A distributed multi-physics co-simulation method

Abstract

The application discloses a distributed multi-physical field cooperative simulation method, and relates to the field of electromechanical system simulation.The method comprises the following steps: configuring independent variable step integrators for physical field subsystems with different time constants respectively; establishing a step mapping function between the subsystems by a main controller, wherein the function is associated with the maximum allowed step size ratio of each subsystem; when a timing alignment module detects that the simulation time of at least two subsystems meets a synchronization condition, activating cross-field boundary condition transmission; if the Lyapunov index of any subsystem exceeds a stability threshold, triggering joint time step rollback of the associated subsystems.The application scheme can break through the limitation of global fixed step size, replace the strong synchronization mode with a dynamic weak coupling strategy driven by timing, and realize the cooperative optimization of calculation efficiency and numerical stability.

Description

Technical Field

[0001] This invention relates to the field of electromechanical system simulation, and in particular to a distributed multiphysics collaborative simulation method. Background Technology

[0002] Multiphysics coupling simulation technology is a core supporting tool for the design and optimization of complex engineering systems. In lumped parameter models, the time constants of electrical, mechanical, and thermodynamic physical fields differ significantly. Traditional methods typically use the minimum time constant as a benchmark to set a fixed global step size, leading to excessive redundant calculations for physical fields with larger time constants due to over-discretization. Especially in scenarios such as power electronic equipment, lithium-ion battery pack management, and high-frequency electromechanical systems, the dynamic interaction of multiphysics fields exhibits strong nonlinearity, multi-scale, and transient abrupt changes, requiring real-time capture of the coupling effects of electromagnetic, thermal, and mechanical fields. However, existing simulation frameworks often rely on steady-state models of single fields or loose coupling strategies, making it difficult to accurately describe the energy transfer and dynamic interaction of boundary conditions between physical fields, thus limiting simulation accuracy and efficiency.

[0003] Existing multiphysics coupling simulation methods suffer from three significant drawbacks: 1. Most methods employ a fixed-step synchronous coupling strategy, failing to dynamically adjust the integration step size based on the subsystem's time constant. For example, in electromechanical coupling systems, the circuit and mechanical subsystems must use a uniform minimum step size, resulting in a waste of over 70% of mechanical field computational resources. Although variable-step techniques have been proposed, their iterative step size reset mechanism relies solely on a nonlinear iteration threshold, lacking quantitative analysis of system stability and error propagation, easily leading to coupling divergence or numerical oscillations. 2. Existing weak coupling strategies rely on preset synchronization times for inter-field data transfer, ignoring the phase consistency of physical quantities. For example, in the thermal and electrical coupling simulation of lithium-ion batteries, electrode heat conduction and current density changes exhibit phase lag; fixed-time synchronization introduces interface flux conservation errors. Furthermore, the lack of flux compensation and gradient continuity constraints at the coupling interface leads to distortion in boundary parameter transfer, exacerbating system-level error accumulation. 3. Traditional local differential equation frameworks struggle to effectively simulate discontinuous processes such as crack propagation and arc mutations. In high-voltage switchgear arc simulation, arc reignition and extinction events require real-time micro-step segmentation. However, existing methods cannot capture instantaneous high-frequency responses due to step-size adjustment lag, leading to transient process distortion. Furthermore, the uncertainty of multi-field coupling lacks efficient quantification methods, affecting the reliability of the digital twin system. Therefore, based on these challenges, this invention proposes a distributed multiphysics collaborative simulation method. Summary of the Invention

[0004] Purpose of the invention

[0005] To address the aforementioned issues, the present invention aims to provide a distributed multiphysics co-simulation method. This method addresses the problem of wasted computational resources caused by differences in the time constants of physical fields in multiphysics coupling simulations using lumped parameter models. While ensuring the coupling accuracy between circuit and mechanical fields, it significantly reduces the computational load of physical fields with large time constants, thereby improving the simulation efficiency of complex systems.

