Research on a Comfort Evaluation Model for High-Speed Trains Based on Variable Weight Theory

Abstract

As a result of the continuous improvement in passengers’ requirements for the quality of train operation, the comfort of high-speed train operation has been paid increasing attention. The evaluation of comfort has gradually changed from the narrow sense of a comfort evaluation model containing only vibration to the generalized evaluation of passengers’ overall satisfaction with the ride environment of specific lines. The factors affecting comfort evaluation include physical, physiological, and psychological aspects. To address the problems that the existing comfort evaluation model has a single index and that the weight determination of some indicators is greatly affected by subjectivity, we built a high-speed train comfort evaluation model based on variable weight theory. Combined with the actual working conditions of the Baolan passenger dedicated line, dynamic detection data and noise monitoring data captured by a track inspection car were combined with a passenger ride comfort questionnaire survey. In addition, the initial weight value of each factor was optimized by constructing an equilibrium function to realize the balance between the various factors, so as to realize the comprehensive fuzzy evaluation of high-speed train comfort. The results show that the comprehensive evaluation result of the comfort degree of the high-speed train on the Tongwei to Lanzhou section of the Baolan passenger dedicated line has a grade of II. The fuzzy scores of the evaluations using variable weights and constant weights were analyzed from the perspective of membership degree. The variable weight optimization avoids the one-sidedness and extremeness of the constant weight calculation. The comprehensive evaluation results are closer to the real situation. The research results can provide a reference for the comfort evaluation of high-speed trains with extreme differences in state values and constant weights and help in the acquisition of more realistic evaluation results.

1. Introduction

As a result of the improvement in people’s living standards, people not only pursue the safety and speed of high-speed trains, but also pay more attention to the comfort of riding. Comfort has gradually become an important basis for choosing travel modes. The comfort of high-speed trains is a concern of experts in many fields. The first step in the study of comfort is to analyze and explore the factors affecting comfort. From the perspective of the research process, a comfort evaluation study was carried out by considering the physiological and psychological feelings of passengers at the beginning of the study [1]. In the middle of the study, some scholars added the physical perception of the vibration of the train while running. This includes not only the vibration of rails and vehicles [2] and various vibration reduction measures applied to vehicle structures [3,4], but also research related to the train vibration caused by external wind loads [5]. At the same time, some scholars have taken passenger demand into account on the basis of the concept of the generalized method of comfort [6]. Wang [7] constructed a multi-dimensional comfort evaluation index system for high-speed trains based on comprehensive physiological feelings, psychological feelings, and physical feelings. At this point, the relevant factors affecting the comfort of the train were basically considered comprehensively. After basically exploring the influencing factors of train comfort, the corresponding evaluation methods were included in the research agenda. Some scholars have analyzed and explored some of the many aspects involved in the influencing factors, such as for example, using biomechanical knowledge to study the comfort of a single seat [8,9,10], using the model simulation method to study the noise in a train [11], and using finite element simulation to study the auditory physiological comfort of a train running in a tunnel [12,13]. Although these evaluation methods are meaningful for the analysis and exploration of some influencing factors, they ignore the coupling effect of various influencing factors and lack the overall evaluation of comfort. Some scholars have also used the combination of the analytic hierarchy process and entropy weight methods [14] and the fuzzy analytic hierarchy process [15] to analyze and evaluate the comfort of trains involving many influencing factors. Among these approaches, fuzzy logic based on multi-factor index values has been applied in comfort evaluation. The fuzziness of index evaluation is studied using the method of the fuzzy set. By using the membership function relationship to deal with the fuzzy relationship, the uncertainty problem in the process of fuzzy judgment is solved. Similarly, the incomplete consideration of influencing factors and the quantitative difficulties in the evaluation processes lead to some limitations of the research results. Faced with the current situation of evaluation difficulties, researchers have also proposed various solutions. Among the typical studies, Chen et al. [16] identified the priority of the influencing factors of cabin ride comfort by collecting feedback from a large number of passengers and using a fuzzy language decision-making method. Peng et al. [17] proposed a machine learning evaluation model for evaluating passenger comfort. These studies further optimized the fuzzy relationship with fuzzy logic using a large amount of training and reduced the logical break in judgment. However, this research process is too cumbersome, and its workload is too large. Therefore, it is not suitable for the high-efficiency requirements of current evaluation. The literature research shows that the trend in studies of the realistic demand for comfort is to carry out a reasonable overall comfort evaluation on the basis of comprehensive influencing factors. In this case, the practical significance and importance of creating a comfort evaluation model are highlighted. The comfort evaluation model can take into account all the multi-dimensional influencing factors and can show the whole evaluation process more intuitively. At the same time, it can effectively reduce the evaluation workload and meet the high-efficiency needs of actual cases. However, when the existing comfort evaluation method determines the index weight, it is often set so that the weight value of each influencing factor does not change in different instances. This leads to a significant difference between the weight value and the state value of the index factors. The final judgment results cannot truly reflect some extreme situations, and it is difficult to ensure the authenticity and accuracy of the comfort evaluation results. Therefore, an optimization method to solve the above problems is urgently needed to scientifically and accurately evaluate the comfort.

