Multi-stress coupling acceleration model construction method based on generalized logarithmic regression model

Abstract

The invention provides a multi-stress coupling acceleration model construction method based on a generalized logarithmic regression model, and the method comprises the following steps: constructing a multi-stress coupling acceleration model based on the generalized logarithmic regression model, and constructing a multi-stress coupling acceleration life distribution model in combination with Weibull distribution; constructing a sample life data set, and performing parameter estimation based on constant multi-stress acceleration test data by using a maximum likelihood estimation method and a least square estimation method based on the multi-stress coupling acceleration life distribution model; correcting the multi-stress coupling accelerated life distribution model based on F-test and t-test; and performing reliability evaluation in a normal use environment based on the corrected multi-stress coupling accelerated life distribution model. According to the method, the multi-stress coupling acceleration model construction and the product reliability evaluation under the normal stress are realized, and the evaluation, identification and assessment work of the product reliability under the complex environment can be effectively supported.

Description

Technical Field

[0001] The present invention is applicable to related technical fields such as the construction of multi-stress coupling acceleration models and reliability assessment, and particularly relates to a method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model. Background Art

[0002] Life test is a key technology for realizing the reliability assessment, identification, and evaluation of products. It examines the law of product failure over time by placing the product under specific test conditions to understand and evaluate the life and reliability of the product. With the rapid development of the manufacturing industry, the quality and reliability of products have been continuously improved, making it difficult to quickly obtain product failure data through traditional life tests. For this reason, the accelerated life test technology has been proposed. Under the condition of keeping the failure mechanism of the product unchanged, it speeds up product failure and data collection by increasing the test stress of the product, and then extrapolates the life level of the product under normal use stress through an acceleration model, so as to realize the efficient and accurate assessment of product reliability.

[0003] The acceleration model is the core of the accelerated life test technology. Since it is difficult to analyze the failure process of products under working conditions and stresses, there are currently only acceleration models describing single stress or double stress such as temperature, humidity, vibration, and electrical stress. However, for products in actual use environments, they are generally affected by the combined action and coupling of three or more types of stresses. For example, in the use state, electrical connectors used for electrical connections between product subsystems are affected by the coupling of multiple types of stresses such as temperature, humidity, and electrical stress, resulting in failure modes such as contact failure, insulation failure, and sealing failure. Since the existing acceleration models fail to effectively describe the influence of the combined action of multi-stresses and their coupling on the life characteristics of products, it is not only difficult to effectively simulate the failure process of products in the actual environment in the laboratory, but also difficult to accurately evaluate the life and reliability levels of products during actual use, hindering the development of product reliability assessment, identification, and evaluation work. Summary of the Invention

[0004] Based on the above background, in view of the problem that it is difficult to accurately evaluate the reliability of products in the actual use environment based on the existing single-stress or double-stress acceleration models due to the combined action and coupling of multiple types of stresses on products during the process of product reliability assessment, identification, and evaluation, the present invention provides a method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model. This method sorts out the sensitive stresses in the actual use environment of the product, constructs a multi-stress acceleration model and an accelerated life distribution model using the generalized logarithmic regression model, estimates the model parameters according to the constant multi-stress acceleration test data, and then conducts model correction using t-tests and F-tests, and finally completes the reliability assessment of products under normal stress. Based on the above ideas, the present invention provides the following technical solutions:

[0005] A method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model, comprising the following steps:

[0006] S1. Construct a multi-stress coupling acceleration model based on the generalized logarithmic regression model, and construct a multi-stress coupling accelerated life distribution model in combination with the Weibull distribution;

[0007] S2. Construct a sample life data set, and based on the multi-stress coupling accelerated life distribution model, use the maximum likelihood estimation method and the least squares estimation method to perform parameter estimation based on the constant multi-stress acceleration test data;

[0008] S3. Modify the multi-stress coupling accelerated life distribution model based on the F-test and t-test;

[0009] S4. Perform reliability assessment under normal use environment based on the modified multi-stress coupling accelerated life distribution model.

