Thermal-mechanical coupling analysis method for inertial microsystems based on physical information neural network

Abstract

The present invention discloses a thermomechanical coupling analysis method for an inertial microsystem based on a physical information neural network, comprising: S1, setting the material parameters and boundary conditions of the inertial microsystem and establishing a thermomechanical coupling analysis model; S2, obtaining the temperature distribution of the inertial microsystem through electrothermal coupling analysis; S3, obtaining the thermal stress distribution of the microsystem through thermomechanical coupling simulation analysis; S4, predicting the temperature field of the microsystem through a physical information neural network; S5, using the temperature field as the boundary condition for the mechanical simulation of the microsystem to obtain the mechanical properties such as stress and strain of the microsystem; S6, performing electromechanical coupling simulation analysis to analyze the influence of structural deformation on various parameters in the electrical properties. The present invention improves the solving accuracy of the neural network through an improved adaptive weight strategy, combines the complete polynomial basis function with the neural network, introduces the expanded basis function to reduce the state dimension, reduces the computational cost and time, realizes the accurate prediction of the temperature field of the microsystem at multiple moments, and calculates the performance of the microsystem under the coupling of electrothermal and mechanical multi-physical fields.

Description

Technical Field

[0001] The present invention relates to the technical field of inertial microsystems, and in particular to a thermal-mechanical coupling analysis method of an inertial microsystem based on a physical information neural network. Background Art

[0002] Inertial microsystems are widely used in various fields due to their advantages such as miniaturization, integration, intelligence, low cost, high performance and mass production. With the continuous deepening of inertial microsystem technology, reliability failure analysis of inertial microsystems has become a weak link in the further development of microsystem packaging technology. The improvement of the integration of inertial microsystem packaging structure makes the interconnection problem become crucial. The reduction of interconnection line size and the increase of layer number will cause the increase of electromagnetic loss, which in turn leads to the increase of internal temperature of the system and the structural reliability problem. Reliability characterization through traditional physical and experimental methods faces great difficulties, and thus reliability analysis and evaluation methods are urgently needed. Therefore, how to accurately present the failure of inertial microsystems through simulation and combine failure analysis to feed back to the engineering has always been a hot issue in inertial microsystem packaging failure analysis.

[0003] When serving in space, inertial microsystems are subject to the synergistic effects of electrical, thermal, and mechanical forces, with energy exchange between these fields. This complex multi-field coupling exacerbates errors in the inertial microsystem, severely impacting its performance. Chinese patent publication number CN108920831A discloses a method for rapidly calculating the effects of high-temperature ablation of a high-speed aircraft cover on the electrical performance of an antenna. This method only analyzes the effects of the thermal field, but fails to consider the engineering application environment of multiple load-stress coupling, nor the mutual influences between thermal and mechanical forces, resulting in inaccurate analysis results. Currently, there is a lack of analysis of the mutual coupling of the three physical fields of electricity, heat, and force in inertial microsystems. Furthermore, most analyses of inertial microsystems only consider thermal or mechanical simulations separately, without considering the harsh operating conditions of multi-field coupling in space service or the mutual influences between heat, force, and electromagnetics. This inability to fully reflect actual operating conditions makes accurate analysis difficult. There is an urgent need for multi-field coupling analysis of inertial microsystems to guide and verify inertial microsystem product design. Summary of the Invention

[0004] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology and provide a thermal-mechanical coupling analysis method for inertial microsystems based on a physical information neural network, thereby achieving high-precision prediction of the temperature field of the inertial microsystem at multiple moments, calculating the performance of the inertial microsystem under the coupling of electrical, thermal and mechanical multi-physical fields, improving the solution accuracy and reliability, and ensuring the reliability of the inertial microsystem in space service.

[0005] The technical solution of the present invention is: a thermomechanical coupling analysis method for inertial microsystems based on physical information neural network, comprising:

[0006] S1. According to the space service conditions, set the material parameters and boundary conditions of the inertial microsystem and establish a thermal-mechanical coupling analysis model for the inertial microsystem;

[0007] S2. Performing electrothermal coupling simulation analysis on the thermomechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under working conditions;

[0008] S3, using the temperature distribution of each device and the power loss of each device obtained in step S2 as heat sources, performing a thermal-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem;

[0009] S4. Based on the temperature distribution and thermal stress distribution obtained in steps S2 and S3, a physical information neural network is established, whose input is position and time and whose output is the temperature field of the inertial microsystem at each moment. The physical information neural network is used to predict the temperature field of the inertial microsystem at different moments. The specific steps include:

[0010] S41. Experimentally measure the temperature of the test point on the inertial microsystem;

[0011] S42, taking position x and time t as input, and taking the complete polynomial coefficient β i As the extended parameters of the physical information neural network, together with the physical information neural network parameter weights and bias values ​​(w i ,b i ) as the output; construct the loss function of the physical information neural network, and integrate the physical information including the temperature value of the measuring point, the control equation and the boundary conditions into the loss function; use the adaptive motion estimation algorithm Adam and the inverse rank two quasi-Newton method LBFGS for training optimization to minimize the loss function and obtain the complete polynomial coefficient β i And weights and bias values ​​(w i ,b i );

[0012] S43, the complete polynomial coefficient β i , weights and bias values ​​(w i ,b i ), substituted into the physical information neural network, thus accurately predicting the temperature field of the inertial microsystem at different times;

[0013] S5, using the temperature fields of the inertial microsystem at different times obtained in step S4 as boundary conditions for mechanical simulation of the inertial microsystem structure, performing mechanical analysis to obtain the mechanical properties of the inertial microsystem structure;

[0014] S6. Feeding the mechanical properties obtained in step S5 back into the electromagnetic simulation, performing electrical performance simulation based on the mechanical properties, analyzing the influence of the mechanical properties on the electrical properties, and obtaining the electrical properties of the inertial microsystem.

[0015] Furthermore, the loss function of the physical information neural network is specifically:

[0016]

[0017]

[0018] Where: W F is the heat conduction weight coefficient, loss F is the residual mean square error of the control equation, W N is the heat flow weight coefficient, loss BCq is the residual mean square error of the boundary heat flow, W U is the temperature term weight coefficient, N BCT 、N RC are the number of coordinates of the corresponding nodes, N t is the number of time nodes, N m is the number of measurement points, loss BCT 、loss RC are the residual sum of squares of the boundary temperature and the initial point temperature, respectively, and loss m is the mean square error of the temperature residual of the measuring point, is the predicted value of the temperature field by the neural network at the measuring point, T m is the temperature corresponding to the measuring point, Γ m is the measurement point boundary, t end The end time of transient calculation.

[0019] Furthermore, the temperature weight coefficient W U and heat flux weight coefficient W N First, iterative calculations are performed using the Adam solver, and the weight coefficient is updated each time. The weight coefficient obtained after multiple updates is used as the optimal weight coefficient of the inertial microsystem. Then, the LBFGS algorithm is used to optimize the parameters of the physical information neural network to minimize the loss function.

[0020] Furthermore, the temperature weight coefficient W U and heat flux weight coefficient W N The update method is as follows:

[0021]

[0022]

[0023] Where: l is the number of iterations, α is the weight coefficient, and are respectively represented as the temperature weight coefficient after the lth iteration, is the average value of the temperature loss term at the lth iteration, and They are respectively expressed as the heat flow weight coefficient after the lth iteration, is the average value of the heat flux loss term at the lth iteration.

[0024] Further, in step S43, the complete polynomial coefficient β obtained in step S422 is i , substituted into the physical information neural network, specifically: using the complete polynomial coefficient β i Update the temperature field heat source g(x,t) parameters in the physical information neural network. The formula is as follows:

[0025]

[0026] Where: λ is the scale factor, φ i (x, t) is the polynomial basis function, s is the number of basis functions, i = 1, 2…s.

[0027] Further, in step S43, the weights obtained in step S422 are combined with the bias value (w i ,b i ) into the physical information neural network, specifically: Substitute the following formula

[0028]

[0029] Where: x1, x2 and x3 represent the x-axis, y-axis and z-axis coordinates of the measuring point respectively, w i 、b i are the unknown parameters that need to be optimized in the neural network model, which are the weights and bias values ​​of the neural network, and k is the number of layers of the physical information neural network;

[0030] The temperature field of the inertial microsystem at different times is predicted using the following formula:

[0031] T=L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1)

[0032] Where: o is a combination operator that changes according to the number of hidden layers and neurons. The above formula is a physical information neural network with a depth of k layers, σ is the Softplus activation function, L k is the kth layer, z k is the parameter of the kth hidden layer of the neural network.

[0033] Furthermore, in step S2, the electrothermal coupling simulation analysis solves the temperature distribution of the inertial microsystem by the following heat conduction equation:

[0034]

[0035] Where: ρ and c are the device material density and specific heat capacity, respectively, k(T1) is the temperature-dependent conductivity of the device material, P is the heat generation power of the device, T1 is the transient spatial temperature field distribution, h is the convective heat transfer coefficient, T is the inertial microsystem temperature, T0 is the initial temperature, t is the node measurement point time, n is the spatial coordinate, and Γa is the convective heat transfer boundary.

