Accelerated degradation test optimization method based on grey correlation

Abstract

The invention discloses an accelerated degradation test optimization method based on grey correlation. The method comprises the following steps: modeling a degradation path by adopting a gamma process to obtain an acceleration model, and setting a (a = 1-n) optimization targets; a test result of the acceleration model in the degradation process is collected, the result comprises a optimization target values and a plurality of variables to be optimized corresponding to the target values, and a groups of sequence data are formed; calculating a difference value between each group of sequence data and the reference sequence to obtain at least one group of difference value sequence; calculating at least one gray incidence coefficient based on the difference value sequence, and calculating a comprehensive gray correlation degree of the a optimization targets based on the at least one gray incidence coefficient; and evaluating the optimality of the test result based on the comprehensive grey correlation degree. According to the method, the defects caused by limitation of test data can be effectively overcome, and the dependency strength between inherent degradation and external random impact can be determined. The model can guarantee the calculation cost and precision of optimization at the same time.

Description

Technical Field

[0001] The invention relates to the technical field of degradation test, and in particular to an accelerated degradation test optimization method based on grey correlation. Background Art

[0002] As an effective method to evaluate reliability characteristics, reliability testing has been widely used in various fields to explore failure mechanisms. Reliability testing can be performed in the laboratory or during operation. When reliability testing is planned in the laboratory, environmental conditions must be simulated to maintain the accuracy of the collected data. In the case of obtaining failure data by testing the performance of service products, the cost burden makes it difficult to be widely used. Therefore, most reliability tests are arranged in the laboratory.

[0003] Traditional reliability test plans collect failure data and model the operating mechanism. However, with the rapid development of science and technology, products are becoming more and more reliable. Failure events may be less likely to occur within a limited time interval. Therefore, collecting sufficient failure data may be much more expensive than previous products. Reliability testing then tends to focus on the degradation process and check the performance level during the test. The above tests can also be called degradation tests. Since intrinsic degradation evolves slowly within the original test stress levels (such as temperature, humidity, and voltage), techniques to accelerate the degradation process are also used to improve the economy of scheduled tests.

[0004] In summary, the most widely used in engineering practice is accelerated degradation testing (ADT). In ADT, the product under test may be subjected to more severe stress than normal under the same failure mechanism to shorten the total test duration. Degradation measurements are used to specify the evolution of the degradation process over time, usually modeled by a random process.

[0005] According to the acceleration technique applied, ADT can be divided into three categories: constant stress ADT, step stress ADT and progressive stress ADT. For constant stress ADT, the test stress value is higher than the normal level and remains unchanged throughout the test. In step stress ADT, the value of the tested stress can be increased at a specific level. For progressive stress ADT, the test stress value is designed to increase step by step.

[0006] The existing literature on ADT can generally be divided into studies on degradation process modeling and techniques for optimizing ADT to improve effectiveness and economy. For the first question, the Wiener process, the gamma process, and the inverse Gaussian process are the most widely used models in degradation data analysis. For the optimal design of ADT, the goal is often to maximize the estimation accuracy in a certain sense under certain constraints. Although there are a large number of studies on optimizing ADT from different perspectives, almost all existing methods only focus on the inherent degradation process, regardless of the external random shocks exposed. Moreover, very little work has estimated the parameters that measure the dependence between the two failure processes. In addition, most of the above methods are based on large sample sizes, and some models have strict constraints on the distribution, and then optimize the characteristic parameters, which are difficult to be widely applied.

[0007] To overcome the above shortcomings, the existing technology introduces the grey incidence analysis (GIA) model, which is an effective tool to measure the similarity between different data sequences, without being constrained by sample size and distribution requirements. Therefore, it has been widely used in many different fields such as optimization and reliability engineering. However, the problem of integrating GIA and exploring the degradation mechanism, the dependency between different types of failure processes, and the optimal values ​​of the characteristic parameters that determine the reliability level still exists. Summary of the invention

[0008] In view of this, the purpose of the present invention is to propose an accelerated degradation test optimization method based on grey correlation, which can effectively overcome the shortcomings brought by the limitation of test data and determine the dependence intensity between inherent degradation and external random shock. The model can simultaneously ensure the optimization of calculation cost and accuracy.

[0009] According to one aspect of the present invention, there is provided an accelerated degradation test optimization method based on grey correlation, comprising:

[0010] The degradation pathway is modeled using the gamma process to obtain an accelerated model, and a (a=1-n) optimization objectives are set;

[0011] Collecting the test results of the acceleration model in the degradation process, the results include a optimization target values ​​and a number of variables to be optimized corresponding to the target values, to form a groups of sequence data; calculating the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequences;

[0012] Calculate at least one grey incidence coefficient based on the difference sequence, and calculate the comprehensive grey correlation degree of a optimization objectives based on the at least one grey incidence coefficient;

[0013] The optimality of the test results was evaluated based on the comprehensive grey relational degree.

[0014] In the above technical solution, the present invention has the following advantages:

[0015] (1) Improve optimization efficiency and accuracy: By using the gamma process to model the degradation path, the present invention can more accurately describe the complex dynamic behavior in the accelerated degradation process, thereby providing a solid mathematical model foundation for optimization. Setting multiple optimization targets (a) and collecting corresponding test results makes the optimization process more comprehensive, and can simultaneously consider multiple performance indicators to improve the overall effect of optimization. Using gray correlation analysis to calculate the comprehensive gray correlation degree can quantify the degree of influence of each variable to be optimized on the optimization target, thereby more accurately guiding the optimization direction and improving the optimization accuracy.

