Product reliability evaluation method and system based on multi-information measurement fusion

Abstract

The invention relates to the technical field of product reliability evaluation, in particular to a product reliability evaluation method and system based on multi-information measurement fusion. The method comprises the following steps: acquiring an unknown parameter of life distribution adapted to an evidence source, generating a parameter interval for the unknown parameter, and generating basic probability distribution associated with the parameter interval based on the evidence source; calculating correlation coefficients between the evidence sources based on the basic probability distribution, and generating importance weights according to a plurality of correlation coefficients of the evidence sources and other evidence sources; calculating the information entropy of the evidence source, and obtaining a credibility weight through normalization based on the information entropy; carrying out normalization on an operation result of the importance weight and the credibility weight to obtain an evidence weight; taking the evidence weight as a weight coefficient of basic probability distribution, and obtaining comprehensive probability distribution through evidence fusion; and carrying out parameter estimation on unknown parameters based on comprehensive probability distribution, and substituting an estimation result into a reliability function to carry out reliability evaluation, so that reliability evaluation under fault-free data is realized.

Description

Technical Field

[0001] This invention relates to the field of product reliability assessment technology, and specifically to a product reliability assessment method and system based on the fusion of multiple information measures. Background Technology

[0002] Traditionally, reliability assessments of long-life products are based on failure data. However, for long-life products with high reliability, long lifespan, and scarce sample sizes, sufficient failure data is difficult to obtain within a reasonable timeframe due to multiple constraints such as testing cycles, life testing costs, R&D cycles, and equipment limitations. Therefore, how to utilize fault-free data as evidence for reliability assessment is a pressing issue that needs to be addressed. Summary of the Invention

[0003] The purpose of this invention is to address the technical problem in existing technologies where it is difficult to obtain failure data of long-life products for reliability assessment using fault-free data. This invention provides a product reliability assessment method and system based on multi-information metric fusion. First, fault-free data following a Weibull distribution is used as evidence sources to obtain unknown parameters of the lifespan distribution. Based on multiple parameter intervals of the unknown parameters, a parameter identification framework is constructed using evidence theory methods. Then, evidence sources are screened by quantifying the differences between them. For the screened evidence sources, information measures are obtained in two aspects: the correlation between evidence sources and the reliability of the evidence sources themselves. When fusing evidence sources, multi-information measures from multiple evidence sources are introduced as coefficients of the corresponding evidence, representing the different degrees of influence of different evidence sources on product reliability assessment. Next, the basic probability assignments of multiple evidence sources are fused into a comprehensive probability assignment, and a probability density function is constructed using this comprehensive probability assignment. Finally, the first-order moment estimation method is used to estimate the parameters based on the probability density function, obtaining estimated values ​​of the unknown parameters. Substituting these estimated values ​​into the reliability function achieves reliability assessment under fault-free data, which helps improve the accuracy of product reliability assessment.

[0004] To achieve the above-mentioned objectives, this application provides the following technical solutions: A product reliability assessment method based on multi-information metric fusion includes: Obtain unknown parameters of the lifetime distribution adapted to the evidence source, generate parameter intervals for the unknown parameters, and generate a basic probability allocation associated with the parameter intervals based on the evidence source; The correlation coefficients between the evidence sources are calculated based on the basic probability allocation, and importance weights are generated based on the correlation coefficients between the evidence source and other evidence sources. Calculate the information entropy of the evidence source, and obtain the credibility weight based on the information entropy through normalization; The results of calculating the importance weight and the credibility weight are normalized to obtain the evidence weight; Using the evidence weights as the weight coefficients for the basic probability allocation, a comprehensive probability allocation is obtained through evidence fusion; based on the comprehensive probability allocation, the unknown parameters are estimated, and the estimation results are substituted into the reliability function for reliability assessment.

[0005] This application also provides a product reliability assessment system based on multi-information metric fusion, including: The evidence module is configured to obtain unknown parameters of the lifetime distribution adapted to the evidence source, generate a parameter range for the unknown parameters, and generate a basic probability allocation associated with the parameter range based on the evidence source. The first measurement module is configured to calculate the correlation coefficient between the evidence sources based on the basic probability allocation, and generate importance weights based on multiple correlation coefficients between the evidence sources and other evidence sources. The second measurement module is configured to calculate the information entropy of the evidence source and obtain the credibility weight based on the information entropy through normalization. The fusion module is configured to normalize the calculation results of the importance weight and the credibility weight to obtain the evidence weight; The evaluation module is configured to use the evidence weights as weight coefficients for the basic probability allocation, obtain a comprehensive probability allocation through evidence fusion, estimate the unknown parameters based on the comprehensive probability allocation, and substitute the estimation results into the reliability function for reliability evaluation.

[0006] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Addressing the challenge of obtaining failure data for reliability assessment of long-life products during testing, this application determines the lifespan distribution using fault-free data acquired during testing. Using this fault-free data as the data source, unknown parameters within the lifespan distribution are estimated. These estimated values ​​are then substituted into a reliability function to achieve product reliability assessment based on fault-free data. Importance weights are obtained by quantifying the correlation between evidence sources, and credibility weights are obtained by quantifying the information content of each evidence source. This measures the information of evidence sources from both their contribution to reliability assessment and their overall reliability. A multi-information measurement fusion formula synthesizes the importance and credibility weights into evidence weights, and the Dempster synthesis rule is used to obtain the basic probability allocation under multi-dimensional information, effectively overcoming the shortcomings of subjective weighting in traditional evidence fusion.

