A data expansion and reliability analysis method and system for avionics equipment

Abstract

This invention discloses a method and system for data expansion and reliability analysis of avionics equipment, comprising: collecting reliability growth test data of avionics equipment to obtain a full sample dataset and a candidate subsample set; evaluating the information content of the candidate subsample set by maximizing Rényi entropy; constructing a dual-objective collaborative optimization model of entropy constraint and distribution distance by minimizing the distribution difference between the candidate subsample set and the full sample set by minimizing the Wasserstein distance metric; determining the globally optimal subsample set and sample reuse degree by using a greedy search to traverse the sample reuse degree; establishing an avionics equipment reliability analysis model based on a two-parameter Weibull distribution; adaptively selecting a hyperparameter estimation method according to prior information conditions and model complexity and constructing a posterior distribution based on Bayes' theorem; and using a step-by-step sampling method for avionics equipment reliability analysis and life prediction. This invention achieves both information content and distribution representativeness in data expansion and reliability analysis.

Description

Technical Field

[0001] This invention relates to the field of reliability data fusion technology, specifically to a data expansion and reliability analysis method and system for avionics equipment, and more specifically to a data expansion and reliability analysis method and system for avionics equipment with entropy constraints and distribution distance optimization. Background Technology

[0002] In recent years, with the rapid development of my country's economy and technology, the scale of the civil aviation industry has continued to expand, and the complexity and reliability requirements of avionics equipment have been continuously increasing. Its reliability is directly related to flight safety and mission execution capabilities.

[0003] Traditional reliability analysis methods that rely on a single data source are gradually revealing their limitations, especially when the sample data is limited, resulting in lower accuracy and reliability of the analysis results. Specifically:

[0004] On the one hand, domestically produced avionics equipment, especially electronic modules based on printed circuit boards (such as flight control computer modules, signal processing modules, and power management modules), has a relatively short development and service life, resulting in extremely limited historical service data. On the other hand, the data provided by reliability prediction manuals such as GJB-299C and MIL-HDBK-217F are mostly based on general operating conditions, which are highly conservative and deviate significantly from the actual operating conditions of specific avionics equipment under multi-stress coupling environments such as temperature, humidity, and electrical stress. This directly leads to a structural lack of fundamental safety data for newly developed avionics equipment, thus restricting the effective implementation of its safety assessment and reliability analysis.

[0005] For key electronic components and functional modules in avionics equipment, reliability growth testing is an important way to obtain reliability data. By implementing reliability growth tests at different stages of product development, data reflecting the performance evolution of devices or modules can be obtained. This type of data can not only serve as an important supplement to traditional data sources, but also comprehensively reveal the changes in product reliability as the development process progresses. However, existing methods generally have the following problems when using this type of data: the sample size of data at each stage is small, and there is an imbalance in the amount of data information and distribution characteristics, making it difficult to achieve unified modeling and collaborative utilization.

[0006] Therefore, in the reliability analysis of electronic components and modules of avionics equipment, how to construct a data augmentation method that takes into account both the amount of information and the representativeness of the distribution and carry out reliability analysis under the conditions of scarce data samples, lack of sufficient prior information and significant differences in data distribution is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of the above problems, the present invention proposes a data expansion and reliability analysis method and system for avionics equipment that overcomes or at least partially solves the above problems. It can significantly improve the accuracy of model parameter estimation and accurately predict the life of avionics equipment without sufficient prior information, and provides an effective data expansion method and modeling means for its safety assessment and reliability analysis.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A method for data augmentation and reliability analysis of avionics equipment includes: S1. Collect reliability growth test data of key electronic components and functional modules in avionics equipment to obtain a full sample dataset, and randomly select a portion of the samples to form a candidate subsample set; S2. The Rényi entropy is used to evaluate the information content of the candidate subsample set. By maximizing the Rényi entropy, the candidate subsample set with high information content is selected. S3. The Wasserstein distance is used to measure the distribution difference between the candidate subsample set and the full sample set. By minimizing the Wasserstein distance, the candidate subsample set approximates the full sample distribution in terms of location, scale and shape features. S4. Construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization, and use a greedy search strategy to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree; S5. Construct prior information based on the optimal subsample set, and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. Adaptively select the hyperparameter estimation method according to the prior information conditions and model complexity, and construct the posterior distribution based on Bayes' theorem. Use the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