[0016] (2) Enhanced robustness and adaptability:

[0017] As an effective method for dealing with uncertainty and fuzzy information, grey correlation analysis can deal with problems such as incomplete data and noise interference in the degradation process and enhance the robustness of the optimization method. By calculating the difference sequence and the grey incidence coefficient, the present invention can capture the slight changes in the degradation process, adjust the optimization strategy in time, and improve the adaptability of the optimization method.

[0018] (3) Simplify and optimize processes and reduce costs:

[0019] The present invention combines grey correlation analysis with accelerated degradation test to form a systematic optimization method, which can simplify the complex steps in the traditional optimization process and improve the optimization efficiency. Through precise mathematical modeling and optimization algorithm, the present invention can achieve the ideal optimization effect while reducing the number of tests and the test cost, and has significant economic benefits.

[0020] (4) Solve the fundamental problem:

[0021] The present invention provides an effective solution to the problem of multiple optimization targets and complex variable relationships in accelerated degradation tests. Through grey correlation analysis, the correlation between each variable to be optimized and the optimization target can be clarified, so as to optimize in a targeted manner and solve the blindness and uncertainty problems in the optimization process. The present invention can also reveal the inherent laws and trends in the degradation process, provide strong support for product reliability design and life prediction, and fundamentally improve the quality and reliability level of the product.

[0022] In summary

[0023] The accelerated degradation test optimization method based on grey correlation proposed in this invention can significantly improve the optimization efficiency and accuracy, enhance robustness and adaptability, simplify the optimization process and reduce costs through precise mathematical modeling, multi-objective optimization and grey correlation analysis and other technical means, and solve the fundamental problems of multiple optimization targets and complex variable relationships in accelerated degradation tests. This method will show significant technical innovation and practical application value in the review, and provide strong support for product reliability design and life prediction.

[0024] In some embodiments, the optimization objectives include:

[0025] 1) Minimize the asymptotic variance of the MTTF estimated in the accelerated degradation test;

[0026] 2) Maximize the parameter values ​​contained in the Fisher information matrix;

[0027] 3) Minimize the ratio of asymptotic variances when varying the input parameters.

[0028] In some embodiments, the constraints of the acceleration model include test resources, and the test resource expression is as follows:

[0029]

[0030] In the formula, c s represents the cost of a sample, N represents the number of samples, c0 represents the unit time cost of the test equipment, d k represents the test duration at the kth level of the selected stress, c m represents the cost of measuring a performance level for a sample and a time, M k Represents the total number of measured tests within a specified stress combination, TC * Represents the maximum cost that reliability testing can provide.

[0031] In some embodiments, test results of the acceleration model in the degradation process are collected, the results including a optimization target values ​​and a number of variables to be optimized corresponding to the target values, forming a set of sequence data, and further including:

[0032] The test results are normalized and preprocessed.

[0033] In some embodiments, the optimality of the test results is evaluated based on the comprehensive grey relational degree, specifically:

[0034] Taking the comprehensive grey correlation degree as the dependent variable, constructing a Kriging model, and predicting the grey incidence based on the Kriging model;

[0035] The optimality of the test results was evaluated based on the grayscale occurrence rate.

[0036] In the above technical solutions, the Kriging model can indeed provide important guidance in the process of searching for the optimal value of the test feature variable and effectively reduce the computational burden. This is mainly reflected in the following aspects:

[0037] 1. High-precision prediction capability

[0038] The Kriging model is a spatial interpolation method based on the principles of geostatistics. It can not only provide the optimal unbiased estimate of the point to be estimated, but also estimate the variance of the estimate, thereby evaluating the prediction accuracy of the model. This high-precision prediction capability enables the Kriging model to more accurately predict the performance under different variable combinations when searching for the optimal value of the test feature variable, providing a reliable basis for optimizing the search process.

[0039] 2. Consider spatial structural characteristics

[0040] The Kriging model takes into full account the spatial position relationship between sample points and the structural characteristics of regionalized variables. When searching for the optimal value of the test feature variable, these spatial structural characteristics often have an important impact on the results. The Kriging model describes this spatial structural feature by constructing a variogram (or semivariogram) and makes full use of this information in the interpolation process to more accurately predict the variable value of the unknown point.

[0041] 3. Reduce the computational burden

[0042] In the process of searching for the optimal value of the test feature variable, a large amount of computational simulation and iterative optimization is often required. If all possible variable combinations are simulated directly, it will consume huge computing resources and time. The Kriging model can approximate the response relationship of the real model by constructing an alternative model (such as the Kriging alternative model). This alternative model can greatly reduce the computational burden and improve the efficiency of the optimization search process while maintaining a high prediction accuracy.

[0043] 4. Guide and optimize search direction

[0044] The Kriging model not only provides the optimal prediction value of the point to be estimated, but also evaluates the uncertainty of the prediction through the variance of the estimated value. This uncertainty information is of great significance in guiding the optimization search direction. During the search process, based on the predicted value and its uncertainty information, the area with better prediction performance and lower uncertainty can be searched in depth, so as to find the optimal value of the test feature variable more efficiently.

[0045] 5. Combined with optimization algorithm

[0046] The Kriging model can also be combined with optimization algorithms (such as genetic algorithms, particle swarm optimization algorithms, etc.) to form a more efficient optimization search strategy. In the optimization search process, the Kriging model is used as a response surface model to approximate the response relationship of the real model, while the optimization algorithm guides the search direction based on the information provided by the response surface model. This combination can make full use of the high-precision prediction ability of the Kriging model and the global search ability of the optimization algorithm, so as to find the optimal value of the test feature variable more quickly.