[0007] 2. The multi-information measure fusion provided in this application quantifies the contribution of an evidence source to product reliability assessment by measuring the cumulative correlation between that evidence source and other evidence sources; and quantifies the reliability of an evidence source to product reliability assessment by measuring its own information content. Then, the evidence weight is determined by the proportion of the evidence source's importance weight and credibility weight among all evidence. By using evidence weights to represent the influence of different evidence sources relative to other evidence sources, this reflects the differences in how different evidence sources support the same proposition, which helps reduce the impact of conflicts between evidence sources on evidence fusion and improves the reliability of the multi-information measure fusion results. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the product reliability assessment system based on multi-information metric fusion in this application; Figure 2 This is a flowchart illustrating the product reliability assessment method based on multi-information metric fusion proposed in this application. Figure 3 This is a flowchart illustrating the process of calculating importance weights in multi-information measure fusion. Figure 4 A comparison curve of the probability density function and the true value obtained by three evidence fusion methods; Figure 5 A comparison curve of the reliability functions and true values ​​obtained from three evidence fusion methods; Figure 6 This is a comparison curve of the reliability function and the true value obtained by the multi-information measurement fusion method and the E-Bayes method. Detailed Implementation

[0009] It should be noted that the following detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments, features, and technical solutions in the embodiments of the present invention can be combined with each other.

[0010] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, it should be noted that the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0011] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0012] For example Figure 1 The diagram shown is a structural schematic of a product reliability assessment system based on multi-information metric fusion provided in this embodiment. In one embodiment of this application, the system includes: The evidence module is configured to obtain unknown parameters of the lifetime distribution adapted to the evidence source, generate parameter intervals for the unknown parameters, and generate a basic probability allocation associated with the parameter intervals based on the evidence source. The first measurement module is configured to calculate the correlation coefficient between evidence sources based on the basic probability allocation, and generate importance weights based on multiple correlation coefficients between the evidence sources and other evidence sources. The second measurement module is configured to calculate the information entropy of the evidence source and obtain the credibility weight based on the information entropy through normalization. The fusion module is configured to normalize the results of the calculation of importance weight and credibility weight to obtain evidence weight; The evaluation module is configured with weight coefficients based on evidence weights as the basic probability allocation, and obtains a comprehensive probability allocation through evidence fusion; based on the comprehensive probability allocation, it performs parameter estimation on unknown parameters, and substitutes the estimation results into the reliability function for reliability assessment.

[0013] The system is used to execute a product reliability assessment method based on multi-information metric fusion provided in this application. For example... Figure 2 The diagram shown is a flowchart illustrating a product reliability assessment method based on multi-information metric fusion provided in this embodiment. In one embodiment of this application, the method includes: Obtain the unknown parameters of the lifetime distribution adapted to the evidence source, generate parameter intervals for the unknown parameters, and generate a basic probability allocation associated with the parameter intervals based on the evidence source. The correlation coefficient between evidence sources is calculated based on the basic probability allocation, and importance weights are generated based on multiple correlation coefficients between the evidence sources and other evidence sources. Calculate the information entropy of the evidence source, and obtain the credibility weight based on the information entropy through normalization; The results of calculating the importance weight and the credibility weight are normalized to obtain the evidence weight; Using evidence weights as the weighting coefficients for the basic probability allocation, a comprehensive probability allocation is obtained through evidence fusion; based on the comprehensive probability allocation, parameter estimation is performed on the unknown parameters, and the estimation results are substituted into the reliability function for reliability assessment.

[0014] Specifically, fault-free data refers to a dataset in which a product has not experienced any failures within a specified testing or observation period. Fault-free data relevant to the reliability assessment of long-life products can be collected through multiple channels, including sensor detection, accelerated life testing, on-site maintenance records, and expert experience reviews. This data includes, but is not limited to, time-truncated test data, fixed-number truncated test data, and continuous operation cumulative time data. Fault-free data undergoes standardized preprocessing, such as removing abnormal data caused by equipment failure or human error, and using linear interpolation to complete missing data.

[0015] In this embodiment, right-truncated data from timed-truncation test data is used as an example. It is assumed that there are n samples in total, divided into k groups, and different truncation times are set for each group of samples. The fault-free data collected by the sensor comes from the monitoring time of the monitoring equipment. and the number of samples that did not fail at that time Composition, including monitoring time As the cutoff time, the fault-free data monitored by the sensor throughout the entire test is represented as follows: ; ; Where i is the index, and i is less than or equal to k; Let be the cutoff time for the i-th sample group. ; Let be the number of samples in the i-th group. The fault-free data (t, n) serves as the k evidence sources for the DS evidence theory. Experts determine the current product's lifetime distribution based on the product failure mechanism, historical data characteristics, and the statistical regularities of fault-free data in engineering scenarios. The lifetime distributions applicable to this application include, but are not limited to, the Weibull distribution, the log-normal distribution, and the Gamma distribution.

