A spring-damper parameterization modeling system

Abstract

The present application relates to the field of computational many-body dynamics and computer-aided engineering simulation, in particular to a spring damping parameterized modeling system, the system comprises: excitation perception and manifold initialization unit, as the input level of the system for coping with non-stationary working conditions, configured to monitor the external excitation signal in real time, based on the current instantaneous geometric state of the system, generate dynamic topological state matrix; topological-parameter bidirectional transient coupling engine, generate transient stiffness / damping field matrix representing parasitic stiffness effect, and perform degree of freedom locking on hyperfinite nodes to modify topological connection matrix, generate reduced topological state data; and adaptive reduced-order manifold solving unit, transmit the solution back to the excitation perception and manifold initialization unit as a feedback signal; the present application effectively avoids the energy virtual increase phenomenon caused by ignoring geometric nonlinearity of traditional model, significantly improves the physical authenticity and simulation accuracy of the system under complex deformation working conditions.

Description

Technical Field

[0001] This invention relates to the field of computational multibody dynamics and computer-aided engineering simulation technology, specifically a parametric modeling system for spring damping. Background Technology

[0002] As flexible multibody systems are increasingly used in complex engineering fields, their operating environment exhibits significant non-stationary and high-frequency random excitation characteristics. The complexity of this operating condition places extremely high demands on the accuracy of system dynamics modeling and simulation, especially in dealing with the evolution of physical properties caused by structural deformation.

[0003] Currently, dynamic simulations of such systems generally employ the traditional lumped parameter method for modeling. This method typically relies on the rigid node assumption, treating spring stiffness coefficients and damping coefficients as preset constants or obtaining them through simple static lookup tables. In terms of computational logic, traditional simulation architectures often treat geometric topology and physical parameters as independent, decoupled variables, meaning that physical properties do not intrinsically change with real-time twisting or folding of the geometric configuration. This traditional modeling method, which relies on the decoupling of static parameters and geometric physics, has significant drawbacks when facing high-frequency impacts or large deformation conditions. Furthermore, it neglects the influence of geometric nonlinearity... The parasitic stiffness effect generated by linearity cannot truly reflect the driving effect of configuration evolution on physical properties. This not only leads to the phenomenon of energy inflation that violates the laws of physics in the simulation results, but also causes the differential equation system to exhibit strong rigidity characteristics due to its inability to adapt to the drastic fluctuations of transient internal forces. This easily leads to divergence in numerical calculations, making it difficult to guarantee the convergence and high fidelity of simulation results. Therefore, how to solve the problems of energy inflation and calculation divergence caused by neglecting geometric nonlinearity in flexible multibody systems under high-frequency non-stationary conditions, and how to achieve real-time coupled modeling of geometric topology and physical parameters, has become an urgent problem to be solved in this field. Summary of the Invention

[0004] To solve the above-mentioned technical problems, the present invention provides a parametric modeling system for spring damping. Specifically, the technical solution of the present invention includes:

[0005] The excitation sensing and manifold initialization unit, as the input stage of the system, is used to deal with non-stationary operating conditions. It is configured to monitor external excitation signals in real time, and when a sudden change in the centroid of the signal is detected, it constructs a dynamic state space equation containing generalized coordinates, topological adjacency and physical parameter mapping relationship based on the current instantaneous geometric state of the system, thereby generating a dynamic topological state matrix.

[0006] The topology-parameter bidirectional transient coupling engine, as the core unit for real-time interlocking of geometric configuration and physical properties, is configured to receive the dynamic topology state matrix, run geometry-driven physical logic, update the system stiffness and damping matrices based on the deformation degree of the geometric configuration through nonlinear constitutive mapping, and generate a transient stiffness / damping field matrix characterizing parasitic stiffness effects; then, it runs physical-locked geometry logic, solves for the transient internal force vectors of the connection points based on the transient stiffness / damping field matrix, compares the magnitude of the vector with the local locking threshold of the connection points, performs degree-of-freedom locking on over-limit nodes to modify the topology connection matrix, and generates reduced-order topology state data;

[0007] The adaptive reduced-order manifold solving unit is configured to receive the reduced-order topology state data, identify the regions marked as locked and merge rigid node variables to dynamically reduce the dimension of the computation matrix, solve for the system state response solution including displacement, velocity and acceleration, and transmit the solution back to the excitation sensing and manifold initialization unit as a feedback signal.