This paper introduces the variable weight theory for the evaluation of train comfort. A high-speed train comfort evaluation model based on variable weight theory was established. This work considered the physical feelings, physiological feelings, and psychological feelings of passengers, combined with the data obtained from a track inspection vehicle, a passenger survey, and noise monitoring under actual working conditions. The variable weight theory was used to dynamically optimize the weight of each factor. As a result, evaluation results closer to the actual situation were obtained.

2. Theoretical Basis of Comprehensive Evaluation Model

Because weight determination is an important part of multi-objective decision-making problems, even small changes may have an important impact on the final evaluation results. Constant weight theory only takes into account the relative importance of various factors of decision making, while ignoring the preference for the state equilibrium. This will lead to the fact that the actual situation cannot be reflected in the final evaluation results when there are extreme situations in the actual value of the index. For example, it is difficult to reflect the influence of an index with a low fixed weight when the actual value is very poor, resulting in distortion of the evaluation results.

The idea of variable weight is a new comprehensive decision-making method proposed by Wang P., a famous scholar in China, when he studied multi objective decision making in the 1980s. An empirical formula for variable weight is given, as shown in (1). The theory is essentially a dynamic modeling principle, considering that the index weight should change from the change in the index value state, so as to eliminate the deviation effect of the constant weight on the actual decision-making in the case of extreme state values [18]. Li [19] conducted in-depth and systematic research on the variable weight theory and gave a strict definition of the factor space. On this basis, he gave the axiomatic system of penalty variable weight, incentive variable weight, and mixed variable weight, which made the variable weight theory more perfect. Then, Liu [20] introduced the utility function of the variable weight theory, proposed a compromise variable weight form, and studied the coordination of variable weights. The compromise variable weight was obtained by the compromise utility function, which expanded the variable weight method. Li [21] proposed a hierarchical variable weight multi-factor decision-making model by using the synthesis of factor states in the factor space.

$$Z={\displaystyle \sum _{i=1}^{\mathrm{m}}{w}_i}(x_1^{{}^0},\cdot \cdot \cdot ,x_{\mathrm{m}}^{{}^0})x_i^{{}^0}$$

(1)

In the equation, Z is the actual evaluation value. $x_i{}^0$ is the state value of factor $x_i$; $w_i\left(x_1^0,x_2^0,\cdot \cdot \cdot ,x_m^0\right)$ is a variable weight of $x$ related to $x_1^0,x_2^0,\cdot \cdot \cdot ,x_m^0$, satisfying condition ${\displaystyle \sum _{i=1}^{\mathrm{m}}{w}_i\left(x_1^0,x_2^0,\cdot \cdot \cdot ,x_m^0\right)}=1$.