[0047] Furthermore, the optimality is determined based on the value of the correlation degree. The following is a detailed explanation of how to withdraw:

[0048] Grey relational degree and embodiment of optimality

[0049] Definition of relevance:

[0050] The correlation is a measure of the correlation between factors (indicators), which quantitatively describes the relative changes between factors. In the process of system development, if the trends of changes in two factors are consistent, that is, the degree of synchronous change is high, then the correlation is large; otherwise, the correlation is small.

[0051] Correlation calculation:

[0052] Grey relational analysis usually involves the following steps:

[0053] 1. Determine the reference sequence and comparison sequence: The reference sequence (also called the parent sequence) is an ideal comparison standard. It can be composed of the optimal value (or the worst value) of each indicator, or other reference values ​​can be selected according to the evaluation purpose. The comparison sequence is the sequence used for comparison with the reference sequence.

[0054] 2. Data preprocessing: Due to the different physical meanings of various factors in the system, the dimensions of the data may not be the same, which makes it difficult to compare. Therefore, dimensionless data processing is generally required when conducting grey relational analysis.

[0055] 3. Calculate the correlation coefficient: Use the calculation formula of grey correlation degree to calculate the correlation coefficient between the reference sequence and the comparison sequence at each time. These correlation coefficients reflect the degree of correlation between the two at each time.

[0056] 4. Calculate the degree of association: Since there is more than one correlation coefficient, the correlation coefficients at each moment are usually concentrated into one value, that is, the average value is calculated as a quantitative representation of the degree of association between the comparison sequence and the reference sequence, that is, the degree of association.

[0057] The embodiment of optimality:

[0058] 1. Sorting and analysis: Sort the evaluation objects according to the calculated correlation value. The object with a larger correlation value indicates that it has a higher degree of correlation with the reference sequence (ideal standard), which means that it is better in a certain sense.

[0059] 2. Establish a correlation sequence: The order of the degree of correlation can form a correlation sequence, which reflects the "superiority" relationship of each subsequence with respect to the parent sequence. For example, in the supplier selection decision, the supplier with the highest degree of correlation is the best choice.

[0060] In some embodiments, the optimality of the test result is evaluated based on the comprehensive grey relational degree, and then further includes:

[0061] According to the optimality of the test results, several groups of variables to be optimized are obtained;

[0062] Several groups of variables to be optimized are used as data input for the PSO algorithm, and the PSO algorithm is used to search for the optimal solution.

[0063] In the above technical solution,

[0064] Steps of combining comprehensive grey relational analysis with PSO algorithm

[0065] 1. Comprehensive grey correlation analysis and evaluation:

[0066] Conduct grey correlation analysis on multiple variables or systems and calculate the correlation between them.

[0067] According to the size of the correlation, the advantages and disadvantages of each variable or system are evaluated to determine which variables are to be optimized (i.e. variables with low correlation or that have not achieved the expected goals).

[0068] 2. Obtain variables to be optimized: Based on the results of grey correlation analysis, select several groups of variables with low correlation or poor performance as objects to be optimized.

[0069] 3.PSO algorithm initialization:

[0070] These variables to be optimized are used as input of the PSO algorithm.

[0071] Initialize a swarm of particles, where each particle represents a possible solution (i.e., an optimized value of a set of variables).

[0072] Set the parameters of the PSO algorithm, such as the number of particles, number of iterations, inertia weight, acceleration factor, etc.

[0073] 4. PSO algorithm optimization process:

[0074] Fitness evaluation: According to the optimization goal (such as improving relevance, reducing costs, improving performance, etc.), define the fitness function to evaluate the quality of each particle.

[0075] Update speed and position: Each particle updates its speed and position according to its own historical optimal position and the global optimal position to find a better solution.

[0076] Iterative optimization: Repeat the fitness evaluation and position update steps until the set number of iterations is reached or the convergence condition is met.

[0077] 5. Result output and analysis:

[0078] Output the optimal solution found by the PSO algorithm, that is, the optimized variable value.

[0079] Substitute the optimized variable values ​​into the original system or model to verify whether its performance is improved.

[0080] Analyze the optimization results, summarize the optimization experience, and provide reference for subsequent optimization work.

[0081] Example

[0082] Suppose we have a system with multiple variables, and through grey correlation analysis, we find that variables A and B have a low correlation. In order to optimize this system, we can input A and B as variables to be optimized into the PSO algorithm. The PSO algorithm will initialize a set of particles, each particle represents a possible value combination of A and B. Then, through the iterative optimization process, the PSO algorithm will find the value combination of A and B that makes the system performance optimal (such as the highest correlation).

[0083] The combination of comprehensive grey correlation analysis and PSO algorithm can give full play to the advantages of both in data processing and optimization solution. Determining the variables to be optimized through grey correlation analysis and then using PSO algorithm for fine optimization can effectively improve the overall performance of the system.

[0084] According to another aspect of the present invention, there is provided an accelerated degradation test optimization device based on grey correlation, based on the above method; comprising:

[0085] A building module is used to model the degradation pathway using a gamma process to obtain an acceleration model and set a (a=1-n) optimization objectives;

[0086] A gray coefficient module is used to collect the test results of the acceleration model in the degradation process, which includes a optimization target value and a number of variables to be optimized corresponding to the target value, forming a group of sequence data; calculating the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequence; calculating at least one gray incidence coefficient based on the difference sequence, and calculating the comprehensive gray correlation degree of a optimization target based on the at least one gray incidence coefficient;

[0087] Evaluation module, used to evaluate the optimality of test results based on the comprehensive grey relational degree.

[0088] In the above technical scheme, in order to better use the above method, the present application proposes an accelerated degradation test optimization device based on grey correlation, each module corresponds to each step of the above method, and its specific principles have been described above and will not be repeated here.

[0089] According to another aspect of the present invention, there is provided an accelerated degradation test optimization device based on grey correlation, comprising:

[0090] at least one processor and a memory communicatively coupled to the at least one processor;

[0091] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the above method.