[0016] Taking the lifetime distribution of fault-free data that follows a Weibull distribution as an example, the three parameters of the Weibull distribution are the shape parameter m, the scale parameter m, and the time distribution. and position parameters In practical engineering, it is generally believed that products gradually fail from the very beginning of operation, meaning that the risk of failure exists at time t=0. The location parameters of the Weibull distribution are only introduced when failure data clearly exists in the initial, failure-free phase. Secondly, the sample size of fault-free data is relatively small, especially considering location parameters. This could make the estimation results abnormally sensitive to the setting of the censoring time. Therefore, this embodiment uses a two-parameter Weibull distribution, treating the timed censoring experiment of the right-truncated data as a successive timed censoring experiment, with the shape parameter m and scale parameter... Under the condition of truncation time Reliability function as a random variable following a Weibull distribution The formula is as follows: ; in, Let i be the cutoff time for the i-th group of products; For unknown parameters m and The resulting vector represents the coefficients that influence the random variable; where, , Let m be the scale parameter and m be the shape parameter. Their values ​​depend on the product's failure mechanism, material properties, manufacturing process, and other inherent attributes. The value of m can be used to distinguish different failure types, such as early failure, accidental failure, and wear-out failure. It is important to note that the unknown parameter vector... The number of vector components in the middle is equal to the number of unknown parameters in the lifetime distribution.

[0017] Based on expert experience or historical lifespan data of similar products, a parameter domain is defined for the unknown parameter vector. This parameter domain is then divided into multiple mutually exclusive parameter intervals to reflect the uncertainty of the unknown parameters. The number of parameter intervals is preset based on expert experience. In this embodiment, the length of each parameter interval is uniformly divided.

[0018] Furthermore, based on the evidence theory approach, for the unknown parameter vector The parameter ranges are combined, and one parameter range is taken from each of the multiple parameter ranges corresponding to each unknown parameter to form a basic element. Multiple basic elements are combined to obtain a parameter recognition framework. Based on the parameter recognition framework, a parameter recognition framework is generated. The power set of subsets, these subsets are propositions, where... Let be the number of basic elements in the parameter identification framework, and be the product of the number of intervals in the parameter interval. By statistically analyzing the probability that fault-free data falls into the parameter interval, the basic probability assignment of fault-free data from the i-th evidence source to the power set is calculated, thus obtaining the evidence corresponding to the i-th evidence source. The propositions corresponding to basic probability assignments greater than 0 in the evidence are the focal elements.

[0019] Furthermore, information measures are used to quantify the relationship between information uncertainty and information content. In this embodiment, the contribution of an evidence source to product reliability assessment relative to other evidence sources, as well as the reliability of the evidence source itself, are used as information measures. The correlation between evidence sources and the information content of each evidence source are calculated as the results of the information measures. Finally, the results of the information measures of multiple evidence sources are used as evidence weights, and the basic probability allocations corresponding to multiple evidence sources are fused into a single basic probability allocation using evidence fusion methods such as Dempster's synthesis rule, thus achieving the fusion of multiple information measures.

[0020] In the DS evidence theory, the degree of support for the same proposition from different sources of evidence may vary due to data source, acquisition method, or noise interference. The higher the correlation between two sources of evidence, the more similar their support for the same proposition, indicating a lower likelihood of conflict when these two sources are integrated. Conversely, the lower the correlation, the greater the difference in support for the same proposition, indicating a significant conflict or non-linear relationship between the two sources. By assigning basic probability to the proposition from the sources of evidence, and using methods such as Pearson correlation coefficient and partial correlation coefficient, the correlation coefficient between any two sources of evidence is calculated. Then, multiple correlation coefficients between one source of evidence and other sources are calculated using statistical methods such as summation and product calculation. The results are used as importance weights, or additional weight coefficients are added to the results to generate importance weights, to represent the contribution of the evidence source to the product reliability assessment.

[0021] The amount of information contained in the evidence source itself also affects product reliability assessment. The more information a evidence source contains, the greater the uncertainty, and the lower the accuracy of the product reliability assessment result. Therefore, by using formulas such as Shannon entropy or Kartley entropy, the information entropy representing the average amount of information in the evidence source is calculated. This information entropy is then normalized using methods such as proportional normalization or min-max normalization to calculate the proportion of an evidence source's information entropy to the total information entropy of all evidence sources. This proportion is used as a credibility weight, or a further weighting coefficient is added to this proportion to generate a credibility weight, thus representing the reliability of the evidence source in the product reliability assessment.

[0022] Furthermore, multi-information measure is a joint measurement of the contribution of multiple evidence sources to product reliability assessment and their own reliability. By constructing a two-factor weighted model, the relative influence of each evidence source in the evidence fusion system is quantified. Multi-information measure operations are performed on the importance weight and credibility weight, such as calculating the statistical results of summation and product. The operation results are then normalized by methods such as proportional normalization or min-max normalization to calculate the proportion of the multi-information measure of one evidence source in the multi-information measures of all evidence sources. This proportion is used as the evidence weight. The formula is as follows: ; in, Let be the importance weight corresponding to the i-th evidence source; is the credibility weight corresponding to the i-th evidence source; k is the number of evidence sources.

[0023] Furthermore, when dealing with multiple conflicting sources of evidence using the Dempster synthesis rule in DS evidence theory, the framework for identifying the same parameter for multiple sources of evidence is discussed. After generating multiple pieces of evidence and calculating the evidence weight for each piece of evidence, the evidence weight is used as the weighting coefficient for the basic probability allocation of the proposition in each piece of evidence. The weighted evidence is then fused using the Dempster synthesis rule, as follows: ; in, The basic probability allocation after synthesizing all evidence is denoted as the comprehensive probability allocation. This refers to all mutually exclusive propositions among the evidence. For the first A proposition, For the first The basic probability distribution of a proposition; This represents the sum of the products of the basic probability assignments of all completely mutually exclusive propositions, used to indicate the overall degree of conflict among all evidence. Conflicting propositions are those that cannot coexist within the parameter identification framework; these propositions contradict each other. The larger the product of the basic probability assignments, the more severe the conflict among the evidence.

