crack detection in welding process using acoustic …310692/fulltext01.pdfmälardalen university...

Abstract: The process of inspecting welds done in production at Volvo Aero in Trollhättan is time

consuming and a lot of this time goes into examining faulty objects. The aim of this thesis is to start

development of a system that analyses acoustic emission from cooling welds to determine the quality

of the weld. Our aim is to be able to detect cracks in the material and to give information on the

cracks using the data gathered by our sensors. To do this we will use methods to locate sound sources

and then rate our findings and do some simplifications on the result of our calculations. We will

analyze our calculated data to find crack signatures and classify our findings and give alarms if we

find cracks that are considered too big for comfort. We will also give insight in to future aspects of our

work and look at ways to improve on our proposed methods. We will discuss our systems pros, cons

and what things have been taken into consideration during design, and what strategies we propose

to handle the results from the system.

Crack Detection in Welding Process

using Acoustic Emission.

Linus Karlsson

Lkn05007

Mälardalen University

Supervisor:

Erik Olsson

Contact at Volvo:

Patrik Boart

Examinator:

Peter Funk


Crack detection in welding process using acoustic emission

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Contents

Introduction ............................................................................................................................................. 4

Background and related work ................................................................................................................. 5

Background .......................................................................................................................................... 5

Related work ....................................................................................................................................... 6

Problems and goals ................................................................................................................................. 7

Working with the data from Volvo .......................................................................................................... 9

The first data set .................................................................................................................................. 9

Examining the non-cracked weld .................................................................................................. 12

Examining the third cracked weld ................................................................................................. 17

Comparing the two welds ............................................................................................................. 21

Conclusion ..................................................................................................................................... 23

The Second Data Set .......................................................................................................................... 24

Non cracked weld .......................................................................................................................... 24

Weld without visible cracks ........................................................................................................... 26

Cracked weld ................................................................................................................................. 29

Comparisons .................................................................................................................................. 33

Conclusion ..................................................................................................................................... 34

Result ................................................................................................................................................. 34

Conclusion ......................................................................................................................................... 34

Proposing solutions for localization and analysis .................................................................................. 36

The problems we face when using multiple microphones ............................................................... 36

Microphone arrays ............................................................................................................................ 38

Designs using two microphones .................................................................................................... 38

Three or more microphones ......................................................................................................... 40

Sound preprocessing ......................................................................................................................... 40

Centering data around zero .......................................................................................................... 41

Singling out sound events ............................................................................................................. 43

Finding a max point to use in calculations .................................................................................... 44

Sound source localization .................................................................................................................. 47

Testing algorithms ............................................................................................................................. 50

Sound data handling and clustering .................................................................................................. 52

First approach ................................................................................................................................ 52

Second approach ........................................................................................................................... 53



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Crack recognition and localization Hypothesis ................................................................................. 54

Results ................................................................................................................................................... 54

Conclusions and Future work ................................................................................................................ 55

Summary ............................................................................................................................................... 55

Referenses ............................................................................................................................................. 56

Appendix A, Matlab ............................................................................................................................... 56

Instructions for using this Appendix .................................................................................................. 56

Preprocessing.m ................................................................................................................................ 57

Get_coordinates.m ............................................................................................................................ 63

Position.m .......................................................................................................................................... 64



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Introduction

In this thesis work we will consider the possibility to detect cracks caused by welding using acoustic

emission. To do this we will focus on sounds generated during the time after the welding is done

when the material hardens, this is done during the cooling of the material and the duration of the

recording will be 5 seconds or more, tough the data provided by Volvo and used for this thesis work

covered somewhere between 5 and 15 seconds.

We will be studying one scenario where we have one microphone and some different situations

using multiple microphones. Our hope is to be able to determine whether cracks can be found with

use of one microphone and determine the reliability of such a system. When using multiple

microphones we will focus on locating sound events that might indicate cracks and also to gather

other usable data by use of acoustic emission.

We will examine data, provided by technicians at Volvo Aero, which has been recorded on actual

welds using one microphone that was mounted on the piece to be welded. Our purpose is to use this

data to determine whether a single microphone is enough to detect cracks in the material. Examining

both cracked and non cracked welds we will try to find any information about the quality of the weld.

Using two or more microphones the acoustic data obtained will be analyzed and our goal is to locate

and pinpoint the sources of individual sounds and then to cluster sounds of similar types from the

same region. We will then analyze this data, searching for areas where sounds indicating a crack are

frequent. To accomplish this we have designed some different approaches and algorithm going in to

different aspects and depths in the problem, trying to find an optimal balance between needed

resources, computing time and accuracy. The problem, proposed solutions, consideration and future

work will be discussed. To accomplish this we will use at least two microphones set up as pairs of

microphones so at least one pair will be used. We will use triangulation between microphones to

deduct the source of the sound in question. We will also examine different sampling rate to see

where the optimum frequency lies in terms of accuracy versus data management.

The first section will deal with related work and some insight in to why this project came about at

Volvo in Trollhättan.

The second section will contain an introduction to the Problem of crack detection, sound data

handling and introduce some difficulties with it.

The Section that follows this is where we look at the data from Volvo and report on our work using

single microphones. In this section we try to find things that indicate whether crack detection can be

done with a single microphone. This section contains two major parts, one dedicated to each data set

provided by Volvo.

The section on multiple microphones contains both a description on problems we face when trying

to use more than one microphone as well a section on sound preprocessing. This section also

contains our approach when trying to use multiple microphones to detect cracks.

In the last chapter we will discuss our findings, our results and what this tells us about using this

approach when dealing with the problem off crack detection. We will also contemplate on how to

improve accuracy and limit the need for computational power. Lastly we will have a summary of the

entire paper which will also hold our conclusions.



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Background and related work

Background

The idea for this project was thought up at Volvo Aero in Trollhättan, Sweden. In their process of

creating airplane parts and related products they do a lot off welding and wanted to improve the

performance of their welding operation, more precisely they wanted to improve their quality

assurance controls and the methods used to validate that any piece of equipment that was delivered

to a customer was according to the requirement specifications.

Their current method of control is time consuming and relies on experts finding faults in the finished

products and as time is money it is in any company’s best interests to limit the time spent on all

processes within its production work and, by doing so, lower their expenses.

Today the method used by Volvo Aero to determine the quality of their work and more precisely to

assure that each finished product is as close to perfect as possible and that it will function at the level

specified in the product specification. Today this is done by sending each finished peace to control

department where the piece is X-rayed and then experts examine the results of these tests to

determine whether a weld is ok or not. As we said this takes time, and since the experts must look at

every finished product, even the ones that are not up to specification, a lot of time goes into

examining pieces that later goes straight into the trash bin.

The test done by these experts gives to important pieces of information. It tells us whether a weld is

good enough or if it should be discarded, secondly it tells us where in the piece there are any faults

and how severe these faults are. This is of course very helpful since it can tell us things about the

welding process and also about the work of individual welder. This information will let us see

reoccurring faults and help us to alter our processes to avoid these faults in the future. However

Volvo wants a system of control that gives as close to the same info as possibly but uses a lot less

time, the main focus of the system however will be to discard faulty pieces before they take up

expensive expert time.

Volvos idea was to examine the quality of welds using acoustic emission and use some method to

detect cracks and also to get as much information about these cracks as possible. One of the main

points of using acoustic emission is that it is a form of non-destructive testing same as X-raying and

therefore it can be used directly on products that are to be delivered rather than samples from the

production line. The main focus of the project and the most important goal is to determine whether

cracks have began growth in the object and if so, are these cracks severe enough to cause a major

difference in performance. If this method can find cracks that are off the dangerous kind they can be

weeded out before going in to X-ray and this is of course the optimal scenario. Another application is

that of finding cracks that are minor or in areas where they have less impact, the pieces indicating

these cracks will still need X-raying but since the analysis of acoustic emission has already localized

an area with suspect acoustic activity the experts will now where to begin their examination in order

to find existing severe faults earlier in the examination process.

When Volvo had gotten this far in their planning of the system and the considerations to be made

they contacted Mälardalen University and introduced their idea to Erik Olsson and Peter Funk who

took an initial look at the project and decided that it would make a good master thesis work for

students at advanced level spanning over 20 weeks. The thesis work was to be done by one student



6

depending on the people at Volvo for expert knowledge, measurement data and other forms of

necessary assistance.

The first focus of the thesis work was to do research in the field of acoustic emission, analysis of

sound data, source localization and crack appearance in welds. This research work was ours main

focus for roughly three weeks and a summary of the earlier work and related subjects will now

follow.

Related work

A lot of research work has been done in the field of analyzing of acoustic emission and we have

limited our research to papers concerning either acoustic emission used as a non destructive testing

method, acoustic emission in the welding process or work on multiple sound source localization. We

have divided this section in two three parts each concerning one aspect of our research.

We began our study of related work by looking at the field of acoustic emission in general. We read

about the theory of using acoustic emission as a method for non destructive testing described by

Baifeng JI and Weilian QU[1]. We then went on to read about using acoustic emission to measure

crack growth caused by welding and stress corrosion in an article by C.E. Hartbower, W.G. Reuter,

C.F. Morais and P.P. Crimmins[2].

We found an article describing how acoustic emission was used to find cracks in welds during their

cool down time. This method described by A. N. Ser’eznov, L. N. Stepanova, E. Yu. Lebedev, S. I.

Kabanov, V. N. Chaplygin, S. A. Laznenko, K. V. Kanifadin, and I. S. Ramazanov used multiple sound

channels and clustering to find events and also gave the location of found events [3].

When we realized the potential of using multiple channels and localization we researched basic

methiods for sound source localization and first read about the music algorithm and clustering in an

article by E. D. Di Claudio, R. Parisi and G. Orlandi[4]. We then went on to examine methods of using

time delays between microphones and difference in amplitudes to locate sound sources and found

two interesting articles. One by Brent C. Kirkwood[6] and one by Ming Jaan, Alex C. Kot and Meng H.

Er[5].



