Flywheel system bearing assembly multi-dimensional rule reduction health state test method

Abstract

The invention discloses a flywheel system bearing assembly multi-dimensional rule reduction health state testing method, and relates to the technical field of flywheel system bearing assembly health state testing. Acquiring an actual measurement data set of the flywheel system bearing assembly; determining a confidence coefficient corresponding to the reference value set and the result, and constructing an initial health state test model based on a confidence rule base; constructing a multi-dimensional rule evaluation framework; performing composite activation on the reduced model; optimizing parameters in the model by adopting an optimization algorithm; and reasoning the model by using an evidence reasoning analysis algorithm to obtain a health test result of the flywheel system bearing assembly, and realizing an accurate health state test through the evidence reasoning algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of flywheel system bearing assembly health state testing, in particular to a flywheel system bearing assembly multi-dimensional rule reduction health state testing method. BACKGROUND

[0002] Flywheel system bearing assemblies have been widely used in key fields such as aerospace, rail transportation and power equipment, and their running state is directly related to the safety and reliability of the system. However, as the complexity of the system continues to increase, the difficulty of testing and managing its health state also significantly increases. Currently, health state testing methods mainly rely on expert experience and traditional statistical models, which often show low efficiency and accuracy when dealing with large-scale, multi-dimensional and dynamically changing data. In addition, traditional models have high computational complexity and lack of explanatory ability for system operation mechanism, which limits their application value in high-risk fields.

[0003] In the research of flywheel system bearing assembly health state testing, rule-based methods have attracted widespread attention due to their high interpretability and flexibility. However, existing rule-based models often face problems such as excessive number of rules, unreasonable weight allocation, and incomplete rule base in practical applications. This not only increases the complexity of the model, but also reduces the reliability of the test results. In addition, current optimization algorithms are prone to local optimization in high-dimensional parameter space, making it difficult to meet the accurate testing needs of flywheel system bearing assemblies.

[0004] To solve the above problems, researchers have proposed some improvement methods, such as optimizing rule weights through sensitivity analysis and introducing dynamic factors to adapt to changes in system state. However, these methods still need to further balance between reducing model complexity and maintaining testing accuracy, especially in high-dimensional data processing, the existence of multi-dimensional redundant rules seriously restricts the practical application ability of the model. Therefore, how to effectively realize multi-dimensional rule reduction while ensuring high accuracy has become an important research direction in the field of flywheel system bearing assembly health state testing.

[0005] To solve the above technical problems, the present application proposes a flywheel system bearing assembly multi-dimensional rule reduction health state testing method, which significantly reduces the model complexity, improves the testing efficiency and accuracy by introducing rule weight optimization, dynamic factor integration and disjunction model, etc., providing a reliable and efficient solution for flywheel system bearing assembly health state testing. SUMMARY

[0006] To solve the above technical problems, the present application proposes a flywheel system bearing assembly multi-dimensional rule reduction health state testing method, which significantly reduces the model complexity, improves the testing efficiency and accuracy by introducing rule weight optimization, dynamic factor integration and disjunction model, etc., providing a reliable and efficient solution for flywheel system bearing assembly health state testing. Step 1: Obtain the measured dataset of the flywheel system bearing assembly; Step 2: Determine the set of reference values ​​and the confidence levels corresponding to the results, and construct an initial health status test model based on the confidence rule base; Step 3: Construct a multi-dimensional rule evaluation framework; Step 4: Perform compound activation on the reduced model; Step 5: Optimize the parameters in the model using optimization algorithms; Step 6: Use the evidence-based reasoning analysis algorithm to reason about the model and obtain the health test results of the flywheel system bearing components.

[0007] In a preferred embodiment, in step two, the health status test model is divided into two forms: conjunction and disjunction. In the antecedent attribute part, different types of information under uncertain conditions are taken as input and transformed into the same confidence structure. In the conclusion part, there are multiple scales, each with a corresponding value, indicating the confidence level of the rule being classified into that scale.

