Equipment-level product reliability real-time evaluation method fusing fault physics and active learning Kriging model

Abstract

The invention relates to an equipment-level product reliability real-time evaluation method fusing fault physics and an active learning Kriging model. The method mainly comprises the following steps: (1) constructing a product parameter uncertainty model; (2) generating a training sample pool and a candidate sample pool; (3) calculating the sample life of the training sample pool in combination with finite element simulation and a fault physical model; (4) constructing a Kriging model based on the training sample pool; (5) predicting the sample life of the candidate sample pool by using a Kriging model; (6) calculating the reliability real-time evaluation accuracy; (7) determining a key sample by using a learning function and adding the key sample into a training sample pool; (8) judging whether each statistical feature meets a stop criterion; and (9) completing reliability real-time evaluation according to a Kriging model life prediction result. The method has the beneficial effects that the product reliability evaluation range is converted from discrete to continuous, the finite element simulation frequency is effectively reduced, and the reliability is evaluated more efficiently in real time while the precision is ensured.

Description

Technical Field

[0001] The present invention belongs to the field of product reliability design and analysis, and particularly relates to a method for real-time evaluation of the reliability of equipment-level products that integrates physics of failure and active learning Kriging model. Background Art

[0002] Failures inevitably exist in the entire life cycle of products, such as thermal fatigue failure of electronic component solder joints, overstress failure of mechanical products, etc. Failures can cause unexpected functions of products, which in turn trigger more serious accidents, resulting in huge property losses and casualties. Therefore, accurate prediction of the time of failure is crucial for ensuring the stable operation of products and reducing safety risks.

[0003] Traditional failure prediction is carried out based on statistical methods. By collecting information on a large number of failed products, the statistical laws of failures are obtained from the data, and the product life is predicted based on this. However, this method cannot explain the real causes and mechanisms of failures, nor can it link the failure data with the design parameters of the products, resulting in the failure prediction results of products not being able to be fed back into the design improvement work. Therefore, a life prediction method based on physics of failure is proposed. This method focuses on the failure causes, failure mechanisms and failure evolution laws of products. By deeply understanding and comprehending the failure modes and failure mechanisms, from the perspective of the microscopic structures of physics and chemistry, a mathematical function model that can quantitatively reflect the relationship between the characteristic parameters (time before failure, failure rate, degradation amount, etc.) of failure occurrence and the geometric dimensions, material parameters, physical responses, etc. of products is constructed, that is, a physics of failure model, and the life assessment and design improvement of products are carried out based on this.

[0004] At the same time, due to the influence of multi-source uncertainties such as materials, processes and environments during the production and processing of products, the parameters in the physics of failure model often have randomness, resulting in fluctuations in the product life. In this case, the probability that the changing product life is greater than the allowable life has received attention, and the reliability analysis of products based on physics of failure has emerged and has been widely studied in engineering. Product reliability analysis methods can be mainly divided into three categories: analytical method, numerical simulation method and surrogate model method. However, as products gradually transform from unit level to equipment level, their structural complexity increases exponentially. In this case, the analytical method and the numerical simulation method expose problems such as expensive computing resources and limited application scenarios. In contrast, the surrogate model method can effectively balance the computing accuracy and cost by constructing an approximate model, and has become an effective analysis means for the reliability problems of equipment-level products. In recent years, the development of active learning has made the surrogate model method based on the active sampling strategy become the mainstream. Among them, the active learning Kriging model stands out among a variety of methods due to its advantages such as simple model, high accuracy and easy optimization.

[0005] However, in existing research, the reliability assessment of device-level products based on the active learning Kriging model only focuses on the probability that the product life is greater than the allowable life, and the reliability calculated at this time is a fixed value. Under different usage scenarios, the allowable life will change according to the severity of the application scenario and the difference in application requirements. At this time, how to analyze the reliability of products under different allowable lives has become the focus of attention of designers and maintainers, and there is an urgent need to develop a new method for real-time assessment of the reliability of device-level products. Summary of the Invention

[0006] To fully consider the reliability issues of device-level products in the scenario of changing allowable life, and to more efficiently conduct real-time assessment of product reliability while ensuring calculation accuracy, the present invention provides a real-time reliability assessment method for device-level products that integrates physics of failure and the active learning Kriging model. This method combines the active learning idea with the Kriging surrogate model. Based on novel learning functions and stopping criteria, by selecting the key samples that have the greatest impact on the accuracy of real-time reliability assessment results in each model iteration update process, the overall accuracy of surrogate model prediction is maximally improved, so that the reliability assessment accuracy of the product at any moment is maximally enhanced. This method can effectively reduce the number of calls to finite element simulations, balance calculation efficiency and accuracy, support rapid assessment of the reliability of products at any moment, and has important theoretical and practical application value for device-level products with complex structures and numerous levels.