[0024] Given the differences in monitoring mechanisms and accuracy among different sensors, the feedback information is uncertain, leading to variations in how different evidence sources support the same proposition. Therefore, when fusing multiple pieces of evidence, the basic probability allocation needs to be corrected. Traditional methods rely solely on domain experts' subjective evaluations of evidence to assign weights. This approach is susceptible to the influence of experts' personal experience and cognitive biases, making it difficult to objectively reflect the actual contribution of each evidence source. The multi-information measure fusion method provided in this application quantifies the contribution of an evidence source to product reliability assessment by measuring the cumulative correlation between that source and other evidence sources; and quantifies the reliability of the evidence source's contribution by measuring its own information content. The weight of the evidence source is then determined by its proportion of importance and credibility weights among all evidence. By using evidence weights to represent the influence of different evidence sources relative to others, this method reflects the differences in how different evidence sources support the same proposition, helping to reduce the impact of conflicts between evidence sources on evidence fusion and improving the reliability of the multi-information measure fusion results.

[0025] Furthermore, after fusing all evidence, parameter estimation is performed based on the comprehensive probability allocation to calculate the estimated values ​​of the unknown parameters. Parameter estimation methods include, but are not limited to, the method of moments (MA) and likelihood estimation. The calculation of unknown parameters relies on statistical inference, but statistical methods require that the data or variables have randomness. Since the divided parameter intervals lack this randomness, it is difficult to directly optimize the parameters. To estimate the unknown parameters in the lifetime distribution and determine the reliability function of the lifetime distribution, it is necessary to separately estimate the unknown parameters m and m. The corresponding multiple parameter intervals are merged and transformed into the parameter domain corresponding to the random variable. The transformation method includes: calculating the probability density function of the parameter interval by the ratio of the comprehensive probability distribution to the first value of the interval length; merging the probability density functions of multiple parameter intervals to obtain the probability density function of the unknown parameter in the parameter domain, thereby transforming the uncertainty of the continuous parameter space into a comprehensive probability distribution of the discrete interval, as shown in the following formula: ; ; Where p is the index of the parameter range, , To combine the parameter intervals into the parameter domain using probability density functions; Indicates the unknown parameter m, The number of focal points in the corresponding evidence; , The table shows the comprehensive probability allocation obtained after the fusion of multiple information measures; , For unknown parameters m, The upper limit of the interval of the p-th parameter, , For unknown parameters m, The lower limit of the interval of the p-th parameter; , For unknown parameters m, The length of the interval of the p-th parameter; , This is an indicator function used to represent m, Whether the overall probability allocation belongs to the corresponding parameter range is determined by the following formula: ; ; In this embodiment, for the unknown parameters in the comprehensive probability allocation, the first-order moment estimation method is used based on the probability density function to solve for the unknown parameters m. The estimated value : ; ; Estimate the unknown parameters Substituting the reliability function into the two-parameter Weibull distribution, the formula is as follows: ; Where t is the truncation time of long-life products, and the reliability assessment is performed by fusing multi-source data through the product's reliability function formula.

[0026] To address the challenge of obtaining failure data for reliability assessment of long-life products during testing, this application determines the lifespan distribution using fault-free data acquired during testing. Using this fault-free data as the data source, unknown parameters within the lifespan distribution are estimated. These estimated values ​​are then substituted into a reliability function to achieve product reliability assessment based on fault-free data. Importance weights are obtained by quantifying the correlation between evidence sources, and credibility weights are obtained by quantifying the information content of each source. This measures the information of evidence sources from both their contribution to reliability assessment and their overall reliability. A multi-information measurement fusion formula synthesizes the importance and credibility weights into evidence weights, and the Dempster synthesis rule is used to obtain the basic probability allocation under multi-dimensional information, effectively overcoming the shortcomings of subjective weighting in traditional evidence fusion.

[0027] In one embodiment of this application, a parameter interval is generated for the unknown parameter, and a basic probability assignment associated with the parameter interval is generated based on the evidence source, including: The parameter domain of the unknown parameters is divided into multiple parameter intervals; the interval likelihood function of the parameter interval is derived based on the likelihood function of the evidence source; a parameter identification framework is constructed using evidence theory with multiple parameter intervals corresponding to multiple unknown parameters; the ratio of the interval likelihood function of the parameter interval to the interval likelihood function of the parameter domain is used as the basic probability allocation of the power set of the evidence source for the parameter identification framework.

[0028] Specifically, if we consider the fault-free data at each truncation time as an independent source of evidence, then the fault-free data following a two-parameter Weibull distribution at each truncation time... Likelihood function of evidence sources for each data point for: ; in, Let be the truncation time for the i-th source of evidence; Let be the number of samples from the i-th evidence source; k is the number of evidence sources.

[0029] Furthermore, for the basic probability allocation of the evidence source (t, n) to the unknown parameters, the basic probability allocation is calculated based on the likelihood function of the corresponding interval of the parameter interval. This is to quantify the degree of matching between the given evidence source and multiple parameter intervals in the associated parameter domain, thereby providing data support and theoretical basis for the fusion of multiple information measures of multiple evidence sources.

[0030] Specifically, obtain the unknown parameter vector in the lifetime distribution adapted to the i-th evidence source. By setting the parameter domain of the unknown parameter vector The parameter domain is uniformly divided into multiple parameter intervals. A parameter identification framework is constructed based on these intervals using evidence theory. This involves: taking one parameter interval from each of the multiple intervals corresponding to each unknown parameter to form an unordered pair; using these unordered pairs as basic elements; and combining all basic elements to obtain the parameter identification framework. It is important to note that the opening and closing conditions of the parameter intervals do not affect the value of the interval likelihood function.

