An all-link multi-physical field "digital twin" simulation method and system

Abstract

The application claims a full-link multi-physical field digital twin simulation method and system, belonging to the technical field of MEMS device design and multi-physical field simulation. The method constructs a four-layer link of "sensitive microstructure - packaging structure - interface circuit - environmental load" of the electro-mechanical-thermal-acoustic-magnetic five-field two-way strong coupling digital twin, and realizes millisecond-level fast solution combined with high-fidelity reduction technology; synchronously injects multi-source composite interference, locates the interference transmission core sensitive node through global sensitivity analysis, completes parallel optimization of anti-interference scheme, and uses an adaptive filtering algorithm to assimilate measured data, realizes online self-calibration and design closed-loop iteration of the twin. The application solves the technical problems of insufficient full-link coupling, imbalance of efficiency and precision, and weak optimization targeting of the existing MEMS anti-interference simulation, has the characteristics of high simulation confidence, high optimization efficiency and wide adaptability, and is suitable for anti-interference design and performance evaluation scenes of various high-precision MEMS sensors.

Description

Technical Field

[0001] This invention belongs to the fields of microelectromechanical systems (MEMS) design, multiphysics simulation and digital twin technology. Specifically, it relates to a full-link multiphysics "digital twin" system-level simulation method and system for anti-interference MEMS design. It is applicable to the shielding effectiveness calibration, interference path tracing, multi-parameter optimization design and service performance evaluation of high-precision capacitive / electromagnetic MEMS inertial sensors, micro resonators, Lorentz force magnetometers and other devices in complex acoustic, vibration, thermal and magnetic composite interference environments. Background Technology

[0002] MEMS devices, with their advantages of small size, low power consumption, and easy integration, have become core sensing units in consumer electronics, smart cars, aerospace, and deep earth exploration. Under harsh conditions such as high temperatures in deep wells, strong vibrations in engine rooms, and strong magnetic fields in power grids, MEMS devices must simultaneously withstand multi-source composite interference, including acoustic noise, mechanical vibration, temperature gradients, stray magnetic fields, and high-frequency electromagnetic radiation. Acoustic noise can penetrate the package and induce structural resonance, modulating the comb tooth gap through pressure film damping; mechanical vibration can propagate along the substrate, causing parasitic vibrations and orthogonal errors; temperature gradients can induce Young's modulus drift and dominant frequency shift through thermal stress; and stray magnetic fields and high-frequency EMI can disrupt the differential bridge balance through electromagnetic coupling, and even trigger cascade degradation of the "magnetic-mechanical-thermal-electrical" system through Joule heating, potentially leading to device failure in severe cases.

[0003] To mitigate these risks during the design phase, the industry commonly employs multiphysics simulation for anti-interference design; however, existing technologies still face significant bottlenecks.

[0004] First, the simulation dimensions are fragmented, lacking the ability to achieve strong coupling across all five fields. Traditional simulations often solve for structural units individually, neglecting the bidirectional reaction of electromagnetic shielding saturation and eddy current thermal effects on structural prestress. They cannot construct an integrated closed loop of "environmental electromagnetic radiation - encapsulation shielding - microstructure multi-field coupling - ASIC circuit matching", making it difficult to accurately predict the anti-interference limit when multiple fields overlap.

[0005] Secondly, it is difficult to balance simulation efficiency and nonlinear accuracy. High-precision three-dimensional finite element simulation involves large computational loads and long cycles, which cannot support large-scale parameter iterations; while traditional linear macro models suffer severe distortion in highly nonlinear scenarios such as large deflection hardening, slip flow damping, and magnetic saturation, making them unsuitable as a basis for high-fidelity design.

[0006] Third, digital twins lack deep self-assimilation capabilities. Due to implicit factors such as micro-nano fabrication deviations, encapsulation leakage, and aging of shielding materials, static simulation models gradually become inaccurate over time. Existing solutions lack effective algorithms to assimilate measured time-series data into a reduced-order model, making it impossible to correct the model's stiffness, damping, and electromagnetic characteristic parameters online.

[0007] Fourth, anti-interference optimization lacks precise targeted guidance. Existing designs mostly rely on trial and error based on experience, and cannot quantify the contribution ratio of each interference path from the output noise, resulting in weak optimization targeting, long R&D cycles, and high costs.

[0008] With the increasing demand for high-precision MEMS devices in complex operating conditions, the industry urgently needs a digital twin simulation solution that combines full-link coupling, high-fidelity order reduction, accurate traceability, and self-updating capabilities.

[0009] A search revealed application CN116644625B, entitled "An Efficient Micromirror Chip Analysis Method Based on Multiphysics Coupling," belonging to the field of microelectromechanical systems (MEMS). The method includes: establishing a mapping relationship between the deflection angle and torque of comb teeth; firstly, applying approximate periodic boundary conditions to the comb teeth to calculate the mapping relationship; then, verifying a single-axis adjustable micromirror electrostatic actuator based on this mapping relationship. Finally, the finite element method is used to simulate a complex dual-axis electrostatic actuator, enabling faster frequency domain analysis of the thermo-viscosistic acoustic and mechanical coupling of the dual-axis electrostatic actuator. This approach allows for more efficient optimization design of dual-axis adjustable micromirror electrostatic actuators.