[0007] To achieve the above object, the present invention proposes a real-time reliability assessment method for device-level products that integrates physics of failure and the active learning Kriging model, including the following steps:

[0008] Step 1: For the key design and production parameters of device-level products (including material parameters, assembly parameters, load parameters, and geometric parameters), sort out the multi-source uncertainty information existing in each parameter, and use uncertainty modeling theory to construct the uncertainty model of each parameter.

[0009] Step 2: Based on the uncertainty models of each parameter constructed in Step 1, first generate a training sample pool through Latin hypercube sampling, and secondly generate a candidate sample pool through Monte Carlo sampling, specifically including the following steps:

[0010] Step 2.1: Based on the uncertainty models of each parameter, generate a training sample pool through Latin hypercube sampling, and the number of samples in the training sample pool is determined by Equation (1):

[0011] N0 = max{12, 2k} (1)

[0012] where N0 is the number of samples in the training sample pool, and k is the number of uncertainty design parameters.

[0013] At this time, the training sample pool can be expressed in the form of Equation (2):

[0014]

[0015] where is the training sample pool, and x ij (i = 1,..., N0; j = 1,..., k) is the j-th design parameter of the i-th sample in the training sample pool;

[0016] Step 2.2: Based on the uncertainty models of the parameters, generate a candidate sample pool containing N (N ≥ N0) groups of samples through Monte Carlo sampling. At this time, the candidate sample pool can be expressed in the form of Equation (3):

[0017]

[0018] where X N×k candidate is the candidate sample pool, and x i ′ j (i = 1,..., N; j = 1,..., k) is the j-th design parameter of the i-th sample in the candidate sample pool.

[0019] Step 3: Based on all the samples in the training sample pool established in Step 2, respectively construct the finite element simulation models of the product, and adopt the method combining multi-physics field coupling simulation and physics of failure model to calculate the product life sets corresponding to each sample, which specifically includes the following steps:

[0020] Step 3.1: For the design parameter values of each sample in the training sample pool , respectively construct the finite element models of the product, conduct finite element simulations, and obtain the finite element response outputs corresponding to each sample;

[0021] Step 3.2: Determine the physics of failure model corresponding to the key failure modes of the product, which can be expressed by Equation (4):

[0022]

[0023] where N f is the product life, X is the finite element response, such as stress, strain, temperature, etc., and θ is the physics of failure model parameter;

[0024] Step 3.3: Use the physics of failure model to calculate the product life sets corresponding to each sample in the training sample pool according to the finite element responses of the samples, which can be expressed by Equation (5):

[0025]

[0026] where is the product life set corresponding to the training sample pool, N fi (i = 1,..., N0) is the product life of the i-th sample in the training sample pool.

[0027] Step 4: Based on the product life set obtained in Step 3, construct a Kriging model for predicting the product life of each sample in the candidate sample pool.

[0028] Specifically, the general expression of the Kriging model is shown in Equation (6). Using the training sample pool and its corresponding product life set the unknown parameters in the Kriging model expression can be estimated.

[0029]

[0030] Among them, G(X) is the performance function, f(X) = [f1(x), f2(x),..., f l (x)] T is the regression function vector, β = [β1, β2,..., β l T is the regression coefficient vector, and z(X) is a stationary Gaussian process with a mean of 0.

[0031] Step 5: Using all the samples in the candidate sample pool established in Step 2 as inputs, use the Kriging model constructed in Step 4 to predict the product life of each sample in the candidate sample pool in turn.

[0032] Specifically, the life prediction result of the Kriging model is a random variable subject to a normal distribution and can be expressed in the form of Equation (7):

[0033]

[0034] Among them, Y N×1 candidate is the Kriging model life prediction result of the candidate sample pool, N' fi (i = 1,..., N) is the Kriging model life prediction result of the i-th sample in the candidate sample pool, which is subject to a normal distribution and can be expressed as μ i and σ i are the mean and standard deviation of the normal distribution, respectively.

