PrefabricatedConcreteComponentGeometryDeviation … · 2021. 3. 22. · togrammetry technology. e...

Research ArticlePrefabricated Concrete Component Geometry DeviationStatistical Analysis

Xiaoyong Luo 12 Hao Long 12 Shuang Dong 1 and Jingyi Wu 3

1Department of Civil Engineering Central South University Changsha 41000 China2Hunan Prefabricated Construction Engineering Technology Research Centre Changsha 41000 China3Hatchip Co Shenzhen 518000 China

Correspondence should be addressed to Hao Long longhaocsueducn

Received 22 March 2021 Revised 26 April 2021 Accepted 5 May 2021 Published 19 May 2021

Academic Editor Jie Chen

Copyright copy 2021 Xiaoyong Luo et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e research objects of this paper were the prefabricated concrete components produced by four enterprises in China and thedimension deviation data of more than 1400 prefabricated concrete components are measured with high-precision 3D pho-togrammetry technology e nonparametric KruskalndashWallis test was carried out for the size deviation of the same type ofcomponents produced by different enterprises e distribution characteristics of geometric parameters of typical components ofprefabricated structures in China such as beams columns wall boards and composite slabs were analyzed by using theprobability statistical method e KolmogorovndashSmirnov goodness-of-fit method was used to test the cumulative distributionfunction of dimension deviation and the size distribution of fabricated components was studied e results showed that therewas no significant difference in the size deviation of the same-type component produced by different enterprises and the range ofgeometric parameter uncertainty random variables was small which was between 099 and 102 Also the fluctuation was smallthe coefficient of variation was below 00093 and the variability of component size deviation was small e transverse dimensionof the component shows a positive deviation the vertical dimension of component shows a negative deviation and the dimensiondeviation of prefabricated concrete components follows the normal distribution

1 Introduction

Prefabricated building is one of the important directions ofbuilding structure development which is conducive to thedevelopment of building industrialization As a crucial partof the prefabricated concrete (PC) structure the quality ofprefabricated components plays an important role in theoverall structural performance [1] In terms of the splicingstructure of prefabricated components if the size of pre-fabricated components is too large it would be difficult toassemble and if the size is too small the joints betweencomponents would be too large causing water seepageproblems From the aspect of stress performance whenanalyzing the reliability of the structure according to theprobability limit state design method the failure probabilityof the structural part or its corresponding reliability index isused as the measurement and the geometrical dimension

variable is one of the aspects that affect the resistance of thestructural part Moreover contemporary buildings havebecome lighter and more vulnerable to building movementand subsequent geometric changes [2] e lack of uni-formity of accuracy between factory-made and in-situcomponents and the higher level of building movements inthe contemporary building are two major factors that affectthe dimensional and geometric accuracy of buildings [3]e conversion of a good design into a good product (eg abuilding) is a matter of keeping dimensional and geometricvariations within tolerances that are predetermined at thedesign stage [4] e acceptability of a product depends onwhether its variations in size and geometry fall within setlimits thus the bridge between design and production istolerance In other words tolerances interlink design withconstruction because without specifying the tolerances it isnot clear whether components and subassemblies (ie

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 9993451 15 pageshttpsdoiorg10115520219993451

connections of two or more components) meet the designintent regarding the accuracy of the final product [5]

At present there are many quality control standards forfabricated components such as German DIN18203 andDIN18202 standards Japanese JASS10 American MNL-116and ACI regulations and Chinese standards GBT51231-2016 and GBT 51232-2016 [6ndash10] Each standard specifiesthe dimensional deviation of prefabricated componentsese standards usually determine the allowable value ofdimensional deviation based on traditional experiences [11]and the deviation allowable value for prefabricated com-ponents is strictly controlled and appropriately modifiedbased on the relevant specifications of cast-in-place concreteScholars do not pay attention to the prefabricated compo-nent manufacturersrsquo production capacity and have notsystematically investigated the dimensional deviation ofprefabricated components [12] To determine the reliabilityof the concrete structure design in the 1970s and 1980s [13]a survey of the size deviation of cast-in-place concretestructures was conducted in China [13] Liu et al [11]conducted the statistical investigation on the size deviationof cast-in-place concrete structures in Beijing and suggestedadjusting the size deviation acceptance index while Mao andShi [14] conducted the statistical investigation and analysison the section size and axis position of cast-in-place concretestructures and they believed that the deviation of concretesection size obeys the normal distribution yet the axisposition deviation obeys the logarithmic distributionNowadays there are many types of research on the sizedeviation of cast-in-situ structures but there are quite fewstatistical studies on the size deviation of prefabricatedconcrete components erefore it is of great significance tosystematically investigate the size deviation of fabricatedcomponents

In this paper the dimensions of fabricated concretecomponents of different companies in China are measuredby 3D photogrammetry technology obtaining a database ofwall board composite slab beam and column size devia-tion e dimensional deviation distribution characteristicsof fabricated components are analyzed

2 Data Acquisition

21 Overview of Sample Acquisition e focus is mainly onthe component forms existing in prefabricated buildingstructures beams columns wall panels and compositeslabs In terms of survey objects components produced byprefabricated component factories in different regions ofChina are mainly selected Random sampling is used foreach type of component Detailed information about thenumber of survey samples is shown in Table 1