[0010] Further, step S1 specifically includes:

[0011] S11. Assume that according to the analysis of the actual use environment profile of the product and the experience of relevant staff, determine the main sensitive stress set S = {S1, S2,..., S n}, where S i (i = 1, 2,..., n) represents the i-th type of stress, such as temperature, humidity, vibration, electrical stress, etc., and n represents the number of stress types;

[0012] S12. Considering the fact that the coupling effect of the third order and above between multiple types of stresses has a generally small impact on the product life, and the complexity of its mathematical form makes it difficult to be actually applied, use the generalized logarithmic regression model to construct the overall framework of the multi-stress coupling acceleration model in a typical multi-stress scenario as shown in Equation (1):

[0013]

[0014] In the formula, L(S) is the life characteristic of the product, such as median life, average life, quantile life, characteristic life, etc.; β0 is a constant, β i (i = 1, 2,..., n) is the first-order action parameter of the stress, β j,k (j = 1, 2,..., n, k = 1, 2,..., n) is the second-order coupling action parameter of the stress, and g(·) is a transformation function, including reciprocal form, logarithmic form, etc. For common temperature, humidity, vibration and electrical stress, the form of the change function is as shown in Equation (2):

[0015]

[0016] S13. Given that the Weibull distribution can be converted into an exponential distribution by adjusting the distribution parameters and can also approximate a normal distribution, thus covering the product life distributions commonly used in actual engineering. Therefore, taking the Weibull distribution as the product life distribution, its probability density function f(t) is as shown in Equation (3):

[0017]

[0018] In the formula, m is the shape parameter; η is the characteristic life, which is affected by environmental stress; I(·) is the indicator function. When the value inside the function is true, I = 1; otherwise, it is 0.

[0019] S14. Substitute η for L(S) in the multi-stress coupling acceleration model in Equation (1) to obtain the multi-stress coupling accelerated life distribution model as shown in Equation (4):

[0020]

[0021] In the formula, η l represents the characteristic life value under the l-th stress level combination, and S i,l , S j,l , S k,l respectively represent the levels of the i-th, j-th, and k-th stresses under the l-th stress level combination.

[0022] Furthermore, in step S2, constructing the sample life data set specifically includes:[[]]

[0023] Assume that a constant stress accelerated life test of a certain product is carried out under L stress level combinations, and H samples are put into each stress level combination. Denote the stress levels in the l-th stress level combination as (S 1,l , S 2,l , …, S n,l ), where l = 1, 2, …, L; S i,l (i = 1, 2, …, n) represents the value of the i-th stress in the l-th stress level combination; denote the sample life data set measured under the l-th stress level combination as X l = (X l,1 , X l,2 , …, X l,H ), where X l,h (h = 1, 2, …, H) represents the life of the h-th sample under the l-th stress level combination. For the multi-stress coupling accelerated life distribution model shown in Equation (4), use the maximum likelihood estimation method and the least squares estimation method to construct a two-step model parameter estimation method.

[0024] Furthermore, step S2 specifically includes:[[]]

[0025] S21. For the sample life data set \(X\) under the \(l\)-th stress level combination l =(X l,1 , X l,2 , …, X l,H ), establish the log-likelihood function of the parameters in the life distribution model of Equation (3) as shown in Equation (5):

[0026]

[0027] where \(\ln L\) represents the log-likelihood function;

[0028] S22. Take the partial derivatives of Equation (5) with respect to the parameters \(m\) and \(\eta\) l respectively, and set them equal to 0 to obtain a system of simultaneous equations as shown in Equation (6):

[0029]

[0030] S23. Use numerical methods to solve Equation (6) to obtain the two parameter estimates of the product life distribution model under the \(l\)-th stress level combination and For the sample life data under all stress level combinations, use the maximum likelihood method to estimate the model parameters in turn, and obtain the sets of estimates of the two parameters under \(L\) stress level combinations as and and let the final estimate of the shape parameter \(m\) be as shown in Equation (7):

[0031]

[0032] S24. For the parameters in the overall framework of the multi-stress coupling acceleration model of Equation (1), according to the least squares estimation method and obtain the estimates of the unknown model parameters as shown in Equation (8):

[0033]

[0034] where

[0035]

[0036] Thus, the estimation of the model parameters under the current multi-stress coupling acceleration model of Equation (1) is completed.

