Complex equipment global reliability analysis method based on physical information neural network

Abstract

The invention discloses a complex equipment global reliability analysis method based on a physical information neural network, and the method comprises the steps: segmenting a sample feasible region through employing a Voronoi region division method, calculating the region sensitivity through the model response in a training process, dividing a sensitive region, carrying out the resampling, dynamically adjusting the distribution of sample points in the training process of the physical information neural network, and carrying out the global reliability analysis of complex equipment. And iteratively updating sample points, constructing a network model, and efficiently predicting the failure probability of any time-space coordinate of the system by utilizing the system global response prediction capability of the physical information neural network and combining a Monte Carlo simulation method. The method can be used for calculating the global failure probability of complex equipment under the comprehensive action of various uncertainties, the problem that traditional reliability analysis depends on a large amount of simulation calculation to obtain experimental samples is solved, the calculation cost is effectively reduced, the limitation to fixed hotspots is overcome, the problem that potential failure areas change at any time and space is solved, and the reliability of the equipment is improved. The analysis efficiency is greatly improved; and the waste of computing resources is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of reliability analysis of complex equipment, and in particular relates to a global reliability analysis method of complex equipment based on physical information neural network. Background Art

[0002] Studying the reliability of complex equipment under various uncertainties in its operation plays a vital role in improving the equipment's operating performance and stability. In recent years, it has also received widespread attention in many cutting-edge engineering fields.

[0003] Based on existing research, researchers' understanding, exploration and practical application of reliability theory are mostly focused on the traditional time-invariant reliability model. This model usually ignores the degradation of structural performance and the influence of dynamic loads, so the reliability of equipment is often regarded as a fixed value. However, in actual engineering, the reliability of complex structural systems will be affected by uncertain factors such as material properties, working conditions, time-varying loads, etc., resulting in its reliability changing with time and space and is no longer a constant value. Therefore, in order to ensure the safety of complex equipment throughout its life cycle, it is urgent to establish a reliability analysis model that can capture the global uncertainty characteristics.

[0004] In order to realize the global reliability analysis of complex structural systems, the Monte Carlo simulation (MCS) method is currently mainly used. The MCS method provides a high-precision reliability analysis method, but it requires a large number of random sample points and obtains the corresponding response through actual models or simulations, which is extremely costly and impractical, especially for complex equipment. Therefore, the proxy model method has become an effective alternative, which replaces the real finite element simulation process by constructing a simplified model.

[0005] However, traditional reliability analysis methods based on surrogate models, such as transient response surface method, usually only focus on certain fixed hotspot locations and fail to fully consider the changes in potential failure areas of complex systems under dynamic conditions on a global scale, especially when the system is in a dynamic operating environment. This deficiency leads to low computational efficiency and may ignore key potential failure points. In addition, existing methods lack uniformity in sample point distribution, resulting in waste of computing resources and excessive costs. Summary of the invention

[0006] In order to solve the shortcomings of the prior art and achieve the purpose of reducing computing costs and reducing the waste of computing resources, the present invention adopts the following technical solutions:

[0007] The global reliability analysis method of complex equipment based on physical information neural network includes the following steps:

[0008] Step S1: Obtain complex system input and system randomness related to complex equipment;

[0009] Step S2: Generate initial sample points according to the distribution of complex system input;

[0010] Step S3: Based on the randomness of the system, a mapping relationship between the system response and the failure form is established, a limit state function for global reliability analysis of the complex system is constructed, and the failure probability of any spatial coordinate point of the complex system is constructed based on the limit state function;

[0011] Step S4: extracting the control equation of the complex system and determining its boundary conditions according to the physical information of the complex system;

[0012] Step S5: Based on the determined boundary conditions, construct a physical information neural network model and perform training, adjust the samples by predicting the system response of the current physical information, and use the updated samples for training;

[0013] Step S6: using the trained physical information neural network model to fit the system response, and using the limit state function of the global reliability analysis of the complex system, the global failure probability of the complex system is calculated based on the Monte Carlo simulation method.