22 Measurement Method Prefabricated building produc-tion and installation have higher precision requirementsthan traditional cast-in-situ concrete structures e tradi-tional measurement method for prefabricated concretebuildings is mainly using steel rulers and there are problemswith the use of steel rulers in measuring the dimensions of

prefabricated concrete components such as insufficientaccuracy large errors and difficulty in measuring the edgecorners of the component dimensions e HL-3DP is amedium-range photogrammetry scanner type It wasdesigned for medium-space applications such as buildingcivil and survey and forensics ree-dimensional photo-grammetry known as HL-3DP was applied for prefabricatedconcrete and the scanned data were managed with theirassociated software HOLON3DP HL-3DP is a high-accu-racy and medium-range photogrammetry system It is as-sociated with a high-resolution camera Table 2 shows thespecification of HL-3DP erefore in this article HL-3DPthree-dimensional photogrammetry was adopted to collectsample data Figure 1 shows the on-site measurement ofprefabricated components e relative error of this methodis less than 5 and the absolute error is less than 001mme measurement of the size of the prefabricated compo-nent thus resulted in high precision in terms of both ex-perimental error and measurement accuracy

23 Accuracy Assessment Accuracy assessment was alsoperformed in this study e findings show that the 3Dphotogrammetry of HL-3DP can provide high accuracy ofthe building structure To get a systematic accuracy as-sessment the evaluation of the estimate accuracy was carriedout using equation (1) where x represents each value in thedataset x represents themean of all values in the dataset andn represents the number of value in the dataset

RMSE

1113936niminus1 (x minus x)

2

n

1113971

(1)

e root-mean-square error (RMSE) was used tomeasure the differences between values observed Accordingto Mao and Shi [14] RMSE is commonly used in the re-search field to describe the accuracy of features and it isacceptable to measure the error and estimate the quality offeatures e lower the RMSE value the better the accuracy

Table 3 shows the dimensional measurement differencebetween the measuring steel tape and photogrammetrysystem Meanwhile the analysis for this study included thecomparison of measurement between the photogrammetrysystem and conventional method (measuring steel tape) withthe design valuee comparison is performed and recordedin Table 4 e RMSE value of the photogrammetry systemdata was 060mm while that of the measuring steel tapemethod was 094mm As the result the tolerance of thephotogrammetry system model is well within the 001-millimeter level e photogrammetry system model has alower tolerance compared to the measuring steel tap isproved that the photogrammetry system method wasaccurate

3 Results of Sample Collection

In the process of statistical analysis of the geometric pa-rameters of the components because the design dimensionsof the components are not the same to analyze and comparethe variation of the dimensions described by the uncertainty

2 Mathematical Problems in Engineering

of the geometric parameters with the random variable KA

[15] which can be expressed as shown in equation (2) wherea is the actual value of the geometric parameter of thecomponent and aK is the standard value of the geometricparameter of the component (usually the design value)

KA a

aK

(2)

When analyzing the variability of the geometric di-mensions of components variables such as length widthand height are regarded as independent random variables

Taking the same type of component produced by the sameenterprise as a matrix its statistical parameters are analyzedwith a subsample of capacity ngt 50 Integrating the statis-tical analysis results of various enterprises the weightedaverage of the same type of component size variation is usedto reflect the variation level of geometric dimensions ispaper is based on the measured data and the number ofsubsamples participating in the statistical analysis is theweight (the capacity is n) [16] Statistical parameters ofrandom variables with uncertain geometric dimensions ofvarious components were obtained as follows

Table 1 Sample number of prefabricated concrete members in different enterprises

Survey objectSample number of prefabricated parts

Beam components Column components Wall panel components Composite slab componentsEnterprise 1 62 66 102 87Enterprise 2 54 129 84 96Enterprise 3 76 94 64 111Enterprise 4 103 85 121 107

Table 2 Specification of 3D photogrammetric HL-3DP

HL-3DP 3D photogrammetric instrument

Range measurement principle scanner control Measurement of noncontact optical tricoordinateRange Up to 20m (minimum range 001m)Field of view 360deghorizontal 360degverticalSignal image 18MB 4Mpixels (1920times1920 pixel)Ranging error plusmn001mm

(a) (b)

Figure 1 3D photogrammetric component size (a) Composite slab 3D measurement (b) 3D measurement of prefabricated columns

Mathematical Problems in Engineering 3

μKA

1113936ni1 niμKAi

1113936ni1 ni

(3)

δKA

1113936ni1 niδKAi

1113936ni1 ni

(4)

where ni is the subsample capacity of the geometric char-acteristic value of a certain construction unit μKA

is theaverage value under capacity ni and δKA

is the coefficient ofvariation under ni capacity According to equations (2) and(3) the statistical parameters of the random variable of thegeometric parameters of the component can be obtained

31 Analysis of Acquisition Results Taking prefabricatedconcrete components produced by different companies asthe research object analyzing the difference in geometricuncertainty of component size in different enterprisesand calculating the average production component KA

maximum minimum upper and lower quartiles of eachenterprise production Figures 2ndash5 give a comparison ofbox plots e figures show the different productionenterprise production ranges of similar artifacts are

similar both in the range of 099 to 102 e abnormalport of beam members accounted for 34 the abnormalpoints of column members accounted for 08 the ab-normal percentage of wall slabs accounts for 34 andthe abnormal percentage of composite slab slabs accountsfor 12 ere are fewer abnormal points which indi-cates that the variability of component size deviation inthe actual production process is small e volume of thebox body represents the dense and discrete degree of datadistribution in the group e length and width of beamscolumns wall panels slabs and width values KA of thebox body are relatively short and the fluctuation is small

Table 5 shows the comparison results of the KA valueamong similar components of different manufacturers ehorizontal size of the components produced by different en-terprises (wall panel height wall panel width composite slablength and composite slab width) dimension uncertainty is lessthan 1 which is biased towards negative deviation and lon-gitudinal member dimensions are greater than 1 which arebiased toward positive deviation e size deviation of similarPC components produced by different companies is not largewhich proves the reliability of the measured data Manufac-turers have less influence on the size of prefabricated PC

Table 4 Comparison of measurement between the measuring steel tape and photogrammetry system

