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The research objects of this paper were the prefabricated concrete components produced by four enterprises in China, and the dimension deviation data of more than 1400 prefabricated concrete components are measured with high-precision 3D photogrammetry technology. The nonparametric Kruskal–Wallis test was carried out for the size deviation of the same type of components produced by different enterprises. The distribution characteristics of geometric parameters of typical components of prefabricated structures in China, such as beams, columns, wall boards, and composite slabs, were analyzed by using the probability statistical method. The Kolmogorov–Smirnov goodness-of-fit method was used to test the cumulative distribution function of dimension deviation, and the size distribution of fabricated components was studied. The results showed that there was no significant difference in the size deviation of the same-type component produced by different enterprises, and the range of geometric parameter uncertainty random variables was small, which was between 0.99 and 1.02. Also, the fluctuation was small, the coefficient of variation was below 0.0093, and the variability of component size deviation was small. The transverse dimension of the component shows a positive deviation, the vertical dimension of component shows a negative deviation, and the dimension deviation of prefabricated concrete components follows the normal distribution.

Prefabricated building is one of the important directions of building structure development, which is conducive to the development of building industrialization. As a crucial part of the prefabricated concrete (PC) structure, the quality of prefabricated components plays an important role in the overall structural performance [

At present, there are many quality control standards for fabricated components, such as German DIN18203 and DIN18202 standards, Japanese JASS10, American MNL-116 and ACI regulations, and Chinese standards GB/T51231-2016 and GB/T 51232-2016 [

In this paper, the dimensions of fabricated concrete components of different companies in China are measured by 3D photogrammetry technology, obtaining a database of wall board, composite slab, beam, and column size deviation. The dimensional deviation distribution characteristics of fabricated components are analyzed.

The focus is mainly on the component forms existing in prefabricated building structures: beams, columns, wall panels, and composite slabs. In terms of survey objects, components produced by prefabricated component factories in different regions of China are mainly selected. Random sampling is used for each type of component. Detailed information about the number of survey samples is shown in Table

Sample number of prefabricated concrete members in different enterprises.

Survey object | Sample number of prefabricated parts | |||
---|---|---|---|---|

Beam components | Column components | Wall panel components | Composite slab components | |

Enterprise 1 | 62 | 66 | 102 | 87 |

Enterprise 2 | 54 | 129 | 84 | 96 |

Enterprise 3 | 76 | 94 | 64 | 111 |

Enterprise 4 | 103 | 85 | 121 | 107 |

Prefabricated building production and installation have higher precision requirements than traditional cast-in-situ concrete structures. The traditional measurement method for prefabricated concrete buildings is mainly using steel rulers, and there are problems with the use of steel rulers in measuring the dimensions of prefabricated concrete components, such as insufficient accuracy, large errors, and difficulty in measuring the edge corners of the component dimensions. The HL-3DP is a medium-range photogrammetry scanner type. It was designed for medium-space applications such as building, civil and survey, and forensics. Three-dimensional photogrammetry known as HL-3DP was applied for prefabricated concrete, and the scanned data were managed with their associated software HOLON3DP. HL-3DP is a high-accuracy and medium-range photogrammetry system. It is associated with a high-resolution camera. Table

Specification of 3D photogrammetric HL-3DP.

HL-3DP 3D photogrammetric instrument | |
---|---|

Range measurement principle scanner control | Measurement of noncontact optical tricoordinate |

Range | Up to 20 m (minimum range 0.01 m) |

Field of view | 360°horizontal, 360°vertical |

Signal image | 1.8 MB, 4Mpixels (1920 × 1920 pixel) |

Ranging error | ±0.01 mm |

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

Accuracy assessment was also performed in this study. The findings show that the 3D photogrammetry of HL-3DP can provide high accuracy of the building structure. To get a systematic accuracy assessment, the evaluation of the estimate accuracy was carried out using equation (

The root-mean-square error (RMSE) was used to measure the differences between values observed. According to Mao and Shi [

Table

Result of dimensional measurement.

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

Prefabricated beam components | Length | 2830 | 2833 | 2831.86 |

Width | 400 | 402 | 400.82 | |

Height | 410 | 413 | 412.03 | |

Prefabricated column components | Length | 2535 | 2539 | 2537.08 |

Width | 500 | 503 | 502.07 | |

Height | 520 | 523 | 520.67 | |

Prefabricated wall panel components | Height | 6630 | 6633 | 6629.84 |

Width | 2600 | 2598 | 2599.24 | |

Thickness | 240 | 238 | 240.65 | |

Prefabricated composite slab | Length | 4350 | 4355 | 4346.06 |

Width | 3930 | 3933 | 3926.95 |

Comparison of measurement between the measuring steel tape and photogrammetry system.