[0036] Furthermore, the thermal stress distribution in the inertial microsystem in step S3 is:

[0037] σ YL =Eε-β(T-T0)

[0038] Where, σ YL is the thermal stress of the inertial microsystem, E is the elastic coefficient, ε is the strain of the inertial microsystem, β is the thermoelastic coefficient, T is the temperature of the inertial microsystem, and T0 is the initial temperature.

[0039] Furthermore, the mechanical properties in step S5 include thermal stress, elastic-plastic strain, fatigue life, creep, deformation, fracture and warping.

[0040] The advantages of the present invention compared with the prior art are:

[0041] The present invention proposes a thermal-mechanical coupling analysis method for inertial microsystems based on a physical information neural network. The method improves the accuracy of the neural network solution through an improved adaptive weight strategy, combines complete polynomial basis functions with the neural network, and introduces expanded basis functions to reduce the state dimension. This method enables high-precision prediction of the microsystem's temperature field at multiple moments, accurately predicting the microsystem's performance under the coupling of electrical, thermal, and mechanical multi-physical fields, and ensuring the reliability of the microsystem in space service. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a flow chart of the inertial microsystem thermal-mechanical coupling analysis method based on physical information neural network of the present invention;

[0043] Figure 2 This is a structural framework diagram of the physical information neural network of the present invention. DETAILED DESCRIPTION

[0044] In order to better understand the technical solutions of the present invention, embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0045] The present invention provides a method for thermomechanical coupling analysis of inertial microsystems based on physical information neural network. Figure 1 As shown, the steps include:

[0046] S1. According to the space service conditions, set the material parameters and boundary conditions of the inertial microsystem and establish a thermal-mechanical coupling analysis model for the inertial microsystem;

[0047] S2. Performing electrothermal coupling simulation analysis on the thermomechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under working conditions;

[0048] In one possible implementation, in the electrothermal coupling simulation analysis in step S2, the temperature distribution of the microsystem is solved by the following heat conduction equation:

[0049]

[0050]

[0051] Where: ρ and c are the device material density and specific heat capacity, respectively, k(T1) is the temperature-dependent conductivity of the device material, P is the heat generation power of the device, T1 is the transient spatial temperature field distribution, h is the convective heat transfer coefficient, T is the inertial microsystem temperature, T0 is the initial temperature, n is the spatial coordinate, and Γa is the convective heat transfer boundary.

[0052] S3, using the temperature distribution of each device and the power loss of each device obtained in step S2 as heat sources, performing a thermal-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem;

[0053] In a possible implementation, the thermal stress distribution in the inertial microsystem in step S3 is:

[0054] σ YL =Eε-β(T-T0)

[0055] Where, σ YL is the thermal stress of the inertial microsystem, E is the elastic coefficient, ε is the strain of the inertial microsystem, β is the thermoelastic coefficient, T is the temperature of the inertial microsystem, and T0 is the initial temperature.

[0056] S4. Based on the temperature distribution and thermal stress distribution obtained in steps S2 and S3, a physical information neural network is established, whose input is position and time and output is the temperature field of the inertial microsystem at each moment. The physical information neural network structure framework is as follows: Figure 2 As shown in Figure 1, the temperature field of the inertial microsystem at different times is predicted using a physical information neural network. The specific steps include:

[0057] S41. Experimentally measure the temperature of the test point on the inertial microsystem;

[0058] S42. Calculate the complete polynomial coefficient β iAnd weights and bias values ​​(w i ,b i )

[0059] S421, taking the position x and time t as input, and the complete polynomial coefficient β i As the extended parameters of the physical information neural network, together with the physical information neural network parameter weights and bias values ​​(w i ,b i ) as the output; construct the loss function of the physical information neural network, and integrate the physical information including the temperature value of the measuring point, the control equation and the boundary conditions into the loss function;

[0060] The loss function of the physical information neural network is:

[0061]

[0062] Where: W F is the heat conduction weight coefficient, loss F is the residual mean square error of the control equation, W N is the heat flow weight coefficient, loss BCq is the residual mean square error of the boundary heat flow, W U is the temperature term weight coefficient, N BCT 、N RC are the number of coordinates of the corresponding nodes, N t is the number of time nodes, N m is the number of measurement points, loss BCT 、loss RC are the residual sum of squares of the boundary temperature and the initial point temperature, respectively, and loss m is the mean square error of the temperature residual of the measuring point, is the predicted value of the temperature field by the neural network at the measuring point, T m is the temperature corresponding to the measuring point, Γ m is the measurement point boundary, t end The end time of transient calculation.