[0008] Preferably, the specific logic for determining the spectral centroid mutation by the excitation sensing and manifold initialization unit is as follows:

[0009] The change in the centroid of the external excitation signal's spectrum per unit time is calculated. If the change exceeds a preset threshold, it is determined that the system has entered a non-stationary operating condition. At this point, the preset static stiffness matrix is ​​stopped, and the process of constructing the dynamic state space equation is started instead.

[0010] Preferably, the construction of dynamic state-space equations is characterized by:

[0011] The spring stiffness coefficient and damping coefficient are defined as intrinsic state variables that evolve in real time with the geometric topology state variables, rather than preset constants, thereby establishing a three-dimensional dynamic mapping relationship between generalized coordinates, topological adjacency and physical parameters.

[0012] Preferably, the geometry-driven physical logic in the topology-parameter bidirectional transient coupling engine specifically includes:

[0013] The system receives node displacement and rotation data in real time and calculates the rate of change of geometric coordinates. When the rate of change exceeds the preset linear range, it determines that the configuration has undergone minor deformation or large-angle folding.

[0014] Based on the current degree of geometric distortion, the element values ​​in the system stiffness matrix and damping matrix are updated instantaneously to reshape the energy dissipation path, thereby obtaining the transient stiffness / damping field matrix.

[0015] Preferably, the physical locking geometry logic in the topology-parameter bidirectional transient coupling engine specifically includes:

[0016] The magnitude of the transient internal force vector of each connection point, obtained based on dynamic calculations, is compared with the local locking threshold of the connection point, which serves as the critical force value for maintaining the flexible motion state of the connection structure.

[0017] When the magnitude of the transient internal force vector exceeds the local locking threshold of the connection point, the connection point is determined to enter a near-rigid state and a degree-of-freedom locking command is triggered.

[0018] Preferably, the execution method of the degree-of-freedom locking instruction is as follows:

[0019] By adding Lagrange multiplier constraints or directly performing matrix row and column reduction operations based on Gaussian elimination, the topological connection matrix of the system is forcibly modified, so that the associated nodes are merged into the same moving rigid body in the current time step, thereby temporarily freezing the relative motion degrees of freedom between the nodes.

[0020] Preferably, the order reduction processing logic of the adaptive order reduction manifold solver is as follows:

[0021] Based on the geometric degrees of freedom locked by physical and mechanical states, an adaptive order reduction operation is performed at the mathematical solution level. By merging nodal variables that are temporarily made rigid, the number of equations to be solved and the condition number of the stiffness matrix are dynamically reduced without sacrificing flexibility accuracy.

[0022] Preferably, it also includes a virtual sensing and state reconstruction unit, which is used to mine data value by utilizing intermediate computational variables, and is configured to simultaneously receive topological distortion data and parameter evolution history generated by the topology-parameter bidirectional transient coupling engine;

[0023] Using the topological distortion data generated during the calculation process as a virtual sensing source, the stress distribution state inside the physical system is calculated by performing inverse deduction based on the physical mapping relationship between the distortion degree of the parameterized topology and the internal stress.

[0024] The output includes an enhanced simulation report containing the conventional dynamic response and the derived internal stress contour plot.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. This invention establishes a dynamic mapping relationship between geometric topology and physical parameters, defining stiffness and damping coefficients as intrinsic state variables that evolve with the configuration, breaking the barrier of decoupling geometry and physics in traditional simulations. This mechanism can capture the parasitic stiffness effect caused by large-angle folding or small deformation in real time, effectively avoiding the energy inflation phenomenon caused by neglecting geometric nonlinearity in traditional models, and significantly improving the physical realism and simulation accuracy of the system under complex deformation conditions.

[0027] 2. This invention introduces a reverse feedback control mechanism based on mechanical state. By comparing the transient internal force vector with the local locking threshold in real time, it can automatically identify overload nodes and trigger degree-of-freedom locking commands. This mechanism uses mathematical constraints to temporarily freeze the relative motion of high-frequency flutter nodes, effectively suppressing noise accumulation and amplification in the numerical integration process, solving the problem of easy divergence of rigid differential equations under large dynamic loads, and ensuring the convergence and stability of calculations under extreme conditions.

[0028] 3. This invention adopts an adaptive reduced-order manifold solution strategy, which can dynamically adjust the dimension of the mathematical model according to the physical locking state; by merging node variables that are transformed into a rigid state, the system significantly reduces the number of equations to be solved and the condition number of the stiffness matrix without losing the accuracy of the key flexible regions; this dynamic management of computational complexity achieves the optimal balance between simulation accuracy and computational efficiency, and supports rapid parameter iteration of complex multibody systems.