Prefabricated | Measuring steel tape (mm) | Photogrammetry system | ||
---|---|---|---|---|

Prefabricated | −3 | 9 | −1.86 | 3.46 |

Beam components | −2 | 4 | −0.82 | 0.67 |

−3 | 9 | −2.03 | 4.12 | |

Prefabricated | −4 | 16 | −2.08 | 4.33 |

Column | −3 | 9 | −2.07 | 4.28 |

Components | −3 | 9 | −0.67 | 0.45 |

Prefabricated wall | −3 | 9 | 0.16 | 0.02 |

Panel components | 2 | 4 | 0.76 | 0.58 |

2 | 4 | −0.65 | 0.42 | |

Prefabricated | −5 | 25 | 3.94 | 15.52 |

Composite slab | −3 | 9 | 3.05 | 9.30 |

Sum | 107 | 43.15 | ||

RMSE | 0.94 | 0.60 |

In the process of statistical analysis of the geometric parameters of the components, because the design dimensions of the components are not the same, to analyze and compare the variation of the dimensions described by the uncertainty of the geometric parameters with the random variable

When analyzing the variability of the geometric dimensions of components, variables such as length, width, and height are regarded as independent random variables. Taking the same type of component produced by the same enterprise as a matrix, its statistical parameters are analyzed with a subsample of capacity

Taking prefabricated concrete components produced by different companies as the research object, analyzing the difference in geometric uncertainty of component size in different enterprises, and calculating the average production component

Box plot of geometric uncertainty of the beam member.

Box plot of geometric uncertainty of the column member.

Box plot of wall panel geometric uncertainty.

Box plot of geometric uncertainty of slab.

Table

Summary of sample statistical.

Prefabricated components | Project | Deviation range (mm) | |||||||
---|---|---|---|---|---|---|---|---|---|

Enterprise 1 | Enterprise 2 | Enterprise 3 | Enterprise 4 | Enterprise 1 | Enterprise 2 | Enterprise 3 | Enterprise 4 | ||

Prefabricated beam member | Length | 1.0011 | 1.0009 | 1.0010 | 1.0065 | [0.04, 5.44] | [−0.77, 5.32] | [0.53, 5.52] | [0.16, 6.78] |

(0.0004) | (0.0005) | (0.0004) | (0.0034) | ||||||

Width | 1.0030 | 1.0067 | 1.0035 | 1.0036 | [−1.05, 3.13] | [−0.81, 6.06] | [−0.09, 3.39] | [−1.48, 4.72] | |

(0.0023) | (0.0038) | (0.0018) | (0.0030) | ||||||

Height | 1.0039 | 1.0061 | 1.0047 | 1.0065 | [−4.74, 5.85] | [−1.25, 5.11] | [−1.56, 5.33] | [−1.09, 7.79] | |

(0.0056) | (0.0032) | (0.0031) | (0.0034) | ||||||

Prefabricated column member | Length | 0.9996 (0.0007) | 0.9991 (0.0007) | 0.9993 (0.0007) | 0.9993 (0.0006) | [−4.53, 4.29] | [−8.06, 1.81] | [−6.54, 1.48] | [−6.16, 1.09] |

Width | 1.0035 (0.0019) | 1.0031 (0.0029) | 1.0033 (0.0029) | 1.0039 (0.0032) | [−0.25, 3.91] | [−1.44, 3.30] | [−1.30, 3.90] | [−1.25, 4.04] | |

Height | 1.0026 (0.0040) | 1.0053 (0.0061) | 1.0033 (0.0029) | 1.0055 (0.0056) | [−1.51, 6.48 ] | [−3.65, 6.21] | [−2.28, 6.81] | [−2.19, 8.23] | |

Prefabricated wall panel components | Height | 0.9996 (0.0002) | 0.9994 (0.0005) | 0.9994 (0.0006) | 0.9992 (0.0006) | [−5.81, 0.24] | [−5.42, 2.16] | [−5.03, 1.15] | [−6.57, 3.29] |

Width | 0.9996 (0.0005) | 0.9997 (0.0004) | 0.9996 (0.0003) | 0.9997 (0.0004) | [−4.75, 2.29 ] | [−4.36, 2.05] | [−3.32, 1.77] | [−4.38, 2.04] | |

