analysis of the main factors influencing the dominant

Research ArticleAnalysis of the Main Factors Influencing the DominantFrequency of Blast Vibration

Da Liu12 Wenbo Lu 12 Yijia Liu12 Ming Chen 12 Peng Yan12 and Pengchang Sun12

1State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan 430072 China2Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering Ministry of Education Wuhan UniversityWuhan 430072 China

Correspondence should be addressed to Wenbo Lu wbluwhueducn

Received 10 December 2018 Revised 27 January 2019 Accepted 7 February 2019 Published 12 March 2019

Academic Editor Yuri S Karinski

Copyright copy 2019 Da Liu et al -is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

At present the study on the dominant frequency of blasting vibration is still a worldwide problem Compared with the matureresearch on the particle peak velocity of blasting vibration the researches on the dominant frequency of blasting vibration aremuch less In this paper by analyzing the main influencing factors of the dominant frequency an attenuation equation of thedominant frequency induced by blasting vibration has been proposed by dimensional analysis combined with the theory of radialspherical wave propagation -e proposed equation is applied to the fitting analysis on the dominant frequency measured inZhoushan Green Petrochemical Base in China which has obtained a favorable fitting correlation Based on the fitting analysis ithas found that the correlation coefficient of radial vibration obtained by the proposed equation is higher than that of verticalvibration which is resulted from the reason that the vibration in vertical is considered to be influenced most by the R-wave on theground and perceived to be quite different from the radial vibration affected by P-wave In generally different components ofblasting waves will affect the attenuation of dominant frequency

1 Introduction

Blasting excavation has been widely used in mining waterand hydropower engineering highway municipal infra-structure construction and other fields [1] Althoughblasting is an indispensable efficient and economical ex-cavation technology it inevitably brings adverse effects onthe surrounding buildings and environment In order tocontrol the blasting vibration it is necessary to predict thevibration induced by blasting [2] In recent years the re-search on blasting vibration velocity has formed a maturesystem and peak particle velocity (PPV) is often used as acriterion for evaluating blasting vibration safety [3] Bycontrast the study on the prediction of blasting vibrationfrequency is much less In fact more and more researchesrevealed that when the dominant frequency of blasting vi-bration is close to the natural frequency of the structure itwill produce resonance effect and easily cause damage to thestructures even if the PPV is in the range of safety standard[4 5] -erefore it is also of great significance to study the

attenuation law of the dominated frequency to keep theunderprotected structure stability and safety

-e dominant frequency induced by blasting is affectedby many factors including characteristics of explosionsource distance away from explosion source and physical-mechanical properties of rock [6] Among them Zhonget al [7] have found that the dominant frequency bandshifts from mid-high frequency to low frequency and thedominant frequency band become more concentrated withthe increase of the distance away from explosion sourcethe charge weight per delay and the decrease of thenumber of delay in millisecond detonation Yang et al [8]has found that the vibration frequency of breaking blast-hole of full-face millisecond delay blasting in undergroundopening excavation increases as the burden decreases Linget al [9] have studied the difference of energy distributioncharacteristics of blasting vibration signals in frequencydomain under single-delay blasting and multidelay milli-second blasting by using wavelet analysis technologyTripathy and Gupta [10] have indicated that the vibration

HindawiShock and VibrationVolume 2019 Article ID 8480905 17 pageshttpsdoiorg10115520198480905

induced by blasting is diversified with the rock and geo-logical condition

-e majority of factors affecting the dominant frequencyof blasting vibration can hardly be described quantitativelyAs a result it is very difficult to accurately obtain the at-tenuation law of the dominant frequency [11] Generallyspeaking the dominant frequency of blasting vibrationdecreases exponentially with the increase of the distanceaway from the explosion source due to the high-frequencyfiltering characteristics of rock [12] In recent years with theprogress of the analysis technique of blasting vibrationspectrum many prediction formulas have been proposed byusing the method of artificial neural network [13] supportvector machine [14] and gene expression programming[15] Although these formulas can obtain favorable fittingcorrelation they are difficult to apply in engineer practicebecause of its too complex fitting parameters and calcula-tion -erefore it is necessary to obtain a simple andpracticable formula which can reflect the changes of thedominant frequency with distance

2 The Attenuation Equation of DominantFrequency Induced by Blasting

21 Analysis of Main Influencing Factors of the DominantFrequency -e explosive releases enormous energy in theprocess of blasting in rock which mainly transforms intoblasting shock wave stress wave and blasting gas In theprocess of stress wave propagation in rock due to the energyattenuation of wave and the damp absorption effect of rockthe properties and waveforms of stress wave will changecorrespondingly with distances It will form the crushingzone cracking zone and elastic zone successively with thedistance far from the blastholes [1] In order to analyze thepropagation and attenuation of blasting seismic wave byusing elastic wave theory the inelastic zone (crushing zoneand cracking zone) near the blastholes is equivalent to theblasting source and the blasting load is acted on theequivalent elastic boundary (cracking boundary ie theouter boundary of the crushing zone) -erefore the the-oretical solution of the elastic wave excited by a sphericalcavity in an elastic medium can be adopted and the theo-retical solution is given by Favreau [16]

Introducing potential function φ to represent radialdisplacement

u zφ(r t)

zr (1)

where u is the radial displacement r represents the distancebetween blasting source with the measuring points and t isthe time

Assuming the load function acting on the inner wall ofthe spherical cavity is p(t)

φ(r t) minusa

ρωr1113946

s

0p(sminus t)e

minusητ sin(ωτ) dτ (2)

s tminusrminus a

CP

(3)

η 1minus 2]1minus ]

CP

a (4)

ω

1minus 2]

radic

1minus ]CP

a (5)

where p(t) is the blasting load acted on elastic cavity λ and μare the constant of Lame ] is Poissonrsquos ratio ρ is the densityCP is the longitudinal wave velocity a is the radius of elasticcavity (cracking zone) ω is the phase of function φ is alsothe natural frequency of the equivalent system and s and ηare intermediate variables

It is often assumed that the law of blasting load p(t) isused in the following form [17]

p(t)

