Reliability design optimization method combining transfer learning and physical information neural network

Abstract

The invention belongs to the technical field of reliability-based design optimization, and particularly relates to a reliability design optimization method combining transfer learning and a physical information neural network. Comprising the following steps: constructing a physical information neural network model by adopting training data of a source domain, and evaluating the reliability of the source domain. A physical information neural network model constructed by adopting training data of a source domain is updated by utilizing a layer freezing and fine tuning technology in transfer learning, so that the reliability of a target domain with different statistical attributes is evaluated, the calculation overhead is saved, and the calculation efficiency is improved. A first-order scoring function is utilized to carry out random sensitivity analysis on the failure probability so as to ensure normal operation of design optimization. And finally, providing estimation reliability, an objective function value and corresponding sensitivity information for an optimizer to obtain a corresponding updated design point. And repeating the iterative design process until the optimal design is realized. The training speed of the physical information neural network model is increased, and the precision of the physical information neural network model is improved.

Description

Technical Field

[0001] The present invention belongs to the field of reliability-based design optimization technology, and in particular, relates to the design optimization of constraint functions expressed in the form of ordinary differential equations or partial differential equations in complex mechanical structures or systems. Specifically, it is a reliability design optimization method combining transfer learning and physical information neural network. Background Art

[0002] Reliability-based design optimization (RBDO) can fully consider the impact of uncertainty on constraints and objectives during the optimization process, and obtain an optimization solution that meets the target reliability, thereby achieving a good balance between the reliability of constraints and the optimization of objectives. In general, the mathematical formula for reliability-based design optimization problems can be expressed as:

[0003]

[0004] In the formula, the random input X is composed of X rv and X rp Two components, namely X = [X rv ,X rp ] T , where X rv =[X1,X2,…,X nd ] T represents the vector of random design variables; X rp =[X nd+1 ,X nd+1 ,…,X nr ] T represents a vector of random parameters, d = [d1, d2, …, d nd ] T is the design vector, which is a vector of random design variables X rv The mean of L and d U denote the lower and upper boundaries of the design vector respectively; is the target failure probability of the jth constraint function; nc, nd and nr represent the number of constraint functions, the number of random design variables and the number of random inputs respectively. It is not difficult to find that in order to obtain the precise optimal design point, it is necessary to accurately evaluate the failure probability of each constraint function. In other words, reliability analysis is performed on each constraint function. The failure probability in reliability analysis is defined as:

[0005]

[0006] where ψ is a vector of distribution parameters, usually including the mean and standard deviation of the random input X; P{·} is a probability measure; f X(x; ψ) represents the joint probability density function (PDF) of X. Formula (2) is usually a multidimensional integration problem, and it is difficult to directly obtain its closed-form solution. In order to solve the multidimensional integration problem with high accuracy, a sampling-based method, such as Monte Carlo simulation, can be used. In this case, Formula (2) can be expressed as:

[0007]

[0008] Where E[·] is the expectation operator; Ω F ={x:G(x)<0} is the failure set. In formula (3), it is called the indicator function and is defined as follows:

[0009]

[0010] Due to the adoption of X rv The mean d of is used as the design vector. When calculating the failure probability in equation (3), the distribution parameter vector ψ can be simply replaced by d.

[0011] The core of the constraint function G(X) of many optimization design problems in science and engineering is driven by the laws of physics and expressed in the form of linear or nonlinear ordinary differential equations / partial differential equations. For space-time phenomena, these equations can be expressed as:

[0012]

[0013] where u(t,s,X) represents the potential (hidden) solution of the PDE, where t represents the time variable and s represents the space variable. t is the partial derivative of u(s,t,X) with respect to t; represents the nonlinear differential operator parameterized by the random variable X; Ω is Therefore, in this case, the constraint function G(X) can be expressed by the potential (hidden) solution u and the threshold u0 as:

[0014] G(X)=g(u)-u0 (6)

[0015] The mathematical formula of RBDO can be reformulated as:

[0016]

[0017] The solution process of the RBDO method is usually designed with two layers of nested optimization. The outer layer is the optimization of the design variables, and the inner layer is the reliability analysis, that is, each design point in the optimization process needs to be evaluated for reliability. Since the constraint functions in actual engineering are usually numerical models with high computational costs, the nested relationship makes the RBDO calculation inefficient. In order to improve the computational efficiency of RBDO, three mainstream methods have been developed to solve the RBDO problem: the double-loop method, the decoupled loop method, and the single-loop method. The double-loop method nests two different levels of optimization processes. The outer layer optimizes the design variables to generate candidate design points, and the inner layer performs reliability analysis. In the decoupled loop method, the RBDO problem is transformed into a series of deterministic optimization problems. The main idea of ​​the single-loop method is to replace the probabilistic constraints with optimality conditions and solve the RBDO problem in a single-loop process.

