Aviation airborne part reliability evaluation method considering unobservable heterogeneity

Abstract

The invention discloses an aviation airborne part reliability evaluation method considering unobservable heterogeneity, and relates to the field of reliability evaluation uncertainty analysis, and the method comprises the following steps: firstly constructing an inverse Gaussian random degradation model, and obtaining an intensity function corresponding to the inverse Gaussian random degradation model; secondly, under the condition of considering unobservable heterogeneity, improving an inverse Gaussian random degradation model based on a fragility factor; then, a maximum likelihood estimation model of the inverse Gaussian random degradation model considering the unobservable heterogeneity is established, the model is used for solving parameters of the improved inverse Gaussian random degradation model, and then the unobservable heterogeneity is quantized; and finally, analyzing the reliability of the aviation airborne part based on an improved inverse Gaussian random degradation model. According to the method provided by the invention, the unobservable difference of the degradation process of different products can be visually reflected, the problem of uncertainty caused by the difference between the products is effectively solved, and the accuracy of reliability evaluation is improved.

Description

Technical Field

[0001] The present invention relates to the field of uncertainty analysis of reliability assessment, and in particular to a method for reliability assessment of aviation airborne parts considering unobservable heterogeneity. Background Art

[0002] Reliability research, especially the reliability research of large-scale equipment such as aviation products, has always been the focus of industry attention. The effectiveness of reliability data itself, as an important data source for airworthiness safety analysis, is particularly crucial. After years of development, the reliability level of China's aviation manufacturing industry has been improved, but there is still a significant gap compared with the advanced foreign level, and there are two prominent problems in front of us.

[0003] Firstly, the airborne equipment of domestic aircraft in China mainly relies on imports. It is an inevitable trend and result to realize the localization of airborne equipment in the future. However, at present, since the localization of airborne equipment is in its infancy, the research and development of new products, the progress of production technology, and the blank of service data all make the underlying reliability data still a gray area. This makes it difficult to apply the traditional statistical analysis method based on failure life. To solve this problem, people have begun to pay attention to degradation data with rich product process information. What is in front of us is no longer the disorderly failure time data with different failure times, but the degradation data with certain physical laws. However, there are many uncertain factors in the real degradation process of products. Ignoring the influence of uncertainty will make the analysis result too ideal. Therefore, how to quantify these uncertain factors has become the key to determining the accuracy of reliability assessment.

[0004] In degradation modeling, the randomness and dynamics in the time dimension are an important source of uncertainty. Common engineering techniques mainly describe degradation information by fitting a degradation path model, while ignoring the influence of uncertainty in the time dimension. In addition, due to the change of materials and the instability of manufacturing levels, units from the same batch may show quite large heterogeneity in their degradation paths. This difference between products is also an important source of uncertainty, and most existing studies will ignore its influence. To sum up, proposing a method for reliability assessment of aviation airborne parts considering unobservable heterogeneity, quantifying the uncertainty in the time dimension through a stochastic process, and quantifying the difference between products through a frailty model, making the modeling itself more in line with the actual situation and improving the accuracy of reliability analysis of target products, has become a real and effective means to supplement the underlying reliability data of domestic aviation airborne parts. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for reliability assessment of aviation airborne parts considering unobservable heterogeneity, which can effectively solve the influence of uncertainty on reliability modeling analysis, thereby improving the accuracy of reliability analysis of target products.

[0006] To achieve the above object, the present invention provides a method for reliability assessment of airborne components considering unobservable heterogeneity, including the following steps:

[0007] Step 1: Construct an inverse Gaussian stochastic degradation model and obtain the intensity function corresponding to the inverse Gaussian stochastic degradation model;

[0008] Step 2: Improve the inverse Gaussian stochastic degradation model constructed in Step 1 based on the frailty factor considering unobservable heterogeneity;

[0009] Step 3: Establish a maximum likelihood estimation model for the inverse Gaussian stochastic degradation model considering unobservable heterogeneity, and use this model to solve the parameters of the improved inverse Gaussian stochastic degradation model in Step 2, and then quantify the unobservable heterogeneity;

[0010] Step 4: Analyze the reliability of airborne components based on the improved inverse Gaussian stochastic degradation model.