0 tltminusτ1

σmax1 + t

τ11113888 1113889 minusτ1 le tle 0

σmax1minus t

τ21113888 1113889 0le tle τ2

0 tgt τ2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

where σmax is the peak value of the blasting load τ1 is therising time of the blasting load and τ2 is the time of blastingload reduction from peak to zero

Bymeans of the Fourier transform the velocity spectrumof blasting vibration in the elastic rock mass can be obtainedas follows [8 17]

F(ω) Sσ(jω)

11138681113868111386811138681113868111386811138681113868aωCP

C2P + r2ω2

1113969

4μr2

CPa( 11138574

+[1minus(λ + 2μ)2μ]ω2 CPa( 11138572

+[(λ + 2μ)4μ]2ω41113969 (7)

Sσ(jω)1113868111386811138681113868

1113868111386811138681113868 σmax

aebeτω211138581 + a2e + b

2e + 2aebe cosωτ

minus 2 ae cos beωτ + be cos aeωτ( 1113857111385912

(8)

where F(ω) is the velocity spectrum of blasting vibrationSσ(ω) is the stress spectrum of blasting load τ τ1 + τ2ae τ1τ and be τ2τ

It can be concluded from equation (7) that the maininfluencing factors of velocity spectrum include threeaspects firstly the distance away from blasting sourcer secondly the parameters of rock λ μ ] and CP andfinally the parameters of blasting such as the radius ofelastic cavity (the cracking zone) a and load parameters aebe and τ

2 Shock and Vibration

In practical compared with spherical charge cylindricalcharge is used in open-pit blasting excavationmore frequentlywhich is in advantage of its more uniform distribution ofexplosive energy in rock mass Although the theoretical so-lution discussed previously is aiming at the spherical charge infact analysis of the experimental data showed that blasts ofcylindrical charges are similar to the processes observed inseismic investigations of blasts with spherical charges [17]-is is because spherical and cylindrical waves excited byspherical or cylindrical explosive sources can be regarded asplane waves when they propagate to the far region [1] If theelastic cavity formed by cylindrical charge blasting is regardedas an equivalent blasting source the blasting load will beapplied to the boundary of the elastic cavity -e radius of theequivalent blasting source will be the radius of the boundary ofthe elastic cavity a as shown in Figure 1

However in the process of cylindrical charge blastingsome explosive energy will propagate in the form of stress wavein rock According to the different propagation paths of waveit can be divided into body wave and surface wave -epropagation of body wave in rock mass can be divided intocompressive wave (P-wave) and shear wave (S-wave) In termsof the existence of the surface free surface the surface wave (S-wave) will also appear on the surface free surface of the semi-infinite space which is the most significant symbol differentfrom the spherical charge blasting in infinite rockmass In factstudies have shown that for vertical hole blasting the P-wave isan important component for both near and far distance and itmainly acts on the horizontal and radial vibrations the S-waveis only the dominant wave in the near zone and its role in thefar zone can be neglected the R-wave grows and developsgradually at a farther distance and it will have a major impacton vertical vibration [2] -erefore if taking the elastic cavityformed by cylindrical blasting as a spherical blasting sourcethe radial vibration induced by the cylindrical blasting sourcewill be closer to the vibration induced by the spherical blastingsource than that of vertical direction as shown in Figure 1

Considering the condition of single-hole blasting themultiple-hole blasting is equivalent to the elastic superpo-sition of each single hole as shown in Figure 2

Figure 3 illustrates the changes of the dominant fre-quency of blasting vibration with distance where the dis-tance away from the blasting source is r1lt r2lt r3 and thedominant frequency of each distance is f1gt f2gt f3 -edominated frequency used to fitting analyzing in this paperis zero-crossing dominant frequency which is also shown inFigure 3 and it is the most commonly used form ofdominant frequency when the waveform has a clear peak [2]

22 Dimensional Analysis of the Dominant Frequency It isknown from the previous analysis that the vibration inducedby elastic spherical cavity mainly depends on the longitu-dinal wave velocity CP the radius of the elastic cavity a thedensity of the rock ρ the charge weight Q and the distancebetween the blasting source with the measuring points r asshown in Table 1

Among all the parameters shown in Table 1 a CP and ρare independent with each other and include three basicdimensions of measurement mass M length L and time T

which are selected as the main parameters of the dominatedfrequency by using the dimensional analysis method

Based on the π-theorem three nondimensional equa-tions are established as follows [18]

π1 aα1Cβ1P ρc1f

π2 aα2Cβ2P ρc2r

π3 aα3Cβ3P ρc3Q

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)

When the dimension of each physical quantity issubstituted according to the principle of dimension ho-mogeneity the dimensionless expression is obtained

π1 fa

CP

π1 Q

a3ρ

π3 r

a

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)

-e functional relationship between dimensionless di-mensions is as follows

f CP

a

Q13

rρ131113888 1113889

αr

a1113874 1113875

β (11)

where α and β are coefficientsUnder the condition of spherical charge the charge

weight can be expressed as follows

Q 43πqa

3 (12)

where q is the unit explosive consumption of rockUnder the condition of cylindrical charge the charge


Q 16πqd

3 (13)

where d is the diameter of the blastholeIt can be seen that a d and Q are not independent

Comparing equations (5) and (11) and considering the re-lationship between a d and Q in (12) the attenuationequation of blasting vibration dominant frequency inducedby spherical explosion can be obtained

f ξCP

Q13Q13

r1113888 1113889

β

(14)

where ξ are β are coefficientsIn fact ξ is a coefficient that included the effect of

properties of rock -e longitudinal wave velocity CP is alsoone of the parameters reflecting the properties of rocks If theeffect of CP is included in the coefficient ξ and the di-mensional consistency of (14) is not considered the cor-relation coefficient of (14) will not be affected and theequation can be further simplified as follows

f ζ

Q13Q13

r1113888 1113889

β

(15)

where ζ is the coefficient

Shock and Vibration 3

e charge weight of the cylindrical charge in benchblasting is

Q qHSB (16)

where Q is the charge weight H is the bench height S is theblastholes spacing and B is the row spacing

In mining bench blasting bench height H is generallyadopted as (15ndash20)B stemming length is (07ndash10)B dril-ling depth is 03B blastholes spacing S (10ndash20)B and rowspacing B and drilling diameter d have a relationship ofB (25ndash35)d [1] So according to the assumption in Section21 and the proportional relationship among dishyerentblasting parameters mentioned above equation (15) is stillvalid for cylindrical charge blasting

