Effectiveness evaluation of complex electromechanical system based on improved analytic hierarchy process - entropy weight method - fuzzy synthesis evaluation method

At present, complex electromechanical systems are widely used in modern society. By evaluating complex electromechanical systems, it is of great value to improve and upgrade them. Given the complex and interrelated characteristics of performance indicators, this paper establishes the performance evaluation indicator system of a complex electromechanical system, proposes to calculate the weight of each indicator by an improved analytic hierarchy process, revises the indicator weight by entropy weight method, and then adopts fuzzy synthesis evaluation method to evaluate the comprehensive effectiveness of a complex electromechanical system quantitatively. Through the example analysis, it is proved that this method provides an effective way for the effectiveness evaluation of complex electromechanical systems.


Introduction
Nowadays, with the progress of society, new demands are placed on various aspects of human life, such as clothing and transportation, forcing several high-effectiveness and high-precision electromechanical equipment to appear.A complex electromechanical system is the product of the intersection and integration of various disciplines, integrating various high and new technologies, composed of subsystems of different levels, and is a complex system integrating multiple physical processes such as machine and electricity [1].Complex systems need not only quantitative analysis but also qualitative analysis.Therefore, a scientific and systematic evaluation of complex electromechanical systems requires the use of multiple evaluation methods.Saaty proposed the Analytic Hierarchy Process (AHP) [2], which covers both qualitative and quantitative indicators for evaluating complex multi-level systems.Yuan et al. used the fuzzy synthesis evaluation method in combination with the analytic hierarchy process [3], calculated the weight by the analytic hierarchy process, and comprehensively evaluated the target by the fuzzy synthesis evaluation method.
Taking the coal mine disaster rescue system as an example, this paper constructs an indicator evaluation system for the coal mine disaster rescue system [4][5][6][7][8][9], and the effectiveness indicators of the rescue system are mainly survivability, action ability, operation ability, etc.The weights of each indicator in the indicator evaluation system are calculated by the improved analytic hierarchy process, and then the entropy weight method is used to modify the indicator weight.Finally, the fuzzy synthesis evaluation method is used to calculate the effectiveness evaluation score of the coal mine disaster rescue system.By analyzing the weight of indicators and effectiveness evaluation score, the relative importance and comprehensive effectiveness level of each indicator of the coal mine disaster rescue system can be obtained, which is convenient for enhancing the comprehensive effectiveness level of the rescue system in the future by improving relatively weak indicators and enhancing relatively important indicators.

Improved analytic hierarchy process-entropy weight method to determine weights
The traditional analytic hierarchy process is a method to determine the weight subjectively and requires a consistency test of the judgment matrix [10].The biggest advantage of the improved analytic hierarchy process compared with the traditional analytic hierarchy process is that it adopts the optimal transfer matrix to ensure that the judgment matrix passes the consistency test.In addition, this paper adopts the entropy weight method to correct weights, which makes the revised index weights more objective and greatly reduces the disadvantages of subjectivity in the AHP.The steps to determine the weight are as follows: ∂ (1) The effectiveness evaluation system of the complex electromechanical system is established according to hierarchical structure.The selection principles of evaluation indicators mainly include scientificity, integrity, consistency, and independence.For complex electromechanical systems, methods such as literature research and expert analysis are used to select indicators.These methods are relatively subjective, and the selected evaluation indicators are more scientific and reasonable.These indicators are constantly revised and improved according to the development of the system to be evaluated.∂ (2) We construct a judgment matrix.Using the 1-9 scale method, the importance of each indicator is compared in pairs, and the judgment matrix A is constructed.
∋ ( ∂ (4) We calculate the weight of the indicators.

Fuzzy synthesis evaluation method
The core of the fuzzy synthesis evaluation method is to determine the factors set and the comments set of the indicators, select the appropriate membership function, and determine the weight of each indicator [11].Among them, the factor set of indicators is determined by the indicator evaluation system, the comment set is determined by experts, the membership function is selected as a triangular distribution type membership function, and the indicator weight is determined by Formulas (1)-( 8).
The steps are as follows: ∂

Indicator weight calculation of complex electromechanical system
Experts in this field analyze all the indicators of the coal mine disaster rescue system evaluation system and quantitatively express the relative importance of each layer of indicators.The judgment matrix constructed by the experts' scoring results and the modified weight results are shown in Tables 2 to 6.