[0018] In RBDO, it is crucial to perform accurate and efficient reliability analysis because it affects the accuracy of the optimal solution as well as the computational cost. Many reliability analysis methods have been proposed for this purpose, including sampling methods (such as Monte Carlo simulation), methods based on most likely points (such as first-order and second-order reliability methods), surrogate model methods, expansion methods, and approximate integral methods. Among them, surrogate models are widely used in various engineering problems due to their simplicity and efficiency. A surrogate model is an easy-to-evaluate model that approximately describes the relationship between the input and output of a system. Different surrogate model techniques, such as support vector machines (SVM), Kriging, artificial neural networks (ANN), and response surface methods (RSM) have been developed. Surrogate models are usually constructed based on given training data and then combined with Monte Carlo simulation to solve the reliability of the system. Solving RBDO problems based on surrogate model methods has also been fully explored in recent years.

[0019] On the other hand, due to the recognition of the physical laws governing the dynamic evolution of control systems, machine learning techniques have also been developed to directly learn the dynamics of the system without using data provided by traditional numerical solvers such as finite element models. One of the most popular recent works is the physical-informed neural network, which is widely used in fields such as fluid mechanics, robotic control, and high-energy physics. It constructs a loss function using the residuals and boundary conditions of partial differential equations. The model is then trained by optimizing the loss function so that the predictions satisfy the physical laws. In this case, the neural network itself can be considered as a physical-informed proxy model to provide solutions to the control equations. Physical-informed neural networks have also emerged in the field of reliability analysis, especially when the control equations of the system are expressed in the form of differential equations. There is still much research to be done on the solution of RBDO problems based on physical-informed neural networks.

[0020] In the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art:

[0021] (1) Although traditional surrogate model methods have been fully explored in the field of RBDO, their essence is to use data-driven surrogate models to solve RBDO problems. The quality of the model and the prediction accuracy directly depend on the training data. Although the size of the database is minimized through various strategies, the original constraint function still needs to be evaluated. In particular, when the constraint function is expressed in the form of a differential equation, the differential equation needs to be solved repeatedly. Usually, methods such as finite element (FE) and finite difference (FD) are required. However, using these methods to solve complex problems can be time-consuming.

[0022] (2) Physical information neural networks have not been fully explored in the field of RBDO, but just as data-driven surrogate models have been used to solve RBDO problems, these methods can be simply integrated into the framework of sampling-based RBDO. However, this simple integration is inefficient, mainly because the physical information neural network models trained by these methods have limited generalization capabilities, resulting in the need to rebuild the physical information neural network model in each iteration to accurately evaluate the reliability of the current design point when solving the RBDO problem. Although the physical information neural network does not need to evaluate the constraint function expressed as a differential equation, that is, "no simulation", it does not mean that the physical information neural network has no computational overhead. In fact, training the physical information neural network is also time-consuming. Therefore, when solving the RBDO problem, rebuilding the physical information neural network model in each iteration also faces huge computational costs. Summary of the invention

[0023] In order to solve the above problems in the prior art, the present invention proposes a reliability design optimization method combining transfer learning and physical information neural network, which mainly solves the problems of computational accuracy and efficiency of RBDO problems represented by partial differential equations. The main problems include: (1) the problem that expensive numerical models make it difficult to obtain sample data for reliability analysis. (2) the generalization problem of physical information neural network caused by covariate offset.