[0010] However, the aforementioned literature is limited to the acoustic-mechanical dual-field coupling simulation of chip-level microstructures in the frequency domain, neglecting the entire interference propagation path formed by packaging structure, interface circuits, and complex environmental loads. It cannot simulate the nonlinear cascading interference effects of electromagnetic shielding degradation, transient thermal stress, and high-frequency EMI in the overall system. Furthermore, as a static offline model, it cannot perform online adaptive calibration for parameter drift caused by manufacturing deviations or material aging. To address these shortcomings, this invention constructs a four-layer link unit covering "sensitive microstructure - packaging structure - interface circuit - environmental load," achieving bidirectional strong nonlinear coupling solution of five fields (mechanical, electrical, thermal, acoustic, and magnetic) in the time domain. Using global sensitivity analysis based on variance decomposition (Sobol), it quantitatively evaluates and accurately locates core sensitive nodes on the interference propagation path. Through a dual-core joint adaptive unscented Kalman filter algorithm, it assimilates the test data of the physical prototype in real time, correcting time-varying implicit parameters such as damping and electromagnetic parameters online, achieving adaptive evolution throughout the model's entire lifecycle and high-fidelity anti-interference design verification. Summary of the Invention

[0011] This invention aims to achieve full-link simulation of strong bidirectional coupling of five fields: mechanical, electrical, thermal, acoustic, and magnetic. It balances accuracy and efficiency through nonlinear high-fidelity order reduction technology, achieves accurate source tracing of interference paths based on Sobol global sensitivity analysis, and constructs a model self-assimilation closed loop based on a dual-core adaptive filtering algorithm, thus promoting the upgrade of MEMS anti-interference design from "experience-based trial and error" to "digital twin-driven".

[0012] The technical solution of the present invention is as follows:

[0013] An anti-interference MEMS end-to-end multiphysics digital twin simulation method includes the following core steps:

[0014] Step 1: Construction of a fully coupled digital twin: For the target MEMS device, the system is divided into four layers of link units: "sensitive microstructure - packaging structure - interface circuit - environmental load". The partial differential control equation model of the physical field corresponding to each unit is established. The strong bidirectional coupling mapping of the five fields of mechanics, electricity, heat, sound and magnetism of each unit is realized through a standardized bidirectional coupling interface to construct a system-level multi-physics digital twin.

[0015] Step 2: Multi-source composite interference quantization injection and transmission simulation: five types of interference signals, namely acoustic noise, mechanical vibration, temperature gradient, stray magnetic field and electromagnetic radiation, are injected into the environmental load layer of the digital twin. Based on the coupling transfer matrix, the attenuation, amplification and multi-field overlapping coupling effect of the interference signal in each link unit are calculated, and the interference response time series data of the key nodes of the entire link are output.

[0016] Step 3: Deep source tracing and performance evaluation of sensitive nodes coupled with multi-physics field: Based on the response data of each probe node in the entire link, the core sensitive nodes on the interference propagation path are located by means of transfer function state identification and global sensitivity analysis based on variance decomposition, and the degree of device performance degradation under different electromagnetic shielding effectiveness and mechanical temperature vibration coupling is quantitatively evaluated.

[0017] Step 4: Anti-interference topology iterative optimization and real-time self-assimilation update of the digital twin: Electromagnetic shielding, structural topology and circuit compensation parameters are optimized in coordination for core sensitive nodes, and imported into the digital twin for parallel simulation verification; measured dynamic interference response data of the physical prototype are collected and fed back to the digital twin; a dual-core joint adaptive unscented Kalman filter algorithm is used to assimilate and correct manufacturing deviations, material degradation and permeability drift parameters in the digital twin online, forming a self-calibration closed loop.

[0018] Furthermore, in step 1, the modeling rules for the four-layer link unit are specifically as follows:

[0019] The sensitive microstructure unit establishes a force-electric-thermal-acoustic-magnetic strongly coupled nonlinear partial differential control model, and its transient control equation is:

[0020]

[0021] Where M, C, and K are the system mass matrix, damping matrix, and stiffness matrix, respectively. Let be the displacement vector of the microstructure nodes. To soften the nonlinear driving force of the electrostatic spring, This is either the Lorentz force or the magnetostrictive strain. Coriolis force and inertial load, For transient thermal stress loads;

[0022] The encapsulation structure unit establishes a three-dimensional "force-sound-thermal-solid-magnetic" strongly coupled solid model, including a metal encapsulation shell, a high permeability shielding layer, a ceramic substrate, an adhesive medium, and bonding leads, which are used to solve stray magnetic field flux saturation, high-frequency EMI skin effect and eddy current effect, as well as the mechanical transmission path of mechanical vibration and sound pressure.

[0023] The interface circuit unit is constructed using an analog hardware description language to establish a circuit immunity degradation model under high-frequency EMI radiation injection, including power supply rejection ratio, common-mode rejection ratio degradation behavior, and differential cancellation active electromagnetic interference compensation network.

[0024] The environmental load unit establishes a standardized import interface for multiple load fields, supporting concurrent loading of acoustic waves, random vibrations, temperature field gradients, triaxial time-varying magnetic fields, and radio frequency EMI loads.

[0025] Furthermore, in step 1, the multi-physics field bidirectional strong coupling mapping is achieved through a nonlinear high-fidelity reduced-order macromodel. Specifically, the feature matrices of the high-dimensional partial differential models of each unit are extracted, and the Arnoldi algorithm is used to construct the multi-output block Krylov subspace projection basis matrix, compressing the system degrees of freedom from millions to tens of dimensions. The eigenorthogonal decomposition method is used to extract the transient feature snapshots of the nonlinear force field, and the nonlinear space super-reduction processing is performed through the discrete empirical interpolation algorithm to construct a nonlinear reduced-order macromodel that retains the effects of electrostatic spring softening, magnetic saturation, and geometric large deflection hardening, thereby achieving efficient and fast solution in the system-level time domain.

[0026] In the damping matrix of the sensitive microstructure unit, the extrusion membrane damping is described by a modified two-dimensional Reynolds equation, and an equivalent flow resistance system for boundary overflow is introduced at the opening side boundary of the electrode. It corrects the pressure loss of the discharge flow and accurately calculates the damping for slip flow and transition flow regions.

[0027] Furthermore, in step 2, the injection method for stray magnetic fields and high-frequency electromagnetic interference is as follows:

[0028] Stray magnetic field interference: A time-varying external magnetic field signal is injected outside the package structure unit. The residual stray magnetic flux density of the internal cavity of the package is calculated by solving the BH magnetization nonlinearity of the package shell material.

