D-brb-based complex system health state evaluation model

Abstract

The application discloses a complex system health state evaluation model based on D-BRB, comprising the following steps: step one, obtaining a complex system measured data set; step two, obtaining feature distribution based on data mining; step three, dynamically constructing a confidence rule base model set; step four, dynamically optimizing the confidence rule base set; step five, using a customized Akaike information criterion to comprehensively evaluate the complexity and precision of the model, and obtaining an optimal model; the application effectively combines multiple uncertain feature indexes by using the confidence rule base, comprehensively integrates complete information, realizes all-around evaluation of the complex system health state, simultaneously, obtains feature distribution through data mining, dynamically constructs a model set, and effectively covers the diverse state and dynamic change of the complex system; in addition, the dynamic optimization method and dynamic optimization strategy effectively improve the model precision and the efficiency of the optimized model set; finally, the model is comprehensively evaluated to obtain a model with consideration of accuracy and complexity.

Description

Technical Field

[0001] This invention relates to the field of health status assessment technology, specifically to a health status assessment model for complex systems based on D-BRB. Background Technology

[0002] In complex systems, health status assessment can determine the system's state and identify potential problems. However, due to the various uncertainties and changes inherent in complex systems, these factors are difficult to assess accurately, making it challenging to construct effective assessment models.

[0003] Confidence rule bases (BRBs) can effectively handle uncertain information using data-driven and knowledge-driven approaches, and are widely used in health status assessment modeling of complex systems. However, expert knowledge may not be able to cover all potential system states and dynamic changes, and traditional BRB models also have limitations in terms of adaptability and parameter tuning in dynamic environments. Therefore, this paper proposes a complex system health status assessment model based on dynamic BRB (D-BRB). Summary of the Invention

[0004] The purpose of this invention is to provide a health status assessment model for complex systems based on D-BRB, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a complex system health status assessment model based on D-BRB, comprising the following steps:

[0006] Step 1: Obtain a measured dataset of complex systems: Measure various indicators of complex systems using different sensors to obtain a relatively comprehensive measured dataset for assessing the health status of complex systems.

[0007] Step 2, obtain feature distribution based on data mining: mine historical data based on K-means++ with error sum of squares constraint to obtain the feature distribution of the measured dataset and construct a new set of reference values;

[0008] Step 3: Dynamically construct a set of confidence rule base models: Based on different numbers of reference values, dynamically construct a set of models for assessing the health status of complex systems. The dynamic changes in the state of complex systems and the complex data distribution are effectively applied to the modeling.

[0009] Step 4, Dynamically optimize the confidence rule base set: A new dynamic optimization strategy was designed to ensure the optimization efficiency of BRB model parameters and model set;

[0010] Step 5: Comprehensive evaluation of the accuracy and complexity of the confidence rule base: A customized Akaike Criterion (AIC) is proposed. AIC ensures that the selected model effectively captures the complex relationships in the data, while not losing its generalization ability due to the complexity of the model, which helps to further improve the effectiveness and reliability of the model in practical applications.

[0011] Step 6: Establishment of a health status assessment model for complex systems based on a dynamic confidence rule base: The AIC criterion is used as the model evaluation index to establish a health status assessment model for complex systems based on a dynamic confidence rule base.

[0012] Preferably, in step one, the indicators include, but are not limited to, system status.

[0013] Preferably, in step two, feature distribution extraction is performed based on data mining. The SSE-KPP algorithm is developed by introducing a minimum SSE constraint at the top of the K-means++ algorithm to achieve reference value mining. The specific implementation process is as follows:

[0014] Step 1: Randomly select initial cluster centers μ1 from the dataset;

[0015] Step 2: Calculate μ from each data point to the current cluster center set. j The shortest distance is calculated as follows:

[0016]

[0017] dist(x i ,μ i )=||χ i -μ i || 2

[0018] Where x i Let μ represent the i-th sample point. i This represents the i-th cluster center, K represents the number of clusters, and dist(·) represents the cluster index;

[0019] Step 3: Select the next cluster center. The probability of each data point being selected as the next cluster center is calculated as follows:

[0020]

[0021] Where X represents the set of all sample points that were not selected, P(x i ) is the data point x i The distance to be selected as the next cluster center;

[0022] Step 4: After selecting the cluster centers, repeat steps 2-4 to select the remaining cluster centers until the clustering is complete;

[0023] Step 5: Update the cluster assigned to each cluster point:

[0024]

[0025] Where c i This indicates the cluster to which the i-th data point belongs;

[0026] Step 6: Update cluster centers. For each cluster center, calculate the average of all data points assigned to it, and then calculate the new cluster center.

[0027]

[0028] Where N j It is assigned to the cluster center μ j The number of data points is counted, and steps 5 and 6 are repeated until the stopping condition is met;

[0029] Step 7: Calculate the sum of squared errors within each cluster. The goal of K-means++ clustering is to minimize the sum of squared distances between all data points and the centers of their respective clusters, i.e., to minimize the loss function:

[0030]

[0031] Where μ ci |is χ i Designated cluster centers;

[0032] Step 8: Set the number of iterations for centroid refinement, gradually approaching a reasonable centroid.