[0006] Technical solution

[0007] To achieve the above objectives, this invention provides a distributed multiphysics co-simulation method. This method configures independent variable step-size strategies for the circuit and mechanical subsystems, dynamically adjusting the step size through nonlinear iterative convergence. When the iteration count overflows, step-size compression and time reset are triggered to avoid numerical divergence. The necessity of mechanical field participation is dynamically determined based on the step-size ratio. Joint iteration of the two fields is activated only when the simulation time is aligned; otherwise, the mechanical field state remains unchanged, reducing redundant computation. A unified equation framework is constructed using the nodal voltage method; the nonlinear equations of the circuit and mechanical subsystems are solved synchronously using the Newton-Rafaelson algorithm; boundary conditions are transferred between the two fields in real time, and joint rollback is performed when divergence occurs.

[0008] In a first aspect, the present invention provides a distributed multiphysics collaborative simulation method, comprising:

[0009] Independent variable-step-size integrators based on the dynamic characteristics of the physical field are configured for physical field subsystems with different time constants;

[0010] A nonlinear step size mapping function is established between subsystems through the main controller, and the function is associated with the maximum allowable step size ratio of each subsystem.

[0011] When the timing alignment module detects that the simulation times of at least two subsystems meet the synchronization condition, it activates the cross-field boundary condition propagation.

[0012] If the Lyapunov exponent of any subsystem exceeds the stability threshold, the joint time step rollback of the associated subsystems is triggered, thereby systematically improving the simulation stability.

[0013] Furthermore, the independent variable step-size integrator dynamically predicts the next step size based on the rate of change of the second norm of the current solution vector. When the decay rate of the nonlinear residual is lower than a preset value, adaptive step-size reduction is performed to maintain computational accuracy in the critical phase transition region. An asynchronous iteration strategy is enabled for subsystems with time constant differences greater than orders of magnitude to alleviate the waiting delay caused by time scale differences between subsystems.

[0014] Furthermore, the synchronization condition is determined by calculating the least common multiple of the next simulation time of each subsystem. The least common multiple is generated based on the current step size of each subsystem and the simulation start time. The phase coincidence time of key physical states is captured by the event-driven engine. By accurately capturing the key coupling moments of the physical process, the number of redundant data exchanges is reduced.

[0015] Furthermore, the joint time step rollback includes recording the first three stable state points of the divergent subsystem, resetting the simulation clock of the associated subsystem based on the maximum stable state point, and reloading the historical cached data of the boundary conditions to restore computational consistency, thereby achieving rapid recovery of system stability and minimizing data loss caused by divergence.

[0016] Secondly, the present invention also provides a distributed multiphysics collaborative simulation system, the system being based on the method described in the first aspect above, comprising:

[0017] The heterogeneous solver cluster contains at least three adaptive step-size solver engines corresponding to electromagnetic, fluid, and structural fields, respectively.

[0018] A dynamic load balancer is used to dynamically allocate computing nodes based on the Jacobian matrix of each engine.

[0019] Cross-field data relay stations are used to perform bidirectional parameter interpolation transmission at synchronization time;

[0020] The stability monitoring center is used to analyze the cumulative energy error of the coupled system in real time.

[0021] Furthermore, the adaptive step-size solving engine includes:

[0022] Implicit iterative accelerators are used to compress matrix solution time and reduce the time required to solve large-scale linear equation systems by employing the preprocessed conjugate gradient method.

[0023] Step size oscillation suppressor is used to optimize step size decisions by using the moving average of historical step size sequences, thereby avoiding convergence oscillations caused by sudden changes in step size.

[0024] The transient event capture unit uses the Lipchitz constant based on the function derivative as a metaphor to identify step size split points, thereby improving the ability to analyze sudden physical processes.

[0025] Furthermore, the dynamic load balancer monitors the stiffness matrix update frequency of each solver engine. When the ratio of nonlinear iteration time to linear solution time exceeds a threshold, it triggers GPU resource reallocation to accelerate the nonlinear convergence process and preloads the boundary data of adjacent subsystems before the synchronization time to eliminate data waiting delay at the synchronization time.

[0026] Furthermore, the working modes of the cross-field data relay station include a gradient-preserving transmission mode that imposes a first-order derivative continuity constraint on the transmission parameters and a conservation correction mode that uses a flux compensation algorithm to eliminate interface numerical dissipation.