[0009] Preferably, the prior information of the candidate subset is expressed as:

[0010] in, is the order parameter of the Rényi entropy; Let be the shape parameter of the Weibull distribution, which follows a uniform distribution and takes values ​​ranging from 1 to 2. ; Let be the scaling parameter of the Weibull distribution, which follows a gamma distribution. .

[0011] Preferably, the first-order Wasserstein distance is:

[0012] in, , These are the probability distributions corresponding to the full sample dataset and the candidate subsample dataset, respectively. The full sample dataset is... The candidate subsample dataset is , , They are respectively , The corresponding empirical cumulative distribution function.

[0013] The preferred dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization is as follows:

[0014] in, Let Rényi entropy be the candidate subsample dataset in the prior distribution. The Wasserstein distance between the full dataset and the candidate subsample dataset. These are weight parameters; Sample reuse of candidate subsamples for:

[0015] in, For the candidate subsample dataset, including One sample, ; For the full sample dataset, including One sample; At the preset sample reuse rate The optimization problem of the dual-objective collaborative optimization model is constrained as follows:

[0016] in, For sample reuse The corresponding optimal subsample set.

[0017] Preferably, the specific method for determining the globally optimal subset of samples and the corresponding optimal sample reuse by traversing sample reuse using a greedy search strategy is as follows: S41. Suppose we start from the original full sample set. Randomly selected From a sample, construct a candidate subset. The corresponding sample reuse rate is , , The number of candidate subsamples; S42. Targeting candidate subsets Each sample point Based on the corresponding reliability index Construct nonlinear constraint equations , For the prior expected moment; S43. Maximize the dual-objective collaborative optimization model function while satisfying the constructed equality constraints and parameter boundary conditions; S44. Repeat steps S41-S43 a preset number of times. If the model function value of the current candidate subset is better than the historical best record, then update the optimal subset. ; S45. Iterate through a set of preset sample reuse rates The performance metrics of the optimal subset under each reuse degree are evaluated in downstream tasks, and the globally optimal sample reuse degree is finally determined. and the corresponding optimal subsample set .

[0018] Preferably, in step S5, the hyperparameter estimation method is adaptively selected based on prior information and model complexity: When the number of hyperparameters to be estimated is greater than the sample size of prior information, the hyperparameter estimation method based on maximum entropy is used. Prior moments are constructed based on known reliability information and a nonlinear constraint optimization problem is established. A multi-level optimization strategy based on random search and post-processing is used to iteratively solve the problem and obtain the estimated hyperparameter values ​​of the highest prior distribution. When the number of hyperparameters to be estimated is less than or equal to the sample size of prior information, the least squares-based hyperparameter estimation method is used to obtain the optimal hyperparameter estimate by minimizing the sum of squared errors between the reliability prior moments and the known reliability data.

[0019] Preferably, in step S5, the observation data is processed according to Bayes' theorem. As sample data, and combined with prior information to construct a posterior distribution, specifically:

[0020] in, β For shape parameters, λ The scaling parameter follows a gamma distribution. , t i For the first i Lifespan data, δ i The failure index, n For the total amount of lifetime data, when δ i When =1, the lifespan data is fault data. δ i When =0, the lifespan data is fault-free data; The specific content of reliability analysis and life prediction of avionics equipment using the step-by-step sampling method is as follows: Set a random seed and use the Metropolis-Hastings algorithm to optimize the shape parameters. Sampling was performed to obtain the sample. The inverse function method was used to measure the scale parameters. Sampling was performed to obtain the sample. Repeat the sampling process until the number of samples for both parameters is obtained. Reaching the preset value; comprehensive analysis of the dual-parameter sampling samples. and The posterior expected values ​​of the two-parameter samples are calculated as parameter estimates. and Reliability analysis is performed based on dual-parameter sampling samples to predict the lifespan of avionics equipment and evaluate related reliability indicators.