[0033] MaxIter=z i

[0034] Where MaxIter is the number of iterations for centroid refinement;

[0035] Step 9: This statistical parameter calculates the SSE from each point in the cluster to the cluster center, using the following formula:

[0036] MaxIter_KPP=z2

[0037]

[0038] output = min(SSE)

[0039] MaxIter_KPP represents the number of algorithm iterations, which calculates the SSE value from each point in the cluster to the cluster center in each operation result, and selects the result with the smallest SSE.

[0040] Step 10: The relevant constraints of the reference values ​​obtained by the SSE-KPP algorithm are described as follows:

[0041]

[0042]

[0043] st

[0044] 2≤m≤9

[0045]

[0046]

[0047]

[0048]

[0049] Where Min(D) A ) and Max(D A ) represent the minimum and maximum values ​​of the attribute reference values, respectively. Min(D) R ) and Max(D R ) represent the minimum and maximum values ​​of the reference values ​​for the results, respectively. and This represents the set of attribute reference values ​​and result reference values ​​generated by the SSE-KPP algorithm, which is indicated as the set of a and r reference values.

[0050] Preferably, in step three, a set of confidence rule base models is dynamically constructed, an evaluation model is built using the BRB confidence rule base, ER rules are used as the inference engine, and a reference value set is introduced to construct the confidence rule base model. The modeling process is as follows:

[0051] (1) Description of BRB Knowledge Base

[0052] The model is constructed using IF-THEN rules, where the k-th confidence rule is defined as follows:

[0053]

[0054] THEN{(D1,β 1,k ),(D2,β 2,k ),.....,(D N ,β N,k )},

[0055] WITH rule weightθ k (k = 1, 2, ..., L)

[0056] AND attribute weightδ i (i = 1, 2, ..., M)

[0057] Where R k This represents the k-th confidence rule in the BRB model; x1, x2, ..., x M This represents M prerequisite attributes; M represents the number of attributes; A1, A2, ..., A M A set of reference values ​​corresponding to M attributes; β 1,k ,β 2,k ,...,β N,k Let D1, D2, ..., D2 represent the confidence distributions corresponding to N outcomes. N Represents N results; θ k δ is the rule weight of the k-th confidence rule; i The weight of the i-th attribute is represented by L; L represents the number of rules.

[0058] (2) BRB reasoning process

[0059] For BRB, ER rules are often used as the inference engine. The specific inference process of the BRB model is as follows:

[0060] Step 1: Input Conversion

[0061] Determining the confidence distribution of the input values ​​corresponding to the reference values ​​is often done using membership functions. The final confidence distribution is described as follows:

[0062] S(x i )={(A i,j ,a i,j ), i = 1,...,M; j = 1,...,T i}

[0063] Where A i,j a represents the j-th reference value in the i-th attribute. i,j x represents i Regarding A i,j Confidence level;

[0064] Step 2: Calculate activation weights

[0065] Step 2.1: Calculate the reference value matching degree:

[0066]

[0067] Where J represents the number of reference values ​​and the reference value matching degree. The matching degree for rule k is calculated as follows:

[0068]

[0069]

[0070] Where α kThis indicates the matching degree corresponding to the k-th rule. This represents the normalized weight of the i-th attribute;

[0071] Step 2.2: Matching degree normalization:

[0072] By aggregating the corresponding matching degrees, the calculation method for the activation rule is obtained:

[0073]

[0074] Where w k Indicates the activation weight of the rule;

[0075] Step 3: Rule Fusion

[0076] Using ER rules for rule fusion, the confidence level for the nth result is:

[0077]

[0078] in This represents the confidence level of the nth result;

[0079] (3) Utility calculation

[0080] Calculate the expected utility value and derive the final output:

[0081]

[0082] Where S(·) represents the set of confidence distributions, A' represents the actual input vector, and μ(D) represents the set of confidence distributions. n ) represents D n The utility, μ(S(A′)) is the final expected utility;

[0083] (4) A new form of BRB set construction

[0084] This study extensively incorporates the obtained attribute reference value set. and result reference value set Constructing a diverse integrated BRB model structure, this approach covers almost all model structures and provides a foundation for selecting the appropriate model structure for different needs. By constructing model integration, the relationship between different sets of reference values ​​is systematically explored, and the optimal model structure is determined. For each model structure, its performance in the evaluation task is evaluated, and the most suitable model structure is selected according to the requirements. This comprehensive consideration of different structures provides greater flexibility and accuracy to adapt to various evaluation needs.

[0085] A new form of BRB set construction is proposed, as shown in the equation:

[0086]

[0087]

[0088] Preferably, in step four, the confidence rule base is combined with dynamic optimization, specifically implemented as follows:

[0089] (1) Dynamic optimization strategy for model set

[0090] When constructing multiple sets of models, if the result parameter set is small, optimization is performed directly on the model set; if the result parameter set is large, the proposed dynamic optimization strategy is used for optimization.

[0091] Assume there are K sets of reference values, and the maximum number of reference values ​​is M. K See the flowchart for the dynamic optimization strategy. Figure 3 The steps are as follows:

[0092] Step 1: When 0 < K < 3, directly construct the entire model; when K ≥ 3, construct the following model:

[0093]

[0094]

[0095]

[0096] Step 2: Optimize the constructed BRB model and perform the following operations:

[0097] Step 2.1: When but

[0098] Step 2.2: When Let temp = K / 2, and perform optimization on the following model:

[0099]

[0100]

[0101] Step 2.3: When

[0102] Given temp = K / 2, perform optimization on the following model:

[0103]

[0104]

[0105] By recursively executing steps 2.1-2.3 for optimization, the final result is determined.