Prefabricated Measuring steel tape (mm) x2 Photogrammetry system x2

Prefabricated minus3 9 minus186 346

Beam components minus2 4 minus082 067minus3 9 minus203 412

Prefabricated minus4 16 minus208 433Column minus3 9 minus207 428Components minus3 9 minus067 045Prefabricated wall minus3 9 016 002

Panel components 2 4 076 0582 4 minus065 042

Prefabricated minus5 25 394 1552Composite slab minus3 9 305 930Sum Σ 107 Σ 4315RMSE

Σ

radic11 094

Σ

radic11 060

Table 3 Result of dimensional measurement

Prefabricated Dimension Design value (mm) Measuring steel tape (mm) Photogrammetry system (mm)

Prefabricated beam componentsLength 2830 2833 283186Width 400 402 40082Height 410 413 41203

Prefabricated column componentsLength 2535 2539 253708Width 500 503 50207Height 520 523 52067

Prefabricated wall panel componentsHeight 6630 6633 662984Width 2600 2598 259924

ickness 240 238 24065

Prefabricated composite slablowast Length 4350 4355 434606Width 3930 3933 392695

lowastSince the thickness direction of the prefabricated composite slab is cast-in-place concrete it was not counted


components e coefficients of variation KA are below 00093and the variation is small indicating that similar componentsproduced by different companies have the same sizecharacteristics

32 Correlation Test of Dimensional Deviation With thesignificant level a 005 as the difference a single factoranalysis of variance on the dimensions of the componentsproduced by the four companies is performed the differ-ences between the components produced by each factory arediscussed and it is evaluated whether the dimensional de-viations of the components can be traced to a certain extentso that the measurement results of different componentfactories are comparable

e KruskalndashWallis test [17] infers whether the samplecomes from the populationmedian or the distribution pattern issignificantly different is method neither requires the data to

obey the normal distribution nor does it require the homo-geneity of variance e KruskalndashWallis test is a nonparametrictest method to test whether multiple population distributionsare the same Firstly samples in multiple groups are mixed andsorted in ascending order to find the rank of each variabl if thevalues show no big difference it can be considered that thedistributions of multiple populations are not significantly dif-ferent on the contrary if the rank means of each group aresignificantly different the data of multiple groups cannot bemixed and if the distributions of multiple samples are signif-icantly different the statistic constructed by the KruskalndashWallistest is the KndashW statistic which is pRiR shown as follows

p 12

N(N + 1)1113944

k

i1ni Ri minus R( 1113857

2

Ri Ri

ni

R N + 12

(5)

where k is the number of sample groups N is the totalsample size Ri is the sum of ranks of the group I Ri is theaverage rank of the group I and R is the total average rank

Assuming that the distribution of the size deviation ofsimilar components is the same in the company category ifplt a the null hypothesis is rejected and the size deviationdistributions of similar components produced by differentcompanies have significant differences on the contrary ifpgt a then accept the null hypothesis which means that thesize deviation distribution of similar components producedby different companies has no significant difference enonparametric KruskalndashWallis test was performed bySPSS190 software and the analysis results are shown inTable 6 e significance value of each component size isgreater than the significance level of 005 accepting theformer hypothesis so there is no significant difference in thesize deviation of similar components produced by different

102

101

100

099

Height Width Length

Rang

e

Enterprise 1Enterprise 2


Figure 2 Box plot of geometric uncertainty of the beam member

103

102

101

100

099

Height Width Length

Rang

e



Figure 3 Box plot of geometric uncertainty of the columnmember


companies e size deviation values of the same types ofcomponents produced by different companies can be used assubsamples to analyze the distribution characteristics of thesize deviations of fabricated components in China

4 Frequency Distribution of Size Deviation

Since there is no significant difference in the size deviation ofthe same type components the size deviations of the same-type components produced by different companies are in-tegrated as a sample of the size deviation and the distri-bution law of size deviation is analyzed using histograms andbox plots

41 Dimensional Deviation Distribution of PrefabricatedBeam Components Calculating the difference between themeasured data and the design value of the prefabricated beamthe sample size is 295 which is divided into 20 groups ehistogram is drawn with the deviation value as the abscissa andthe measured frequency as the ordinate as shown in Figure 6

As seen in Figure 6 the dimensional deviation distributionhistogram for the beam decreases from the center to the sidesand it can be seen from Figure 6 that the dimensional deviationdistribution histogram of the beam is a normal distribution

e length deviation of beam components mainlyconcentrated in the range of 0ndash6mm e most frequentdeviation is 2ndash4mm the mean is 302mm and the varianceis 191 e width deviation range is mainly concentrated inthe range of 0-3mm the mean value is 157mm and thevariance is 156 e height deviation is mainly concentratedin the range of 0ndash5mm the mean value is 244mm and thevariance is 327

e maximum minimum upper quartile lower quartileand median of the size deviations are compared using boxplots as shown in Figure 7 e characteristic values of thethree-dimensional dimensional deviation of prefabricatedbeam components are all significantly different and the di-mensional deviations are basically positive deviations ere isno abnormal value in the length dimension deviation themedian is located in the center of the upper and lower quartilesand the box chart is symmetrical about the median line in-dicating that the length dimension deviation is symmetricallydistributed Both height and width deviations have abnormalvalues e height deviation abnormal values are concentratedon the smaller value side and the median tends to the upperquartile indicating that the height size deviation distribution isright-skewed distribution e width size deviation abnormalvalues are concentrated on the larger value side and themediantends to the lower quartile indicating that the width deviationdistribution is left-skewed distribution