[0037] After obtaining the multi-stress coupling acceleration model, it is necessary to conduct a significance test on the overall multi-stress coupling acceleration model and a significance test on each stress action term through the F-test and t-test respectively, and gradually delete the insignificant stress action terms to complete the correction of the multi-stress coupling acceleration model.

[0038] Furthermore, step S3 specifically includes:

[0039] S31. Conduct an overall significance test on the multi-stress coupling accelerated life distribution model based on the F-test, and construct the test null hypothesis as shown in Equation (9):

[0040] H0: β0 = β1 = … = βx = β 1,1 = … = β n,n = 0 (9)

[0041] When the null hypothesis of Equation (9) holds, it indicates that all stress effect terms are not significant for the characteristic life;

[0042] S32. Construct an F-statistic as shown in Equation (10) to determine the overall significance of the multi-stress coupling acceleration model:

[0043]

[0044] where, represents the logarithmic characteristic life of the product under the l-th stress level combination predicted by the current multi-stress coupling acceleration model; when the null hypothesis (9) holds, the F-statistic in Equation (10) follows an F-distribution with degrees of freedom (p, L - p - 1); for a given significance level α, when F > F α (p, L - p - 1) in Equation (10), reject the null hypothesis, consider the multi-stress coupling acceleration model significant, and proceed to S33; otherwise, accept the null hypothesis, consider the multi-stress coupling acceleration model not significant, and determine that this product is not suitable for constructing a multi-stress coupling acceleration model using the generalized logarithmic regression model;

[0045] S33. Conduct a significance test on each stress effect term of the multi-stress coupling acceleration model based on the t-test. For the u-th (u = 1, 2, …, p) term in the multi-stress coupling acceleration model, construct the test null hypothesis as shown in Equation (11):

[0046] H 0u : β u = 0 (11)

[0047] When the null hypothesis (11) holds, it indicates that this stress effect term is not significant for the characteristic life;

[0048] S34. To determine the significance of each stress effect term, construct a t-statistic as shown in Equation (12):

[0049]

[0050] where, c uu is the element in the u-th row and u-th column of the matrix (Z T Z) -1 , When the null hypothesis (11) holds, the t-statistic in Equation (12) follows a t-distribution with degrees of freedom L - p - 1; for a given significance level α, when holds, the null hypothesis is rejected, and it is considered that the u-th term of the multi-stress coupling acceleration model is significant; otherwise, the null hypothesis is accepted, and it is considered that the u-th term of the multi-stress coupling acceleration model is not significant; when there is a stress action term with a non-significant test result, go to S35; otherwise, output the current multi-stress coupling acceleration model;

[0051] S35. For the stress action term with a non-significant test result, according to the magnitude of its t-test statistic value |t u |, delete the stress action term corresponding to the smallest |t u | value, and repeat steps S2 and S33 and S34 in step S3 until all stress action terms pass the significance test, and complete the correction of the multi-stress coupling acceleration model.

[0052] Further, step S4 specifically includes:

[0053] S41. Assume that the corrected multi-stress coupling accelerated life distribution model is as shown in Equation (13):

[0054]

[0055] In the formula, n1, n2, n3 represent 3 subsets of the set {1, 2,..., n};

[0056] S42. Based on the corrected model, form the final reliability function of the product as shown in Equation (14):

[0057]

[0058] S43. Assume that the stress level combination under normal stress is (S 1,0 , S 2,0 , …, S n,0 ), then the reliability function of the product under normal use environment is as shown in Equation (15):

[0059]

[0060] So far, the construction of the product multi-stress coupling acceleration model and the reliability evaluation under normal stress are completed.