[0106] (2) D-BRB optimization

[0107] At the current stage of research, many high-performance algorithms have been used in the model optimization process. A commonly used optimization algorithm for the BRB model is the P-CMA-ES algorithm, and the steps of the P-CMA-ES algorithm are as follows:

[0108] Step 1: Determine the initial set of optimization parameters w 0 =Ω 0 ,

[0109] Ω 0 ={θ1,...,θ L ,β 1,1 ,...,β L,N ,δ1,…,δ M}

[0110] Where Ω 0 For the initial optimization parameter vector, w 0 This is the initial average value;

[0111] Step 2: Determine the objective function and constraints. The mean squared error (MSE) represents the modeling accuracy of BRB, and the calculation formula is:

[0112]

[0113] Where T is the amount of observed data, and result autual It is the actual output of the system, result predict This is the diagnosis result of BRB;

[0114] Based on the above definition, the objective function and constraints are as follows:

[0115] minMSE(θ k ,β n,k ,δ i )

[0116] st0≤θ k ≤1,0≤β n,k ≤1,

[0117]

[0118] k=1,2,...,L,n=1,2,...,N,i=1,2,...,M;

[0119] Step 3: Perform the sampling operation.

[0120]

[0121] in Let ε represent the i-th solution in the (g+1)-th generation, and let ε represent the step size. Let C represent a normal distribution. g Denotes the covariance matrix in the g-th generation;

[0122] Step 4: Perform a projection operation to satisfy the constraints.

[0123]

[0124] Among them, the hyperplane is used It means that n e This represents the number of variables with equality constraints in the solution, where j = 1, ..., N+1. The number of equality constraints in the solution, A e =[1…1] 1×N Represents a parameter vector;

[0125] Step 5: Perform a selection operation to update the average value. h i This represents the weight coefficient of the i-th solution. Let represent the i-th solution in the (g+1)-th λ-solution, and τ represent the size of the offspring population;

[0126] Step 6: Perform the adaptation operation to update the covariance matrix.

[0127]

[0128]

[0129] The step size is updated using the following formula:

[0130]

[0131]

[0132] Where c1 and c2 are defined as learning rates, p c Defined as an evolutionary path, c c Defined as the backward time span of an evolutionary path;

[0133] Step 7: Recursively execute the above process until the optimal solution Ω is obtained. optimal .

[0134] Preferably, in step five, a customized Akaike Criterion (AIC) is proposed to comprehensively evaluate the accuracy and complexity of the confidence rule base, and its specific derivation process is as follows:

[0135] For a given linear model, there exists a relation:

[0136] z = h0 + h1χ1 + h2χ2 + ... + h N χ N+e

[0137] Where z represents the data output, h N Indicates the input, χ N Let n represent the nth model parameter, and e represent the model perturbation;

[0138] Akaike proposed the following criteria to determine the minimum order (or number of independent parameters) of a model:

[0139] AIC = -2logL(χ) ML )+2N

[0140] in, The parameter χ = [χ1, χ2, ..., χ] represents the parameter χ. N The maximum likelihood estimate of ] express The likelihood function is given by N, where N represents the number of independent parameters in the model. The steps for introducing BRB into AIC will be explained in detail below.

[0141] Suppose {(X,Y)} is a training dataset, where X is the input and Y is the output. X has two dimensions: the size P of the training dataset and the number N of independent parameters. Therefore, we have... Y has one dimension, which is the number of training datasets, therefore Y = [y1, y2, ..., y]. p ] T The output model of BRB is:

[0142]

[0143] Where, ω n φ represents the weight of the nth independent parameter, n = 1, 2, ..., N. n (X p f(X) represents the mapping correlation between the BRB input and estimated output with respect to the nth independent parameter and the pth set of training data. p ) represents the estimated output of BRB, with X as the input. p ;

[0144] Let ε p f(X) p ) and y p The error between them, assuming ε p Follows a normal distribution, ε p ~N{0,σ 2 The BRB output is represented as follows:

[0145]

[0146] Based on the above formula The likelihood estimation formula is expressed as:

[0147]

[0148] Where W = [ω1, ω2, ..., ω n ] T ;

[0149] Through logarithmic transformation, the likelihood estimation formula can also be written as:

[0150]

[0151] For ω n and σ 2 Calculating the partial derivatives, the typical equation is expressed as:

[0152]

[0153] The partial derivatives are calculated, and the solution is as follows:

[0154] W = [ω1, ω2, ..., ω n ] T

[0155] W and σ 2 The maximum likelihood estimate is calculated using the following method:

[0156] W = (G′G) -1 G′Y

[0157]

[0158] in Based on the above calculations, the likelihood estimation formula after logarithmic transformation can also be written as:

[0159]

[0160] Therefore, the AIC calculation formula has been updated as follows:

[0161]

[0162] Right now:

[0163] AIC BRB =Pln(σ 2 )+2N+C

[0164] Where C = Pln(2π) + P is a constant, independent of N;

[0165] When comparing different models, the constant C is omitted; therefore, AIC BRB writing:

[0166] AIC BRB =Pln(P·MSE)+2N

[0167] via AIC BRB The BRB is evaluated to ensure the complexity and modeling accuracy of the model.