[0092] In the above technical solution, in order to better run and process the method, the above method is stored in a memory, and the stored method is executed by a processor. It should be noted that the principle and effect of each step have been described above and will not be described in detail here.

[0093] According to another aspect of the present invention, there is provided a computer-readable storage medium storing a computer program, wherein the computer program implements the above method when executed by a processor.

[0094] In the above technical solution, in order to better run and use the method, the above method is stored in a computer-readable storage medium, and the above method is implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be described in detail here. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0096] Figure 1 It is a flow chart of an embodiment of an accelerated degradation test optimization method based on grey correlation according to the present invention;

[0097] Figure 2 It is a PSO flow diagram of an embodiment of an accelerated degradation test optimization method based on grey correlation of the present invention;

[0098] Figure 3 The invention discloses a degradation test device for an electric spindle according to an embodiment of an accelerated degradation test optimization method based on grey correlation.

[0099] Figure 4 It is a schematic diagram of an embodiment of an accelerated degradation test optimization device based on grey correlation of the present invention. DETAILED DESCRIPTION

[0100] The present invention will be further described in detail below in conjunction with the accompanying drawings and examples. It is particularly noted that the following examples are only used to illustrate the present invention, but are not intended to limit the scope of the present invention. Similarly, the following examples are only partial embodiments of the present invention rather than all embodiments, and all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention.

[0101] The present invention provides an accelerated degradation test optimization method based on grey correlation, which can effectively overcome the disadvantages caused by the limitation of test data and determine the dependence intensity between inherent degradation and external random shock. The model can simultaneously ensure the optimization calculation cost and accuracy.

[0102] Embodiment 1

[0103] See also Figure 1 , an accelerated degradation test optimization method based on grey correlation, comprising:

[0104] S1. Model the degradation path using the gamma process to obtain an acceleration model, and set a (a=1-n) optimization targets;

[0105] In this embodiment, the gamma process has been widely used in existing literature and engineering practice due to its advantages in describing non-negative increments and Markov increments of degradation characteristics. Since the degradation processes considered in this study (such as wear, corrosion, cracks, erosion, creep and fatigue) accumulate monotonically over time, we choose the gamma process to model the degradation process.

[0106] The gamma process {X(t), t≥0}, with shape parameter α and scale parameter β, is a continuous time random process with the following properties: the probability of X(0)=0 is 1; X(t) has independent and non-negative increments; X(t)-X(s)~G(α(ts),β), in summary t>s≥0.

[0107] When the degradation behavior is modeled by a gamma process, the reliability can be expressed as:

[0108]

[0109] Wherein, Γ(α(t)), Γ(α(t), βH) represent the function and the incomplete function, respectively. H represents the critical threshold, and the expected value of the process at time t can be expressed as E[X(t)] = α(t)β′, which can also be defined as the degradation rate. In addition to the inherent polymorphic degradation, random shocks caused by environmental factors can also reduce the operating efficiency of components in a more extreme way, that is, the arriving shocks may cause the components to fail suddenly. Each arriving shock may cause some damage to the components, but the ability of the components to resist these arriving damages is different. Once the shock load exceeds the threshold of a specific component, the component under consideration will fail suddenly.

[0110] Since it is difficult to accurately predict the changes in external factors, we use a truncated normal distribution NN to describe the potential impact load. Not only the mean μ and standard deviation σ of the impact load are considered, but also the actual positive value characteristics of the impact load are ensured by limiting the range of (0,∞). This method effectively reflects the uncertainty of external random impact and provides a more accurate impact load simulation for degradation tests, thereby improving the accuracy and reliability of the test.

[0111] As mentioned above, both the inherent polymorphic degradation and the random shock caused by external factors may make the component fail. Therefore, these two failure-suffering processes are competing to cause the failure of each component. That is, once any of these two failure processes occurs, the considered component will fail. In addition, a large number of research and engineering practices have proved that there is a dependency relationship between the above two different failure processes, that is, the arriving random shock may accelerate the intrinsic degradation process.

[0112] In order to reduce the total duration of the degradation test, the considered stresses will be intensified without changing the failure mechanism. Therefore, both the external random shocks and the enhanced stresses in the test will accelerate the degradation process, making the test product more likely to fail. In order to explicitly model the acceleration of the above factors, the shape function of the gamma process is chosen. In fact, when modeling the degradation process, any shape function α(t) can satisfy its requirement of being a non-decreasing, right-continuous, real-valued function. Therefore, the shape function is mathematically expressed as:

[0113]

[0114] Where α(t) represents the value of the shape function when stress is not increased and no impact arrives.

[0115] s k =(s 1k ,s 2k , ..., s hk ) represents the accelerated stress group in the kth stage. H is the total number of stresses considered in the accelerated degradation test. Parameter pr and p h Aims to illustrate how random impact and accelerated stress affect degradation and to estimate it through accelerated degradation tests.

[0116] In order to evaluate the parameters involved in equation (2), test data collected from different stages will be considered simultaneously. Specifically, there are N samples tested simultaneously. There are exactly H types of stress, each with k levels. In order to explore how the tested sample degrades, the performance of the considered sample may have to be measured multiple times within the specified range of stress level combinations. The total number of measurements to be performed, under the condition that the test stress is at the kth level, is M k Then the degradation can be expressed as ΔX i.k.j =X ik.j -X ik.j-1 , where X ik.j It represents the performance level of the i-th (i=1, ..., N) test sample within the k-th (k=1, ..., K) level. ΔX ik·j It can be seen as a performance change caused by degradation.

