Multi-output system sensitivity analysis method based on evidence theory and decision-making method thereof

Abstract

A multi-output system sensitivity analysis method based on an evidence theory comprises the following steps: firstly, setting a system input variable, a system output variable and a value range of the system input variable of a multi-output system, then carrying out uniform Latin hypercube sampling in the value range to obtain a sampling result, and finally, calculating the sensitivity of the multi-output system according to the sampling result. Substituting a sampling result and a system output variable into a multi-output system for training to obtain an input-output data sample set; parameter sensitivity information output by each system is obtained based on the proxy model and Sobol global sensitivity analysis; on the basis of the main effect and the interaction effect of each piece of parameter sensitivity information, corresponding evidence information is constructed, all evidence information is obtained through summarizing, and an evidence information set is obtained; and fusing the evidence information set by using an evidence synthesis rule to obtain comprehensive evidence information, namely system level variable sensitivity information of the multi-output system. According to the invention, the sensitivity of a plurality of variables can be integrally evaluated.

Description

Technical Field

[0001] The present invention relates to an improvement of a multi-output system analysis technology, belongs to the field of data analysis, and in particular to a multi-output system sensitivity analysis method and a decision-making method thereof based on evidence theory. Background Art

[0002] Sensitivity analysis is a method to study the sensitivity of system output to changes in system input or parameters. Sensitivity analysis aims to understand how the system output changes with changes in input or parameters, and to help identify which inputs or parameters have a significant impact on system results. Existing systems can only conduct global sensitivity analysis of variables for a certain output and obtain variable sensitivity information for a specific output, but cannot integrate sensitivity information for multiple outputs to form a comprehensive understanding of the overall impact of the system input variables on multiple outputs.

[0003] A Chinese patent application with application number CN 202211610981.2 and application date December 14, 2022 discloses a sensitivity analysis method for a flexural electric cantilever beam structure based on Sobol sequence sampling, comprising the following steps: S1: establishing a flexural electric cantilever beam structure model; S2: parameter uncertainty analysis of the flexural electric cantilever beam structure model based on Sobol sequence sampling; S3: substituting the extracted samples into the corresponding model to calculate the mean and standard measurement of the output representation, and analyzing and studying the output performance. This scheme not only points out the direction for optimizing the structural performance of the flexural electric cantilever beam considering parameter randomness, but also provides the necessary theoretical and experimental basis for the application of the flexural electric cantilever beam as the main structural unit for flexural electric signal output in the next generation of micro-nano electromechanical systems. However, the above scheme does not solve the problem of the inability to integrate and evaluate the sensitivity of multiple variables.

[0004] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of this patent application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0005] The purpose of the present invention is to overcome the problem in the prior art that it is impossible to perform an integrated overall evaluation of the sensitivities of multiple variables, and to provide a multi-output system sensitivity analysis method and a decision-making method based on evidence theory that can perform an integrated overall evaluation of the sensitivities of multiple variables.

[0006] To achieve the above objectives, the technical solution of the present invention is: a multi-output system sensitivity analysis method based on evidence theory, the multi-output system sensitivity analysis method based on evidence theory comprises the following steps:

[0007] Step 1: first set the system input variables and system output variables of the multi-output system, then set the value range of the system input variables, and then sample the system input variables within the value range using uniform Latin hypercube to obtain the sampled system input variables, and then substitute the sampled system input variables into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set;

[0008] Step 2: First, a preliminary model is constructed for each system output value in the input-output data sample set based on a regression machine learning algorithm, and then the input variables corresponding to the system output value are substituted into the preliminary model for training to obtain a proxy model corresponding to the system output value;

[0009] Step 3: With the help of the proxy model, Sobol global sensitivity analysis is performed on each system output value to obtain the corresponding parameter sensitivity information;

[0010] Step 4: Based on the main effects and interaction effects of all parameter sensitivity information, construct corresponding evidence information, and summarize all the evidence information to obtain an evidence information set;

[0011] Step 5: Use evidence synthesis rules to fuse the evidence information set to obtain comprehensive evidence information, that is, the system-level variable sensitivity information of the multi-output system.