[0061] The multi-stress coupling acceleration model construction method based on the generalized logarithmic regression model proposed by the present invention has the following advantages:

[0062] ① The present invention aims at constructing a multi-stress coupling acceleration model under the joint action of multiple stresses and their coupling action, establishes a multi-stress coupling acceleration model based on the generalized logarithmic regression model, constructs a multi-stress coupling acceleration distribution model in combination with the Weibull distribution, and uses the F-test and t-test to carry out the overall significance test of the model and the significance test of each stress action item, thereby realizing the gradual correction of the multi-stress coupling acceleration model, and finally realizing the construction of the multi-stress coupling acceleration model and the product reliability evaluation under normal stress, which can effectively support the evaluation, identification and assessment of product reliability in complex environments.

[0063] ② The principle and calculation of the method proposed in the present invention are simple to understand and easy to implement, which is convenient for engineering and technical personnel to master and use, and is easy to apply and promote. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0065] The following takes the construction of a multi-stress coupling acceleration model of a certain type of electrical connector as an example. Figure 1 , the present invention is described in further detail.

[0066] A certain type of electrical connector will be affected by temperature, humidity and electrical stress in working state, resulting in contact failure, insulation failure, sealing failure and other failure modes, which will cause the electrical signal between product subsystems to be unable to be transmitted, affecting the normal operation of the product. In order to effectively support the optimization of maintenance strategies for this type of electrical connector, it is necessary to accurately evaluate its reliability in actual use environment. In a certain test, 90 electrical connectors were evenly divided into 18 groups, and accelerated life tests were carried out under 18 combinations of temperature, humidity and electrical stress. The stress levels in each stress level combination are shown in Table 1, and the life data of the electrical connectors collected under each stress level are shown in Table 2. In addition, the normal working stress of this type of electrical connector is: absolute temperature 298.15, relative humidity 50%, voltage 12V.

[0067] Table 1

[0068] Combination number of stress levels Absolute temperature (K) Relative humidity (%) Voltage (V) 1 353.15 60 18 2 353.15 60 24 3 353.15 75 18 4 353.15 75 30 5 353.15 90 24 6 353.15 90 30 7 373.15 60 18 8 373.15 60 30 9 373.15 75 24 10 373.15 75 30 11 373.15 90 18 12 373.15 90 24 13 393.15 60 24 14 393.15 60 30 15 393.15 75 18 16 393.15 75 24 17 393.15 90 18 18 393.15 90 30

[0069] Table 2

[0070]

[0071]

[0072] Based on the above example, the embodiment of the present invention proposes a method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model, and its specific implementation steps are as follows (the formulas (1)-(15) involved are described in the above invention content):

[0073] Step 1: Construction of multi-stress coupling acceleration model and accelerated life distribution model.

[0074] Since the main sensitive stresses of this type of electrical connector in the combat readiness duty state are temperature, humidity, and electrical stress, the set of main sensitive stresses of the product is determined as S = {S1 = temperature, S2 = humidity, S3 = voltage}. According to formula (1) and formula (2), the overall framework of the multi-stress coupling acceleration model under three stress scenarios is constructed using the generalized logarithmic regression model as shown in formula (16):

[0075]

[0076] In the formula, T represents the absolute temperature, RH represents the relative humidity, and V represents the voltage.

[0077] Using the Weibull distribution to characterize the life distribution of this type of electrical connector, according to formula (4) and formula (16), the multi-stress coupling accelerated life distribution model of this type of electrical connector under temperature, humidity, and electrical stress is as shown in formula (17):

[0078]

[0079] In the formula, T l , RH l , V l respectively represent the absolute temperature level, relative humidity level, and voltage level under the l-th stress level combination.

[0080] Step 2: Parameter estimation based on constant multi-stress acceleration test data.

[0081] Based on the test data in Table 2, the model parameter estimation is carried out using the maximum likelihood estimation method and the least squares estimation method.

[0082] In the first step, for the life data under each stress level combination in Table 2, using the maximum likelihood estimation method, the estimated values of the life distribution parameters m and η l are calculated according to formula (6), and the results are shown in Table 3.