[0021] A data expansion and reliability analysis system for avionics equipment, based on the aforementioned data expansion and reliability analysis method for avionics equipment, includes: a data acquisition and processing module, a dual-objective collaborative optimization module, and a reliability analysis module; The data acquisition and processing module is used to collect reliability growth test data of key electronic components and functional modules in avionics equipment, obtain a full sample dataset, and randomly select a portion of the samples to form a candidate subsample set. The dual-objective collaborative optimization module is used to construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization. Rényi entropy is used to evaluate the information content of candidate subsample sets. By maximizing Rényi entropy, high-information candidate subsample sets are selected. Wasserstein distance is used to measure the distribution difference between candidate subsample sets and the full sample set. By minimizing Wasserstein distance, the candidate subsample sets approximate the full sample distribution in terms of position, scale, and shape features. A greedy search strategy is used to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree. The reliability analysis module is used to construct prior information based on the optimal subsample set and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. It adaptively selects the hyperparameter estimation method according to the prior information conditions and model complexity, constructs the posterior distribution based on Bayes' theorem, and uses the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

[0022] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned data augmentation and reliability analysis method for avionics equipment.

[0023] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned data expansion and reliability analysis method for avionics equipment. As can be seen from the above technical solution, compared with the prior art, the present invention discloses a data expansion and reliability analysis method and system for avionics equipment, which effectively avoids the limitations of traditional subjective prior and empirical Bayesian methods under small sample conditions, significantly balances the model's fitting ability and generalization ability, and enhances the robustness and credibility of reliability analysis results; under the condition that there is no prior information for newly developed avionics equipment, it can effectively extract the reliability characteristics and life distribution information of the target avionics equipment. The obtained reliability indicators and life prediction results can be used to supplement the missing underlying safety basic data in the safety assessment process, and have clear engineering practical value and promotion significance. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0025] Figure 1 This is a flowchart of a data expansion and reliability analysis method for avionics equipment provided in an embodiment of the present invention; Figure 2 This is a flowchart of the greedy search strategy provided in the embodiments of the present invention; Figure 3 This is a flowchart of the step-by-step sampling method provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of a sample dataset that follows a two-parameter Weibull distribution, as provided in an embodiment of the present invention. Figure 5 This is a comparison chart of MREs for each sample dataset under different sample reuse degrees provided in this embodiment of the invention; Figure 6 This is a graph showing the reliability growth test data of a certain Weibull-type avionics equipment provided in an embodiment of the present invention; Figure 7 This is a standard error diagram of shape parameters under different random seeds provided in the embodiments of the present invention; Figure 8 This is a histogram of two-parameter sampling provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Example 1 This invention discloses a method for data augmentation and reliability analysis of avionics equipment, such as... Figure 1 ,include: S1. Collect reliability growth test data of key electronic components and functional modules in avionics equipment to obtain a full sample dataset, and randomly select some samples to form a candidate subsample set; S2. The Rényi entropy is used to evaluate the information content of the candidate subsample set. By maximizing the Rényi entropy, the candidate subsample set with high information content is selected. S3. The Wasserstein distance is used to measure the distribution difference between the candidate subsample set and the full sample set. By minimizing the Wasserstein distance, the candidate subsample set approximates the full sample distribution in terms of location, scale and shape features. S4. Construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization, and use a greedy search strategy to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree; S5. Construct prior information based on the optimal subsample set, and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. Adaptively select the hyperparameter estimation method according to the prior information conditions and model complexity, and construct the posterior distribution based on Bayes' theorem. Use the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

[0028] In this embodiment, for step S1, a reliability growth test is conducted on the key electronic components in a certain type of newly developed aerospace equipment to obtain life data under high stress. Based on the Arrhenius model, the life under high stress is converted to normal stress conditions to obtain a full sample dataset containing all valid test data. The test adopts an accelerated high-temperature life test bench. A portion of the samples are randomly selected from the full sample dataset to form a candidate subsample set.