Thickness | 1.0071 (0.0093) | 1.0121 (0.0089) | 1.0076 (0.0070) | 1.0054 (0.0084) | [−3.45, 5.88 ] | [−0.67, 5.98] | [−1.09, 4.48] | [−4.28, 5.98] | |

Prefabricated composite slab | Length | 0.9994 (0.0006) | 0.9994 (0.0003) | 0.9993 (0.0003) | 0.9992 (0.0005) | [−5.99, 3.10] | [−4.84, 1.12] | [−5.23, 0.23] | [−5.41, 0.92] |

Width | 0.9994 (0.0004) | 0.9993 (0.0003) | 0.9994 (0.0004) | 0.9991 (0.0004) | [−4.88, 1.22] | [−6.20, 0.09] | [−3.89, 2.13] | [−3.48, 1.10] |

With the significant level

The Kruskal–Wallis test [

Assuming that the distribution of the size deviation of similar components is the same in the company category, if

Kruskal–Wallis inspection of component size deviation.

Prefabricated components | Project | |||||
---|---|---|---|---|---|---|

Prefabricated beam member | Length | 295 | 584.07 | 146.02 | 0.131 | 0.05 |

Width | 295 | 611.65 | 152.91 | 0.177 | ||

Height | 295 | 575.88 | 143.97 | 0.123 | ||

Prefabricated column member | Length | 368 | 765.93 | 191.48 | 0.401 | |

Width | 368 | 741.33 | 185.33 | 0.231 | ||

Height | 368 | 727.64 | 181.91 | 0.090 | ||

Prefabricated wall panel components | Height | 404 | 818.47 | 204.61 | 0.061 | |

Width | 404 | 818.34 | 204.59 | 0.053 | ||

Thickness | 404 | 821.64 | 205.41 | 0.077 | ||

Prefabricated composite slab | Length | 401 | 808.91 | 202.23 | 0.097 | |

Width | 401 | 796.64 | 199.16 | 0.081 |

Since there is no significant difference in the size deviation of the same type components, the size deviations of the same-type components produced by different companies are integrated as a sample of the size deviation, and the distribution law of size deviation is analyzed using histograms and box plots.

Calculating the difference between the measured data and the design value of the prefabricated beam, the sample size is 295, which is divided into 20 groups. The histogram is drawn with the deviation value as the abscissa and the measured frequency as the ordinate, as shown in Figure

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

The length deviation of beam components mainly concentrated in the range of 0–6 mm, The most frequent deviation is 2–4 mm, the mean is 3.02 mm, and the variance is 1.91. The width deviation range is mainly concentrated in the range of 0-3 mm, the mean value is 1.57 mm, and the variance is 1.56, The height deviation is mainly concentrated in the range of 0–5 mm, the mean value is 2.44 mm, and the variance is 3.27.

The maximum, minimum, upper quartile, lower quartile, and median of the size deviations are compared using box plots, as shown in Figure

Box plot of beam size deviation distribution.

Calculating the difference between the measured data and the design value of the prefabricated column, the sample size is 374, which is divided into 20 groups. The histogram is drawn with the deviation value as the abscissa and the measured frequency as the ordinate, as shown in Figure

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

The length deviation of the column components mainly concentrated in the range of −5-1 mm, the most frequent deviation is −3-1 mm, the mean value is −2.05 mm, and the variance is 3.74; the width deviation mainly concentrated in the range of −1-3.5 mm, the most frequent deviation is 0.7–1.5 mm, the mean value is 1.34 mm, and the variance is 1.21; the height deviation is mainly concentrated in the range of −2–5 mm, the most frequent deviation is 1.5–2.5 mm, the average is 1.88 mm, and the variance is 4.34.

The maximum, minimum, upper quartile, lower quartile, and median of the size deviations are compared using box plots, as shown in Figure

Box plot of column size deviation distribution.

Calculating the difference between the measured data and the design value of the prefabricated wall panel, the sample size is 371, which is divided into 20 groups. The histogram is drawn with the deviation value as the abscissa and the measured frequency as the ordinate, as shown in Figure

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

The height deviation size of prefabricated wall panels is mainly concentrated in the range of −5-0 mm, the most frequent deviation is −3.5-2.8 mm, the average is −2.39 mm, and the variance is 2.91. The width deviation mainly concentrated in the range of −3-0.5 mm, the most frequent deviation was −1-0.6 mm, the mean value was −1.13 mm, and the variance was 1.57. The thickness deviation is mainly concentrated in the range of −1.5-4 mm, the most frequent deviation is 1.0–1.6 mm, the average is 1.81 mm, and the variance is 4.13.

