Evaluation Method of Traffic Safety Maintenance of High-Grade Highway

This part is mainly composed of road shoulders and pavements, among others. The common damages of road shoulders include poor surface flatness, improper width setting of the shoulders, and staggering. The common damages of road pavements are ruts and breakages on the road surface, insufficient slip resistance, and water accumulation.

This part is mainly composed of central separation zones, separation zones for motor-driven vehicle and non-motor-driven vehicles, roadside guardrails, crossroad marks, anti-glare facilities, sightline guidance facilities, etc. Common damages mainly include poor sight distance, missing parts, poor reflectivity, poor visibility, weakened retroreflectivity, etc.

This part mainly refers to traffic markings, signs, signal lights, street lights, etc. Common damages are severely worn facilities, insufficient anti-slip resistance, poor retroreflectivity, missing parts, or damaged, tilt, reduced visibility, unreasonable location settings, and insufficient or overloaded information.

Channelling is the use of diversion islands or marking lines to separate or control conflicting vehicle flow. The common damages are improper channelling, damages of channelling diversion islands, worn channelling marks, and poor visibility.

Greening refers to the planting of trees and flowers on both sides or in the middle of the road, aiming to improve the traffic environment. The major common damages are the inappropriate selection of greening tree species which negatively affect the viewing distance.

The high-grade highway maintenance evaluation system is a complex system, with each subsystem depending, influencing, and impacting every other. In the safety evaluation process, if the mutual influence between the relevant subsystems is ignored, the evaluation results will not be comprehensive, objective, or reliable. The comprehensive evaluation system consists of three functional modules, namely the data acquisition module, the subsystem performance evaluation module, and the comprehensive evaluation module, as shown in Figure 1 below.

Fig. 1

The comment set is made for each evaluation indicator according to a certain scale. In this research, in order to facilitate calculation and analysis, the vector comment set of each indicator corresponds to and is consistent with the system's safety level. The comment level is shown as z = (z₁, z₂, z₃, z₄) = (Level 1, Level 2, Level 3, Level 4). In order to make the evaluation process rational and reasonable, it is necessary to standardise the sample matrix. In this paper, four gray classes are determined according to the four security levels, and the corresponding whitening weight function is established as shown in Table 3.

For the evaluation index u_ij, the evaluation objects belong to the gray evaluation coefficient of the evaluation gray class: (1) Xije=∑n=1lfe(dijn) {X_{ije}} = \sum\limits_{n = 1}^l {f_e}({d_{ijn}})

For the evaluation index u_ij, the evaluation objects belong to the total gray evaluation coefficient of every evaluation gray class: (2) Xij=∑g=1eXijg {X_{ij}} = \sum\limits_{g = 1}^e {X_{ijg}} The evaluation objects belong to the gray evaluation power of the e-gray class: (3) rije=Xije/Xij {r_{ije}} = {X_{ije}}/{X_{ij}}

The evaluation index u_ij corresponds to the gray evaluation weight matrix of each evaluation gray class: (4) Ri=[ri11⋯rile⋮⋮rin1rine] {R_i} = \left[ {\matrix{ {{r_{i11}}} & \cdots & {{r_{ile}}}\cr \vdots & {} & \vdots\cr {{r_{in1}}} & {} & {{r_{ine}}}\cr } } \right] Standardise the second-level indicators under the first-level indicators according to the gray evaluation weight vector, and obtain the evaluation vector as k_ij = (k_ij1, k_ij2 . . . , k_ije), thus forming an evaluation matrix: (5) Ki=[ki11⋯kile⋮⋮kin1kine] {K_i} = \left[ {\matrix{ {{k_{i11}}} & \cdots & {{k_{ile}}}\cr \vdots & {} & \vdots\cr {{k_{in1}}} & {} & {{k_{ine}}}\cr {}& {} & {} \cr } } \right] In the formula: kij={rij1rij¯,rij2rij¯,…,rijerij¯},rij¯=max(rij1,rij2,…,rije) {k_{ij}} = \left\{ {{{{r_{ij1}}} \over {\overline {{r_{ij}}} }}} \right.,{{{r_{ij2}}} \over {\overline {{r_{ij}}} }}, \ldots ,\left. {{{{r_{ije}}} \over {\overline {{r_{ij}}} }}} \right\},\overline {{r_{ij}}} = \max ({r_{ij1}},{r_{ij2}}, \ldots ,{r_{ije}})

Subjective weighting method and objective weighting method are commonly adopted to determine the weight value of each indicator, namely: A = (a_l, a₂, ..., a_n), where a_i > 1 and Σa_i = 1. The determination of the weights in this section is still obtained through expert investigation and AHP. In the actual investigation, the judgement matrix returned by some experts cannot pass the consistency test. In this research, an optimisation algorithm was selected to adjust the consistency matrix A.