[0027] Furthermore, the stability monitoring center detects the exponential growth behavior of the subsystem's state variables, reduces the probability of coupled system collapse, constructs an error propagation matrix for cross-field parameter transfer, and automatically selects the optimal recovery point based on the state space trajectory, avoiding the risk of secondary divergence caused by traditional fixed rollback points.

[0028] Thirdly, the present invention also provides the application of a distributed multiphysics collaborative simulation system in real-time simulation of high-frequency electromechanical systems, including:

[0029] Electromagnetic fields and structural vibration fields are deployed to physically isolated computing nodes to avoid the impact of electromagnetic interference on precision structural calculations.

[0030] Sub-microsecond time synchronization accuracy is achieved by synchronizing the clock signals of each node through a phase-locked loop circuit.

[0031] When the electromagnetic force spectrum energy is detected to be concentrated in a specific frequency band, the solution step size of the dynamically compressed structural field is used to accurately capture the electromechanical coupling effect in the resonant frequency band.

[0032] This invention discloses a distributed multiphysics co-simulation method. It configures adaptive step-size strategies for the circuit and mechanical subsystems respectively, independently solving nonlinear equations using the Newton-Rafaelin algorithm, and triggering step-size reset upon iteration overflow. Based on the alignment of the step-size ratio with the simulation time, it selectively activates the mechanical field to participate in the iteration, performing joint solution of the two fields only when their time sequences coincide; otherwise, it maintains the mechanical field state unchanged. The parameters of the two fields are transmitted in real time, and the simulation time is synchronously reset when either subsystem diverges, ensuring coupling stability.

[0033] This method significantly optimizes computational resource allocation through asynchronous variable step size and selective coupling mechanisms. The mechanical subsystem participates in iteration only during time alignment, avoiding redundant calculations caused by traditional global fixed small step sizes, reducing the computational load on the mechanical field by approximately 70%. A unified equation framework is constructed based on the nodal voltage method, combined with Newton's iterative convergence criterion and a joint rollback mechanism to ensure the accuracy of boundary condition transfer in dual-field coupling, while effectively suppressing the risk of numerical divergence. It is suitable for transient analysis of electromechanical systems, providing an efficient solution for complex multiphysics simulation.

[0034] Beneficial effects

[0035] By implementing the distributed multiphysics collaborative simulation method provided by the present invention, the following technical effects are achieved:

[0036] (1) To address the time constant difference between the circuit and mechanical subsystems, an independent variable step size strategy and a selective coupling mechanism are adopted. By dynamically determining the necessity of the mechanical field participating in the iteration, the joint solution is activated only when the simulation time is aligned, which significantly reduces the computational redundancy of physical fields with large time constants. This design breaks through the global fixed step size limitation and significantly optimizes the efficiency of computational resource allocation while ensuring coupling accuracy.

[0037] (2) A dual fault-tolerant system is constructed based on Lyapunov stability theory. When a single-field iteration overflows, the local step size is reset, and when the global energy error exceeds the limit, a joint state rollback is initiated. By backtracking historical steady-state data points and reconstructing the initial boundary conditions, numerical divergence caused by error accumulation is effectively suppressed. This mechanism significantly improves the robustness of multi-field coupled systems, especially ensuring simulation continuity during strongly nonlinear transient processes.

[0038] (3) By dynamically generating synchronization thresholds instead of a fixed time-step alignment strategy, the timing accuracy of cross-field boundary condition propagation is significantly optimized. This strategy effectively suppresses boundary parameter propagation distortion caused by phase mismatch, especially in electromagnetic and mechanical coupling scenarios, where the energy conservation error between physical fields is systematically compressed. Simultaneously, this mechanism intelligently filters non-critical synchronization points based on the dominant frequency component, significantly reducing the frequency of invalid data exchanges in subsystems with large time constants, thereby improving the resource allocation efficiency of heterogeneous computing clusters and achieving a significant optimization of overall simulation efficiency.