Fuzzy comprehensive evaluation calculation of complex electromechanical systems
First, according to the indicator of the coal mine disaster rescue system, this paper establishes the comment set

ζ |
V excellent medium bad < .Secondly, 10 experts in this field are invited to get comments on the qualitative indicators using expert scores.The specific comment values of qualitative indicators are shown in Table 7.For quantitative indicators, it is necessary to use measured data to calculate the membership degree of quantitative indicators using a membership function.Some quantitative indicator evaluation standards and measured data are shown in Table 8.Taking the "continuous working time" in Table 8 as an example to calculate its membership degree, it is known that 1 1 a < , 2 3 a < , 3 5 a < , and . According to the membership function of triangular distribution, we can get: Therefore, the membership vector of "continuous working time" is (0, 0.4, 0.6).This means that "continuous working time" is 0% likely to be bad, 40% likely to be medium, and 60% likely to be excellent.
The fuzzy comment matrix 1 R of "viability" calculated in the above way is: In the same way, the fuzzy vectors of "motion", "work capacity", and "communication capability" are calculated respectively, and the fuzzy comment matrix R of the first-level indicator is constructed, the final evaluation result vector S is obtained by multiplying the indicator weight of A-B layer with the fuzzy comment matrix R .

Conclusions
This paper studies the effective evaluation of complex electromechanical systems based on an improved analytic hierarchy process -entropy weight method -fuzzy synthesis evaluation method.
Taking the coal mine disaster rescue system as an example, the effectiveness evaluation system of the coal mine disaster rescue system is established according to the hierarchical structure.The improved analytic hierarchy process and entropy weight method are used to calculate the weights.Compared with the AHP, this method is more objective.The weights of the indicator can reflect the importance of each indicator to the coal mine disaster rescue system.For example, the weight value of "work capacity" is the largest among the second-level indicators, which indicates that it is the most important to the coal mine disaster rescue system.In the future, we can focus on improving "work capacity".In this paper, the final evaluation score is between medium and good, which indicates that the overall effectiveness of the coal mine disaster rescue system is relatively good and can meet the requirements of use.However, some indicators need to be focused on to avoid the failure or the reduction of work efficiency of the rescue system.
In the process of building the performance indicator system, we have investigated a lot of relevant literature and consulted experts in this field, but the method of constructing the indicator system is highly subjective and the constructed index system may not be perfect, so in the future, more objective methods are needed to screen the performance indicator of the complex electromechanical system and establish more objective and perfect performance indicator system.

∂ ( 3 )
The antisymmetric matrix, the optimal transfer matrix, and the quasi-optimal consistent matrix are calculated sequentially.

∂ ( 6 )
We calculate the entropy value of the evaluation indicators.

∂ ( 2 )
We construct a fuzzy comment matrix, calculate the membership degree of quantitative indicators through a triangular distribution type membership function, and obtain the membership degree of qualitative indicators through expert consultation.After obtaining the membership degrees of indicators at each level, a fuzzy comment matrix with m rows and n columns can be constructed.The image of the triangular distribution type membership function is shown in Figure1.

Figure 1 .
Figure 1.Triangular distribution type membership function (a, b, c, and d represent the critical value of membership function of indicator).

Table 2 .
Judgment matrix and relative weight table of A-B indicator layer.

Table 3 .
Judgment matrix and relative weight table of B1-C indicator layer.

Table 4 .
Judgment matrix and relative weight table of B2-C indicator layer.

Table 5 .
Judgment matrix and relative weight table of B3-C indicator layer.

Table 6 .
Judgment matrix and relative weight table of B4-C indicator layer.

Table 7 .
Qualitative indicator comment values.

Table 8 .
Part of quantitative indicator evaluation standards and measured data.
In the above weight method, the known weight of "viability" (B1-C) is 7