A fuzzy evaluation method of road vehicle automatic weighing instrument in dynamic force metrological performance

Abstract

The measurement performance of road vehicle automatic weighing instrument installed on highways is directly related to the safety of roads and bridges. The fuzzy number indicates that the uncertain quantization problem has obvious advantages. By analyzing the factors affecting the metrological performance of the road vehicle automatic weighing instrument, combined with the fuzzy mathematics theory, the weight evaluation model of the dynamic performance evaluation of the road vehicle automatic weighing instrument is proposed. The factors of measurement performance are summarized and calculated, and the comprehensive evaluation standard of the metering performance of the weighing equipment is obtained, so as to realize the quantifiable analysis and evaluation of the metering performance of the dynamic road vehicle automatic weighing instrument in use, and provide data reference for adopting a more scientific measurement supervision method.

Keywords

Road vehicle automatic weighing instrument metrological performance fuzzy evaluation

1. Introduction

Traffic is the artery of the national economy. Zhejiang is located on the coast and the road network is developed. With the implementation of “The Belt and Road”, the road transport throughput of goods has grown tremendously [1]. The road vehicle automatic weighing instrument is installed in the exit lane of the highway toll station. The road vehicle automatic weighing instrument is the key measuring instrument for national highway toll collection [2], and its dynamic force metrological performance directly affects the safety of road traffic and the fairness of the toll collection. Because the equipment is in a high-intensity environment, its dynamic force metrological performance has been greatly different from that at the beginning of the factory [3]. It needs to be adjusted during the measurement verification process. After adjusting the parameters, it can be qualified, and some of them are difficult to adjust to the maximum tolerance after repeated adjustments. Factors that determine the dynamic force metrological performance of the equipment, in addition to the conventional metering performance under laboratory conditions, the adaptability of the vehicle, the adaptability of the road condition, the adaptability of the driving state, etc. are also very important in the actual installation and use [4]. Importantly, these factors all affect the accuracy of the weighing data, but these factors are difficult to quantify. Based on this, we hope to find a method for the dynamic force metrological performance of the road vehicle automatic weighing instrument that include installation conditions, the environmental conditions and the different driving modes.

2. Evaluation mode of road vehicle automatic weighing instrument

The fuzzy theory indicates that the uncertain quantitative problem has obvious advantages [5]. It can decompose the problem into different constituent factors, and combine the factors according to the interrelated influences and subordination factors to form a multi-level analytical structure model [6,7]. Based on the analysis of the factors affecting the dynamic force metrological performance of the road vehicle automatic weighing instrument (RVAWI), a fuzzy evaluation method of road vehicle automatic weighing instrument is proposed to calculate the factors affecting the measurement performance. The method realizes a quantifiable analysis and evaluation of the metrological performance of the road vehicle automatic weighing instrument in use. The influencing factors of measurement performance are compared as evaluation indicators, and the level of evaluation indicators is distinguished. The experts with rich practical experience give scientific and reasonable evaluation to the evaluation indicators. After calculating and comparing the selection goals, the quantitative value description of the qualitative problem is reached.

Fig. 1.

Factors hierarchical graph.

The factors affecting dynamic force metrological performance are divided into different levels. The factors in the same layer are subordinated to the upper layer and have influence on the upper factors. At the same time, the factors underlying the next layer are affected by the lower factors. The dynamic force metrological performance of the instrument (U) includes the adaptability of the vehicle type (U₁), adaptability of the driving status (U₂), and stationary load status (U₃). The hierarchical structure model of 12 parameters is shown in Fig. 1. According to the existing verification data analysis and the expert scoring judgment, determine the scale of the analytic hierarchy, and the obtained pairwise comparison matrix is the judgment matrix. The analytic scale is based on a 1–9 scale [8]. The larger the scale, the more important the former is relative to the latter. The importance scale of factor i and factor j is u_ij, and the importance scale of factor j and factor i is 1∕u_ij. The equivalence matrix values of the normalized vector are the weights of the corresponding factors of the layer to the previous level.