[0029] Electromagnetic radiation interference: Inject high-frequency alternating radio frequency electromagnetic fields, calculate the electromagnetic induction effect of the package wall and bonding wires, and extract the induced voltage and parasitic charge noise of sensitive microstructure electrodes and interface circuits.

[0030] The coupling transfer matrix is ​​a multiple-input multiple-output transfer function matrix. The matrix elements correspond to the interference transfer coefficients between different link units and different physical fields. It is used to quantitatively characterize the attenuation factor, amplification gain and multi-field coupling superposition coefficient of the interference signal when it passes through the interface of each unit.

[0031] Furthermore, in step 3, the specific process of deep tracing the electromagnetic-multi-field coupled sensitive node is as follows:

[0032] Dynamic response signals from N nodes across the entire link are collected to construct a multi-input multi-output transfer matrix. Based on the Sobol global sensitivity analysis algorithm using variance decomposition, the contribution rate of parameter fluctuations at each node to the total variance of the device's final electrical zero-point drift and scaling error is calculated, yielding the first-order sensitivity index for each node. With the total sensitivity index Nodes whose total sensitivity index exceeds a preset threshold are marked as core sensitive nodes, and an interference full-link energy transfer topology is drawn.

[0033] Furthermore, the twin construction module is used for full-link multi-physics digital twin modeling; the interference simulation module has a built-in multi-source interference database for simulation of concurrent injection and propagation of multiple types of interference; the interference analysis module has a built-in transfer function identification and Sobol variance decomposition unit for tracing interference paths and sensitive nodes; the optimization iteration module has a built-in multi-objective optimization engine and a dual-core adaptive unscented Kalman estimator for collaborative optimization and online parameter assimilation; and the data interaction module is used for bidirectional data transmission between the system and the physical prototype.

[0034] A full-link multiphysics digital twin simulation system for interference-resistant MEMS design includes a twin construction module, an interference simulation module, an interference analysis module, an optimization iteration module, and a data interaction module.

[0035] The twin construction module is used to perform full-link mechanical-electrical-thermal-acoustic-magnetic five-field digital twin modeling;

[0036] The interference simulation module has a built-in multi-source, multi-field interference database, which is used to perform simulations of concurrent injection and transmission of multiple types of interference.

[0037] The interference analysis module has a built-in transfer function identification and Sobol global variance decomposition unit, which is used to perform interference path and sensitive node source tracing analysis.

[0038] The optimization iteration module incorporates a multi-objective optimization engine and a dual-core joint adaptive unscented Kalman estimator to perform collaborative optimization and online assimilation and evolution of model parameters.

[0039] The data interaction module is used to realize real-time bidirectional data transmission between the digital twin simulation system and the physical prototype testing platform.

[0040] Furthermore, the twin construction module includes a three-dimensional unit structure library for MEMS devices, an asymmetric packaging library, an active demagnetizing shield model library, and an ASIC interface circuit behavior model library including charge amplification, active mode matching, and EMI filtering conditioning.

[0041] The interference simulation module supports the streaming import of custom geomagnetic changes, interference sound fields, broadband vibration power spectra, temperature change curves, and high-voltage EMI transient pulse signals, which can be used to reproduce multi-field coupling extreme scenarios under complex working conditions.

[0042] The optimization iteration module supports heterogeneous multi-core parallel simulation and can schedule transient coupled solution tasks for more than a number of reduced-order models, achieving a hundredfold improvement in efficiency for large-scale parameter optimization.

[0043] An anti-interference MEMS sensor, wherein the sensitive microstructure, packaging structure and interface circuit of the MEMS sensor are optimized for anti-interference design and performance verification using any of the described full-link multi-physics digital twin simulation methods.

[0044] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the described end-to-end multiphysics digital twin simulation methods.

[0045] The advantages and beneficial effects of this invention are as follows:

[0046] 1. Strong coupling across multiple fields in the entire link, with high simulation confidence: A four-layer digital twin is constructed to achieve strong bidirectional coupling of multiple physical fields, fully reproduce the entire transmission path of interference and cascade effects, and accurately predict the anti-interference limit under extreme conditions.

[0047] 2. Precise source tracing of sensitive nodes and targeted optimization: By combining transfer function identification and Sobol global variance decomposition, the contribution ratio of each interference path and parameter to performance degradation is quantified, and core sensitive nodes are located, providing a precise basis for anti-interference optimization.

[0048] 3. High-fidelity nonlinear order reduction, balancing accuracy and efficiency: It integrates block Krylov subspace projection and POD-DEIM nonlinear super-reduction technology, retaining strong nonlinear characteristics such as large deflection hardening, magnetic saturation, and slip flow damping, compressing simulation time from hours to milliseconds, and supporting parallel optimization of multiple sets of parameters.

[0049] 4. Self-assimilation closed-loop calibration, supporting dynamic self-correction: Adopting a dual-core joint adaptive unscented Kalman filter algorithm, it can assimilate measured data online and dynamically correct implicit parameters such as process deviations and material aging, ensuring high confidence throughout the entire life cycle of the digital twin and taking into account the needs of design and development as well as service monitoring.

[0050] Steps 1 to 4 of this invention construct an efficient self-assimilation closed loop of "modeling-simulation-source tracing-optimization-calibration," with strong synergistic dependencies between each step. Traditional MEMS simulation and physical testing are independent, and anti-interference design often relies on blind trial and error with full-parameter sweeps. In this invention, the four-layer link (sensitive microstructure-packaging structure-interface circuit-environmental load) five-field strongly coupled model constructed in step 1 provides a high-fidelity physical foundation for the time-domain transient simulation of multi-source composite interference (acoustic, vibration, temperature, magnetic, and electrical sources) in step 2; the dynamic response time-series data output in step 2 is the data source for the Sobol global sensitivity analysis based on variance decomposition implemented in step 3; step 3 calculates the first-order sensitivity index of the nodes. With the total sensitivity index This method precisely identifies the "core sensitive nodes" that contribute the most to the electrical bias and scaling error of the device, directly providing targeted guidance for the anti-interference topology iteration (electromagnetic shielding, structural decoupling, and active circuit compensation) in step 4. Step 4 utilizes the measured dynamic interference response of the physical prototype for online assimilation using a dual-core Kalman filter, dynamically correcting manufacturing deviations, material degradation, and permeability drift that are difficult to measure directly in the model of step 1, enabling the digital twin of step 1 to be dynamically updated throughout its service life. This full-lifecycle self-calibration closed-loop collaboration solves the technical deadlock of static simulation models becoming inaccurate over time.