[0024] The complete technical solution of the present invention includes:

[0025] The sample space and its distribution based on the initial design point are called the source domain, and the sample space and its distribution based on the current design point are called the target domain. First, the training data of the source domain is used to build a physical information neural network model, and the reliability of the source domain is evaluated. Secondly, in order to evaluate the reliability of the target domain with different statistical properties, the layer freezing and fine-tuning techniques in transfer learning are used to update the physical information neural network model built with the training data of the source domain, instead of reconstructing a physical information neural network model with the training data of the target domain to save computational overhead. Thirdly, in order to ensure the normal progress of the design optimization, a random sensitivity analysis of the failure probability is performed using a first-order scoring function. Finally, the estimated reliability, objective function value and corresponding sensitivity information are provided to the optimizer to obtain the corresponding updated design point. The iterative design process will be repeated until the optimal design is achieved.

[0026] The complete technical solution of the present invention includes:

[0027] A reliability design optimization method combining transfer learning and physical information neural network includes the following steps:

[0028] (1) Define the initial design point of RBDO;

[0029] (2) generating source domain configuration points, wherein the source domain is a sample space and its distribution based on the initial design points in step (1), and Latin hypercube sampling is used to generate source domain configuration points; generating configuration points for constructing a physical information neural network model At the same time, the configuration points for source domain reliability assessment are generated

[0030] (3) Construct a physical information neural network model for source domain reliability analysis;

[0031] (4) Source domain reliability analysis and sensitivity analysis: The constructed physical information neural network model is used to predict the configuration points The response of the constraints is analyzed and reliability analysis is performed on them. At the same time, a first-order scoring function is used to perform random sensitivity analysis.

[0032] (5) Update the design point: By providing the optimizer with the estimated failure probability, objective function value, and corresponding sensitivity information, the updated design point is obtained;

[0033] (6) Generate target domain configuration points: The target domain is a sample space and its distribution based on the updated design points, and Latin hypercube sampling is used to generate target domain configuration points; Generate configuration points for transfer learning At the same time, the configuration points for reliability evaluation in the target domain are generated

[0034] (7) performing transfer learning on the physical information neural network model used for source domain reliability analysis; the transfer learning includes first adopting layer freezing and then fine-tuning to update the physical information neural network model;

[0035] (8) Target domain reliability analysis and sensitivity analysis: Using updated physical information neural network model to predict configuration points The response of the constraints is analyzed and reliability analysis is performed on them. At the same time, a first-order scoring function is used to perform random sensitivity analysis.

[0036] (9) Check the convergence condition: If the convergence condition is met, stop the iteration process and output the optimal design; otherwise, return to step (5) and repeat the iteration process until the convergence condition is met.

[0037] Furthermore, in step (1), the initial design point of RBDO is the optimal solution under deterministic optimization.

[0038] Furthermore, in step (2), the configuration points for constructing the physical information neural network model include initial condition configuration points Boundary Condition Configuration Points and the residual collocation points of the partial differential equation

[0039] Furthermore, in step (3), the process of constructing a physical information neural network model for source domain reliability analysis includes: first initializing a deep neural network model, then using an automatic differentiation mechanism to satisfy initial conditions, boundary conditions and partial differential equations, and finally minimizing the training data loss of physical information.

[0040] Furthermore, in step (6), the configuration point for transfer learning is Include initial condition configuration points Boundary Condition Configuration Points and the residual collocation points of the partial differential equation

[0041] Furthermore, in step (6), the layer freezing includes freezing some layers of the physical information neural network model used for source domain reliability analysis, and then freezing the layers of the physical information neural network model used for source domain reliability analysis in the training data. The remaining layer parameters are updated.

[0042] Further, in step (6), the fine-tuning includes unfreezing the entire model or part of the model obtained above, and then Retrain the model with a lower learning rate.

[0043] Furthermore, the lower learning rate is 0.0001.

[0044] Furthermore, the reliability design optimization method is used to optimize the system structure.

[0045] Furthermore, the system includes a force-bearing component.

[0046] Furthermore, the system is a cylindrical straight rod, an undamped single-degree-of-freedom system, or a thin plate subjected to uneven loads.

[0047] The advantages of the present invention over the prior art are:

[0048] (1) The present invention uses a physical information neural network for reliability analysis, and efficiently solves the reliability design optimization problem of complex engineering structures expressed in the form of ordinary differential equations or partial differential equations. The physical information neural network adds physical equations as constraints to the neural network, which not only makes the fitting results more in line with physical laws, but also avoids the simulation of traditional numerical solution methods such as finite element analysis, and realizes efficient uncertainty quantification.