Vehicle type adaptability U₁ = [U₁₁, U₁₂, U₁₃], according to JJG907-2006 “Verification Regulations of Automatic Instruments for Weighing Road Vehicles in Motion”, in addition to rigid vehicles, other vehicles are required [9]. The two-axis, three-axis and five-axis vehicles are actually equipped during the verification process, assuming different models during the verification process. The actual maximum error is Δ, and the maximum allowable error of the specification is MPEV. The adaptability of driving status U₂ = [U₂₁, U₂₂, U₂₃] and stationary load U₃ = [U₃₁, U₃₂, U₃₃] are similar to the evaluation indicators of vehicle adaptability U₁.

2.1. Weight calculation

Assigning the importance of the indicators of the criteria in the domain U. The method is to compare the indicators in each criterion, and assign them scientifically and reasonably according to their relative importance [10], and then obtain the pairwise comparison matrix C_k of the indicators in the criterion. $\begin{eqnarray}\displaystyle C_{k}=\left[\begin{array}{@{}cccc@{}}1 & u_{k2} & \cdots ∼ & u_{kj}\\ 1/u_{k2} & 1 & & u_{k+1,j+1}\\ \vdots & \vdots & \ddots & \vdots \\ 1/u_{kj} & \cdots ∼ & & 1\\ \end{array}\right]. & & \displaystyle\end{eqnarray}$ (1)

According to the pairwise comparison matrix C_k, weight vector A_k can be obtained. Before constructing the square matrix C_k, use meaning of scale values table list the relative importance of each indicator (Table 2). According to the importance of the evaluation index, the expert group gives the pairwise comparison matrix C_k of each index’s excellent degree of the target. To ensure the non-negative weight, the eigenvector corresponding to the maximum eigenvalue is used. Therefore, on this basis, the maximum eigenvalues of the square matrix C_k and the corresponding eigenvectors ω_k are also solved, and the eigenvectors are normalized.

2.2. Consistency check

In the construction process of pairwise comparison matrices, it is not required to judge whether the matrix has consistency, which is determined by the complexity of objective things and the diversity of human cognition. However, it is necessary to judge that there is general consistency. Therefore, after obtaining the maximum eigenvalue 𝜆_max, a consistency check is required. The steps are as follows:

(1) Computational consistency indicator CI $\begin{eqnarray}\displaystyle CI=({\lambda}_{\text{max}}-n)/(n-1). & & \displaystyle\end{eqnarray}$ (2)

(2) Query average random consistency index

Constructing 500 sample matrices by random method Calculate the consistency index value CI for each of 500 random sample matrices of 1–9 order, and then take the arithmetic mean value to obtain the evaluation random consistency index value. For the 1–9 order judgment matrix, the value RI of the evaluation random consistency index is as shown in Table 3.

(3) Calculate the consistency ratio

When CR = CI∕RI < 0.1, the pairwise comparison matrix is considered to have satisfactory consistency, and the weights sought are acceptable.

2.3. Fuzzy comparison

Because there are many fuzzy factors, based on the relevant evaluation indicators, this paper compares and analyzes according to the fuzzy comparison method, and provides data support for the selection. The fuzzy comparison method carries out the fuzzy comparison of the corresponding levels according to the evaluation level. The two-level fuzzy comparison described in this paper includes the comparison of the first level indicators and the second level comprehensive comparison.