[0168] Preferably, in step six, a complex system health status assessment model with dynamic optimization and high accuracy is established based on a dynamic confidence rule base.

[0169] The advantages compared to existing technologies are as follows:

[0170] This invention proposes a health status assessment model for complex systems based on D-BRB. This model constructs a series of BRB model sets, adjusting the model structure to adapt to the application environment and decision-makers' preferences. In addition, a dynamic modeling strategy is proposed, which effectively improves modeling efficiency. This research lays the foundation for the further application and development of BRB in the field of health status assessment of complex systems, and is expected to enhance the understanding of system design in practical applications, thereby optimizing system performance and reducing potential risks. Attached Figure Description

[0171] Figure 1 This is a step diagram of the present invention;

[0172] Figure 2 This is a flowchart of the method of the present invention;

[0173] Figure 3 This is a schematic diagram of the reasoning process of the confidence rule base of the present invention;

[0174] Figure 4 This is a flowchart of the data mining method of the present invention;

[0175] Figure 5 This is a schematic diagram of the confidence rule base set construction method of the present invention;

[0176] Figure 6 This is a schematic diagram of the dynamic optimization strategy of the present invention. Detailed Implementation

[0177] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0178] Please see Figure 1-6 This invention provides a health status assessment model for complex systems based on D-BRB, comprising the following steps:

[0179] Step 1: Obtain a measured dataset of complex systems: Measure various indicators of complex systems using different sensors to obtain a relatively comprehensive measured dataset for assessing the health status of complex systems.

[0180] Step 2, obtain feature distribution based on data mining: mine historical data based on K-means++ with error sum of squares constraint to obtain the feature distribution of the measured dataset and construct a new set of reference values;

[0181] Step 3: Dynamically construct a set of confidence rule base models: Based on different numbers of reference values, dynamically construct a set of models for assessing the health status of complex systems. The dynamic changes in the state of complex systems and the complex data distribution are effectively applied to the modeling.

[0182] Step 4, Dynamically optimize the confidence rule base set: A new dynamic optimization strategy was designed to ensure the optimization efficiency of BRB model parameters and model set;

[0183] Step 5: Comprehensive evaluation of the accuracy and complexity of the confidence rule base: A customized Akaike Criterion (AIC) is proposed. AIC ensures that the selected model effectively captures the complex relationships in the data, while not losing its generalization ability due to the complexity of the model, which helps to further improve the effectiveness and reliability of the model in practical applications.

[0184] Step 6: Establishment of a health status assessment model for complex systems based on a dynamic confidence rule base: The AIC criterion is used as the model evaluation index to establish a health status assessment model for complex systems based on a dynamic confidence rule base.

[0185] In step one, the indicators include, but are not limited to, system status.

[0186] In step two, feature distribution extraction is performed based on data mining. The SSE-KPP algorithm is developed by introducing a minimum SSE constraint at the top of the K-means++ algorithm to achieve reference value mining. The specific implementation process is as follows:

[0187] Step 1: Randomly select initial cluster centers μ1 from the dataset;

[0188] Step 2: Calculate μ from each data point to the current cluster center set. j The shortest distance is calculated as follows:

[0189]

[0190] dist(x i ,μ i )=||χ i -μ i || 2

[0191] Where x i Let μ represent the i-th sample point. i This represents the i-th cluster center, K represents the number of clusters, and dist(·) represents the cluster index;

[0192] Step 3: Select the next cluster center. The probability of each data point being selected as the next cluster center is calculated as follows:

[0193]

[0194] Where X represents the set of all sample points that were not selected, P(x i ) is the data point x i The distance to be selected as the next cluster center;

[0195] Step 4: After selecting the cluster centers, repeat steps 2-4 to select the remaining cluster centers until the clustering is complete;

[0196] Step 5: Update the cluster assigned to each cluster point:

[0197]

[0198] Where c i This indicates the cluster to which the i-th data point belongs;

[0199] Step 6: Update cluster centers. For each cluster center, calculate the average of all data points assigned to it, and then calculate the new cluster center.

[0200]

[0201] Where N j It is assigned to the cluster center μ j The number of data points is counted, and steps 5 and 6 are repeated until the stopping condition is met;

[0202] Step 7: Calculate the sum of squared errors within each cluster. The goal of K-means++ clustering is to minimize the sum of squared distances between all data points and the centers of their respective clusters, i.e., to minimize the loss function:

[0203]

[0204] Where μ ci |is χ i Designated cluster centers;

[0205] Step 8: Set the number of iterations for centroid refinement, gradually approaching a reasonable centroid.

[0206] MaxIter=z i

[0207] Where MaxIter is the number of iterations for centroid refinement;

[0208] Step 9: This statistical parameter calculates the SSE from each point in the cluster to the cluster center, using the following formula:

[0209] MaxIter_KPP=z2

[0210]

[0211] output = min(SSE)

[0212] MaxIter_KPP represents the number of algorithm iterations, which calculates the SSE value from each point in the cluster to the cluster center in each operation result, and selects the result with the smallest SSE.