In the formula:

W is the relative weight vector of the original judgement matrix A, W = (W_a, W₂, ⋯, W_n)^T;

P is solved by the minimum closeness, and the calculation formulas are shown in formulas (7) and (8).

According to the hierarchical relationship of highway safety maintenance and its subsystems given in Tables 1 and 2 above, the weight of each parameter is summarised and shown in Figures 2 and 3 below. There are 16 sub-indicators in the highway section and 23 sub-indicators in the plane crossroads.

Fig. 2

Fig. 3

In the actual evaluation process, if there are missing items to be evaluated, the weights are adjusted according to the following formula (9).

In the formula:

W_iⁿ represents the adjusted weights of the i facility;

Taking the correlation between the first-level evaluation indicator vector and the relatively most indicator vector as the evaluation indicator, the gray evaluation matrix of the first-level indicator is obtained.

Obtain the traffic safety service level D of evaluation vector of the first-level indicator U: (12) D=W∘⋅C=(ω1,ω2,...,ωm)∘[C1,C2,...,Ce]T=(z1,z2,...,ze) D = {W^ \circ } \cdot C = ({\omega _1},{\omega _2},...,{\omega _m}{)^ \circ }{\left[ {{C_1},{C_2},...,{C_e}} \right]^T} = ({z_1},{z_2},...,{z_e})

To facilitate analysis, D is normalised, that is: (13) D={D1∑i=1eDi,D2∑i=1eDi,D3∑i=1eDi,...,De∑i=1eDi} D = \left\{ {{{{D_1}} \over {\sum\limits_{i = 1}^e {D_i}}}} \right.,{{{D_2}} \over {\sum\limits_{i = 1}^e {D_i}}},{{{D_3}} \over {\sum\limits_{i = 1}^e {D_i}}},...,\left. {{{{D_e}} \over {\sum\limits_{i = 1}^e {D_i}}}} \right\}

According to the principle that evaluating and analysing is based on the maximum degree of membership, the comments of corresponding max_iD are the final comprehensive evaluation results.

Based on the objective and operable principle, and in reference to the road maintenance standards and literature, the 23 indicators selected for the crossroads safety maintenance evaluation system and the 16 indicators selected for the road section maintenance safety evaluation system are determined in detail. The scoring standards are shown in Table 4. The score of each indicator is deducted from the full score of 100 points, and the safety evaluation score of each indicator is obtained after deducting the lost points from 100 points.

In order to measure the influence of the evaluator's subjective factors on the indicator score and ensure the impartiality, the objectivity of the evaluation data needs to be verified. The general model of the single factor problem is as follows. There is a factor A, which has k levels: 1, 2, ..., k. The n experiments are conduced when i is taken horizontally to obtain data X_i1, X_i2, ..., X_in. Assume that each X_ij has a normal distribution: N(μi,σ2) j=1,2,...,ni.e.,level1:x11,x12,...,x1j,...,x1n ≈N(μ1,σ2)level2:x21,x22,...,x2j,...,x2n ≈N(μ2,σ2)…………levelk:xk1,xk2,...,xkj,...,xkn ≈N(μk,σ2) \matrix{ {N({\mu _i},{\sigma ^2})\;j = 1,2,...,n} \cr {i.e.,level1:{x_{11}},{x_{12}},...,{x_{1j}},...,{x_{1n}}\;\;\; \approx N({\mu _1},{\sigma ^2})} \cr {level2:{x_{21}},{x_{22}},...,{x_{2j}},...,{x_{2n}}\;\;\; \approx N({\mu _2},{\sigma ^2})} \cr { \ldots \ldots \ldots \ldots } \cr {levelk:{x_{k1}},{x_{k2}},...,{x_{kj}},...,{x_{kn}}\;\;\; \approx N({\mu _k},{\sigma ^2})} \cr }

It is necessary to test the hypotheses that H0:μ1=μ2=...=μk↔H1:μ1,μ2,...,μk are not all the same. {H_0}:{\mu _1} = {\mu _2} = ... = {\mu _k} \leftrightarrow {H_1}:{\mu _1},{\mu _2},...,{\mu _k}\;\;{\rm{are}}\;{\rm{not}}\;{\rm{all}}\;{\rm{the}}\;{\rm{same}}{\rm{.}} If H₀ is rejected, the influence of the factor on the test indicator is considered significant; if H₀ is accepted, the influence of the factor on the test indicator is considered insignificant.