[0039] (4) By adaptively selecting the optimal rollback point through a joint curvature and stability weight model, the risk of secondary divergence caused by traditional fixed-history-point rollback is fundamentally suppressed. In strongly nonlinear transient processes, the recovered state-space trajectory can quickly converge to a stable manifold, significantly shortening the iterative recovery cycle. At the same time, the state variable jump error when overloaded boundary data is effectively controlled, ensuring the global controllability of error accumulation in long-term simulations, thereby enhancing the system's robustness and continuous simulation capabilities. Attached Figure Description

[0040] To make the above-described distributed multiphysics collaborative simulation method of the present invention more obvious and understandable, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0041] Figure 1 This is a flowchart illustrating the method described in this application;

[0042] Figure 2 This diagram illustrates the system architecture and parallel flowchart.

[0043] Figure 3This represents the flowchart of the joint rollback mechanism. Detailed Implementation

[0044] Example 1:

[0045] A distributed multiphysics co-simulation method is provided, the method flow is as follows: Figure 1 As shown, it includes:

[0046] Independent variable-step-size integrators based on the dynamic characteristics of the physical field are configured for physical field subsystems with different time constants;

[0047] A nonlinear step size mapping function is established between subsystems through the main controller, and the function is associated with the maximum allowable step size ratio of each subsystem.

[0048] When the timing alignment module detects that the simulation times of at least two subsystems meet the synchronization condition, it activates the cross-field boundary condition propagation.

[0049] If the Lyapunov exponent of any subsystem exceeds the stability threshold, a joint time step rollback of the associated subsystems is triggered.

[0050] The independent variable step-size integrator dynamically predicts the next step size based on the rate of change of the second norm of the current solution vector. When the decay rate of the nonlinear residual is lower than the preset value, it performs adaptive step-size reduction to maintain computational accuracy in the critical phase transition region and enables an asynchronous iteration strategy for subsystems with time constant differences greater than orders of magnitude.

[0051] The synchronization condition is determined by calculating the least common multiple of the next simulation time of each subsystem. The least common multiple is generated based on the current step size of each subsystem and the simulation start time, and the phase coincidence time of key physical states is captured by the event-driven engine.

[0052] The joint time step rollback includes recording the first three stable state points of the divergent subsystem, resetting the simulation clock of the associated subsystem based on the maximum stable state point, and reloading the historical cached data of the boundary conditions to restore computational consistency.

[0053] A distributed multiphysics collaborative simulation system is also provided, the system architecture and parallel process of which are as follows: Figure 2 As shown, it includes:

[0054] The heterogeneous solver cluster contains at least three adaptive step-size solver engines corresponding to electromagnetic, fluid, and structural fields, respectively.

[0055] A dynamic load balancer is used to dynamically allocate computing nodes based on the Jacobian matrix of each engine.

[0056] Cross-field data relay stations are used to perform bidirectional parameter interpolation transmission at synchronization time;

[0057] The stability monitoring center is used to analyze the cumulative energy error of the coupled system in real time.

[0058] The adaptive step-size solving engine includes:

[0059] Implicit iterative accelerators are used to compress matrix solution time using the preprocessed conjugate gradient method;

[0060] A step size oscillation suppressor is used to optimize step size decisions by using a moving average of historical step size sequences.

[0061] The transient event capture unit uses the analogy of the Lipchitz constant based on the function derivative to identify step size segmentation points.

[0062] The dynamic load balancer monitors the stiffness matrix update frequency of each solver engine. When the ratio of nonlinear iteration time to linear solution time exceeds a threshold, it triggers GPU resource reallocation to accelerate the nonlinear convergence process and preloads the boundary data of adjacent subsystems before the synchronization time.

[0063] The working modes of the cross-field data relay station include a gradient-preserving transmission mode that adds a first-order derivative continuity constraint to the transmission parameters and a conservation correction mode that uses a flux compensation algorithm to eliminate interface numerical dissipation.

[0064] The stability monitoring center detects the exponential growth of subsystem state variables, reduces the probability of coupled system collapse, constructs an error propagation matrix for cross-field parameter transfer, and automatically selects the optimal recovery point based on the state space trajectory.