[0014] Furthermore, step S3 includes the following steps:

[0015] Step S3.1: Analyze the potential failure modes of the complex system, establish the mapping relationship between the current system response and the failure mode, and construct the limit state function of the global reliability analysis of complex equipment:

[0016] G(U,ω,t)=u0-u(U,ω,t)

[0017] Among them, U represents the system randomness including random variables, random fields and time-varying random processes, u0 represents the threshold of reliability analysis, u(*) represents the response of the system in different time and space coordinates, ω represents the system space coordinates, and t represents time;

[0018] Step S3.2: Calculate the failure probability of any spatial coordinate point of the complex system:

[0019]

[0020] Among them, P{*} represents the failure probability function, T represents the time upper limit of the global reliability analysis of the complex system, and Ω represents the spatial domain of the reliability analysis of the complex system.

[0021] Furthermore, the step S4 comprises the following steps:

[0022] Step S4.1: Determine the applicable physical model based on the physical properties and behaviors of the complex system. The system response of the complex system often satisfies some specific form of control equations, which are usually based on basic physical laws (such as Newtonian mechanics, the first law of thermodynamics, conservation of mass, etc.);

[0023] Step S4.2: Simplify the form of the control equations for the complex system by reasonable simplifying assumptions (such as steady state or quasi-steady state, ignoring minor physical effects, assuming uniform material properties, etc.);

[0024] Step S4.3: Parameterize the control equation of the complex system and substitute the parameters related to the system reliability (such as material properties, geometric dimensions, external forces, etc.) into the control equation;

[0025] Step S4.4: Analyze the physical properties of the complex system, determine the nature and type of the boundary of the complex system control equation (such as Dirichlet boundary conditions, Neumann boundary conditions, etc.), and construct appropriate boundary conditions.

[0026] Furthermore, in step S4.2, the complex system control equation in the form of a partial differential equation is as follows:

[0027]

[0028] in, represents a nonlinear operator for a partial differential equation, They represent the partial derivatives of the system response u(*) with respect to ω and t respectively, and λ is the parameter of the partial differential equation.

[0029] Furthermore, the step S5 comprises the following steps:

[0030] Step S5.1: Initialize the physical information neural network structure and parameters, construct the initial physical information neural network model, and run network training;

[0031] Step S5.2: Based on the system response predicted by the current physical information neural network model, the training sample points are adjusted to obtain new training samples;

[0032] Step S5.3: Use the updated training sample points for training;

[0033] Step S5.4: Determine whether the network training convergence condition is met. If not, repeat steps S5.1 to S5.2; if it is met, execute step S6.

[0034] Furthermore, the step S5.1 includes the following steps:

[0035] Step S5.1.1: Construct a multi-layer perceptron, including an input layer, a hidden layer, and an output layer. Each layer of neurons contains an activation layer. The output of the neurons in the first layer is:

[0036] z (l) =W (l) h (l-1) +b (l)

[0037] Among them, z (l) represents the output of the lth layer, W (l) and b (l) They represent the parameters and bias terms of the lth layer, h (l-1) Represents the output of the l-1th layer after the activation function:

[0038] h (l-1) =σ(z (l-1) )

[0039] Among them, σ(*) represents the activation function;

[0040] Step S5.1.2: Construct the physical information neural network loss function, which is expressed as follows

[0041] L=L f +λ BC ·L BC +λ IC ·L IC

[0042]

[0043] Among them, L f , L BC and L IC are different components of the network loss function, representing the partial differential equation residual, boundary conditions and initial conditions, respectively, BC and λ IC Respectively represent L BC and L IC The Laplace multiplier of the term, N f 、N BC and N IC Represent the sample points of different components of the loss function, represents the predicted value, u BC and u IC It represents the actual value of the corresponding part of the loss function, which is generally obtained through theoretical derivation or simulation.