[0011] Preferably, the process of constructing the inverse Gaussian stochastic degradation model and obtaining the intensity function corresponding to the inverse Gaussian stochastic degradation model in Step 1 is as follows:

[0012] S11: Represent the degradation process {D(t), t≥0} based on the inverse Gaussian, and the expression is as follows:

[0013] D(t)~IG(Λ θ (t),ηΛ 2 θ (t));

[0014] In the formula, D(t) represents the degradation state of the sample at time t, IG represents the inverse Gaussian, η represents the scale parameter (diffusion rate), θ represents the degradation parameter (drift rate), and Λ θ (t) = θt represents the time scale function that reflects the fluctuations generated during degradation and satisfies Λ θ (0) = 0;

[0015] S12: Calculate the degradation increment, and the calculation expression is as follows:

[0016] X = D(t + Δt) - D(t);

[0017] In the formula, X represents the degradation increment, which is a random variable, and Δt represents the time interval;

[0018] S13: According to the independent increment property, obtain the inverse Gaussian stochastic degradation model, and the expression is as follows:

[0019] X~IG(ΔΛ θ (t),η[ΔΛ θ (t)] 2 );

[0020] S14. Combine the obtained inverse Gaussian random degradation model with the failure rate in the survival model to obtain the probability that the degradation increment no longer changes, and derive the final intensity function. The expression is as follows:

[0021]

[0022]

[0023] In the formula, h(x|ΔΛ θ (t), η) represents the intensity function under the failure rate, h IG (x|ΔΛ θ (t), η) represents the intensity function under the inverse Gaussian random degradation model, Φ represents the cumulative distribution function of the standard normal distribution, and x represents the specific value of the degradation increment.

[0024] Preferably, in step 2, when considering unobservable heterogeneity, the process of improving the inverse Gaussian random degradation model constructed in step 1 based on the frailty factor is as follows:

[0025] S21. Build a generalized inverse Gaussian frailty model based on the frailty factor;

[0026] S22. Introduce the frailty factor into the degradation analysis to improve the inverse Gaussian random degradation model constructed in step 1.

[0027] Preferably, the process of building a generalized inverse Gaussian frailty model based on the frailty factor in S21 is as follows:

[0028] S211. Calculate the expectation and variance of the frailty factor z according to its probability density function. The calculation expressions are as follows:

[0029]

[0030] In the formula, f(z; a, b, λ) represents the probability density function of the frailty factor z, E[z] represents the expected value of the frailty factor z, Var[z] represents the variance value of the frailty factor z, a represents scale parameter 1, b represents scale parameter 2, λ represents the shape parameter, K λ (x) is the modified Bessel function of the second kind, and a > 0, b > 0;

[0031] S212. Obtain the generalized inverse Gaussian frailty model. The expression is as follows:

[0032] h(t|z) = zh0(t);

[0033] Wherein, z represents a frailty factor and z≥0, and z follows the generalized inverse Gaussian distribution mentioned in S211, z~f(z;a,b,λ), and h0(t) represents the baseline hazard function. It can be intuitively understood from the formula that for different individuals, the greater the vulnerability, the easier it is to be damaged.

[0034] Preferably, in S22, the frailty factor is introduced into the degradation analysis, and the process of improving the inverse Gaussian random degradation model constructed in step 1 is as follows:

[0035] S221. Improve the intensity function of the degradation amount of a single sample, and the expression is as follows:

[0036]

[0037] Wherein, h i (x|ΔΛ θ (t),η,z i ) represents the improved intensity function;

[0038] S222. Obtain the survival function based on the intensity function improved in S221, and the expression is as follows:

[0039]

[0040] Wherein, R i (x|ΔΛ θ (t),η,z i ) represents the survival function of the degradation amount of a single component considering the frailty factor, H IG (x|ΔΛ θ (t),η) represents the cumulative intensity function, and R i (x|ΔΛ θ (t),η,a,b,λ) represents the unconditional survival function.

[0041] Preferably, in step 3, a maximum likelihood estimation model of the inverse Gaussian random degradation model considering unobservable heterogeneity is established, and the expression for solving the parameters of the improved inverse Gaussian random degradation model in step 2 using this model is as follows:

[0042]

[0043] Wherein, L i represents the unconditional likelihood function, h IG (x ij |ΔΛ(t ij ),η,z i ) represents the intensity function considering the frailty z i of each component and the degradation increment x ij observed for each component, and R i (x ij|ΔΛ(t ij ),η,z i ) represents the intensity function considering the vulnerability z i of each component and the degradation increment x ij observed for each component. f(z i ; a, b, λ) represents the probability function that each component's vulnerability factor z i obeys. H IG (x ij |ΔΛ(t ij ),η) represents the cumulative intensity function derived based on h IG (x ij |ΔΛ(t ij ),η,z i ). L 1i = h IG (x ij |ΔΛ(t ij ),η),

[0044] Preferably, the expression for quantifying the unobservable heterogeneity is as follows:

[0045]

[0046] where f(z i |X) represents the posterior probability distribution of each vulnerability factor z i given the observed degradation increment X. f α (z i ) represents the prior probability density function of the vulnerability factor z i . p(x ij |z i ) represents the probability of the observed degradation increment X given the latent variable z i . p(x ij ) represents the marginal probability of the observed degradation increment X. L(Λ θ (t), η, α, λ) represents the overall unconditional maximum likelihood function considering the vulnerability factor.