Moreover with the increase of the distance away fromthe blasting source the wave front formed by the blasting

seismic wave is cylindrical wave front Revised from thetheory of cylindrical waves in reference to the attenuationformula of PPV [19] equation (15) can be rewritten asfollows

f αQ12

Q12

r( )

β

(17)

where α and β are coecients

3 Fitting of Frequency Attenuation Law ofOpen-Pit Blasting in ZhoushanPetrochemical Base

31 Engineering Background Zhoushan Green Petrochem-ical Base is located in Zhoushan City Zhejiang ProvinceChina As shown in Figure 4 the project plans to reclaim 41square kilometers of land area with Dayu Mountain as its

Elastic cavity boundary

(cracking zone) Blasting hole

a

Stemming

Explosive

ri

rj

Surface wave

Body wave

Body waveh

Figure 1 Schematic diagram of single-hole blasting


(cracking zone)

Blasting hole

Stemming

ri

rj

Surface wave

Body wave

Body wave

Explosive

h

a

Figure 2 Schematic diagram of multiple-hole blasting

r1

Δt1 Δt2 Δt3

r2 r3

f1 = 12Δt1 f2 = 12Δt2 f3 = 12Δt3

Figure 3 e dominant frequency of blasting vibration decreaseswith distance increasing

Table 1Main inuencing parameters and dimensions of dominantfrequency

Parameter Unit (dimension)Longitudinal wave velocity ms (LTminus1)Radius of elastic cavity m (L)Distance between the blasting sourcewith the measuring points m (L)

Charge weight per delay kg (M)Density of rock kgm3 (MLminus3)


core and build an island-type modern and ecologicalpetrochemical base -e base is built in two phases wherephase II is under excavation as shown in Figure 5 -esquare quantity exploited by blasting is about 47 millioncubic meters and the open-pit excavation period is about20months in phase II

Two blasting sites have been arranged in phase II asshown in Figure 6 -ere are two blasting experiments ineach of the both blasting sites which have been analyzed inorder to verify the effectiveness of the proposed equation-e dominant frequency of the field measured blasting from1 and 2 experiments in 3 massif to 3 and 4 experimentsin 5 massif will be selected to fitting analyze -e vibrationlogging and analysis system used in field observation con-sists of three parts three-axis velocity transducers a blastingvibration intelligent monitor (Blast-UM) and computersinstalled with Blast-UM software used to withdraw andprocess test data Typical blasting measuring points anddevices are shown in Figure 7

32 Experiments in 3 Massif 1 and 2 experiments areconducted in the platform with elevation of 16m in 3massif 1 experiment is located on the northwest side of theplatform and 2 experiment is located on the north side ofthe platform -e diameter of the blasting holes is 115mmand the diameter of the explosive is 90mm -e detailedblasting parameters of the two experiments are shown inTable 2

In 1 and 2 experiment a single-hole blasting was set inthe last delay of the multiple-hole blasting to observe thedominant frequency attenuation law of single-hole blastingand multiple-hole blasting respectively Among them sixand eight surface blasting vibration measurement pointswere arranged in 1 and 2 experiment respectively -emultiple-hole blasting is detonated by holes MS3 detonatorsare used between holes MS5 detonators are used betweenrows and single-hole blasting and multiple-hole blasting areseparated by theMS10 detonator MS3MS5MS10 representthe millisecond with 50110650ms as shown in Figures 8and 9 And a stereo sketch of the layout of measuring pointsis provided in the red-dotted frame

Figure 10 gives the typical time history curves of blastingvibration of the 1 measuring point in 1 experiment as anexample Blasting vibration is divided into two parts thefront part is multiple-hole blasting and the rear part is single-hole blasting In order to facilitate observation differentcolors are used to indicate the blasting vibration -edominant frequency of the two parts is marked in the figure

-e values of dominant frequency of single-hole andmultiple-hole blasting are given in Table 3

Since both 1 and 2 experiments were carried out in3 massif they were fitted together Multiple-hole blastingis different from single-hole blasting in vibration wave-form and spectrum characteristics due to the superposi-tion and the influence of detonator delay As a resultsingle-hole blasting and multiple-hole blasting are fittedseparately -e fitting results of the attenuation rule for thedominant frequency of single-hole and multiple-holeblasting by equation (16) are presented in Figures 11and 12 and Table 4

-e proposed equation (17) generally has obtained afavorably correlation coefficient in 3 massif -e dominantfrequency of blasting vibration in multiple-hole blasting isdecaying faster than that in single-hole blasting which is alsoconfirmed by Zhang et al [20] In addition the fittingcorrelation coefficient of dominant frequency in X-directionis generally higher than that of the other two directions andthe vertical direction obtains the worst relevance which is incompliance with previous discussion that the radial vibra-tion is normally perceived to be related to the P-wave whilethe vibration in vertical is normally considered to beinfluenced most by the R-wave reflected by the free face onthe ground [2] As a result for surface vibration the fittingcorrelation coefficient of radial vibration is higher than thatof vertical vibration

33 Experiments in 5 Massif 3 and 4 experiments areconducted in the platform with elevation of 30m in 5massif 3 experiment is located on the northeast side of theplatform and 4 experiment is located on the north side ofthe platform -e diameter of the blasting holes is 115mmand the diameter of the explosive is 90mm -e detailed

ZhoushanChina

Zhejiang

Figure 4 Location of Zhoushan Green Petrochemical Base


blasting parameters of the two experiments are shown inTable 5

In 3 and 4 experiment besides the multiple-holeblasting a single-hole blasting was also set up to observe

the dominant frequency attenuation law of single-holeblasting and multiple-hole blasting respectively Amongthem seven and ve surface blasting vibration measurementpoints were arranged in 3 and 4 experiments respectively

Phase I Phase II

Demarcation line

Figure 5 Photograph of Zhoushan Green Petrochemical Base

Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site

1 Experiment2 Experiment

3 Experiment

4 Experiment

(b)