[0044] Furthermore, the step S5.2 comprises the following steps:

[0045] Step S5.2.1: Use the Voronoi region partitioning method to partition the feasible domain of the complex system input and divide the existing initial sample points into corresponding Voronoi partitions;

[0046] Step S5.2.2: Calculate the sensitivity index of each area and divide the sensitive areas;

[0047] The sensitivity index calculated for each area is used to determine whether the area belongs to a sensitive area. The sensitivity index S of the sensitive area is m Satisfaction tar ≤S m ≤1-γ tar , γ tar represents the partition threshold hyperparameter;

[0048] Step S5.2.3: resampling is performed in the divided sensitive area to obtain the upper and lower limits of the values ​​of each input variable in the divided sensitive area; based on the Latin hypercube sampling method, a batch of new training sample points are randomly and uniformly selected in the sensitive area, while ensuring that the number of selected training sample points does not exceed a certain proportion (such as 20%) of the total number of original training samples;

[0049] Step S5.2.4: Re-divide the existing area. First, determine whether the number of currently divided areas exceeds the set upper limit. For the Voronoi partitions determined as non-sensitive areas, randomly select sample points in the partitions as new Voronoi region partition seed points. For the Voronoi partitions determined as sensitive areas, select the points that make the system limit state function The sample point with the value closest to 0 is taken as the new Voronoi region partition seed point to achieve refined partitioning near the failure boundary.

[0050] Furthermore, in step S5.2.2, for partition R m , assuming that the set of sample points it contains is X m , calculate the partition R m Sensitivity index:

[0051]

[0052] Among them, N m Indicates region R m The total number of sample points included in represents the system limit state function constructed based on the physical information neural network model in the current training stage, X i m Represents partition R m A sample within, I(*) represents the indicator function, when its internal When the value is greater than zero, I takes the value of 1, otherwise I takes the value of 0.

[0053] Furthermore, in step S5.4, the convergence condition is as follows:

[0054]

[0055] When the network is trained, the loss value of epoch i, i ≥ 100 is Loss i When the above formula is met, the network training is considered to have converged.

[0056] Furthermore, step S6 includes the following steps:

[0057] Step S6.1: Determine the area of ​​concern in the reliability assessment of the complex system, and discretize the time and space coordinate points of the area;

[0058] Step S6.2: using the optimal linear expansion method to discretize the random process or random field variable into multiple standard random variables;

[0059] Step S6.3: Based on the fully trained physical information neural network model, construct the limit state function of the system global reliability analysis:

[0060]

[0061] in, represents the system response fitted by the network model, N represents the physical information neural network model constructed, θ represents the network model parameters, U represents the system randomness including random variables, random fields and time-varying random processes, u0 represents the threshold of reliability analysis, u(*) represents the response of the system in different space-time coordinates, ω represents the system space coordinates, and t represents time;

[0062] Step S6.4: Based on the Monte Carlo simulation method, calculate the failure probability of the system at different time and space coordinates, as follows:

[0063]

[0064] Among them, N MCS represents the number of sample points of the Monte Carlo simulation method, I(*) represents the indicator function, when its internal When the value is less than zero, I takes the value of 1, otherwise I takes the value of 0.

[0065] The advantages and beneficial effects of the present invention are:

[0066] In view of the high cost of complex equipment experiments, the difficulty in obtaining global responses, and the small amount of failure sample data, the method of the present invention starts from the partial differential equations that describe the response of complex equipment systems, applies physical information neural network technology, integrates the partial differential equations that constrain the response of the system into the loss function of network model training, uses the network model to predict the actual response of the system, and builds performance equations based on this, which solves the problem that traditional reliability analysis relies on a large number of simulation calculations to obtain experimental samples, effectively reduces the calculation cost, and at the same time, thanks to the physical information neural network's ability to predict the global response of the system, it innovatively combines the spatial and temporal changes of random variables and / or random fields, and can perform global reliability analysis at any time and space position. Through this method, not only the limitations of fixed hotspots in traditional methods are overcome, but also the problem of potential failure areas changing with time and space is effectively solved, which greatly improves the analysis efficiency and reduces the waste of computing resources. This global spatiotemporal reliability analysis provides a new solution for the reliability assessment of complex systems under dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.

[0068] Figure 2a Schematic diagram of the reliability analysis area of ​​Implementation Example 1 of the present invention.

[0069] Figure 2b This is a failure probability distribution heat map of the global reliability analysis in the first implementation example of the present invention.

[0070] Figure 3a Schematic diagram of the laser cladding area after grid division in the second implementation case of the present invention.

[0071] Figure 3b This is a finite element simulation diagram of the temperature distribution in the cladding area after laser irradiation for 0.8s in the second implementation case of the present invention.