[0008] In a preferred embodiment, the k-th confidence rule is described as follows: (1); (2); in, Indicates the first Confidence rules, This represents the premise attribute used in the k-th confidence rule. Indicating the k-th confidence rule The reference value corresponding to each prerequisite attribute, The k-th confidence rule Each rating level Indicates the first Under the confidence rule, each rating level The corresponding confidence level; and These represent the number of rules in rule base 1 and rule base 2, respectively. and They represent the first The rule weights of rule base 1 and rule base 2 under the confidence rule. and These represent the attribute weights of each prerequisite attribute. This indicates that the confidence rule is constructed using the conjunctive activation method. This indicates how the confidence rule is constructed under the disjunctive hypothesis.

[0009] In a preferred embodiment, step three includes the following steps: 3.1 Gradually reduce the rule weight of each rule until it reaches 0; 3.2 Using the mean squared error of the model as the target output, record the change of MSE relative to the initial rule weights when the rule weights are reduced N times; 3.3 The average change in MSE for each rule is recorded as the initial importance assessment metric for the rule. : (3); Among them, MSE L The MSE represents the output result before reducing the rule weights. This represents the MSE of the output result after reducing the rule weights; 3.4. Initial importance assessment indicators Combined with the rule weight coefficient k and the number of activations t, the comprehensive evaluation index R is calculated: (4); 3.5 Sort the comprehensive evaluation index R, delete rules with low importance, and optimize the rule base.

[0010] In a preferred embodiment, in step four, the activation method is a conjunctive activation method: (5); in," "" indicates that the confidence rule is constructed under the conjunction activation method.

[0011] 6. The multi-dimensional rule reduction health status test method for flywheel system bearing assemblies according to claim 5, characterized in that: the activation calculation follows these steps: 4.1.1 Calculate the rule matching degree; for input data , No. The first rule under the rule The matching degree of each attribute is calculated as follows: (6); in, This represents the matching degree of the i-th attribute of the k-th rule. and This indicates that the input data is located at two adjacent reference values ​​of the i-th attribute. The rule is activated when the matching degree of all attributes of the rule is not zero. 4.1.2 Calculate the rule activation weight; the calculation of activation weights is based on the rule matching degree, taking into account both attribute weights and rule weights, emphasizing the impact of different rule matching degrees on the final result: (7); in, The rule weight represents the k-th rule, when The k-th rule is activated; In a preferred embodiment, in step four, the activation method employs a disjunction approach to activate the rule, as follows: (8); in, This indicates how the confidence rule is constructed under the disjunctive hypothesis.

[0012] In a preferred embodiment, the following steps are followed when activating computation: 4.2.1 Consider an input vector of test data. ,in To determine the number of prerequisite attributes, the disjunction rule will assign each input... The rule activation matching table converts the reference value of the i-th prerequisite attribute into the input data. : (9); (10); express Attribute input data For reference values likelihood yes The number of reference values ​​for the prerequisite attribute; 4.2.2 Calculate the activation weight of each prerequisite attribute using a weighted method: (11).

[0013] In a preferred embodiment, in step five, an adaptive projection covariance matrix algorithm is used to optimize the rule weights, attribute weights, and confidence levels in the model. The result of this health status test model is as follows: (12); express The utility value, The reference value representing the nth result. The confidence level of the nth result. The final output value is represented by N, which represents the total number of results, and the mean squared error is 0. This represents the modeling accuracy of the health status test model, where the rule weights and attribute weights are optimized parameters; Represented as: (13); in For the amount of training data, This represents the actual output value of the system.