[0012] In step 1, the sampled system input variables are then substituted into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set, specifically:

[0013] S = {X, y1, y2, ..., y k},X∈R n×d ;

[0014] Where n is the sample size, d is the number of system variables, and y k is a column vector of length n, representing the output vector consisting of the kth output of the system corresponding to the input sample matrix X.

[0015] In the step 1, the variable value range is set to ±20% of the initial setting value of the system.

[0016] In step 2, the accuracy of the proxy model is verified by goodness of fit. When the goodness of fit of the proxy model test is greater than 0.8, it is considered that the model can be used for the next step of analysis. Otherwise, new training samples are added to improve the model accuracy. The goodness of fit expression is shown in the following formula:

[0017]

[0018] Among them, N is the number of test validation samples, y k，iis the response value of the i-th validation sample of the k-th output, is the predicted value of the proxy model of the k-th output for the i-th validation sample, Output the mean of all validation sample response values ​​for the kth time.

[0019] In step 3, Sobol global sensitivity analysis is performed on each system output value with the assistance of the surrogate model to obtain the corresponding parameter sensitivity information. Specifically, according to the surrogate model and Sobol global sensitivity analysis, the parameter sensitivity information of each system input variable to the system output variable is obtained. The main effect and second-order interaction effect of the variable corresponding to the kth output are marked as and in is the i-th variable x i The main effect of is the i-th variable x i and the jth variable x j interaction effect.

[0020] According to the main effect and interaction effect of the variables corresponding to each output obtained in step 3, the basic probability distribution corresponding to different outputs is generated, that is, the evidence information corresponding to different outputs.

[0021] In the fourth step, based on the main effects and interaction effects of all parameter sensitivity information, corresponding evidence information is constructed, and all evidence information is summarized to obtain an evidence information set, which is specifically: the set of events that have an impact on the system output can be constituted by the independent input variables of the system Θ = {x1, x2, ..., x d}, that is, the parameter sensitivity identification framework. The power set of all subsets of the parameter sensitivity identification framework is shown as follows:

[0022]

[0023] According to the variable main effect and second-order interaction effect corresponding to the k-th output, they are marked as and The basic probability distribution of the kth piece of evidence can be determined according to the rules defined in the following formula:

[0024]

[0025]

[0026] In step 5, the variable sensitivity information at the system level is extracted based on the comprehensive evidence information, as follows:

[0027]

[0028] The decision-making method makes decisions based on the above-mentioned system-level variable sensitivity information.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. In the sensitivity analysis method of a multi-output system based on evidence theory and its decision-making method, information fusion is performed based on the global sensitivity information of multiple variables corresponding to multiple outputs, and various aspects of parameter sensitivity information are comprehensively considered. The uncertainty of information can be handled through evidence theory, and evidence information from different sources can be reasonably integrated to obtain more comprehensive and reliable variable sensitivity information at the system level, which provides effective decision support for the identification of important variable parameters of the multi-output system and can be applied to the identification of the importance of parameters of complex multi-output systems. Therefore, the present invention can integrate and evaluate the sensitivity of multiple variables as a whole.

[0031] 2. In the multi-output system sensitivity analysis method and decision-making method based on evidence theory of the present invention, the proxy model can replace the complex multi-output system model to a certain extent, especially when the original system has high computational cost or is difficult to analyze directly, the proxy model can quickly give approximate results, thereby improving the analysis efficiency. Therefore, the present invention has high analysis efficiency and convenient analysis.

[0032] 3. In the sensitivity analysis method of a multi-output system based on evidence theory and its decision method, the Sobol global sensitivity analysis can comprehensively evaluate the influence of each parameter on the multi-output system, and can consider the influence of the parameter in the entire value range, so as to more accurately identify the key parameters, which is helpful to determine the priority parameters in system optimization, fault diagnosis and other aspects, and improve the accuracy of decision-making. Therefore, the present invention has comprehensive analysis and high decision-making accuracy.