[0047] Preferably, the process of analyzing the reliability of aviation airborne parts based on the improved inverse Gaussian stochastic degradation model in step 4 is as follows:

[0048] S41. Obtain the first passage time when the degradation amount first reaches or exceeds the failure threshold ρ of the degradation amount, and the expression is as follows:

[0049] T = inf{t|D(0) ≤ ρ ≤ D(t)};

[0050] S42. Obtain the CDF of the product life based on the degradation model according to the first passage time, and the expression is as follows:

[0051] F T F(t) = P(D(t) ≥ ρ) = 1 - F(x = ρ|Λ θ (t), η);

[0052] S43. Calculate the PDF of the product life, and the expression is as follows:

[0053]

[0054] S44. Based on the generalized inverse Gaussian frailty factor, obtain the unconditional PDF of the life of the aviation airborne parts considering frailty, and the calculation expression is as follows:

[0055]

[0056] In the formula, represents the probability density function of the life considering the frailty factor, represents the probability density function of the life without considering the frailty factor, K1 represents the Bessel function 1, K2 represents the Bessel function 2, H IG (x = ρ|ΔΛ θ (t), η) represents the cumulative intensity function when the degradation amount reaches the failure threshold ρ, R IG (x = ρ|ΔΛ θ (t), η) represents the survival function when the degradation amount reaches the failure threshold ρ.

[0057] Therefore, the present invention adopts the above-mentioned reliability evaluation method for aviation airborne parts considering unobservable heterogeneity, and has the following beneficial effects:

[0058] (1) The method proposed by the present invention can reasonably quantify the uncertainty problem caused by unit differences, and comprehensively observe various heterogeneities in the degradation process of samples (such as degradation rate, environmental effects, etc.) as a whole, improving the accuracy of product reliability analysis;

[0059] (2) The generalized inverse Gaussian frailty model proposed by the present invention can include more random states compared with the traditional frailty model, capture more random effects, and be closer to the actual situation;

[0060] (3) The reliability information and life information of the target product obtained by the present invention, as effective input and supplement for the underlying data in the safety analysis process, have practical significance in the safety analysis project.

[0061] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0062] Figure 1It is the overall flowchart of a reliability evaluation method for aviation airborne parts considering unobservable heterogeneity according to the present invention;

[0063] Figure 2 It is the original degradation path diagram of 21 samples in the embodiment of the present invention;

[0064] Figure 3 It is the degradation path diagram of the crack data of 21 samples after conversion in the embodiment of the present invention;

[0065] Figure 4 It is the comparison diagram of the frequency distribution histogram and normal fitting based on the sample degradation data in the embodiment of the present invention;

[0066] Figure 5 It is the schematic diagram of the degradation relationship corresponding to different vulnerabilities in the embodiment of the present invention;

[0067] Figure 6 It is the P-P test diagram of the vulnerability factors corresponding to 21 samples in the embodiment of the present invention;

[0068] Figure 7 It is the PDF comparison diagram of the lifetimes of 21 samples under different models in the embodiment of the present invention;

[0069] Figure 8 It is the CDF comparison diagram of the lifetimes of 21 samples under different models in the embodiment of the present invention. Detailed implementation manners

[0070] The following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts fall within the scope of protection of the present invention.

[0071] Please refer to Figure 1 , a reliability evaluation method for aviation airborne parts considering unobservable heterogeneity, comprising the following steps:

[0072] S1. Construct an inverse Gaussian stochastic degradation model and obtain the intensity function corresponding to the inverse Gaussian stochastic degradation model;

[0073] S1.1. Collection and processing of degradation data

[0074] Before performing degradation modeling analysis, it is necessary to collect degradation data obtained from target sample tests or actual use. In this case, taking metal fatigue crack degradation data as an example, the detailed steps will be elaborated to verify the effectiveness and accuracy of the proposed method for capturing and quantifying heterogeneity in stochastic degradation modeling using the frailty model. A total of 21 samples were tested for crack length, and the test frequency was 120,000 cycles. When the crack length of a sample exceeded 1.6 inches, the sample was considered failed. As Figure 2 shows the degradation paths and degradation thresholds of 21 samples.