42 Dimensional Deviation Distribution of PrefabricatedColumn Components Calculating the difference betweenthe measured data and the design value of the prefabricatedcolumn the sample size is 374 which is divided into 20groups e histogram is drawn with the deviation value asthe abscissa and the measured frequency as the ordinate asshown in Figure 8 As seen in Figure 8 the dimensionaldeviation distribution histogram for the column decreasesfrom the center to the sides and it can be seen from Figure 8that the dimensional deviation distribution histogram of thecolumn is a normal distribution

e length deviation of the column components mainlyconcentrated in the range of minus5-1mm the most frequentdeviation is minus3-1mm the mean value is minus205mm and thevariance is 374 the width deviation mainly concentrated in therange of minus1-35mm themost frequent deviation is 07ndash15mmthe mean value is 134mm and the variance is 121 the heightdeviation is mainly concentrated in the range of minus2ndash5mm themost frequent deviation is 15ndash25mm the average is 188mmand the variance is 434

e maximum minimum upper quartile lower quartileandmedian of the size deviations are compared using box plotsas shown in Figure 9 e characteristic values of the three-dimensional dimensional deviation of prefabricated columncomponents are all significantly differentere is no abnormalvalue for the width dimension deviation the median deviationof width is located in the center of the upper and lower quartiles

104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e



Figure 4 Box plot of wall panel geometric uncertainty

1002

1000

0998

Width Length

Rang

e



Figure 5 Box plot of geometric uncertainty of slab


and the square box chart is symmetrical about the median linewhich means that the dimension deviation is symmetricallydistributed e abnormal values of height deviation are con-centrated on the side of the larger value and the median de-viation tends to the upper quartile indicating that the heightdimension deviation is right-skewed distribution Althoughthere are outliers on both sides of the length deviation the boxchart is symmetrical about the median and the proportion ofthe outliers in the upper and lower quartiles is consistenttherefore it can be considered that the length deviation issymmetrical

43DimensionalDeviationDistribution of PrefabricatedWallPanel Components Calculating the difference between themeasured data and the design value of the prefabricated wall

panel the sample size is 371 which is divided into 20 groupse histogram is drawn with the deviation value as theabscissa and the measured frequency as the ordinate asshown in Figure 10 As seen in Figure 10 the dimensionaldeviation distribution histogram for the wall panel decreasesfrom the center to the sides and it can be seen from Fig-ure 10 that the dimensional deviation distribution histogramof the wall panel is a normal distribution

e height deviation size of prefabricated wall panels ismainly concentrated in the range of minus5-0mm the most fre-quent deviation is minus35-28mm the average is minus239mm andthe variance is 291 e width deviation mainly concentratedin the range of minus3-05mm themost frequent deviationwasminus1-06mm the mean value was minus113mm and the variance was157 e thickness deviation is mainly concentrated in the

Table 5 Summary of sample statistical

Prefabricatedcomponents Project

μkmm(δk)

Deviation range (mm)

Enterprise1

Enterprise2 Enterprise 3 Enterprise

4 Enterprise 1 Enterprise 2 Enterprise 3 Enterprise 4

Prefabricatedbeammember

Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)

Width 10030 10067 10035 10036 [minus105 313] [minus081 606] [minus009 339] [minus148 472](00023) (00038) (00018) (00030)

Height 10039 10061 10047 10065 [minus474 585] [minus125 511] [minus156 533] [minus109 779](00056) (00032) (00031) (00034)

Prefabricatedcolumnmember

Length 09996(00007)

09991(00007)

09993(00007)

09993(00006) [minus453 429] [minus806 181] [minus654 148] [minus616 109]

Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)

10055(00056) [minus151 648 ] [minus365 621] [minus228 681] [minus219 823]

Prefabricatedwall panelcomponents

Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)


Prefabricatedcompositeslab

Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)


Table 6 KruskalndashWallis inspection of component size deviation

Prefabricated components Project N Ri Ri p alowast

Prefabricated beam memberLength 295 58407 14602 0131

005

Width 295 61165 15291 0177Height 295 57588 14397 0123

Prefabricated column memberLength 368 76593 19148 0401Width 368 74133 18533 0231Height 368 72764 18191 0090

Prefabricated wall panel componentsHeight 404 81847 20461 0061Width 404 81834 20459 0053

ickness 404 82164 20541 0077

Prefabricated composite slab Length 401 80891 20223 0097Width 401 79664 19916 0081

lowastSignificance is progressive significance and the significance level is 005


range of minus15-4mm the most frequent deviation is10ndash16mm the average is 181mm and the variance is 413

e maximum minimum upper quartile lower quartileandmedian of the size deviations are compared using box plotsas shown in Figure 11 e characteristic values of the three-dimensional dimensional deviation of prefabricated wall panelcomponents are all significantly different e characteristicvalues of the wallboard size deviation are significantly differente height and width deviations are basically negative devia-tions and the thickness deviations are basically positive devi-ations e abnormal values of height and width deviations areconcentrated on the larger value side and the median deviationtends to the upper quartile indicating that the height dimensiondeviation and width dimension deviation are right-skeweddistribution and the thickness deviation abnormal values areconcentrated on the smaller value side which means that thethickness deviation distribution is left-skewed distribution

44 Dimensional Deviation Distribution of PrefabricatedComposite Slab Components Because the thickness direc-tion of the composite slab is cast-in-place concrete the

thickness of the composite slab is not counted Calculatingthe difference between the measured data and the designvalue of the prefabricated composite slab components thesample size is 401 which is divided into 20 groups ehistogram is drawn with the deviation value as the abscissaand the measured frequency as the ordinate as shown inFigure 12 As seen in Figure 12 the dimensional deviationdistribution histogram for composite slab decreases from thecenter to the sides and it can be seen from Figure 12 that thedimensional deviation distribution histogram of the com-posite slab is a normal distribution

e length deviation size of the composite slab is mainlyconcentrated in the range of minus5-0mm the most frequentdeviation is minus26-20mm the mean value is minus244mm andthe variance is 221 e width deviation mainly concen-trated in the range of 0ndash3mm the most frequent deviation isminus25-20mm the mean value is 134mm and the variance is121

e maximum minimum upper quartile lowerquartile and median of the size deviations are comparedusing box plots as shown in Figure 13 e dimensional

ndash3 ndash2 ndash1 0 1 2 3 4 5 6 7 8 9Length deviation (mm)