[0072] Figure 3c This is a heat map of the failure probability distribution of the global reliability analysis in the second implementation case of the present invention. DETAILED DESCRIPTION

[0073] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0074] The complex equipment time-varying reliability analysis method based on adaptive sampling physical information neural network of the present invention uses Latin hypercube sampling to sample input variables, adopts Voronoi region partitioning method to divide sample feasible domain, uses model response in training process to calculate regional sensitivity, divides sensitive area and resamples, dynamically adjusts sample point distribution in physical information neural network training process, iteratively updates sample points, constructs network model, and uses the system global response prediction capability of physical information neural network, combined with Monte Carlo simulation method, to efficiently predict the failure probability of the system under the combined effect of various uncertainties at any time and space coordinates. Figure 1 As shown, the specific steps include:

[0075] Step S1: extracting system inputs related to complex equipment and random processes that vary with time or space;

[0076] Step S2: Generate initial sample points according to the distribution of system input;

[0077] Step S3: Analyze the failure form of the complex system and construct the limit state function of the global reliability analysis of the complex system;

[0078] Step S3.1: Analyze the potential failure modes of the complex system, establish the mapping relationship between the current system response and the failure mode, construct the global reliability analysis limit state function G of the complex equipment, as shown below, and further calculate the system failure probability.

[0079] G(U,ω,t)=u0-u(U,ω,t)

[0080] Among them, U represents the system randomness including random variables, random fields and time-varying random processes, u0 represents the threshold of reliability analysis, u(*) represents the response of the system in different space-time coordinates, ω represents the system space coordinates, and t represents time.

[0081] Step S3.2: Construct the failure probability calculation expression of any spatial coordinate point of the system, as follows:

[0082]

[0083] Where T represents the time upper limit of the system global reliability analysis, and Ω represents the spatial domain of the system reliability analysis.

[0084] Step S4: extracting system control equations;

[0085] Step S4.1: Determine the appropriate physical model based on the complex physical properties and behaviors of the system. The system response of a complex system often satisfies some specific form of control equations, usually based on basic physical laws (such as Newtonian mechanics, the first law of thermodynamics, conservation of mass, etc.).

[0086] Step S4.2: Simplify the form of the complex system control equations by reasonable simplifying assumptions (such as steady state or quasi-steady state, ignoring minor physical effects, assuming uniform material properties, etc.). Complex system control equations in the form of partial differential equations

[0087] The expression is as follows

[0088]

[0089] in, represents a nonlinear operator for a partial differential equation, They represent the partial derivatives of the system response u(*) with respect to ω and t respectively, and λ is the parameter of the partial differential equation.

[0090] Step S4.3: Parameterize the control equation of the complex system and substitute the parameters related to the system reliability (such as material properties, geometric dimensions, external forces, etc.) into the control equation.

[0091] Step S4.4: Analyze the physical properties of the complex system, determine the nature and type of the boundary of the complex system control equation (such as Dirichlet boundary conditions, Neumann boundary conditions, etc.), and construct appropriate boundary conditions.

[0092] Step S5: Based on the determined boundary conditions, a physical information neural network model is constructed and trained, the sample is adjusted by predicting the system response of the current physical information, and the updated sample is used for training, including the following steps:

[0093] Step S5.1: Initialize the physical information neural network structure and parameters, construct the initial physical information neural network model, and run network training;

[0094] Step S5.1.1: Multilayer perceptron construction. Multilayer perceptron is also called fully connected neural network, which consists of input layer, hidden layer and output layer. There is an activation layer between each layer of neurons. The expression of the output of the lth layer of neurons is as follows:

[0095] z (l) =W (l) h (l-1) +b (l)

[0096] Among them, z (l) represents the output of the lth layer, W (l) and b (l) They represent the parameters and bias terms of the lth layer, h (l-1) It represents the output of the l-1th layer after the activation function, and the expression is as follows

[0097] h (l-1) =σ(z (l-1) )

[0098] Among them, σ(*) represents the activation function.