Comparison of the first-level indicators: The single-index comparison is performed according to the elements of each factor subset U_k. The method is based on the relative importance of each factor in each subset U_k, and is assigned according to the scale shown in Table 2. The matrix C_k, by calculating the weight vector A_k, and the single factor evaluation result in the k subset is composed of the index evaluation matrix R_k. Finally, the pros and cons of the corresponding subset are obtained by the following formula: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle A_{k}=C_{k}\cdot {\omega}_{k}\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle B_{k}=A_{k}R_{k}=[b_{k1},b_{k2}].\end{eqnarray}$ (4)

The second-level comprehensive comparison is similar to the first-level comprehensive comparison. Each factor subset is compared as a single factor, and the final evaluation is obtained by the following formula: $\begin{eqnarray}\displaystyle B=AR=[b_{1},b_{2}]. & & \displaystyle\end{eqnarray}$ (5)

3. Evaluation application of road vehicle automatic weighing instrument

The following is the error value measured by three evaluation categories of a road vehicle automatic weighing instrument installed in the lane of Zhejiang Hangchang Expressway. Δ_a and Δ_b represent the absolute value of the error measured by RVAWI A under the three evaluation categories U₁, U₂ and U₃ (unit of measurement: ton), where the values of U₁₁, U₁₂ and U₁₃ are respectively expressed as two, three and five axes vehicles under standard measurement conditions The absolute value between the weight of the vehicle and the known standard value after the test vehicle passed RVAWI A. The Δ_a values of U₂₁, U₂₂ and U₂₃ are respectively expressed as the absolute value of the difference between the measured value and the standard value after the five-axis test vehicle passes RVAWI A under three different vehicle motion states of uniform speed, variable speed, and curved driving. MPEV is the maximum value allowed by JJG907-2006 technical specifications. The judgment matrix is obtained according to the error value.

3.1. Comparison of primary indicators

3.1.1. The adaptability of the vehicle type

As shown in Table 4, the three indicators of the two-axle, three-axle and four-axle vehicles of the two dynamic road vehicles are assigned $R_{{\rm\Delta}}=\left[\begin{array}{@{}cc@{}}{\rm\Delta}_{a} & {\rm\Delta}_{b}\end{array}\right]$ $\begin{eqnarray}\displaystyle R_{i}=1-{\rm\Delta}_{ai}/({\rm\Delta}_{ai}+{\rm\Delta}_{bi}). & & \displaystyle\end{eqnarray}$ (6)

According to the formula (6), normalize the results of the model evaluation in Table 5. The membership degree of each indicator of the two road vehicle automatic weighing instrument is obtained, and the judgment matrix is R₁, it is showed in Table 6.

Table 1

Assignment criteria

Level	Very poor	Poor	Middle	Good	Excellent
Assignment criteria	1	3	5	7	9

Table 2

Meaning of scale values

Scale value (u_ij)	Relationship
1	Equally good
3	The former is better than the latter
5	The former is slightly better than the latter
7	The former is stronger than the latter
9	The former is extremely superior to the latter
2, 4, 6, 8	An adjacent state indicating the above state

Table 3

The mean random consistency index RI

Level	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.46

Table 4

Road vehicle automatic weighing instrument evaluation sets

		RVAWI A		RVAWI B
Criteria	Indicators	Δ_a (t)	MPEV (t)	Δ_b (t)	MPEV (t)
Vehicle type (U₁)	2 axles (U₁₁)	0.02	0.17	0.03	0.17
	3 axles (U₁₂)	0.14	0.62	0.21	0.62
	5 axles (U₁₃)	0.26	0.89	0.39	0.89
Road vehicle drive status (U₂)	Uniform speed (U₂₁)	0.66	0.89	0.41	0.89
	Variable speed (U₂₂)	0.46	0.89	0.62	0.89
	“S” style (U₂₃)	0.74	0.89	0.72	0.89
Stationary load (U₃)	Zero point (U₃₁)	0.01	0.05	0.01	0.05
	Weighing range (U₃₂)	0.05	0.15	0.10	0.15
	Repeatability (U₃₃)	0.05	0.10	0	0.10

Table 5

The evaluation indexes R_Δ of vehicle type

	Goal
Indicators	RVAWI A	RVAWI B
2 axles (U₁₁)	0.02	0.03
3 axles (U₁₂)	0.14	0.21
5 axles (U₁₃)	0.26	0.39