[0029] 4. This invention possesses adaptive sensing and virtual sensing capabilities, enabling automatic switching between static and dynamic modeling processes based on the frequency domain characteristics of external excitation signals, thus achieving on-demand allocation of computing resources. Simultaneously, by utilizing topological distortion data as a virtual sensing source, the system can inversely deduce the unmeasurable stress distribution state within the physical structure, outputting an enhanced report containing dynamic response and internal stress cloud diagrams, providing rich data support for structural health assessment. Attached Figure Description

[0030] The present invention will be further explained below with reference to the accompanying drawings and embodiments:

[0031] Figure 1 This is a structural diagram of the system of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments;

[0033] Example 1:

[0034] Please see Figure 1 A parametric modeling system for spring damping includes:

[0035] The excitation sensing and manifold initialization unit, as the input stage of the system, is used to deal with non-stationary operating conditions. It is configured to monitor external excitation signals in real time, and when a sudden change in the centroid of the signal is detected, it constructs a dynamic state space equation containing generalized coordinates, topological adjacency and physical parameter mapping relationship based on the current instantaneous geometric state of the system, thereby generating a dynamic topological state matrix.

[0036] The topology-parameter bidirectional transient coupling engine, as the core unit for real-time interlocking of geometric configuration and physical properties, is configured to receive the dynamic topology state matrix, run geometry-driven physical logic, update the system stiffness and damping matrices based on the deformation degree of the geometric configuration through nonlinear constitutive mapping, and generate transient stiffness / damping field matrices characterizing parasitic stiffness effects; run physical-locked geometry logic, solve for the transient internal force vectors of connection points based on the transient stiffness / damping field matrices, compare the magnitude of the vector with the local locking threshold of the connection points, perform degree-of-freedom locking on over-limit nodes to modify the topology connection matrix, and generate reduced-order topology state data;

[0037] The adaptive reduced-order manifold solver is configured to receive reduced-order topology state data, identify regions marked as locked, merge rigid node variables to dynamically reduce the dimension of the computation matrix, calculate the system state response solution including displacement, velocity, and acceleration, and transmit the solution back to the excitation sensing and manifold initialization unit as a feedback signal.

[0038] A spring-damped parameterized modeling system is constructed as a unified modeling architecture that can simultaneously characterize the continuous evolution of geometric topology and the discrete abrupt changes of physical parameters. It aims to solve the problem of energy inflation caused by the neglect of geometric nonlinearity in the traditional lumped parameter method when flexible multibody systems encounter high-frequency random excitation.

[0039] The excitation sensing and manifold initialization unit, serving as the full-time domain signal acquisition and analysis interface, connects to an external excitation signal source. This unit does not passively receive signals but continuously performs spectral characteristic analysis. It detects drastic fluctuations in the frequency components of the input signal, thus determining that the system has entered a non-stationary operating condition, and constructs a three-dimensional dynamic mapping relationship accordingly. This mapping relationship constructs a high-dimensional parametric manifold space, tightly binding physical parameters as fibers on the manifold with the geometric state space as the base manifold, outputting a dynamic topological state matrix containing initial conditions. This dynamic topological state matrix is ​​instantiated in computer memory as a three-dimensional nested data structure: the first dimension stores the generalized coordinate data of the nodes, i.e., the geometric state; the second dimension stores... A topological adjacency index table between nodes; a third dimension stores memory address pointers to physical parameter objects, with pointers directly associated with the geometric coordinates of the first dimension, enabling addressing operations on the geometric state to directly access the corresponding stiffness and damping parameters through pointer offsets, thereby achieving physical and geometric binding at the data structure level; in this invention, the manifold concept is specifically represented at the computer implementation level as the dynamic topological state matrix, which is constructed as a nested linked list or structure data structure that can dynamically map geometric state addresses and physical parameter addresses in real time through pointer offsets; the dynamic topological state matrix is ​​a composite data structure that not only contains node position information but also embeds connection relationships and parameter definitions that evolve over time;

[0040] The topology-parameter bidirectional transient coupling engine receives the above matrix, breaking the barrier between geometry and physics decoupling in traditional simulations and executing bidirectional interlocking logic: the engine corrects stiffness and damping values ​​in real time according to the degree of distortion of the geometry, and captures parasitic stiffness; it freezes geometric degrees of freedom in reverse according to mechanical load to prevent numerical divergence.