[0083] Table 3

[0084]

[0085]

[0086] Therefore, according to formula (7), it can be known that the final estimated value of the shape parameter m is

[0087] Step ②: Using the estimated values of the characteristic life under each stress level combination in Table 3, according to the least squares estimation method and formula (8), the estimated values of the multi-stress coupling acceleration model parameters are obtained as shown in Table 4.

[0088] Table 4

[0089] Parameter Estimated value <![CDATA[β0]]> 96.8627 <![CDATA[β1]]> <![CDATA[-5.3006×10 4 > <![CDATA[β2]]> 3.6150 <![CDATA[β3]]> -23.5666 <![CDATA[β 1,1 > <![CDATA[6.3934×10 6 > <![CDATA[β 1,2 > 332.8578 <![CDATA[β 1,3 > <![CDATA[8.0517×10 3 > <![CDATA[β 2,2 > -0.3513 <![CDATA[β 2,3 > -0.6698 <![CDATA[β 3,3 > 0.6589

[0090] Thus, the estimation of the model parameters under the current multi-stress coupling acceleration model with Equation (16) is completed.

[0091] Step 3: Modification of the multi-stress coupling acceleration model based on F-test and t-test.

[0092] To test the overall significance of the multi-stress coupling acceleration model shown in Equation (16) and the significance of each stress term, the F-test and t-test of model (16) are respectively carried out, and the multi-stress coupling acceleration model is modified. Specifically as follows:

[0093] Step ①: Conduct an overall significance test of the multi-stress coupling acceleration model based on the F-test. Construct the test null hypothesis as shown in Equation (18):

[0094] H0:β0=β1=β2=β3=β 1,1 =β 1,2 =β 1,3 =β 2,2 =β 2,3 =β 3,3 =0 (18) According to formula (10), the value of the F-test statistic is calculated as F = 271.0570. Looking up the table, at the significance level α = 0.1, F 0.1 (10,7)=0.4143, and it satisfies F>F 0.1 (10,7). Therefore, the null hypothesis is rejected, and it is considered that the current multi-stress coupling acceleration model is significant, and proceed to step ②.

[0095] Step ②: Conduct a significance test of each stress term of the multi-stress coupling acceleration model based on the t-test. Respectively for each stress term in the multi-stress coupling acceleration model (16), construct the test null hypothesis as shown in Equation (19)

[0096] H 0u :β u =0, where u = 1,2,…,10 (19) According to formula (12), the values of the t-statistics of each coefficient of the multi-stress coupling acceleration model are calculated as shown in Table 5.

[0097] Table 5

[0098] Parameter t-statistic value <![CDATA[β0]]> 3.0669 <![CDATA[β1]]> -4.3245 <![CDATA[β2]]> 0.3665 <![CDATA[β3]]> -4.1079 <![CDATA[β 1,1 > 3.0738 <![CDATA[β 1,2 > 0.2975 <![CDATA[β 1,3 > 9.0596 <![CDATA[β 2,2 > -0.3317 <![CDATA[β 2,3 > -1.0589 <![CDATA[β 3,3 > 0.9807

[0099] From the table, at the significance level α = 0.1, t 0.1 / 2 (7) = 1.8946. Therefore, the parameters β2, β 1,2 , β 2,2 , β 2,3 and β 3,3 cannot pass the significance test.

[0100] Step ③, modification of the multi-stress coupling acceleration model. Since β 1,2 has the smallest absolute value of the t-statistic, after removing this stress action term from model (17), the updated multi-stress coupling acceleration model in the first round is shown in Equation (20):

[0101]

[0102] According to Equation (20) and the data listed in Table 3, using Equation (8), the parameter estimation values in the multi-stress coupling acceleration model (20) are shown in Table 6.

[0103] Table 6

[0104]

[0105]

[0106] Re-execute Step ②, and the values of the t-statistics of the coefficients in the multi-stress coupling acceleration model (20) are shown in Table 7.