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Problems and goals

In this section we will take a close look at the basic problem and a lot of the things that we have

taken in to consideration. We will examine our different approaches and why they were chosen and

also why some things where not taken into account when facing the task. We will start by addressing

some main points of the problem and then go into more detail on the points that will be handled in

more depth throughout the thesis.

The basic problem we face is to use some sort of acoustic analyze to discern a crack created during a

welding process and to locate it if that is possible. This consists both of localizing the sound source

and to determine how to determine whether what we see is a crack or not. Another aspect of the

problem is to do this with small resources and without taking up large amounts of time. Tradeoffs in

accuracy and robustness might be preferable to make the system light, fast and as easy to handle as

possible. To accommodate this we have chosen simple and straight forward methods throughout the

thesis work to keep the performance requirements low.

The situation that we face is a weld that occurs and cools off in a given area. We will be able to

mount our microphones the way we see fit in and around that area, and given that, we can basically

choose any microphone array setup. However there is much to gain in having a microphone array

that takes up little space and the optimal solution stated by Volvo is for the final crack detector to be

as close to fully portable as possible.

Because of the above mentioned problems we also encounter another problem when it comes to

detection and localization. The task of finding a crack and its location might be possible by use of two

different approaches. We either, first find a crack signature in the sound data and then pin points its

location or we map all sounds and sources and the search for cracks.

One of the main goals with our thesis work is to determine whether the single microphone approach

is applicable on the problem as specified by Volvo. To determine this we will examine data from both

non cracked and cracked welds and try to determine if there are any indicators for cracks or the

absence of cracks that can be found with relatively low computational power.

If, after our analysis we find that we have difficulties determining whether a weld is cracked or not

from a single microphone we will start work on simple algorithms for sound source localization using

simplified methods that will work on the given problem. We will also discuss clustering and sound

data handling for the multiple microphone approach.

If these two methods are usable then they each have their own pros and cons, the problem with the

first approach is that of miss localization which will lead to insecurities when giving the position for

found cracks, and also the problem with determining the size of the crack and if there are multiple

signs of crack growth in the object.

The major problem with the second approach is data handling and computer power, though this

does not need to become a major problem it will still use up more power than the first approach. The

good thing with the first approach is that it gives us fast and easy indication of cracks and that it

requires very little computer power to do so. The major advantage with the second approach is the

amount of information it could give us, the accuracy and also the fact that we can alter this approach

in many beneficial ways, improving our different criteria and methods as we go along. The second

approach also offers the ability to use different clustering strategies that allow us to rate different

parts of the welding area according to their level of sound generating activity.



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Apart from the task specific obstacles we have discussed so far we also face problems related to

recording acoustic emission such as background noise, random noise, microphone precision and also

delays caused by other factors than the distance to the source of a sound. As for background noise

the normal strategy is to choose threshold values to sort out noise that do not meet required levels

of amplitude. When it comes to random noise the problem is a little trickier, since a random noise

could have the same signature as any other type of event. Microphone precision is a big factor when

deciding the maximum resolution of the system, since we will be relying on differences in amplitude

and arrival times between microphones to deduct the source location we can only have as fine a

precision as our microphones allow. When considering delays from unknown factors we have two

cases one is a constant delay which can easily be taken care of, therefore it is not a big issue, and the

other is a random delay which might greatly hinder our work. Preferably we must remove all random

delays in the system and this will have to be taken care of before calculations take place.



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Working with the data from Volvo

When using one single microphone we will focus on analyzing sound data based on frequency and by

observing the pressure curves generated by the microphones. The major problem here is to

determine what kind of sounds a crack will result in and if these can be perceived and singled out by

sound data manipulating and in the long run an autonomic approach.

In this section we use authentic weld data provided by Volvo and our goal is to determine whether a

crack can be found using only one microphone mounted on the piece to be welded. This means that

we will analyze data from cracked and non cracked welds and compare the results to see if we find

any key differences that provide information on crack appearances and growth.

Data was provided by Volvo in two separate sets. The second data set was recorded after our initial

analyzes of the first set and therefore the measurement parameters and experimental approach was

altered for the second recording.

The first data set

The first data set we got from Volvo contained a total of nine recordings with eight being welds and

seven of these included some cool down time. In our analysis our focus will be on the seven data sets

that included cool down time.

Title Sensitivity Length in seconds Comments

First cracked weld 50mV/div 13:33 With another setup than

the other welds

Second cracked weld 10mV/div 13:39

Third cracked weld 5mV/div 13:48

Fourth cracked weld 5mV/div 14:02

Fifth cracked weld 5mV/div 14:07 With air mounted

microphone

Non-cracked weld 5mV/div 13:45 Table 1, here we see information about the measurement data provided by Volvo.

This data was recorded on welds made on a test piece set up with a sound sensing device mounted

on the piece. All welds where done in a small area of the piece and should therefore be comparable

when analyzing sound pressure amplitudes.



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Figure 1, the setup used by the people at Volvo to record data set 1.

In figure 1 we see the setup that was used at Volvo to make the recordings. At the point marked A in

the top left half of the figure we see the microphone mounted on the piece. At point B in the right

part of the figure is where the welding took place. All welds where made in the polished area and

where made from top to bottom given the perspective of the figure.



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Figure 2, the welds after they have had time to cool down.

Figure 2 shows us the welds made in area B from a perpendicular angle. The two welds placed to the

right are the welds that are not cracked. These welds are somewhat closer to the microphone tough

we hope that this will not affect our measurements too much. One of these non cracked welds

where made without recording cool down time and has therefore been omitted from analysis.

When considering the non cracked weld there is however one thing that we must take in

consideration and that is that the welding apparatus was no turned off directly as was done with all

other welds but rather it was toned out over a period of about ten seconds. The impact of this on our

data is not fully determined, this happened due to a communications problem between us and the

testing team, since our focus lies in the seconds after welding apparatus is off and technicians had a

higher focus on time when it was on. We hope that this does not make our data invalid, and we will

take steps to avoid this in future measurements.

After the first cracked weld was completed the piece that was welded on and also the sensor was

rearranged. Also, as we can see, throughout the testing the sensitivity of the equipment was altered

with the first and second cracked weld having different sensitivities from the other four welds. In all

the recordings the initial seconds consist of recording while the welder is on, it is then turned off and

we have data on the initial seconds of the material cooling down. We will show our work on

examining the welds using the third cracked weld and the non-cracked weld, beginning with the non-

cracked weld.



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Examining the non-cracked weld

The first step we took when examining the sound data was naturally to look at a plot of the sound

pressure over time.

Figure 3, the non cracked weld shown as sound pressure over time.

Above in figure 3 we see the data plot and we can notice the change around index 7 on the X-axis,

this is where the welding apparatus was turned off. Since we will want to take closer look on the part

of the data that was gathered after the weld was turned off we cut that data out and worked on it

exclusively. This leaves us with a new array consisting of indexes 7000000 to 10000000 of the original

data array.

Figure 4, the last part of our sound data, recorded with welding apparatus off.



13

In figure 4 we first noticed five clear and visible audio spikes in the later part of the sound and also a

higher level of noise in the earlier parts of the recording. Our first step in trying to get more

information from the data was to run it through a FFT analysis, which will let us see how the

amplitudes of spikes and noise are divided over frequency. First we simply looked at all the data over

all our frequencies.

Figure 5, the first FFT plot. Sound amplitude, shown over time and frequency

In this figure the right-hand axis indexed from 0 to 300 shows frequency with our full range of 200

KHz split into 256 equal parts indexed from lowest to highest. Sharing origo with this axis is the time

axis indexed from 0 to 6000 where each million indexes in our sound data is represented as 2000

points in this graph. The last axis indexed from 0 to 0.01 is the amplitude axis showing the amplitude

of the sounds we are seeing placed at their correct time and frequency.

When studying this graph we find some interesting points to note, firsthand we see that almost all of

the noise occurs at the low end of the frequency register and therefore should be fairly easy to

remove or at least to omit from our analytic methods. We can also note that the five spikes seen in

the first data plot are not shown in this graph, which tells us that they are of a higher frequency than

200 KHz.



14

Figure 6, the second FFT plot. The data with the lowest frequency omitted.

We removed the lowest frequencies and redid the plot and ended up with the graph seen in figure 6.

We found a second smaller section of noise placed just above the first one in frequency. Now that

the resolution on the amplitude axis is a lot higher we could also see some low amplitude spikes in

the higher ends of the frequency spectrum.

Figure 7, the third FFT plot. This graph shows data from the 246 highest groups of frequencies.

We redid the FFT plot omitting enough of the low frequencies to filter away the noise and the results

can be seen in figure 7. To arrive at this plot we removed 10 of the 256 groups of frequencies thus

omitting roughly four percent of the sound data. If we cross reference this data plot to the amplitude

plot of the whole data in figure 4 we can see that the spikes seen in the higher frequency spectrum of

figure 7 occur at the same time as the spikes seen in figure 4.



15

Studying the spike in figure 7 we see that they grow in amplitude towards the higher end of the

frequency spectrum and that they do so continuously suggesting that it is not a result of filtering

where we would have seen a much sharper start to our spikes. The spikes observed in this graph also

differ from the ones observed in figure 8 when it comes to amplitude and are a lot smaller than those

observed in the other plot. To better determine the characteristics of the spikes, and also the spikes

amplitude contra noise amplitude, we singled out the last and biggest spike and redid the initial plot

and the FFT yet again and this time plotting indexes 9850000 to 9860000.

Figure 8, indexes 9850000 to 0860000 of the data shown as amplitude over time.

Figure 9, the top 246 frequency slots of indexes 9850000 to 9860000 with amplitude shown over time and frequency



16

In figures 8 and 9 we see a smaller portion of the data represented in three different ways. First in

figure 8 we see the data one again as sound pressure amplitude over time, in this graph we can see

the spikes from figure 8 but this time the resolution of the axis has changed and we also see that the

start of the spike is really fast whilst it ends by fading out.