[0033] 4. In the sensitivity analysis method of a multi-output system based on evidence theory and its decision-making method, uniform Latin hypercube sampling helps to obtain sampling points more evenly within the value range of the system input variables, which can better cover the entire input space, so that the obtained input-output training data set is more representative, ensuring a high-quality data foundation when building a proxy model, and comprehensively capturing the relationship between various variables in the system, so that the data obtained can reflect this complex correlation. Therefore, the sampling of the present invention is uniform, and the relationship between the data is more accurately reflected. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the present invention.

[0035] Figure 2 It is a flow chart of the sensitivity information fusion method in the present invention. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0037] See also Figure 1 to Figure 2 A multi-output system sensitivity analysis method based on evidence theory, the multi-output system sensitivity analysis method based on evidence theory comprises the following steps:

[0038] S1. First, set the system input variables and system output variables of the multi-output system, then set the value range of the system input variables, and then sample the system input variables within the value range using uniform Latin hypercube to obtain the sampled system input variables, and then substitute the sampled system input variables into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set;

[0039] S2. First, a preliminary model is constructed for each system output value in the input-output data sample set based on a regression machine learning algorithm, and then the input variables corresponding to the system output value are substituted into the preliminary model for training to obtain a proxy model corresponding to the system output value;

[0040] S3, with the assistance of the proxy model, perform Sobol global sensitivity analysis on each system output value to obtain the corresponding parameter sensitivity information;

[0041] S4. Based on the main effects and interaction effects of all parameter sensitivity information, corresponding evidence information is constructed, and all evidence information is summarized to obtain an evidence information set;

[0042] S5. Use evidence synthesis rules to fuse the evidence information set to obtain comprehensive evidence information, that is, the system-level variable sensitivity information of the multi-output system.

[0043] In step 1, the sampled system input variables are then substituted into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set, specifically:

[0044] S = {X, y1, y2, ..., y k},X∈R n×d ;

[0045] Where n is the sample size, d is the number of system variables, and y k is a column vector of length n, representing the output vector consisting of the kth output of the system corresponding to the input sample matrix X.

[0046] In the step 1, the variable value range is set to ±20% of the initial setting value of the system.

[0047] In step 2, the accuracy of the proxy model is verified by goodness of fit. When the goodness of fit of the proxy model test is greater than 0.8, it is considered that the model can be used for the next step of analysis. Otherwise, new training samples are added to improve the model accuracy. The goodness of fit expression is shown in the following formula:

[0048]

[0049] Among them, N is the number of test validation samples, y k，i is the response value of the i-th validation sample of the k-th output, is the predicted value of the proxy model of the k-th output for the i-th validation sample, Output the mean of all validation sample response values ​​for the kth time.

[0050] In step 3, Sobol global sensitivity analysis is performed on each system output value with the assistance of the surrogate model to obtain the corresponding parameter sensitivity information. Specifically, according to the surrogate model and Sobol global sensitivity analysis, the parameter sensitivity information of each system input variable to the system output variable is obtained. The main effect and second-order interaction effect of the variable corresponding to the kth output are marked as and in is the i-th variable x i The main effect of is the i-th variable x i and the jth variable x j interaction effect.

[0051] According to the main effect and interaction effect of the variables corresponding to each output obtained in step 3, the basic probability distribution corresponding to different outputs is generated, that is, the evidence information corresponding to different outputs.

[0052] In the fourth step, based on the main effects and interaction effects of all parameter sensitivity information, corresponding evidence information is constructed, and all evidence information is summarized to obtain an evidence information set, which is specifically: the set of events that have an impact on the system output can be constituted by the independent input variables of the system Θ = {x1, x2, ..., x d}, that is, the parameter sensitivity identification framework. The power set of all subsets of the parameter sensitivity identification framework is shown as follows:

[0053]

[0054] According to the variable main effect and second-order interaction effect corresponding to the k-th output, they are marked as and The basic probability distribution of the kth piece of evidence can be determined according to the rules defined in the following formula:

[0055]

[0056] In step 5, the variable sensitivity information at the system level is extracted based on the comprehensive evidence information, as follows:

[0057]

[0058] The decision-making method makes decisions based on the above-mentioned system-level variable sensitivity information.