[0014] In a preferred embodiment, the minimum value is found through continuous iteration. The value, and the specific process are as follows: 5.1 Initialization operation, initial parameters are as follows: (14); in Represents the initial parameter set. Represents the set of rule weights. Represents the set of attribute weights. Represents the set of confidence levels; 5.2 Sampling operation: The initial population is determined in the following way: (15); in Indicates the first The first generation of offspring One solution. Represents the population mean. Indicates the step size; It follows a normal distribution; For the first The covariance matrix of the generation; Indicates the number of child solutions; 5.3 Perform projection operations to satisfy the following constraints: (16); A hyperplane is represented as ,in Representing the solution The number of constraint variables in the middle form. Representing the solution The number of constraints in the middle form, and Represents a parameter vector; 5.4. Perform the selection operation to update the average value using the following formula: (17); in Indicates the first Weighting coefficients for each equation; Indicates the ( The first in the substitution solution One solution; Indicates the size of the offspring population; 5.5. Update the covariance matrix through adaptive computation to determine the population search range and direction; the calculation process is shown in the following formula: (18); in and Indicates the learning rate; This represents the evolution path of the covariance, with the initial evolution path being 0. and For the first and the The covariance matrix of the generation, Indicates the first The weighting coefficients of the equations Indicates the first The mean of generations, Indicates the first The step size of the generation, where T is the amount of training data. Indicates the size of the offspring population. This indicates the number of child solutions.

[0015] In a preferred embodiment, step six includes the following steps: 6.1 Calculate the degree of matching between the input sample information and the confidence rules. The first input The rule adaptability of a rule is calculated as follows: (19); 6.2 Calculate the first... Activation weight w of the rule i : (20); in, Indicates the first The attribute weights of each evaluation indicator; 6.3. Use the ER algorithm for inference to obtain the final confidence level. : (twenty one); (twenty two); 6.4 Calculate the expected utility value: (twenty three); Where S() represents the set of confidence distributions. This represents the actual input vector. express The effect, Represents the final expected utility; the final confidence distribution. The description is as follows: (twenty four).

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: By constructing a multi-dimensional rule evaluation framework, the rule base is efficiently reduced, which not only improves the simplicity and performance of the model, but also significantly enhances the transparency of the rule base; the introduction of two kinds of activation mechanisms of conjunction and disjunction solves the problem of rule missing caused by rule reduction while ensuring the completeness of the rule base, so that the model has stronger adaptability and robustness; combined with the projection covariance matrix adaptive optimization algorithm (P-CMA-ES), the rule weight, attribute weight and confidence are comprehensively optimized, and the accurate health state test is realized through the evidence reasoning algorithm, thereby providing an efficient, flexible and generalizable solution for the modeling and health state test of the flywheel system bearing assembly.

[0017] Formula section (next section) description of drawings Figure 1 The flywheel system bearing assembly multi-dimensional rule reduction health state test method of the application is shown in the figure. Figure 2 The flywheel system bearing assembly multi-dimensional rule reduction health state test method of the application is shown in the figure. Figure 3 The multi-dimensional rule reduction method of the application is shown in the figure. Figure 4 The model parameter optimization method of the application is shown in the figure. DETAILED DESCRIPTION The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0018] Reference Figures 1-2 The flywheel system bearing assembly multi-dimensional rule reduction health state test method of the application includes the following steps: Step 1: Obtain the measured data set of the flywheel system bearing assembly.

[0019] The real-time test data of shaft temperature and rotating speed of the flywheel system bearing assembly under different loads and operating conditions are collected by sensors, and the data are pretreated such as cleaning and normalization.

[0020] Step 2: Determine the reference value set and the confidence corresponding to the result, and construct the initial health state test model based on the belief rule base (BRB).

[0021] According to expert knowledge, the reference value set and the confidence corresponding to the result are determined, and the initial health state test model based on the belief rule base (BRB) is constructed. The model is divided into two forms of conjunction and disjunction.

[0022] In the antecedent attributes section, different types of information under uncertain conditions are taken as input and transformed into the same confidence structure; in the conclusion section, there are multiple scales, each with a corresponding confidence level, indicating the degree of confidence that the rule is classified into that scale.

[0023] Its k-th confidence rule is described as follows: (1); (2); in, Indicates the first Confidence rules, This represents the premise attribute used in the k-th confidence rule. Indicating the k-th confidence rule The reference value corresponding to each prerequisite attribute, The k-th confidence rule Each rating level Indicates the first Under the confidence rule, each rating level The corresponding confidence level. Confidence level is used to quantify the degree of trust in rules and evidence. In rule-based reasoning, confidence level is used to guide decision-making. and These are the number of rules in rule base 1 and rule base 2, respectively. and They represent the first The rule weights of rule base 1 and rule base 2 under a confidence rule, i.e., the importance of this rule relative to other rules. and Each attribute represents the weight of the prerequisite attribute, that is, the importance of the attribute relative to other attributes.