Studying figure 9 we see the spike and how it is fading out and how that spreads over the frequency

slots. We that the highest amplitude in the spike is found at the high end of the observed frequency

slots, this leads us to assume that an even higher peak can be found at higher frequencies. Since we

still cannot see peaks to match those of figure 4 we will have to keep searching or do other

measurements.

In the close up in figure 9 we can also see some effects from the noise climbing its way up in

frequency. The affect is fading and it is fixed in frequency which will make it easier to suppress if that

turns out to be necessary.

Assuming that the peaks fades away in a similar fashion to that seen in figure 4 we will not examine

that in the FFT graph. We will instead study how the spike grows over frequency slots. To better be

able to do this we will first isolate the highest of the peaks, showing only that peaks behavior over

the frequency slots. Focusing on indexes 9852500 to 9853524, frequency sots above 150 and

examining the peaks as amplitude over frequency we arrive at figure 10.

Figure 10, the top 106 frequency slots of indexes 9852500 to 9853524.



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From the way the observed amplitudes in figure 10 behave we assume that the biggest amplitude

can be found at higher frequencies. This leads us to speculate whether the amplitude spikes seen in

figure 4 are located at an even higher frequency than the ones covered by our measurements. From

the figure we also see that the relationship between frequency and amplitude is varying and it seems

that there are peaks at higher and higher frequencies but also smaller peaks at frequencies in

between. From the figure it is not possible to approximate a frequency at which we will find our

sought after amplitude peaks. We do believe however since we see amplitudes of varying height over

the frequencies, but still all growing with the frequency that, there might be waves carried by each

other. To determine if this is the case we made a high-resolution close up of the peak as amplitude

over time, similar to figure 4.

Figure 11, a close up of the spike seen as sound pressure amplitude over time.

From figure 11 we can clearly determine that there are multiple frequencies collaborating to produce

the spikes we have observed with only single peaks being responsible for the really high amplitudes.

This explains why they were omitted from the FTT which only focuses on the frequencies which can

be fully covered by a sample rate of 500 KSS, those frequencies that lie below 250 KHz.

Examining the third cracked weld

As with the non cracked weld our first task when examining the recording of the cracked weld was to

look at the sound data as sound pressure amplitude over time.



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Figure 12, Sound data from the cracked weld shown as pressure over time.

The graph in figure 12 shows us that there are not as many spikes in this data as in the data from the

non cracked weld. There are some clear spikes around index 5000000 in the graph which we hope

will give us some information. There is also some activity around index 5000000 and 8000000 in the

graph which we want to take a closer look at. We will begin with examining the relation between

spikes and background noises through a FFT focused on the part of the recording that contains the

spike and the other sound activity, indexes 4500000 to 8000000, showing all frequencies.

Figure 13, amplitude shown over time and frequency for indexes 4500000 to 8000000.

We see that when looking at frequencies which we can fully cover given our sampling rate the spike

is not to be seen against the noise. We will omit the lowest frequencies to get a view of the sound

activity as amplitude plotted over time and frequency.



19

Figure 14, showing a closer look at the activity found between indexes 4500000 and 8000000.

By studying figure 14 we see that the activity can be described as two clear spikes beginning

somewhere in the top 50 frequency slots and also noise and seemingly random activity at roughly

the same frequency. The activity that we observe is of rather low amplitude and does not account for

the spikes seen in the plot off sound pressure amplitude over time. This tells us that the spikes

appear at a higher frequency and the same goes for the noise seen in the figure.

We will now single out the highest of the spikes observed in the sound pressure over time graph to

examine it in more detail, focusing on indexes 5105000 to 5115000.

Figure 15, indexes 5105000 to 5115000 of the cracked weld shown as sound pressure amplitude over time.

We see in figure 15 that the event begins sharply and then fades out which I consistent with a spike

and we also see things to indicate that it is an event that acts throughout different frequencies. We



20

will examine it in more detail with the use of yet another FFT focused on the same indexes as figure

15.

Figure 16, the spike between indexes 5105000 and 5115000 shown as amplitude over time and frequency.

Figure 16 shows us how the spike behaves through the various frequency slots. We see that it grows

in amplitude towards the higher end of the frequency slots and also that that the amplitudes fade

independently throughout the frequency slots. We will conclude our study off the data from the

cracked weld by examining how steeply the amplitude grow over frequency, this is done, as in the

non cracked case, by narrowing down our view on the spike itself and examine only the two indexes

that make up the spike. We focus our last modified FFT on the cracked data on indexes 5108400 to

5109424.



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Figure 17, Shows how the amplitude grows with frequency in the spike between indexes 5108400 and 5109424.

In figure 17 we see that there can be many estimates for the growth of amplitude over frequency

and that it is hard to make a clear calculation of the frequency at which we might find the high

amplitudes found in the figures showing the data as plain pressure amplitude over time.

Comparing the two welds

In this section we will make a comparison between our two recorded sound data and try to reason

our way around similarities and differences in the two sound data recordings. We will begin by

simply showing the data as sound pressure amplitude over time.

Figure 18, a comparison between the two welding data. The non cracked weld is seen in its entirety to the right and the

cracked weld is shown to the left.

Observing figure 18 we see a lot off differences between the two sets of sound event data. The first

and most obvious difference is the difference in focus between the two recordings. Both are of

similar length but in the case of the non cracked weld recording roughly 70% is recorded whilst the

welding apparatus is still turned on compared to around 35% in the case of the cracked weld.

The transmission from the part where the welding apparatus is on to the part where it is turned off

also looks a lot different between the two recordings. In the data from the non cracked weld we see



22

what looks like an immediate turning of off the apparatus, the transition from on to off is done in one

single step and in a very small timeframe. Whereas in the case of the cracked weld the apparatus is

turned off successively through several steps and also the turning of takes up more time than in the

recording from the non cracked weld. It is not clear if and how this affects our data but the issue has

been noted and will be taken into account when conducting the recordings for our second data set.

Another thing that we can see clearly from the figure is the difference in behaviors of the spikes

between the two recordings. There are clear spikes in both cases but there are big differences

between them both in number, frequency and amplitude. (Notice that frequency in this sense

corresponds to the number of spikes and their relative timing rather than the frequency of the

sounds that generate the spikes). In the recording from the non cracked weld we see a number of

high to medium amplitude spikes with short time in between beginning roughly two seconds after

the apparatus is turned off. In the recording from the cracked weld we see one medium amplitude

spike and some small spikes spaced out throughout the recording with the highest spike at about 3

seconds after the apparatus is turned off.

In both recordings we see some noises that differ from the base level of noise though it appears at

different timing in the recordings and also varies in length between them.

These differences are consistent throughout all the data with all recordings from cracked welds

showing medium to low amplitude spikes and not as many occurrences as in the case of the non

cracked weld.

Note worthy similarities between our recordings on this stage is that the sound pressure amplitude

recorded whilst the apparatus is on and also the noise when it has been turned off is at close to the

same level and also that it acts the same which tells us that the experiments have been conducted

with roughly the same environmental parameters.

Figure 19, Showing the two recording as amplitude over time and frequency.

Taking a closer look on the data as amplitude over time and frequency as shown in figure 19 we can

also note and discuss some differences and similarities. The first and most obvious difference is that

of amplitude between the two recordings. As when the data is shown as sound pressure over time

the amplitudes observed in the data from the non cracked weld have much higher amplitude than

the data taken from the recording of the cracked weld. This affects the resolution and reference

values of the axis set on the plot by Matlab and gives the impression that the cracked weld contains a



23

lot more noise spread out over the frequencies. This however in not true it is merely the higher

resolution in the graph showing that data that gives the illusion of a higher noise.

We note that the noise seen in the pressure over time graphs described as deviating from the

background noises can be observed at the high end of the frequency slot in both graphs and is visible

in the non cracked weld data even though the resolution is lower than in the cracked weld data. This

noise is seen prior to the spikes in the data from the non cracked weld and directly after the spikes in

the data recorded on the cracked weld.

Furthermore we can also see that the spikes, apart from the difference in amplitude, are similar in

both data sets. Particularly their growth and the behavior of their respective amplitude as the

frequency increases are very similar. We will take a closer look at the spikes to conclude our

comparison of the two data sets.

Figure 20, a close up FFT made on the largest spikes from both data sets, the one from the non cracked weld is shown to

the left and the data from the cracked weld is to the right.

Examining the two graphs in figure 20 we see a lot of similarities between the two spikes. We see

that their behavior regarding both time and frequency is very much alike and this gives strength to

our theories that claim that the events in themselves are similar. The only significant difference is yet

again the amplitude and a small variation to the fading out of the sound pressure at high frequencies,

though this can be explained by the difference in resolution.

Conclusion

We conclude that, as far as we can see in this data, the same type off sound generating events occur

in both cracked and non cracked welds and that we will have to achieve measurements that give us a

larger number of spikes to work with from both kinds of welds, preferably the new data will have the

same consistency in amplitude as we have so far observed in behavior.

We will also want new data with a higher sampling rate so that we can observe the whole sound

events. Preferably we want to include frequencies where the spikes are no longer active so that we

can watch their behaviors over all the frequencies that they inhabit.

So far we see no difference between cracked and non cracked welds and we lean towards the idea

that we need to categorize number of sound events and use some sort of localization techniques to

determine whether cracks are present or not, work on the second data set will help to confirm or

deny this hypothesis.



24

The Second Data Set

The second data set we received from Volvo contained a total of six recordings and five of these

where recorded during welding. A similar equipment setup as for the first data set was used apart

from the recording in itself which was done with other parameters.

For this data set they used a sample rate of two million samples per second which is four times the

sampling rate used for the first dataset. All recordings where done with the same microphone

sensitivity and again at roughly the same distance. The sensitivity was set to 20 mV per div.

One of the welds in the set was made with a long shutdown time for the welding apparatus and all

the other used a short shutdown time. Some differences occurs even among the welds said to have

the same shutdown sequence and this is yet to be explained by Volvo, since this occurs at the

beginning of the recording we have not given it to much weight with our focus still lying on the later

part of the recording.