[0107] Table 7

[0108] Parameter t-statistic value <![CDATA[β0]]> 3.4398 <![CDATA[β1]]> -4.7581 <![CDATA[β2]]> 0.5125 <![CDATA[β3]]> -4.3273 <![CDATA[β 1,1 > 3.2483 <![CDATA[β 1,3 > 9.6427 <![CDATA[β 2,2 > -0.3455 <![CDATA[β 2,3 > -1.1671 <![CDATA[β 3,3 > 1.0014

[0109] From the table, at the significance level α = 0.1, t 0.1 / 2 (8) = 1.8595. Therefore, the parameters β2, β 2,2 , β 2,3 and β 3,3 cannot pass the significance test. Since β 2,2 has the smallest absolute value of the t-statistic, after removing this stress action term from model (20), the updated multi-stress coupling acceleration model in the second round is shown in Equation (21):

[0110]

[0111] According to Equation (21) and the data listed in Table 3, using Equation (8), the parameter estimation values in the multi-stress coupling acceleration model (21) are shown in Table 8.

[0112] Table 8

[0113]

[0114]

[0115] Re - execute step ②, and the t - statistic values of the coefficients in the multi - stress coupling acceleration model (21) are shown in Table 9 as follows.

[0116] Table 9

[0117] Parameter t-statistic value <![CDATA[β0]]> 5.6221 <![CDATA[β1]]> -4.9957 <![CDATA[β2]]> 0.8612 <![CDATA[β3]]> -4.5652 <![CDATA[β 1,1 > 3.4005 <![CDATA[β 1,3 > 10.2388 <![CDATA[β 2,3 > -1.2149 <![CDATA[β 3,3 > 1.0486

[0118] Looking up the table, at the significance level α = 0.1, t 0.1 / 2 (9)=1.8331. Therefore, the parameters β2, β 2,3 and β 3,3 cannot pass the significance test. Since β2 has the smallest absolute value of the t - statistic, after removing this stress effect term from the model (21), the updated multi - stress coupling acceleration model in the third round is shown in Equation (22) as follows:

[0119]

[0120] According to Equation (22) and the data listed in Table 3, using Equation (8), the parameter estimation values in the multi - stress coupling acceleration model (22) are shown in Table 10 as follows.

[0121] Table 10

[0122]

[0123]

[0124] Re - execute step ②, and the t - statistic values of the coefficients in the multi - stress coupling acceleration model (22) are shown in Table 11 as follows.

[0125] Table 11

[0126] Parameter t-statistic value <![CDATA[β0]]> 6.6309 <![CDATA[β1]]> -5.0003 <![CDATA[β3]]> -6.0876 <![CDATA[β 1,1 > 3.3547 <![CDATA[β 1,3 > 10.6812 <![CDATA[β 2,3 > -5.5757 <![CDATA[β 3,3 > 1.0611

[0127] Looking up the table, at the significance level α = 0.1, t 0.1 / 2 (10)=1.8125. Therefore, only the parameter β 3,3 cannot pass the significance test. After removing this stress effect term from the model (22), the updated multi - stress coupling acceleration model in the fourth round is shown in Equation (23) as follows:

[0128]

[0129] According to Equation (23) and the data listed in Table 3, using Equation (8), the parameter estimation values in the multi - stress coupling acceleration model (23) are shown in Table 12 as follows.

[0130] Table 12.

[0131]

[0132]

[0133] Re - execute step ②, and the t - statistic values of the coefficients in the multi - stress coupling acceleration model (23) are shown in Table 13 as follows.

[0134] Table 13

[0135] Parameter t-statistic value <![CDATA[β0]]> 6.6737 <![CDATA[β1]]> -4.9743 <![CDATA[β3]]> -10.7581 <![CDATA[β 1,1 > 3.3372 <![CDATA[β 1,3 > 10.6256 <![CDATA[β 2,3 > -5.5467

[0136] By looking up the table, it can be obtained that when the significance level α = 0.1, t 0.1 / 2 (11)=1.7959. Therefore, all parameters have passed the significance test, the multi - stress coupling acceleration model is corrected, and formula (23) is determined as the final multi - stress coupling acceleration model.

[0137] Step Four: Reliability assessment under normal use environment.