[0049] (2) The present invention uses a first-order scoring function to analyze the sensitivity of the failure probability. By providing the optimizer with the estimated reliability, the objective function value and the corresponding sensitivity information, the corresponding updated design point can be obtained.

[0050] (3) The present invention introduces transfer learning technology, which effectively solves the generalization problem caused by covariate shift when the physical information neural network method is used to deal with design optimization problems. The layer freezing technology in transfer learning, on the one hand, retains the useful physical information in the physical information neural network model constructed in the source domain; on the other hand, it reduces the gradients that need to be calculated to update the physical information neural network model, thereby speeding up the training of the physical information neural network model. The fine-tuning technology in transfer learning further improves the accuracy of the physical information neural network updated by the layer freezing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flowchart of the design optimization method for simulation-free reliability combining transfer learning and physical-informed neural network models.

[0052] Figure 2 Architecture for physical information neural networks.

[0053] Figure 3 Schematic diagram of layer freezing technology.

[0054] Figure 4 Schematic diagram of fine-tuning technology.

[0055] Figure 5 This is a structural schematic diagram of the design optimization method for non-simulation reliability combining transfer learning and physical information neural network model proposed in the present invention.

[0056] Figure 6 Schematic diagram of the cylindrical straight rod of Example 1. DETAILED DESCRIPTION

[0057] The present invention is described in detail below in conjunction with the embodiments and drawings, but it should be understood that the embodiments and drawings are only used to exemplify the present invention and do not constitute any limitation on the protection scope of the present invention. All reasonable changes and combinations within the scope of the inventive concept of the present invention fall within the protection scope of the present invention.

[0058] Figure 1 and Figure 5 The flowchart and structural schematic diagram of the embodiment of the non-simulation reliability design optimization method combining transfer learning and physical information neural network of the present invention are shown in the figure, which includes the following steps:

[0059] S1 defines the initial design point.

[0060] Generally speaking, the initial design point of reliability-based optimization design is the optimal solution under deterministic optimization.

[0061] S2 generates source domain configuration points.

[0062] The sample space and its distribution based on the initial design point is called the source domain, and Latin hypercube sampling is used to generate the source domain configuration points. Generate the configuration points used to build the physical information neural network model Include initial condition configuration points Boundary Condition Configuration Points and the residual collocation points of the partial differential equation At the same time, the configuration points for source domain reliability assessment are generated

[0063]

[0064] The present invention uses Latin hypercube sampling to generate collocation points. For the time variable t and the space variable s, the collocation points are generated using uniform distribution. For the random variable X, according to the source domain D S This method generates a total of

[0065] Configuration Points include PDE residual collocation points Initial condition configuration points Boundary condition configuration points in:

[0066]

[0067] The values ​​of initial conditions and boundary conditions at the configuration points can be calculated and are expressed as in:

[0068]

[0069] At the same time, the configuration points for source domain reliability assessment are generated The present invention mainly focuses on specific spatiotemporal reliability analysis and reliability-based design optimization problems, which means that for time variable t=t0 and space variable s=s0, where:

[0070]

[0071] S3 builds a physical information neural network model for source domain reliability analysis. Figure 2 shown.

[0072] S301 uses a deep neural network model to represent the approximate solution. The deep neural network model needs to be initialized, including parameters and hyperparameters, such as the number of hidden layers and the number of neurons. The approximate hidden solution using the deep neural network model can be expressed as:

[0073]

[0074] S302 uses an automatic differentiation mechanism to satisfy initial conditions, boundary conditions and partial differential equations. The loss functions that violate the partial differential equations, initial conditions and boundary conditions can be expressed as:

[0075]

[0076] Therefore, the loss function of the physical information neural network model for source domain reliability analysis can be expressed as:

[0077]

[0078] S303 minimizes the loss function. In order to calculate the parameter θ S , including W S and b S , minimizing the loss function in formula (18) can be expressed as:

[0079]

[0080] S4 Source domain reliability analysis and sensitivity analysis, including:

[0081] S401 Source Domain Reliability Analysis. Once the network is trained, it can be used to predict the partial differential equations at the collocation point The solution of . Thus, the probability distribution function of the estimated response is obtained, which is used for source domain reliability analysis, where the configuration point The estimated response is divided into two categories: failure and safety, expressed as:

[0082]