[0051] II. The nonlinear order reduction method based on Krylov subspace projection and POD-DEIM spatial super-reduction, and the boundary equivalent flow resistance coefficient. The modified two-dimensional Reynolds equations, combined, form a simulation method that balances computational efficiency with high nonlinear accuracy. Traditional high-fidelity five-field strongly coupled methods involve millions of degrees of freedom, resulting in extremely high computational costs, making them unsuitable for direct application to global Sobol analysis requiring tens of thousands of iterations or for time-sensitive online filtering. This invention, while performing projection order reduction, introduces a drag coefficient at the opening boundary of the Reynolds equations to address the high-frequency extrusion film damping between the plates. By accurately repairing pressure leakage errors under slip flow and transition flow conditions, the computational dimension is significantly compressed, and the large displacement geometric deflection hardening, electromagnetic force and damping nonlinearity are fully reproduced, overcoming the inherent technical conflict between "high-precision nonlinear multiphysics coupling" and "high-throughput rapid iterative solution".

[0052] Thirdly, a dual-core joint adaptive Kalman filter architecture for parallel estimation of state variables and implicit physical characteristic parameters is proposed. Conventional filtering algorithms are often used for real-time estimation of first-order physical states. This invention, addressing the susceptibility of MEMS devices to environmental stress and service aging, innovatively employs dual-core estimation: the first core filter is used for real-time estimation of the high-frequency motion state of sensitive microstructure units, while the second core filter is used to simultaneously identify and track implicit physical drift parameters such as manufacturing corrosion deviations, material stiffness degradation, vacuum micro-leakage, and packaging demagnetization at low-frequency scales. By dynamically adjusting the noise covariance using the covariance matching method, the divergence of coupled filters with multiple nonlinear parameters is avoided, solving the industry problem of the inability to identify and calibrate multiple implicit physical attenuations online during MEMS operation. Attached Figure Description

[0053] Figure 1 This is an overall flowchart of the end-to-end multiphysics digital twin simulation method described in this invention;

[0054] Figure 2 A schematic diagram of multiphysics coupling modeling and order reduction principle for a full-link four-layer unit;

[0055] Figure 3 A schematic diagram illustrating the principle of multi-source interference injection and sensitive node tracing;

[0056] Figure 4 This is a module architecture diagram of the digital twin simulation system described in this invention;

[0057] Figure 5 This is a schematic diagram of the structural decomposition of a microsystem under strong coupling of multiple physics fields as described in an embodiment of the present invention;

[0058] Figure 6 This is a comparison diagram of the reduced-order model and the original model in terms of degrees of freedom and time domain response, as described in this embodiment of the invention. Figure 6 (a) Comparison of degrees of freedom compression Figure 6 (b) Comparison of time-domain responses;

[0059] Figure 7 This is a radar map showing the location of the core sensitive nodes based on Sobol global sensitivity analysis in an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0061] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0062] Step 1: Construction of a full-link five-field coupled digital twin

[0063] The system is constructed from the bottom up, consisting of four layers: sensitive microstructure, encapsulation structure, interface circuit, and environmental load. Corresponding physical field coupling models are established for each layer, and bidirectional mapping is achieved through a standardized interface. The core transient control equation is:

[0064]

[0065] This equation comprehensively covers the structural inertia, damping, and stiffness characteristics, as well as the multi-source load coupling of electrostatic force, electromagnetic force, inertial force, and thermal stress. The stiffness matrix changes in real time with temperature, and the damping matrix dynamically adjusts with gas pressure and plate displacement, accurately describing nonlinear effects such as large deflection hardening and electrostatic softening. The packaging structure unit establishes a three-dimensional "acoustic-thermal-solid-magnetic" strongly coupled model, fully replicating the packaging shell, high-permeability shielding layer, ceramic substrate, and bonding leads. It can solve for the BH nonlinear magnetization of stray magnetic fields, flux distribution, and shielding effectiveness attenuation, as well as the skin effect and eddy current Joule heat conduction characteristics of high-frequency EMI. It also simulates the transmission paths of sound pressure and mechanical vibration to the internal microstructure. The interface circuit unit uses Verilog-A to construct a behavioral-level macromodel, covering core circuits such as differential charge amplification, synchronous detection, and mode matching closed-loop. It integrates common-mode rejection ratio and power supply rejection ratio degradation operators under high-frequency EMI and incorporates a differential electromagnetic common-mode compensation network, achieving bidirectional mapping between the mechanical and circuit domains. The environmental load unit constructs standardized load boundaries, supporting independent or concurrent loading of five types of loads: acoustic, vibration, temperature, magnetic field, and RF EMI, and is compatible with the import of standard signals and measured operating condition signals. To balance simulation accuracy and efficiency, high-fidelity order reduction processing is performed on the entire system finite element model: the block Arnoldi algorithm is used to construct the Krylov subspace projection basis, compressing the linear dynamics and electromagnetic diffusion equations with millions of degrees of freedom to tens of orders; for strongly nonlinear characteristics such as electrostatic force, Lorentz force, and magnetic saturation, transient snapshots are extracted through eigenorthogonal decomposition, and a small number of characteristic control nodes are selected by discrete empirical interpolation to complete the solution of the nonlinear force field.