[0075] In addition, the present invention also transforms the crack data through the Paris law used to describe crack growth to describe the law in the stable crack growth region. The transformed degradation amount D′(t) is:

[0076]

[0077] In the formula, D(t) represents the degradation state of the sample at time t. After transformation, the initial degradation amount of the crack data is 0, the degradation threshold is 0.5754, and the product fails after 0.117 million cycles. The transformed degradation path is as Figure 3 shown. Through Figure 2 and Figure 3 comparison, it can be seen that the degradation path after transforming the data is significantly more linear.

[0078] S1.2. Construction of the stochastic degradation model;

[0079] To elaborate on the stochastic degradation model in detail, in this case, the inverse Gaussian degradation process is taken as an example for detailed elaboration.

[0080] Let D(t) represent the degradation state of the sample at time t. Assume that the degradation process {D(t), t ≥ 0} follows an inverse Gaussian (inverse Gaussian process, IG) process, that is, D(t) ∼ IG(Λ θ (t), ηΛ 2 θ (t)). Let the degradation increment X = D(t + Δt) - D(t). According to the independent increment property, then X ∼ IG(ΔΛ θ (t), η[ΔΛ θ (t)] 2 ). Then the probability density function (PDF) of the degradation increment can be expressed as:

[0081]

[0082] The cumulative distribution function (CDF) of the degradation increment is as follows:

[0083]

[0084] where Φ(·) is the cumulative distribution function of the standard normal distribution;

[0085] S1.3. Derivation of the Degradation Intensity Function

[0086] Based on the determined degradation model and the definition of the degradation intensity function, the expression of the specific intensity function can be derived. First, according to the cumulative distribution function of the degradation increment, the survival function of the degradation increment can be obtained as:

[0087] R IG (x|ΔΛ θ (t),η) = 1 - F IG (x|ΔΛ θ (t),η);

[0088] Furthermore, the intensity function of the specific degradation amount can be obtained, and the expression is as follows:

[0089]

[0090] The corresponding cumulative degradation intensity function can be defined as:

[0091]

[0092] S1.4. Comparison of the Goodness of Fit of Different Models

[0093] The present invention adopts a comprehensive test method of AIC and BIC tests to comprehensively judge whether the data meets the model premise assumptions through AIC and BIC. First, a frequency distribution histogram of the degradation conversion data is drawn, and a comparison of normal fitting is carried out. As Figure 4 shown, the results show that this group of crack degradation data does not strictly satisfy the normal distribution but is left-skewed. In order to compare the goodness of fit of different degradation models to this group of real data, the AIC and BIC values of different models are calculated respectively in this case as shown in Table 1. Among the three models, the AIC value and BIC value corresponding to the inverse Gaussian degradation model are the smallest, which also proves that the inverse Gaussian degradation model has the best goodness of fit and is more suitable for describing the random degradation process of this group of data.

[0094] Table 1 Test Results of the AIC and BIC Criteria for Degradation Models

[0095] Distribution AIC BIC Log-likelihood gamma -1268.02 -1267.06 636.01 winner -1225.19 -1218.23 614.59 IG -1334.51 -1327.62 669.24

[0096] S2. Improve the constructed inverse Gaussian stochastic degradation model based on the frailty factor considering unobservable heterogeneity.

[0097] S2.1. Construction of the generalized inverse Gaussian frailty model

[0098] In order to consider the impact of unobservable heterogeneity on the model, the present invention uses the frailty model to quantify and describe the differences between units. Compared with the traditional frailty model, the present invention proposes a new method for constructing a frailty model, namely the generalized inverse Gaussian frailty model. The specific construction idea is shown as follows. As one of the representative non - negative and asymmetric distributions, the generalized inverse Gaussian (GIG) distribution is widely used in modeling and data analysis due to its flexibility in mathematical analysis. In traditional frailty models, it is usually considered that the frailty factor z follows a gamma distribution (b = 0, λ > 0) or an inverse Gaussian distribution. Both of these two distributions are special cases of the generalized inverse Gaussian. Therefore, using the generalized inverse Gaussian distribution adopted by the present invention to fit the frailty can ensure its flexibility in mathematical processing and capture more random effects. When z ∼ GIG(a, b, λ), the probability density function of the non - negative random variable z is:

[0099]

[0100] where a > 0, b > 0, K λ (x) is the modified Bessel function of the second kind, that is