[0029] To further implement the above technical solution, the prior information of the candidate subsample set is represented as follows:

[0030] in, is the order parameter of the Rényi entropy; Let be the shape parameter of the Weibull distribution, which follows a uniform distribution and takes values ​​ranging from 1 to 2. ; Let be the scaling parameter of the Weibull distribution, which follows a gamma distribution. ; In this embodiment, Rényi entropy is introduced as an information metric to quantify the information content of candidate subsamples. Rényi entropy is a generalized form of Shannon entropy, which can be flexibly adjusted by the order parameter to be sensitive to the tail of the probability distribution. It has a stronger information discrimination ability in small sample scenarios. By maximizing Rényi entropy, the optimal selection of the information content of the candidate subsample set is achieved, ensuring that the selected subsamples contain as much effective information as possible.

[0031] To further implement the above technical solution, the first-order Wasserstein distance is:

[0032] in, , These are the probability distributions corresponding to the full sample dataset and the candidate subsample dataset, respectively. The full sample dataset is... The candidate subsample dataset is , , They are respectively , The corresponding empirical cumulative distribution function.

[0033] This embodiment ensures that the candidate subsample set approximates the full sample distribution in terms of location, scale, and shape by minimizing the Wasserstein distance between the full sample dataset and the candidate subsample dataset, thereby reducing the risk of prior modeling distortion caused by sample bias.

[0034] To further implement the above technical solution, a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization is proposed as follows:

[0035] in, Let Rényi entropy be the candidate subsample dataset in the prior distribution. The Wasserstein distance between the full sample dataset and the candidate subsample dataset; These are weighting parameters, which are set in practice based on task requirements through cross-validation or experience. To describe the size of the subsample selection and clarify its representativeness in the full sample, the sample reuse degree of the candidate subsample is defined. for:

[0036] in, For the candidate subsample dataset, including One sample, ; For the full sample dataset, including One sample; At the preset sample reuse rate The optimization problem of the dual-objective collaborative optimization model is constrained as follows:

[0037] in, For sample reuse The corresponding optimal subsample set.

[0038] To obtain the global optimal solution, this embodiment adopts a greedy search strategy, traversing a set of discrete sample reuse degrees and independently optimizing the model under each reuse degree. By comparing the performance indicators of each set of subsamples in downstream tasks, the global optimal subsample set and its corresponding optimal sample reuse degree are finally determined. This can achieve joint optimization of information richness and distribution representativeness, while taking into account the robustness and accuracy of downstream model performance.

[0039] To further implement the above technical solutions, such as Figure 2 The specific method for determining the globally optimal subset of samples and the corresponding optimal sample reuse by traversing the sample reuse degree using a greedy search strategy is as follows: S41. Suppose we start from the original full sample set. Randomly selected From a sample, construct a candidate subset. The corresponding sample reuse rate is , , The number of candidate subsamples; S42. Targeting candidate subsets Each sample point Based on the corresponding reliability index Construct nonlinear constraint equations , For the prior expected moment; S43. Maximize the dual-objective collaborative optimization model function while satisfying the constructed equality constraints and parameter boundary conditions; S44. Repeat steps S41-S43 a preset number of times. If the model function value of the current candidate subset is better than the historical best record, then update the optimal subset. ; S45. Iterate through a set of preset sample reuse rates The performance metrics of the optimal subset under each reuse degree are evaluated in downstream tasks, and the globally optimal sample reuse degree is finally determined. and the corresponding optimal subsample set .