[0066] Step 2: Simulation of Quantization Injection and Transmission of Multi-Source Composite Interference

[0067] The reduced-order macro model is imported into the system-level simulator, and multi-source composite interference is synchronously injected through the environmental load unit to carry out full-link transmission simulation.

[0068] Acoustic and vibration interference: Sound pressure loads are applied to the outer surface of the package, and random vibration loads are applied to the mounting base. The parasitic vibrations of the microstructure are excited through acoustic-solid coupling and structural transmission, respectively.

[0069] Temperature disturbance: Applying a steady-state or transient temperature gradient can induce changes in structural thermal stress and material properties through heat conduction, leading to a shift in the resonant frequency;

[0070] Magnetic field and EMI interference: Apply time-varying stray magnetic field, solve the nonlinear magnetic saturation of the shielding layer and the residual magnetic flux in the cavity; inject high-frequency radio frequency EMI, calculate the lead-induced voltage and eddy current Joule heating, and the temperature fluctuations caused by Joule heating are further fed back to the structural domain, forming a multi-field cascade effect.

[0071] The system solver concurrently solves the transient equations of the entire system and outputs timing response data for all nodes in the entire link, including magnetic induction of the encapsulation shielding layer, shear strain of the anchor point, displacement of the comb teeth, noise at the front end of the circuit, and the final output voltage.

[0072] Step 3: In-depth source tracing and performance evaluation of electromagnetic-multi-field coupled sensitive nodes

[0073] Based on end-to-end response data, interference propagation path identification and global sensitivity analysis are conducted.

[0074] First, the attenuation factor and transfer function of the interference in different frequency bands and at different physical interfaces are extracted using a frequency response identification algorithm, thus preliminarily clarifying the impedance distribution of the interference transmission.

[0075] Subsequently, a global sensitivity analysis based on variance decomposition was employed, selecting the core physical parameters of the entire link as input random vectors and using device zero-point drift and scaling error as output targets. The first-order sensitivity index of each parameter was calculated through quasi-Monte Carlo sampling. With the total sensitivity index The first-order exponent reflects the independent contribution of a single parameter to the output error, while the total sensitivity index encompasses the combined effect of the parameter after being coupled through multiple cascaded fields.

[0076] Nodes whose total sensitivity index exceeds a preset threshold are marked as core sensitive nodes and visualized in the 3D model as heat maps. At the same time, an interference energy transfer topology map is generated to quantify the contribution ratio of each path, providing targeted guidance for subsequent optimization.

[0077] Step 4: Iterative optimization of anti-interference scheme and self-assimilation update of twin.

[0078] Based on the source tracing results of sensitive nodes, multi-objective collaborative optimization and model self-calibration closed loop are carried out.

[0079] The optimization phase uses the geometry, materials, and circuit parameters of core sensitive nodes as optimization variables, with the objective functions of "maximizing the composite interference suppression ratio, minimizing zero-point drift, and minimizing circuit power consumption." Utilizing a millisecond-level reduced-order simulation engine, a multi-objective genetic algorithm is invoked for parallel optimization, outputting a Pareto optimal solution set to support the coordinated optimization of structural topology, shielding design, and circuit compensation. The self-assimilation update phase constructs a dual-core joint adaptive unscented Kalman filter online estimator: microstructure displacement and velocity are used as state vectors, while implicit parameters such as etching asymmetry deviation, cavity air pressure degradation, and shielding layer permeability shift are used as parameter vectors, forming a joint extended state-space model. The measured output waveform of the physical prototype is transmitted back in real time through a data interaction module. Unscented transformation is used to synchronously update the state and parameter estimates, and the noise covariance matrix is ​​adaptively adjusted online based on residual information using the Sage-Husa mechanism to avoid filter divergence under high dynamic interference. After calibration, the relative error between the model and the measured data can be stably controlled within a scientific range, enabling the digital twin to continuously self-evolve as it progresses in service. Furthermore, the present invention also provides a corresponding digital twin simulation system, which includes five major modules: twin construction, interference simulation, interference analysis, optimization iteration, and data interaction. The functions of each module correspond one-to-one with the above-mentioned method steps, realizing the integration of the entire process of modeling-simulation-analysis-optimization.

[0080] Furthermore, this embodiment takes the acoustic-vibration-thermal-magnetic composite interference immunity design of a high-precision MEMS tuning fork gyroscope as a scenario to describe the implementation process of the method in detail:

[0081] Implementation Step 1: Constructing a full-link digital twin of the MEMS gyroscope

[0082] For the target MEMS tuning fork gyroscope, five-field coupling modeling is carried out according to a four-layer architecture:

[0083] Sensitive microstructure unit: A three-dimensional structural model including a driving beam, a detection beam, comb-tooth electrodes, and a central anchor point is established. Single-crystal silicon material parameters are set, and the temperature dependence of Young's modulus is defined. A micro-conductive coil is integrated to characterize the Lorentz force effect. The damping term uses a modified two-dimensional Reynolds equation to describe the extrusion film damping effect, and an equivalent flow resistance coefficient for boundary overflow is introduced at the electrode opening side boundary. The pressure loss of the gas leakage is corrected to adapt to the accurate calculation of damping in the slip flow and transition flow regions, ensuring that the calculation error of the quality factor Q value is ≤3%. The specific form of the corrected two-dimensional extruded membrane Reynolds equation is as follows:

[0084]

[0085] In the formula, The thickness of the gas film between the electrodes. For gas dynamic viscosity, For air film pressure distribution, The coordinates are orthogonal coordinates in the plane of the electrode. It is a time variable.

[0086] To address the gas overflow effect on the open side of the electrode, an equivalent flow resistance coefficient for boundary overflow is introduced. The pressure boundary condition at the open boundary is modified, and the modified pressure condition at the open boundary is as follows:

[0087]

[0088] In the formula, This refers to the air pressure in the cavity. This represents the gas flow rate per unit length of the open boundary.