[0031] In this embodiment, the unknown parameter vector Represented as: ; Where y is the index of the unknown parameter, and y is less than or equal to the number of unknown parameters z; Let y be the y-th unknown parameter. For example, in this embodiment, when the fault-free data follows a two-parameter Weibull distribution, , In other implementations, for example, if fault-free data follows a normal distribution, , The parameter domain of the unknown parameter vector. Represented as: ; in, Let y be the minimum value of the y-th unknown parameter. This represents the maximum value of the y-th unknown parameter. Therefore, for the unknown parameter... The parameter domain can be divided into multiple parameter intervals as follows: ; Where p is the index of the parameter interval, and p is less than or equal to the number of intervals Y of the parameter interval; Let be the interval boundary of the p-th parameter interval for the y-th unknown parameter. The interval length of each parameter interval is equal, i.e. .

[0032] Accordingly, for the i-th source of evidence, let Let be the upper limit of the interval of the p-th parameter of the unknown parameter vector. Let be the lower bound of the interval of the p-th parameter of the unknown parameter vector. Correspondingly, this can be determined through the unknown parameters. The upper and lower limits are represented as follows: ; ; in, Let be the upper limit of the interval of the p-th parameter for the y-th unknown parameter. Let be the lower bound of the interval of the p-th parameter of the y-th unknown parameter. Therefore, the interval of the unknown parameter can be expressed as: A parameter identification framework built on parameter ranges. Represented as: ; The number of basic elements in the parameter recognition framework ,in Let be the number of intervals for the y-th unknown parameter. Accordingly, the parameter identification framework can be simplified to... .

[0033] Furthermore, based on the likelihood function corresponding to fault-free data For multiple parameter ranges of unknown parameters Define the interval likelihood function , is used to represent the degree of support of the evidence source for the corresponding parameter range, and the formula is as follows: ; in, Let p be the vector of unknown parameters corresponding to the p-th parameter interval. Let p be the evidence source corresponding to the p-th parameter interval. The degree of support of the evidence source for the parameter interval is measured using a data-driven interval likelihood function. Since the parameter domain and parameter interval settings are the same for each evidence source and in the parameter identification framework, the ratio of the interval likelihood function of each parameter interval to the interval likelihood function of the entire parameter domain is used as the basic probability allocation of the evidence source for the power-set propositions of the parameter identification framework. The formula is as follows: ; in, It is the interval likelihood function of the unknown parameter across the entire parameter domain; Let be the interval likelihood function for the p-th parameter interval in the parameter domain.

[0034] In one embodiment of this application, after generating a basic probability allocation based on the evidence source and the parameter range, the method further includes: calculating a difference measure based on the basic probability allocation between evidence sources, and using evidence sources with a difference measure less than a difference threshold for evidence fusion.

[0035] Specifically, in this embodiment, the Jousselme distance is preferably used to quantify the differences between evidence sources, so as to use the degree of conflict between evidence sources as a key basis for multi-information fusion and screening. Specifically, for the parameter identification framework... The two pieces of evidence below have the following basic probability assignments: and The formula for calculating the Jousselme distance between these two pieces of evidence is as follows: ; in, This is a similarity matrix, where elements in the matrix... For evidence, Jiao Yuan and The Jaccard similarity coefficient between the two is used to represent the similarity between subsets of the power set of the parameter recognition framework. The calculation formula is as follows: ; in, Power set for parameter identification framework The number of all subsets in The number of basic elements in the parameter identification framework.

[0036] It is important to note that a piece of evidence is a set of basic probability assignments for multiple subsets. Therefore, in other embodiments, evidence can be viewed as a vector, and the quantification method for measuring the difference between evidence sources can be to calculate the cosine similarity between the evidence sources using this vector; or to calculate the Euclidean distance based on the difference between the confidence function and the similarity function between the evidence sources using the confidence function and the similarity function corresponding to the basic probability assignments.

[0037] Because evidence fusion generates a corresponding piece of evidence from each source, and each piece of evidence contains multiple focal elements used to calculate the product of basic probability assignments, the computational workload increases. To reduce the occurrence of focal element explosion, evidence sources are filtered based on their differences. The smaller the difference between two evidence sources, the higher the similarity. By calculating the difference between evidence through basic probability assignments, evidence sources with higher similarity are selected, which helps improve the accuracy of the multi-information fusion process and also reduces computational complexity.

[0038] For example Figure 3 As shown, in one embodiment of this application, importance weights are generated based on multiple correlation coefficients between the evidence source and other evidence sources, including: After calculating the correlation coefficient, a correlation matrix is ​​constructed with the evidence sources as rows and columns, and the correlation coefficients as elements. The sum of the correlation coefficients between any evidence source and other evidence sources in the correlation matrix is ​​used as the importance weight.

[0039] Specifically, in the DS evidence theory, the degree to which different sources of evidence support the same proposition may vary due to differences in data source, acquisition method, or noise interference. The higher the correlation between sources of evidence, the closer their support for the same proposition, and the lower the likelihood of conflict during fusion; the lower the correlation, the more significant the conflict or non-linear relationship between the sources of evidence, making fusion difficult and requiring screening or further analysis.