0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt

ndash2 ndash1 0 1 2 3 4 5 6 7ndash3Width deviation (mm)

(b)

Cou

nt

ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3 4 5 6 7 8ndash6 109Height deviation (mm)

60

50

40

30

20

10

0

(c)

Figure 6 Histogram of beam member size deviation distribution (a) Statistical histogram of beam length deviation (b) Statisticalhistogram of beam width deviation (c) Statistical histogram of beam height deviation


deviation characteristic values of the composite slab slabsare all significantly different and the dimensional devi-ations are basically negative deviations there are ab-normal values in the length and height deviation elength deviation abnormal value is concentrated on the

larger value side which means that the length deviationdistribution is skewed to the left-skewed distribution andthe width deviation abnormal values are concentrated onthe side of the smaller value which means that the widthdeviation distribution is right-skewed distribution

Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)

Figure 7 Box plot of beam size deviation distribution

ndash8 ndash7 ndash6 ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3 4 5ndash9Length deviation (mm)

0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt

ndash1 0 1 2 3 4 5ndash2Width deviation (mm)

(b)

0

10

20

30

40

50

60

70

Cou

nt

ndash4 ndash3 ndash2 ndash1 0 1 2 3 4 5 6 7 8ndash5 9Height deviation (mm)

(c)

Figure 8 Histogram of column member size deviation distribution (a) Statistical histogram of column length deviation (b) Statisticalhistogram of column width deviation (c) Statistical histogram of column height deviation


45 Frequency Distribution Inspection of DimensionalDeviation In statistics the KolmogorovndashSmirnov test (KStest) [18 19] is used to test whether two empirical

distributions are the same or whether one empirical dis-tribution is different from another ideal distribution As-suming that X1 X2 XN and Y1 Y2 YN are two

Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)

Figure 9 Box plot of column size deviation distribution

ndash8 ndash7 ndash6 ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3 4 5 6ndash9Height deviation (mm)

0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt

ndash4 ndash3 ndash2 ndash1 0 1 2 3 4ndash5Width deviation (mm)

(b)

ndash4 ndash3 ndash2 ndash1 0 1 2 3 4 5 6 7 8ndash5ickness deviation (mm)

0

10

20

30

40

50

Cou

nt

(c)

Figure 10 Histogram of wall panel size deviation (a) Statistical histogram of wall panel height deviation (b) Statistical histogram of wallpanel width deviation (c) Statistical histogram of wall panel thickness deviation


different samples KndashS can be used to test whether the twosamples belong to the same population and it depends onthe value of the test statistic D e D value is defined as

D max SX(x) minus SY(x)1113868111386811138681113868

1113868111386811138681113868 (6)

Among them SX(x) and SY(x) are the cumulative dis-tribution functions of the two samples respectively If the valueofD is small it can be judged that the two samples are from thesame population Taking into account that the versatility of thenormal probability distribution to random variables and thegeneral significance of Weibullrsquos theory in analyzing the sizeeffect of concrete [20] these two probability statistical distri-butions are compared with the size deviation values of fabri-cated components By using Matlab the normal distributionfunction y normrnd(X σ m n) is used to generate a samplethat conforms to the normal distribution with the average valueX and the standard deviation σ e Weibull distributionfunction y weibrnd(X a b) is used to generate a sample thatconforms to the Weibull distribution with X as the averagewhere a is the scale parameter and b is the shape parameter

Figures 14ndash17 are the curve fitting diagram of the cumu-lative distribution function of different component size devi-ations eWeibull cumulative distribution function curve andthe normal distribution function curve are similar to thecomponent size deviation cumulative distribution functioncurve Intuitively the length deviation cumulative distributionand the width size deviation fit well with the normal distri-bution but are significantly different with the Weibull distri-bution In the deviation distribution of wallboard height andwallboard thickness the Weibull cumulative distribution andthe normal cumulative distribution function curve are in goodagreement To accurately compare and determine the bestdistribution it is necessary to further calculate the maximumabsolute deviation among the theoretical distribution functionthe empirical distribution function and the probability P ofmaking the first type of error e specific results are shown inTable 4 Among themD is calculated according to equation (6)and the value of P is calculated under the hypothesis of theKolmogorov distribution of the limit distribution of D

e KS test results of size deviation frequency normaldistribution and Weibull distribution are shown in Table 7

Height Width Thicknessndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)

Figure 11 Box plot of wall panel size deviation distribution

0

20

40

60

80

Cou

nt

ndash7 ndash6 ndash5 ndash4 ndash3Length deviation (mm)

ndash2 ndash1 0 1 2 3 4

(a)

0

20

40

60

80

Cou

nt

ndash6 ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3ndash7Width deviation (mm)

(b)

Figure 12 Histogram of composite slab size deviation distribution (a) Statistical histogram of length deviation of composite slab(b) Statistical histogram of width deviation of the composite slab


Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)

Figure 13 Box plot of composite slab size deviation distribution

10

08

06

04

02

00

Prob

abili

ty

ndash1 0 1 2 3 4 5 6 7Dimension deviation value (mm)

Cumulative distributionfunctionNormal distributionWeibull distribution

(a)

10

08

06

04

02

00

Prob

abili

ty

ndash2 ndash1 0 1 2 3 4 5 6Width deviation value (mm)