Figure 6 Layouts of experiment in Zhoushan Green Petrochemical Base (a) Phase I (b) Phase II


ree-axis velocity transducer

Blasting vibrationintelligent monitor

Figure 7 Typical blasting measuring points and devices

Table 2 Drilling and blasting parameters for the blast in 3 massif

Blast site 3 massifExperiment 1 2Blastholes Multiple Single Multiple SingleBlasthole diameter (mm) 115 115 115 115Blasthole length (m) 132ndash149 148 127ndash147 142Blasthole spacing (m) 45 mdash 45 mdashRow spacing (m) 45 mdash 45 mdashCharge diameter (mm) 7090 90 7090 90Charge weight per hole (kg) 66ndash90 90 69ndash93 87Stemming length (m) 40ndash55 40 45 45Number of rows 4 mdash 4 mdashNumber of blastholes 116 1 126 1

Measuring pointsXYZ Directions of transducer

DetonatorSingle-hole blastingGroup-hole blasting

MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting

Figure 8 Blast design and layout of measuring points in 1 experiment


e multiple-hole blasting is detonated by holes MS3detonators are used between holes MS5 detonators are usedbetween rows and single-hole blasting and multiple-holeblasting are separated by the MS10 detonator MS3MS5MS13 represent the millisecond with 50110650ms as

shown in Figures 13 and 14 And a stereo sketch of the layoutof measuring points is also provided in the red-dotted frame

Figure 15 gives the typical time history curves of blastingvibration of the 3 measuring point in 3 experiment as anexample Blasting vibration is divided into two parts the



281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz

Group-hole blastingSingle-hole blasting

ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz


ndash220ndash160ndash100

ndash402080

140

(c)

Figure 10 Blast-induced velocity-time histories recorded at the 1 measurement point (a) X-direction (b) Y-direction (c) Vertical


front part is multiple-hole blasting and the rear part is single-hole blasting In order to facilitate observation dishyerentcolors are used to indicate the blasting vibration edominant frequency of the two parts is marked in the gure

e values of dominant frequency of single-hole blastingand multiple-hole blasting are given in Table 6

e tting results of the dominant frequency by equation(17) are presented in Figures 16 and 17 and Table 7

Table 3 Dominant frequency of single vibration signals in 3 massif

Experiment Blasthole DirectionDominant frequency (Hz)

1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2

SingleX 833 893 847 546 476 526 mdash mdashY 1111 893 535 352 532 521 mdash mdash

Vertical 725 833 725 355 442 435 mdash mdash

MultipleX 1667 1087 1136 843 685 426 mdash mdashY 1563 2000 833 333 588 588 mdash mdash


y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )

ndash26 ndash22 ndash18ndash3ln (Q12R)

(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)

Figure 11 Fitting analysis of the dominant frequency of single-hole blasting by (17) (a) X-direction (b) Y-direction (c) Vertical


e proposed equation (17) also has obtained a fa-vorable correlation coecient in 5 massif And the ttingcorrelation coecient of dominant frequency in X-di-rection is still higher than the vertical direction Moreoverboth of the amplitude and the attenuation speed of thedominant frequency in X-direction are larger than that invertical direction which is also in compliance with pre-vious discussion that the radial vibration is more related tothe P-wave while the vibration in vertical is normallyconsidered to be inuenced most by the R-wave In factthe amplitude and attenuation speed of the P-wave arelarger than that of the R-wave It can be seen that dishyerent

wave components have an important inuence on thefrequency

4 Comparison with Other Formulas

In recent years although the frequency of blasting vibration isbeing paid more attention and most of blasting vibrationcontrol standards are frequency-dependent the prediction offrequency is still the most dicult in terms of the numerousinuencing factors which is dicult to quantify But manyscholars still have conducted quantities of in-depth studiese blasting vibration frequency was initially put forward by

y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )

ndash25 ndash15ndash3 ndash2ln (Q12R)

(a)

y = 2632x + 12715R2 = 06979

Y-direction

ndash3 ndash25 ndash2 ndash15ln (Q12R)

45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)

Figure 12 Fitting analysis of the dominant frequency of multiple-hole blasting by (17) (a) X-direction (b) Y-direction (c) Vertical

Table 4 Fitting equation of the dominant frequency in 3 massif

Equation BlastholesX-direction Y-direction Vertical

Equation Correlationcoecient Equation Correlation

coecient Equation Correlationcoecient

(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642

Multiple f ((273E + 5)Q12)(Q12r)253 r2 0733 f ((333E + 5)Q12)

(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ

Stereo sketchBlasting region

Cast direction

13m

Group-hole blastingSingle-hole blastingDetonator

Measuring pointsDirections of transducerXYZ



Measuring pointsDirections of transducer

MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued


Blast site 5 massifExperiment 3 4Blastholes Multiple Single Multiple SingleBlasthole diameter (mm) 115 115 115 115Blasthole length (m) 106ndash133 130 144 148Blasthole spacing (m) 60 mdash 61 mdashRow spacing (m) 36 mdash 35 mdashCharge diameter (mm) 90 90 90 90Charge weight per hole (kg) 60ndash72 72 8496108 96Stemming length (m) 45 45 50 50Number of rows 5 mdash 6 mdashNumber of blastholes 40 1 54 1


ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)



Experiment Blasthole DirectionMeasuring points number

1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4

SingleX 685 568 347 459 368 mdash mdashY 735 543 455 365 370 mdash mdash

Vertical 667 549 543 495 372 mdash mdash

MultipleX 847 459 360 325 377 mdash mdashY 781 633 538 311 345 mdash mdash



X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)



Sadovskij [21] which is only considered the distance awayfrom explosion source and ignored other factors

f k1log r( )minus1 (18)

where f is the blast-induced dominant vibration frequencyk1 is the nonnegative site specic tting coecient and r isthe distance between blasting source and measuring point

Meng and Guo [22] have deduced the prediction for-mula of the dominant frequency of blasting seismic wavepropagating in the viscoelastic medium as follows

f k1Q13 + k2r

2( )minus1 (19)

where k1 and k2 are uncertain parameters related to chargestructures and Q is the maximum explosive charge per delay

Zhang and Yu [23] obtained the prediction formula ofdominant frequency of blasting vibration by dimensionalanalysis as follows

f k1r

( )Q13

r( )

k2

(20)