Axiomatic definition of variable weight [22]: let $X=\left(x_1^0,x_2^0,\cdot \cdot \cdot ,x_m^0\right)$ be the state vector of factor $\left(x_1^0,x_2^0,\cdot \cdot \cdot ,x_m^0\right)$; let $W=\left(w_1,w_2,\cdot \cdot \cdot w_m\right)$ be the constant weight vector of factor $w_1,w_2,\cdot \cdot \cdot ,w_m$; $S\left(X\right)=\left(S_1\left(X\right),S_2\left(X\right),\cdot \cdot \cdot ,S_{\mathrm{m}}\left(X\right)\right)$ is a state variable weight vector.

The variable weight vector $W\left(X\right)=\left(w_1\left(X\right),w_2\left(X\right),\cdot \cdot \cdot ,w_{\mathrm{m}}\left(X\right)\right)$ of factor $x_1,x_2,\cdot \cdot \cdot ,x_m$ can represent the normalized Hadamard product of $W$ and $S\left(X\right)$, as follows:

$$W\left(X\right)=\frac{W·S\left(X\right)}{{\displaystyle \sum _{i=1}^{\mathrm{m}}{w}_i{S}_i\left(X\right)}}=\frac{\left(w_1{S}_1\left(X\right),\cdot \cdot \cdot ,w_m{S}_m\left(X\right)\right)}{{\displaystyle \sum _{i=1}^{\mathrm{m}}{w}_i{S}_i\left(X\right)}}$$

(2)

Variable weight theory can be a reasonable study of the imbalance of selected indicators, reference to practical experience to select the equilibrium function is as follows.

$${\displaystyle \sum {}_T}\left(x_1,x_2,\cdot \cdot \cdot ,x_m\right)={\displaystyle \sum _{}^m{x}_j^{\alpha }},\left(0<\alpha \le 1\right)$$

(3)

Based on the existing variable weight theory and the research content of this paper, the variable weight formula suitable for the comfort evaluation of high-speed trains is obtained as follows.

$$w_j\left(x_1,x_2,\cdot \cdot \cdot ,x_m\right)=\frac{w_j^0{x}_j^{\alpha -1}}{{\displaystyle \sum _{k=1}^{\mathrm{m}}{w}_k^0{x}_k^{\alpha -1}}}$$

(4)

In the equation, $w_j^0$, $x_j$, $m$, and $w_j$ are the constant weight, state value, evaluation index number, and variable weight of secondary index, respectively; α is the equilibrium coefficient that should be given to the secondary index, which indicates the requirement of the evaluator for the equilibrium degree between the indexes. According to experience, α is generally taken as 0.2~0.3 in engineering [23].

3. Establishing the Model of Evaluating

We comprehensively analyze many factors affecting the comfort of high-speed trains. We classify the physical, psychological, and physiological indicators that may cause changes in passengers’ feelings during the ride. Based on the analytic hierarchy process, variable weight theory, and fuzzy comprehensive evaluation, a comfort evaluation model of high-speed train is established (Figure 1).

3.1. Comprehensive Evaluation Index System of High-Speed Train Comfort

In this paper, the evaluation index system of high-speed train comfort is established by referring to the practical experience of engineering and the research results of existing scholars [7]. As shown in Figure 2, the top layer is the target layer A, which is the total index to evaluate the comfort of high-speed trains. The middle layer is the criterion layer B, which generally includes three aspects: physical comfort, physiological comfort, and psychological comfort.

In terms of expansion, it can be divided into five first-level indicators: operating performance B₁, noise and pressure B₂, air quality B₃, vehicle decoration environment B₄, and personalized service B₅. The bottom layer is the measure layer C, which can be divided into 22 secondary indicators according to the specific evaluation content of the first-level indicators.

3.2. High-Speed Train Comfort Index Classification

According to the comfort evaluation index system of high-speed train, the comfort degree is divided into five grades: grade I, grade II, grade III, grade IV, and grade V. Comfort level progresses from Class V to Class I on high-speed trains. Grade V indicates that passengers feel very uncomfortable during the ride due to poor physical, physiological, and psychological stimuli. Grade I indicates that passengers feel very good stimuli regarding physical, physiological, and psychological aspects during the ride, making people feel very comfortable. The specific classification is shown in

Table 1. Comfort Classification.