[0213] Step 10: The relevant constraints of the reference values ​​obtained by the SSE-KPP algorithm are described as follows:

[0214]

[0215]

[0216] st

[0217] 2≤m≤9

[0218]

[0219]

[0220]

[0221]

[0222] Where M in (D A ) and Max(D A ) represent the minimum and maximum values ​​of the attribute reference values, respectively. Min(D) R ) and Max(D R ) represent the minimum and maximum values ​​of the reference values ​​for the results, respectively. and This represents the set of attribute reference values ​​and result reference values ​​generated by the SSE-KPP algorithm, which is indicated as the set of a and r reference values.

[0223] In step three, a set of confidence rule base models was dynamically constructed. The evaluation model was built using the BRB confidence rule base, with ER rules serving as the inference engine. A reference value set was also introduced to construct the confidence rule base model. The modeling process is as follows:

[0224] (1) Description of BRB Knowledge Base

[0225] The model is constructed using IF-THEN rules, where the k-th confidence rule is defined as follows:

[0226]

[0227] THEN{(D1,β 1,k ),(D2,β 2,k ),.....,(D N ,β N,k )},

[0228] WITH rule weightθ k (k = 1, 2, ..., L)

[0229] AND attribute weightδ i (i = 1, 2, ..., M)

[0230] Where R k This represents the k-th confidence rule in the BRB model; x1, x2, ..., x M This represents M prerequisite attributes; M represents the number of attributes; A1, A2, ..., A M A set of reference values ​​corresponding to M attributes; β 1,k ,β 2,k ,...,β N,k Let D1, D2, ..., D2 represent the confidence distributions corresponding to N outcomes. N Represents N results; θ k δ is the rule weight of the k-th confidence rule; i The weight of the i-th attribute is represented by L; L represents the number of rules.

[0231] (2) BRB reasoning process

[0232] For BRB, ER rules are often used as the inference engine. The specific inference process of the BRB model is as follows:

[0233] Step 1: Input Conversion

[0234] Determining the confidence distribution of the input value corresponding to the reference value is often done using a membership function. The final confidence distribution is described as follows:

[0235] S(x i )={(A i,j ,a i,j ), i = 1,...,M; j = 1,...,T i}

[0236] Where A i,j a represents the j-th reference value in the i-th attribute. i,j x represents i Regarding A i,j Confidence level;

[0237] Step 2: Calculate activation weights

[0238] Step 2.1: Calculate the reference value matching degree:

[0239]

[0240] Where J represents the number of reference values ​​and the reference value matching degree. The matching degree for rule k is calculated as follows:

[0241]

[0242]

[0243] Where α k This indicates the matching degree corresponding to the k-th rule. This represents the normalized weight of the i-th attribute;

[0244] Step 2.2: Matching degree normalization:

[0245] By aggregating the corresponding matching degrees, the calculation method for the activation rule is obtained:

[0246]

[0247] Where w k Indicates the activation weight of the rule;

[0248] Step 3: Rule Fusion

[0249] Using ER rules for rule fusion, the confidence level for the nth result is:

[0250]

[0251] in This represents the confidence level of the nth result;

[0252] (3) Utility calculation

[0253] Calculate the expected utility value and derive the final output:

[0254]

[0255] Where S(·) represents the set of confidence distributions, A' represents the actual input vector, and μ(D) represents the set of confidence distributions. n ) represents D n The utility, μ(S(A′)) is the final expected utility;

[0256] (4) A new form of BRB set construction

[0257] This study extensively incorporates the obtained attribute reference value set. and result reference value set Constructing a diverse integrated BRB model structure is a method that covers almost all model structures and provides a basis for selecting the appropriate model structure for different needs. By constructing model integration, the relationship between different sets of reference values ​​is systematically explored and the optimal model structure is determined. For each model structure, its performance in the evaluation task is evaluated, and the most suitable model structure is selected according to the requirements. This comprehensive consideration of different structures provides greater flexibility and accuracy to adapt to various evaluation needs.

[0258] A new form of BRB set construction is proposed, as shown in the equation:

[0259]

[0260]

[0261] In step four, the confidence rule base is combined with dynamic optimization, specifically implemented as follows:

[0262] (1) Dynamic optimization strategy for model set

[0263] When constructing multiple sets of models, if the result parameter set is small, optimization is performed directly on the model set; if the result parameter set is large, the proposed dynamic optimization strategy is used for optimization.

[0264] Assume there are K sets of reference values, and the maximum number of reference values ​​is M. K See the flowchart for the dynamic optimization strategy. Figure 3 The steps are as follows:

[0265] Step 1: When 0 < K < 3, directly construct the entire model; when K ≥ 3, construct the following model:

[0266]

[0267]

[0268]

[0269] Step 2: Optimize the constructed BRB model and perform the following operations:

[0270] Step 2.1: When but

[0271] Step 2.2: When Let temp = K / 2, and perform optimization on the following model:

[0272]

[0273]

[0274] Step 2.3: When

[0275] Given temp = K / 2, perform optimization on the following model:

[0276]

[0277]

[0278] By recursively executing steps 2.1-2.3 for optimization, the final result is determined.