[0065] Example 2:

[0066] To address the issue that traditional synchronization determination relies on a fixed least common multiple time point, this paper proposes a method to dynamically generate a synchronization threshold by analyzing the dominant frequency components of the subsystems in real time. Based on the short-time Fourier transform, the instantaneous frequencies of the physical field boundary parameters are extracted. Synchronization is triggered when the rate of change of the phase difference between the dominant frequencies of the two subsystems approaches zero, thus avoiding invalid data exchange caused by fixed time intervals. The formula is as follows:

[0067]

[0068] In the formula, The phase difference change rate of the dual-field dominant frequency band; For subsystem A at frequency time The power spectral density; For subsystem B at frequency time The power spectral density; Entropy of the spectrum energy distribution; Effective bandwidth; This represents the average historical synchronization interval.

[0069] A real-time spectrum analysis unit is embedded in the boundary condition transfer channel, and the dominant frequency component is calculated once every 5 local steps;

[0070] According to the current and energy entropy Adjusting the threshold automatically reduces high-frequency oscillation scenarios. To improve synchronization sensitivity;

[0071] when When the threshold is below the threshold for three consecutive times, cross-field data transmission is activated.

[0072] Verification shows that, while achieving an average error similar to the aforementioned embodiments, in motor control system simulations, the frequency of mechanical vibration field participation in iterations is reduced by 42%, the electrode interface flux conservation error decreases from 5.1% to 1.3%, communication overhead is reduced by 37%, and the computational efficiency of the heterogeneous cluster is improved by 28%. The results demonstrate that this scheme significantly optimizes the timing accuracy of cross-field data transfer. The distortion in boundary condition transmission caused by traditional fixed-step synchronization is effectively suppressed, especially in electromagnetic and mechanical coupling scenarios, where parasitic oscillations caused by inaccurate phase alignment of the mechanical vibration field are fundamentally improved. The energy conservation error between physical fields is significantly reduced, and the improved fidelity of boundary flux transmission allows the coupled system to maintain stable interaction during transient changes. Simultaneously, this mechanism significantly reduces the frequency of invalid calculations in subsystems with large time constants by intelligently filtering non-critical synchronization points, systematically optimizing the resource utilization of the heterogeneous computing cluster, and significantly improving overall simulation efficiency and reducing redundant communication overhead.

[0073] Example 3:

[0074] Traditional joint rollback relies on fixed historical points for recovery, which can easily lead to secondary divergence in highly nonlinear regions. This paper addresses this issue by constructing a curvature analysis model of the state-space trajectory and selecting the curvature extremum point as the optimal rollback reference point. Stability weights are constructed using the product of the Lyapunov exponential rate of change and the trajectory curvature to achieve adaptive recovery point decision-making.

[0075]

[0076] In the formula, This is the optimal rollback point; For a moment The rate of change of the Lyapunov index; For the state space trajectory in Curvature at that point; Let be the system energy gradient norm.

[0077] The joint rollback mechanism process is as follows: Figure 3As shown, the state-space trajectory vectors of the 10 most recent stable state points of each subsystem are stored in a circular manner. Lyapunov index and system energy function ;

[0078] The five-point differential method is used to approximate the solution. This avoids high-order computational overhead.

[0079] For each divergence event detected, select from the cache points. And reload the boundary data at that moment.

[0080] For example, suppose the circuit subsystem is an RLC oscillating circuit. , , initial voltage The mechanical subsystem is a mass-spring-damping system. , , initial displacement The coupling relationship is electromagnetic force. , Current Acting on the mass; back electromotive force , , The velocity of the mass block in the mechanical subsystem is fed back to the circuit.

[0081] exist Apply step disturbance voltage This leads to an exponential increase in the displacement response of the mechanical subsystem, triggering a joint rollback mechanism.

[0082] The experimental results are shown in Table 1.

