application of error analysis in engeering

8/7/2019 Application of Error Analysis in Engeering

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APPLICATION OF ERRORANALYSIS IN ENGEERING

GROUP MEMBER:FAIZA MUSHTAQ UW 07 EE-01ALEENA ZAFARUW 07 EE-02

SAHAR KHALIDUW 07 EE-03HAMMAD RIAZUW 07 EE 04


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ANALYSIS

Analysis is when you tell your results prove or disprove your original guess or hypothesis.Explain why your results turned out this way

NUMERICAL ANALYSIS:The study of approximation techniques forsolving mathematical problems, taking intoaccount the extent of possible error. The branchof mathematics concerned with obtainingnumerical answers by approximations, ratherthan by analytic solution.


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ERROR ANALYSIS

Error analysis is the study and evaluation of uncertainty in measurement. No experiment,however carefully made, can be completelyfree of uncertainties.The same error analysis can be used for anyset of repeated measurements whether theyarise from random processes or not.


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CONT .

In the solution of a problem on a digital computer, the estimation of the cumulativeeffect of rounding or truncation errorsassociated with basic arithmetic operations


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TYPES OF ERROR ANALYSIS

Gross error:

Errors that occur when a measurement processis subject occasionally to large inaccuracies. It is occur due to human or person.Rand om error:

Random errors are errors in measurement

that lead to measurable values beinginconsistent when repeated measures of aconstant attribute or quantity are taken.


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System a tic error:

Systematic errors are caused by imperfect

calibration of measurement instruments or imperfect methods of observation , or interference of the environment with themeasurement process, and always affect theresults of an experiment in a predictabledirection


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App roxim a tio n error:

The approximation error in some data is thediscrepancy between an exact value and someapproximation to it. An approximation errorcan occur because

1. The measurement of the data is not precise

(due to the instruments), or2. Approximations are used instead of the real

data .


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Ab solute error:

The absolute error is the magnitude of the

difference between the exact value and theapproximation.

Given some value v and its approximationvapprox, the absolute error is


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Rel a tive error:

The relative error is the absolute error divided

by the magnitude of the exact value.where the vertical bars denote the absolute

value . If the relative error is


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P erce n t ag e error:

The percent error is the relative error expressed

in terms of per 100and the percent error is


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APPLICATIONS IN DIFFERENT FIELDSof engineering:

Electrical engineeringMechanical engineering:

Software engineering:Marine engineering


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MARINE engineering:

In marine engineering error analysis technique isalso used .for example a ship is cruising in theocean .in ships ultrasonic rays are propagatedinto water and reflected back if any hurdles arecome. If hurdles are come then ship deviate or

change its path. Here we use the error will comebetween the original path and deviated path. Soerror analysis technique is used here.


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CONT


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E lectro n ics e ng in eeri ngIn Venire calipers:Instrument error refers to the combined accuracy and precision of a measuring instrument , or the differencebetween the actual value and the value indicated by the instrument ( error ). Measuring instruments are usuallycalibrated on some regular frequency against a standard . The most rigorous standard is one maintained by astandards organization such as NISTin the United States , or the ISO in European countries. However, in physicsprecision, accuracy, and error are computed based upon the instrument and the measurement data. Precision is to1/2 of the granularity of the instrument's measurement capability. Precision is limited to the number of significantdigits of measuring capability of the coarsest instrument or constant in a sequence of measurements andcomputations. Error is the granularity of the instrument's measurement capability. Error magnitudes are alsoadded together when making multiple measurements for calculating a certain quantity. When making acalculation from a measurement to a specific number of significant digits, rounding (if needed) must be doneproperly. Accuracy might be determined by making multiple measurements of the same thing with the sameinstrument, and then calculating the result with a certain type of math function, or it might mean for example, afive pound weight could be measured on a scale and then the difference between five pounds and the measuredweight could be the accuracy. The second definition makes accuracy related to calibration, while the firstdefinition does not.The instrument error is not like random error , that can't be removed. Sometimes the removal of instrument errorsare very easy, but it is case dependent. In Engineering instruments, like voltmeter or ammeter for example, theinstrument error is very difficult to remove. Ammeter has built in resistance, which can't be removed either way.So the only way is to minimize it. On the other hand, the removal of error of a thermometer is a bit simple. Onlythe calibration has to be removed and then again calibrate it carefully. Sometimes, the user doesn't care forremoval of error from the instrument, else he compensates it in calculation, for example, the zero error in VernierCaliper is eliminated by proper calculation