[0041] The adaptive reduced-order manifold solver performs dimensionality reduction at the mathematical level, calculates the dynamic response of the system in a very short time step, and feeds back the system state response solution containing displacement, velocity and acceleration to the input stage to complete the closed-loop iteration.

[0042] This embodiment overcomes the failure problem of traditional rigid node assumptions when dealing with high-frequency impacts by establishing a closed-loop architecture of excitation sensing, bidirectional coupling and adaptive solution. It explicitly introduces physical locking and parameter evolution mechanisms into the computational logic, enabling the system to automatically identify and simulate parasitic effects caused by large geometric deformations, avoiding the phenomenon of energy inflation that violates physical laws, and ensuring the convergence and high fidelity of simulation results under extreme conditions.

[0043] Example 2:

[0044] The specific logic for determining spectral centroid mutations in the excitation sensing and manifold initialization unit is as follows:

[0045] The change in the centroid of the external excitation signal's spectrum per unit time is calculated. If the change exceeds a preset threshold, it is determined that the system has entered a non-stationary operating condition. The system stops calling the preset static stiffness matrix and instead starts the process of constructing the dynamic state space equation.

[0046] This embodiment employs a dynamic discrimination protocol based on time-frequency analysis to identify sudden changes in operating conditions. The unit continuously samples the input external excitation signal through a sliding window and applies short-time Fourier transform to calculate the degree of drift of the signal frequency range in the current time step relative to the previous time step. The specific calculation logic for the frequency change is as follows: perform spectral analysis on the signal within the current sliding window to calculate the weighted average frequency of the spectral energy distribution, i.e., the spectral centroid; perform a difference operation between the spectral centroid of the current time step and the spectral centroid of the previous time step, and take the absolute value of the difference as the frequency change.

[0047] The unit internally stores a preset threshold, which is determined based on statistical analysis of a large amount of historical operating data and expert experience: three times the standard deviation of frequency fluctuation under stable operating conditions is taken as the critical value; when the calculated frequency change is lower than this threshold, the system maintains low-power static model operation; when the change exceeds this threshold, the unit immediately triggers an interrupt mechanism, forcibly stopping the invocation of the preset, fixed static stiffness matrix, and instead activating the high-precision dynamic state space equation construction process; this design ensures that computing resources are accurately allocated to the moments when high-fidelity simulation is most needed.

[0048] By setting a clear logic for discriminating abrupt changes in the spectral centroid, the system achieves intelligent scheduling for on-demand modeling; it ensures computational efficiency under stable operating conditions and guarantees instantaneous switching to high-precision mode under non-stationary operating conditions, thus achieving an optimal balance between simulation accuracy and computational cost.

[0049] Example 3:

[0050] The construction of dynamic state-space equations is characterized by:

[0051] The spring stiffness coefficient and damping coefficient are defined as intrinsic state variables that evolve in real time with the geometric topology state variables, rather than preset constants, thereby establishing a three-dimensional dynamic mapping relationship between generalized coordinates, topological adjacency and physical parameters.

[0052] This unit innovates the way traditional physical laws are expressed. When establishing the mathematical model, it abandons the traditional practice of treating the spring stiffness coefficient and damping coefficient as constants obtained from looking up tables. This unit defines these two physical parameters as intrinsic state variables, that is, sets them as functions that change in real time with the geometric topology state variables of the system, thereby reflecting the nonlinear physical characteristics caused by configuration distortion. On this basis, this unit establishes a three-dimensional dynamic mapping relationship covering generalized coordinates, topological adjacency and physical parameters. With every tiny change in the geometric configuration during the simulation, the coefficient terms in the equation will evolve accordingly according to the preset nonlinear constitutive equation, without the need for external manual intervention or reset.

[0053] By internalizing physical parameters as state variables, this invention successfully captures the nonlinear physical nature of parameter evolution with configuration; this enables the model to accurately describe the essential changes in the stiffness characteristics of a spring when it undergoes complex deformations such as bending and folding, greatly improving the physical realism of the model when dealing with geometric nonlinear problems.

[0054] Example 4:

[0055] The geometry-driven physical logic in the topology-parameter bidirectional transient coupling engine specifically includes:

[0056] The system receives node displacement and rotation data and generalized velocity vectors in real time, and calculates the rate of change of geometric coordinates. When the rate of change exceeds the preset linear range, it determines that the configuration has undergone minor deformation or large-angle folding.