(b)

10

08

06

04

02

00Pr

obab

ility

ndash4 ndash2 0 2 4 6 8Height deviation value (mm)


(c)

Figure 14 e cumulative distribution function of beam size deviation (a) e cumulative distribution function of beam length deviation(b) e cumulative distribution function of beam width deviation (c) e cumulative distribution function of beam height deviation

10

08

06

04

02

00

Prob

abili

ty

ndash8 ndash6 ndash4 ndash2 0 2 4Dimension deviation value (mm)


(a)

10

08

06

04

02

00

Prob

abili

ty

ndash2 ndash1 0 1 2 3 4Width deviation value (mm)


(b)

10

08

06

04

02

00

Prob

abili

ty

ndash4 ndash2 0 2 4 86Height deviation value (mm)


(c)

Figure 15 e cumulative distribution function of column size deviation (a) e cumulative distribution function of column lengthdeviation (b) e cumulative distribution function of column width deviation (c) e cumulative distribution function of column heightdeviation


It can be seen from Table 7 that in the two distributions themaximum absolute value of the normal distribution D is thesmallest and the P value of the normal distribution is the

smallest If the significance is taken at the level of 005 thefitting effects of normal distribution and Weibull distribu-tion are both acceptable and it is obvious that the former is

10

08

06

04

02

00

Prob

abili

ty

ndash6 ndash4 ndash2 0 2Dimension deviation value (mm)


(a)

10

08

06

04

02

00

Prob

abili

ty

ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3Width deviation value (mm)


(b)

Figure 17 e cumulative distribution function of sample value deviation of superimposed slab size (a) e cumulative distributionfunction of length deviation of composite (b) e cumulative distribution function of height deviation of composite slab

10

08

06

04

02

00

Prob

abili

ty

ndash8 ndash6 ndash4 ndash2 0 2 4Height deviation value (mm)


(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty

ndash4 ndash2 0 2 4 6ickness deviation value (mm)


(c)

Figure 16e cumulative distribution function of sample value of wall panel size deviation (a)e cumulative distribution function of wallpanel height deviation (b) e cumulative distribution function of wall panel width deviation (c) e cumulative distribution function ofwall panel thickness deviation


better It shows that the dimensional deviation of fabricatedcomponents conforms to the null hypothesis and normaldistribution

5 Conclusions

In this paper three-dimensional surveys of more than 1400prefabricated components in China were carried out andthe geometric parameters of the components were statisti-cally analyzed using probability and statistics methodshence obtaining the following conclusions

(1) e range of the geometric parameter uncertaintyrandom variable of the same component size pro-duced by different enterprises shows little differenceand the fluctuation is small ranging from 099 to102 e geometric parameter uncertainty coeffi-cient of variation is below 00093 and the compo-nent size deviation variability is small

(2) e significance of the correlation degree of theprefabricated component size deviation is greaterthan the level of 005 and there is no significantdifference among the size deviations of similarcomponents produced by different companies

(3) e histogram of the frequency distribution ofprefabricated component size deviation decreasesfrom the center to both sides and the fitting curvehas only one peake geometric uncertainties of thetransverse dimensions of the components are all lessthan 1 which tend to be negative deviations and thegeometric uncertainties of the longitudinal dimen-sions are all greater than 1 which tend to be positivedeviations

(4) e size deviation of fabricated components does notrefuse to obey the normal distribution and theWeibull distribution but it is more inclined to obeythe normal distribution

Data Availability

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

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors gratefully acknowledge the financial support forthis research by the applied basic research program ofChinarsquos 13th Five-Year Plan (2016YFC0701705-1)

References

[1] T Song Study on quality control of prefabricated concretestructure PhD dissertation Xirsquoan University of Architectureand Technology Xian China 2017

[2] C T Milberg and I D Tommelein ldquoMethods for managingtolerance compatibilityWindows in cast-in-place concreterdquoJournal of Construction Engineering and Managementvol 146 no 2 Article ID 04019105 2020

[3] S Talebi ldquoImprovement of dimensional tolerance manage-ment in constructionrdquo PhD dissertation University ofHudderfield Huddersfield WY UK 2019

[4] C Liu S Shirowzhan S M E Sepasgozar and A KabolildquoEvaluation of classical operators and fuzzy logic algorithmsfor edge detection of panels at exterior cladding of buildingsrdquoBuildings vol 9 no 2 p 40 2019

[5] S Talebi L Koskela P Tzortzopoulos M Kagioglou andA Krulikowski ldquoDeploying geometric dimensioning andtolerancing in constructionrdquo Buildings vol 10 no 4 p 622020

[6] DIN18203-1997 Tolerances for Building Part1 PrefabricatedOrdinary Reinforced and Prestressed Concrete ComponentsDeutsches Institut fur Normung EV (DIN) Berlin Ger-many 1997

[7] PCI MNL-116 Manual for Quality Control for Plants andProduction of Prefabricated and Prestressed Concrete ProductsPrestressed Concrete Institute Chicago IL USA 2nd edition1977

[8] ACI 117M-06 and ACI Committee 117 Specifications forTolerances for Concrete Construction and Materials andCommentarythe United States American Concrete InstituteFarmington Hills MI USA 2006

[9] GB50204-2015 Code for Quality Acceptance of ConcreteStructure Construction China Architecture amp Building PressBeijing China 2015

Table 7 KS inspection result of size deviation

Prefabricated components ProjectNormal distribution Weibull distributionD P D P

Prefabricated beam memberLength 0038 0592 0213 0039Width 0177 0187 0098 0028Height 0044 0331 0052 0311



ickness 0035 0377 0051 0293

Prefabricated composite slablowast Length 0087 0199 0199 0038Width 0019 0211 0227 0031