[0059] The supplementary description of the present invention is as follows:

[0060] This method aims at the variable sensitivity information decision-making problem of multi-output systems. It forms corresponding evidence information based on the variable sensitivity information of each system output, and obtains the variable sensitivity information at the system level through evidence synthesis rules. This method can be applied to the identification of the importance of parameters of complex multi-output systems.

[0061] Embodiment 1:

[0062] A multi-output system sensitivity analysis method based on evidence theory, the multi-output system sensitivity analysis method based on evidence theory comprises the following steps:

[0063] Step 1: first set the system input variables and system output variables of the multi-output system, then set the value range of the system input variables, and then sample the system input variables within the value range using uniform Latin hypercube to obtain the sampled system input variables, and then substitute the sampled system input variables into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set;

[0064] Step 2: First, a preliminary model is constructed for each system output value in the input-output data sample set based on a regression machine learning algorithm, and then the input variables corresponding to the system output value are substituted into the preliminary model for training to obtain a proxy model corresponding to the system output value;

[0065] Step 3: With the help of the proxy model, Sobol global sensitivity analysis is performed on each system output value to obtain the corresponding parameter sensitivity information;

[0066] Step 4: Based on the main effects and interaction effects of all parameter sensitivity information, construct corresponding evidence information, and summarize all the evidence information to obtain an evidence information set;

[0067] Step 5: Use evidence synthesis rules to fuse the evidence information set to obtain comprehensive evidence information, that is, the system-level variable sensitivity information of the multi-output system.

[0068] Embodiment 2:

[0069] Embodiment 2 is substantially the same as Embodiment 1, except that:

[0070] This case is a simple system with two inputs and two outputs. The system input-output relationship model is as follows:

[0071]

[0072] It can be seen from the formula that the influence of x1 on y1 is consistent with the influence of x2 on y2, and the influence of x2 on y1 is consistent with the influence of x2 on y1. Therefore, from the system level, the above variables x1 and x2 have the same influence on the system;

[0073] In step one, 20 samples are obtained by uniform Latin hypercube sampling for system variables and given variable value ranges, and the system is run to obtain system output values ​​of the 20 samples to form a training sample set.

[0074] In step 2, proxy models are established for the system outputs y1 and y2 respectively, and the accuracy of the proxy models is verified by the leave-one-out validation method. Since the system is relatively simple, the leave-one-out validation R-squared values ​​of the proxy models of y1 and y2 are both 1, that is, the proxy models can approximate the system without error.

[0075] In step 3, Sobol sensitivity analysis is performed with the aid of the surrogate model to obtain the main effects and interaction effects of the variables for the system outputs y1 and y2. The main effects and interaction effects of the variables for the system outputs y1 and y2 are shown in the sensitivity information in Table 1.

[0076] Table 1. Results of sensitivity analysis of multi-output systems

[0077]

[0078] In step 4, the original evidence is constructed with the variable sensitivity information of y1 and y2 respectively. The basic probability distribution constructed by the main effect and interaction effect of the system output variables y1 and y2 is shown in the original evidence m1(·) and m2(·) in Table 1. In step 5, the original evidence from multiple sources is synthesized according to the evidence synthesis rule to obtain the synthesized evidence, and the Pignistic probability is calculated based on the basic probability distribution of the synthesized evidence. Table 1 shows the basic probability distribution of the synthesized evidence and the Pignistic probability, and thus the main effect and interaction effect of the variables at the system level are given, that is, the comprehensive sensitivity information in Table 1. The Pignistic probability reflects the total effect of the variables at the system level. BetP(x1)=BetP(x2)=0.5 indicates that from the system level, the variables x1 and x2 in the case have the same influence on the system.

[0079] Embodiment 3:

[0080] Embodiment 3 is substantially the same as Embodiment 1, except that:

[0081] This embodiment is also a simple system with two inputs and two outputs. The system input-output relationship model is as follows:

[0082]

[0083] It can be seen from the formula that y1=-y2, so the variable sensitivity information of y1 is consistent with the variable sensitivity information of y2.