[0024] Step 3: Construct a multi-dimensional rule evaluation framework to reduce the health status test model constructed in Step 2.

[0025] The quantity and quality of rules directly impact the modeling capability and simplicity of rule-based models. In flywheel system health status testing models, an appropriate number of rules is crucial. However, BRB models often contain redundant and inefficient rules, reducing model performance and transparency. The goodness of fit of a BRB model is negatively correlated with the quantity and quality of rules. Therefore, this step constructs a multi-dimensional rule evaluation framework for rule reduction. The construction of this multi-dimensional rule evaluation framework aims to comprehensively consider the quantity, quality, sensitivity, and practical application of rules to optimize rule base construction and improve model performance.

[0026] The construction steps of the multidimensional rule evaluation framework are as follows: 3.1 Gradually reduce the rule weight of each rule until it is 0.

[0027] 3.2 Using the mean squared error (MSE) of the model as the target output, record the change of MSE relative to the initial rule weights when the rule weights are reduced N times.

[0028] 3.3 The average change in MSE for each rule is recorded as the initial importance assessment metric for the rule. : (3); Among them, MSE L The MSE represents the output result before reducing the rule weights. This represents the MSE of the output result after reducing the rule weights; 3.4. Initial importance assessment indicators Combined with the rule weight coefficient k and the number of activations t, the comprehensive evaluation index R is calculated: (4); 3.5 Sort the comprehensive evaluation index R, delete rules with low importance, and optimize the rule base.

[0029] Step 4: Perform compound activation on the reduced health status test model.

[0030] After reducing the rules in the health status test model in step three, an inevitable problem arises: it is difficult to find a matching rule for some input data, resulting in a lack of completeness in the originally complete rule-based system.

[0031] To address this issue and ensure the completeness of the health status testing model, this step proposes a novel composite rule activation method.

[0032] This compound rule activation method is divided into conjunctive activation and disjunctive activation, with the conjunctive activation method as follows: (5); The original confidence rule base activates rules using conjunctive activation. Formula (5) represents the rules under the conjunctive activation method. This indicates that the confidence rule is constructed using the conjunctive activation method. The prerequisite properties are conjunctive, meaning that the confidence rule is activated only when both properties are activated.

[0033] Based on this confidence rule, BRB integrates expert knowledge and historical data to handle different types of information under uncertain conditions, following these steps when conjunctive activation occurs: 4.1.1 Calculate the rule matching degree.

[0034] For input data The matching degree between the k-th rule and the reference value under the i-th attribute is calculated as follows: (6); in, This represents the matching degree of the i-th attribute of the k-th rule. and This indicates that the input data is located between two adjacent reference values ​​of the i-th attribute, and K is the total number of rules. The sequence used to represent reference values, i.e. This is the current reference value. This represents the next reference value. A rule is activated when all attributes of that rule have a non-zero match rate.

[0035] 4.1.2 Calculate the activation weights according to the rules.

[0036] The activation weight wk is calculated based on rule matching degree, taking into account both attribute weights and rule weights, emphasizing the impact of different rule matching degrees on the final result. This method ensures that more matching rules have a greater impact on the final result.

[0037] (7); in, The rule weight represents the k-th rule. Representing the The rule weight of a rule, when The k-th rule is activated.

[0038] Because the rules are reduced in step three, the conjunction form cannot guarantee that a rule will be activated for every input data point in subsequent inference calculations in some cases. Therefore, in such cases, the disjunctive method is used to activate the rules, in the following form: (8); Formula (8) is the disjunction rule. This indicates that the confidence rule is constructed under the disjunctive activation method, which means that the rule is activated if the input data satisfies any one of the attribute conditions.