[0089] Boundary overflow equivalent flow resistance coefficient The calculation method is as follows:

[0090]

[0091] In the formula, The initial gap between the plates. Knudsen number, used to characterize the degree of slip in gas flow; This is the slip correction factor, whose value is related to the aspect ratio of the electrode opening. For a comb-tooth electrode structure, The value ranges from 1.0 to 1.5 and can be obtained through experimental calibration or direct simulation fitting.

[0092] Packaging structure unit: Establish a complete model of metal packaging shell, permalloy shielding layer, ceramic substrate, and gold wire bonding, set up multiple coupling interfaces of acoustic-solid, thermal-structural, and magnetic-solid, and calculate the magnetic saturation, eddy current heat and vibration transmission characteristics of the shielding layer.

[0093] Interface circuit unit: A Verilog-A behavioral model is built for charge amplification, phase-sensitive detection, and mode matching closed loop, and EMI common-mode interference and power supply rejection ratio degradation models are incorporated.

[0094] Environmental load unit: Standardized loading interface configured with five types of interference.

[0095] To visually demonstrate the microsystem physical model under the aforementioned end-to-end multiphysics strong coupling and environmental loads, this embodiment constructs the following... Figure 5 The diagram shows a breakdown of the microsystem structure.

[0096] The block Arnoldi algorithm and the POD-DEIM method are used to reduce the order of the model, compressing degrees of freedom while preserving nonlinear characteristics. To verify the beneficial effects of the above-mentioned high-fidelity reduced-order macromodel based on the POD-DEIM method on computational efficiency and accuracy, this embodiment provides the following... Figure 6The diagram shows a comparison of the degrees of freedom and time-domain response. It can be seen that the degree-of-freedom compression factor reaches approximately 10. 5 The computation time is significantly reduced to the millisecond level. The gyroscope output curve of the nonlinear order reduction method (POD-DEIM) of this invention matches well with the initial peak value of the full-degree-of-freedom finite element simulation (FEM), successfully preserving the nonlinear effect and avoiding the distortion of the traditional linear order reduction model (ROM).

[0097] Implementation Step 2: Simulation of Multi-Source Composite Interference Injection and End-to-End Transmission

[0098] Multi-source composite interference signals are synchronously injected into the environmental load layer, including: acoustic noise signals with preset sound pressure levels and corresponding frequency sweep ranges, broadband random vibration loads with preset total root mean square acceleration, time-varying transient temperature gradient loads, multi-axis time-varying external stray magnetic field loads, and high-frequency radio frequency alternating electromagnetic field interference with preset radio frequency frequencies and radiated electric field strengths.

[0099] The system solver concurrently solves the multi-field coupled transient response: acoustic waves excite the packaging shell to resonate and are transmitted to the anchor point; vibrations induce parasitic deformation of the structure through the substrate; temperature gradients induce thermal stress and stiffness drift; stray magnetic fields are attenuated by shielding and act on the coil to generate Lorentz force; EMI induces common-mode noise at the lead end and is accompanied by eddy current Joule heating; the thermal effect further reacts on the structural stiffness.

[0100] The simulation process synchronously collects timing data from 12 key nodes, including package surface vibration, anchor point strain, comb tooth displacement, circuit front-end noise, and final output voltage, to form a full-link response dataset.

[0101] To accurately assess the multi-field cascade degradation effect under combined disturbances and provide design comparison, this embodiment includes a single-physics field decoupling disturbance simulation comparison step, in addition to concurrently solving the multi-field coupled transient response through the system solver:

[0102] First, by independently injecting temperature gradient disturbance through the environmental load unit, the first component of zero-point drift caused by changes in material properties induced by thermal stress is calculated separately. Next, by independently injecting stray magnetic field disturbance, the second component of zero-point drift caused by the Lorentz force generated on the coil by the residual magnetic flux is calculated separately. Similarly, the single-field zero-point drift response components under the independent action of each of the remaining single-physics fields are calculated separately.

[0103] The comparison of the calculation results shows that if the zero-point drift response components induced by each individual physical field in an isolated state are superimposed using conventional linear algebra, the theoretical superposition value is significantly smaller than the composite interference zero-point drift response output when the five types of interference signals are injected synchronously and solved concurrently. This comparison clearly reveals from a mechanistic perspective that when multiple sources of interference occur concurrently, the encapsulation will trigger a cascade amplification effect across physical fields such as "magnetism-mechanics-thermal-electricity," and the performance degradation caused by the overlapping coupling of multiple fields is far greater than the simple linear superposition of the effects of each individual field. This decoupling comparison process, from the perspective of system thermodynamics and dynamics coupling, intuitively demonstrates the high confidence and irreplaceable nature of full-link five-field bidirectional strong coupling simulation in anti-interference design.

[0104] Implementation Step 3: Source Tracing and Performance Evaluation of Interference-Sensitive Nodes

[0105] A global sensitivity analysis of the full-link response dataset was conducted using Sobol. Several key geometric and multi-field physical parameters, including shielding layer geometric thickness, anchor beam structural parameters, bonding wire spacing, cavity filling pressure, and interface circuit gain, were selected as input random variables. The zero-point drift of the device's final output was used as the target output function. Multidimensional numerical integration was performed through quasi-Monte Carlo sampling to output the first-order sensitivity index of each parameter and the total sensitivity index.

[0106] Figure 7 This is an example of sensitivity analysis results; the actual parameters and calculated results are dynamically adjusted according to the device structure and operating conditions. For example... Figure 7 This specific example illustrates the overall sensitivity index of the shielding layer's geometric thickness among multiple random variables, including the selected combination of damping coefficients and the stiffness of the anchor beam structure. It reached a maximum of 0.9, and was identified as a core sensitive node in the system.

[0107] Accordingly, the system-level simulator automatically marks the encapsulation shielding layer and anchor structure whose total sensitivity index exceeds the preset tolerance threshold as core sensitive nodes in the whole-link system, and the interference analysis module generates an interference energy transfer path topology map to clearly identify two core interference paths that overlap across physical fields: "external stray magnetic field - encapsulation shielding attenuation - cavity residual magnetic flux - microstructure Lorentz force - electrical orthogonal error" and "external mechanical vibration - encapsulation and substrate anchor transfer - microstructure parasitic vibration - output zero drift".