[0084] In step 1, 20 samples are obtained by uniform Latin hypercube sampling for the system variables and the given variable value range, and the system is run to obtain two system output values ​​of the 20 samples to form a training sample set S.

[0085] In step 2, proxy models are established for the system outputs y1 and y2 respectively, and the accuracy of the proxy models is verified by the leave-one-out validation method. Since the system is relatively simple, the leave-one-out validation R-squared values ​​of the proxy models of y1 and y2 are both 1, that is, the proxy models can approximate the system without error.

[0086] In step three, Sobol sensitivity analysis is performed with the assistance of the surrogate model to obtain the main effects and interaction effects of the variables for the system outputs y1 and y2. The main effects and interaction effects of the variables for the system outputs y1 and y2 are shown in the sensitivity information in Table 2. Since y1 = -y2, the main effects and interaction effect information of the variables for y1 and y2 are the same, and the impact of x2 on the system outputs y1 and y2 is greater than the impact of x2 on the system outputs y1 and y2.

[0087] Table 2. Results of sensitivity analysis of multi-output systems

[0088]

[0089] In step 4, the original evidence is constructed with the variable sensitivity information of y1 and y2, and the system outputs the basic probability distribution of the variable main effects and interaction effects of y1 and y2 as shown in the original evidence m1(·) and m2(·) in Table 2;

[0090] In step five, the original evidence from multiple sources is synthesized according to the evidence synthesis rules to obtain the synthesized evidence, and the Pignistic probability is calculated based on the basic probability distribution of the synthesized evidence. Table 2 gives the basic probability distribution of the synthesized evidence and the Pignistic probability, and thus gives the main effects and interaction effects of the variables at the system level, that is, the comprehensive sensitivity information in Table 2. BetP(x1)<BetP(x2) indicates that from the system level, the impact of the variable x2 on the system in the case is greater than the impact of x1 on the system. Since the impact of x2 on the system outputs y1 and y2 is greater than the impact of x2 on the system outputs y1 and y2, this impact gap will be further amplified from the system level.

[0091] Embodiment 4:

[0092] Embodiment 4 is substantially the same as Embodiment 1, except that:

[0093] This embodiment is a relatively complex system with four inputs and three outputs. The system input-output relationship model is as follows:

[0094]

[0095] Where x i ∈[0, 1], the output expression of the system is relatively complex, and it is difficult to intuitively obtain the impact of the variable on the system;

[0096] In step 1, 40 samples are obtained by uniform Latin hypercube sampling for the system variables and the given variable value range, and the system is run to obtain two system output values ​​of the 40 samples to form a training sample set S;

[0097] In step 2, Kriging proxy models with second-order polynomial as trend function and Gaussian equation as correlation function are established for system outputs y1, y2 and y3 respectively. The accuracy of the proxy model is verified by leave-one-out validation method. The leave-one-out validation R-square values ​​of the proxy models of y1, y2 and y3 are all 1, that is, the proxy model can approximate the system without error.

[0098] In step three, Sobol sensitivity analysis is performed with the assistance of the surrogate model to obtain the main effects and interaction effects of the system outputs y1, y2 and y3. The main effects and interaction effects of the system outputs y1, y2 and y3 are shown in the sensitivity information in Table 3.

[0099] In step 4, the original evidence is constructed with the variable sensitivity information of y1, y2, and y3, and the system outputs the basic probability distribution of the variable main effects and interaction effects of y1, y2, and y3 as shown in the original evidence m1(·), m2(·), and m3(·) in Table 3;

[0100] In step 5, the original evidence from multiple sources is synthesized according to the evidence synthesis rules to obtain the synthesized evidence, and the Pignistic probability is calculated based on the basic probability distribution of the synthesized evidence. Table 3 gives the basic probability distribution of the synthesized evidence and the Pignistic probability, and thus gives the main effect and interaction effect of the variables at the system level, that is, the comprehensive sensitivity information in Table 3. According to the comprehensive sensitivity information in the table, it can be seen that the variable with the most significant impact on the system is x3, followed by x1, and the impact of the interaction between variables on the system is almost negligible.