[0279] (2) D-BRB optimization

[0280] At the current stage of research, many high-performance algorithms have been used in the model optimization process. A commonly used optimization algorithm for the BRB model is the P-CMA-ES algorithm, and the steps of the P-CMA-ES algorithm are as follows:

[0281] Step 1: Determine the initial set of optimization parameters w 0 =Ω 0 ,

[0282] Ω 0 ={θ1,...,θ L ,β 1,1 ,...,β L,N ,δ1,…,δ M}

[0283] Where Ω 0 For the initial optimization parameter vector, w 0 This is the initial average value;

[0284] Step 2: Determine the objective function and constraints. The mean squared error (MSE) represents the modeling accuracy of BRB, and the calculation formula is as follows:

[0285]

[0286] Where T is the amount of observed data, and result autual It is the actual output of the system, result predict This is the diagnosis result of BRB;

[0287] Based on the above definition, the objective function and constraints are as follows:

[0288] minMSE(θ k ,β n,k ,δ i )

[0289] st0≤θ k≤1,0≤β n,k ≤1,

[0290]

[0291] k=1,2,...,L,n=1,2,...,N,i=1,2,...,M;

[0292] Step 3: Perform the sampling operation.

[0293]

[0294] in Let ε represent the i-th solution in the (g+1)-th generation, and let ε represent the step size. Let C represent a normal distribution. g Denotes the covariance matrix in the g-th generation;

[0295] Step 4: Perform a projection operation to satisfy the constraints.

[0296]

[0297] Among them, the hyperplane is used It means that n e This represents the number of variables with equality constraints in the solution, where j = 1, ..., N+1. The number of equality constraints in the solution, A e =[1…1] 1×N Represents a parameter vector;

[0298] Step 5: Perform a selection operation to update the average value. h i This represents the weight coefficient of the i-th solution. Let represent the i-th solution in the (g+1)-th λ-solution, and τ represent the size of the offspring population;

[0299] Step 6: Perform the adaptation operation to update the covariance matrix.

[0300]

[0301]

[0302] The step size is updated using the following formula:

[0303]

[0304]

[0305] Where c1 and c2 are defined as learning rates, p c Defined as an evolutionary path, c cDefined as the backward time span of an evolutionary path;

[0306] Step 7: Recursively execute the above process until the optimal solution Ω is obtained. optimal .

[0307] In step five, a customized Akaike Criterion (AIC) is proposed to comprehensively evaluate the accuracy and complexity of the confidence rule base. Its specific derivation process is as follows:

[0308] For a given linear model, there exists a relation:

[0309] z = h0 + h1χ1 + h2χ2 + ... + h N χ N +e

[0310] Where z represents the data output, h N Indicates the input, χ N Let n represent the nth model parameter, and e represent the model perturbation;

[0311] Akaike proposed the following criteria to determine the minimum order (or number of independent parameters) of a model:

[0312] AIC = -2logL(χ) ML )+2N

[0313] in, The parameter χ = [χ1, χ2, ..., χ] represents the parameter χ. N The maximum likelihood estimate of ] express The likelihood function is given by N, where N represents the number of independent parameters in the model. The steps for introducing BRB into AIC will be explained in detail below.

[0314] Suppose {(X,Y)} is a training dataset, where X is the input and Y is the output. X has two dimensions: the size P of the training dataset and the number N of independent parameters. Therefore, we have... Y has one dimension, which is the number of training datasets, therefore Y = [y1, y2, ..., y]. p ] T The output model of BRB is:

[0315]

[0316] Where, ω n φ represents the weight of the nth independent parameter, n = 1, 2, ..., N. n (X p f(X) represents the mapping correlation between the BRB input and estimated output with respect to the nth independent parameter and the pth set of training data. p) represents the estimated output of BRB, with X as the input. p ;

[0317] Let ε p f(X) p ) and y p The error between them, assuming ε p Follows a normal distribution, ε p ~N{0,σ 2 The BRB output is represented as follows:

[0318]

[0319] Based on the above formula The likelihood estimation formula is expressed as:

[0320]

[0321] Where W = [ω1, ω2, ..., ω n ] T ;

[0322] Through logarithmic transformation, the likelihood estimation formula can also be written as:

[0323]

[0324] For ω n and σ 2 Calculating the partial derivatives, the typical equation is expressed as:

[0325]

[0326] The partial derivatives are calculated, and the solution is as follows:

[0327] W = [ω1, ω2, ..., ω n ] T

[0328] W and σ 2 The maximum likelihood estimate is calculated using the following method:

[0329] W = (G′G) -1 G′Y

[0330]

[0331] in Based on the above calculations, the likelihood estimation formula after logarithmic transformation can also be written as:

[0332]

[0333] Therefore, the AIC calculation formula has been updated as follows:

[0334]

[0335] Right now:

[0336] AIC BRB =Pln(σ 2 )+2N+C

[0337] Where C = Pln(2π) + P is a constant, independent of N;

[0338] When comparing different models, the constant C is omitted; therefore, AIC BRB writing:

[0339] AIC BRB =Pln(P·MSE)+2N

[0340] via AIC BRB The BRB is evaluated to ensure the complexity and modeling accuracy of the model.

[0341] In step six, a complex system health status assessment model with dynamic optimization and high accuracy is established based on a dynamic confidence rule base.

