Inertial microsystem thermal-mechanical coupling analysis method based on physical information neural network

Abstract

The invention discloses an inertial microsystem thermal coupling analysis method based on a physical information neural network, and the method comprises the steps: S1, setting material parameters and boundary conditions of an inertial microsystem, and building a thermal coupling analysis model; s2, performing electrothermal coupling analysis to obtain temperature distribution of the inertial microsystem; s3, thermal stress distribution of the microsystem is obtained through thermal-mechanical coupling simulation analysis; s4, predicting a temperature field of the microsystem through the physical information neural network; s5, taking the temperature field as a boundary condition of mechanical simulation of the microsystem to obtain mechanical properties such as stress and strain of the microsystem; and S6, performing mechanical-electric coupling simulation analysis, and analyzing the influence of structural deformation on each parameter in electrical performance. According to the method, the neural network solving precision is improved through the improved adaptive weight strategy, the complete polynomial basis function is combined with the neural network, the state dimension is reduced by introducing the expansion basis function, the calculation cost and time are reduced, accurate prediction of the micro-system multi-moment temperature field is achieved, and the micro-system performance under electric heating power multi-physics field coupling is calculated.

Description

Technical Field

[0001] The 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 the development of inertial microsystem technology, the 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 structures makes the interconnection problem extremely important. The reduction in the size of interconnection lines and the increase in the number of layers will cause an increase in electromagnetic losses, which in turn leads to an increase in the internal temperature of the system, causing structural reliability problems. 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 methods and combine failure analysis to feed back to the project has always been a hot issue in inertial microsystem packaging failure analysis.

[0003] When the inertial microsystem is in service in space, it is affected by the synergistic effects of physical fields such as electricity, heat, and mechanical forces, and there is energy exchange between various physical fields. It is a complex multi-field coupling system. The multi-physical field coupling makes the inertial microsystem error aggravated, seriously affecting the performance of the inertial microsystem. The Chinese patent with publication number CN108920831A discloses a fast calculation method for the influence of high-temperature ablation of the cover of a high-speed aircraft on the electrical performance of the antenna. It only analyzes the influence of the thermal field. This method does not consider the engineering application environment of multi-load stress coupling, nor can it consider the mutual influence between thermal forces, resulting in inaccurate analysis results. At present, there is a lack of mutual coupling analysis of the three physical fields of electricity, heat and force in the inertial microsystem, and most of the inertial microsystems only consider thermal simulation or mechanical simulation separately in the analysis, and do not consider the harsh working conditions of multi-physical field coupling in space service, nor the mutual influence between heat, force and electromagnetic, which cannot fully reflect its actual working conditions, and the analysis results are difficult to be accurate. It is urgent to conduct multi-physical field coupling analysis on the inertial microsystem to guide and verify the product design of the inertial microsystem. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, to provide an inertial microsystem thermal-mechanical coupling analysis method based on a physical information neural network, to achieve high-precision prediction of the temperature field of the inertial microsystem at multiple moments, to calculate the performance of the inertial microsystem under the coupling of electrical-thermal-mechanical multi-physical fields, to improve the solution accuracy and reliability, and to ensure the reliability of the inertial microsystem in space service.

[0005] The technical solution of the present invention is: a thermal-mechanical coupling analysis method of an inertial microsystem based on a 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 of the inertial microsystem;

[0007] S2. Performing an electrothermal coupling simulation analysis on the thermal-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under the working state;

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

[0009] S4. According to 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, and the temperature field of the inertial microsystem at different moments is predicted by using the physical information neural network. The specific steps include:

[0010] S41, experimentally measure the temperature of the test point on the inertial microsystem;

[0011] S42, taking the position x and time t as input, the complete polynomial coefficient β i As the extended parameters of the physical information neural network, it is related to 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, so as to accurately predict the temperature field of the inertial microsystem at different times;

[0013] S5, using the temperature field of the inertial microsystem at different times obtained in step S4 as the boundary conditions of the inertial microsystem structural mechanics simulation, performing mechanical analysis, and obtaining the mechanical properties of the inertial microsystem structure;

[0014] S6. Feeding back the mechanical properties obtained in step S5 to the electromagnetic simulation, performing electrical properties 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:

[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 , firstly perform iterative calculations through the Adam solver, update the weight coefficient once each time, and use the weight coefficient obtained after multiple updates as the optimal weight coefficient of the inertial microsystem, and then use the LBFGS algorithm to optimize the physical information neural network parameters 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 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 represented as the heat flux 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 weight obtained in step S422 and the bias value (w i ,b i ) into the physical information neural network, specifically: Substitute the following formula

[0028]

[0029] Where: x 1 、x 2 and x 3 Respectively represent the x-axis, y-axis and z-axis coordinates of the measuring point, 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 ) k-1 (z k-1 )o…oσoL 1 (z 1 )

[0032] Where: o is a combination operator, which 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 kis 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 using the following heat conduction equation:

[0034]

[0035] Where: ρ, c are the device material density and specific heat capacity, respectively, k(T 1 ) is the conductivity of the device material that changes with temperature, P is the heating power of the device, T 1 is the transient spatial temperature field distribution, h is the convection heat transfer coefficient, T is the inertial microsystem temperature, T 0 is the initial temperature, t is the node time, n is the spatial coordinate, and Γa is the convective heat transfer boundary.