Table 6

The evaluation matrix R₁ of vehicle type

	Goal
Indicators	RVAWI A	RVAWI B
2 axles (U₁₁)	0.6	0.4
3 axles (U₁₂)	0.62	0.38
5 axles (U₁₃)	0.54	0.46

Referring to the criteria shown in Table 1, the importance of the two indicators of the two axes (U₁₁) three axes (U₁₂) five axes (U₁₃) in the vehicle type is compared and paired according to the criteria shown in Table 2, so that Pairwise comparison matrix C₁ of each indicator for the vehicle adaptability can be obtained. From Table 2, in terms of vehicle type, based on past experience, we believe that the impact of the U₁₁ symmetry weight result is higher than U₁₂, and we give it a value of 7, then the symmetry weight result of U₁₂ to U₁₁, The value is 1∕7. In the same way, in the degree of influence of the symmetry weight result, U₁₁ is slightly higher than U₁₃, we give it a value of 5, then the importance of U₁₃ relative to U₁₁ is 1∕5, compared with U₁₂ and U₁₃. To the extent that U₁₃ is more important than U₁₂ and we give it a value of 3, the importance of U₁₂ over U₁₃ is 1∕3. The pairwise comparison matrix C₁ is showed in Table 7.

Table 7

The pairwise comparison matrix C₁ of vehicle type

C ₁	U ₁₁	U ₁₂	U ₁₃
U ₁₁	1	7	5
U ₁₂	1∕7	1	1∕3
U ₁₃	1∕5	3	1

The maximum eigenvalue 𝜆_max = 3.065, the corresponding eigenvector ${\omega}=\left[\begin{array}{@{}ccc@{}}0.963 & 0.107 & 0.248\end{array}\right]$ .

By formula (2), the consistency ratio CR = (3.065 −3)∕[(3 −1) × 0.58] = 0.056 < 0.1.

By formula (3), formula (4), through the consistency test, the weight vector of each indicator of vehicle adaptability A₁ and the comparison results of vehicle adaptability of two dynamic road vehicles automatic weighing instruments B₁ are obtained. $\begin{eqnarray}A_{1}=\left[\begin{array}{@{}ccc@{}}1 & 7 & 5\\ 1/7 & 1 & 1/3\\ 1/5 & 3 & 1\end{array}\right]\left[\begin{array}{@{}c@{}}0.963\\ 0.107\\ 0.248\end{array}\right]=\left[\begin{array}{@{}c@{}}2.951\\ 0.327\\ 0.761\end{array}\right]B_{1}=\left[\begin{array}{@{}ccc@{}}2.951 & 0.327 & 0.761\end{array}\right]\left[\begin{array}{@{}cc@{}}0.6 & 0.4\\ 0.62 & 0.38\\ 0.54 & 0.46\end{array}\right]=\left[\begin{array}{@{}cc@{}}2.38 & 1.65\end{array}\right].\end{eqnarray}$

In the same way, the comparison result between driving state and static weighing can be obtain, it is showed in Table 9.

Table 8

The pairwise comparison matrix C of U₁, U₂, U₃

C	U ₁	U ₂	U ₃
U ₁	1	3	2
U ₂	1∕3	1	1∕3
U ₃	1∕2	3	1

Table 9

Indicators layer evaluation summary

Matrix
Alternatives	C₁, C₂, C₃			R₁, R₂, R₃		ω₁, ω ₂, ω ₃	A₁, A₂, A₃	B₁, B₂, B₃
U ₁₁	1	7	5	0.6	0.4	0.963	2.951
U ₁₂	1/7	1	1/3	0.62	0.38	0.107	0.327	2.38	1.65
U ₁₃	1/5	3	1	0.54	0.46	0.248	0.761
U ₂₁	1	6	2	0.38	0.62	0.885	2.654
U ₂₂	1/6	1	1/3	0.57	0.43	0.147	0.442	1.91	2.51
U ₂₃	1/2	3	1	0.49	0.51	0.442	1.327
U ₃₁	1	7	4	0.5	0.5	0.952	2.886
U ₃₂	1/7	1	1/3	0.66	0.34	0.114	0.345	1.67	2.42
U ₃₃	1/4	3	1	0	1	0.285	0.864