[0342] This invention proposes a health status assessment model for complex systems based on D-BRB. This model constructs a series of BRB model sets, adjusting the model structure to adapt to the application environment and decision-makers' preferences. In addition, a dynamic modeling strategy is proposed, which effectively improves modeling efficiency. This research lays the foundation for the further application and development of BRB in the field of health status assessment of complex systems, and is expected to enhance the understanding of system design in practical applications, thereby optimizing system performance and reducing potential risks.

[0343] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for assessing the health status of complex systems based on D-BRB, characterized in that, Includes the following steps: Step 1: Obtain a measured dataset of complex systems: Measure various indicators of complex systems using different sensors to obtain a relatively comprehensive measured dataset for assessing the health status of complex systems. Step 2, obtain feature distribution based on data mining: mine historical data based on K-means++ with error sum of squares constraint to obtain the feature distribution of the measured dataset and construct a new set of reference values; Step 3: Dynamically construct a set of confidence rule base models: Based on different numbers of reference values, dynamically construct a set of models for assessing the health status of complex systems. The dynamic changes in the state of complex systems and the complex data distribution are effectively applied to the modeling. Step 4, Dynamically optimize the confidence rule base set: A new dynamic optimization strategy was designed to ensure the optimization efficiency of BRB model parameters and model set; Step 5: Comprehensively evaluate the accuracy and complexity of the confidence rule base: a customized Akaike criterion is proposed; Step 6: Establishment of a health status assessment model for complex systems based on a dynamic confidence rule base: The AIC criterion is used as the model evaluation index to establish a health status assessment model for complex systems based on a dynamic confidence rule base. In step five, the specific derivation process of the customized Akaike Criterion is as follows: For a given linear model, there exists a relation: Where z represents the data output. Indicates input, This represents the nth model parameter. Indicates model perturbation; Akaike proposed the following criteria to determine the minimum order or number of independent parameters of a model: in, Indicates parameters Maximum likelihood estimate express The likelihood function is given by N, where N represents the number of independent parameters in the model. The steps for introducing BRB into AIC will be explained in detail below. Assumption This is a training dataset, where X is the input and Y is the output. X has two dimensions: the size of the training dataset P and the number of independent parameters N. Therefore, we have Y has one dimension, namely the number of training datasets, therefore we have The output model of BRB is: in, This represents the weight of the nth independent parameter. , This represents the mapping correlation between the BRB input and the estimated output regarding the nth independent parameter and the pth set of training data. This represents the estimated output of BRB, with the input being... ; set up for and The error between them, assuming Follows a normal distribution. The BRB output is represented as: Based on the above formula The likelihood estimation formula is expressed as: in ; Through logarithmic transformation, the likelihood estimation formula can also be written as: right and Calculating the partial derivatives, the typical equation is expressed as: The partial derivatives are calculated, and the solution is as follows: W and The maximum likelihood estimate is calculated using the following method: in Based on the above calculations, the likelihood estimation formula after logarithmic transformation can also be written as: Therefore, the AIC calculation formula has been updated as follows: Right now: in It is a constant and is independent of N; When comparing different models, the constant C is omitted; therefore... writing: pass The BRB is evaluated to ensure the complexity and modeling accuracy of the model.

2. The method for assessing the health status of complex systems based on D-BRB according to claim 1, characterized in that: In step one, the indicators include, but are not limited to, system status.

3. The method for assessing the health status of complex systems based on D-BRB according to claim 1, characterized in that: In step two, feature distribution extraction is performed based on data mining. The SSE-KPP algorithm is developed by introducing a minimum SSE constraint at the top of the K-means++ algorithm to achieve reference value mining. The specific implementation process is as follows: Step 1: Randomly select initial cluster centers from the dataset ; Step 2: Calculate the distance from each data point to the current cluster center set. The shortest distance is calculated as follows: in This represents the i-th sample point. Let K represent the i-th cluster center, and K represent the number of clusters. Represents a clustering index; Step 3: Select the next cluster center. The probability of each data point being selected as the next cluster center is calculated as follows: Where X represents the set of all sample points that were not selected. Data points The distance to be selected as the next cluster center; Step 4: After selecting the cluster centers, repeat steps 2-4 to select the remaining cluster centers until the clustering is complete; Step 5: Update the cluster assigned to each cluster point: in This indicates the cluster to which the i-th data point belongs; Step 6: Update cluster centers. For each cluster center, calculate the average of all data points assigned to it, and then calculate the new cluster center. in It is assigned to the cluster center The number of data points is counted, and steps 5 and 6 are repeated until the stopping condition is met; Step 7: Calculate the sum of squared errors within each cluster. The goal of K-means++ clustering is to minimize the sum of squared distances between all data points and the centers of their respective clusters, i.e., to minimize the loss function: in yes Designated cluster centers; Step 8: Set the number of iterations for centroid refinement, gradually approaching a reasonable centroid. in This represents the number of iterations for centroid refinement. Step 9: This statistical parameter calculates the SSE from each point in the cluster to the cluster center, using the following formula: in This represents the number of algorithm iterations. It calculates the SSE value from each point in the cluster to the cluster center in each operation result and selects the result with the smallest SSE. Step 10: The relevant constraints of the reference values ​​obtained by the SSE-KPP algorithm are described as follows: in and These represent the minimum and maximum values ​​of the attribute reference values, respectively. and These represent the minimum and maximum values ​​of the reference result, respectively. and This represents the set of attribute reference values ​​and result reference values ​​generated by the SSE-KPP algorithm, which is indicated as the set of a and r reference values.