[0083] in, represents the approximate solution obtained by the physical information neural network model. Then, according to the number of failure samples and the configuration points The reliability is approximated by the ratio of the size, which is expressed as:

[0084]

[0085] S402 Source Domain Sensitivity Analysis. In order to find the optimal solution, the failure probability P F (d) Sensitivity information is necessary. The failure probability for the i-th design variable d i Find partial derivatives:

[0086]

[0087] According to Leibniz's differential law, the integral operator and the differential operator are interchangeable, and equation (22) can be written as:

[0088]

[0089] because Not i The logarithmic function of the joint PDF in formula (23) is i The partial derivative of i The first-order scoring function can be expressed as:

[0090]

[0091] Therefore, formula (23) can be reformulated as:

[0092]

[0093] The sensitivity can be directly approximated based on the identified failure Monte Carlo samples as:

[0094]

[0095] Among them, n mcs is the number of Monte Carlo sample populations. Formula (26) can effectively approximate the sensitivity information of failure probability to design variables without incurring additional computational costs. Therefore, the sensitivity in the source domain can be expressed as:

[0096]

[0097] S5 updates the design point.

[0098] By providing the optimizer with the estimated failure probability, the objective function value, and the corresponding sensitivity information, an updated design point can be obtained.

[0099] S6 generates a target domain configuration point.

[0100] The sample space and its distribution based on the updated design point are called the target domain, and Latin hypercube sampling is used to generate the source domain collocation points. For the time variable t and the space variable s, the collocation points are generated using a uniform distribution. For the random variable X, according to the target domain D S This method generates a total of Configuration Points include PDE residual collocation points Initial condition configuration points Boundary condition configuration points in:

[0101]

[0102]

[0103] The values ​​of initial conditions and boundary conditions at the configuration points can be calculated and are expressed as in:

[0104]

[0105] At the same time, the configuration points for reliability evaluation in the target domain are generated in:

[0106]

[0107] S7 performs transfer learning on the physical information neural network model for source domain reliability analysis.

[0108] S701 layer freezing

[0109] The initial values ​​of the parameters in the physical information neural network model used for target domain reliability analysis are set to the parameter values ​​in the physical information neural network model used for source domain reliability analysis, which means that the physical information neural network model used for target domain reliability analysis and the physical information neural network model used for source domain reliability analysis have the same architecture. The model is trained on the basis of the last few layers of the physical information neural network model, and the parameters corresponding to the last few layers are updated instead of the parameters corresponding to all layers. Figure 3 As shown, it can be expressed as:

[0110]

[0111] in, represents the weights and biases that are allowed to be updated during the layer freezing process. The loss functions that violate the partial differential equations, initial conditions, and boundary conditions can be expressed as:

[0112]

[0113] Therefore, the loss function of the physical information neural network model for target domain reliability analysis can be expressed as:

[0114]

[0115] To calculate the parameters include Minimizing the loss function in equation (38) can be expressed as:

[0116]

[0117] Layer freezing is implemented using a custom function. In this function, the model.parameters() method is first used to return an iterator to traverse all the parameters of the model. Then the requires_grad attribute is used to set whether each parameter requires a gradient. The layer freezing technology, on the one hand, retains the useful physical information in the physical information neural network model constructed in the source domain. On the other hand, it reduces the gradients that need to be calculated to update the physical information neural network model, speeding up the training of the physical information neural network model.

[0118] S702 fine-tuning.

[0119] Fine-tuning involves unfreezing the entire model (or part of the model) obtained above and then running it on the training data. The model is retrained with a lower learning rate (e.g. 0.0001), as Figure 4 As shown, it can be expressed as:

[0120]

[0121] in, They represent the weights and biases that are allowed to be fine-tuned. The training data of the fine-tuning process and the layer freezing process are consistent. Therefore, the loss function that violates the partial differential equations, initial conditions and boundary conditions in the fine-tuning process can also be expressed by equations (35), (36) and (37). The loss function of the physical information neural network model for target domain reliability analysis can be expressed as:

[0122]

[0123] To calculate the parameters include Minimizing the loss function in equation (41) can be expressed as:

[0124]

[0125] Typically, the number of iterations of fine-tuning is a small value to prevent overfitting. Fine-tuning further improves the prediction accuracy of the model.

[0126] S8 Target domain reliability analysis and random sensitivity analysis.