[0101] At this time, the expectation and variance of the frailty factor z are:

[0102]

[0103] The generalized inverse Gaussian frailty model is obtained, and the expression is as follows:

[0104] h(t|z) = zh0(t);

[0105] where z represents the frailty factor and z ≥ 0, and h0(t) represents the baseline hazard function;

[0106] Based on the above derivation, when the frailty factor follows the generalized inverse Gaussian distribution, the unconditional reliability function of the product is:

[0107]

[0108] S2.2. Degradation model considering the frailty factor

[0109] After establishing the frailty model and the random degradation model, the present invention considers combining the two models to quantify the impact and improvement of unobservable heterogeneity on the model in actual degradation. The specific derivation is as follows:

[0110] According to the definition of the frailty factor, the higher the frailty of a product, the higher the probability that the product will have a large degradation increment.

[0111] As Figure 5 shows the degradation paths corresponding to three different frailties z. It can be intuitively seen from the figure that the component with a larger frailty factor value reaches the same degradation amount in a shorter time and has a larger overall degradation amount; the component with a smaller frailty factor value takes a longer time to reach the failure threshold and has a relatively smaller overall degradation amount. When considering the generalized inverse Gaussian frailty factor in the inverse Gaussian degradation process, the unconditional survival function of the degradation increment of each component is:

[0112]

[0113] From a mathematical perspective of the formula, it is easy to analyze that when the degradation increment x is very large, the corresponding survival function R IG (x|ΔΛ θ (t),η,) approaches 0, and the corresponding cumulative degradation intensity function H IG (x|ΔΛ θ (t),η,) approaches infinity; when the degradation increment x is very small, the corresponding survival function R IG (x|ΔΛ θ (t),η,) approaches 1, and the corresponding cumulative degradation intensity function H IG (x|ΔΛ θ (t),η,) approaches 0. Therefore, to fit different conditions, the unconditional survival function of the degradation increment of the component in actual situations is:

[0114]

[0115] From this, the unconditional CDF of the degradation increment of the component considering frailty can be obtained:

[0116] F i (x|ΔΛ θ (t),η,a,b,λ)=1 - R i (x|ΔΛ θ (t),η,a,b,λ);

[0117] Correspondingly, by taking the derivative of the degradation amount x therein, the unconditional PDF of the degradation increment of the component considering frailty can be obtained:

[0118]

[0119] So far, the construction of the model has been completed, and the analysis of unobservable heterogeneity has been successfully introduced into the degradation model, making the overall analysis closer to reality and laying a foundation for subsequent reliability analysis.

[0120] S3. Establish a maximum likelihood estimation model for the inverse Gaussian stochastic degradation model considering unobservable heterogeneity, use this model to solve the parameters of the improved inverse Gaussian stochastic degradation model, and then quantify the unobservable heterogeneity;

[0121] S3.1. Maximum likelihood estimation model for the stochastic degradation model considering unobservable heterogeneity;

[0122] Based on the models established in S1 and S2, it is necessary to use parameter estimation methods to solve the unknown parameters of the model. To achieve reliability index extrapolation, the maximum likelihood estimation method (MLE) is a parameter estimation method that provides a way to evaluate model parameters using given observed data. Due to its generality and stability, it is widely used in the field of reliability data analysis. Since the complexity of the overall model increases after considering the frailty factor in the present invention, a maximum likelihood estimation method for a distribution is proposed. Specifically as follows:

[0123]

[0124] In this case analysis, it is considered that there are n samples at time t ij (j = 1,... n i ) and the degradation increment of each product can be observed as The frailty z of each device i (i = 1,... n) are independent of each other and follow the distribution of f(z i ; a, b, λ). Then, by integrating z i , the overall unconditional likelihood function can be obtained as:

[0125]

[0126] After considering the generalized inverse Gaussian frailty factor, the unconditional likelihood function of any product is deduced as:

[0127]

[0128] Through the step-by-step processing of the above formula, it can be observed that L 1i does not contain frailty, and the random effect of frailty mainly acts on L 2i . Therefore, the overall unconditional likelihood function can be abbreviated as:

[0129]

[0130] After taking the logarithm, the overall unconditional log-likelihood function can be obtained as:

[0131]

[0132] In the case analysis of this time, the maximum likelihood function L 2i Specifically:

[0133]

[0134] Among them

[0135] In the process of parameter solving, based on the basic property that the derivative of the maximum point of the maximum likelihood estimation is 0, the mathematical solving method of the maximum likelihood estimation can also be used for calculation, that is, the partial derivative of each parameter is set to 0 to construct an optimization model, and then the solution is carried out. However, in order to solve the parameters of the model simultaneously, an artificial intelligence algorithm is used in the present invention for parallel estimation and solution of multiple parameters, which improves the efficiency of parameter solving of the model. The iterative process of the artificial intelligence algorithm is as follows:

[0136] (1) Select an intelligent algorithm for parallel calculation;

[0137] (2) Selection of the adaptive process of the algorithm;

[0138] (3) Global and local exploration control;

[0139] (4) Update the individual positions of the parameters;

[0140] (5) Stop iteration and obtain the parameter results.