4. The method for assessing the health status of complex systems based on D-BRB according to claim 1, characterized in that: In step three, a set of confidence rule base models is dynamically constructed. The BRB confidence rule base is used to build the evaluation model, ER rules are used as the inference engine, and a reference value set is introduced to construct the confidence rule base model. The modeling process is as follows: (1) Description of BRB knowledge base The model is constructed using IF-THEN rules, where the k-th confidence rule is defined as follows: in This represents the k-th confidence rule in the BRB model; This indicates M prerequisite attributes; M represents the number of attributes. A set of reference values ​​corresponding to M attributes; This represents the confidence distribution corresponding to N results; Represents N results; It is the rule weight of the k-th confidence rule; The weight of the i-th attribute is represented by L; L represents the number of rules. (2) BRB reasoning process For BRB, ER rules are often used as the inference engine. The specific inference process of the BRB model is as follows: Step 1: Input Conversion Determining the confidence distribution of the input value corresponding to the reference value is often done using a membership function. The final confidence distribution is described as follows: in This represents the j-th reference value in the i-th attribute. express about Confidence level; Step 2: Calculate activation weights Step 2.1: Calculate the reference value matching degree: Where J represents the number of reference values ​​and the reference value matching degree. The matching degree for the k-th rule is calculated as follows: in This indicates the matching degree corresponding to the k-th rule. This represents the normalized weight of the i-th attribute; Step 2.2: Matching degree normalization: By aggregating the corresponding matching degrees, the calculation method for the activation rule is obtained: in Indicates the activation weight of the rule; Step 3: Rule Fusion Using ER rules for rule fusion, the confidence level for the nth result is: in This represents the confidence level of the nth result; (3) Utility calculation Calculate the expected utility value and derive the final output: in Represents a set consisting of confidence distributions. This represents the actual input vector. express The effect, It is the ultimate expected utility; (4) A new form of BRB set construction This study extensively incorporates the obtained attribute reference value set. and result reference value set This approach constructs a diverse integrated BRB model structure, which covers almost all model structures and provides a basis for selecting the appropriate model structure for different needs. By constructing model integration, the relationship between different sets of reference values ​​is systematically explored, and the optimal model structure is determined. For each model structure, its performance in the evaluation task is evaluated, and the most suitable model structure is selected according to the requirements. This comprehensive consideration of different structures provides greater flexibility and accuracy to adapt to various evaluation needs. A new form of BRB set construction is proposed, as shown in the equation: 。 5. The method for assessing the health status of complex systems based on D-BRB according to claim 1, characterized in that: In step four, the confidence rule base is combined with dynamic optimization, specifically implemented as follows: (1) Dynamic optimization strategy for model set When constructing multiple sets of models, if the result parameter set is small, optimization is performed directly on the model set; if the result parameter set is large, the proposed dynamic optimization strategy is used for optimization. Assume there are K sets of reference values, with a maximum number of reference values. The flowchart of the dynamic optimization strategy is shown in Figure 3, and the steps are as follows: Step 1: When At that time, the entire model is built directly. Construct the following model: ； Step 2: Optimize the constructed BRB model and perform the following operations: Step 2.1: When ,but ; Step 2.2: When ,make Perform optimizations on the following models: ； Step 2.3: When , Perform optimizations on the following models: ； By recursively executing steps 2.1-2.3 for optimization, the final result is determined. ; (2) D-BRB optimization At the current stage of research, many high-performance algorithms have been used in the model optimization process. A commonly used optimization algorithm for the BRB model is the P-CMA-ES algorithm, and the steps of the P-CMA-ES algorithm are as follows: Step 1: Determine the initial set of optimization parameters , in For the initial optimization parameter vector, This is the initial average value; Step 2: Determine the objective function and constraints. The mean squared error (MSE) represents the modeling accuracy of BRB, and the calculation formula is as follows: Where T is the amount of observed data, It is the actual output of the system. This is the diagnosis result of BRB; Based on the above definition, the objective function and constraints are as follows: ； Step 3: Perform the sampling operation. in This represents the i-th solution in the (g+1)-th generation. Indicates the step size. Indicates a normal distribution. Denotes the covariance matrix in the g-th generation; Step 4: Perform a projection operation to satisfy the constraints. Among them, the hyperplane is used express, This indicates the number of variables in the solution that represent equality constraints. express The number of equality constraints in the solution. Represents a parameter vector; Step 5: Perform a selection operation to update the average value. , This represents the weight coefficient of the i-th solution. Represents the (g+1)th generation The i-th solution in the solution, Indicates the size of the offspring population; Step 6: Perform the adaptation operation to update the covariance matrix. The step size is updated using the following formula: in, , Defined as the learning rate, Defined as an evolutionary path, Defined as the backward time span of an evolutionary path; Step 7: Recursively execute the above process until the optimal solution is obtained. .

6. The method for assessing the health status of complex systems based on D-BRB according to claim 1, characterized in that: In step six, a complex system health status assessment model with dynamic optimization and high accuracy is established based on a dynamic confidence rule base.

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