[0127] S801 Target Domain Reliability Analysis. Once the network is trained, it can be used to predict the partial differential equations at the configuration point The solution of . Thus, the probability distribution function of the estimated response is obtained, which is used for target domain reliability analysis, where the configuration point The estimated response is divided into two categories: failure and safety, expressed as:

[0128]

[0129] in, represents the approximate solution obtained by the physical information neural network model. Then, according to the number of failure samples and the configuration points The reliability is approximated by the ratio of the size, which is expressed as:

[0130]

[0131] S802 Target domain sensitivity analysis. Similar to the sensitivity analysis in the source domain, the sensitivity in the target domain can be expressed as:

[0132]

[0133] S9 checks the convergence condition. If convergence is achieved, the iteration process stops and the optimal design is output; otherwise, the iteration process returns to S5.

[0134] Through the method proposed in the present invention, the reliability design optimization of engineering structures is achieved with high precision and high efficiency. The high precision of the proposed method is due to the following two main reasons: First, the layer freezing technology in transfer learning overcomes the generalization problem caused by statistical differences in the process of solving the RBDO problem by the physical information neural network model; second, on the basis of the physical information neural network model updated by the layer freezing technology, the model is retrained by the fine-tuning technology in transfer learning, which further improves the prediction accuracy of the model. The high efficiency of the proposed method is due to the following two main reasons: First, compared with the direct solution of the RBDO problem by the data-driven neural network model, the proposed method makes full use of the physical prior information and avoids the call of the traditional expensive numerical simulation model. Secondly, compared with the direct solution of the RBDO problem by the physical information neural network model, the proposed method retains the useful physical information in the previous physical information neural network model through the layer freezing technology, and there is no need to retrain the physical information neural network model in each optimization process, which greatly reduces the training overhead of the physical information neural network model.

[0135] Example 1

[0136] Taking a cylindrical straight rod as an example, the present invention is further described. Figure 6 As shown, the length of the cylindrical straight rod is l = 5, the left side is fixed, and the right side bears the load F. Young's modulus E, cross-sectional area A and load F are considered as random variables, among which the cross-sectional area A is a random design variable, and the rest are non-design variables and are considered as random parameters. The distribution information of all random variables is shown in Table 1.

[0137] Table 1 Distribution information of random variables in Example 1

[0138] random variable Mean Standard Deviation distributed F 100 10 normal distribution A <![CDATA[d1]]> 0.1 normal distribution E 206 15 normal distribution

[0139] The optimization goal is to minimize the mass of the cylindrical rod, which is equivalent to minimizing the cross-sectional area. The maximum allowable displacement of the rod is u max =1.5. The RBDO problem is expressed as:

[0140]

[0141] in, u0=1.5. In this embodiment, the initial point is set to d0=1.500, and it is assumed that the standard deviation of the random design variable remains unchanged, and the method proposed in the present invention is used to solve the RBDO problem.

[0142] In this embodiment, the sample space based on the initial design point d0 and its distribution are called the source domain. In order to perform reliability analysis on the source domain, firstly, 2100 collocation points are generated by Latin hypercube sampling, including 2000 partial differential equation residual collocation points and 100 boundary condition collocation points, which are used to train the physical information neural network model. This means Generate 10 at a time 5 configuration points for reliability evaluation, which means Secondly, a physical information neural network model is constructed, denoted as SD-PINN. The network structure contains 3 hidden layers, each with 50 neurons. Except for the last layer, the activation function of the remaining layers adopts the tanh activation function. Thirdly, the constructed physical information neural network model is used to evaluate the failure probability of the source domain. Finally, a first-order scoring function is used to perform a random sensitivity analysis on the failure probability. By providing the optimizer with the estimated failure probability, the objective function value and the corresponding sensitivity information, the updated design point d1=1.9146 can be obtained.