[0099] Step S5.1.2: Construct the physical information neural network loss function, which is expressed as follows

[0100] L=L f +λ BC ·L BC +λ IC ·L IC

[0101]

[0102] Among them, L f , L BC and L IC are different components of the network loss function, representing the partial differential equation residual, boundary conditions, and initial conditions respectively. BC and λ IC Respectively represent L BC and L IC The Laplace multiplier of the term. f 、N BC and N IC Respectively represent the sample points of different components of the loss function, u BC and u IC It represents the actual value of the corresponding part of the loss function, which is generally obtained through theoretical derivation or simulation.

[0103] Step S5.2: adjusting the training sample points based on the system response predicted by the current physical information neural network model to obtain new training samples;

[0104] Step S5.2.1: Use the Voronoi region partitioning method to partition the feasible domain of the existing system input and divide the existing initial sample points into corresponding Voronoi partitions;

[0105] Step S5.2.2: Calculate the sensitivity index of each area and divide the sensitive areas; for partition R m , assuming that its package

[0106] The set of sample points is X m , partition R m The sensitivity index S m The calculation formula is as follows:

[0107]

[0108] Among them, N m Indicates region R m The total number of sample points included in represents the system limit state function constructed based on the physical information neural network model in the current training stage, X i m Represents partition R m I(*) indicates the indicator function. When the value is greater than zero, I takes the value of 1, otherwise I takes the value of 0.

[0109] The sensitivity index calculated for each area is used to determine whether the area belongs to a sensitive area. The sensitivity index S of the sensitive area is m Satisfaction tar ≤S m ≤1-γ tar , γ tar Represents the split threshold hyperparameter.

[0110] Step S5.2.3: resampling is performed in the divided sensitive area to obtain the upper and lower limits of the values ​​of each input variable in the divided sensitive area, and a batch of new training sample points are randomly and uniformly selected in the sensitive area based on the Latin hypercube sampling method, while ensuring that the number of selected training sample points does not exceed 20% of the total number of original training samples;

[0111] Step S5.2.4: Re-divide the existing area. First, determine whether the number of currently divided areas exceeds the set upper limit. For the Voronoi partitions determined as non-sensitive areas, randomly select sample points in the partitions as new Voronoi region partition seed points. For the Voronoi partitions determined as sensitive areas, select the points that make the system limit state function The sample point with the value closest to 0 is used as the seed point for the new Voronoi region partition to achieve fine partitioning near the failure boundary;

[0112] Step S5.3: Use the updated training sample points for training;

[0113] Step S5.4: Determine whether the network training convergence condition is met. If not, repeat steps S5.1 to S5.2; if it is met, execute step S6;

[0114] The convergence condition is as follows: when the i-th (i≥100) epoch loss value Loss is i The network training is considered to have converged when the following formula is met;

[0115]

[0116] Step S6: Calculate the global failure probability of the system based on the physical information neural network model generated in step S5.

[0117] Step S6.1: Determine the area of ​​interest in the system reliability assessment, and discretize the time and space coordinate points of the area;

[0118] Step S6.2: Use the optimal linear expansion method to discretize the random process / random field variables into multiple standard random variables; Step S6.3: Construct the limit of the global reliability analysis of the system based on the fully trained physical information neural network model

[0119] The state function is as follows:

[0120]

[0121] in, Represents the system response fitted by the network model, N represents the constructed physical information neural network model, and θ represents the network model parameters.

[0122] Step S6.4: Based on the Monte Carlo simulation method, the failure probability of the system at different time and space coordinates is calculated as follows:

[0123]

[0124] Among them, N MCS represents the number of sample points of the Monte Carlo simulation method, I(*) is the indicator function, when its internal When the value is less than zero, I takes the value of 1, otherwise I takes the value of 0.

[0125] Embodiment 1

[0126] In order to verify the effectiveness of the method of the present invention, this example adopts the reliability analysis method based on adaptively trained physical information neural network (adaptively trained PINN for reliability analysis, AT-PINN-RA) given by Zhang et al. (Zhang C, Shafieezadeh A. Simulation-free reliability analysis with active learning and Physics-Informed Neural Network [J]. Reliability Engineering & System Safety, 2022, 226: 108716.) and the reliability analysis method based on physical information neural network (PI-DNN for reliability analysis, PI-DNN-RA) given by Chakraborty (Chakraborty S. Simulation free reliability analysis: A physics-informed deep learning based approach [J]. arXiv preprint arXiv: 2005.01302, 2020.) Model and data are brought into the method of the present invention. Where t represents the time parameter that varies in [0,1], ω=[x,y] is the spatial coordinate, Y(t) is the Gaussian process, Z(ω) is the random field, and the specific distribution parameters are shown in Table 1.