[0141] In order to comprehensively compare the superiority of the model proposed in the present invention, the overall analysis dimension of the model is two layers. First, the influence of considering vulnerability and not considering vulnerability on the analysis accuracy of the model is compared. Second, the difference in the estimation accuracy of the model between the generalized inverse Gaussian vulnerability model (IG-GIGF) and the traditional inverse Gaussian vulnerability model (IG-IGF) is compared. Table 2 gives the results of the overall maximum likelihood estimation of each parameter under different models.

[0142] Table 2 Parameter Estimation Results under Different Models

[0143]

[0144]

[0145] It can be seen from Table 2 that the η estimated by the two vulnerability-considering models is higher than the value under the inverse Gaussian model, which indicates that the degradation rate of the components increases significantly after considering vulnerability. Ignoring the influence of heterogeneity between components will make the overall estimated parameter value too idealized, resulting in inaccurate final life analysis.

[0146] S3.2. Bayesian Estimation of Independent Vulnerability Factors;

[0147] The framework of Bayesian parameter estimation is a method centered around Bayes' theorem and updating the initially available information based on new observed data. To precisely quantify the heterogeneity of different samples, the present invention proposes that after estimating the overall parameter results through the maximum likelihood estimation method, the Bayesian theory can be combined with the degradation data observed for each sample to infer the vulnerability factors of each individual. The specific steps are as follows:

[0148] After calculating the corresponding unknown parameters Θ = {α, λ, η, θ} in the model through an optimization algorithm, Bringing in the prior distribution of the vulnerability factor, the PDF of the individual vulnerability can be derived as:

[0149]

[0150] Simplifying it, it can be obtained that under the conditions of the actual degradation process of each sample, the independent vulnerability factors of the samples satisfy:

[0151]

[0152] For the convenience of further analysis, based on the simplified model, the expectation and variance of the vulnerability factor z can be derived as:

[0153]

[0154] Among them,

[0155]

[0156] According to the parameter estimation results in Table 2, combined with the Bayesian theory, the independent vulnerabilities of 21 components are estimated. Table 3 shows the independent vulnerabilities of the 21 components and the corresponding cumulative degradation amounts in this case. It can be seen from Table 3 that the vulnerability of the components is generally directly related to the degradation amount, that is, the higher the cumulative degradation amount of the component, the larger the corresponding vulnerability factor, which proves the view proposed in this paper that the more vulnerable individuals are more likely to degenerate. In addition, the vulnerability model not only considers the degradation amount but also the cumulative degradation related to time. It can be observed from Table 3 that the degradation amount of Component 1 is not the highest, but the vulnerability of Component 1 is the largest because Component 1 reaches the degradation threshold first and has a fast degradation rate, which can also be understood as Component 1 having the shortest lifespan.

[0157] Table 3 Independent vulnerability factors of 21 components

[0158]

[0159]

[0160] Due to the small number of actual components, this paper uses the method of parametric bootstrap sampling to generate 100 samples based on the vulnerabilities of 21 components that have been calculated. Figure 6 Figure 6 shows the P-P plot of the normality test of the vulnerabilities of these 100 samples. It can be observed from the P-P plot that the samples show a convex curvature compared to the normal distribution, indicating that the distribution of vulnerabilities should be left-skewed. Therefore, it is more reasonable to describe the vulnerabilities with a generalized inverse Gaussian distribution with a skewed distribution.

[0161] S4. Analyze the reliability of aviation airborne components based on the improved inverse Gaussian random degradation model;

[0162] For the reliability analysis method based on the improved degradation model proposed in this invention, in order to achieve more reasonable life analysis results, the overall idea of the model life analysis is now elaborated from the following two aspects. First, based on the initial random degradation model, a degradation threshold is introduced for life extrapolation. In this case, taking the inverse Gaussian degradation process as an example, the product life CDF that satisfies the inverse Gaussian degradation process without considering unit heterogeneity can be obtained as:

[0163]

[0164] The PDF of the product life is:

[0165]

[0166] where φ(·) represents the probability density function of the standard normal distribution.