Title Sensitivity Length in seconds Comments

Non cracked weld 20mV/div 13:29 Longer turning off of

welding apparatus

First cracked weld 20mV/div 13:33

No visible cracks 20mV/div 13:36

Second cracked weld 20mV/div 14:41

Third cracked weld 20mV/div 14:44

Fourth cracked weld 20mV/div 13:48 Table 2, this table shows the welds from data set 2.

At first glance we cannot see any clear spikes in the data from the two welds without visible cracks

but still see clear spikes in the cracked welds. Since all the cracked welds are very similar to one

another we will use one of these to represent them all and we will also examine the non cracked

weld and the weld without visible cracks, beginning with the non cracked weld. For all welds we

divided the plotting of the data into two parts, one showing the time when the welding apparatus

was on and the turning of off the apparatus, the other parts shows the interesting data gathered

from the initial cooling of the material.

Non cracked weld

We began by examining the data that was recorded during the non cracked weld. This weld was done

with a longer tone out of the welding apparatus. We plotted the data in two parts with the first

containing the turning of off the apparatus and the other focusing on the interesting part where the

material starts to cool down. The two parts of the data is shown with different values for the Y-axis

to get a better understanding of both the noise produced by the welding apparatus and the sound

data recorded during cooling.



25

Figure 21, the data from when the welding apparatus was on and the turning of off the apparatus.

Figure 22, this data follows after the last figure and shows what was recorded during the initial cool down.

The first thing to notice is the lack of visible spikes, which were seen in all data from data set 1.

Failure to notice any spikes in this non cracked weld might give us useful information. We do

however see some noise in the beginning of the second half of the data as well as in the end of the

first part. To get more information from this data we will use an FFT focus on the ending of the

observed noise, indexes 2 to 6 million, without the first 50 frequency slots, in figure 19.



26

Figure 23, an FFT of indexes 2 to 6 million in the second half of the data.

From figure 23 we learn that there are no clear spikes in the figure however the noise observed

earlier is visible in the beginning of the frequency field of approximately 1 MHz, with the first 20%

omitted to remove background noise that puts the sounds seen in the picture at around 200 KHz.

In the figure we can also observe some sound activity higher up in the frequency field, at around 600

KHz we see something similar to the bigger sound events but at much lower amplitude. This activity

is at a high enough frequency to have been missed last time and we will search for similar

phenomena in all our data from the second data set.

The lack of visible spikes in this data and also the noise seen and its amplitude and behavior will be

noted as we go on to examination of the other two data sets chosen for inspection.

Weld without visible cracks

We had the same approach with the weld that had no visible cracks; we first looked at the two halves

of the recording and tried to find points of interest to investigate further, once again they are shown

with different Y-axis for a clearer view and a better understanding.



27

Figure 24, the first part of the data from the weld with no visible cracks.

Figure 25, the second part of the weld with no visible cracks.

There are few distinguishing features in both halves of the recording though some noises and one

small spike can be seen in the second half of the data. We will focus on the part with the spike in the

second half and also the beginning of the noise seen in the beginning of the second half. First we will

look at the beginning of the noise focusing on the data between index 8000000 in the first halt and

2000000 in the second half, shown as a FFT.



28

Figure 26, a FFT showing the beginning of the noise observed in figures 24 and 25.

We can see in figure 26 that the noise is taking place in the frequencies where we have earlier

observed spikes and noises that were not deemed a part of the background noise. We can also see

that the nose gain in amplitude at the same point in time as in figure 25. We also note that the rise in

amplitude can be observed on the high amplitude reflection as well and that it seems to be of around

the same magnitude as the rise in the low frequency data.

We will not look at the only resemblance of spike that we have observed in the data from this weld,

found around index 8 million in the second half of the data. The spike can be observed at this index in

figure 25 and we will now show it in a FFT showing indexes 7000000 to 9000000 of the second half of

the data.



29

Figure 27, an FFT of the small spike seen in figure 25.

We can clearly see the spike emerging from the noise and roughly at the same frequency. We can

also notice that the highest amplitude of the spike is located at a slightly higher frequency than the

top amplitude of the noise. Also visible at a close up of the figure is a reflection of the spike in the

reflection of the noise at the higher frequency of about 600 KHz.

This spike that was no seen in the data from the non cracked weld might give us information

regarding non seen cracks in the weld. However from the first data set we did not observe spikes to

be exclusive to cracked welds.

We will however not the behavior of this crack and note at where in the data set it took place and

move on to the final examination in the second data set.

Cracked weld

We choose to use the third cracked weld for our examination of the cracked welds in the second data

set. At first glance we saw that it was only in the cracked welds that we observed clear spikes and we

will try to see if we can match their behavior to the spikes earlier observed in data set 1.



30

Figure 28, the first half of the data from the cracked weld.

Figure 28 shows us the first half off the data from the cracked weld. We can note that the part that

shows the welding apparatus being turned off has a different look than in the other recording from

the same data set.

Figure 29, the second part of the recording from the cracked weld.

In this figure we see a lot of spikes and also a rise in noise level as observed in the earlier recordings.

We will narrow down our examination on the last 2000000 indexes of the data set and focus on the

rise in noise amplitude and the largest of the spikes. We will begin by examining it all with a FFT.



31

Figure 30, a FFT of indexes 18 million to 20 million of the cracked weld data.

As we look at figure 30 we see the spikes clearly at around 200-300 KHz which is where we hoped to

find them, we also see some low amplitude activity around the same frequencies that grows towards

the end of the recording. This matches the rise in noise amplitude that we observed in figure 29.

If we look at the higher amplitudes we again see a reflection of the activity around 200-300 KHz

appearing at lower amplitude and with a frequency of about 600-700 KHz.

We can also note that the spikes appear within the same areas where we also note a higher noise

level. It might indicate that something is indeed taking place in the material during these times of

higher noises and that the spikes give us information about this process.

We will take a closer look on the largest of the spikes to better study its behaviors over frequency

and also its companion at higher frequency. First we will view it in a plain graph as amplitude over

time.



32

Figure 31, the largest spike from the cracked weld shown as amplitude over time.

When we examine the spike more closely as in figure 31 we see that I fades out in stages, the fist

max point stands alone but after it comes 5 points that reach about the same height and then I fades

again to a number of points in the next category of amplitude. I we look at the lower spikes, the

minimum points we also see roughly the same behavior, though the time of their lowest point does

not match that of the top point.

Figure 32, a FFT of the largest spike in the data from the cracked weld.

Now that we can see the spike in more detail in figure 32 we can study its behavior more closely. We

see that the event peaks at around 200 KHz which means that we were close to seeing the peak in

the first data set. The over tone at 600KHZ is a reflection of the first sound and was of course omitted



33

earlier. Now that we have identified a so clear a spike in the data and also noted that it lies within a

period of higher noises we are starting to assume that a correlation between spikes and a rise in the

noise level, only measuring noise around 100-200 KHz might actually indicate an event taking place in

the material.

Comparisons

The first thing we want to look at in our comparison is the part of the data where the welding

apparatus was turned off. This is also a point on which the three cracked welds look alike and

therefore we will again look at the first half of the three examined data sets.

Figure 33, the turning of off the apparatus as it was recorded in the three examined welds.

As we can see from the graphs in figure 33 the welding apparatus seems to have been turned off in a

different manner between the cracked and non cracked welds. We also note that the noise produced

by the welding apparatus looks a bit different in the data from the non cracked weld as compared to

the two others; this might have something to do with the manner of turning off the apparatus. Volvo

specified that a longer tone out was used for the non cracked weld and that must be what we see in

the recording.

We will assume that the difference between the welds will not affect our work but we will still advise

to remove these differences from future measurements.

We will also look at the rise in noises at around 150 KHz shown as pressure over time in the three

welds. Since we have already concluded that the noise appears at those frequencies we will now just

compare it between the welds.

Figure 34, the rise in noise shown in all three welds.

In figure 34 we see the data from all three welds beginning with the non cracked weld followed by

the weld without visible cracks and the lastly data from the cracked weld.



34

In the first data, from the non cracked weld, we see the whole rise in amplitude come and go. We see

that it spans over roughly 10 000 000 indexes which means roughly 5 seconds. We can also see that

the activity is a smooth one without any strange occurrences apart from the rise in noise.

In the data without visible cracks the noise begins in the second part and we see 9-10 000 000

indexes off it; we do not see the end of the activity. During the observed part of the sound activity it

looks smooth except for a few smaller spikes which could mean that something is happening inside

the material for example the beginning of a small crack.

In the data from the cracked weld we see the last 6 000 000 indexes, about 3 seconds, and see a rise

in the noise level even if it is not as distinct as in the other two recordings. We do however not that

the spikes seen appear in conjunction with the rise in noise beginning roughly at the same time as we

can note a difference in noise levels and then gaining in amplitude as the noise rises. This is

interesting and leads us to believe that activity in the material leads to height in noise level and that

distinct events leads to different events that can be observed in the recordings.

Conclusion

In the second data set we saw no spikes in the non cracked weld but clear and obvious spike from

the cracked weld data and also a high level of similarity between all cracked welds. When we looked

at the data from the weld without visible cracks we see something that might indicate some minor

activity taking place in the material. Based on the second data set alone we could reach the

conclusion that cracks are indicated by spikes that appear around 200 KHz and are mirrored at

roughly 600 KHz.

Result

After we have examined both data sets provided by Volvo we are a bit split as to how to read the

results. On one hand we have the second data set and parts of the first data set that indicates that

the spikes observed at around 200 KHz do indicate cracks or related phenomena in the material. On

the other hand we have the non cracked welds in the first data set and also some of the cracked

welds that contradict this conclusion.

Of course some of these might be problems with equipment or other noises that destroy the

reliability of our data but this cannot be decided upon with only the given data.