[0127] Table 1 Parameter distribution of numerical cases

[0128]

[0129] The failure model corresponding to the input variable is G(Y(t),Z(ω),ω)

[0130] G(Y(t),Z(ω),ω)=S th -S(ω,Y(t),Z(ω))

[0131]

[0132] Where u and v are the displacements of the plate in the x and y directions respectively;

[0133] In this test case, the initial training sample points for network training are set to 4×10 4 The network training uses the Adam optimizer, and the initial learning rate is set to 1×10 -3 .like Figure 2aAs shown in the figure, the value range of the spatial coordinates x and y of the case setting is [-1,1]. It is assumed that the reliability analysis is performed on the entire plane area, and the observation points are evenly distributed on the plane at intervals of 0.1. The failure probability of all observation points is calculated during the global reliability analysis process.

[0134] The solution of the Monte Carlo simulation method is used as the benchmark solution. The number of sample points used in the Monte Carlo simulation method is 10 4 The results obtained by the method of the present invention are compared with the failure probability results obtained by the method proposed by Zhang et al. and the method proposed by Chakraborty, as shown in Table 2.

[0135] Table 2 Comparison of calculation results of implementation case 1

[0136] method Training rounds Training time (seconds) Average failure probability error Real solution - - 0.1812 - PI-DNN-RA 25000 6147 0.1883 3.92％ AT-PINN-RA 25000 6256 0.1876 3.56％ Method of the present invention 25000 6523 0.1857 2.46％

[0137] Under the same initial conditions and the same test case, the method of the present invention does not need to obtain training sample points through numerical simulation means such as simulation. Compared with the reliability analysis method based on physical neural network proposed by Chakraborty and the reliability analysis method based on adaptive training physical information neural network proposed by Zhang et al., the method of the present invention significantly improves the accuracy of solving global reliability analysis problems, which shows that the method of the present invention can greatly improve the efficiency and accuracy of global reliability analysis. This is mainly because the method adjusts the network training samples based on the global system response during the training process of the physical information neural network, collects more sample points near the failure boundary, thereby improving the prediction accuracy of the network model for reliability problems.

[0138] Figure 2b This is the calculation result of the global reliability of this case, which shows the failure probability distribution of different areas in the plate space under the action of uncertain loads. Through this heat map, we can clearly know the failure risks of different areas of the plate. In the actual engineering design process, it can provide effective support and reference for the subsequent optimization design links.

[0139] Embodiment 2

[0140] The method of the present invention is applied to the reliability analysis of the laser cladding process, thereby proving the effectiveness of the method of the present invention. In the process of laser cladding of materials, there are usually requirements for the temperature of the molten pool generated by laser heating. During the cladding process, due to the uneven distribution of the material surface, the material parameters in different areas may be different, and there is also uncertainty in the working state of the laser itself. Figure 3a to Figure 3cAs shown in the figure, it is a finite element simulation model of the laser cladding process. Therefore, it is assumed that during the laser cladding process, the material surface reflection coefficient η is a random field, the laser power P0 is a random process, and the coordinates of the laser focus point (X dx ,X dy ) is a random variable, t represents the time parameter that varies in [0,1], and the specific distribution parameters are shown in Table 3.

[0141] Table 3 Parameter distribution during laser cladding process

[0142]

[0143] The parameters are input into the finite element model, and the temperature distribution on the material surface during the cladding process is obtained by simulation calculation and compared with the minimum temperature required by the cladding process. Figure 2a , Figure 2b is the finite element simulation model of the laser cladding process. Therefore, its failure model is:

[0144] G(X dx ,X dy ,P(t),η(ω),ω)=T(ω,X dx ,X dy ,P(t),η(ω))-T th

[0145] Where T(*) is the temperature at any spatial coordinate, and the threshold T th =1700K.