[0063] S422, use the adaptive motion estimation algorithm Adam and the inverse rank two quasi-Newton method LBFGS for training optimization to minimize the loss function and obtain the complete polynomial coefficient β i And weights and bias values ​​(w i ,b i );

[0064] Step S422: The temperature weight coefficient W in the weight coefficient of the neural network loss function U and heat flux weight coefficient W N, the Adam solver is used for iterative calculation, and the weight coefficient is updated once each calculation. The weight coefficient obtained after multiple updates is used as the optimal weight coefficient of the inertial microsystem, and then the LBFGS algorithm is used to optimize the neural network parameters to minimize the loss function.

[0065] Temperature weight coefficient W U and heat flux weight coefficient W N The update method is as follows:

[0066]

[0067]

[0068] In the formula, l is the number of iterations, α is the weight coefficient, and They are respectively represented as the temperature weight coefficient after the lth iteration, is the average value of the temperature loss term at the lth iteration, and They are respectively expressed as the heat flow weight coefficient after the lth iteration, is the average value of the heat flux loss term at the lth iteration.

[0069] S43, the complete polynomial coefficient β i , weights and bias values ​​(w i ,b i ), substituted into the physical information neural network, thus accurately predicting the temperature field of the microsystem at different times;

[0070] The complete polynomial coefficient β obtained in step S422 is used i , update the temperature field heat source g(x,t) parameters in the physical information neural network, specifically:

[0071]

[0072] Where: λ is the scale factor, φ i (x, t) is the polynomial basis function, s is the number of basis functions, i = 1, 2…s.

[0073] The polynomial basis function is introduced to reduce the temperature field state dimension of the neural network and realize high-precision prediction of the temperature field of the microsystem at multiple moments.

[0074] The weights and bias values ​​(w i ,b i )Substitution:

[0075]

[0076] Where: x1, x2 and x3 represent the x-axis, y-axis and z-axis coordinates of the measuring point respectively, t is the measuring time, w i 、b i are the unknown parameters that need to be optimized in the neural network model, which are the weights and bias values ​​of the neural network, and k is the number of layers of the physical information neural network;

[0077] The temperature field of the microsystem at different times is predicted using the following formula:

[0078] T=L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1)

[0079] In the formula, o is a combination operator that changes according to the number of hidden layers and neurons. The above formula is a physical information neural network with a depth of k layers, σ is the Softplus activation function, and L k is the kth layer, z k is the parameter of the kth hidden layer of the neural network.

[0080] S5, using the temperature fields of the microsystem at different times obtained in step S4 as boundary conditions for the inertial microsystem structural mechanics simulation, performing mechanical analysis to obtain the mechanical properties of the microsystem structure;

[0081] The mechanical properties in step S5 include thermal stress, elastic-plastic strain, fatigue life, creep, deformation, fracture and warping.

[0082] S6. Feeding the mechanical properties obtained in step S5 back into the electromagnetic simulation, performing electrical performance simulation based on the mechanical properties, analyzing the influence of the mechanical properties on the electrical properties, and obtaining the electrical properties of the microsystem.

[0083] It will be understood that the present invention is described by way of example, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and any embodiment that falls within the scope of the claims of this application is intended to be within the scope of protection of the present invention.

[0084] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A thermal-mechanical coupling analysis method for inertial microsystems based on physical information neural network, characterized in that: include: According to the space service conditions, the material parameters and boundary conditions of the inertial microsystem are set, and the thermal-mechanical coupling analysis model of the inertial microsystem is established; Conduct electrothermal coupling simulation analysis on the thermomechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under working conditions; The temperature distribution and power loss of each device in the inertial microsystem are used as heat sources to perform thermal-mechanical coupling simulation analysis to obtain the thermal stress distribution of the inertial microsystem. Based on the obtained temperature distribution and thermal stress distribution, a physical information neural network is established with position and time as input and temperature field of the inertial microsystem at each moment as output. The physical information neural network is used to predict the temperature field of the inertial microsystem at different moments. The specific steps include: Experimentally measure the temperature of the test point on the inertial microsystem; Taking position x and time t as input, the complete polynomial coefficient β i As the extended parameters of the physical information neural network, together with the physical information neural network parameter weights and bias values ​​(w i ,b i ) as the output; construct the loss function of the physical information neural network, and integrate the physical information including the temperature value of the measuring point, the control equation and the boundary conditions into the loss function; use the adaptive motion estimation algorithm Adam and the inverse rank two quasi-Newton method LBFGS for training optimization to minimize the loss function and obtain the complete polynomial coefficient β i And weights and bias values ​​(w i ,b i ); The complete polynomial coefficient β i , weights and bias values ​​(w i ,b i ), substituted into the physical information neural network, thus accurately predicting the temperature field of the inertial microsystem at different times; The predicted temperature fields of the inertial microsystem at different times are used as boundary conditions for the structural mechanics simulation of the inertial microsystem. Mechanical analysis is performed to obtain the mechanical properties of the inertial microsystem structure. The obtained mechanical properties of the inertial microsystem structure are fed back into the electromagnetic simulation, and electrical performance simulation based on the mechanical properties is performed to analyze the influence of the mechanical properties on the electrical properties and obtain the electrical properties of the inertial microsystem.

2. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The loss function of the physical information neural network is: Where: W F is the heat conduction weight coefficient, loss F is the residual mean square error of the control equation, W N is the heat flow weight coefficient, loss BCq is the residual mean square error of the boundary heat flow, W U is the temperature term weight coefficient, N BCT 、N RC are the number of coordinates of the corresponding nodes, N t is the number of time nodes, N m is the number of measurement points, loss BCT 、loss RC are the residual sum of squares of the boundary temperature and the initial point temperature, respectively, and loss m is the mean square error of the temperature residual of the measuring point, is the predicted value of the temperature field by the neural network at the measuring point, T m is the temperature corresponding to the measuring point, Γ m is the measurement point boundary, t end The end time of transient calculation.

3. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 2, characterized in that: Temperature weight coefficient W U and heat flux weight coefficient W N First, iterative calculations are performed using the Adam solver, and the weight coefficient is updated each time. The weight coefficient obtained after multiple updates is used as the optimal weight coefficient of the inertial microsystem. Then, the LBFGS algorithm is used to optimize the parameters of the physical information neural network to minimize the loss function.

4. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 3, characterized in that: Temperature weight coefficient W U and heat flux weight coefficient W N The update method is as follows: Where: l is the number of iterations, α is the weight coefficient, and are respectively represented as the temperature weight coefficient after the lth iteration, is the average value of the temperature loss term at the lth iteration, and They are respectively expressed as the heat flow weight coefficient after the lth iteration, is the average value of the heat flux loss term at the lth iteration.

5. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The obtained complete polynomial coefficient β i , substituted into the physical information neural network, specifically: using the complete polynomial coefficient β i Update the temperature field heat source g(x,t) parameters in the physical information neural network. The formula is as follows: Where: λ is the scale factor, is the polynomial basis function, s is the number of basis functions, i=1,2…s.

6. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The obtained weight and bias value (w i ,b i ) into the physical information neural network, specifically: Substitute the following formula Where: x1, x2 and x3 represent the x-axis, y-axis and z-axis coordinates of the measuring point respectively, w i 、b i are the unknown parameters that need to be optimized in the neural network model, which are the weights and bias values ​​of the neural network, and k is the number of layers of the physical information neural network; The temperature field of the inertial microsystem at different times is predicted using the following formula: T=L k (z k )oσoL k-1 (z k-1 )o…oσoL1(z1) Where: o is a combination operator that changes according to the number of hidden layers and neurons. The above formula is a physical information neural network with a depth of k layers, σ is the Softplus activation function, L k is the kth layer, z k is the parameter of the kth hidden layer of the neural network.

7. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The electrothermal coupling simulation analysis of the thermal-mechanical coupling analysis model of the inertial microsystem is performed, and the temperature distribution of the inertial microsystem is solved by the following heat conduction equation: Where: ρ and c are the device material density and specific heat capacity, respectively, k(T1) is the temperature-dependent conductivity of the device material, P is the heat generation power of the device, T1 is the transient spatial temperature field distribution, h is the convective heat transfer coefficient, T is the inertial microsystem temperature, T0 is the initial temperature, t is the node measurement point time, n is the spatial coordinate, and Γa is the convective heat transfer boundary.

8. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The thermal stress distribution of the inertial microsystem is: s YL =Eε-β(T-T0) Where σ YL is the thermal stress of the inertial microsystem, E is the elastic coefficient, ε is the strain of the inertial microsystem, β is the thermoelastic coefficient, T is the temperature of the inertial microsystem, and T0 is the initial temperature.

9. The method for thermomechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 1, characterized in that: The mechanical properties of inertial microsystem structures include thermal stress, elastic-plastic strain, fatigue life, creep, deformation, fracture and warping.

Images