Comfort Grade	I	II	III	IV	V
Score Values	[90,100]	[70,90)	[50,70)	[30,50)	[0,30)
State Evaluation	Very Comfortable	Comfortable	Nearly Comfortable	Uncomfortable	Very Uncomfortable

. Referring to the relevant evaluation criteria and norms in China, the evaluation criteria of some indicators can be obtained in

Table 2. Evaluation Criteria for Some Indicators.

Index	Evaluation Criterion
Riding Steadiness	W ≤ 2.5 (Excellent)	2.5 < W ≤ 2.75 (Good)			2.75 < W ≤ 3.0 (Qualified)
Riding Comfort	N < 1 (Very comfortable)	1≤ N < 2 (Comfortable)	2 ≤ N < 4 (Nearly comfortable)	4 ≤ N < 5 (Uncomfortable)	N ≥ 5 (Very uncomfortable)
Transverse Acceleration	<2.5 m/s2
Vertical Acceleration	<2.5 m/s2
Passenger Room Noise	≤65 dB(A)
Driver Room Noise	≤76 dB(A)
Passing Platform Noise	≤78 dB(A)

.

We establish a membership function $S\left(x\right)$ based on the comfort levels in Table 1. Grade I membership function $S_1\left(x\right)$ is shown as follows in Equation (5). II~IV level membership function $S_i\left(x\right)$ general formula is shown as follows in Equation (6).

$$S_1\left(x\right)=\left\{\begin{array}{cc}1& x\ge 100\\ \frac{x-90}{100-90}& 90\le x<100\\ 0& x<90\end{array}\right.$$

(5)

$$S_i\left(x\right)=\left\{\begin{array}{cc}0& x\ge a_1 or x<a_3\\ \frac{a_2-x}{a_1-a_2}& a_2\le x<a_1\\ \frac{x-a_3}{a_2-a_3}& a_3\le x<a_2\end{array}\right.$$

(6)

Among them, $a_1, a_2, a_3$ are the endpoint values of the evaluation interval, and different values are taken as the evaluation level changes, as follows:

$$\left\{\begin{array}{cc}i=2& a_1=100, a_2=90, a_3=70\\ i=3& a_1=90, a_2=70, a_3=50\\ i=4& a_1=70, a_2=50, a_3=30\end{array}\right.$$

Grade V membership function $S_5\left(x\right)$ is as follows:

$$S_1\left(x\right)=\left\{\begin{array}{cc}0& x\ge 50\\ \frac{50-x}{50-30}& 30\le x<50\\ 1& 0\le x<30\end{array}\right.$$

(7)

According to the membership function established above and the calculated value of the index, the membership degree of each index value belonging to grade I, II, III, IV, and V can be calculated in turn. According to the principle of fuzzy comprehensive score and maximum membership degree, the final comfort evaluation result can be determined. At the same time, the corresponding indexes can be analyzed and discussed according to the membership degree of the obtained indexes, which provides theoretical and data support for the comparison of the advantages and disadvantages of the evaluation in the two states of variable weight and constant weight.

The membership degree of the calculated m indexes about n grade intervals is composed of the membership degree matrix R:

$$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{12}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right]$$

(8)

4. Engineering Examples

According to the comfort evaluation model of high-speed trains based on variable weight theory established in this paper, the first high-speed railway through the Silk Road Economic Belt on the Baoji to Lanzhou passenger line is selected for comfort evaluation. The Baoji to Lanzhou passenger-dedicated line starts in Baoji in the east and reaches Lanzhou in the west. It is the western section of the Xuzhou to Lanzhou passenger-dedicated line in the national medium- and long-term railway network planning. The design speed is 250 km/h, and the length of the main line is about 401 km. The length in Gansu Province accounts for 88.58% of the total length of the line. The line is connected to the Xi’an to Baoji section of the Xuzhou to Lanzhou high-speed railway through the Baoji South Station to the east and to the west is connected to the Lanzhou–Xinjiang passenger-dedicated line through the Lanzhou West Station. In order to facilitate the accuracy of survey statistics and investigation, this paper only selects the Tongwei to Lanzhou section of Baolan passenger-dedicated line as the research section.