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rror ana ys s n mo ecu ar ynam cssimulation:

In molecular dynamics (MD) simulations, there areerrors due to inadequate sampling of the phase spaceor infrequently occurring events, these lead to thestatistical error due to random fluctuation in themeasurements.For a series of M measurements of a fluctuatingproperty A, the mean value is:formula

When these M measurements are independent.


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Propagation of uncertainty:

propagation of error (or propagation of uncertainty) is the effect of variables ' uncertainties (or errors ) on the uncertainty of a functionbased on them.When the variables are the values of experimental measurementsthey have uncertainties due to measurement limitations (e.g.instrument precision ) which propagate to the combination of variables in the function.The uncertainty is usually defined by the absolute error .Uncertainties can also be defined by the relative error ( x)/x, whichis usually written as a percentage.Most commonly the error on a quantity, x, is given as the standarddeviation , . Standard deviation is the positive square root of variance , 2. The value of a quantity and its error are oftenexpressed as x x.


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Autocorrelation:

Autocorrelation is the cross-correlation of asignal with itself. Informally, it is the similaritybetween observations as a function of thetime separation between them.By this we can find the error in the delayversion of orignal data.


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Error analysis of electronic instrumenttransformers:

The system error characteristics are analyzed to improvethe measurement accuracy of electronic instrumenttransformers. The noise characteristics of the electronicinstrument transformers are related to the error

characteristics of front-amplifiers, A/D converters, andsignal processing units on the low-voltage side. The analysisidentifies the key factors influencing the systemmeasurement accuracy. Criteria are then developed forcomponent selection and system design of thetransformers with a 220 kV electronic current transformerdeveloped and tested. The results show that the currenttransformer meets the IEC 0.2 class accuracy requirements,has a ratio the range of error of less than 0.1% and aphase error of less than 2 at the range of-30 to +70 .


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in mech an ic a l e ng in eeri ng :

Error analysis is used during the stabilization

of different mechanical body such as segways.means when the error occur due to instabilityof body the accelerometer or gyroscope areused for apply the control algorithmic.


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Telecommu n ic a tio n :

In information theory and coding theory withapplications in computer science andtelecommunication , error detection and correction orerror control are techniques that enable reliabledelivery of digital data over unreliable communicationchannels . Many communication channels are subjectto channel noise , and thus errors may be introducedduring transmission from the source to a receiver. Errordetection techniques allow detecting such errors, whileerror correction enables reconstruction of the originaldata


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In numerical modeling:

In numerical simulation or modeling of realsystems, error analysis is concerned with thechanges in the output of the model as theparameters to the model vary about a mean.For instance, in a system modeled as afunction of two variables . Error analysis dealswith the propagation of the numerical errorsin and (around mean values and ) to error in(around a mean ).


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In numerical analysis, error analysis comprisesboth forward error analysis and backward erroranalysis. Forward error analysis involves the

analysis of a function which is an approximation(usually a finite polynomial) to a function todetermine the bounds on the error in theapproximation; i.e., to find such that . Backward

error analysis involves the analysis of theapproximation function , to determine thebounds on the parameters such that the result


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See Figure 12 Forward error propagation: difficult andusually leads to overestimates (pessimistic).Backward error propagation: How much error in inputwould be required to explain all output error?Assumes that approximate solution to problem is goodIF IT IS THE exact solution to a ``nearby'' problem.Example Want to approximate . We evaluate itsaccuracy at .


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application of error analysis in engeering

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