[0057] Based on the current degree of geometric distortion, the values ​​of the elements in the system stiffness matrix and damping matrix are updated instantaneously to reshape the energy dissipation path, thereby obtaining the transient stiffness / damping field matrix.

[0058] This embodiment aims to accurately map macroscopic geometric deformations into microscopic parameter fluctuations; the logic continuously receives system node displacement and rotation data from the previous time step and calculates the derivatives of these geometric coordinates with respect to time, i.e., the rate of change, in real time.

[0059] The nonlinear constitutive algorithm specifically performs the following mathematical operations: reads the degree of geometric distortion at the current time step, i.e., the relative rotation angle of the nodes. Call the pre-stored material hardening coefficient and damping nonlinear coefficient Material hardening coefficient With damping nonlinear coefficient The data is calibrated based on the physical tensile test data of the spring material, or pre-entered into the system database by the user according to the material property table; based on the formula and Simultaneously calculate the updated stiffness and damping values, where... , These are the initial stiffness and initial damping coefficient, respectively; , These are the updated stiffness matrix and damping matrix elements, respectively; The value in radians represents the relative rotation angle of the node. and The coefficients are dimensionless coefficients related to material properties; the calculation process is performed on all deformed nodes at each time step; the module immediately calls the preset nonlinear constitutive algorithm, using the current degree of geometric distortion as the independent variable, to recalculate and update each corresponding element in the system stiffness matrix and damping matrix; this process mathematically reshapes the energy dissipation path of the system, and the generated transient stiffness / damping field matrix is ​​a data set that accurately characterizes the additional mechanical properties caused by geometric distortion at the current moment;

[0060] This logic can capture and quantify the unidirectional driving effect of geometric nonlinearity on physical properties in real time. By updating matrix elements in real time, the system successfully simulates the stiffness strengthening or softening phenomenon caused by structural deformation in the real physical world, eliminating the simulation error caused by fixed parameters in traditional models.

[0061] Example 5:

[0062] The physical locking geometry logic in the topology-parameter bidirectional transient coupling engine specifically includes:

[0063] The magnitude of the transient internal force vector of each connection point, obtained based on dynamic calculations, is compared with the local locking threshold of the connection point, which serves as the critical force value for maintaining the flexible motion state of the connection structure.

[0064] When the magnitude of the transient internal force vector exceeds the local locking threshold of the connection point, the connection point is determined to enter a near-rigid state and a degree-of-freedom locking command is triggered.

[0065] In this embodiment, the system continuously monitors the potential restoring force of the locked node. When the calculated potential restoring force or relative motion trend is lower than the preset restoring threshold, a degree of freedom release command is triggered to release the rigid body merging state and restore the independent degree of freedom of the node, thereby forming a bidirectional switching logic with hysteresis characteristics. The above logic constitutes a key mechanism to prevent high-frequency vibration divergence. This logic performs dynamic calculations to calculate the magnitude and direction of the internal force borne by each connection point at the current instant, i.e., the transient internal force vector.

[0066] The logic compares the magnitude of the vector with a preset local locking threshold for each connection point. The local locking threshold is not the material's fracture limit, but a critical force value that characterizes the connection structure's ability to maintain its flexible motion characteristics. This value is set based on the physical test data of the connectors or the results of high-precision finite element analysis. When the transient internal force magnitude of a connection point exceeds this threshold, the system identifies that the node can no longer maintain a flexible response and has entered a high-frequency flutter-like rigid state. The logic immediately triggers a degree-of-freedom locking command, forcibly intervening in subsequent geometric calculations.

[0067] This reverse feedback control mechanism based on mechanical state endows the model with the ability to protect itself; by identifying and locking those nodes that bear overload internal forces, the system effectively curbs the accumulation and amplification of high-frequency noise in the numerical integration process, solving the industry pain point of difficult and easy divergence in solving rigid differential equations.

[0068] Example 6:

[0069] The specific execution method of the degree-of-freedom locking instruction is as follows:

[0070] By adding Lagrange multiplier constraints or directly performing matrix row and column reduction operations based on Gaussian elimination, the topological connection matrix of the system is forcibly modified, so that the associated nodes are merged into the same moving rigid body in the current time step, thereby temporarily freezing the relative motion degrees of freedom between the nodes.