[0040] In a preferred embodiment, when fusing multiple evidence sources, the basic probability distribution of focal elements in the evidence from two different sources is obtained, and the covariance and standard deviation are calculated respectively. Then, the Pearson correlation coefficient between the two pieces of evidence is calculated as the correlation coefficient to quantify the degree of linear correlation between the evidence sources. (Pearson correlation coefficient) The calculation formula is as follows: ; in, , Assign basic probabilities to evidence i and evidence j; Let i and j be the covariances; , The average of the basic probability assignments for evidence i and evidence j; , The variance is assigned to the basic probabilities of evidence i and evidence j. A correlation matrix is ​​constructed, representing the global correlation level, with the evidence sources as row and column elements and the Pearson correlation coefficient as matrix element values.

[0041] ; in, This is a correlation matrix; N is the number of pieces of evidence. The Pearson correlation coefficient is used. In this embodiment, based on the basic probability allocation of evidence, the sum of the correlation coefficients between any one evidence source and other evidence sources is used as the importance weight. That is, the first result is obtained by summing the correlation coefficients of each row in the correlation matrix, and the first result is used as the importance weight of the evidence source corresponding to each row. It should be noted that this embodiment can also be applied to the fusion of two evidence sources.

[0042] In another implementation, if the number of evidence sources is less than 3, the Pearson correlation coefficient between the evidence sources can be directly calculated as the importance weight.

[0043] Furthermore, a correlation matrix is ​​constructed based on the correlation coefficients, including: The correlation coefficient matrix is ​​obtained by using the correlation coefficients as matrix elements. Treat the evidence sources as graph nodes. If the correlation coefficient between two evidence sources is greater than zero, connect the corresponding graph nodes with undirected edges. Generate a weighted undirected graph by associating the correlation coefficient with the undirected edges. Generate an adjacency matrix based on the weighted undirected graph and use the adjacency matrix as the correlation matrix.

[0044] Specifically, when the Pearson correlation coefficient is less than or equal to 0, it indicates that the two pieces of evidence are negatively correlated or uncorrelated. The correlation coefficients of these two evidence sources show different levels of support for the same proposition, therefore, calculating the importance weight is meaningless. To reduce computational complexity, in this embodiment, when constructing the correlation matrix based on the correlation coefficient, the evidence sources are used as row and column elements, and the Pearson correlation coefficient is used as the matrix element value to construct the correlation coefficient matrix. Each evidence source is used as a graph node, and the correlation coefficient matrix is ​​mapped to an adjacency matrix of a weighted undirected graph to obtain the contribution of positively correlated evidence sources. Specifically, if the Pearson correlation coefficient between two evidence sources is greater than zero, an undirected edge is connected between the corresponding graph nodes; otherwise, no connection is made between the graph nodes. The correlation coefficient and the undirected edge are associated; for example, the weight value of the undirected edge is set to the Pearson correlation coefficient. An adjacency matrix is ​​constructed based on the weighted undirected graph. : ; In this context, the rows and columns of the adjacency matrix represent evidence. Let be the absolute value of the Pearson correlation coefficient between the evidence sources; N be the number of evidence sources. The adjacency matrix is ​​used as the correlation matrix. The sum of the correlation coefficients between one piece of evidence and all other evidence in the correlation matrix, i.e., the sum of the Pearson correlation coefficients in the i-th row, is used as the importance weight. By calculating the Pearson correlation coefficients between each pair of evidence sources, undirected edges are connected between the graph nodes corresponding to positively correlated evidence. This maps the correlation coefficients between multiple pieces of evidence into the adjacency matrix of a weighted undirected graph, enabling the filtering of positive correlations between evidence sources. This helps reduce the interference of negative and no correlations, improving the accuracy of quantifying the contribution of evidence sources to product reliability assessment.

[0045] Furthermore, the sum of the correlation coefficients between any one source of evidence and other sources of evidence in the correlation matrix is ​​used as the importance weight, including: Obtain the correlation coefficient between any evidence source and other evidence sources, count the first number of all non-zero correlation coefficients, and use the product of the first number and the importance weight as the new importance weight.

[0046] Specifically, the higher the similarity of a particular source of evidence to other sources of evidence, the greater its contribution and influence in product reliability assessment, and therefore it should be given a larger weight. Thus, in this embodiment, after constructing a correlation matrix using correlation coefficients, the Pearson correlation coefficient in the i-th row of the correlation matrix is ​​obtained. The first count of non-zero Pearson correlation coefficients in the i-th row is then calculated. The sum of the Pearson correlation coefficients in the i-th row is then used to obtain a second result. The product of the first count and the second result is taken as the importance weight of the i-th source of evidence, as shown in the following formula: ; in, This represents the first count of non-zero elements in the i-th row. These are matrix elements in the correlation matrix.

[0047] In one embodiment of this application, generating a credibility weight for an evidence source based on information entropy includes: using the ratio of the information entropy of any evidence source to the sum of the information entropies of all evidence sources as the credibility weight.

[0048] Specifically, in this embodiment, information entropy is used to reflect the amount of information contained in the evidence source, and is set as the credibility weight of the evidence source. A higher entropy value indicates a stronger uncertainty about the proposition from the evidence source, and provides less effective information; conversely, a lower entropy value indicates a weaker uncertainty about the proposition from the evidence source, and provides more explicit information. Based on the basic probability allocation of each proposition corresponding to the evidence source, the corresponding information entropy is calculated using the Shannon entropy formula. To quantify the uncertainty of evidence sources, the formula is as follows: ; in, For the corresponding parameter range The basic probability distribution; The number of propositions. When dealing with sources of evidence with uncertainty, reducing the credibility weight of sources with lower credibility can effectively accelerate the fusion process of multiple information measures. Credibility weights are obtained based on proportional normalization of information entropy. The formula is as follows: ; in, The information entropy of the i-th evidence source; the credibility weight. The range of values ​​is .