4.1. Constant Weight Calculation

The comfort of high-speed trains from the Tongwei to Lanzhou section of the Baolan passenger-dedicated line is evaluated reasonably by obtaining relevant basic data and seeking expert evaluation. The nine-scale method is used to evaluate the importance of the first-level and second-level indicators of the high-speed train comfort evaluation model. Then, the corresponding judgment matrix is constructed, and the consistency is verified. Finally, the constant weight of the first-level index and the second-level index are calculated. The calculation results are shown in

Table 3. Constant weight calculation and consistency test.

Category	Judgment Matrix	Consistency Check	Wi
A-Bi	$\left[\begin{array}{ccccc}1& 2& 5& 7& 5\\ 1/2& 1& 4& 5& 4\\ 1/5& 1/4& 1& 3& 2\\ 1/7& 1/5& 1/3& 1& 1/3\\ 1/5& 1/4& 1/2& 3& 1\end{array}\right]$	λmax = 5.1905 CR = 0.0425 < 0.10	0.4599
			0.2981
			0.1120
			0.0451
			0.0849
B1-C14	$\left[\begin{array}{cccc}1& 4& 1/5& 1/5\\ 1/4& 1& 1/6& 1/6\\ 5& 6& 1& 1\\ 5& 6& 1& 1\end{array}\right]$	λmax = 4.1846 CR = 0.0684 < 0.10	0.1129
			0.0515
			0.4178
			0.4178
B2-C25	$\left[\begin{array}{ccccc}1& 3& 6& 4& 3\\ 1/3& 1& 5& 3& 2\\ 1/6& 1/5& 1& 1/4& 5\\ 1/4& 1/3& 4& 1& 1/2\\ 1/3& 1/2& 5& 2& 1\end{array}\right]$	λmax = 5.2236 CR = 0.0499 < 0.10	0.4440
			0.2401
			0.0422
			0.1059
			0.1678
B3-C34	$\left[\begin{array}{cccc}1& 1& 3& 2\\ 1& 1& 2& 2\\ 1/3& 1/2& 1& 1/4\\ 1/2& 1/2& 1& 1\end{array}\right]$	λmax = 4.1943 CR = 0.0720 < 0.10	0.3532
			0.3192
			0.1020
			0.2257
B4-C43	$\left[\begin{array}{ccc}1& 7& 4\\ 1/7& 1& 1/4\\ 1/4& 4& 1\end{array}\right]$	λmax = 3.0764 CR = 0.0659 < 0.10	0.6955
			0.0754
			0.2290
B5-C56	$\left[\begin{array}{cccccc}1& 1/3& 1/4& 3& 4& 5\\ 3& 1& 1/3& 4& 5& 6\\ 4& 3& 1& 6& 5& 5\\ 1/3& 1/4& 1/6& 1& 2& 2\\ 1/4& 1/5& 1/5& 1/2& 1& 2\\ 1/5& 1/6& 1/5& 1/2& 1/2& 1\end{array}\right]$	λmax = 6.3839 CR = 0.0619 < 0.10	0.1549
			0.2631
			0.4131
			0.0732
			0.0550
			0.0408

.

4.2. Fuzzy Membership Matrix and Variable Weight Calculation

The indicator state value x_ij⁰ is obtained in two ways: first, through the track inspection vehicle dynamic detection data and noise monitoring data referenced in Table 1 and Table 2 to determine the state value (

Table 4. Detection data and corresponding state values.