[0108] The quantitative output of the system's comprehensive evaluation unit indicates that, under the current unoptimized initial configuration, the nonlinear cascade amplification effect of the aforementioned core interference transmission paths causes the device to exhibit service performance degradation indicators such as zero-point drift under combined interference environments, which have exceeded the preset design tolerance and cannot meet the requirements of high-precision operating conditions. Therefore, it is urgent to carry out targeted collaborative optimization for the identified core sensitive nodes.

[0109] Implementation Step 4: Anti-interference scheme optimization and twin self-assimilation update

[0110] For the core sensitive nodes located in step 3, the shielding layer geometric thickness, shielding material nonlinear permeability, anchor beam structural stiffness parameters, and encapsulation cavity internal air pressure are selected as core optimization variables. With "minimizing the zero-point drift of composite interference, controlling the attenuation of device sensitivity, and optimizing the power consumption of interface circuit" as the collaborative constraint objectives, a heterogeneous multi-core parallel optimization engine is called to perform multi-objective genetic algorithm optimization. Parallel simulations of multiple parameter combinations are carried out in the parameter space, and finally, the Pareto optimal solution set that satisfies the multi-dimensional performance constraints is output.

[0111] The optimal engineering configuration scheme was selected from the solution set. This was achieved by increasing the design thickness of the shielding layer, using a high-permeability shielding material, widening the anchor beam to improve structural stiffness, and appropriately adjusting the internal air pressure of the encapsulation cavity. Verification using a reduced-order macromodel showed that after adopting this optimized configuration scheme, the core performance indicators of the device under combined interference conditions, such as zero-point drift, were significantly improved compared to before optimization, successfully exceeding the preset design requirements. A corresponding physical prototype was fabricated and subjected to experimental evaluation under multi-source combined interference scenarios to obtain experimental dynamic interference response data of the physical prototype under harsh conditions. The measured time-series waveforms and environmental load data were transmitted back to the digital twin simulation system in real time, and the Joint-AUKF algorithm was initiated for online assimilation calibration: using the transient displacement and velocity of the sensitive microstructure motion as the state vector, and the etching deviation caused by the manufacturing process, the actual permeability drift of the material, and the air pressure degradation of the encapsulation cavity as implicit parameter vectors, an extended state-space model was constructed for synchronous estimation.

[0112] During calibration iterations, if abnormal disturbances in the innovation cause the covariance matrix to become out of positive definite, the system automatically activates an anti-divergence mechanism: introducing a strong tracking fading factor and diagonalizing the covariance matrix to ensure model positive definiteness and avoid filter divergence under high dynamic disturbances. After cyclic step-by-step iterations, the relative error between the model simulation output and the prototype measured data converges quickly and smoothly to within the preset high-precision engineering error threshold, completing the full lifecycle online self-calibration update of the digital twin. Thus, a complete digital twin simulation and optimization of the entire MEMS anti-interference design process is completed.

[0113] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0114] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0115] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0116] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A full-link multiphysics digital twin simulation method, characterized in that, Includes the following steps: Step 1: Construction of a fully coupled digital twin: For the target MEMS device, the system is divided into four layers of link units: "sensitive microstructure - packaging structure - interface circuit - environmental load". The partial differential control equation model of the physical field corresponding to each unit is established. The strong bidirectional coupling mapping of the five fields of mechanics, electricity, heat, sound and magnetism of each unit is realized through a standardized bidirectional coupling interface to construct a system-level multi-physics digital twin. Step 2: Multi-source composite interference quantization injection and transmission simulation: five types of interference signals, namely acoustic noise, mechanical vibration, temperature gradient, stray magnetic field and electromagnetic radiation, are injected into the environmental load layer of the digital twin. Based on the coupling transfer matrix, the attenuation, amplification and multi-field overlapping coupling effect of the interference signal in each link unit are calculated, and the interference response time series data of the key nodes of the entire link are output. Step 3: Deep source tracing and performance evaluation of sensitive nodes coupled with multi-physics field: Based on the response data of each probe node in the entire link, the core sensitive nodes on the interference propagation path are located by means of transfer function state identification and global sensitivity analysis based on variance decomposition, and the degree of device performance degradation under different electromagnetic shielding effectiveness and mechanical temperature vibration coupling is quantitatively evaluated. Step 4: Anti-interference topology iterative optimization and real-time self-assimilation update of the digital twin: Electromagnetic shielding, structural topology and circuit compensation parameters are optimized in coordination for core sensitive nodes, and imported into the digital twin for parallel simulation verification; measured dynamic interference response data of the physical prototype are collected and fed back to the digital twin; a dual-core joint adaptive unscented Kalman filter algorithm is used to assimilate and correct manufacturing deviations, material degradation and permeability drift parameters in the digital twin online, forming a self-calibration closed loop.

2. The end-to-end multiphysics digital twin simulation method according to claim 1, characterized in that, In step 1, the modeling rules for the four-layer link unit are as follows: The sensitive microstructure unit establishes a force-electric-thermal-acoustic-magnetic strongly coupled nonlinear partial differential control model, and its transient control equation is: Where M, C, and K are the system mass matrix, damping matrix, and stiffness matrix, respectively. Let be the displacement vector of the microstructure nodes. To soften the nonlinear driving force of the electrostatic spring, This is either the Lorentz force or the magnetostrictive strain. Coriolis force and inertial load, For transient thermal stress loads; The encapsulation structure unit establishes a three-dimensional "force-sound-thermal-solid-magnetic" strongly coupled solid model, including a metal encapsulation shell, a high permeability shielding layer, a ceramic substrate, an adhesive medium, and bonding leads, which are used to solve stray magnetic field flux saturation, high-frequency EMI skin effect and eddy current effect, as well as the mechanical transmission path of mechanical vibration and sound pressure. The interface circuit unit is constructed using an analog hardware description language to establish a circuit immunity degradation model under high-frequency EMI radiation injection, including power supply rejection ratio, common-mode rejection ratio degradation behavior, and differential cancellation active electromagnetic interference compensation network. The environmental load unit establishes a standardized import interface for multiple load fields, supporting concurrent loading of acoustic waves, random vibrations, temperature field gradients, triaxial time-varying magnetic fields, and radio frequency EMI loads.