[0117] When the cumulative degradation level is represented as a gamma process, the degradation increment within a specified time interval follows a gamma distribution, i.e., ΔXi,j,k ~ Ga[a(Sk,r,t)Δt;,β], where Δt represents the jth measurement and the (j-1)th measurement. Therefore, the probability density function of ΔXi,j,k can be mathematically expressed as:

[0118]

[0119] Then, the likelihood function of the degradation test can be derived as:

[0120]

[0121] Among them, θ Ga =(Pr,P1,pz,..,pH,β) represents the parameter vector of the accelerated degradation gamma process. These parameters need to be estimated through test data.

[0122] In this embodiment, the optimization objectives include:

[0123] 1) Minimize the asymptotic variance of the MTTF estimated in the accelerated degradation test;

[0124] 2) Maximize the parameter values ​​contained in the Fisher information matrix;

[0125] 3) Minimize the ratio of asymptotic variances when varying the input parameters.

[0126] The goal is to design functions that represent the parameters with estimation accuracy and stability to fully represent the gamma process. In summary, the first goal is to obtain the estimation accuracy of the life cycle. Then, the parameters representing the accelerated degradation model are accurately evaluated so that the estimated model plays an important role in the reliability design and allocation of the system. In order to obtain reasonable results with limited resources, it is also necessary to consider the sensitivity of the estimated reliability to parameter changes. In degradation testing, several goals need to be achieved, namely, evaluating the expected MTTF (mean time to failure) to specify how long the product under consideration will meet the required performance; estimating the parameters representing the degradation process and the factors affecting external shocks; improving the robustness of the model used to describe the degradation process.

[0127] Therefore, the objectives considered can be summarized as 1) minimizing the asymptotic variance corresponding to the estimated MTTF in the accelerated degradation test; 2) maximizing the parameter values ​​contained in the Fisher information matrix; 3) minimizing the ratio of the asymptotic variance when changing the input parameters. More specifically, as a measure of the deviation of the estimated parameters, the asymptotic variance can be used to indicate the estimation accuracy, especially when the estimation must be performed in multiple stages. The first objective function is expressed mathematically. The expression is expressed as:

[0128]

[0129] Among them I Ga represents the Fisher matrix, as shown in equation (6). And, H Ga The matrix can be obtained as shown in (7)

[0130]

[0131] The length of the confidence intervals for the estimated parameters of the degradation process and their dependence on the random shocks is determined by the determinant of the Fisher matrix. Moreover, the larger the determinant of the Fisher matrix, the more precise the parameters are. To improve the robustness of the reliability test, a third objective is specified as the rate of change of the asymptotic variance after modifying the parameters. Moreover, the lower the rate of change, the more robust the test / model.

[0132] Most importantly, the objective function under consideration can be mathematically specified as

[0133] Among them, Avar * (MTTF Ga ) represents the minimum level of the asymptotic variance of MTTF. Avar(MTTF Ga ) is the asymptotic variance value after random modification to the optimal parameters that characterize the degradation process and its correlation with random shocks.

[0134] In this embodiment, the constraints of the acceleration model include test resources, and the test resource expression is as follows:

[0135]

[0136] In the formula, c s represents the cost of a sample, N represents the number of samples, c0 represents the unit time cost of the test equipment, d k represents the test duration at the kth level of the selected stress, C m represents the cost of measuring a performance level for a sample and a time, M k Represents the total number of measured tests within a specified stress combination, TC * Represents the maximum cost that reliability testing can provide.

[0137] In order to optimally arrange the reliability test, the constraints considered are specified as costs. Specifically, the entire cost can be divided into three parts: sample cost, test resource cost, and performance measurement cost. The cost of the sample can be expressed as CS=cs*N, where cs is the cost of a sample. The test resource cost refers to the cost of the test equipment, which is determined by the test duration. Therefore, the expression can be expressed as CR=C0*∑dkKk=1, where C0 represents the unit time usage cost of the test equipment, and dkis represents the test duration at the kth level of the selected stress. The total cost of performance measurement can be expressed as CM=N*cm*∑KMk, where cm is the cost of measuring the performance level of a product and a time. In summary, the constraint can be comprehensively expressed as:

[0138]

[0139] In the formula, c s represents the cost of a sample, N represents the number of samples, c0 represents the unit time cost of the test equipment, d k represents the test duration at the kth level of the selected stress, c m represents the cost of measuring a performance level for a sample and a time, M k Represents the total number of measured tests within a specified stress combination, TC * Represents the maximum cost that reliability testing can provide.

[0140] S2. Collect the test results of the acceleration model in the degradation process, which include a optimization target values ​​and a number of variables to be optimized corresponding to the target values, to form a group of sequence data; calculate the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequence; calculate at least one grey incidence coefficient based on the difference sequence, and calculate the comprehensive grey correlation degree of the a optimization targets based on the at least one grey incidence coefficient;

[0141] In this embodiment, when dealing with multi-objective optimization, traditional methods usually transfer multiple considered objectives into a comprehensive objective. Moreover, all objectives must be weighted to clarify their importance. However, the functions corresponding to different objectives vary from person to person. Therefore, it is almost impossible to search for a unified evaluation of objective weights. In order to overcome the above shortcomings, this section introduces a grayscale incidence model, considering three objective functions at the same time. And the gray correlation degree is used to measure the optimality of the results. When integrating gray correlation analysis into accelerated test optimization, the following steps can be applied.

[0142] Step 1: Data Collection In this step, it is necessary to test the target values ​​under different levels of the variables to be optimized to obtain the mapping function between the target value and the variables.

[0143] Step 2: Data preprocessing Since the measured dimensions of the three targets are inconsistent with each other, the collected data of the three targets need to be standardized to consider them together. For the first and third targets (asymptotic variance and RV), the normalization equation is expressed as

[0144]

[0145] Among them, v i Indicates the i-th value of the collected target value. u i is the normalized value of the target. max and v min Respectively represent the maximum and minimum levels of the collected target values.