What we can decide on however is that sound data gathered in this way has a high potential of being

valuable and that we should continue with recording using the same sampling frequency as in the

second data set. We can also note that we want to strive to eliminate any and all differences in

procedure between measurements on cracked and non cracked welds so that future data will be

even more reliable.

Conclusion

From the observed data it is hard to draw a good conclusion. When we consider the data from the

first set we can observe that the spikes in the non cracked weld, in figure 3, that are of the highest

amplitude observed for spikes do not follow the behavior suggested by other data in that they do not

occur in conjunction with the noise generating event. The difference in amplitude relative other

sounds in that data set also stands alone from other data sets and this leads to suspicion of this data

being off rather than other observations. Since the observed spikes are so similar to the spikes vied in



35

other data this might be because other welds are cooling off in the vicinity of the non cracked weld

or just a result of the difference in equipment sensitivity.

The conclusion we reach is that we spikes that lie within the field of heightened noise with both

spikes and noise have frequencies at around 200 KHz might very well indicate crack growth in the

material. The next step in measurements will be to conduct larger scale experiments with more cases

in each one and also to keep allowing time in between welds for the material too properly cool off

and therefore avoid any eventual interference.



36

Proposing solutions for localization and analysis

When considering solutions to our problem we have taken a lot of things into consideration and we

have looked at a lot off possible answers. We have compared many different ideas in theory and

come up with a few different approaches to go on and test in real life situations. After our own initial

tests, which will be done on mundane data with acoustic data that lies within the hearable spectrum,

we will go on to apply the real test data on the proposed solutions that produce the results we are

looking for.

In this section we will focus on our work on design solutions for the microphone array design, the

algorithms used for sound localization, sound data handling and also on our work on recognizing

cracks in the output from the first two algorithms. The work put into these three areas will be

presented in that order, first array design then source localization followed by data handling and

lastly analyzing the data to find cracks. We will begin by taking a closer look at the some of the

problems we face.

When doing this thesis work we had some problems with measurements at Volvo and therefore we

were unable to obtain data recorded with multiple microphones, we also had problems with

determining what kind of equipment would be used. This leads to cut downs in some of the work in

this theoretical section. Mostly in the section of clustering and data handling for Volvo data, also we

have been unable to determine what filters and sound data algorithms we need to apply to the data

before applying our own methods for sound preprocessing.

The problems we face when using multiple microphones

One main problem when using multiple microphones to pinpoint a sound event source is that we

must first match sound events between our microphones. Matching sounds is a task that can run in

to a lot of problems, such as sound events taking place at times close to each other or sounds that

are low enough in amplitude to be represented very differently in the two microphones.

When we examine the acoustic patterns that are emitted from the cooling weld we will discover

sounds varying in frequency and this might help us determine the nature of the events that

generated the sound that we are looking at. This fact will also be useful in figuring out which sound

event corresponds to which between the different microphones. A problem we face here is that

sounds can arrive in different sequences at different microphones and cause confusion as to which

measured event corresponds to a given sound generating event. This can be helped by avoiding

certain microphone array designs and also by examining the frequencies of measured sounds to

better identify its source. Some risk of this phenomena occurring will still be in the system but it will

be much reduced and we will implement some different tactics to handle it.

As we have just discussed, problems in array design for the placement of the microphones in

conjunction with an inability to discern different sound sources given only the data in one

microphone can lead to problems in source localization. A problem is that two sounds generated at

roughly the same time might arrive at the different microphone in another order than the order of

appearance. This will lead to our algorithms, using the wrong data, producing false positions for both

the sources.



37

Figure 35: This figure is used to illustrate the problem sound switching order between microphones

In figure 35 we see a setup that uses two microphones set at opposing sides of the welding area,

marked as grey in the figure. The two microphones M1 and M2 Will both be recording all sound

generated in the target area. For the case of our example we assume that two similar sounds arise at

points P1 and P2 at about the same time. This will be measured in both microphones as soon as the

sound waves arrive. Given that both sounds are closer two one of the microphones than the other

this will lead to the sounds from a Point arriving at different times in the two microphones. We will

call the sound generated by events P1 S1 and sounds from P2 S2.

Figure 9: This figure will help us see how the sounds generated at P1 and P2 are represented in the measurement data

from the microphones M1 and M2.

In figure 36 we see the result of measurements for both our microphones M1 and M2 presented in

the form off a wave with amplitude on the Y-axis and the time of arrival at the X-axis. As we can see

in the figure a situation has occurred where the two sounds has arrived in different order to the

microphones and there by introduced the problem of identifying which sound corresponds to which

particular event. In the section on proposed solutions we will discuss ways to limit the effects of this

problem.



38

Microphone arrays

We started out with a lot of theoretical work in considering different approaches to designing our

microphone array. We arrived at the problem, described in the problem section, of sounds arriving in

different order to different microphones and began work with trying to figure out how to design an

array where this is less likely to happen.

Designs using two microphones

We began however with the basic concept of two microphones each positioned at opposite sides of

the welding area; it was by considering this design that we realized the problem of arrival time.

When considering this area the only thing we need to keep track of is the distance D between the

microphones.

Figure 37: our first attempt at array design which led to our discovery of the problem of sounds changing their order in

different microphones

The array in figure 37 was discarded due to the problem associated with it that we have described

and we started thinking on what changes could be made to this design. Still working with only two

microphones and still wanting to keep them at opposing sides of the weld we came up with the idea

of using an offset. Using an offset and a more limited weld area would let us guarantee the distance

to one of the microphones would always be greater than the distance to the other microphone, using

this design we would lessen the risk of arrival time problems. For this design we will have to know

both the distance between microphones D and the offset do which is the difference in length from

the center of the welding area. We will also have to limit the width of the welding are to insure that

the distance will always be greater to one of the microphones.



39

Figure 38: In this figure we can see how a design could look when we use a limited weld area and a microphone off-set.

The last two microphone solution we will look as is also the one we choose for our algorithm testing,

in this method we use two microphones positioned at the same side of the weld area. This will allow

us to keep a wider weld area but we will still profit from keeping it as small as possible. What we do

in this approach is to use the distance D between our two microphones as a reference and with that

we can go on to positioning algorithms. One problem with this design is choosing the size of D, we

want to keep D as large as possible to give us a bigger accuracy when measuring distance from the

microphones to each other and to sound sources, at the same time we want D to be as small as

possible to be able to measure small enough time changes to be able to estimate the frequency of

the sound. This minimum length of the distance D will vary depending on how high frequencies we

want to monitor but will be equal to the wave length of the examined sound.

Figure 10: Here we see a two microphone design that has both microphones on the same side as the weld.

In this design there is theoretically the least risk of running in to the arrival time problem and also

since our microphones are close to each other the effects of random noises and acoustic activity

from outside of the weld area should be roughly the same in each microphone and therefore easier

to handle.

When considering designs using only two microphones we have chosen to proceed with this design

using two microphones on the same side of the welding area. With choosing this design for our two

microphone testing we hope to minimize the effects of the arrival time problem and also limit the

effects of background noises and random interrupting acoustic emission. One thing to take into



40

account however is that when using microphones that have longer distances between each other we

can filter some background and random noise by comparing between microphones, this takes up

fairly large amount of computing power however and we much prefer to just treat these as we would

other sounds and later omit sounds that are calculated to have originated outside of the weld area.

We also look at the fact that this is the most portable solution and also one that is fairly easy to set

up. We see this as the optimal way of configuring two microphones in terms of accuracy, noise

handling and also in sorting for arrival times.

Three or more microphones

If we have the opportunity to use more than two microphones our strategy will be to build many

pairs of microphones, and also in a case of for example 3 microphones, use them as three pairs.

When setting up our microphone arrays we will also consider having different pairs of microphones

working from various angels relative to the welding are. And when we have microphones set up to

one side of the field as preferred when using two microphones we can also try different approaches

off pairing. For example we can pair microphones from different sides of the weld are and use that

data in conjunction with data obtained from a single side to get as much info as we possibly can.

The big win when using microphones from two side of the weld is that the distance between them is

greater and therefore the points for which we can decide their origin will be located with higher

precision. The drawback is as we have discussed that sounds can be wrongly matched and sounds

may end up in false positions.

Sound preprocessing

When we take a first look at recorded sound we will see that most often it comes with a few

problems that must be taken care off. Such as the sound curve being of centre, small noises, peaks

and fluctuations due to equipment and environmental factors.

To solve these issues we have constructed some tools for pre processing of sound data that will be

applied to data just before it goes to other computations, if for instance we want to use filters to

single out or remove certain frequencies that will be done before applying the methods shown in this

section. To describe our methods and show their functionality we have applied the step by step to a

test data, this data was created to be easily presented and a good example.



41

Figure 40, we see the sound data directly after recording

In figure 40 we see the sound data plotted directly after recording and we will now discuss what

needs to be corrected and also how we have chosen to do it. As we can see the data in the graph is

not centered at zero, this gives us some problems with further calculations and there for we will try

to align the data around zero

Centering data around zero

To get the data centered we must find out the distance from the data base line, the line that

represents no sound events, to zero and then adjust all points in the data array with this distance.

This is done by counting how many reorientations there are of each possible distance to the center

and then chose the most common one. To do this we will first chose a resolution of our analysis

based on how many decimals we want to use. In the chosen example we have chosen to round to the

second decimal, since it gives a good enough accuracy. We now round all numbers and then

determine how many there are of each one; wherever we find the most numbers we have our base

line.



42

Figure 41, this is the frequency with which each distance is appearing.

In figure 41 we see a graph representing the number of findings for each distance to zero in the

sound data, the peak value of 28 means the distance in 0.28 from our min value which is -0.35. This

gives us the distance -0.07 in our example. If we subtract that from each element en the sound data

array we will receive an array where the values have been normalized around zero.

Figure 42, the sound data has now been normalized around zero

Now that our sound data is normalized around zero we can begin working on sorting out background

noise and smaller spikes so that we can identify and analyze important sound events.



43

Singling out sound events

Now that the values all revolve around zero we may calculate a Root mean squared value for the

data and use that to set up appropriate threshold values.