Equation BlastholesX-direction Y-direction Vertical direction

Formula Correlationcoecient Formula Correlation

coecient Formula Correlationcoecient

(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642

Multiple f (1657Q12)(Q12r)073 r2 0794 f (1570Q12)

(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038

ndash4 ndash35 ndash3 ndash25 ndash2

ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)

Figure 18 Fitting analysis of the dominant frequency ofmultiple-hole blasting in 3massif by dishyerent formulas (a) Equation (18) (b) Equation(19) (c) Equation (20) (d) Equation (21) Note equation (22) is tted by multiple linear regression so there is no tting diagram provided


where k1 is defined as the site coefficient which is related torock properties and blasting parameters k2 is an attenuationcoefficient of blasting vibration

Jiao [24] proposed the formula for calculating thedominant frequency of ground particle vibration caused byblasting as follows

f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)

where k1 is defined as the site coefficient which is related to thedominant frequency of blasting vibration and usually rangesfrom 001 to 03Cs denotes the shear wave velocity in the rock

Li et al [25] has provided a prediction formula ofblasting dominant frequency based on a combination of greyrelational analysis and dimensional analysis as follows

f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)

where k1 k2 k3 and k4 are nondimensional constantswhich are related to the rock density and the wave velocityH denotes the relative elevation and V is the peak particlevelocity

In order to observe the difference of fitting effect betweenequation (17) and other formulas (18)ndash(22) the dominantfrequency of blasting vibration measured in ZhoushanGreen Petrochemical Base are fitted and compared with eachother As the length of the article is limited Figure 18 onlygives the fitting analysis curve of multiple-hole blasting of X-direction in 1 experiment Table 8 gives a complete list ofthe fitting parameters and correlation coefficients of eachexperiment by each formula

It can be seen from Table 8 that equation (17) generallyperforms better than most of other formulas and the fittingcorrelation coefficient is only lower than equation (22)However it is worth noting that although the fitting corre-lation coefficient obtained by equation (22) is generally the

Table 8 -e fitting results of different formulas

Equation Blasthole Direction3 massif 5 massif

k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)

SingleX 329Eminus 3 815Eminus 7 0028 297Eminus 3 284Eminus 7 0433Y 327Eminus 3 762Eminus 7 0011 428Eminus 3 minus353Eminus 7 0519Z 352Eminus 3 606Eminus 7 0007 445Eminus 3 minus265Eminus 7 0645

MultipleX 384Eminus 3 902Eminus 7 0589 minus176Eminus 2 107Eminus 5 0266Y 358Eminus 3 864Eminus 7 0679 minus516Eminus 3 410Eminus 6 0322Z 434Eminus 3 597Eminus 7 0271 226Eminus 2 minus101Eminus 5 0435

(20)

SingleX 100E+ 4 018 0042 117671 minus039 0527Y 239E+ 4 047 0155 108572 minus043 0651Z 166E+ 4 038 0119 67194 minus060 0805

MultipleX 894E+ 5 154 0504 131901 minus028 0381Y 119E+ 6 165 0475 119171 minus035 0530Z 778E+ 4 081 0312 57317 minus059 0855

(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)

SingleX 293 013 104 minus787 0683 162E+ 4 000 071 246 0862Y 520E+ 7 minus033 170 702 0704 509E+ 4 minus020 086 289 0925Z 300E+ 8 010 130 1011 0673 954E+ 3 minus045 092 071 0906

MultipleX 353 010 229 minus1167 0758 301E+ 3 074 minus034 402 0875Y 705Eminus 5 051 121 minus1845 0890 116E+ 3 minus013 075 minus050 0782Z 739Eminus 8 026 129 minus2608 0876 482E+ 3 011 025 246 0760

(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726


highest it is difficult to apply in engineer practice in result ofits too complex fitting parameters and calculation which needfour unknown parameters and multiple linear regression Incomparison equation (17) can not only obtain a favorablefitting correlation but also simple and brief in form

5 Conclusion

Based on the theoretical derivation of the attenuationequation of the dominant frequency induced by blasting andthe fitting analysis of the dominant frequency in ZhoushanGreen Petrochemical Base the following conclusions can bedrawn

(1) An equation reflecting the change of dominantfrequency induced by blasting has been derived bydimensional analysis combined with the theory ofradial spherical wave propagation Based on thefitting analysis of dominant frequencies measured inZhoushan Green Petrochemical Base favorablecorrelation coefficients have been obtained whichproves the feasibility of the proposed equation Bycomparing the different prediction formulas ofdominant frequency with equation (17) it is foundthat equation (17) performs better in general whichcan not only obtain a favorable fitting correlation butalso simple and brief in form

(2) -e fitting correlation coefficient of dominantfrequency in radial direction is generally higherthan the vertical direction which is resulted fromthe existence of surface free surface in cylindricalcharge blasting -e vibration in vertical is con-sidered to be influenced most by the R-wave re-flected by the free face on the ground which isperceived to be quite different from the radial vi-bration affected by the P-wave In other wordsdifferent types of waves will affect the dominantfrequency of blasting vibration

-is paper has proposed an attenuation formula fordominant frequency and it has found that the attenuationof dominant frequency is influenced by the component ofthe blasting wave Although the proposed equation hasobtained a favorable fitting correlation it has adoptedmany simplified assumptions such as that the rock isassumed to be linear elastic and the influence of freesurface in semi-infinite space is neglected -erefore theproposed equation still needs to be further improved andoptimized

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the National Natural ScienceFund Project of China (51779190) and Hubei ProvinceTechnical Innovation Program (2017ACA102) -e authorswish to express their thanks to all supporters

References

[1] W Hustrulid ldquoBlasting principles for open pit miningrdquoMining Engineering vol 1 2004

[2] C H Dowding ldquoConstruction vibrationsrdquo Shock amp Vibra-tion 1995

[3] J H Yang W B Lu Z G Zhao P Yan andM Chen ldquoSafetydistance for secondary shotcrete subjected to blasting vi-bration in Jinping-II deep-buried tunnelsrdquo Tunnelling andUnderground Space Technology vol 43 no 7 pp 123ndash1322014

[4] P K Singh and M P Roy ldquoDamage to surface structures dueto blast vibrationrdquo International Journal of Rock Mechanicsand Mining Sciences vol 47 no 6 pp 949ndash961 2010