3.1.2. Second-level comprehensive comparison

The comparison result $B_{1}=\left[\begin{array}{@{}cc@{}}2.38 & 1.65\end{array}\right]$ of thevehicle adaptability, the comparison result $B_{2}=\left[\begin{array}{@{}cc@{}}1.91 & 2.51\end{array}\right]$ of thedriving adaptability, and the comparison result $B_{3}=\left[\begin{array}{@{}cc@{}}1.67 & 2.42\end{array}\right]$ of thestatic weighing are combined to obtain a normalized comprehensive evaluation matrix $R=\left[\begin{array}{@{}cc@{}}0.59 & 0.41\\ 0.43 & 0.57\\ 0.41 & 0.59\end{array}\right]$ of the criteria of the dynamic highway vehicle automatic weighing instrument.

The importance of the three criteria of vehicle adaptability, driving adaptability and static weighing is compared and assigned according to the scale shown in Table 2, so that the matrix C of the dynamic highway vehicle automatic weighing instrument can be obtained, it is showed in Table 8.

The maximum eigenvalue of C, 𝜆_max = 3.054, the corresponding eigenvector ${\omega}=\left[0.826\ \ 0.218\ \ 0.520\right]$ .

By formula (3), formula (5), the weight vector A and the comprehensive fuzzy comparison results B of two dynamic road vehicle automatic weighing instruments is $\begin{eqnarray}\displaystyle A=\left[\begin{array}{@{}ccc@{}}1 & 3 & 2\\ 1/3 & 1 & 1/3\\ 1/2 & 3 & 1\end{array}\right]\left[\begin{array}{@{}c@{}}0.826\\ 0.218\\ 0.520\end{array}\right]=\left[\begin{array}{@{}c@{}}2.521\\ 0.667\\ 1.588\end{array}\right]B=\left[\begin{array}{@{}ccc@{}}2.521 & 0.667 & 1.588\end{array}\right]\left[\begin{array}{@{}cc@{}}0.59 & 0.41\\ 0.43 & 0.57\\ 0.41 & 0.59\end{array}\right]=\left[\begin{array}{@{}cc@{}}2.43 & 2.35\end{array}\right]. & & \displaystyle \nonumber\end{eqnarray}$

According to the fuzzy evaluation results, the dynamic measurement performance of the dynamic RVAWI A is better than RVAWI B.

4. Comprehensive evaluation conclusion

In this paper, fuzzy comparison method is applied to the measurement performance evaluation of dynamic highway vehicle automatic weighing instrument, and the fuzzy evaluation model is established. The basic calculation steps of fuzzy comparison method are established. Taking the measurement performance evaluation problem of the dynamic road vehicle automatic weighing instrument installed in the long-distance toll lane of Hangchang Expressway as an example, according to the indicators such as vehicle adaptability, adaptability of driving conditions and static weighing, the fuzzy comparison method is adopted. For comparison, the following conclusions can be drawn:

1. From the perspective of vehicle adaptability, the dynamic measurement performance of the RVAWI A is better than that of the RVAWI B The dynamic metering performance of the RVAWI B is superior to the RVAWI A from the perspective of the adaptability of the driving conditions. Considering the static weighing performance alone, the dynamic metering performance of the RVAWI B is better than that of the RVAWI A. Considering all the above factors, the dynamic measurement performance of the RVAWI A is better than that of the RVAWI B.

2. The focus of this comparison method is the determination of the index assignment and the comparison matrix. In the application process, it is necessary to organize a number of technical personnel with practical experience to form an assessment working group. On the basis of fully understanding the problems, each member will ultimately influence the decision-making problem. The evaluation index, evaluation criteria, relative importance of the indicators, and the relative importance of the principles are scientifically and reasonably evaluated according to the evaluation criteria, which is essential for ensuring the scientific rationality of the final comparison results.

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