3. The end-to-end multiphysics digital twin simulation method according to claim 1, characterized in that, In step 1, the multi-physics bidirectional strong coupling mapping is achieved through a nonlinear high-fidelity reduced-order macromodel. Specifically, the feature matrices of the high-dimensional partial differential models of each unit are extracted, and the Arnoldi algorithm is used to construct the Krylov subspace projection basis matrix of the multi-output block, compressing the system degrees of freedom from millions to tens of dimensions. The eigenorthogonal decomposition method is used to extract the transient feature snapshots of the nonlinear force field, and the nonlinear space super-reduction processing is performed through the discrete empirical interpolation algorithm to construct a nonlinear reduced-order macromodel that retains the effects of electrostatic spring softening, magnetic saturation, and geometric large deflection hardening, thereby achieving efficient and fast solution in the system-level time domain. In the damping matrix of the sensitive microstructure unit, the extrusion membrane damping is described by a modified two-dimensional Reynolds equation, and an equivalent flow resistance system for boundary overflow is introduced at the opening side boundary of the electrode. It corrects the pressure loss of the discharge flow and accurately calculates the damping for slip flow and transition flow regions.

4. The end-to-end multiphysics digital twin simulation method according to claim 1, characterized in that, In step 2, the injection method for stray magnetic fields and high-frequency electromagnetic interference is as follows: Stray magnetic field interference: A time-varying external magnetic field signal is injected outside the package structure unit. The residual stray magnetic flux density of the internal cavity of the package is calculated by solving the BH magnetization nonlinearity of the package shell material. Electromagnetic radiation interference: Inject high-frequency alternating radio frequency electromagnetic fields, calculate the electromagnetic induction effect of the package wall and bonding wires, and extract the induced voltage and parasitic charge noise of sensitive microstructure electrodes and interface circuits. The coupling transfer matrix is ​​a multiple-input multiple-output transfer function matrix. The matrix elements correspond to the interference transfer coefficients between different link units and different physical fields. It is used to quantitatively characterize the attenuation factor, amplification gain and multi-field coupling superposition coefficient of the interference signal when it passes through the interface of each unit.

5. The end-to-end multiphysics digital twin simulation method according to claim 1, characterized in that, In step 3, the specific process of deep tracing the electromagnetic-multi-field coupled sensitive node is as follows: Dynamic response signals from N nodes across the entire link are collected to construct a multi-input multi-output transfer matrix. Based on the Sobol global sensitivity analysis algorithm using variance decomposition, the contribution rate of parameter fluctuations at each node to the total variance of the device's final electrical zero-point drift and scaling error is calculated, yielding the first-order sensitivity index for each node. With the total sensitivity index ; Nodes whose total sensitivity index exceeds a preset threshold are marked as core sensitive nodes, and an interference full-link energy transfer topology diagram is drawn.

6. The end-to-end multiphysics digital twin simulation method according to claim 1, characterized in that, The twin construction module is used for full-link multi-physics digital twin modeling; the interference simulation module has a built-in multi-source interference database for simulation of concurrent injection and transmission of multiple types of interference; the interference analysis module has a built-in transfer function identification and Sobol variance decomposition unit for tracing interference paths and sensitive nodes. The optimization iteration module incorporates a multi-objective optimization engine and a dual-core adaptive unscented Kalman estimator for collaborative optimization and online parameter assimilation; the data interaction module is used for bidirectional data transmission between the system and the physical prototype.

7. A full-link multiphysics digital twin simulation system for interference-resistant MEMS design, characterized in that, It includes a twin construction module, an interference simulation module, an interference analysis module, an optimization iteration module, and a data interaction module; The twin construction module is used to perform full-link mechanical-electrical-thermal-acoustic-magnetic five-field digital twin modeling; The interference simulation module has a built-in multi-source, multi-field interference database, which is used to perform simulations of concurrent injection and transmission of multiple types of interference. The interference analysis module has a built-in transfer function identification and Sobol global variance decomposition unit, which is used to perform interference path and sensitive node source tracing analysis. The optimization iteration module incorporates a multi-objective optimization engine and a dual-core joint adaptive unscented Kalman estimator to perform collaborative optimization and online assimilation and evolution of model parameters. The data interaction module is used to realize real-time bidirectional data transmission between the digital twin simulation system and the physical prototype testing platform.

8. The digital twin simulation system according to claim 7, characterized in that, The twin construction module includes a three-dimensional unit structure library for MEMS devices, an asymmetric packaging library, an active demagnetizing shield model library, and an ASIC interface circuit behavior model library including charge amplification, active mode matching, and EMI filtering conditioning. The interference simulation module supports the streaming import of custom geomagnetic changes, interference sound fields, broadband vibration power spectra, temperature change curves, and high-voltage EMI transient pulse signals, which can be used to reproduce multi-field coupling extreme scenarios under complex working conditions. The optimization iteration module supports heterogeneous multi-core parallel simulation and can schedule transient coupled solution tasks for more than a number of reduced-order models, achieving a hundredfold improvement in efficiency for large-scale parameter optimization.

9. An anti-interference MEMS sensor, characterized in that, The sensitive microstructure, packaging structure, and interface circuit of the MEMS sensor are optimized for anti-interference design and performance verification using the full-link multi-physics digital twin simulation method described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the end-to-end multiphysics digital twin simulation method according to any one of claims 1-6.

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