Index	Detecting Data		Status Value
Riding Steadiness	Transverse (Maximum/Average)	1.13/0.81	90.00
	Vertical (Maximum/Average)	1.39/1.02
Riding Comfort	Maximum/Average	1.15/0.86	91.38
Vehicle Vibration Acceleration	Transverse (Maximum/Average)	0.74/0.62 (m/s2)	89.19
	Vertical (Maximum/Average)	0.43/0.30 (m/s2)	89.88
Passenger Room Noise	Average	62 dB(A)	86.50
Driver Room Noise	Average	72 dB(A)	88.75
Passing Platform Noise	Average	75 dB(A)	86.88

). The second is to investigate the indicators involved in comfort evaluation models of high-speed trains established in this paper through the form of questionnaires (Figure A1). The higher the index score, the better the comfort of the index. The arithmetic mean of the status scores of the remaining indicators calculated by the questionnaire is the state value. In view of the impact on the new coronavirus epidemic, the questionnaire was carried out in a combination of online and offline forms. We distributed a total of 400 questionnaires. Finally, 386 valid questionnaires were collected. The effective questionnaire recovery rate was 96.5%, with the conditions and needs for further analysis. The arithmetic mean of the status scores of the remaining indicators calculated by the questionnaire is the state value.

Finally, combined with the obtained state value, the variable weight theory is used to optimize the index weight [24]. The equilibrium coefficient is selected to be 0.3, and the variable weight of the indexes are calculated. The results are shown in

Table 5. Index weight calculation results.

Bi	Wi	Cij	Wij0	Constant Weight Comprehensive Weight	xij0	Wij	Variable Weight Comprehensive Weight	Weight Change Rate/%	Comfort Grade
									I	II	III	IV	V
B1	0.4599	C11	0.1129	0.0520	90.00	0.1126	0.0518	−0.38	0.00	1.00	0.00	0.00	0.00
		C12	0.0515	0.0237	91.38	0.0509	0.0234	−1.27	0.14	0.86	0.00	0.00	0.00
		C13	0.4178	0.1921	89.19	0.4199	0.1931	0.52	0.00	0.96	0.04	0.00	0.00
		C14	0.4178	0.1921	89.88	0.4166	0.1916	−0.26	0.00	0.99	0.01	0.00	0.00
B2	0.2981	C21	0.4440	0.1323	86.50	0.4467	0.1332	0.68	0.00	0.83	0.18	0.00	0.00
		C22	0.2401	0.0716	88.75	0.2377	0.0709	−0.98	0.00	0.94	0.06	0.00	0.00
		C23	0.0422	0.0126	86.88	0.0424	0.0126	0.00	0.00	0.84	0.16	0.00	0.00
		C24	0.1059	0.0316	87.56	0.1057	0.0315	−0.32	0.00	0.88	0.12	0.00	0.00
		C25	0.1678	0.0500	87.63	0.1675	0.0499	−0.20	0.00	0.88	0.12	0.00	0.00
B3	0.1120	C31	0.3532	0.0396	90.75	0.3503	0.0392	−1.01	0.08	0.93	0.00	0.00	0.00
		C32	0.3192	0.0357	89.00	0.3215	0.0360	0.84	0.00	0.95	0.05	0.00	0.00
		C33	0.1020	0.0114	88.88	0.1027	0.0115	0.88	0.00	0.94	0.06	0.00	0.00
		C34	0.2256	0.0253	89.88	0.2255	0.0253	0.00	0.00	0.99	0.01	0.00	0.00
B4	0.0451	C41	0.6955	0.0314	89.13	0.6980	0.0315	0.32	0.00	0.96	0.04	0.00	0.00
		C42	0.0755	0.0034	89.19	0.0758	0.0034	0.00	0.00	0.96	0.04	0.00	0.00
		C43	0.2290	0.0103	91.00	0.2262	0.0102	−0.97	0.10	0.90	0.00	0.00	0.00
B5	0.0849	C51	0.1549	0.0131	83.25	0.1577	0.0134	2.29	0.00	0.66	0.34	0.00	0.00
		C52	0.2631	0.0223	84.94	0.2633	0.0224	0.45	0.00	0.75	0.25	0.00	0.00
		C53	0.4130	0.0351	86.31	0.4100	0.0348	−0.85	0.00	0.82	0.18	0.00	0.00
		C54	0.0732	0.0062	87.25	0.0721	0.0061	−1.61	0.00	0.86	0.14	0.00	0.00
		C55	0.0550	0.0047	79.56	0.0574	0.0049	4.26	0.00	0.48	0.52	0.00	0.00
		C56	0.0408	0.0035	88.63	0.0395	0.0033	−5.71	0.00	0.93	0.07	0.00	0.00