The maximum, minimum, upper quartile, lower quartile, and median of the size deviations are compared using box plots, as shown in Figure

Box plot of wall panel size deviation distribution.

Because the thickness direction of the composite slab is cast-in-place concrete, the thickness of the composite slab is not counted. Calculating the difference between the measured data and the design value of the prefabricated composite slab components, the sample size is 401, which is divided into 20 groups. The histogram is drawn with the deviation value as the abscissa and the measured frequency as the ordinate, as shown in Figure

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.

The length deviation size of the composite slab is mainly concentrated in the range of −5-0 mm, the most frequent deviation is −2.6-2.0 mm, the mean value is −2.44 mm, and the variance is 2.21; The width deviation mainly concentrated in the range of 0–3 mm, the most frequent deviation is −2.5-2.0 mm, the mean value is 1.34 mm, and the variance is 1.21.

The maximum, minimum, upper quartile, lower quartile, and median of the size deviations are compared using box plots, as shown in Figure

Box plot of composite slab size deviation distribution.

In statistics, the Kolmogorov–Smirnov test (KS test) [

Among them,

Figures

The cumulative distribution function of beam size deviation. (a) The cumulative distribution function of beam length deviation. (b) The cumulative distribution function of beam width deviation. (c) The cumulative distribution function of beam height deviation.

The cumulative distribution function of column size deviation. (a) The cumulative distribution function of column length deviation. (b) The cumulative distribution function of column width deviation. (c) The cumulative distribution function of column height deviation.

The cumulative distribution function of sample value of wall panel size deviation. (a) The cumulative distribution function of wall panel height deviation. (b) The cumulative distribution function of wall panel width deviation. (c) The cumulative distribution function of wall panel thickness deviation.

The cumulative distribution function of sample value deviation of superimposed slab size. (a) The cumulative distribution function of length deviation of composite. (b) The cumulative distribution function of height deviation of composite slab.

The KS test results of size deviation frequency, normal distribution, and Weibull distribution are shown in Table

KS inspection result of size deviation.

Prefabricated components | Project | Normal distribution | Weibull distribution | ||
---|---|---|---|---|---|

Prefabricated beam member | Length | 0.038 | 0.592 | 0.213 | 0.039 |

Width | 0.177 | 0.187 | 0.098 | 0.028 | |

Height | 0.044 | 0.331 | 0.052 | 0.311 | |

Prefabricated column member | Length | 0.073 | 0.429 | 0.189 | 0.033 |

Width | 0.098 | 0.373 | 0.167 | 0.048 | |

Height | 0.031 | 0.333 | 0.094 | 0.309 | |

Prefabricated wall panel components | Height | 0.055 | 0.419 | 0.193 | 0.037 |

Width | 0.061 | 0.380 | 0.313 | 0.018 | |

Thickness | 0.035 | 0.377 | 0.051 | 0.293 | |

Prefabricated composite slab | Length | 0.087 | 0.199 | 0.199 | 0.038 |

Width | 0.019 | 0.211 | 0.227 | 0.031 |

In this paper, three-dimensional surveys of more than 1,400 prefabricated components in China were carried out, and the geometric parameters of the components were statistically analyzed using probability and statistics methods, hence obtaining the following conclusions:

The range of the geometric parameter uncertainty random variable of the same component size produced by different enterprises shows little difference and the fluctuation is small, ranging from 0.99 to 1.02. The geometric parameter uncertainty coefficient of variation is below 0.0093, and the component size deviation variability is small.

The significance of the correlation degree of the prefabricated component size deviation is greater than the level of 0.05, and there is no significant difference among the size deviations of similar components produced by different companies.

The histogram of the frequency distribution of prefabricated component size deviation decreases from the center to both sides, and the fitting curve has only one peak. The geometric uncertainties of the transverse dimensions of the components are all less than 1, which tend to be negative deviations, and the geometric uncertainties of the longitudinal dimensions are all greater than 1, which tend to be positive deviations.

The size deviation of fabricated components does not refuse to obey the normal distribution and the Weibull distribution, but it is more inclined to obey the normal distribution.

The [xls] data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The authors gratefully acknowledge the financial support for this research by the applied basic research program of China’s 13th Five-Year Plan (2016YFC0701705-1).