[0035] Step 6: Based on the product life prediction results obtained in Step 5, perform real-time evaluation of the product reliability and measure the accuracy of the reliability evaluation results, which specifically includes the following steps:

[0036] ​Step 6.1: Based on the product life prediction results obtained in Step 5, apply Equation (8) to conduct real-time evaluation of the reliability of the product under the current training samples:

[0037]

[0038] where is the real-time evaluation result of the reliability of the product under the current training samples, μ i is the mean of the Kriging model life prediction results of the i-th sample in the candidate sample pool, and I{μ i ≤t} is an indicator function, which can be expressed in the form of Equation (9):

[0039]

[0040] Step 6.2: Calculate the variance of the real-time evaluation result of the reliability under the current training samples, as shown in Equation (10), to measure the accuracy of the evaluation result:

[0041]

[0042] where σ i is the standard deviation of the Kriging model life prediction results of the i-th sample in the candidate sample pool, and Φ(·) is the cumulative distribution function of the standard normal distribution.

[0043] Step 7: For all samples in the candidate sample pool, use the learning function to determine the key samples that have the greatest impact on the accuracy of the real-time evaluation result of the reliability obtained in Step 6, and add them to the training sample pool, which specifically includes the following steps:

[0044] Step 7.1: Calculate the values of each sample in the candidate sample pool under the learning function shown in Equation (11) respectively:

[0045]

[0046] where L i is the value of the i-th sample in the candidate sample pool under the learning function;

[0047] Step 7.2: As shown in Equation (12), calculate the maximum value of {L i |i = 1, 2,... N}, and determine the corresponding sample as the key sample and add it to the training sample pool:

[0048]

[0049] where i index is the sample serial number corresponding to the maximum value of the learning function , and x new is the key sample determined to be added to the training sample pool.

[0050] Step 8: Repeat Steps 3 - 7, continuously adding new key samples to the training sample pool until the statistical features based on the Kriging model life prediction results in Step 5 meet the stopping criterion, specifically including the following steps:

[0051] Step 8.1: Based on the life prediction results of the Kriging model in Step 5, calculate the values of each statistical feature (including the product life mean, product life standard deviation, and kernel density estimate of the product life probability density). The specific calculation process is shown in Equations (13) - (15):

[0052]

[0053] where, is the product life mean when the number of new samples added to the training sample pool is p.

[0054]

[0055] where, is the product life standard deviation when the number of new samples added to the training sample pool is p.

[0056]

[0057] where, is the kernel density estimate of the product life probability density function when the number of new samples added to the training sample pool is p, h is the bandwidth, and K(·) is the kernel function, which can be expressed by Equation (16):

[0058]

[0059] where u is the standardized variable, representing the difference between the data point and the position of the estimated density, and is normalized by the bandwidth;

[0060] Step 8.2: For the product life mean product life standard deviation and the kernel density estimate of the product life probability density When there exists an integer M ≥ m such that for any p ∈ {M - m + 1,..., M}, Equations (17) - (19) are simultaneously satisfied, it can be considered that each statistical feature based on the Kriging model life prediction results meets the stopping criterion. At this time, the model converges and Steps 3 - 7 are no longer repeated.

[0061]

[0062] where ε is the convergence threshold, which can be taken as [10 -4 , 10 -2, where m is any integer not less than 2, determined according to the requirement for the accuracy of real-time reliability assessment of the product. The higher the requirement for accuracy, the larger the value of m.

[0063] Step 9: Based on the training sample pool obtained in Step 8, use the Kriging model obtained in Step 4 to predict the product life results corresponding to each sample in the candidate sample pool, calculate the real-time reliability of the product, and complete the real-time assessment of the product reliability.

[0064] Specifically, use Equation (15) to estimate the probability density function of the product life, then based on Equation (20), conduct real-time assessment of the product reliability, and use Equation (21) to calculate the mean time to failure of the product:

[0065]

[0066] Among them, is the probability density function of the product life, R(t) is the real-time reliability of the product, and MTTF is the mean time to failure of the product.