. In the table, Weight change rate = (Variable weight comprehensive weight − Constant weight comprehensive weight)/Constant weight comprehensive weight × 100%. Using the membership function in Section 3.2 to calculate the membership matrix of each secondary index, the results are shown in Table 5.

4.3. Fuzzy Comprehensive Score and Result Analysis

The fuzzy comprehensive evaluation matrix of the first-level indicators and the overall goal under the constant weight state is calculated by using the fuzzy comprehensive evaluation theory (its basic principle and application steps can refer to the research of Yang [25]). Combined with the selected corresponding grade parameter vector $V={\left(95,80,60,40,15\right)}^T$, the fuzzy comprehensive scores of each first-level index and the total target layer under the constant weight state can be calculated, respectively. Similarly, the fuzzy evaluation matrix and fuzzy comprehensive score of relevant indicators under variable weight state can be calculated (

Table 6. Multi-level index fuzzy comprehensive operation results.

	Constant Weight State	Variable Weight State	Score Change Rate/%
First-level Index Fuzzy Comprehensive Score	79.6904	79.6877	−0.003
	77.6768	77.6726	−0.005
	80.2197	80.2108	−0.0011
	79.7267	79.7203	−0.008
	75.3103	75.2810	−0.039
Total Target Fuzzy Comprehensive Score	78.7792	78.7729	−0.008

). In the table, Score change rate = (Variable weight fuzzy comprehensive score − Constant weight fuzzy comprehensive score)/Constant weight fuzzy comprehensive score × 100%.

The Table 6 calculation results show that intuitively from the rating interval, regardless of constant weight state or variable weight state, the Tongwei–Lanzhou section of the Baolan passenger-dedicated line has a high-speed train comfort evaluation result of grade II. This is consistent with the recent evaluation results of the management unit. At the same time, the fuzzy comprehensive score of each first-level index also shows that the operating performance, noise and pressure, air quality, vehicle decoration environment, and personalized service comfort of the section are also grade II in both cases. However, the score obtained by using variable weight theory is always lower than that of constant weight fuzzy calculation. This shows that the introduction of variable weight theory makes the adjustment and optimization of state value on constant weight receive attention. Because the evaluation state value of the section is relatively consistent with the constant weight, the adjustment degree reflected on the variable weight result is relatively small.

From the perspective of index membership, the grade II membership degree of the evaluation results of the section under the constant weight state is 0.4390, and the grade III membership degree is 0.5610; the grade II membership degree of the evaluation results of this section under variable weight is 0.4386, and the grade III membership degree is 0.5614. This shows that the comfort evaluation results of high-speed trains from Tongwei to Lanzhou are closer to grade III, and the degree of grade III is greater in the variable weight state. The membership degree of the fuzzy comprehensive score of the index in the criterion layers shows that under the two states, with the exception that the air quality B₃ is closer to grade II, the other indexes are closer to grade III. The tendency is more obvious under the variable weight state. As mentioned above, the comprehensive evaluation results of high-speed train comfort on the Tongwei–Lanzhou section of the Baolan passenger-dedicated line of variable weight state are closer to the real situation.