[0143] The sample space and its distribution based on the updated design point d1 are called the target domain. In order to perform reliability analysis on the target domain with different distribution properties, firstly, 2100 collocation points are generated by Latin hypercube sampling, including 2000 partial differential equation residual collocation points and 100 boundary condition collocation points, which are used to update the physical information neural network model. This means Generate 10 at a time 5 configuration points for target domain reliability evaluation, which means Secondly, the layer freezing and fine-tuning techniques are used to update the physical information neural network model, which are denoted as FL-PINN and FT-PINN respectively. In this problem, the updated layers are allowed to be set to the last two layers. In addition, in order to compare the efficiency, the training data of the target domain is directly used to construct the physical information neural network model, which is denoted as TD-PINN. Thirdly, the updated physical information neural network model is used to evaluate the failure probability of the target domain. Finally, a first-order scoring function is used to perform a random sensitivity analysis on the failure probability. By providing the optimizer with the estimated failure probability, the objective function value and the corresponding sensitivity information, the updated design point d2=1.9872 can be obtained. The iterative design process will be repeated until an optimal design point d is obtained. opt =2.0077.

[0144] The above applications are only some implementation methods of the present application. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present application, and these all belong to the protection scope of the present application.

Claims

1. A reliability design optimization method combining transfer learning and physical information neural network, characterized in that: The steps include: (1) Define the initial design point of RBDO; (2) generating source domain configuration points, wherein the source domain is a sample space and its distribution based on the initial design points in step (1), and Latin hypercube sampling is used to generate source domain configuration points; generating configuration points for constructing a physical information neural network model At the same time, the configuration points for source domain reliability assessment are generated (3) Construct a physical information neural network model for source domain reliability analysis; (4) Source domain reliability analysis and sensitivity analysis: The constructed physical information neural network model is used to predict the configuration points The response of the constraints is analyzed and reliability analysis is performed on them. At the same time, a first-order scoring function is used to perform random sensitivity analysis. (5) Update the design point: By providing the optimizer with the estimated failure probability, objective function value, and corresponding sensitivity information, the updated design point is obtained; (6) Generating target domain configuration points: the target domain is a sample space and its distribution based on the updated design points, and Latin hypercube sampling is used to generate the target domain configuration points; Generate configuration points for transfer learning At the same time, the configuration points for reliability evaluation in the target domain are generated (7) performing transfer learning on the physical information neural network model used for source domain reliability analysis; the transfer learning includes first adopting layer freezing and then fine-tuning to update the physical information neural network model; (8) Target domain reliability analysis and sensitivity analysis: Using updated physical information neural network model to predict configuration points The response of the constraints is analyzed and reliability analysis is performed on them. At the same time, a first-order scoring function is used to perform random sensitivity analysis. (9) Check the convergence condition: If the convergence condition is met, stop the iteration process and output the optimal design; otherwise, return to step (5) and repeat the iteration process until the convergence condition is met.

2. The reliability design optimization method combining transfer learning and physical information neural network according to claim 1 is characterized in that: In step (1), the initial design point of RBDO is the optimal solution under deterministic optimization.

3. The reliability design optimization method combining transfer learning and physical information neural network according to claim 2 is characterized in that: In step (2), the configuration points for constructing the physical information neural network model include the initial condition configuration points Boundary Condition Configuration Points and the residual collocation points of the partial differential equation 4. The reliability design optimization method combining transfer learning and physical information neural network according to claim 3 is characterized in that: In step (3), the process of constructing the physical information neural network model for source domain reliability analysis includes: first initializing a deep neural network model, then using the automatic differentiation mechanism to satisfy the initial conditions, boundary conditions and partial differential equations, and finally minimizing the training data loss of physical information.

5. The reliability design optimization method combining transfer learning and physical information neural network according to claim 4 is characterized in that: In step (6), the configuration point used for transfer learning Include initial condition configuration points Boundary Condition Configuration Points and the residual collocation points of the partial differential equation 6. The reliability design optimization method combining transfer learning and physical information neural network according to claim 5 is characterized in that: In step (6), the layer freezing includes freezing some layers of the physical information neural network model used for source domain reliability analysis, and then The remaining layer parameters are updated.

7. The reliability design optimization method combining transfer learning and physical information neural network according to claim 6 is characterized in that: In step (6), the fine-tuning includes unfreezing the entire model or part of the model obtained above, and then Retrain the model with a lower learning rate.

8. The reliability design optimization method combining transfer learning and physical information neural network according to claim 7, characterized in that: The lower learning rate is 0.0001.

9. A reliability design optimization method combining transfer learning and physical information neural network according to any one of claims 1 to 8, characterized in that: The reliability design optimization method is used to optimize the system structure.

10. The reliability design optimization method combining transfer learning and physical information neural network according to claim 9, characterized in that: The system includes a stressed component.

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