[0083] Table 1. Summary of Experimental Results

[0084]

[0085] Verification shows that, while achieving a similar average error to the aforementioned embodiments, the number of iterations required for convergence after rollback is reduced by 58%. In crack propagation simulation, the system collapse probability decreases from 15.7% to 2.1%, and the state quantity recovery accuracy improves to 99.2%. Experimental results demonstrate that the curvature-driven joint rollback strategy exhibits superior fault-tolerant recovery capabilities in the experimental environment. The secondary divergence problem caused by traditional fixed-history-point rollback is effectively curbed, and the system collapse probability in the strongly nonlinear region is significantly reduced. This mechanism accurately locates the optimal recovery point through the joint weighting of curvature and stability, enabling the state-space trajectory after rollback to converge rapidly to a stable manifold, significantly shortening the iteration cycle required for system recovery. Simultaneously, the state quantity jump error under heavy boundary data is effectively suppressed, the historical consistency of cross-field parameter transfer is improved, ensuring that error accumulation remains within a controllable threshold during long-term simulations, and significantly enhancing the continuous simulation capability for complex transient processes.

Claims

1. A distributed multi-physics co-simulation method, characterized in that, Comprising: independent variable step-size integrators are configured for physical field subsystems with different time constants respectively; a step-size mapping function between subsystems is established by a master controller, the function associates the maximum allowed step-size ratio of each subsystem; a synchronization condition is dynamically generated by a timing alignment module, the condition is determined based on real-time spectral feature analysis of boundary parameters of each subsystem; when the timing alignment module detects that the simulation time of at least two subsystems meets the synchronization condition, a cross-field boundary condition transfer is activated; if the Lyapunov exponent of any subsystem exceeds a stability threshold, a joint time step rollback of the associated subsystem is triggered, the rollback includes adaptive selection of an optimal rollback reference point based on state space trajectory curvature analysis of historical stable state points of the divergent subsystem.

2. The method of claim 1, wherein: the independent variable step-size integrators dynamically predict the next step-size based on the second order norm change rate of the current solution vector, perform adaptive step-size reduction when the decay rate of the nonlinear residual is lower than a preset value, and enable an asynchronous iteration strategy for subsystems with time constant difference greater than an order of magnitude.

3. The method of claim 1, wherein: the synchronization condition is determined by calculating the least common multiple time point of the next simulation time of each subsystem, the least common multiple is generated based on the current step-size and the simulation start time of each subsystem, and the phase coincidence time of the key physical state is captured by an event-driven engine.

4. The method of claim 1, wherein: the joint time step rollback includes recording the first three stable state points of the divergent subsystem, resetting the simulation clock of the associated subsystem based on the largest stable state point, and reloading the historical cache data of the boundary condition to restore computational consistency.

5. The method of claim 4, wherein: the joint time step rollback adaptively selects the optimal rollback reference point by the following formula: wherein is the optimal rollback point; is the time is the rate of change of Lyapunov exponent of is the curvature of the state space trajectory at is the curvature of the state space trajectory at is the system energy gradient norm.

6. A distributed multi-physics co-simulation system, characterized in that: The implementation of the system is based on the method of any one of claims 1-5, comprising: a heterogeneous solver cluster containing at least three adaptive step-size solving engines corresponding to electromagnetic, fluid, and structural fields respectively; a dynamic load balancer for dynamically distributing computing nodes based on the Jacobian matrix of each engine; a cross-field data relay station for bidirectional parameter interpolation transmission at synchronization time; a stability monitoring center for real-time analysis of energy error accumulation of the coupled system.

7. The system of claim 6, wherein: the adaptive step-size solving engine includes: an implicit iteration accelerator for compressing matrix solving time using a preconditioned conjugate gradient method; a step-size oscillation suppressor for optimizing step-size decision through a sliding average of historical step-size sequence; a transient event capture unit for identifying step-size segmentation points based on the Lipchitz constant of function derivatives.

8. The system of claim 6, wherein: the dynamic load balancer monitors the stiffness matrix update frequency of each solving engine, triggers GPU resource reallocation when the ratio of nonlinear iteration time consumption to linear solving time consumption exceeds a threshold, and preloads adjacent subsystem boundary data before synchronization time.

9. The system of claim 6, wherein: the working mode of the cross-field data relay station includes a gradient preserving transmission mode with first derivative continuity constraint on the transfer parameters and a conserved quantity correction mode with a flux compensation algorithm to eliminate numerical dissipation at the interface.

10. The system of claim 6, wherein: the stability monitoring center detects the super-exponential growth behavior of the state quantities, constructs the error transfer matrix of the cross-field parameter transfer, and automatically selects the optimal recovery point according to the state space trajectory.

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