[0146] For the second objective (determinant of the Fisher matrix), the normalization can be expressed as

[0147]

[0148] Step 3: Transform the sequence structure of normalized data into Y j , which is the target value set in the jth test. j Contains three elements representing three goals, namely Y j (I) and Y j (II) and Y j (III).

[0149] Step 4: Calculate the difference between the different sequences can be calculated as

[0150] Δ j (l)=|Y0(I)-Y j (I)|, l = I, II, III (11)

[0151] Among them, Δ j (l) indicates Y jThe difference between the first value in Y0 and the first value in Y0. Y0(I) is a reference sequence in which all elements reach the optimal value.

[0152] Step 5: Search for the maximum and minimum differences:

[0153]

[0154] Step 6: Calculate the gray incidence coefficient

[0155]

[0156] Among them, Y 0j (l) indicates Y j The grey relational coefficient between ξ∈(0,1) and the first value in Y0.

[0157] Step 7: Calculate the degree of grayscale correlation

[0158]

[0159] As shown in the above steps, by comparing the gray-incidence rate Y 0j , the optimal sequence containing the considered objective value can be obtained. However, the underlining function between the variable to be optimized and the value of the considered objective remains undiscovered.

[0160] S3. Evaluate the optimality of the test results based on the comprehensive grey correlation degree.

[0161] In this embodiment, the optimality of the test results is evaluated based on the comprehensive grey relational degree, specifically:

[0162] Taking the comprehensive grey correlation degree as the dependent variable, constructing a Kriging model, and predicting the grey incidence based on the Kriging model;

[0163] The optimality of the test results was evaluated based on the grayscale occurrence rate.

[0164] The Kriging model is used to explore the degradation between the functional test characteristic variables (such as the total type of stress, the total amount of test duration and the total level of stress considered) and the sequence of optimal target levels close to the target value of the target. Proposed by Danic Krige, the Kriging model is designed to obtain a perfect nonlinear function. The mechanism of underlining is to minimize the variance of the unbiased estimate. According to the Kriging model, the expression can be expressed as:

[0165] y(x)=f T (x)β+z(x) (15)

[0166] Among them, x is the independent variable. y is the dependent variable. β is the regression variable. f T(x) is the relationship function. z(x) represents the random error value.

[0167] In this embodiment, S3 evaluates the optimality of the test result based on the comprehensive grey correlation degree, and then further includes:

[0168] According to the optimality of the test results, several groups of variables to be optimized are obtained;

[0169] Several groups of variables to be optimized are used as data input for the PSO algorithm, and the PSO algorithm is used to search for the optimal solution.

[0170] By obtaining the above optimal function through the Kriging model, the particle swarm optimization (PSO) algorithm can be introduced to search for the optimal values ​​of the characteristic parameters representing the degradation test.

[0171] The PSO algorithm is an intelligent algorithm for global random search for optimal solutions, designed to simulate its biological characteristics and inherent swarm intelligence. In PSO, a set of specified possible values ​​of variables to be optimized is regarded as a particle. The fitness value of a particle is the mapping value in the objective function. In order to effectively find the best particle with the best fitness value, all particles are designed to randomly change their positions in the constraint area. Then, the perfect particle can be selected by comparing their fitness values. Under the condition that the selected perfect particle remains the same in different search paths, the optimal value of the variable can be specified. The application flow chart of PSO is as follows Figure 2 As shown. In the original PSO, the velocity and position vectors can be derived into the following equations.

[0172]

[0173] Among them, Xik = {xik1, xik2, ..., xiik} represents the vector of the position value of the i-th particle in the k-th generation d-dimensional search space. W is the inertial weight. Vik = {vik1, vik2, ..., viik} is the vector of the velocity value of the i-th particle in the k-th generation d-dimensional search space. Pik = {pik1, pik2, ..., piik} is the vector of the best position of each particle. It is also called the best position. Pgk = {pgk1, pgk2, ..., pgkg} represents the best set of particles found so far in the k-th generation, which is called the gbest position.

[0174] In order to better understand the present invention, an electric spindle is used for illustration.

[0175] As a complex electromechanical system, the electric spindle has been widely used in various engineering fields. In this section, an electric spindle is introduced to clearly show how the effective algorithm can be applied. A degradation test of the electric spindle is planned to accurately estimate its reliability level and explore its degradation mechanism. The test is scheduled on Figure 3 A large number of studies and engineering practices have shown that factors such as temperature, speed, torque and free radical stress can have an adverse effect on the performance efficiency of the electric spindle.

[0176] To consider the spindle, due to its design structure, the torque is weak. And there is a cooling subsystem that prevents the electric spindle from generating thermal loads. However, a sudden change in voltage could make the considered spindle more susceptible to the degradation processes suffered. In summary, the rotational speed and radial stress were selected as the stresses to be tested. The sudden change in voltage is considered as a random shock that adversely affects the performance of the sp.

[0177] As a measure of degradation, the degradation characteristic aims to derive a mapping function between the test stress and the assessed reliability level. There are three principles for selecting a perfect degradation characteristic, namely 1) the characteristic is measurable; 2) the characteristic should reflect the mechanism of degradation; 3) the selected value characteristic changes monotonically over time. First, radial runout is selected as the degradation characteristic for accelerated degradation testing.