[0049] In one embodiment of this application, to verify the effectiveness and rationality of the product reliability assessment method based on multi-information metric fusion proposed in this application in processing fault-free data scenarios, the multi-information metric fusion method is compared and analyzed with two other methods. Parameters used. , 600 random number samples were generated and sorted in ascending order to construct an ordered set of 60 data groups, each containing 10 observations. The first 10 data groups were selected, and the minimum value within each group was taken. A number slightly smaller than this minimum value was selected as the cutoff point, which can be considered as a point at which no failure is expected. In the simulation example, assuming 55 electric spindle systems were tested, with the sample size of electric spindles decreasing sequentially in each group, a set of fault-free data for electric spindles was obtained. Specific data is shown in Table 1. Table 1. Trouble-free data of the electric spindle ; Based on expert knowledge and historical experience, the unknown parameters m and are given for this fault-free dataset. parameter domain For example, as shown in Table 2, Table 2 Parameter Field Settings ; To avoid focal explosion, the original evidence sources were screened based on Jousselme distance, ultimately selecting data with sample numbers 1, 5, and 10 as core evidence sources, which were further evaluated quantitatively based on their importance and credibility. For the unknown parameter m, the parameter domain was evenly divided into 5 parameter intervals with an interval of 0.1; for the unknown parameter... The parameter domain was evenly divided into 5 parameter intervals at intervals of 120 pairs. The basic probability distribution of the parameter intervals calculated according to Dempster's composition rule is shown in Table 3. Table 3 Basic probability distribution of parameter intervals ; The evidence weights of the three evidence sources using multi-information measures are calculated, as shown in Table 4. Table 4. Weight of Evidence ; It can be seen that evidence source 5 is optimal. Based on the reliability function formula of the two-parameter Weibull distribution, the point estimates of the unknown parameters are calculated. and .

[0050] In this embodiment, to verify the rationality of multi-information measure fusion in product reliability assessment, the multi-information measure fusion method is compared with two DS evidence fusion methods using relative error (MRE). Relative error (MRE) is an important indicator for measuring the degree of difference between the estimated value and the true value. It compares the absolute error with the true value and expresses the magnitude of this difference as a percentage. The comparison results are shown in Table 5. Table 5. Comparison of parameter estimation results for the three DS evidence fusion methods ; in, For iterative fusion methods, For information fusion methods with equal weights, This is a multi-information measure fusion method. It can be seen that the multi-information measure fusion method... It is more accurate in parameter estimation results and has a lower relative error compared to iterative fusion methods. Equal-weight information fusion method Multi-information measurement fusion method The relative errors after fusion are all less than This indicates that evidence screened using the Jousselme distance as a measure of dissimilarity is more representative. Furthermore, the multi-information measure fusion method... The relative error is less than that of the equal-weighted information fusion method. This demonstrates that the multi-information fusion method, which considers importance and credibility, is effective and reasonable, and also shows that this fusion method can more effectively improve the accuracy of parameter estimation.

[0051] Point estimates of unknown parameters and Substituting the probability density function of fault-free data, the formula is as follows: ; A comparison of the probability density function curves of three DS evidence fusion methods and the true value (True), for example. Figure 4 As shown. Point estimates of unknown parameters. and Substituting the reliability function of fault-free data, the formula is as follows: ; A comparison of the reliability function curves for three DS evidence fusion methods and the true value (True), for example. Figure 5 As shown in Table 5 and Figure 5 It can be seen that the estimated value obtained by using DS evidence multi-information measure fusion is closer to the true value, indicating that using multi-information measure fusion to estimate the unknown parameters of fault-free data is effective and feasible.

[0052] In another embodiment, to evaluate the superiority of the proposed method in a fault-free data scenario, multi-information metric fusion is compared with the E-Bayes method. The comparison results are shown in Table 6. Table 6 Comparison of parameter estimation results between E-Bayes and multi-information metric fusion ; It can be seen that multi-information measure fusion is more accurate in parameter estimation results, with a lower relative error. Based on the parameter estimation results, the reliability function of the E-Bayes method can be derived. Reliability function of M3, a multi-information fusion method for evidence based on DS. Calculate the value at each time t. , Reliability function under the true value True The deviation proportionality, where the deviation proportionality The calculation formula is: ; The reliability deviation results for each test time are shown in Table 7, for example. Table 7 Results of the proportionality of time deviation for each test ; A comparison of reliability function curves for the multi-information metric fusion methods M3 and E-Bayes, and the true value True, for example. Figure 6 As shown in Table 7, the reliability curve of the multi-information measure fusion method consistently maintains a closer fit to the true value curve, more accurately reflecting the reliability trend over time, which aligns with engineering practice. Table 7 also shows that the reliability deviation ratio between the two methods gradually increases with time. Comparing all time points, the deviation ratio of the DS evidence multi-information measure fusion method is smaller than that of the E-Bayes method, indicating that the proposed method has smaller errors and higher accuracy during calculation, further highlighting the superiority of multi-information measure fusion.