[0138] According to formula (14), formula (23) and the parameter estimation results in Table 12, it can be known that the final reliability function of the product is as shown in formula (24):

[0139]

[0140] Substitute the stress level combination under normal stress (T0 = 298.15, RH0 = 50, V0 = 12) into formula (24), and the reliability function of this type of electrical connector under normal use environment can be obtained as shown in formula (25):

[0141]

[0142] So far, the construction of the multi - stress coupling acceleration model for this type of electrical connector and the reliability assessment under normal stress are completed.

[0143] To sum up, the method for constructing a multi - stress coupling acceleration model based on the generalized logarithmic regression model disclosed in the present invention aims at the construction of a multi - stress coupling acceleration model under the combined action and coupling action of multiple stresses. A multi - stress coupling acceleration model based on the generalized logarithmic regression model is established, a multi - stress coupling acceleration distribution model is formed by combining with the Weibull distribution, and the overall significance test of the model and the significance test of each stress action term are carried out by using F - test and t - test. The multi - stress coupling acceleration model is gradually corrected, and finally the construction of the multi - stress coupling acceleration model and the reliability assessment of the product under normal stress are realized, which can effectively support the evaluation, identification and assessment of product reliability under complex environments.

Claims

1. A method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model, characterized in that: The steps include: S1. Construct a multi-stress coupling accelerated model based on the generalized logarithmic regression model, and construct a multi-stress coupling accelerated life distribution model in combination with the Weibull distribution; S2. Constructing a sample life data set, and based on the multi-stress coupled accelerated life distribution model, using the maximum likelihood estimation method and the least squares estimation method, performing parameter estimation based on the constant multi-stress accelerated test data; S3, modifying the multi-stress coupling accelerated life distribution model based on F-test and t-test; S4. Reliability assessment under normal use environment is carried out based on the modified multi-stress coupling accelerated life distribution model.

2. The method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model according to claim 1, characterized in that: Step S1 specifically includes: S11. According to the actual environmental profile analysis and empirical data of the product, determine the main sensitive stress set S = {S1, S2, ..., S n }, where S i (i=1,2,…,n) represents the i-th type of stress, and n represents the number of stress types; S12. Using the generalized logarithmic regression model, the overall framework of the multi-stress coupling acceleration model under typical multi-stress scenarios is constructed as shown in formula (1): Where L(S) is the life characteristic of the product, β0 is a constant, and β i (i=1,2,…,n) is the first-order stress parameter, β j，k (j = 1, 2, ..., n, k = 1, 2, ..., n) is the second-order coupling parameter of stress, g(·) is the transformation function, and the form is shown in formula (2): S13. Taking Weibull distribution as the product life distribution, its probability density function f(t) is shown in formula (3): Where m is the shape parameter; η is the characteristic life, which is affected by environmental stress; I(·) is the indicative function, when the value in the function is true, I = 1; otherwise, it is 0; S14, replace L(S) of the multi-stress coupling acceleration model in formula (1) with η, and obtain the multi-stress coupling accelerated life distribution model as shown in formula (4): Where η l It represents the characteristic life value under the lth stress level combination, S i，l , S j，l , S k，l They represent the levels of the i-th, j-th, and k-th stresses under the l-th stress level combination respectively.

3. The method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model as claimed in claim 2, characterized in that: In step S2, constructing a sample life data set specifically includes: Assume that a constant stress accelerated life test of a product is conducted under L stress level combinations, and H samples are put into each stress level combination, and each stress level in the lth stress level combination is recorded as (S 1，l， S 2，l , …, S n，l ), where l = 1, 2, ..., L; S i，l (i=1,2,…,n) represents the value of the i-th stress in the l-th stress level combination; the sample life data set measured under the l-th stress level combination is recorded as X l =(X l，1 , X l，2 , …, X l,H ), where X l，h (h=1,2,…,H) represents the life of the hth sample under the lth stress level combination.