[0178] Table 1 Step stress levels i n test

[0179] tested stress type normal level maximum level step interval rotational speed(rpm) 4000 5500 25 radial stress(N) 30 60 0.5

[0180] In order to make full use of limited resources, the test stress is gradually accelerated (as shown in Table 1), which can shorten the total duration of the test. In addition, the maximum level of the test stress is set to a value that does not change the failure mechanism. The parameter values ​​representing the cost constraints are specified as cs=2.5, c0=0.02, cm=0.02, TT*=0.02. The variables that need to be optimized are summarized as the test sample N, the test duration within all specified stress levels Δtk, and the total number of measured tests Mk within the specified stress combination.

[0181] In order to explore the function between the test feature variables and the considered objectives, a total of 30 accelerated degradation tests were performed. The results of the conducted tests are shown in Table 2. In order to calculate the grayscale incidence rate, the optimal values ​​of all different objectives were selected as the optimal sequence, i.e., Y0 = [4.286, 13.766, 0.61].

[0182] The results in Table 2 are divided into two categories, namely, the first group contains 25 samples, which obtain the optimal relationship between the variable to be optimized and the grayscale comprehensiveness; the remaining samples are designed to test the accuracy of the fitting function obtained in the first group.

[0183] Table II result of degradation test

[0184] order N K <![CDATA[Δt k ]]> <![CDATA[M k ]]> <![CDATA[Avar(MF Ga )(×10 5 )]]> <![CDATA[|H Ga |(×10 4 )]]> RV γ 1 13 22 49.53 44 5.102 11.285 0.897 0.478 2 15 30 45.25 57 4.810 13.776 0.948 0.672 3 16 29 43.58 55 4.990 10.731 0.690 0.574 4 12 30 34.76 47 5.184 10.726 0.836 0.473 5 16 22 37.92 48 5.880 9.802 0.886 0.388 6 12 23 51.08 52 5.026 9.289 0.977 0.419 7 16 21 47.25 50 5.282 9.751 0.721 0.500 8 15 25 50.68 55 4.863 13.436 0.692 0.735 9 16 22 46.51 60 5.630 10.641 0.825 0.441 10 16 26 48.54 53 4.749 13.468 0.847 0.671 11 14 25 43.70 58 5.358 9.690 0.913 0.410 12 11 24 40.20 41 6.150 12.019 0.670 0.559 13 11 29 36.19 53 5.175 11.328 0.687 0.576 14 14 30 47.77 43 6.093 12.365 0.845 0.476 15 12 21 50.98 52 4.972 11.227 0.728 0.563 16 14 25 36.92 63 4.814 12.472 0.892 0.567 17 16 26 34.95 43 5.762 12.185 0.713 0.549 18 13 28 35.51 41 5.755 10.203 0.868 0.408 19 14 21 50.51 46 5.645 10.505 0.944 0.401 20 16 25 34.98 60 5.501 10.165 0.657 0.547 21 16 26 39.51 61 4.286 10.286 0.707 0.693 22 11 23 44.78 50 4.533 9.889 0.721 0.605 23 12 29 36.13 42 5.062 11.417 0.885 0.490 24 12 22 39.90 42 5.594 11.549 1.016 0.421 25 13 22 49.53 44 5.102 11.285 0.897 0.478 26 12 19 49.36 56 5.259 11.175 0.915 0.454 27 14 25 43.06 51 5.166 10.271 0.812 0.472 28 14 25 44.88 53 4.984 12.062 0.706 0.610 29 13 26 40.36 48 5.597 9.076 0.911 0.384 30 15 28 40.38 52 5.301 13.090 0.610 0.751

[0185] To apply the Kriging model, the DACE toolbox in Matlab was used. The input variables (also called independent variables) include the test sample N, the test duration within all specified stress levels Δttkk, and the total number of measured tests Mk within the specified stress combination. The dependent variable is the calculated grayscale incidence rate. Then, the results obtained by the Kriging model are shown in Table III. In order to test the validity of the Kriging model, the coefficient is also calculated as R2=∑(γ ll -γ)2 5 ii=1∑(γii-y)2 5ii=1=0.9222, where γ is the average value of the last 5 gray dispersions in Table 3. ll It is the grayscale incidence predicted by the Kriging model. Under the condition of R2>0.9, the Kriging model can effectively represent the mapping function between the feature parameters to be optimized and the grayscale incidence.

[0186] Table III Comparison result of Kriging model and collected data

[0187] order gray incidence degree by Kriging original gray incidence degree 1 0.446 0.454 2 0.493 0.472 3 0.663 0.610 4 0.402 0.384 5 0.696 0.751

[0188] The optimization results are shown in Table IV and the comparative analysis.

[0189] Table IV Optimization results with alternative methods

[0190]

[0191] Comparison 1 refers to the optimization method without introducing the Kriging model. In this case, the total number of iterations has been significantly increased, which leads to a high computational burden. The underlined mechanism can be explained as the Kriging model can provide guidance for searching for the optimal value of the variable to be optimized, making it easier to obtain the optimal value.

[0192] Comparison 2 corresponds to the optimization techniques considering the three objectives simultaneously and separately. Under the above conditions, the asymptotic variance and RV values ​​both increase, while the determinant value of the Fisher matrix decreases compared to this method. This means that this result is not as optimal as the newly developed model. The reason that can be proposed is that the optimization objectives are not centralized, which makes it difficult to achieve the optimal values ​​of all the considered objectives. Most importantly, this method obtains better values ​​of the considered objectives with less computational effort.