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

[0037] σ YL =Eε-β(T-T 0 )

[0038] In the formula, 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, T 0 is the initial temperature.

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

[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 an inertial microsystem based on a physical information neural network. The accuracy of the neural network solution is improved by an improved adaptive weight strategy. The complete polynomial basis function is combined with the neural network, and an expanded basis function is introduced to reduce the state dimension. This enables high-precision prediction of the temperature field of the microsystem at multiple moments, and accurate prediction of the performance of the microsystem under the coupling of electrical-thermal-mechanical multi-physical fields, thereby ensuring the reliability of the microsystem in space service. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0043] Figure 2 It 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 solution of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0045] The present invention provides a thermal-mechanical coupling analysis method for an inertial microsystem based on a 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 of the inertial microsystem;

[0047] S2. Performing an electrothermal coupling simulation analysis on the thermal-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under the working state;

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

[0049]

[0050]

[0051] Where: ρ, c are the device material density and specific heat capacity, respectively, k(T 1 ) is the conductivity of the device material that changes with temperature, P is the heating power of the device, T 1 is the transient spatial temperature field distribution, h is the convection heat transfer coefficient, T is the inertial microsystem temperature, T 0 is the initial temperature, n is the spatial coordinate, and Γa is the convection 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 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-T 0 )

[0055] In the formula, 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, T 0 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 whose 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, 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 i And weights and bias values ​​(w i ,b i )

[0059] S421, taking the position x and time t as input, the complete polynomial coefficient β i As the extended parameters of the physical information neural network, it is related to the physical information neural network parameter weights and bias values ​​(w i ,b i ) as 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, using the adaptive motion estimation algorithm Adam and the inverse rank two quasi-Newton method LBFGS for training optimization, so that the loss function is minimized, and the complete polynomial coefficient β is obtained 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 time. 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 represented as the heat flux 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, so as to accurately predict the temperature field of the microsystem at different times;

[0070] Using the complete polynomial coefficient β obtained in step S422 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 times.

[0074] The weight obtained in step S422 and the bias value (w i ,b i ) Substitution:

[0075]

[0076] Where: x 1 、x 2 and x 3 They represent the x-axis, y-axis and z-axis coordinates of the measuring point respectively, t is the measuring point 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 ) k-1 (z k-1 )o…oσoL 1 (z 1 )

[0079] In the formula, o is a combination operator, which 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 field of the microsystem at different times obtained in step S4 as the boundary condition of the inertial microsystem structural mechanics simulation, performing mechanical analysis, and obtaining 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 warpage.

[0082] S6. Feed the mechanical properties obtained in step S5 back into the electromagnetic simulation, perform electrical properties simulation based on the mechanical properties, analyze the influence of the mechanical properties on the electrical properties, and obtain the electrical properties of the microsystem.

[0083] It is to be understood that the present invention is described by way of embodiments, and it is known to 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 by the specific embodiments disclosed herein, and embodiments that can fall within the scope of the claims of this application all fall within the scope protected by 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 an inertial microsystem based on a 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 thermal-mechanical coupling analysis model of the inertial microsystem to obtain the temperature distribution of each component in the inertial microsystem under working conditions; Taking the temperature distribution and power loss of each device in the inertial microsystem as the heat source, a thermal-mechanical coupling simulation analysis is performed 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 coefficients β i As the extended parameters of the physical information neural network, it is related to 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, so as to accurately predict the temperature field of the inertial microsystem at different times; The predicted temperature fields of the inertial microsystem at different times are used as the boundary conditions of the inertial microsystem structural mechanics simulation, and 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 the electrical performance simulation based on the mechanical properties is carried out to analyze the influence of the mechanical properties on the electrical properties, and the electrical properties of the inertial microsystem are obtained.

2. The method for thermal-mechanical 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 thermal-mechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 2 is characterized in that: Temperature weight coefficient W U and heat flux weight coefficient W N , firstly perform iterative calculations through the Adam solver, update the weight coefficient once each time, and use the weight coefficient obtained after multiple updates as the optimal weight coefficient of the inertial microsystem, and then use the LBFGS algorithm to optimize the physical information neural network parameters to minimize the loss function.

4. The method for thermal-mechanical coupling analysis of an inertial microsystem based on a physical information neural network according to claim 3 is 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 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 represented as the heat flux weight coefficient after the lth iteration, is the average value of the heat flux loss term at the lth iteration.

5. The method for thermal-mechanical 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, φ i (x, t) is the polynomial basis function, s is the number of basis functions, i = 1, 2…s.

6. The method for thermal-mechanical 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, which 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 thermal-mechanical 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 is performed on the thermal-mechanical coupling analysis model of the inertial microsystem, 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 conductivity of the device material that changes with temperature; 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 thermal-mechanical 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) In the formula, 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 thermal-mechanical 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.

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