[5] M P Roy P K Singh M Sarim and L S Shekhawat ldquoBlastdesign and vibration control at an underground metal minefor the safety of surface structuresrdquo International Journal ofRock Mechanics and Mining Sciences vol 83 pp 107ndash1152016

[6] A E Alvarez-Vigil C Gonzalez-Nicieza F Lopez Gayarreand M I Alvarez-Fernandez ldquoPredicting blasting propaga-tion velocity and vibration frequency using artificial neuralnetworksrdquo International Journal of Rock Mechanics amp MiningSciences vol 55 no 10 pp 108ndash116 2012

[7] G Zhong L Ao and K Zhao ldquoInfluence of explosion pa-rameters on wavelet packet frequency band energy distri-bution of blast vibrationrdquo Journal of Central South Universityvol 19 no 9 pp 2674ndash2680 2012

[8] J H Yang W B Lu Q H Jiang C Yao and C B ZhouldquoFrequency comparison of blast-induced vibration per delayfor the full-face millisecond delay blasting in undergroundopening excavationrdquo Tunnelling and Underground SpaceTechnology vol 51 pp 189ndash201 2016

[9] T Ling X Li T Dai and Z Peng ldquoFeatures of energydistribution for blast vibration signals based on wavelet packetdecompositionrdquo Journal of Central South University vol 12no 1 pp 135ndash140 2015

[10] G R Tripathy and I D Gupta ldquoPrediction of groundvibrations due to construction blasts in different types ofRockrdquo Rock Mechanics and Rock Engineering vol 35 no 3pp 195ndash204 2002

[11] C Gonzalez Nicieza and M I Alvarez Fernandez ldquoBlastingpropagation velocityrdquo in Rock Mechanics and Engineeringvol 3 of Analysis Modeling ampDesign Taylor amp Francis OnlineLondon UK 2017

[12] J Zhou W Lu P Yan M Chen and G Wang ldquoFrequency-dependent attenuation of blasting vibration wavesrdquo RockMechanics and Rock Engineering vol 49 no 10 pp 4061ndash4072 2016

[13] Z Y Zhong and J Xiaoguang ldquoPrediction of peak velocity ofblasting vibration based on artificial neural network opti-mized by dimensionality reduction of FA-MIVrdquo Mathe-matical Problems in Engineering vol 2018 Article ID8473547 12 pages 2018

[14] M Khandelwal P Kankar and S Harsha ldquoEvaluation andprediction of blast induced ground vibration using support


vector machinerdquo Mining Science and Technology vol 20no 1 pp 64ndash70 2010

[15] R S Faradonbeh D J Armaghani M Z A Majid et alldquoPrediction of ground vibration due to quarry blasting basedon gene expression programming a new model for peakparticle velocity predictionrdquo International Journal of Envi-ronmental Science amp Technology vol 13 no 6 pp 1453ndash14642016

[16] R F Favreau ldquoGeneration of strain waves in rock by anexplosion in a spherical cavityrdquo Journal of Geophysical Re-search vol 74 no 17 pp 4267ndash4280 1969

[17] A A Kuzmenko V D Vorobev I I Denisyuk andA A Dauetas Seismic Effects of Blasting in Rock RoutledgeLondon UK 1993

[18] W B Lu J R Zhou and M Chen ldquoStudy on attenuationformula of dominant frequency of blasting vibrationrdquo En-gineering Blasting vol 21 no 6 pp 1ndash6 2015 in Chinese

[19] J P Devine and W I Duvall ldquoEffect of charge weight onvibration levels for millisecond delayed quarry blastsrdquoEarthquake Notes vol 34 no 2 pp 17ndash24 1963

[20] Z Y Zhang L F Luan Z Q Yin et al ldquoEffects of detonationways on energy distribution for different frequency bands ofbench blastingrdquo Blasting vol 25 no 2 pp 21ndash25 2008 inChinese

[21] M A Sadovskij ldquoEvaluation of seismically dangerous zones inblasting seismic institute of the academy of sciences In onthe effects of blast-induced vibrationsrdquo Bulletin of SubalpinaMining Association 1966

[22] H L Meng and F Guo ldquoExperimental research on the masterfrequency of blasting seismic waverdquo Journal of Railway En-gineering Society vol 11 no 11 pp 81ndash83 2009 in Chinese

[23] L G Zhang and Y L Yu ldquoResearch on the relationship ofmain vibration frequency of blasting vibration and peakparticle velocityrdquo Nonferrous metals (Mine Section) vol 57no 4 pp 32ndash34 2005 in Chinese

[24] Y B Jiao ldquoResearch on the standard of blasting seismic safetyassessmentrdquo Blasting vol 12 no 3 pp 45ndash47 1995 inChinese

[25] H Li X Li J Li X Xia and XWang ldquoApplication of coupledanalysis methods for prediction of blast-induced dominantvibration frequencyrdquo Earthquake Engineering and Engineer-ing Vibration vol 15 no 1 pp 153ndash162 2016


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

induced by blasting is diversified with the rock and geo-logical condition

-e majority of factors affecting the dominant frequencyof blasting vibration can hardly be described quantitativelyAs a result it is very difficult to accurately obtain the at-tenuation law of the dominant frequency [11] Generallyspeaking the dominant frequency of blasting vibrationdecreases exponentially with the increase of the distanceaway from the explosion source due to the high-frequencyfiltering characteristics of rock [12] In recent years with theprogress of the analysis technique of blasting vibrationspectrum many prediction formulas have been proposed byusing the method of artificial neural network [13] supportvector machine [14] and gene expression programming[15] Although these formulas can obtain favorable fittingcorrelation they are difficult to apply in engineer practicebecause of its too complex fitting parameters and calcula-tion -erefore it is necessary to obtain a simple andpracticable formula which can reflect the changes of thedominant frequency with distance