[0167] Then, by introducing the generalized inverse Gaussian vulnerability factor, the unconditional PDF of the product life considering vulnerability can be directly obtained as:

[0168]

[0169] where

[0170] Figure 7 and Figure 8 As shown, they are the PDF and CDF graphs of the life of this component. It can be observed from the PDF image of the life that the life distributions of the three models are all unimodal and symmetric. However, considering vulnerability, the overall estimated life is more centered around the median, and the model estimation is more accurate. In addition, it can also be clearly seen from the image that the PDF and CDF images of the life distribution will shift to the left after considering vulnerability, indicating that when evaluating the life without considering the heterogeneity between components, the overall estimated life value will be too large. When quantifying this random uncertainty through the vulnerability factor and then performing life estimation, the mean time to failure of the model will be shortened, making it closer to the real situation.

[0171] As a statistical measure describing the life of a sample, the median life has important research value in reliability analysis. Table 4 compares the results between the median life values estimated under three models and the true values. It can be clearly seen from the comparison results that the product life estimated under the IG-GIGF model is closest to the true value, and the model estimation is the most accurate.

[0172] Table 4 Comparison of Median Life Values of Different Models

[0173] Model Median life (cycles / million) Absolute error Relative error IG 0.131 0.014 11.966％ IG-IGF 0.127 0.010 8.547％ IG-GIGF 0.124 0.007 5.983％

[0174] Therefore, by adopting the above-mentioned reliability evaluation method for aviation airborne components considering unobservable heterogeneity, the present invention can intuitively reflect the unobservable differences in the degradation processes of different products, effectively solve the uncertainty problems caused by the differences between products, improve the accuracy of reliability evaluation, and make the reliability evaluation of products closer to reality. At the same time, the reliability information and life information of the target product obtained through the new method can effectively support the underlying safety analysis of aviation airborne components and have important engineering application value.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A reliability assessment method for aviation airborne components considering unobservable heterogeneity, characterized in that: The following steps are involved: Step 1, construct an inverse Gaussian random degradation model and obtain an intensity function corresponding to the inverse Gaussian random degradation model; Step 2: Considering the unobservable heterogeneity, the inverse Gaussian random degradation model constructed in step 1 is improved based on the fragility factor; Step 3: Establish a maximum likelihood estimation model of the inverse Gaussian random degradation model considering unobservable heterogeneity, and use the model to solve the parameters of the improved inverse Gaussian random degradation model in step 2, and then quantify the unobservable heterogeneity; Step 4: Analyze the reliability of aviation airborne components based on the improved inverse Gaussian random degradation model.

2. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 1 is characterized in that: The process of constructing the inverse Gaussian random degradation model in step 1 and obtaining the intensity function corresponding to the inverse Gaussian random degradation model is as follows: S11. Based on the inverse Gaussian, the degradation process {D(t), t≥0} is expressed as follows: D(t)~IG(Λ θ (t),ηΛ 2 θ (t)); Where D(t) represents the degradation state of the sample at time t, IG represents inverse Gaussian, η represents the scale parameter, θ represents the degradation parameter, and Λ θ (t) = θt represents the fluctuations generated when the time scale function reacts to degradation and satisfies Λ θ (0) = 0; S12. Calculate the degradation increment. The calculation expression is as follows: X = D(t+Δt)-D(t); In the formula, X represents the degradation increment, which is a random variable, and Δt represents the time interval; S13. According to the independent increment property, the inverse Gaussian random degradation model is obtained, and the expression is as follows: X~IG(DL θ (t),η[ΔΛ θ (t)] 2 ); S14. Combine the obtained inverse Gaussian random degradation model with the failure rate in the survival model to obtain the probability that the degradation increment will no longer change, and obtain the final strength function, which is expressed as follows: h(x|DΛ θ (t),η)= Δ l x I → m0P{x<X≤x+Δx}; In the formula, h(x|ΔΛ θ (t),η) represents the intensity function under failure rate, h IG (x|ΔΛ θ (t),η) represents the intensity function under the inverse Gaussian random degradation model, Φ represents the cumulative distribution function of the standard normal distribution, and x represents the specific value of the degradation increment.

3. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 2 is characterized in that: In step 2, the process of improving the inverse Gaussian random degradation model constructed in step 1 based on the fragility factor while considering unobservable heterogeneity is as follows: S21. Construct a generalized inverse Gaussian fragility model based on fragility factors; S22. Introduce the fragility factor into the degradation analysis and improve the inverse Gaussian random degradation model constructed in step 1.

4. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 3 is characterized in that: The process of building a generalized inverse Gaussian fragility model based on fragility factors in S21 is as follows: S211. Calculate the expectation and variance of the fragility factor z according to its probability density function. The calculation expression is as follows: Where f(z; a, b, λ) represents the probability density function of the fragile factor z, E[z] represents the expected value of the fragile factor z, Var[z] represents the variance of the fragile factor z, a represents the scale parameter 1, b represents the scale parameter 2, λ represents the shape parameter, and K λ (x) is the modified Bessel function of the second kind, And a>0, b>0; S212. Obtain the generalized inverse Gaussian fragile model, expressed as follows: h(t|z)=zh0(t); In the formula, z represents the vulnerability factor and z ≥ 0, and z obeys the generalized inverse Gaussian distribution mentioned in S211, z ~ f(z; a, b, λ), h0(t) represents the baseline risk function.

5. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 4 is characterized by: In S22, the fragility factor is introduced into the degradation analysis, and the process of improving the inverse Gaussian random degradation model constructed in step 1 is as follows: S221. The intensity function of the degradation amount of a single sample is improved, and the expression is as follows: In the formula, h i (x|ΔΛ θ (t),η,z i ) represents the improved intensity function; S222. Based on the improved intensity function of S221, the survival function is obtained, and the expression is as follows: In the formula, R i (x|ΔΛ θ (t),η,z i ) represents the residual function of the degradation of a single component after considering the vulnerability factor, H IG (x|ΔΛ θ (t),η) represents the cumulative intensity function, R i (x|ΔΛ θ (t),η,a,b,λ) represents the unconditional survival function.

6. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 5 is characterized by: In step 3, a maximum likelihood estimation model of the inverse Gaussian random degradation model considering unobservable heterogeneity is established, and the expression of the parameters of the improved inverse Gaussian random degradation model in step 2 is solved using this model as follows: Where, L i represents the unconditional likelihood function, h IG (x ij |ΔΛ(t ij ),η,z i ) means considering the vulnerability of each component z i and the observed degradation increment x for each component ij The intensity function, R i (x ij |ΔΛ(t ij ),η,z i ) means considering the vulnerability of each component z i and the observed degradation increment x for each component ij The intensity function, f(z i ; a, b, λ) represents the fragility factor z of each component i The probability function of compliance, H IG (x ij |ΔΛ(t ij ),η) represents the value based on h IG (x ij |ΔΛ(t ij ),η,z i ) derived cumulative intensity function, L 1i =h IG (x ij |ΔΛ(t ij ),η), 7. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 6 is characterized in that: The expression to quantify the unobservable heterogeneity is as follows: In the formula, f(z i |X) means that given the observed degradation increment X, each fragility factor z i The posterior probability distribution of α (z i ) represents the fragility factor z i The prior probability density function, p(x ij |z i ) represents the latent variable z i Under the condition of ij ) represents the observed degradation increment X edge probability, L(Λ θ (t),η,α,λ) represents the overall unconditional maximum likelihood function after considering the fragility factor.

8. The reliability assessment method for aviation airborne components considering unobservable heterogeneity according to claim 7 is characterized in that: The process of analyzing the reliability of aviation airborne components based on the improved inverse Gaussian random degradation model in step 4 is as follows: S41, obtaining the first arrival time when the degradation amount reaches or exceeds the failure threshold value ρ of the degradation amount for the first time, which is expressed as follows: T=inf{t|D(0)≤ρ≤D(t)}; S42. The CDF of the product life based on the degradation model is obtained according to the first arrival time. The expression is as follows: F T (t)=P(D(t)≥ρ)=1-F(x=ρ|Λ θ (t),h); S43. Calculate the PDF of product life, the expression is as follows: S44. Based on the generalized inverse Gaussian fragility factor, the unconditional PDF of the life of aviation airborne components after considering fragility is obtained. The calculation expression is as follows: In the formula, f TIGF represents the probability density function of life after considering the fragility factor, f TIG (t) represents the probability density function of life without considering the fragility factor, K1 represents Bessel function 1, K2 represents Bessel function 2, H IG (x=ρ|ΔΛ θ (t),η) represents the cumulative strength function when the degradation reaches the failure threshold ρ, R IG (x=ρ|ΔΛ θ (t),η) represents the survival function when the degradation reaches the failure threshold ρ.

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