[0040] To further implement the above technical solution, in step S5, a hyperparameter estimation method is adaptively selected based on prior information and model complexity: When the number of hyperparameters to be estimated exceeds the sample size of prior information, the least squares estimation can only utilize limited prior information, resulting in low fitting accuracy. In this case, the maximum entropy method can effectively address the problem of scarce prior information by introducing additional constraints, thereby reducing estimation bias caused by insufficient information. Therefore, the maximum entropy-based hyperparameter estimation method is used in this case. Prior moments are constructed based on known reliability information, and a nonlinear constraint optimization problem is established. A multi-level optimization strategy based on random search and post-processing is used for iterative solution to obtain the hyperparameter estimates of the highest prior distribution. In this embodiment, given limited prior information, the prior distribution that best fits the known constraints is constructed by maximizing information entropy, thereby reducing estimation bias caused by a lack of prior information; the prior moments constructed based on known reliability information are expressed as:

[0041]

[0042]

[0043] in, It is a hypergeometric function; Establish a nonlinear constrained optimization problem as follows , For known reliability data points; When the number of hyperparameters to be estimated is less than or equal to the sample size of prior information, using the maximum entropy method introduces too many complex nonlinear constraints, increasing computational complexity and reducing computational efficiency. Since least squares estimation is computationally simple and can efficiently fit model parameters, a least squares-based hyperparameter estimation method is used. This method obtains the optimal hyperparameter estimate by minimizing the sum of squared errors between the reliability prior moments and the known reliability data. The optimal hyperparameter estimate is expressed as:

[0044] in, Prior moments constructed for known reliability information, These are known reliability data points.

[0045] To further implement the above technical solution, in step S5, based on Bayes' theorem, the observation data... As sample data, and combined with prior information to construct a posterior distribution, specifically:

[0046] in, β For shape parameters, λ The scaling parameter follows a gamma distribution. , t i For the first i Lifespan data, δ i The failure index, n For the total amount of lifetime data, when δ i When =1, the lifespan data is fault data. δ i When =0, the lifespan data is fault-free data; Due to the complexity of the posterior distribution of the two-parameter Weibull distribution, it is difficult to solve directly using analytical methods, such as... Figure 3 The specific content of reliability analysis and life prediction of avionics equipment using the step-by-step sampling method is as follows: Set a random seed and use the Metropolis-Hastings algorithm to optimize the shape parameters. Sampling was performed to obtain the sample. The inverse function method was used to measure the scale parameters. Sampling was performed to obtain the sample. Repeat the sampling process until the number of samples for both parameters is obtained. Reaching the preset value; comprehensive analysis of the dual-parameter sampling samples. and The posterior expected values ​​of the two-parameter samples are calculated as parameter estimates. and Reliability analysis is performed based on dual-parameter sampling samples to predict the lifespan of avionics equipment and evaluate related reliability indicators.

[0047] Example 2 This embodiment uses the Markov chain Monte Carlo method to generate a simulated dataset that conforms to the assumed distribution. It assumes the data follows a two-parameter Weibull distribution. By setting different parameter combinations, multiple sets of sample data are constructed. Specifically: First, extract two sets of shape parameters. True scale parameters The sample datasets are 1 and 2, with a sample size of 1. Specific sampled samples are as follows Figure 4 As shown in Figures a and b, when the shape parameter of the two-parameter Weibull distribution... When the shape parameter changes, its distribution transforms into an exponential distribution. In this case, extract true scale parameters respectively and Sample datasets 3 and 4, with a sample size of [number missing]. Specific sampled samples are as follows Figure 4 As shown in Figures c and d, the applicability of the method in Example 1 can be more comprehensively verified by using multiple datasets with different parameter configurations, thereby enhancing the credibility of the analysis results.

[0048] The dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization, constructed through Example 1, is based on... Figure 2 The greedy search strategy is adopted to optimize the reuse rate of a set of discrete samples. The process involves iterating through the data and continuously optimizing the dual objective function to obtain the optimal solution for each sample reuse degree. Furthermore, the optimal solution is obtained through Bayesian prior modeling and posterior inference. Performance evaluation results in downstream tasks.

[0049] In this embodiment, the mean relative error (MRE) between the estimated and actual characteristic lifetimes is selected as the core evaluation index, defined as follows:

[0050] in, To utilize the optimal solution The Bayesian estimated characteristic lifetime value, This represents the true characteristic lifetime value; The feature lifetime estimates and MREs of the four sample datasets are shown in Tables 1 to 4, and their visualization results are as follows: Figure 5 As shown; Table 1. Parameter estimates and MREs for the first sample dataset.