[0039] The disjunction rule uses an improved similarity metric to transform the input data into a distribution likelihood of the reference values. It follows these steps during activation computation: 4.2.1 Consider an input vector of test data. ,in The number of prerequisite attributes. The disjunction rule will assign each input... Convert the reference value of the i-th prerequisite attribute into a rule activation matching table with the input data.

[0040] (9); (10); in, This represents the input data for the i-th attribute. For reference values The likelihood. is the number of reference values ​​for the j-th prerequisite attribute, and M represents the total number of attributes. The rule activation matching table indicates the relationship between the reference value and the input data.

[0041] 4.2.2 Calculate the activation weight w of each prerequisite attribute using a weighted method. j The calculation formula is as follows: (11); Step 5: Optimize the parameters in the model using optimization algorithms.

[0042] After building the model through steps two, three, and four, and reducing redundant rules in the multi-model system, the Projection Covariance Matrix Adaptive Algorithm (P-CMA-ES) is used to optimize the rule weights, attribute weights, and confidence levels in the model. The output result of this health status test model can then be determined as follows: (12); express The utility value, The reference value representing the nth result. The confidence level of the nth result. The final output value is represented by N, which represents the total number of results, and the mean squared error is 0. This represents the modeling accuracy of the health status testing model. In this part, the rule weights and attribute weights are optimized parameters, hence the modeling accuracy... Represented as: (13); in, For the amount of training data, This represents the actual output value of the system; therefore, the optimization objective is to find the minimum value through continuous iteration. The value, and the specific process are as follows: 5.1 Initialization operation.

[0043] The initial parameters are as follows: (14); in Represents the initial parameter set. Represents the set of rule weights. Represents the set of attribute weights. This represents the set of confidence levels.

[0044] 5.2 Sampling operation.

[0045] The initial population can be determined in the following ways: (15); in Indicates the first The first generation of offspring One solution. Represents the population mean. Indicates the step size; It follows a normal distribution; For the first The covariance matrix of the generation; This indicates the number of child solutions.

[0046] 5.3 Perform projection operations to satisfy the constraints.

[0047] The solution generated by the sampling operation does not satisfy the constraints, so a projection operation is performed to satisfy the following constraints: (16); in Indicates the first The first generation of offspring There are solutions, and a hyperplane can be represented as... ,in Representing the solution The number of constraint variables in the middle form. Representing the solution The number of constraints in the middle form, and This represents a parameter vector.

[0048] 5.4. Update the average value by selecting an operation.

[0049] Specifically, the selection operation is performed using the following formula: (17); in Indicates the first Weighting coefficients for each equation; Indicates the ( The first in the substitution solution One solution; Indicates the size of the offspring population. This indicates the number of child solutions.

[0050] 5.5 Finally, the covariance matrix is ​​updated through adaptive computation to determine the population search range and direction.

[0051] The calculation process is shown in the following formula: (18); in and Indicates the learning rate; This represents the evolution path of the covariance, with the initial evolution path being 0. and For the first and the The covariance matrix of the generation, Indicates the first The weighting coefficients of the equations Indicates the first The mean of generations, Indicates the first The step size of the generation, where T is the amount of training data. Indicates the size of the offspring population. This indicates the number of child solutions.

[0052] Step Six: Use the evidence-based reasoning analysis algorithm to reason about the model after parameter optimization in Step Five to obtain the health test results of the flywheel system bearing components.

[0053] The Evidence-Based Reasoning (ER) algorithm is applied to reason about the model after parameter tuning in step five to obtain the health status test results of the flywheel system bearing components.

[0054] The reasoning process is as follows: First, the activation weights of the rules are calculated, and then the ER inference engine is used to perform reasoning to obtain the expected utility value, thereby obtaining the output result of the health status test model.

[0055] The specific process is as follows: 6.1 Calculate the degree of matching between the input sample information and the confidence rule, i.e., the rule fit.