[0067] Compared with the prior art, the advantages of the present invention are as follows:

[0068] A real-time reliability assessment method for equipment-level products that integrates physics of failure and active learning Kriging model provided by the present invention effectively combines the idea of active learning with the Kriging surrogate model. Based on novel learning functions and stopping criteria, by selecting the key samples that have the greatest impact on the accuracy of real-time reliability assessment results in each model iteration update process, the overall accuracy of surrogate model prediction is maximally improved, so that the accuracy of reliability assessment of the product at any moment is maximally enhanced. This method can effectively reduce the number of calls to finite element simulations, balance computational efficiency and accuracy, save computational resource occupancy and computational time, and thus more efficiently assess the product reliability while ensuring computational accuracy. In addition, the method provided by the present invention converts the product reliability assessment range from discrete to continuous, broadens the application range of the active learning Kriging model in the field of product reliability analysis, and makes up for the deficiencies of existing models in real-time reliability assessment problems. Compared with traditional Monte Carlo simulation method, Kriging model method under single sampling, and active learning Kriging model method only applicable to single-point reliability analysis, the method provided by the present invention has higher efficiency. When applied to equipment-level products with complex structures, numerous levels, and strong parameter dispersion, the advantages of the method provided by the present invention in terms of efficiency can be more prominent. Description of the Drawings

[0069] Figure 1 is a flowchart of a real-time reliability assessment method for equipment-level products that integrates physics of failure and active learning Kriging model provided by the present invention;

[0070] Figure 2 This is the finite element model of the diaphragm sensor in the differential pressure type pressure transmitter in the embodiment of the present invention;

[0071] Figure 3 This is the change trend of the mean and standard deviation of the fatigue life of the diaphragm sensor with the number of newly added samples in the training sample pool in the embodiment of the present invention;

[0072] Figure 4 This is the change trend of the probability density function of the fatigue life of the diaphragm sensor with the number of newly added samples in the training sample pool in the embodiment of the present invention;

[0073] Figure 5 This is the real-time reliability evaluation result of the diaphragm sensor in the embodiment of the present invention. Specific implementation manner

[0074] The present invention will be further described in conjunction with the accompanying drawings and specific embodiments.

[0075] Taking the diaphragm sensor in a certain type of differential pressure type pressure transmitter as the analysis object, based on Figure 1 the method flow shown, apply a real-time reliability evaluation method for equipment-level products that combines failure physics and active learning Kriging model proposed by the present invention. This embodiment mainly includes the following contents:

[0076] Step 1: For the key design and production parameters of equipment-level products (including material parameters, assembly parameters, load parameters, and geometric parameters), sort out the multi-source uncertainty information existing in each parameter, and use uncertainty modeling theory to construct the uncertainty model of each parameter.

[0077] Specifically, for the diaphragm sensor, its main material types are 316L steel and structural steel, the main input load is the medium pressure, and the main assembly parameter is the pre-strain on the central measuring diaphragm. Therefore, a total of 6 key design parameters are considered, namely the elastic modulus E of structural steel S , the Poisson's ratio v of structural steel S , the elastic modulus E of 316L steel L and the Poisson's ratio v of 316L steel L , the medium pressure P, and the pre-strain D.

[0078] Furthermore, use the normal distribution probability statistical model to characterize the uncertainty of each design parameter. The probability density function of the normal distribution is shown in Equation (22):

[0079]

[0080] Among them, μ is the mean of the normal distribution, and σ is the standard deviation of the normal distribution.

[0081] For each design parameter, the respective nominal value is used as the mean of the normal distribution, and the standard deviation of the normal distribution is determined with a coefficient of variation of 0.05. The distribution parameters of the uncertainty models for the above six design parameters are shown in Table 1.

[0082] Table 1 Distribution parameters of the multi-source uncertainty model of the diaphragm box sensor

[0083]

[0084] Step 2: Based on the uncertainty models of each parameter constructed in Step 1, first generate a training sample pool through Latin hypercube sampling, and then generate a candidate sample pool through Monte Carlo sampling, which specifically includes the following steps:

[0085] Step 2.1: Based on the uncertainty models of the six design parameters in Step 1, generate a training sample pool through Latin hypercube sampling. The number of samples in the training sample pool is determined by Equation (23):

[0086] N0 = max{12, 2k} (23)

[0087] where k is the number of uncertainty parameters determined in Step 1. In this case, k = 6, and N0 is the number of samples in the training sample pool. In this case, it is calculated that N0 = 12.

[0088] At this time, the training sample pool can be expressed in the form of Equation (24). The specific parameter values of the samples in the training sample pool are shown in Table 2.