[0051] Table 2. Parameter estimates and MREs for the second group.

[0052] Table 3. Parameter estimates and MREs for Group 3

[0053] Table 4. Parameter estimates and MREs for Group 4

[0054] The results show that the performance evaluation results of using the dual-objective collaborative optimization strategy to select the optimal subsample set remain consistent under different parameter configurations. Specifically, when the sample reuse rate is 80%, the feature lifetime estimate (MRE) is minimized. This indicates that developing the optimal subsample set at this reuse rate can most fully represent the statistical characteristics of the entire sample set and contain the richest information. The optimal sample reuse degree is defined for subsequent Bayesian prior modeling and posterior inference; this shows that the strategy can effectively suppress the interference of abnormal data on the Bayesian inference process, reduce the risk of model overfitting, and thus improve the accuracy of parameter estimation, providing a theoretical basis for the reliability analysis of newly developed domestic avionics equipment under conditions without prior information.

[0055] This embodiment is used to verify the applicability of the method in Embodiment 1 of the present invention in actual engineering. Figure 6 As shown, reliability growth test data of a certain Weibull-type avionics system was selected as the observation data, with reference to... Figure 2 The optimal subset of samples was obtained by using a greedy search strategy. .

[0056] Based on this, an adaptive method selection mechanism is adopted to select and determine the hyperparameter estimation method. In this embodiment, since the relationship between the sample size of prior information and the number of parameters to be estimated meets the applicable conditions of the least squares method, the least squares estimation method is selected to estimate the hyperparameters, and the results are shown in Table 5.

[0057] Table 5 Hyperparameter estimates

[0058] Subsequently, based on the constructed prior distribution, Bayesian posterior inference is performed using observed data. Due to the complexity of the two-parameter posterior distribution, referencing... Figure 3 The step-by-step sampling method shown applies shape parameters respectively. and scale parameters Sampling, setting the number of samples To ensure the accuracy and repeatability of the sampling results, shape parameters were obtained under random seed values ​​ranging from 0 to 100. The standard error of the sampled samples is used to select the random seed with the smallest standard error for final sampling, such as... Figure 7 As shown, the optimal random seed for shape parameter sampling is 8. Finally, the histograms of the two-parameter sampling are obtained, as shown below. Figure 8 As shown in Figures a and b, the corresponding parameter estimates are shown in Table 6.

[0059] Table 6 Parameter Estimates

[0060] To further verify the performance of the method of this invention, it was compared with the Maximum Likelihood Estimation (MLE) method and the Empirical Bayes (EB) method. The MLE method, as a classic parameter estimation method, has the advantages of not relying on prior information and being simple to implement. However, when the target product data is sparse, the estimation results often exhibit instability. In contrast, the EB method effectively improves the stability of the estimation through a full-sample data-driven strategy, but it is highly dependent on the data distribution and has a certain risk of overfitting. Therefore, by comparing the method of this invention with these two representative methods, we can not only verify its ability to filter and transmit prior information under limited data conditions, but also systematically evaluate its advantages in estimation stability and generalization performance. The specific numerical values ​​of parameter estimation using the MLE method and the EB method are shown in Table 7.

[0061] Table 7 Parameter estimates for MLE and EB methods

[0062] Considering that the estimation of scale parameters depends on the estimation results of shape parameters, this embodiment selects the standard error of shape parameter estimation as the performance evaluation index. Table 8 shows the standard error of shape parameters for the three methods.

[0063] Table 8 Standard errors of shape parameters for each method

[0064]

[0065] The results show that the standard error of the shape parameters estimated by the method of this invention is significantly smaller than that of the MLE and EB methods. This indicates that the method of this invention can significantly reduce the uncertainty of parameter estimation and improve the accuracy of parameter estimation. Therefore, the method of this invention can effectively reduce the uncertainty of parameter estimation and improve the accuracy and stability of parameter estimation under the condition of scarce data, showing a more significant advantage than traditional methods, and providing a more scientific and reliable basis for the prediction of the life of newly developed domestic avionics equipment.