�� ∑�

Now we will calculate a value P relative to the Root mean squared value for each data point and then

compare that value to an appropriate threshold.

� � ��

We will use the threshold value to sort out as much background noise as possible, for testing

algorithms we will set the threshold manually to a value that takes away an appropriate amount of

background noise. In our example P was set to 3.5. If we apply this as a upper and lower limit to the

data and remove points that fall within these limits we will get a data output that holds sound data

that will be considered sound events, and also a few stray sounds that will be removed in later

stages.

Figure 43, our sound data after background sounds are removed.

Now, the next thing to do is to decide which of the sounds we see corresponds to a given sound

event and also if any of these sounds can be omitted as single peaks. We will demand of any sound

that is still left in the data at this point to have other sounds within 500 indexes in the array, which

means roughly 0.01 seconds. Sound peaks that occur within that time frame are considered as part

of the same sound event and peaks which fail to fall within 0.01 seconds of at least one other peak

are omitted.



44

Figure 44, showing our sound data with an indicator on what constitutes as one sound event.

Here we see the result off our sound event localization technique. The positive flank in the green line

marks the beginning of the sound event and the negative flank marks the end. These two points are

what we need to locate the sound when we want to use it for various calculations.

Finding a max point to use in calculations

The next thing to do is to try to approximate a max point to use for later calculations. The problem

we face here is the phenomena explained as waves in waves. That is, sound waves of various

frequencies that lies within each other and thereby makes our approximations more complex. We

might also get a good approximation by using the max point within the timeslot though this will

require that our sampling rate is big enough.

When approximate the max value we will also look at the negative values since max points might be

found amongst them as well. Therefore we will set all values within our timeslot to positive values by

use of the root square method. And also we will do our calculations in a new array and shed the old

indexes.



45

Figure 45, the sound event shown in figure 27 after all values have been made positive.

We will now try to find points suitable for curve fitting that lie within the singled out time slot. To do

this we will begin with the first maximum point in the field and from that point search for the next

maximum point that has higher amplitude. We will continue this search for all maximum points

higher than the last max point until we reach the highest point in the timeslot. When the highest

point has been reach we will redo the same thing starting at the end of the time slot and work

ourselves back to the maximum point. All points that are not found to be a local maximum higher

than the last local maximum will be set to 0.

Figure 46, shows us the points we will use to approximate the maximum amplitude of the event.



46

Our idea at this point is to try to fit a polynomial to this data and to fit it as tight as possible around

the maximum point. Since the length of the data should have no affect on the max point and the

fading out part of the data is as irrelevant we have focused all our effort on the maximum points and

3-5 points to every side of it.

After experimenting and calculating we descried to use a second degree polynomial focused on the

maximum point and its two nearest neighbors as our approximation.

Of course the quality of our approximation is a key issue for our future calculations and work can be

done in this section for years to come. We have chosen a direct and fast approach so that we can

move on for now and examine the whole problem.

Figure 47, our second degree polynomial seen in red against the sound event data shown in blue.

The data from our approximation is stored and we now have a time for the sound event and also the

approximated maximum amplitude that can be seen in the event.

The final work done on sound preprocessing was to put in a safeguard against single sound peaks

breaching our threshold. To handle these kinds of situations we set a simple select statement that

forbids events with less than three points above the threshold from entering the approximation

calculation.



47

Figure 48, an example of a case where some of the found sounds will be omitted from the approximation calculation.

In this sections final figure, figure 48, we see an example of the above explained phenomena. The last

sound event shown will be omitted on account of being too small for calculations.

Sound source localization

In this part we will look at the task of localizing sound sources using difference in amplitude and

arrival time, we will assume that sound activity is arriving in order at both microphones; if this is

untrue in some of our cases we will take care of this later by use of clustering to eliminate stray

sounds.

We will first look at the easiest available case where we have two microphones set up at one side of

the weld area.

Using two microphones

When using two microphones set up at opposite sides of the weld area sound source localization is a

process of calculating the distances from the two microphones to the source. This is done by

comparing the sound data in each microphone and treating these as hypotenuses in two triangles

that share one side, the y value.



48

Figure 49: Two microphones used to create triangles for positioning.

Since we will now the difference in arrival time and amplitude we know both the relation between

the two Hypotenuses and their difference in length.

Figure 50: In this figure we see the readout from the two microphones

With the use of this information we can began calculations to determine the position of the source of

the analyzed sound. First we will look at the known constants and correlation between variables. We

will name the variables for the distance from our microphones to the point P on the X-axis X1 and X2.

And the distance on the Y-axis, which is the same for both microphones will simply be called Y. Our

output value for X will be the same as X1. When looking at our two X values we see from the figure

that:

� � � � �

We also know from earlier reasoning that we can determine the relation in length between the

hypotenuses as the inverse of the relation between measured amplitudes.

� � � ��

The difference in length Q between our two hypotenuses is given by multiplying the speed of sound

with their difference in arrival times, and knowing that H2 will always be longer that H1 gives us:



49

� �� ∆� � �

In this equation c represents the speed of sound. Knowing this we can now set up a simple equation

system to give us the length of each of our hypotenuses. Solving for H2 in both our equations gives us

two equations:

� � � � �

� � � � �

Putting these two together it is possible to calculate the value of H1:

� � � � � � �

� � � � � � �

� �� 1� � �

� � �� 1� Now that we have calculated the value of H1 we can use that in any of our first two equations to

calculate H2. When this is done we can go on to the actual task of identifying that position in terms of

X and Y values of the point P. As we already know the relation between X1 and X2 and also that the

two triangles share one side it is possible to create a new equation system to solve for the reaming

unknown variables. The system will consist of these equations which we also show with the proper

values having been solved out:

� � � � �

� � � � � ��

� � � � � We will now put these three together in the first equation to solve for X1:

� � � � � � ��

� � � �� 2��

� � ��2��

� � � �� 2�

We can now calculate the value of X1 and use it in the first equation to calculate the value of Y. We

now have the full set off position coordinates for P.

As we see, calculating the position of P using two microphones consists of identifying relationship

between the distances from point P for both microphones and combining this knowledge with some

prior knowledge about the relation between microphones on the X-axis. This gives us a rather simple



50

equation system to solve. When this is done we have identified the point P which is the point where

the examined sound originated.

Testing algorithms

We will now test our localization algorithms on some test data that we created by use of a stereo

microphone, a ball pen, a ruler and some paper. We recorded a sound at a set distance from the

microphone and will now try our algorithms for sound source localization on it. The same sound is

also used to illustrate and show our sound preprocessing techniques, tough in that case we only

looked at one channel at a time.

Figure 51, the two sound data sets shown at the same time.

The first thing to do now is to put both our sound data sets through the sound preprocessing. When

we do this we will be able to see how they relate to each other in terms of number of sound events

and their respective behaviors.



51

Figure 52, here we see the sound data after preprocessing.

From observing figure 52 we see that the number of found sound events in our two sets off data do

not match each other. In the data from the lower channel we have observed more sounds with

amplitude above the threshold values. The last sound is so small that it will be omitted from curve

fitting but we still end up with two sounds in one of our data sets and just one sound in the other.

To handle this and similar cases with multiple sounds in one data set per sound in the other set, we

have decided to set requirements for matching sounds based on arrival time. We use the same

timeslot as when deciding if two spike are of the same event, and decide that for two sounds two be

matched against each other they have to have a starting time no more than 500 indexes(0.01

seconds) apart.

We examine the data that is provided by our preprocessing for the two data sets to see what values

we have for the observed sound events.

Event number / Data set The top Channel (time) The lower channel (time)

# 1 16326 16315

# 2 - 25506 Table 3, showing the timing data provided on our sound events by the sound preprocessing.

Event number / Data set The top channel (amplitude) The lower channel (amplitude)

#1 0.4964 0.3190

#2 - 0.0149 Table 4, showing the amplitude data provided on our sound events by the sound preprocessing.

Now we simply match the data from the top channel to the first data in the lower channel and run

that through a function written to calculate the position as describe earlier in this section.

When we did our testing we were unable to get consistent positive results. We had problems with

calculating the positions of sound sources since the data we worked with was incompatible with the

algorithms. We did however find the causes of these problems which we contribute to the following.



52

• We had a fixed distance between our microphones that was far too small. This was due to

the construction of the stereo microphone we used and therefore beyond our control. We

did not have time and resources to acquire a new microphone due to testing being

scheduled at the end of the project.

• Our approximations on max points within sound events might be a little too inaccurate,

though this should not be given too much weight.

• We used a standard microphone and also standard software to do our testing and face some

problems with time resolution. This lead to problems with distances being too small and our

equipment not exact enough to give the necessary precision in measurements then passed

on to calculations.

We did however see some positive results and saw enough coherencies to validate our calculations.

We hope to continue our work with testing out our algorithm using more precise measurement

equipment and more favorable situations.

Sound data handling and clustering

When the position of the source of each off our registered sound events have been calculated we

save the data as coordinate information. Given this information we can make numerous types of

presentations of the data such as, plotting all points as a representation of the welding area or focus

on certain areas or sounds of certain amplitudes.

When it comes to strategies of clustering there are different ways to go about the task. We have

considered two different approaches. One discrete focusing on sorting our events based on their

position and another less discrete method focusing on amplitude and position relative to other

events.

First approach

In this approach what we do is simply to divide our weld area into fields off a set appropriate size,

and the simply add to value to fields which holds many points. In this approach we go through all

coordinates that we have gathered from sound data and allocate a point to the area from where it

came. In the end we have a field matrix representation of the welding area that has higher points

where there are many sound generating events. Here the size of our fields and the number of fields

decide the resolution of our clustering process.

We can then omit fields that have none or few points and focus our attention on areas where there

are higher points.



53

Figure 53, an example off clustering done with the suggested approach.

An alternative to this approach is to use a similar version where points are given to the fields with

regards to the amplitude of the sound event. This might include categorizing amplitudes into

different classes which yield different amounts of points or simply add the amplitude of the event as

points to the field.