2 The Attenuation Equation of DominantFrequency Induced by Blasting

21 Analysis of Main Influencing Factors of the DominantFrequency -e explosive releases enormous energy in theprocess of blasting in rock which mainly transforms intoblasting shock wave stress wave and blasting gas In theprocess of stress wave propagation in rock due to the energyattenuation of wave and the damp absorption effect of rockthe properties and waveforms of stress wave will changecorrespondingly with distances It will form the crushingzone cracking zone and elastic zone successively with thedistance far from the blastholes [1] In order to analyze thepropagation and attenuation of blasting seismic wave byusing elastic wave theory the inelastic zone (crushing zoneand cracking zone) near the blastholes is equivalent to theblasting source and the blasting load is acted on theequivalent elastic boundary (cracking boundary ie theouter boundary of the crushing zone) -erefore the the-oretical solution of the elastic wave excited by a sphericalcavity in an elastic medium can be adopted and the theo-retical solution is given by Favreau [16]

Introducing potential function φ to represent radialdisplacement

u zφ(r t)

zr (1)

where u is the radial displacement r represents the distancebetween blasting source with the measuring points and t isthe time

Assuming the load function acting on the inner wall ofthe spherical cavity is p(t)

φ(r t) minusa

ρωr1113946

s

0p(sminus t)e

minusητ sin(ωτ) dτ (2)

s tminusrminus a

CP

(3)

η 1minus 2]1minus ]

CP

a (4)

ω

1minus 2]

radic

1minus ]CP

a (5)

where p(t) is the blasting load acted on elastic cavity λ and μare the constant of Lame ] is Poissonrsquos ratio ρ is the densityCP is the longitudinal wave velocity a is the radius of elasticcavity (cracking zone) ω is the phase of function φ is alsothe natural frequency of the equivalent system and s and ηare intermediate variables

It is often assumed that the law of blasting load p(t) isused in the following form [17]

p(t)

0 tltminusτ1

σmax1 + t

τ11113888 1113889 minusτ1 le tle 0

σmax1minus t

τ21113888 1113889 0le tle τ2

0 tgt τ2

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

where σmax is the peak value of the blasting load τ1 is therising time of the blasting load and τ2 is the time of blastingload reduction from peak to zero

Bymeans of the Fourier transform the velocity spectrumof blasting vibration in the elastic rock mass can be obtainedas follows [8 17]

F(ω) Sσ(jω)

11138681113868111386811138681113868111386811138681113868aωCP

C2P + r2ω2

1113969

4μr2

CPa( 11138574

+[1minus(λ + 2μ)2μ]ω2 CPa( 11138572

+[(λ + 2μ)4μ]2ω41113969 (7)

Sσ(jω)1113868111386811138681113868

1113868111386811138681113868 σmax

aebeτω211138581 + a2e + b

2e + 2aebe cosωτ

minus 2 ae cos beωτ + be cos aeωτ( 1113857111385912

(8)

where F(ω) is the velocity spectrum of blasting vibrationSσ(ω) is the stress spectrum of blasting load τ τ1 + τ2ae τ1τ and be τ2τ

It can be concluded from equation (7) that the maininfluencing factors of velocity spectrum include threeaspects firstly the distance away from blasting sourcer secondly the parameters of rock λ μ ] and CP andfinally the parameters of blasting such as the radius ofelastic cavity (the cracking zone) a and load parameters aebe and τ










π1 aα1Cβ1P ρc1f

π2 aα2Cβ2P ρc2r

π3 aα3Cβ3P ρc3Q

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)


π1 fa

CP

π1 Q

a3ρ

π3 r

a

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


f CP

a

Q13

rρ131113888 1113889

αr

a1113874 1113875

β (11)



Q 43πqa

3 (12)



Q 16πqd

3 (13)



f ξCP

Q13Q13

r1113888 1113889

β

(14)



f ζ

Q13Q13

r1113888 1113889

β

(15)




Q qHSB (16)





f αQ12

Q12

r( )

β

(17)






a

Stemming

Explosive

ri

rj

Surface wave

Body wave

Body waveh



(cracking zone)

Blasting hole

Stemming

ri

rj

Surface wave

Body wave

Body wave

Explosive

h

a


r1

Δt1 Δt2 Δt3

r2 r3

f1 = 12Δt1 f2 = 12Δt2 f3 = 12Δt3















ZhoushanChina

Zhejiang






Phase I Phase II

Demarcation line


Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site


3 Experiment

4 Experiment

(b)










MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










π1 aα1Cβ1P ρc1f

π2 aα2Cβ2P ρc2r

π3 aα3Cβ3P ρc3Q

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(9)


π1 fa

CP

π1 Q

a3ρ

π3 r

a

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)


f CP

a

Q13

rρ131113888 1113889

αr

a1113874 1113875

β (11)



Q 43πqa

3 (12)



Q 16πqd

3 (13)



f ξCP

Q13Q13

r1113888 1113889

β

(14)



f ζ

Q13Q13

r1113888 1113889

β

(15)




Q qHSB (16)





f αQ12

Q12

r( )

β

(17)






a

Stemming

Explosive

ri

rj

Surface wave

Body wave

Body waveh



(cracking zone)

Blasting hole

Stemming

ri

rj

Surface wave

Body wave

Body wave

Explosive

h

a


r1

Δt1 Δt2 Δt3

r2 r3

f1 = 12Δt1 f2 = 12Δt2 f3 = 12Δt3















ZhoushanChina

Zhejiang






Phase I Phase II

Demarcation line


Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site


3 Experiment

4 Experiment

(b)










MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Q qHSB (16)





f αQ12

Q12

r( )

β

(17)






a

Stemming

Explosive

ri

rj

Surface wave

Body wave

Body waveh



(cracking zone)

Blasting hole

Stemming

ri

rj

Surface wave

Body wave

Body wave

Explosive

h

a


r1

Δt1 Δt2 Δt3

r2 r3

f1 = 12Δt1 f2 = 12Δt2 f3 = 12Δt3















ZhoushanChina

Zhejiang






Phase I Phase II

Demarcation line


Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site


3 Experiment

4 Experiment

(b)










MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











ZhoushanChina

Zhejiang






Phase I Phase II

Demarcation line


Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site


3 Experiment

4 Experiment

(b)










MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Phase I Phase II

Demarcation line


Petrochemical plant

(a)

1 Massif2 Massif

3 Massif

4 Massif

5 Massif

6 Massif

Blasting site


3 Experiment

4 Experiment

(b)










MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









MS3

MS5

MS10

336m

08m288m

12

220m128m

6 34

67m

5

X

Y

XYZ

Stereo sketch

Blasting region

Cast direction

13m

10-hole blasting

12-hole blasting








281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







281m82m64m177m128m

12 MS3

MS5

MS10

125m48m413m

678 345

45m

X

Y XYZ

Stereo sketch

Blasting region

Cast direction

13m11-hole blasting

11-hole blasting


0 500 1000 1500 2000

Velo

city

(cm

s)

Time (ms)

f = 1351Hz f = 980Hz


ndash200ndash140

ndash80ndash20

40100160

(a)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1923Hz f = 781Hz


ndash180ndash120

ndash600060

120180

(b)

Velo

city

(cm

s)

0 500 1000 1500 2000

Time (ms)

f = 1250Hzf = 1000Hz



ndash402080

140

(c)








1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







1 2 3 4 5 6 7 8

1

SingleX 980 617 500 677 633 505 391 407Y 581 847 794 769 538 345 333

Vertical 1000 704 476 704 481 435 355 355

MultipleX 1351 806 1513 1368 1389 632 282 266Y 1923 1087 943 1315 1042 549 304 306

Vertical 1250 1000 1020 1042 893 481 384 302

2





y = 1175x + 9077R2 = 06600

X-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(a)

y = 1474x + 9740R2 = 06430

Y-direction

5

55

6

65

7

75

ln (f

Q1

2 )


(b)

y = 1382x + 9447R2 = 06422

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)







y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






y = 2528x + 12518R2 = 07326

X-direction

45

55

65

75

85

ln (f

Q1

2 )


(a)

y = 2632x + 12715R2 = 06979

Y-direction


45

55

65

75

85

ln (f

Q1

2 )

(b)

y = 1797x + 10618R2 = 06887

Vertical direction


5

55

6

65

7

75

ln (f

Q1

2 )

(c)






(17)Single f ((875E + 3)Q12)

(Q12r)118 r2 0660 f ((170E + 4)Q12)(Q12r)147 r2 0643 f ((127E + 4)Q12)

(Q12r)138 r2 0642


(Q12r)263 r2 0698 f ((409E + 4)Q12)(Q12r)180 r2 0689


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


261m147m160m232m229m391m

123567 4

202m

MS5

MS3

MS10

X

YY

XZ


Cast direction

13m






MS5

MS3

MS10

306m402m113m133m534m

12345X

YY

XZ


Castdirection

13m

XYZ


ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

1800

Time (ms)

f = 368Hz f = 435Hz

600 1000 1400


(a)

Figure 15 Continued




ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ndash60

ndash30

00

30

60

200V

eloc

ity (c

ms

)Time (ms)

f = 424Hz f = 521Hz

600 1000 18001400


(b)

ndash60

ndash30

00

30

60

200

Vel

ocity

(cm

s)

Time (ms)

f = 405Hz f = 595Hz

600 1000 18001400


(c)




1 2 3 4 5 6 7

3

SingleX 758 939 435 562 427 281 250Y 781 mdash 521 719 463 309 260

Vertical 602 549 595 603 490 338 278

MultipleX 943 485 368 413 367 225 187Y 893 483 424 385 342 314 219

Vertical 647 485 405 467 455 275 265

4






X-direction

y = 0618x + 7361R2 = 07395

ln (fQ

12 )

55

5

65

6

7

(a)


ln (fQ

12 )

55

5

65

6

7

Y-direction

y = 0578x + 7313R2 = 07740

(b)

Figure 16 Continued


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ln (fQ

12 )

55

5

65

6

7


Vertical direction

y = 0412x + 6966R2 = 06421

(c)


X-direction


55

45

65

75

ln (fQ

12 )

y = 0725x + 7413R2 = 07941

(a)

Y-direction


55

45

65

75

ln (fQ

12 )

y = 0665x + 7359R2 = 07966

(b)

Vertical direction

ln (fQ

12 )


55

5

65

6

7

y = 0415x + 6797R2 = 07263

(c)







f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






f k1Q13 + k2r

2( )minus1 (19)



f k1r

( )Q13

r( )

k2

(20)





(17)Single f (1573Q12)

(Q12r)062 r2 0740 f (1500Q12)(Q12r)058 r2 0774 f (1060Q12)

(Q12r)041 r2 0642


(Q12r)067 r2 0797 f (859Q12)(Q12r)042 r2 0726

X-direction

y = 154x + 1370R2 = 05038


ln (fr)

ln (Q13r)

8

86

92

98

f

X-direction

y = 013x ndash 38248R2 = 06569

0

40

80

120

160

200

2500 3000 3500 4000 4500 5000(Cs75Q13)(Q13r)25

X-direction

y = 19289xR2 = 01375

0

40

80

120

160

200

044 046 048 05 052 054 056

f

1ln (r)

X-direction

y = 60412x ndash 5670R2 = 05894

0

200

400

600

800

0 05 1 15

fQ1

3

fr2 times 106

(a) (b)

(c) (d)





f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




f k1C75

s

Q131113888 1113889Q13

r1113888 1113889

25

(21)



f k1Vk2

Q131113888 1113889Q13

r1113888 1113889

k3 Q13

H1113888 1113889

k4

(22)






k1 k2 k3 k4 r2 k k1 k2 k4 r2

(18)

SingleX 9575 0212 12588 0461Y 9566 0178 12540 0540Z 9401 0176 11457 0595

MultipleX 8515 0138 19289 0463Y 8951 0116 19250 0489Z 7990 0155 14705 0691

(19)



(20)



(21)

SingleX 0047 0642 0017 0360Y 0057 0636 0017 0303Z 0049 0596 0016 0299

MultipleX 0026 0240 0011 0645Y 0026 0204 0011 0652Z 0020 0272 0010 0780

(22)



(17)

SingleX 875E+ 3 118 0660 1573 062 0740Y 170E+ 4 147 0643 1500 058 0774Z 127E+ 4 138 0642 1060 041 0642

MultipleX 273E+ 5 253 0733 1657 073 0794Y 333E+ 5 263 0698 1570 067 0797Z 409E+ 4 180 0689 859 042 0726



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



5 Conclusion





Data Availability




Acknowledgments


References































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


analysis of the main factors influencing the dominant

Documents