[0193] Degradation tests have been widely used to explore their degradation mechanisms. The tested stresses are generally designed to be gradually accelerated to make full use of limited resources. This paper proposes an optimization algorithm for accelerated degradation testing based on grayscale association. The gamma process is used to simulate the inherent degradation process. The shape function is extended to the gamma process, which explicitly simulates the effects of sudden changes in external environmental conditions. The three goals to be achieved are to improve the accuracy of system reliability, the influencing parameters in the gamma process framework, and the robustness of the model describing the degradation mechanism. The gray incidence analysis method is introduced to comprehensively combine these three goals. This paper also applies the Kriging model to explore the mapping function between the variables to be optimized and the comprehensive objectives. The particle swarm optimization (PSO) method is used to globally search for the optimal values ​​of the characteristic parameters describing the degradation process. Finally, an example about an electric spindle is given to demonstrate the effectiveness and advantages of this method.

[0194] Embodiment 2

[0195] See also Figure 4 , an accelerated degradation test optimization device based on grey correlation, based on the method described in one of the embodiments; comprising:

[0196] A building module is used to model the degradation pathway using a gamma process to obtain an acceleration model and set a (a=1-n) optimization objectives;

[0197] A collection module is used to collect the test results of the acceleration model in the degradation process, the results including a optimization target values ​​and a number of variables to be optimized corresponding to the target values, forming a group of sequence data; calculating the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequence;

[0198] A gray coefficient module, used for calculating at least one gray incidence coefficient based on a difference sequence, and calculating a comprehensive gray correlation degree of a optimization target based on at least one gray incidence coefficient;

[0199] Evaluation module, used to evaluate the optimality of test results based on the comprehensive grey relational degree.

[0200] In this embodiment, in order to better use the method described in one of the embodiments, the present application proposes an accelerated degradation test optimization device based on grey correlation, and each module corresponds to each step of the above method. The specific principles have been described above and will not be repeated here.

[0201] Embodiment 3

[0202] An accelerated degradation test optimization device based on grey correlation, comprising:

[0203] at least one processor and a memory communicatively coupled to the at least one processor;

[0204] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method described in one of the embodiments.

[0205] In this embodiment, in order to better run and process the method described in one of the embodiments, the above method is stored in a memory, and a processor is used to execute the stored method. It should be noted that the principle and effect of each step have been described above and will not be described in detail here.

[0206] Embodiment 3

[0207] A computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, the method described in one of the embodiments is implemented.

[0208] In this embodiment, in order to better run and use the method described in one of the embodiments, the method is stored in a computer-readable storage medium and implemented by a processor. It should be noted that the principle and effect of each step have been described above and will not be described in detail here.

[0209] The above descriptions are only some embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any equivalent device or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. An accelerated degradation test optimization method based on grey correlation, characterized in that: The degradation pathway is modeled using the gamma process to obtain an accelerated model, and a (a=1-n) optimization objectives are set; Collect the test results of the acceleration model in the degradation process, which include a optimization target values ​​and a number of variables to be optimized corresponding to the target values, to form a set of sequence data; Calculating the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequence; calculating at least one grey incidence coefficient based on the difference sequence, and calculating the comprehensive grey correlation degree of a optimization objectives based on the at least one grey incidence coefficient; The optimality of the test results was evaluated based on the comprehensive grey relational degree.

2. The accelerated degradation test optimization method based on grey correlation as claimed in claim 1, characterized in that: The optimization objectives include: 1) Minimize the asymptotic variance of the MTTF estimated in the accelerated degradation test; 2) Maximize the parameter values ​​contained in the Fisher information matrix; 3) Minimize the ratio of asymptotic variances when varying the input parameters.

3. The accelerated degradation test optimization method based on grey correlation as claimed in claim 1, characterized in that: The constraints of the acceleration model include test resources, which are expressed as follows: In the formula, c s represents the cost of a sample, N represents the number of samples, c0 represents the unit time cost of the test equipment, d k represents the test duration at the kth level of the selected stress, c m represents the cost of measuring a performance level for a sample and a time, M k Represents the total number of measured tests within a specified stress combination, TC * Represents the maximum cost that reliability testing can provide.

4. The accelerated degradation test optimization method based on grey correlation as claimed in claim 1, characterized in that: Collect the test results of the acceleration model in the degradation process, which include a optimization target values ​​and a number of variables to be optimized corresponding to the target values, forming a set of sequence data, and also include: The test results are normalized and preprocessed.

5. The accelerated degradation test optimization method based on grey correlation as claimed in claim 1, characterized in that: The optimality of the test results is evaluated based on the comprehensive grey correlation degree, specifically: Taking the comprehensive grey correlation degree as the dependent variable, constructing a Kriging model, and predicting the grey incidence based on the Kriging model; The optimality of the test results was evaluated based on the grayscale occurrence rate.

6. The accelerated degradation test optimization method based on grey correlation as claimed in claim 5, characterized in that: The optimality of the test results is evaluated based on the comprehensive grey correlation degree, followed by: According to the optimality of the test results, several groups of variables to be optimized are obtained; Several groups of variables to be optimized are used as data input for the PSO algorithm, and the PSO algorithm is used to search for the optimal solution.

7. An accelerated degradation test optimization device based on grey correlation, characterized in that: A method according to any one of claims 1 to 6; comprising: A building module is used to model the degradation pathway using a gamma process to obtain an acceleration model and set a (a=1-n) optimization objectives; Gray coefficient module, used to collect the test results of the acceleration model in the degradation process, the results include a optimization target value and a number of variables to be optimized corresponding to the target value, forming a group of sequence data; Calculating the difference between each group of sequence data and the reference sequence to obtain at least one group of difference sequence; calculating at least one grey incidence coefficient based on the difference sequence, and calculating the comprehensive grey correlation degree of a optimization objectives based on the at least one grey incidence coefficient; Evaluation module, used to evaluate the optimality of test results based on the comprehensive grey relational degree.

8. An accelerated degradation test optimization device based on grey correlation, characterized in that: include: at least one processor and a memory communicatively coupled to the at least one processor; The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method as claimed in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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