[0089]

[0090] where, X 12×6 training is the training sample pool, and x ij (i = 1,..., 12; j = 1,..., 6) is the j-th design parameter of the i-th sample in the training sample pool;

[0091] Table 2 Training sample pool

[0092]

[0093] Step 2.2: Based on the uncertainty models of the six design parameters in Step 1, generate a candidate sample pool containing N = 2×10 5 groups of samples through Monte Carlo sampling. At this time, the candidate sample pool can be expressed in the form of Equation (25). The specific parameter values of the samples in the candidate sample pool are shown in Table 3.

[0094]

[0095] where, X 200000×6 candidateis the candidate sample pool, x' ij (i = 1,..., 2×10 5 ; j = 1,..., 6) is the j-th design parameter of the i-th sample in the candidate sample pool.

[0096] Table 3 Candidate Sample Pool

[0097]

[0098] Step 3: Based on all the samples in the training sample pool established in Step 2, respectively construct the finite element simulation models of the product, and adopt the method combining multi-physics field coupling simulation and physics of failure model to calculate the product life set corresponding to each sample, specifically including the following steps:

[0099] Step 3.1: For the design parameter values of each sample in the initial sample pool X 12×6 training in the initial sample pool, respectively construct the finite element models of the product, conduct finite element simulations, and obtain the finite element response outputs corresponding to each sample.

[0100] Specifically, the bellows sensor is composed of an isolation diaphragm, a central measuring diaphragm and a metal shell, and its internal transmission medium is silicone oil. According to the size of each structure, establish the geometric digital prototype model of the bellows sensor, conduct mesh division, apply load boundary conditions and degree-of-freedom constraints, and establish a finite element model, as Figure 2 shown.

[0101] Furthermore, inject the design parameter values of each sample in the training sample pool into the finite element model of the bellows sensor respectively, conduct random finite element simulations, and record the maximum von-Mises strain value Δε of the central measuring diaphragm in the finite element simulation results of each sample;

[0102] Step 3.2: Determine that the key failure mode of the bellows sensor is fatigue fracture of the central measuring diaphragm, and its corresponding physics of failure model is the Coffin-Manson model, which can be expressed by Equation (26):

[0103]

[0104] where, is the total strain amplitude, taking half of the maximum von-Mises strain value in the finite element simulation results, σ f is the fatigue strengthening coefficient, E S is the elastic modulus of the structural steel material, b is the fatigue strength index, ε f is the fatigue ductility coefficient, c is the fatigue ductility index, N f is the fatigue life. The values of each parameter in the model are shown in Table 4;

[0105] Table 4 Parameter Values of Coffin-Manson Failure Physics Model

[0106]

[0107] Step 3.3: Using the Coffin-Manson failure physics model, according to the maximum von-Mises strain value Δε of the central measurement diaphragm in the finite element simulation results of each sample, calculate the fatigue life set corresponding to each sample in the training sample pool, which can be expressed by Equation (27). When considering that the pressure acts on the diaphragm at a frequency of once per minute, the samples in the training sample pool and their corresponding fatigue lives are shown in Table 5.

[0108]

[0109] Among them, Y 12×1 training is the fatigue life set corresponding to the training sample pool, and N fi (i = 1,..., 12) is the fatigue life of the i-th sample in the training sample pool.

[0110] Table 5 Samples in the Training Sample Pool and Their Corresponding Fatigue Lives

[0111]

[0112]

[0113] Step 4: Based on the product life set obtained in Step 3, construct a Kriging model to predict the product life of each sample in the candidate sample pool.

[0114] Specifically, the general expression of the Kriging model is shown in Equation (28). Using the training sample pool X 12×6 training and its corresponding fatigue life set Y 12×1 training , the unknown parameters in the Kriging model expression can be estimated.

[0115] G(X) = β T f(X) + z(X) (28)

[0116] Among them, G(X) is the performance function, f(X) = [f1(x), f2(x),..., f l (x)] T is the regression function vector, β = [β1, β2,..., β l T is the regression coefficient vector, and z(X) is a stationary Gaussian process with a mean of 0.

[0117] ​Step 5: Using all the samples in the candidate sample pool established in Step 2 as inputs, predict the product life of each sample in the candidate sample pool in turn using the Kriging model constructed in Step 4.