5. Discussion

The comfort evaluation of high-speed trains generally shows the trend of physical comfort, physiological comfort, and psychological comfort, as shown in Figure 3. This trend is consistent with the results of the literature research. This shows that the performance of the train itself is the main influencing factor of comfort evaluation, and the proportion of other additional services is relatively small. Among them, the weight of running performance is the largest, indicating that passengers are more intuitive and sensitive to the running performance when riding high-speed trains. The weight ratio of train noise and pressure in the vehicle is second. The real-time data feedback on noise monitoring shows that the focus is on the noise generated during train operation. This is mainly due to the fact that there are 74 new tunnels in the whole Baolan Passenger Dedicated Line restricted by terrain, a total of 272.4 km, accounting for 68% of the length of the line, resulting in aerodynamic noise caused by the high-speed operation of the train in the tunnel most of the time. This is consistent with the research in Reference [13]. It is worth mentioning that the weight calculation results show that people’s requirements for personalized service quality such as catering, network, and ticket purchase in the process of riding are gradually improving. Therefore, in terms of personalized service, we should adhere to the concept of customer-oriented and comprehensively improve the quality of service.

The results show that there are differences in physical, physiological, and psychological aspects of passenger comfort, which provides a basis of further targeted guidance and improvement. In terms of physical feelings, the four indicators are basically maintained near the lower limit of the very comfortable range. The transverse and vertical acceleration indexes are below the lower limit; especially the transverse acceleration is far away from the maximum, and the comfort level is relatively low. In terms of physiological feelings, except for the vehicle temperature entering the very comfortable level, the other indicators are in the comfort level. Among them, the evaluation of passenger room noise and passing platform noise score poorly in comfort. In terms of psychological feelings, the interior lighting index is the most satisfactory for passengers. The comfort level of the leisure and recreation index is the lowest, only in the middle and lower position of the comfort level interval, with a large room for improvement.

The change of the weight of each secondary Index in the evaluation model before and after optimization is shown in Figure 4. It can be seen that after the introduction to variable weight theory, the weight values of each secondary index have changed into different ranges. This also reflects the sensitivity of the weight of each influencing factor to the change in the state value of the factor. Among them, the weight value of VIP services C₅₆, guide service C₅₄, and other indicators decreased relatively large. This shows that in this section, the fixed weight assigned to the above indicators is too large and needs to be weakened to a certain extent. Leisure and entertainment C₅₅, catering services C₅₁, and other indicators of the weight value increase relatively large. This means that these indicators have a greater impact on the comprehensive evaluation of comfort and are easily affected by other factors at the same level. It is necessary to strengthen the fixation of such indicators and increase the degree of attention. The change trend of the index is in line with the actual demand direction found in the literature research. In order to obtain more scientific, reasonable, and reliable evaluation results, enough attention should be paid to the secondary indicators whose weights have changed greatly before and after optimization.

6. Conclusions

This paper presents an evaluation model of high-speed train comfort based on variable weight theory through the dynamic detection data, noise monitoring data, and passenger ride comfort questionnaire survey obtained under actual working conditions. From the perspective of combining subjective and objective indicators, variable weight theory is used to optimize the fixed weight determined by the analytic hierarchy process. The model is verified by the case study of Tongwei to Lanzhou section of Baolan passenger-dedicated line. The following conclusions can be drawn:

• The fuzzy score of evaluation under variable weight state and constant weight state is analyzed from the perspective of membership degree. After variable weight optimization, the one-sidedness and extremeness of constant weight calculation are avoided, and the comprehensive evaluation results are closer to the real situation.
• According to the calculation of the model, the analysis and discussion of indicators at all levels to provide a certain reference for the subsequent improvement work. The weight changes rate before and after optimization reflect the strength of variable weight calculation to fixed weight. It also reflects the sensitivity of the index weight to the index state value. Therefore, some attention should be paid to the indicators with large changes.
• The model is an effective comprehensive evaluation model of high-speed train comfort. This study can provide some theoretical support for the comfort evaluation of high-speed trains with extreme differences in state values and constant weights.

In this study, only the most important and critical parts are considered in data acquisition, but in fact the branches of influencing factors will be more complex and diverse. Therefore, in order to analyze the comfort evaluation of high-speed trains more accurately, a questionnaire containing more information will be considered in the follow-up study. It includes various levels of information such as the age level of the passengers, the reasons for the ride (leisure, business, and back to school), and the degree of education.