[0066] Example 3 A data augmentation and reliability analysis system for avionics equipment, based on a data augmentation and reliability analysis method for avionics equipment, includes: a data acquisition and processing module, a dual-objective collaborative optimization module, and a reliability analysis module; The data acquisition and processing module is used to collect reliability growth test data of key electronic components and functional modules in avionics equipment, obtain a full sample dataset, and randomly select a portion of the samples to form a candidate subsample set. The dual-objective collaborative optimization module is used to construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization. Rényi entropy is used to evaluate the information content of candidate subsample sets. By maximizing Rényi entropy, high-information candidate subsample sets are selected. Wasserstein distance is used to measure the distribution difference between candidate subsample sets and the full sample set. By minimizing Wasserstein distance, the candidate subsample sets approximate the full sample distribution in terms of position, scale, and shape features. A greedy search strategy is used to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree. The reliability analysis module is used to construct prior information based on the optimal subsample set and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. It adaptively selects the hyperparameter estimation method according to the prior information conditions and model complexity, constructs the posterior distribution based on Bayes' theorem, and uses the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

[0067] Example 4 A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a data augmentation and reliability analysis method for avionics equipment.

[0068] Example 5 A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a data expansion and reliability analysis method for avionics equipment.

[0069] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0070] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for data augmentation and reliability analysis of avionics equipment, characterized in that, include: S1. Collect reliability growth test data of key electronic components and functional modules in avionics equipment to obtain a full sample dataset, and randomly select some samples to form a candidate subsample set; S2. The Rényi entropy is used to evaluate the information content of the candidate subsample set. By maximizing the Rényi entropy, the candidate subsample set with high information content is selected. S3. The Wasserstein distance is used to measure the distribution difference between the candidate subsample set and the full sample set. By minimizing the Wasserstein distance, the candidate subsample set approximates the full sample distribution in terms of location, scale and shape features. S4. Construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization, and use a greedy search strategy to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree; S5. Construct prior information based on the optimal subsample set, and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. Adaptively select the hyperparameter estimation method according to the prior information conditions and model complexity, and construct the posterior distribution based on Bayes' theorem. Use the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

2. The data expansion and reliability analysis method for avionics equipment as described in claim 1, characterized in that, The prior information of the candidate subset is represented as: in, is the order parameter of the Rényi entropy; Let be the shape parameter of the Weibull distribution, which follows a uniform distribution and takes values ​​ranging from 1 to 2. ; Let be the scaling parameter of the Weibull distribution, which follows a gamma distribution. .

3. The data expansion and reliability analysis method for avionics equipment as described in claim 1, characterized in that, The first-order Wasserstein distance is: in, , These are the probability distributions corresponding to the full sample dataset and the candidate subsample dataset, respectively. The full sample dataset is... The candidate subsample dataset is , , They are respectively , The corresponding empirical cumulative distribution function.

4. The data expansion and reliability analysis method for avionics equipment as described in claim 1, characterized in that, The dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization is as follows: in, Let Rényi entropy be the candidate subsample dataset in the prior distribution. The Wasserstein distance between the full sample dataset and the candidate subsample dataset. These are weight parameters; Sample reuse of candidate subsamples for: in, For the candidate subsample dataset, including One sample, ; For the full sample dataset, including One sample; At the preset sample reuse rate The optimization problem of the dual-objective collaborative optimization model is constrained as follows: in, For sample reuse The corresponding optimal subsample set.