[0118] Specifically, the fatigue life prediction result of the Kriging model is a random variable obeying a normal distribution and can be expressed in the form of Equation (29):

[0119]

[0120] where Y 200000×1 candidate is the fatigue life prediction result of the Kriging model for the candidate sample pool, and N′ fi (i = 1,..., 2×10 5 ) is the fatigue life prediction result of the Kriging model for the i-th sample in the candidate sample pool, which obeys a normal distribution and can be expressed as μ i and σ i are the mean and standard deviation of the normal distribution, respectively.

[0121] Step 6: Based on the product life prediction results obtained in Step 5, perform real-time evaluation of the reliability of the product and measure the accuracy of the reliability evaluation results, which specifically includes the following steps:

[0122] Step 6.1: Based on the fatigue life prediction results obtained in Step 5, apply Equation (30) to perform real-time evaluation of the reliability of the bellows sensor under the current training samples:

[0123]

[0124] where is the real-time evaluation result of the reliability of the bellows sensor under the current training samples, μ i is the mean of the fatigue life prediction results of the Kriging model for the i-th sample in the candidate sample pool, and I{μ i ≤ t} is an indicator function and can be expressed in the form of Equation (31):

[0125]

[0126] Step 6.2: Calculate the variance of the real-time evaluation result of the reliability of the bellows sensor under the current training samples, as shown in Equation (32), to measure the accuracy of the evaluation results:

[0127]

[0128] where σ i is the standard deviation of the fatigue life prediction results of the Kriging model for the i-th sample in the candidate sample pool, and Φ(·) is the cumulative distribution function of the standard normal distribution.

[0129] Step 7: For all samples in the candidate sample pool, use the learning function to determine the key samples that have the greatest impact on the accuracy of the real-time reliability evaluation result obtained in Step 6, and add them to the training sample pool, which specifically includes the following steps:

[0130] Step 7.1: Calculate the value of each sample in the candidate sample pool under the learning function shown in Equation (33) respectively:

[0131]

[0132] where L i is the value of the i-th sample in the candidate sample pool under the learning function;

[0133] Step 7.2: As shown in Equation (34), calculate the maximum value of {L i | i = 1, 2,... 2×10 5}, and determine the corresponding sample as the key sample and add it to the training sample pool.

[0134] x new = X 200000×6 candidate (i index )

[0135]

[0136] where i index is the sample number corresponding to the maximum value of the learning function , and x new is the key sample determined to be added to the training sample pool.

[0137] Step 8: Repeat Step 3 - Step 7, continuously add new key samples to the training sample pool until each statistical feature based on the Kriging model life prediction result in Step 5 meets the stopping criterion, which specifically includes the following steps:

[0138] Step 8.1: Based on the fatigue life prediction result of the Kriging model in Step 5, calculate the values of each statistical feature (including the mean value of the fatigue life of the bellows sensor, the standard deviation of the fatigue life, and the kernel density estimate of the fatigue life probability density), and the specific calculation process is shown in Equations (35) - (37):

[0139]

[0140] where is the mean value of the fatigue life when the number of new samples in the training sample pool is p.

[0141]

[0142] Among them, is the standard deviation of fatigue life when the number of newly added samples in the training sample pool is p.

[0143]

[0144] Among them, is the kernel density estimate of the probability density function of fatigue life when the number of newly added samples in the training sample pool is p, h is the bandwidth, and K(·) is the kernel function, which can be expressed by Equation (38):

[0145]

[0146] Among them, u is the standardized variable, representing the difference between the data point and the position of the estimated density, and is normalized by the bandwidth;

[0147] Step 8.2: For the mean fatigue life of the bellows sensor standard deviation of fatigue life and the kernel density estimate

[0148]

[0149] If there exists an integer M≥m such that for any p∈{M - m + 1,..., M}, Equations (39) - (41) are simultaneously satisfied, it can be considered that each statistical feature of the fatigue life prediction result based on the Kriging model meets the stopping criterion. At this time, the model converges and Steps 3 - 7 are not repeated: -3 , where ε is the convergence threshold, and in the case, ε = 10 -3 , m is any integer not less than 2, which is determined according to the requirement for the accuracy of real-time reliability assessment of the product. The higher the requirement for accuracy, the larger the value of m. In this case, m = 5.

[0150] Specifically, for the bellows sensor, when each statistical feature of the fatigue life prediction result based on the Kriging model meets the stopping criterion, the number of newly added samples is 85, that is, the total number of samples in the training sample pool is 97. The samples and corresponding fatigue lives in the training sample pool when the model converges are shown in Table 6.