4. The method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model as claimed in claim 3, characterized in that: Step S2 specifically includes: S21, for the sample life data set X under the lth stress level combination l =(X l，1 , X l，2 , …, X l，H ), the log-likelihood function of the parameters in the life distribution model (3) is established as shown in (5): Where, lnL represents the log-likelihood function; S22, for equation (5) with respect to parameters m and η l Find the partial derivative and set it equal to 0, and get the system of simultaneous equations as shown in equation (6): S23. Use numerical methods to solve equation (6) and obtain the estimated values ​​of two parameters of the product life distribution model under the lth stress level combination: and For the sample life data under all stress level combinations, the model parameters are estimated using the maximum likelihood method, and the estimated value sets of the two parameters under L stress level combinations are obtained as follows: and And let the final estimated value of shape parameter m be as shown in formula (7): S24. For the parameters in the overall framework of the multi-stress coupling acceleration model (1), according to the least squares estimation method and The estimated values ​​of the unknown parameters of the model are shown in formula (8): In the formula, Thus, the model parameter estimation under the current multi-stress coupling acceleration model is completed using formula (1).

5. The method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model as claimed in claim 4, characterized in that: Step S3 specifically includes: S31. Based on the F-test, the overall significance test of the multi-stress coupling accelerated life distribution model is carried out, and the test null hypothesis is constructed as shown in formula (9): H0：β0＝β1＝…＝β n ＝β 1，1 ＝…＝β n，n ＝0 (9) When the null hypothesis (9) holds, it means that all stress terms have no significant effect on the characteristic life; S32. Construct the F-statistic as shown in formula (10) to determine the overall significance of the multi-stress coupling acceleration model: In the formula, represents the logarithmic characteristic life of the product under the lth stress level combination predicted by the current multi-stress coupling acceleration model; when the null hypothesis (9) holds, the F-statistic in formula (10) obeys the F distribution with the degree of freedom (p, Lp-1); for a given significance level α, when F>F in formula (10) α (p, Lp-1), reject the original hypothesis, consider the multi-stress coupling acceleration model to be significant, and proceed to S33; otherwise, accept the original hypothesis, consider the multi-stress coupling acceleration model to be insignificant, and determine that the product is not suitable for constructing the multi-stress coupling acceleration model using the generalized logarithmic regression model; S33. Based on the t-test, the significance test of each stress action item of the multi-stress coupling acceleration model is performed. For the u-th item (u=1, 2, ..., p) in the multi-stress coupling acceleration model, the original hypothesis of the test is constructed as shown in formula (11): H 0u ：β u ＝0 (11) When the original hypothesis (11) is established, it means that the stress effect term has no significant effect on the characteristic life; S34. To determine the significance of each stress action term, construct the t-statistic as shown in formula (12): In the formula, c uu is the matrix (Z T Z) -1 The u-th row and u-th column element of When the null hypothesis (11) holds, the t-statistic in formula (12) follows a t-distribution with a degree of freedom of Lp-1; for a given significance level α, when When , reject the original hypothesis and consider the u-th term of the multi-stress coupling acceleration model to be significant; otherwise, accept the original hypothesis and consider the u-th term of the multi-stress coupling acceleration model to be insignificant; when there is a stress action term with an insignificant test result, enter S35; otherwise, output the current multi-stress coupling acceleration model; S35. For stress terms with insignificant test results, according to their t-test statistic value |t u | size, will have the smallest |t u The stress action term corresponding to the value of | is deleted, and steps S2 and S33 and S34 in step S3 are repeated until all stress action terms pass the significance test, and the correction of the multi-stress coupling acceleration model is completed.

6. The method for constructing a multi-stress coupling acceleration model based on a generalized logarithmic regression model as claimed in claim 5, characterized in that: Step S4 specifically includes: S41. Assume that the modified multi-stress coupling accelerated life distribution model is as shown in formula (13): Where n1, n2, n3 represent three subsets of the set {1, 2, ..., n}; S42. The final reliability function of the product is formed based on the modified model as shown in formula (14): S43, Assume that the stress level combination under normal stress is (S 1，0 , S 2，0 , …, S n，0 ), then the reliability function of the product under normal use environment is shown in formula (15): At this point, the construction of the product's multi-stress coupling acceleration model and reliability assessment under normal stress have been completed.

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