5. The data expansion and reliability analysis method for avionics equipment as described in claim 1, characterized in that, The specific method for determining the globally optimal subset of samples and the corresponding optimal sample reuse by traversing sample reuse using a greedy search strategy is as follows: S41. Suppose we start from the original full sample set. Randomly selected From a sample, construct a candidate subset. The corresponding sample reuse rate is , , The number of candidate subsamples; S42. Targeting candidate subsets Each sample point Based on the corresponding reliability index Construct nonlinear constraint equations , For the prior expected moment; S43. Maximize the dual-objective collaborative optimization model function while satisfying the constructed equality constraints and parameter boundary conditions; S44. Repeat steps S41-S43 a preset number of times. If the model function value of the current candidate subset is better than the historical best record, then update the optimal subset. ; S45. Iterate through a set of preset sample reuse rates The performance metrics of the optimal subset under each reuse degree are evaluated in downstream tasks, and the globally optimal sample reuse degree is finally determined. and the corresponding optimal subsample set .

6. The data expansion and reliability analysis method for avionics equipment as described in claim 1, characterized in that, In step S5, the hyperparameter estimation method is adaptively selected based on prior information and model complexity: When the number of hyperparameters to be estimated is greater than the sample size of prior information, the hyperparameter estimation method based on maximum entropy is used. Prior moments are constructed based on known reliability information and a nonlinear constraint optimization problem is established. A multi-level optimization strategy based on random search and post-processing is used to iteratively solve the problem and obtain the estimated hyperparameter values ​​of the highest prior distribution. When the number of hyperparameters to be estimated is less than or equal to the sample size of prior information, the least squares-based hyperparameter estimation method is used to obtain the optimal hyperparameter estimate by minimizing the sum of squared errors between the reliability prior moments and the known reliability data.

7. The data augmentation and reliability analysis method for avionics equipment as described in claim 1, characterized in that, In step S5, according to Bayes' theorem, the observation data... As sample data, and combined with prior information to construct a posterior distribution, specifically: in, β For shape parameters, λ The scaling parameter follows a gamma distribution. , t i For the first i Lifespan data, δ i The failure index, n For the total amount of lifetime data, when δ i When =1, the lifespan data is fault data. δ i When =0, the lifespan data is fault-free data; The specific content of reliability analysis and life prediction of avionics equipment using the step-by-step sampling method is as follows: Set a random seed and use the Metropolis-Hastings algorithm to optimize the shape parameters. Sampling was performed to obtain the sample. The inverse function method was used to measure the scale parameters. Sampling was performed to obtain the sample. Repeat the sampling process until the number of samples for both parameters is obtained. Reaching the preset value; comprehensive analysis of the dual-parameter sampling samples. and The posterior expected values ​​of the two-parameter samples are calculated as parameter estimates. and Reliability analysis is performed based on dual-parameter sampling samples to predict the lifespan of avionics equipment and evaluate related reliability indicators.

8. A data expansion and reliability analysis system for avionics equipment, characterized in that, A data expansion and reliability analysis method for avionics equipment based on any one of claims 1-7 includes: a data acquisition and processing module, a dual-objective collaborative optimization module, and a reliability analysis module; The data acquisition and processing module is used to collect reliability growth test data of key electronic components and functional modules in avionics equipment, obtain a full sample dataset, and randomly select a portion of the samples to form a candidate subsample set. The dual-objective collaborative optimization module is used to construct a dual-objective collaborative optimization model based on entropy constraints and distribution distance optimization. Rényi entropy is used to evaluate the information content of candidate subsample sets. By maximizing Rényi entropy, high-information candidate subsample sets are selected. Wasserstein distance is used to measure the distribution difference between candidate subsample sets and the full sample set. By minimizing Wasserstein distance, the candidate subsample sets approximate the full sample distribution in terms of position, scale, and shape features. A greedy search strategy is used to traverse the sample reuse degree to determine the globally optimal subsample set and the corresponding optimal sample reuse degree. The reliability analysis module is used to construct prior information based on the optimal subsample set and establish a reliability analysis model for avionics equipment based on the two-parameter Weibull distribution. It adaptively selects the hyperparameter estimation method according to the prior information conditions and model complexity, constructs the posterior distribution based on Bayes' theorem, and uses the step-by-step sampling method to perform reliability analysis and life prediction of avionics equipment.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements a data expansion and reliability analysis method for avionics equipment as described in any one of claims 1 to 7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a data expansion and reliability analysis method for avionics equipment as described in any one of claims 1 to 7.

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