[10] GBT51231-2016 Technical Code for Prefabricated ChinaArchitecture amp Building Press Beijing China 2016

[11] K Liu Y Z Wang and G Liu ldquoe statistic and analysis ofthe dimension deviation of cast-in-situ concreterdquo Construc-tion Technology vol 01 no 1 pp 98ndash100 2008

[12] W C Zhang ldquoe Research on the Control Indicators ofConstruction Erection Variation of Prefabricated ConcreteStructurerdquo PhD dissertation North China University ofScience and Technology Tangshan China 2019

[13] Research Group on Reliability of Reinforced ConcreteStructural Members ldquoInvestigation and statistical analysis ofthe dimensional tolerances reinforced concrete structuralmembersrdquo Journal of Building Structures vol 6 no 4 pp 2ndash91985

[14] H X Mao and W Z Shi ldquoNew methodology of representingthe positional error of non-point features in GISrdquo e In-ternational Archives of the Photogrammetry Remote Sensingand Spatial Information Sciences vol 37 pp 1503ndash1508 2008

[15] M X Zhang ldquoInvestigation and study on constructionalquality control of concrete structure in Siturdquo PhD disser-tation Zhejiang University Hangzhou Zhejiang China2004

[16] X P Hu ldquoInvestigation and statistical analysis on resistanceof building structural members and reliability analysis onresidential buildingsrdquo PhD dissertation Xirsquoan University ofArchitecture and Technology Xian China 2005

[17] X C Li ldquoInvestigation and statistical analysis on resistance ofreinforced concrete structure in Xianyang regionrdquo PhDDissertation Xirsquoan University of Architecture and Technol-ogy Xian China 2015

[18] E F Acar and L Sun ldquoA generalized kruskal-wallis testincorporating group uncertainty with application to geneticassociation studiesrdquo Biometrics vol 69 no 2 pp 427ndash4352013

[19] L D Ong and P C Leclare ldquoe KolmogorovndashSmirnov testfor the log-normality of sample cumulative frequency dis-tributionsrdquo Health Physics vol 14 no 4 p 376 1968

[20] A Ghasemi and S Zahediasl ldquoNormality tests for statisticalanalysis a guide for non-statisticiansrdquo International Journalof Endocrinology and Metabolism vol 10 no 2 pp 486ndash4892012


connections of two or more components) meet the designintent regarding the accuracy of the final product [5]

At present there are many quality control standards forfabricated components such as German DIN18203 andDIN18202 standards Japanese JASS10 American MNL-116and ACI regulations and Chinese standards GBT51231-2016 and GBT 51232-2016 [6ndash10] Each standard specifiesthe dimensional deviation of prefabricated componentsese standards usually determine the allowable value ofdimensional deviation based on traditional experiences [11]and the deviation allowable value for prefabricated com-ponents is strictly controlled and appropriately modifiedbased on the relevant specifications of cast-in-place concreteScholars do not pay attention to the prefabricated compo-nent manufacturersrsquo production capacity and have notsystematically investigated the dimensional deviation ofprefabricated components [12] To determine the reliabilityof the concrete structure design in the 1970s and 1980s [13]a survey of the size deviation of cast-in-place concretestructures was conducted in China [13] Liu et al [11]conducted the statistical investigation on the size deviationof cast-in-place concrete structures in Beijing and suggestedadjusting the size deviation acceptance index while Mao andShi [14] conducted the statistical investigation and analysison the section size and axis position of cast-in-place concretestructures and they believed that the deviation of concretesection size obeys the normal distribution yet the axisposition deviation obeys the logarithmic distributionNowadays there are many types of research on the sizedeviation of cast-in-situ structures but there are quite fewstatistical studies on the size deviation of prefabricatedconcrete components erefore it is of great significance tosystematically investigate the size deviation of fabricatedcomponents

In this paper the dimensions of fabricated concretecomponents of different companies in China are measuredby 3D photogrammetry technology obtaining a database ofwall board composite slab beam and column size devia-tion e dimensional deviation distribution characteristicsof fabricated components are analyzed

2 Data Acquisition

21 Overview of Sample Acquisition e focus is mainly onthe component forms existing in prefabricated buildingstructures beams columns wall panels and compositeslabs In terms of survey objects components produced byprefabricated component factories in different regions ofChina are mainly selected Random sampling is used foreach type of component Detailed information about thenumber of survey samples is shown in Table 1

22 Measurement Method Prefabricated building produc-tion and installation have higher precision requirementsthan traditional cast-in-situ concrete structures e tradi-tional measurement method for prefabricated concretebuildings is mainly using steel rulers and there are problemswith the use of steel rulers in measuring the dimensions of

prefabricated concrete components such as insufficientaccuracy large errors and difficulty in measuring the edgecorners of the component dimensions e HL-3DP is amedium-range photogrammetry scanner type It wasdesigned for medium-space applications such as buildingcivil and survey and forensics ree-dimensional photo-grammetry known as HL-3DP was applied for prefabricatedconcrete and the scanned data were managed with theirassociated software HOLON3DP HL-3DP is a high-accu-racy and medium-range photogrammetry system It is as-sociated with a high-resolution camera Table 2 shows thespecification of HL-3DP erefore in this article HL-3DPthree-dimensional photogrammetry was adopted to collectsample data Figure 1 shows the on-site measurement ofprefabricated components e relative error of this methodis less than 5 and the absolute error is less than 001mme measurement of the size of the prefabricated compo-nent thus resulted in high precision in terms of both ex-perimental error and measurement accuracy

23 Accuracy Assessment Accuracy assessment was alsoperformed in this study e findings show that the 3Dphotogrammetry of HL-3DP can provide high accuracy ofthe building structure To get a systematic accuracy as-sessment the evaluation of the estimate accuracy was carriedout using equation (1) where x represents each value in thedataset x represents themean of all values in the dataset andn represents the number of value in the dataset