[0053] Simulation results show that the evidence-screened multi-information measure fusion method outperforms the E-Bayes method, demonstrating significant advantages in small-sample, high-uncertainty scenarios. The multi-information measure fusion method proposed in this application shows advantages in both estimation accuracy and uncertainty handling, providing a new approach and method for reliability assessment of fault-free data. Future research can further explore optimization strategies to eliminate evidence conflicts, improve evidence synthesis rules, and expand the application of the method in multi-type data, such as the fusion of faulty and fault-free data, thereby enhancing the model's universality and robustness. The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. A product reliability assessment method based on multi-information metric fusion, characterized in that, include: Obtain unknown parameters of the lifetime distribution adapted to the evidence source, generate parameter intervals for the unknown parameters, and generate a basic probability allocation associated with the parameter intervals based on the evidence source; The correlation coefficients between the evidence sources are calculated based on the basic probability allocation, and importance weights are generated based on the correlation coefficients between the evidence source and other evidence sources. Calculate the information entropy of the evidence source, and obtain the credibility weight based on the information entropy through normalization; The results of calculating the importance weight and the credibility weight are normalized to obtain the evidence weight; Using the evidence weights as the weight coefficients for the basic probability allocation, a comprehensive probability allocation is obtained through evidence fusion; Based on the comprehensive probability allocation, the unknown parameters are estimated, and the estimation results are substituted into the reliability function for reliability assessment.

2. The product reliability assessment method based on multi-information metric fusion according to claim 1, characterized in that, The step of generating a parameter range for the unknown parameters and generating a basic probability assignment associated with the parameter range based on the evidence source includes: The parameter domain of the unknown parameter is divided into multiple parameter intervals; the interval likelihood function of the parameter interval is derived based on the likelihood function of the evidence source; a parameter identification framework is constructed using evidence theory with multiple parameter intervals corresponding to the multiple unknown parameters; the ratio of the interval likelihood function of the parameter interval to that of the parameter domain is used as the basic probability allocation of the power set of the evidence source to the parameter identification framework.

3. The product reliability assessment method based on multi-information metric fusion according to claim 1, characterized in that, The step of generating importance weights based on multiple correlation coefficients between the evidence source and other evidence sources includes: Using the evidence sources as rows and columns, a correlation matrix is ​​constructed based on the correlation coefficients as elements. The sum of the correlation coefficients between any one of the evidence sources and the other evidence sources in the correlation matrix is ​​used as the importance weight.

4. The product reliability assessment method based on multi-information metric fusion according to claim 3, characterized in that, The construction of a correlation matrix based on the correlation coefficient includes: The correlation coefficients are used as matrix elements to obtain the correlation coefficient matrix; Using the evidence sources as graph nodes, if the correlation coefficient between two evidence sources is greater than zero, connect the corresponding graph nodes with undirected edges, and generate a weighted undirected graph by associating the correlation coefficient with the undirected edges; generate an adjacency matrix based on the weighted undirected graph, and use the adjacency matrix as the correlation matrix.

5. A product reliability assessment method based on multi-information metric fusion according to claim 3 or 4, characterized in that, The step of using the sum of the correlation coefficients between any one of the evidence sources in the correlation matrix and the other evidence sources as the importance weight includes: Obtain the correlation coefficient between any one of the evidence sources and the other evidence sources, count the first number of all non-zero correlation coefficients, and use the product of the first number and the importance weight as the new importance weight.

6. The product reliability assessment method based on multi-information metric fusion according to claim 1, characterized in that, The process of obtaining the credibility weight based on the information entropy through normalization includes: credibility weight based on information entropy. The formula is as follows: ； in, The basic probability assignment for the i-th evidence source; The information entropy of the i-th evidence source; The number of basic elements in the parameter identification framework formed based on the parameter range.

7. A product reliability assessment method based on multi-information metric fusion according to any one of claims 1-6, characterized in that, After generating the basic probability assignment associated with the parameter range based on the evidence source, the method further includes: A difference measure is calculated based on the basic probability allocation among the evidence sources, and evidence sources whose difference measure is less than a difference threshold are used for evidence fusion.

8. The product reliability assessment method based on multi-information metric fusion according to claim 1, characterized in that, The parameter estimation of the unknown parameters based on the comprehensive probability allocation includes: Obtain the parameter interval in which the comprehensive probability assignment is located, calculate the first ratio of the comprehensive probability assignment to the interval length to obtain the probability density function of the parameter interval; merge the probability density functions of multiple parameter intervals to obtain the probability density function of the unknown parameter in the parameter domain; perform parameter estimation based on the unknown parameter and the probability density function to obtain the estimation result.

9. The product reliability assessment method based on multi-information metric fusion according to claim 1, characterized in that, The evidence weight is obtained by normalizing the result of the calculation of the importance weight and the credibility weight, including: the normalization is proportional normalization.

10. A product reliability assessment system based on multi-information metric fusion, characterized in that, include: The evidence module is configured to obtain unknown parameters of the lifetime distribution adapted to the evidence source, generate a parameter range for the unknown parameters, and generate a basic probability allocation associated with the parameter range based on the evidence source. The first measurement module is configured to calculate the correlation coefficient between the evidence sources based on the basic probability allocation, and generate importance weights based on multiple correlation coefficients between the evidence sources and other evidence sources. The second measurement module is configured to calculate the information entropy of the evidence source and obtain the credibility weight based on the information entropy through normalization. The fusion module is configured to normalize the calculation results of the importance weight and the credibility weight to obtain the evidence weight; The evaluation module is configured to use the evidence weights as weight coefficients for the basic probability allocation, and obtain a comprehensive probability allocation through evidence fusion; Based on the comprehensive probability allocation, the unknown parameters are estimated, and the estimation results are substituted into the reliability function for reliability assessment.

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