[0056] For input data The matching degree between the k-th rule and the reference value under the i-th attribute is calculated as follows: (19); in, This represents the matching degree of the i-th attribute of the k-th rule. and This indicates that the input data is located between two adjacent reference values ​​of the i-th attribute, and K is the total number of rules. The sequence used here to represent the reference value is... `l+1` represents the current reference value, and `l+1` represents the next reference value. A rule is activated when the match degree of all its attributes is not zero.

[0057] 6.2 Calculate the first... Activation weight of the rule The calculation method is as follows: (20); in, Indicates the first The attribute weights of each evaluation indicator; The rule weight represents the k-th rule. Representing the The rule weight of a rule, when The k-th rule is activated.

[0058] 6.3. Use the Evidence Reasoning (ER) algorithm to perform reasoning and obtain the final confidence level. The calculation method is as follows: (twenty one); (twenty two); Where N represents the number of results and L represents the number of rules. Represents the activation weight of the l-th rule. Used for calculation Required intermediate parameters. This represents the confidence level of the nth result in the l-th rule. This represents the confidence level of the k-th result in the l-th rule.

[0059] 6.4 Finally, the expected utility value is calculated, and the final output result is as follows: (twenty three); in, Describes a set consisting of confidence distributions. This represents the actual input vector. express The effect, Represents the final expected utility value; the final confidence distribution. The description is as follows: (twenty four); Obtain utility value The final output value of the model is the health test result of the model. Relevant technical personnel can use the confidence distribution y to verify the test status of the model.

[0060] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for testing the health status of a flywheel system bearing assembly using multidimensional rule reduction, characterized in that: Includes the following steps: Step 1: Obtain the measured dataset of the flywheel system bearing assembly; Step 2: Determine the set of reference values ​​and the confidence levels corresponding to the results, and construct an initial health status test model based on the confidence rule base; Step 3: Construct a multi-dimensional rule evaluation framework; Step 4: Perform compound activation on the reduced model; Step 5: Optimize the parameters in the model using optimization algorithms; Step 6: Use the evidence-based reasoning analysis algorithm to reason about the model and obtain the health test results of the flywheel system bearing components.

2. The method for testing the health status of a flywheel system bearing assembly using multidimensional rule reduction as described in claim 1, characterized in that: In step two, the health status test model is divided into two forms: conjunction and disjunction. In the antecedent attribute part, different types of information under uncertain conditions are taken as input and transformed into the same confidence structure. In the conclusion part, there are multiple scales, each with a corresponding value, which indicates the confidence level of the rule being classified into the scale. Its k-th confidence rule is described as follows: (1)； (2)； in, Indicates the first Confidence rules, This represents the premise attribute used in the k-th confidence rule. Indicating the k-th confidence rule The reference value corresponding to each prerequisite attribute, The k-th confidence rule Each rating level Indicates the first Under the confidence rule, each rating level The corresponding confidence level; and These represent the number of rules in rule base 1 and rule base 2, respectively. and They represent the first The rule weights of rule base 1 and rule base 2 under the confidence rule. and These represent the attribute weights of each prerequisite attribute. This indicates that the confidence rule is constructed using the conjunctive activation method. This indicates how the confidence rule is constructed under the disjunctive hypothesis.

3. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 1, characterized in that: Step three includes the following steps: 3.1 Gradually reduce the rule weight of each rule until it reaches 0; 3.2 Using the mean squared error of the model as the target output, record the change of MSE relative to the initial rule weights when the rule weights are reduced N times; 3.3 The average change in MSE for each rule is recorded as the initial importance assessment metric for the rule. : (3)； Among them, MSE L The MSE represents the output result before reducing the rule weights. This represents the MSE of the output result after reducing the rule weights; 3.

4. Initial importance assessment indicators Combined with the rule weight coefficient k and the number of activations t, the comprehensive evaluation index R is calculated: (4)； 3.5 Sort the comprehensive evaluation index R, delete rules with low importance, and optimize the rule base.

4. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 1, characterized in that: In step four, the activation method is the conjunctive activation method: (5)； in," "" indicates that the confidence rule is constructed under the conjunction activation method.

5. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 4, characterized in that: Follow these steps to activate the calculation: 4.1.1 Calculate the rule matching degree; for input data , No. The first rule under the rule The matching degree of each attribute is calculated as follows: (6)； in, This represents the matching degree of the i-th attribute of the k-th rule. and This indicates that the input data is located at two adjacent reference values ​​of the i-th attribute. The rule is activated when the matching degree of all attributes of the rule is not zero. 4.1.2 Calculate the rule activation weight; the calculation of activation weights is based on the rule matching degree, taking into account both attribute weights and rule weights, emphasizing the impact of different rule matching degrees on the final result: (7)； in, Represents the rule weight of the k-th rule, when The k-th rule is activated.

6. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 4, characterized in that, In step four, the activation method uses a disjunctive approach to activate the rule, and its form is as follows: (8)； in, This indicates how the confidence rule is constructed under the disjunctive hypothesis.

7. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 6, characterized in that, Follow these steps when activating the computation: 4.2.1 Consider an input vector of test data. ,in To determine the number of prerequisite attributes, the disjunction rule will assign each input... The rule activation matching table converts the reference value of the i-th prerequisite attribute into the input data. : (9)； (10)； express Attribute input data For reference values likelihood yes The number of reference values ​​for the prerequisite attribute; 4.2.2 Calculate the activation weight of each prerequisite attribute using a weighted method: (11)。 8. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 5, characterized in that, In step five, the projective covariance matrix adaptive algorithm is used to optimize the rule weights, attribute weights, and confidence scores in the model. The result of this health status test model is as follows: (12)； express The utility value, The reference value representing the nth result. Let n be the confidence level of the nth result. The final output value is represented by N, which represents the total number of results, and the mean squared error is 0. This represents the modeling accuracy of the health status test model, where the rule weights and attribute weights are optimized parameters; Represented as: (13)； in For the amount of training data, This represents the actual output value of the system.

9. The multi-dimensional rule-reduction health status test method for flywheel system bearing assemblies according to claim 8, characterized in that, Find the minimum through continuous iteration. The value, and the specific process are as follows: 5.1 Initialization operation, initial parameters are as follows: (14)； in Represents the initial parameter set. Represents the set of rule weights. Represents the set of attribute weights. Represents the set of confidence levels; 5.2 Sampling operation: The initial population is determined in the following way: (15)； in Indicates the first The first generation of offspring One solution. Represents the population mean. Indicates the step size; It follows a normal distribution; For the first The covariance matrix of the generation; Indicates the number of child solutions; 5.3 Perform projection operations to satisfy the following constraints: (16)； A hyperplane is represented as ,in Solution The number of constraint variables in the middle form. Solution The number of constraints in the middle form, and Represents a parameter vector; 5.

4. Perform the selection operation to update the average value using the following formula: (17)； in Indicates the first Weighting coefficients for each equation; Indicates the ( The first in the substitution solution One solution; Indicates the size of the offspring population; 5.

5. Update the covariance matrix through adaptive computation to determine the population search range and direction; the calculation process is shown in the following formula: (18)； in and Indicates the learning rate; This represents the evolution path of the covariance, with the initial evolution path being 0. and For the first and the The covariance matrix of the generation, Indicates the first The weighting coefficients of the equations Indicates the first The mean of generations, Indicates the first The step size of the generation, where T is the amount of training data. Indicates the size of the offspring population. This indicates the number of child solutions.

10. The method for testing the multidimensional rule-reduction health status of flywheel system bearing assemblies according to claim 1, characterized in that, Step six includes the following steps: 6.1 Calculate the degree of matching between the input sample information and the confidence rules. The first input The rule adaptability of a rule is calculated as follows: (19)； 6.2 Calculate the first... Activation weight w of the rule i : (20)； in, Indicates the first The attribute weights of each evaluation indicator; 6.

3. Use the ER algorithm for inference to obtain the final confidence level. : (21)； (22)； 6.4 Calculate the expected utility value: (23)； Where S() represents the set of confidence distributions. This represents the actual input vector. express The effect, Represents the final expected utility; the final confidence distribution. The description is as follows: (24)。

Images