[0151] Table 6 Samples and corresponding fatigue lives in the training sample pool when the model converges

[0152]

[0153] Furthermore, the mean and standard deviation of the fatigue life of the bellows sensor during the model update and iteration process are shown in Table 7, and their changing trends with the number of newly added samples in the training sample pool are as Figure 3 shown.

[0154] Table 7 Mean and Standard Deviation of the Fatigue Life of the Bellows Sensor during Model Update Iteration

[0155]

[0156] In addition, the variation trend of the probability density function of the fatigue life of the bellows sensor with the number of newly added samples in the initial training sample pool is as Figure 4 shown. It can be seen that the mean value of the fatigue life of the bellows sensor, the standard deviation of the fatigue life, and the probability density function of the fatigue life change significantly when the number of newly added samples is less than 40, while they gradually tend to be stable after the number of newly added samples is greater than 40. Finally, the stopping criterion is met when there are 85 newly added samples, and the statistical characteristics hardly change any more, indicating that the real-time reliability evaluation result has converged at this time, and the prediction accuracy of the model reaches the maximum value. This can highlight the efficiency and superiority of the real-time reliability evaluation method for equipment-level products proposed in the present invention, which combines physics of failure and active learning Kriging model.

[0157] Step 9: Based on the training sample pool obtained in Step 8, use the Kriging model obtained in Step 4 to predict the product life results corresponding to each sample in the candidate sample pool, and calculate the real-time reliability of the product to complete the real-time evaluation of the product reliability.

[0158] Specifically, by using Equation (37) to estimate the probability density function of the fatigue life of the bellows sensor, the probability density function of the fatigue life of the bellows sensor can be obtained as shown in Equation (42):

[0159]

[0160] where is the probability density function of the fatigue life of the bellows sensor.

[0161] Furthermore, use Equation (43) to perform real-time evaluation of the reliability of the bellows sensor, and the result is as Figure 5 shown.

[0162]

[0163] where R(t) is the real-time reliability of the bellows sensor.

[0164] At the same time, calculate the mean time to failure of the bellows sensor as shown in Equation (44):

[0165]

[0166] where MTTF is the mean time to failure of the bellows sensor.

Claims

1. A real-time evaluation method for the reliability of device-level products that integrates physics of failure and active learning Kriging model, characterized in that It includes the following steps: Step 1: For the key design and production parameters of device-level products (including material parameters, assembly parameters, load parameters, and geometric parameters), sort out the multi-source uncertainty information existing in each parameter, and construct an uncertainty model for each parameter using uncertainty modeling theory; Step 2: Based on the uncertainty models of each parameter constructed in Step 1, first generate a training sample pool through Latin hypercube sampling, and secondly generate a candidate sample pool through Monte Carlo sampling; Step 3: Based on all the samples in the training sample pool established in Step 2, construct a finite element simulation model of the product respectively, and use the method combining multi-physics field coupling simulation and physics of failure model to calculate the product life set corresponding to each sample; Step 4: Based on the product life set obtained in Step 3, construct a Kriging model to predict the product life of each sample in the candidate sample pool; Step 5: Using all the samples in the candidate sample pool established in Step 2 as inputs, use the Kriging model constructed in Step 4 to predict the product life of each sample in the candidate sample pool in turn; Step 6: Based on the product life prediction results obtained in Step 5, conduct real-time assessment of the product's reliability, and measure the accuracy of the reliability assessment results; Step 7: For all the samples in the candidate sample pool, use a learning function to determine the key samples that have the greatest impact on the accuracy of the real-time reliability assessment results obtained in Step 6, and add them to the training sample pool; Step 8: Repeat Steps 3 - 7, continuously add new key samples to the training sample pool until the statistical characteristics based on the life prediction results of the Kriging model in Step 5 meet the stopping criteria; Step 9: Based on the training sample pool obtained in Step 8, use the Kriging model obtained in Step 4 to predict the product life results corresponding to each sample in the candidate sample pool, calculate the real-time reliability of the product, and complete the real-time assessment of the product's reliability.