[0146] The initial training sample points for network training are set to 4×10 4 The network training uses the Adam optimizer, and the initial learning rate is set to 1×10 -3 The range of x and y values ​​of the laser cladding area in the case setting is [-0.1, 0.1]. It is assumed that a global reliability analysis is performed on the cladding area, and the observation points are evenly distributed at intervals of 0.05 on the plane. The failure probability of all observation points is calculated during the global reliability analysis. Because it involves a real finite element simulation process, the use of Monte Carlo simulation will consume a lot of computing time. Therefore, the results obtained by the method of the present invention are compared with the failure probability results solved by the method proposed by Zhang et al. and the method proposed by Chakraborty, as shown in Table 4.

[0147] Table 4 Comparison of calculation results of implementation case 2

[0148]

[0149]

[0150] When the same initial conditions and the same test case are used, the calculation method of the present invention does not require obtaining training sample points through numerical simulation means such as simulation. And thanks to the prediction ability of the physical information neural network for the global response of the system, the method proposed in the invention can realize the global reliability analysis of the system, further improving the practicality of reliability analysis in the actual design verification and fault analysis process.

[0151] Figure 3c The calculation result of the global reliability of this case shows the failure probability distribution of the laser cladding area under the influence of material uncertainty and heat source uncertainty. Through this heat map, the failure risk of different positions in the cladding area can be clearly known. In the actual engineering design process, it can provide effective support and reference for the subsequent optimization design links.

[0152] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A global reliability analysis method for complex equipment based on physical information neural network, characterized by The steps include: Step S1: Obtain complex system input and system randomness related to complex equipment; Step S2: Generate initial samples according to the distribution of complex system input; Step S3: Based on the randomness of the system, a mapping relationship between the system response and the failure form is established, a limit state of global reliability analysis of the complex system is constructed, and the failure probability of any spatial coordinate of the complex system is constructed based on the limit state; Step S4: extracting the control equation of the complex system and determining its boundary conditions according to the physical information of the complex system; Step S5: Based on the determined boundary conditions, construct a physical information neural network model and perform training, adjust the samples by predicting the system response of the current physical information, and use the updated samples for training; Step S6: using the trained physical information neural network model to fit the system response, and through the limit state of the global reliability analysis of the complex system, calculating the global failure probability of the complex system based on the Monte Carlo simulation method.

2. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 1 is characterized by: The step S3 comprises the following steps: Step S3.1: Analyze the potential failure modes of the complex system, establish the mapping relationship between the current system response and the failure mode, and construct the limit state function of the global reliability analysis of complex equipment: G(U,ω,t)=u0-u(U,ω,t) Among them, U represents the randomness of the system, u0 represents the threshold of reliability analysis, u(*) represents the response of the system in different time and space coordinates, ω represents the spatial coordinate of the system, and t represents time; Step S3.2: Calculate the failure probability of any spatial coordinate point of the complex system: Among them, P{*} represents the failure probability function, T represents the time upper limit of the global reliability analysis of the complex system, and Ω represents the spatial domain of the reliability analysis of the complex system.

3. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 1 is characterized by: The step S4 comprises the following steps: Step S4.1: Determine the appropriate physical model based on the physical properties and behaviors of the complex system; Step S4.2: Simplify the form of the control equations for the complex system through reasonable simplifying assumptions; Step S4.3: parameterize the complex system control equations and substitute the parameters related to system reliability into the control equations; Step S4.4: Analyze the physical properties of the complex system and determine the nature and type of the boundary of the complex system control equation to construct appropriate boundary conditions.

4. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 3 is characterized by: In step S4.2, the complex system control equation in the form of a partial differential equation is as follows: in, represents a nonlinear operator for a partial differential equation, They represent the partial derivatives of the system response u(*) with respect to ω and t respectively, and λ is the parameter of the partial differential equation.

5. The complex equipment global reliability analysis method based on physical information neural network according to claim 1 is characterized by: The step S5 comprises the following steps: Step S5.1: Initialize the physical information neural network structure and parameters, construct the initial physical information neural network model, and run network training; Step S5.2: Based on the system response predicted by the current physical information neural network model, the training sample points are adjusted to obtain new training samples; Step S5.3: Use the updated training sample points for training; Step S5.4: Determine whether the network training convergence condition is met. If not, repeat steps S5.1 to S5.2; if it is met, execute step S6.

6. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 5 is characterized by: The step S5.1 comprises the following steps: Step S5.1.1: Construct a multi-layer perceptron, including an input layer, a hidden layer, and an output layer. Each layer of neurons contains an activation layer. The output of the neurons in the first layer is: z (l) =W (l) h (l-1) +b (l) Among them, z (l) represents the output of the lth layer, W (l) and b (l) They represent the parameters and bias terms of the lth layer, h (l-1) Represents the output of the l-1th layer after the activation function: h (l-1) =σ(z (l-1) ) Among them, σ(*) represents the activation function; Step S5.1.2: Construct the physical information neural network loss function, which is expressed as follows L=L f +λ BC ·L BC +λ IC ·L IC Among them, L f , L BC and L IC are different components of the network loss function, representing the partial differential equation residual, boundary conditions and initial conditions, respectively, BC and λ IC Respectively represent L BC and L IC The Laplace multiplier of the term, N f 、N BC and N IC Represent the sample points of different components of the loss function, represents the predicted value, u BC and u IC Represents the actual value of the corresponding part of the loss function.

7. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 5 is characterized by: The step S5.2 comprises the following steps: Step S5.2.1: Use the Voronoi region partitioning method to partition the feasible domain of the complex system input and divide the existing initial sample points into corresponding Voronoi partitions; Step S5.2.2: Calculate the sensitivity index of each area and divide the sensitive areas; The sensitivity index calculated for each area is used to determine whether the area belongs to a sensitive area. The sensitivity index S of the sensitive area is m Satisfaction tar ≤S m ≤1-γ tar , γ tar represents the partition threshold hyperparameter; Step S5.2.3: resampling is performed in the divided sensitive area to obtain the upper and lower limits of the values ​​of each input variable in the divided sensitive area; based on the Latin hypercube sampling method, a batch of new training sample points are randomly and uniformly selected in the sensitive area, while ensuring that the number of selected training sample points does not exceed a certain proportion of the total number of original training samples; Step S5.2.4: Re-divide the existing area. First, determine whether the number of currently divided areas exceeds the set upper limit. For the Voronoi partitions determined as non-sensitive areas, randomly select sample points in the partitions as new Voronoi region partition seed points. For the Voronoi partitions determined as sensitive areas, select the points that make the system limit state function The sample point with the value closest to 0 is used as the new Voronoi region partition seed point.

8. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 7 is characterized by: In step S5.2.2, for partition R m , assuming that the set of sample points it contains is X m , calculate the partition R m Sensitivity index: Among them, N m Indicates region R m The total number of sample points included in represents the system limit state function constructed based on the physical information neural network model in the current training stage, X i m Represents partition R m A sample within, I(*) represents the indicator function, when its internal When the value is greater than zero, I takes the value of 1, otherwise I takes the value of 0.

9. The method for global reliability analysis of complex equipment based on physical information neural network according to claim 5 is characterized by: In step S5.4, the convergence condition is as follows: When the network is trained, the loss value of epoch i, i ≥ 100 is Loss i When the above formula is met, the network training is considered convergence.

10. The complex equipment global reliability analysis method based on physical information neural network according to claim 1 is characterized by: The step S6 comprises the following steps: Step S6.1: Determine the area of ​​concern in the reliability assessment of the complex system, and discretize the time and space coordinate points of the area; Step S6.2: discretize the random process or random field variable into multiple standard random variables using the optimal linear expansion method; Step S6.3: Based on the fully trained physical information neural network model, construct the limit state function of the system global reliability analysis: in, represents the system response fitted by the network model, N represents the constructed physical information neural network model, θ represents the network model parameters, U represents the system randomness, u0 represents the threshold of reliability analysis, u(*) represents the response of the system in different space-time coordinates, ω represents the system space coordinate, and t represents time; Step S6.4: Based on the Monte Carlo simulation method, the failure probability of the system at different time and space coordinates is calculated as follows: Among them, N MCS represents the number of sample points of the Monte Carlo simulation method, I(*) represents the indicator function, when its internal When the value is less than zero, I takes the value of 1, otherwise I takes the value of 0.

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