[0101] Table 3. Results of sensitivity analysis of multi-output system

[0102]

[0103] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A sensitivity analysis method for a multi-output system based on evidence theory, characterized in that: The multi-output system sensitivity analysis method based on evidence theory comprises the following steps: Step 1: first set the system input variables and system output variables of the multi-output system, then set the value range of the system input variables, and then sample the system input variables within the value range using uniform Latin hypercube to obtain the sampled system input variables, and then substitute the sampled system input variables into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set; Step 2: First, a preliminary model is constructed for each system output value in the input-output data sample set based on a regression machine learning algorithm, and then the input variables corresponding to the system output value are substituted into the preliminary model for training to obtain a proxy model corresponding to the system output value; Step 3: With the help of the proxy model, Sobol global sensitivity analysis is performed on each system output value to obtain the corresponding parameter sensitivity information; Step 4: Based on the main effects and interaction effects of all parameter sensitivity information, construct corresponding evidence information, and summarize all the evidence information to obtain an evidence information set; Step 5: Use evidence synthesis rules to fuse the evidence information set to obtain comprehensive evidence information, that is, the system-level variable sensitivity information of the multi-output system.

2. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 1, characterized in that: In step 1, the sampled system input variables are then substituted into the multi-output system to obtain the corresponding system output values, thereby obtaining an input-output data sample set, specifically: S={X,y1,y2,...,y k },X∈R n×d ; Where n is the sample size, d is the number of system variables, and y k is a column vector of length n, representing the output vector consisting of the kth output of the system corresponding to the input sample matrix X.

3. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 2, characterized in that: In the step 1, the variable value range is set to ±20% of the initial setting value of the system.

4. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 1, characterized in that: In step 2, the accuracy of the proxy model is verified by goodness of fit. When the goodness of fit of the proxy model test is greater than 0.8, it is considered that the model can be used for the next step of analysis. Otherwise, new training samples are added to improve the model accuracy. The goodness of fit expression is shown in the following formula: Among them, N is the number of test validation samples, y k，i is the response value of the i-th validation sample of the k-th output, is the predicted value of the proxy model of the k-th output for the i-th validation sample, Output the mean of all validation sample response values ​​for the kth time.

5. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 1, characterized in that: In step 3, Sobol global sensitivity analysis is performed on each system output value with the assistance of the surrogate model to obtain the corresponding parameter sensitivity information. Specifically, according to the surrogate model and Sobol global sensitivity analysis, the parameter sensitivity information of each system input variable to the system output variable is obtained. The main effect and second-order interaction effect of the variable corresponding to the kth output are marked as and in is the i-th variable x i The main effect of is the i-th variable x i and the jth variable x j interaction effect.

6. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 5, characterized in that: According to the main effect and interaction effect of the variables corresponding to each output obtained in step 3, the basic probability distribution corresponding to different outputs is generated, that is, the evidence information corresponding to different outputs.

7. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 1, characterized in that: In the fourth step, based on the main effects and interaction effects of all parameter sensitivity information, corresponding evidence information is constructed, and all evidence information is summarized to obtain an evidence information set, which is specifically: the set of events that have an impact on the system output can be constituted by the independent input variables of the system Θ = {x1, x2, ..., x d }, that is, the parameter sensitivity identification framework. The power set of all subsets of the parameter sensitivity identification framework is shown as follows:

8. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 7, characterized in that: According to the variable main effect and second-order interaction effect corresponding to the k-th output, they are marked as and The basic probability distribution of the kth piece of evidence can be determined according to the rules defined in the following formula: m k ({x i ,x j })≥0,∑m k (·)=1 9. The method for sensitivity analysis of a multi-output system based on evidence theory according to claim 8, characterized in that: In step 5, the variable sensitivity information at the system level is extracted based on the comprehensive evidence information, as follows:

10. A decision-making method for the multi-output system sensitivity analysis method based on evidence theory according to claim 1, characterized in that: The decision-making method makes decisions based on the system-level variable sensitivity information in claim 1 above.

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