RMSE

1113936niminus1 (x minus x)

2

n

1113971

(1)

e root-mean-square error (RMSE) was used tomeasure the differences between values observed Accordingto Mao and Shi [14] RMSE is commonly used in the re-search field to describe the accuracy of features and it isacceptable to measure the error and estimate the quality offeatures e lower the RMSE value the better the accuracy

Table 3 shows the dimensional measurement differencebetween the measuring steel tape and photogrammetrysystem Meanwhile the analysis for this study included thecomparison of measurement between the photogrammetrysystem and conventional method (measuring steel tape) withthe design valuee comparison is performed and recordedin Table 4 e RMSE value of the photogrammetry systemdata was 060mm while that of the measuring steel tapemethod was 094mm As the result the tolerance of thephotogrammetry system model is well within the 001-millimeter level e photogrammetry system model has alower tolerance compared to the measuring steel tap isproved that the photogrammetry system method wasaccurate

3 Results of Sample Collection

In the process of statistical analysis of the geometric pa-rameters of the components because the design dimensionsof the components are not the same to analyze and comparethe variation of the dimensions described by the uncertainty




KA a

aK

(2)









(a) (b)



μKA

1113936ni1 niμKAi

1113936ni1 ni

(3)

δKA

1113936ni1 niδKAi

1113936ni1 ni

(4)















Σ

radic11 094

Σ

radic11 060






ickness 240 238 24065








p 12

N(N + 1)1113944

k


2

Ri Ri

ni

R N + 12

(5)



102

101

100

099

Height Width Length

Rang

e




103

102

101

100

099

Height Width Length

Rang

e















104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e




1002

1000

0998

Width Length

Rang

e











μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


















KA a

aK

(2)









(a) (b)



μKA

1113936ni1 niμKAi

1113936ni1 ni

(3)

δKA

1113936ni1 niδKAi

1113936ni1 ni

(4)















Σ

radic11 094

Σ

radic11 060






ickness 240 238 24065








p 12

N(N + 1)1113944

k


2

Ri Ri

ni

R N + 12

(5)



102

101

100

099

Height Width Length

Rang

e




103

102

101

100

099

Height Width Length

Rang

e















104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e




1002

1000

0998

Width Length

Rang

e











μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293
















μKA

1113936ni1 niμKAi

1113936ni1 ni

(3)

δKA

1113936ni1 niδKAi

1113936ni1 ni

(4)















Σ

radic11 094

Σ

radic11 060






ickness 240 238 24065








p 12

N(N + 1)1113944

k


2

Ri Ri

ni

R N + 12

(5)



102

101

100

099

Height Width Length

Rang

e




103

102

101

100

099

Height Width Length

Rang

e















104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e




1002

1000

0998

Width Length

Rang

e











μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293




















p 12

N(N + 1)1113944

k


2

Ri Ri

ni

R N + 12

(5)



102

101

100

099

Height Width Length

Rang

e




103

102

101

100

099

Height Width Length

Rang

e















104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e




1002

1000

0998

Width Length

Rang

e











μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


























104

102

100

098

104

102

100

098

1002

1000

0998

Height Width Length

Rang

e




1002

1000

0998

Width Length

Rang

e











μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293






















μkmm(δk)


Enterprise1




Length 10011 10009 10010 10065 [004 544] [minus077 532] [053 552] [016 678](00004) (00005) (00004) (00034)




Length 09996(00007)

09991(00007)

09993(00007)


Width 10035(00019)

10031(00029)

10033(00029)


Height 10026(00040)

10053(00061)

10033(00029)



Height 09996(00002)

09994(00005)

09994(00006)


Width 09996(00005)

09997(00004)

09996(00003)


ickness 10071(00093)

10121(00089)

10076(00070)



Length 09994(00006)

09994(00003)

09993(00003)


Width 09994(00004)

09993(00003)

09994(00004)





005

Width 295 61165 15291 0177Height 295 57588 14397 0123



ickness 404 82164 20541 0077











0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293























0

10

20

30

40C

ount

(a)

60

40

20

0

Cou

nt


(b)

Cou

nt


60

50

40

30

20

10

0

(c)





Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


















Length Width Height

ndash6

ndash4

ndash2

0

2

4

6

8

10

Rang

e (m

m)



0

10

20

30

40

50

60

70

Cou

nt

(a)

0

10

20

30

40

50

Cou

nt


(b)

0

10

20

30

40

50

60

70

Cou

nt


(c)





Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


















Length Width Width

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)



0

10

20

30

40

50

60

Cou

nt

(a)

0

20

40

60

Cou

nt


(b)


0

10

20

30

40

50

Cou

nt

(c)





1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


















1113868111386811138681113868 (6)





ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Rang

e (m

m)


0

20

40

60

80

Cou

nt



(a)

0

20

40

60

80

Cou

nt


(b)



Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293
















Length Widthndash8

ndash6

ndash4

ndash2

0

2

4

Rang

e (m

m)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00Pr

obab

ility



(c)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)





10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293


















10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)


10

08

06

04

02

00

Prob

abili

ty



(a)

10

08

06

04

02

00

Prob

abili

ty



(b)

10

08

06

04

02

00

Prob

abili

ty



(c)




5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293

















5 Conclusions






Data Availability




Acknowledgments


References















ickness 0035 0377 0051 0293
















PrefabricatedConcreteComponentGeometryDeviation … · 2021. 3. 22. · togrammetry technology. e...

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Transcript of PrefabricatedConcreteComponentGeometryDeviation … · 2021. 3. 22. · togrammetry technology. e...