Calculate the sample variance S_i² of n figures at each level, obtain a total of k estimated sample variances of σ², and take the average to get the arithmetic mean of the variance σ² within the group as: S2=1k(n-1)∑i=1k∑j=1n(Xij-X¯i)2 {S^2} = {1 \over {k(n - 1)}}\sum\limits_{i = 1}^k \sum\limits_{j = 1}^n {({X_{ij}} - {\bar X_i})^2} The estimated average μ_i of level i is X̄_i. The greater the difference is between X̄_i, the greater the difference will be between μ_i and between each level. Consequently, the calculated group variance of X̄_i reflects the impact of the difference between the levels: S*2=1k-1∑i=1k(Xi-X¯)2 {S^{*2}} = {1 \over {k - 1}}\sum\limits_{i = 1}^k {({X_i} - \bar X)^2} Taking the rationality of channelling as an example, this research invites highway maintenance personnel, traffic safety researchers, and drivers to conduct a verification test and select a plane crossroad of Jiangsu Provincial Highway 321. A total of 18 investigators deduct points based on the indicators, as shown in Table 5.

The research conducts a one-way analysis of variance on the data in Table 5, assuming that for a given α = 0.05, and calculates F value and F_0.95 (2,15) value whose result is 0.27, satisfying F < F_0.95 (2,15). Therefore, H₀ is accepted by all, that is, there is no significant difference in deduction points of different types of personnel, which verifies the objectivity of the evaluation data.

Common methods for model rationality verification include subjective evaluation, fitting test, residual plot method, regression analysis, etc. In this research, the score of the plane crossroads section and road section used the subjective evaluation method, while the linear correlation between the model's score and the subjective score used regression analysis. The rationality of the model is verified by the results.

(1) Verification test

The test section is selected first, which mainly includes two parts, namely model calculation and subjective scoring. Among them, the model calculation is to access the evaluation indicator scores of the selected test sections, and to score each evaluation object and comprehensive evaluation object according to the above safety maintenance evaluation model; the subjective scoring is to organise a batch of experienced experts in safety maintenance evaluation to make a subjective and quantitative evaluation of the safety maintenance quality of the test section, for which the specific deduction criteria are shown in Table 6.

Table 6

Interval partition of grade.

Type	Grade	Score	Type	Grade	Score
Road section	Grade 1	87–100	Crossroad	Grade 1	89–100
	Grade 2	85–87		Grade 2	87–89
	Grade 3	83–85		Grade 3	84–87
	Grade 4	0–83		Grade 4	0–80

In order to verify the effectiveness of the model, the expert scoring panel offers each indicator's score and the total score on the road section every 2 km on the S321 test highway. Validation data of rationality of road section evaluation model is shown in Figures 4 and 5 below.

Fig. 4

Fig. 5

(2) Model rationality verification

By analysing the correlation between Figures 4 and 5, it can be seen that the absolute error of most validation data is within 5 points, as shown in Figures 6–10. The result is indicating that the model has strong rationality,

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

In order to make the scoring results of the above model reflect the safety and service status of the high-level highways of the evaluation object in a more visual manner, this research uses the cumulative frequency curve method to divide the safety service level. The research selects 50 sections and 40 crossroads of high-grade highways in Jiangsu Province for data collection, using the model to score and accumulating frequencies in an order from low to high. Points with a cumulative frequency of 0 ∼ 15% are selected as the classification criteria for grade 4; points with a cumulative frequency of 15–50% as the classification criteria for grade 3; points with a cumulative frequency of 50–85% as the classification criteria for grade 2; and points with a cumulative frequency of 85–100% as the classification criteria grade level 1. The results are shown in Table 6.