Second approach

The Second approach we suggest is based on the distance between events. And we try to find

groupings of sound events by searching for events that are stringed together by small distances.

Our idea is to choose any event and see if it has any other events close by if it does we mark them as

connected and redo the search for the connecting events, when we can no longer find new points

within the chosen distance we consider our cluster to be completed.

When we have a cluster we use the relative amplitude of all events in the cluster to calculate the

clusters center of mass and use this to pinpoint the cluster on our representation of the welding are.

Clusters that consist of only one or few events are omitted from the search and will not be marked in

the welding area.

Figure 54, a figure showing clustering with the second approach

When the data has been clustered as in figure 54 we do calculations for the clusters center of mass

based on the distances between cluster, their relative positions and amplitudes. The cluster is then

marked in a representation on the weld are by its center of mass.



54

Crack recognition and localization Hypothesis

Our theory concerning the detection on localization of cracks and other related events in the

material is to some extent inspired by the work by A. N. Ser’eznov, L. N. Stepanova, E. Yu. Lebedev, S.

I. Kabanov, V. N. Chaplygin, S. A. Laznenko, K. V. Kanifadin, and I. S. Ramazanov[3].

As in their work we want to use information given by our multi sensor system to calculate the

locations of all sound generating events and then use different clustering methods to gain

information about what goes on in the material. We want to track different types of sound events

and use different clustering strategies to try to get as much useful information as possible.

We also believe that different clustering and analysis methods may give new information on the

same data, one strategy might detect cracks while one might detect welds not cooling properly in

other ways.

What we need to do now is improve our hypotheses by beginning work on recording done with

multiple microphones and start evaluating different clustering approaches and also the analysis tools

used to interpret results from clustering.

Results

After examining the data from Volvo we arrived at a split decision, either the presence of spikes are

not coherent with the presence of cracks or they are in which case some recordings from the first

data set must be discarded as false data. To better determine this we must do more measurements

and it would also help to get a grasp of how much time has been allowed between welds.

According to A. N. Ser’eznov, L. N. Stepanova, E. Yu. Lebedev, S. I. Kabanov, V. N. Chaplygin, S. A.

Laznenko, K. V. Kanifadin, and I. S. Ramazanov[3] the cool down time for a weld is somewhere

around 10 minutes long and sounds will be generated throughout the whole cool down period. This

means that sounds generated in the end of one welds cool down might interfere with the recording

of another weld. To prevent this we must allow enough time between welds so that sound

generating activity is only taking place in the weld that we want to examine.

Since the sensitivity of the equipment was changed during the recording of the first data set it is

possible that spikes belonging to another weld were recorded in the non cracked data at such high

amplitude.

From the theoretical work our result is a set of algorithms and methods that will preprocess and do

calculations in sound data. The algorithms did not do well in our initial tests but too many

parameters in the test were unfavorable and some measurements done on the equipment where

inaccurate.



55

Conclusions and Future work

We will conclude that there is a strong relationship between sound activity occurring at around 150-

200 KHz and changes taking place in the material. Spikes and similar events will be considered as

indications for events taking place inside the cooling materials as long as the spikes occur in

conjunction with a rise in noise at the specified frequency.

We also conclude that experiments must continue and that we need more data to solidify our

theories and also that we will want to use multichannel recording devices so that we can gather

more data from our welds and also try to locate the sources of spikes and other occurrences that we

observe in our data.

We want to keep up experiments at Volvo and keep doing calculations and examinations on the data,

we also want to start development on our localization techniques and gather data to use with our

clustering theory to see how much data can be gathered in this fashion.

We want to explore the field of air transmitted emission and see if we can get data in this way, if that

is possible there is vast potential for development of small hand held devices that can help us control

weld quality, both in industrial environments and in home environments.

The first step of our future work is to gather more data in the same way as we obtained data set 1

and 2 and strive for even more similar procedures for all the welds done in these experiments. We

also want to do measurements over an extended period of time for one single weld to see for how

long it will emit sounds so that we can improve our experiments and reduce that risk of welds

interfering with one another.

We also want to start working with multichannel systems and therefore we want to gather data that

will allow us to get started in that field.

Summary

In this rapport we examined the data provided by Volvo recorded from actual welds in their

laboratory. The data was divided into two sets with the second one being done after initial testing

was performed on the first one which led to some differences in method. We made some interesting

observations in the data and found spikes and noises that might indicate events inside the material.

We had a large section on sound data handling where we also covered how we might track changes

in the material through acoustic emission. We looked at algorithms for sound preprocessing and

sound source location. We also discussed clustering and our theories on how to use the acquired

data to find cracks and other defects within the material.

We finished the rapport with a conclusion and suggestions for future work. The conclusion made

where that given the provided data we lean against a theory where the spikes observed in the

acoustic data do indicate cracks but that we will need more data to confirm this and that we also

need to understand how some of the recording that were made that go against this theory came

about.



56

Referenses

[1] Baifeng JI*, Weilian QU, “The Research of Acoustic Emission Techniques for Non Destructive

Testing and Health Monitoring on Civil Engineering Structures!”, Hubei Key laboratory of

Roadway Bridge&Structure Engineering., Wuhan University of Technology, Wuhan 430070, China

[2] C.E. Hartbower, W.G. Reuter, C.F. Morais and P.P. Crimmins. “Use of Acoustic Emission for

the Detection of Weld and Stress Corrosion Cracking”. Acoustic emission STP 505, American

society for Testing and Material 1972.

[3] A. N. Ser’eznov, L. N. Stepanova, E. Yu. Lebedev, S. I. Kabanov, V. N. Chaplygin, S. A.

Laznenko, K. V. Kanifadin, and I. S. Ramazanov. “Acoustic-Emission Study of the Possibilities

of Localizing Flaws of a Welded Joint during Cooling”. Chaplygin Siberian Research Institute of

Aviation, ul. Polzunova 21, Novosibirsk, 630051 Russia Received November 17, 2008

[4] E. D. Di Claudio, R. Parisi and G. Orlandi, “MULTI-SOURCE LOCALIZATION IN REVERBERANT

ENVIRONMENTS BY ROOT-MUSIC AND CLUSTERING”, INFOCOM Dpt. University of Rome “La

Sapienza” Via Eudossiana 18,I-00184 ROMA RM Italy

[5] Ming Jaan, Alex C. Kot, Meng H. Er, “PERFORMANCE STUDY OF TIME DELAY ESTIMATION IN A ROOM ENVIRONMENT”, Centre for Signal Processing School of Electrical and Electronic

Engineering Nanyang Technological University, Nanyang Avenue, Singapore 639798

[6] Brent C. Kirkwood, “Acoustic Source Localization Using Time-Delay Estimation”, Technical

University of Denmark, August 4, 2003

Appendix A, Matlab

Instructions for using this Appendix

This appendix consists of a number of Matlab .m-files. To use them as intended follow the following

steps:

1. Load appropriate sound data into a variable called data. Appropriate sound data means data

recorded using two parallel channels(Stereo)

2. Copy the entire code of the file Preprocessing.m and paste it at the end of itself, then make

the following changes to it:

at line 9 change: A=data(:,1); into A=data(:,2);

at line 339 change Top_Channel_Time = Event_time; into Low_Channel_Time = Event_time;

at line 340 change Top_Channel_Amp = Event_peak; into Low_Channel_Amp = Event_peak;

3. Run Preprocessing.m

4. You now have the data you need for position calculation in the variables

Low_Channel_time, containing event times for channel B

Top_Channel_time, containing event times for channel A

Low_Channel_Amp, containing event amplitudes for channel B

Top_Channel_Amp, containing event amplitudes for channel A

5. Run Get_coordinates.m



57

6. Examine your result in Pos_X and Pos_Y, two vectors containing the coordinates for found

points listed in chronological order.

Preprocessing.m % all Matlab code for the sound preprocessing, if you mean to use this % code, read through the instructions in: Appendix Matlab code clear Top_channel_Time; %clear these for reruns of the program

clear Top_channel_Amp; clear Event_time; clear Event_peak;

A=data(:,1);% this whole section is run twice in this M-file, the second

run is omitted from appendix % second run: A=data(:,2); % the ending part where the data is saved at line 320 and 321 % is also altered in the second run

%The first step is to find max and min in the array made up by sound data, %multiply these with our resolution and round them.

resolution = 100; %100 means second decimal Ma = max(A); Mi = min(A);

Ma = Ma*resolution; Mi = Mi*resolution;

Ma = round(Ma); Mi = round(Mi);

size_F = Ma - Mi; %determines the size of the field used to count

frequencies.

%create an array of the the appropriate size with indexes from 1..X

%This array will be used to find out which values are most common in the %examined sound and thereby find the base level from which the sound data %oscillates. clear Freq_field; Freq_field(size_F+1) = 0;

%for all elements: %multiply by a hundred, round and subtract the min value to get x %add one to the array index(x+1).

%First we get the size of A size_A_vec= size(A); size_A = size_A_vec(1);

for ind=1:size_A, x = A(ind); x = round(resolution*x) - Mi;



58

Freq_field(x+1) = Freq_field(x+1) +1; end

[C,I] = max(Freq_field); %now we find out which index(distance) that has gotten most "votes".

distance = (Mi + I-1)/resolution; B=A; for ind=1:size_A, B(ind)=B(ind)-distance; end

%output is stored in an array called B %B contains the data from array A recalculated to oscillate a lot closer to %0.

MaZ = B; size_MaZ = size_A; %we have an array around zero and want upper and lower thresholds.

%the Array is called MaZ and its known size is in size_MaZ sum = 0; for ind=1:size_MaZ, % here we do! x=MaZ(ind); x = x^2; x = sqrt(x); sum = sum + x; end %to calculate treshold values we will use the formula for peaks relative to %rms.

%Xf=P/RMS formula for calculating the threshold.