2. The real-time evaluation method for the reliability of equipment-level products integrating physics of failure and active learning Kriging model according to claim 1, characterized in that The first step of generating a training sample pool through Latin hypercube sampling and the second step of generating a candidate sample pool through Monte Carlo sampling described in Step 2 specifically include the following steps: Step 2.1: Based on the uncertainty models of each parameter, generate a training sample pool through Latin hypercube sampling, and the number of samples in the training sample pool is determined by Equation (1): N0 = max{12, 2k} (1) where N0 is the number of samples in the training sample pool, and k is the number of uncertainty design parameters; At this time, the training sample pool can be expressed in the form of Equation (2): Among them, is the training sample pool, and x ij (i = 1, ..., N0; j = 1, ..., k) is the j-th design parameter of the i-th sample in the training sample pool; Step 2.2: Based on the uncertainty models of each parameter, generate a candidate sample pool containing N (N ≥ N0) groups of samples through Monte Carlo sampling. At this time, the candidate sample pool can be expressed in the form of Equation (3): Among them, X N×k candidate is the candidate sample pool, and x′ ij (i = 1,..., N; j = 1,..., k) is the j-th design parameter of the i-th sample in the candidate sample pool.

3. The real-time evaluation method for the reliability of device-level products integrating physics of failure and active learning Kriging model according to claim 1, wherein The step of conducting real-time assessment of the product's reliability based on the product life prediction results obtained in Step 5 and measuring the accuracy of the reliability assessment results described in Step 6 specifically includes the following steps: Step 6.1: Based on the product life prediction results obtained in Step 5, apply Equation (4) to conduct real-time assessment of the product's reliability under the current training samples: Among them, is the real-time evaluation result of product reliability under the current training sample, and μ i is the mean of the Kriging model life prediction results of the i-th sample in the candidate sample pool. I{μ i ≤t} is an indicator function and can be expressed in the form of Equation (5): Step 6.2: Calculate the variance of the real-time reliability evaluation results under the current training samples, as shown in Equation (6), to measure the accuracy of the evaluation results: Among them, σ i is the standard deviation of the Kriging model life prediction result of the i-th sample in the candidate sample pool, and Φ(·) is the cumulative distribution function of the standard normal distribution.

4. The real-time evaluation method for the reliability of equipment-level products integrating physics of failure and active learning Kriging model according to claim 1, characterized in that, For all samples in the candidate sample pool described in Step 7, use the learning function to determine the key samples that have the greatest impact on the accuracy of the real-time reliability evaluation results obtained in Step 6, and add them to the training sample pool. The specific steps are as follows: Step 7.1: Calculate the value of each sample in the candidate sample pool under the learning function shown in Equation (7) respectively: Among them, L i is the value of the i-th sample in the candidate sample pool under the learning function; Step 7.2: As shown in Equation (8), calculate the maximum value of {L i |i = 1, 2,... N}, and determine the corresponding sample as the key sample, and add it to the training sample pool: where i index is the learning function is the sample number corresponding to the maximum value of dt, and x new is the key sample to be added to the training sample pool.

5. The real-time evaluation method for the reliability of device-level products integrating physics of failure and active learning Kriging model according to claim 1, characterized in that, The steps described in Step 8 until the statistical features based on the Kriging model life prediction results in Step 5 meet the stopping criteria. The specific steps are as follows: Step 8.1: Based on the life prediction results of the Kriging model in Step 5, calculate the values of each statistical feature (including the product life mean, the product life standard deviation, and the kernel density estimate of the product life probability density). The specific calculation process is as shown in Equations (9)-(11): Among them, is the mean value of the product life when the number of new samples added to the training sample pool is p; Among them, is the standard deviation of the product life when the number of new samples added to the training sample pool is p; Among them, is the kernel density estimate of the product life probability density function when the number of new samples added to the training sample pool is p; h is the bandwidth; K(·) is the kernel function, which can be expressed by Equation (12): where u is the standardized variable, representing the difference between the data point and the position of the estimated density, and is normalized by the bandwidth; Step 8.2: For the mean value of product life Standard deviation of product life And the kernel density estimation value of the product life probability density When there exists an integer M ≥ m such that for any p ∈ {M - m + 1,..., M}, equations (13) - (15) are simultaneously satisfied, it can be considered that all statistical characteristics of the life prediction result based on the Kriging model meet the stopping criterion. At this time, the model converges and steps 3 - 7 are not repeated: where ε is the convergence threshold, which can take values in the range of [10 -4 , 10 -2 ; m is an integer not less than 2, which is determined according to the requirement for the accuracy of real-time reliability assessment of the product. The higher the requirement for accuracy, the larger the value of m.

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