%we will set a certain value for Xf. % we are looking for RMS*X where Xf is the factor, Xf = 3.50; % value chosen to fit the problem and give manageable data. % this value gives a simple curve for trying out our further solutions and % algorithms. for ind=1:size_MaZ, Upper_T(ind) = Xf*(sum/size_MaZ); Lower_T(ind) = Xf*((sum/size_MaZ)*-1); end

%now we have the values for our threshold stored in an array matching %indexes so that we can plot them in nice understandable graphs hold off subplot(2,2,1); plot(A)

%Also plots the field where we counted the number of entries per value so %that we can see it and get a better feel for it. subplot(2,2,2); plot(Freq_field) subplot(2,2,3); plot(B)

%here we create and array that we will use later when plotting found sound



59

%activity: Activity = MaZ;

% this loop exists to set all sound events that do not clear our threshold % values to 0. for ind=1:size_MaZ, activity(ind)=0; if MaZ(ind) < Upper_T(ind) && MaZ(ind) > Lower_T(ind) MaZ(ind) = 0;

end end %Now we plot our trimmed data with the thresholds plotted in red subplot(2,2,4); hold off plot(MaZ) hold on plot(Upper_T,'Color','red') plot(Lower_T,'Color','red')

%now we shall figure out where we have sound activity, that is where we %should apply our analytic tools.

%In the activity array values are paired giving the first and last index in %each sound event.

%copy for plotting, this is only here to help make understandable plots plot_act = activity;

activity_p = 1; % is an activity array pointer(pointing at where data

should go)

found = 0; %variables for finding activity. has_length = 0;

%describing this loop: %The point of this loop is two move through the data until it finds %activity over the threshold(any non 0 value). When this is found it shall %search for further values and see which corresponds to the same event. %An event is considered over when more than 500 indexes has passed since %last activity(at our Sampling rate of ~44KHz this means around 0.01 %seconds). %the loops should also exclude sounds that are alone for 500 indexes in any %direction. for ind=1:size_MaZ, if MaZ(ind)==0 && found==0 %no sound

elseif MaZ(ind)~=0 && found==0 %found sound from no sound found = 1; activity(activity_p) = ind; activity_p = activity_p + 1; elseif MaZ(ind)~= 0 && found==1 && has_length==0 if ind - activity(activity_p-1) > 500 %single peak, no find activity_p = activity_p-1; found = 0; else %found something activity(activity_p)=ind; has_length = 1; end



60

elseif MaZ(ind) ~= 0 && found ==1 && has_length ==1 %gives two cases, either it’s the end of previous sound or the

beginning %of a new one

if ind - activity(activity_p) > 500 %compares against end of sound %means its a new sound has_length = 0; activity_p = activity_p+1; activity(activity_p) = ind; activity_p = activity_p + 1; %now it is ready to examine the sound as if it were a new one else activity(activity_p) = ind; end else

end

end

% now we want to make it plot able in some nice and understandable way

using % plot_act found = 0; activity_p =1; nr_of_s = 0;

%This only makes a plot able line that is high when we are inside a sound %event and then it is low when we are outside of registered sound events. for ind=1:size_MaZ, if ind < activity(activity_p) && found ==0 % no activity plot_act(ind) = 0.1; elseif ind == activity(activity_p) && found == 0 %start of activity nr_of_s = nr_of_s +1; %record new sounds found = 1; activity_p = activity_p+1; plot_act(ind) = 0.2; elseif ind < activity(activity_p) && found ==1 plot_act(ind) = 0.2; elseif ind == activity(activity_p) && found == 1 found = 0; activity_p = activity_p+1; plot_act(ind) = 0.1; else plot_act(ind) = 0.1; end end

%Here we plot the line that shows us where we have activity. plot(plot_act,'Color','green')

%sound events now have begginings and ends.

%both will be created when needed

% we study all sounds one by one to determine their peaks and also their



61

% times(times will be their start times).

%To place them in correct order we will need a peak index, showing where to %put information calculated from the currently examined peak. Peak_index = 1; %points initially to the first index.

for ind=1:nr_of_s, Event_start = activity(ind*2 -1); Event_end = activity(ind*2); Event_array = MaZ(Event_start:Event_end); %copys the data from within

the time slot to a new array.

for index=1:size(Event_array), Event_array(index) = sqrt(Event_array(index)^2); end %Event array now only contains positive values

%here is where we mark the points that are both local maximum points and

higher than the proceeding point. %We begin with the first point and move on until we find a point that is %both a local max point and higher than the start point, we den redo %this from the new point and keep on until we reach the maximum point.

%this is then done once again in reverse form the end of the data field.

%we begin by saving the index for the whole intervals maximum point [Toss,Glob_Max] = max(Event_array); %we define a target array(we might as well just keep the points but %this helps in showing our results Found_points = Event_array; Found_points(1) = Event_array(1); % loads the first point into the

array %and a variable to save the amplitude of the last maximum point. Last_amp = Event_array(1); %This loops goes from first index to global maximum for index=2:Glob_Max, % begins at the second index since the first index

is atomically a max point %first we find out if what we see is a max point if Event_array(index-1) < Event_array(index) && Event_array(index+1)

< Event_array(index) %we have a max point if Event_array(index) > Last_amp Last_amp = Event_array(index); Found_points(index) = Event_array(index); else Found_points(index) = 0; end else Found_points(index) = 0; end end

%Now we are to reset our variables to search for the other way around %first we set the last point size_Event_array_vec= size(Event_array); End_point = size_Event_array_vec(1); Found_points(End_point) = Event_array(End_point); %we then set Last_amp to that point: Last_amp = Event_array(End_point); %now we set the end point for our loop



62

Loop_end_index = End_point - Glob_Max; %for convenience we also store the size of the array in a variable

%now we loop for index=1:Loop_end_index, % begins at the second index since the

first index is atomically a max point %first we find out if what we see is a max point Act_index = End_point-index; if Event_array(Act_index+1) < Event_array(Act_index) &&

Event_array(Act_index-1) < Event_array(Act_index) %we have a max point if Event_array(Act_index) > Last_amp Last_amp = Event_array(Act_index); Found_points(Act_index) = Event_array(Act_index); else Found_points(Act_index) = 0; end else Found_points(Act_index) = 0; end end

%to continue with curve plotting we shall arrange our points into two %vectors, one for X and one for Y_values. X_Y_Vec_I = 1; clear X_values; clear Y_values; for index=1:size(Found_points), if Found_points(index) == 0; else

X_values(X_Y_Vec_I) = index; Y_values(X_Y_Vec_I) = Found_points(index); X_Y_Vec_I = X_Y_Vec_I + 1;

end end %does what its supposed to

%ensure that no stray sounds are measured if X_Y_Vec_I > 4 %code to find Max values in the two arrays and focus in on them and their %closest neighbors. [Max_in_Y,index_of_max] = max(Y_values);

low = index_of_max-1; high = index_of_max+1; TEsting = X_values; X_values = X_values(low:high); Y_values = Y_values(low:high);

p = polyfit(X_values,Y_values,2); X_vector = 1:150; clear y; y = polyval(p,X_vector); Event_max = max(y);

%Now we report on our findings: Event_time(Peak_index) = Event_start; Event_peak(Peak_index) = Event_max; Peak_index = Peak_index + 1;



63

else end

end %This saves our findings for future calculations Top_channel_Time = Event_time; Top_channel_Amp = Event_peak;

Get_coordinates.m %Get coordinates from the Time/amplitude arrays.

%When this file is run you should have the following variables: %Low_Channel_Time, containing event times for channel B %Top_Channel_Time, containing event times for channel A %Low_Channel_Amp, containing event amplitudes for channel B %Top_Channel_Amp, containing event amplitudes for channel A

% our strategie here is a loop within a loop wich hangs at a value in the % first data set(hanging on Time values) %we then compare times with time from the other microphone, when we find %the closest value in time(that lies within 500 indexes(0.01sec)) we do our %calculations.

size_Top_vec= size(Top_channel_Time); size_Top = size_Top_vec(2)

size_Low_vec= size(Low_channel_Time); size_Low = size_Low_vec(2)

Out_put_index = 1; ind_L = 1;

for ind_T=1:size_Top, Loop_break = 0; while ind_L < size_Low && Loop_break == 0, % we will fiorst see if we have a match right of the bat

if Top_channel_Time(ind_T) - Low_channel_Time(ind_L) < 500 &&

Top_channel_Time(ind_T) - Low_channel_Time(ind_L) > -500 % they match eahother %here we will make a call to the function pos which takes the %following arguments as input: %AVin, Is the Amplitude of the microphone that is furthest away %from the weld %TVin,Time fro the microphone that is furthest away %AHin, Amplitude for the closer microphone %THin, Time for the closer microphone %din, distance between microphones in mm.

% in our data the lower channel was closer to the test sound % events. [Pos_Y(Out_put_index) Pos_X(Out_put_index)] =

pos(Top_channel_Amp(ind_T),Top_channel_Time(ind_T),Low_channel_Amp(ind_L),L

ow_channel_Time(ind_L),10); Out_put_index = Out_put_index + 1;



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Loop_break = 1; elseif Top_channel_Time(ind_T) > Low_channel_Time(ind_L) % case

here we need to advance the second channel so do nothing Ind_L = Ind_L + 1; else Loop_break = 1; end end end

Position.m function [y x] = pos(AVin,TVin,AHin,THin,din)

%Calculations as seen in the rapport.

AmpV = AVin; %closest microphone Amplitude TidV = TVin; %Closest microphone Time AmpH = AHin; %Furthest away microphopne Amplitude TidH = THin; %Furthest away microphopne Time d = din; %Distance between te microphones in millimeters

R = AmpV/AmpH; %amplitudes

Q = (TidH-TidV)*330/1000; %Time in nano seconds, results in millimeters

Hb = Q/(R-1) Ha = Hb*R

b = (Ha^2-Hb^2+d^2)/(2*d); a = d - b; %our x value h = sqrt(Hb^2-b^2); %our y value

x = b; y = h;

end

crack detection in welding process using acoustic …310692/fulltext01.pdfmälardalen university...

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