[0071] This embodiment directly operates on the underlying mathematical model to achieve real-time reduction of computational dimensions. When the locking command is triggered, the system selects one of two execution paths based on the current computational resources and accuracy requirements: introduce Lagrange multiplier constraints into the equation system to add additional constraint equations to force the distance between two nodes to be constant; or directly perform matrix row elimination operation to merge the variables of related nodes in the stiffness matrix.

[0072] Regardless of the path taken, the result is a forced modification of the system's topology connection matrix, making two or more originally independent nodes appear as an indivisible moving rigid body in the current time step. This operation temporarily freezes the relative displacement and relative rotation degrees of freedom between nodes, eliminating the degree of freedom components that cause high-frequency oscillations.

[0073] This execution method provides an effective means of handling high-frequency rigid problems at the numerical level. By temporarily transforming the flexible connection of high-frequency oscillation into a rigid connection, it not only avoids the requirement of extremely small integration step size, but also significantly reduces the condition number of the stiffness matrix, thereby improving the solution efficiency and numerical stability of the linear equation system.

[0074] Example 7:

[0075] The order reduction processing logic of the adaptive order reduction manifold solver is as follows:

[0076] This embodiment is based on the geometric degrees of freedom locked by physical and mechanical states. It performs an adaptive order reduction operation at the mathematical solution level. By merging the nodal variables that are temporarily made rigid, it dynamically reduces the number of equations to be solved and reduces the condition number of the stiffness matrix without losing the flexibility accuracy.

[0077] Based on the determined locking state, an intelligent equation optimization strategy is executed; the unit scans the incoming topology state data and identifies those geometric degrees of freedom that are marked as locked.

[0078] Based on these markings, when assembling the dynamic equations, the unit no longer assigns solution variables to each node individually, but performs an adaptive order reduction operation: the group of nodes that have been physically merged into a rigid body is mathematically mapped to a single generalized coordinate variable; this process dynamically reduces the total number of differential equations to be solved; due to the elimination of the maximum stiffness term that leads to numerical instability, the condition number of the stiffness matrix is ​​significantly reduced, making the matrix more inclined to a benign state;

[0079] This order reduction logic enables dynamic management of computational complexity; it allows the system to automatically simplify calculations for locally stiffened regions while ensuring the accuracy of key flexible regions, thereby significantly shortening the computation time without sacrificing the overall simulation reliability and achieving millisecond-level parameter iteration for complex multibody systems.

[0080] Example 8:

[0081] A virtual sensing and state reconstruction unit, configured to mine data value using intermediate computational variables, is as follows:

[0082] Receive topology distortion data and parameter evolution history generated by the topology-parameter bidirectional transient coupling engine;

[0083] This embodiment uses the topological distortion data generated during the calculation process as a virtual sensing source, and performs reverse deduction based on the physical mapping relationship between the distortion degree of the parameterized topology and the internal stress to calculate the stress distribution state inside the physical system.

[0084] The output includes an enhanced simulation report containing the conventional dynamic response and the derived internal stress contour plot.

[0085] It serves as a module for extracting deep physical information; this unit does not directly participate in the forward iteration of dynamics, but is connected in parallel to the calculation process to receive topological distortion data and parameter evolution history from the coupling engine;

[0086] Using this data as a virtual sensing source, the unit runs a set of reverse physical deduction logic: through polynomial fitting or table lookup interpolation, based on the calibrated deformation-stress constitutive relationship that has been determined and stored in the database through offline high-precision finite element simulation calculations or physical experiments, the calculated degree of topological distortion is mapped back to the physical space to deduce the internal stress state required to cause the distortion; the unit visualizes this internal information that is difficult to measure directly through physical sensors and outputs an enhanced simulation report, which not only includes conventional displacement and velocity curves, but also overlays a dynamically evolving internal stress cloud map;

[0087] This design endows the simulation system with the ability to probe its internal state. Without increasing any hardware costs or physical intrusion, this invention successfully reconstructs the unmeasurable stress distribution inside the physical system by utilizing intermediate variables in the calculation process. This provides engineers with richer and more instructive structural health status assessment data than traditional black-box simulation, enhancing the engineering application value of the simulation.

[0088] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A parametric modeling system for spring damping, characterized in that, include: The excitation sensing and manifold initialization unit, as the input stage of the system, is used to deal with non-stationary operating conditions. It is configured to monitor external excitation signals in real time, and when a sudden change in the centroid of the signal is detected, it constructs a dynamic state space equation containing generalized coordinates, topological adjacency and physical parameter mapping relationship based on the current instantaneous geometric state of the system, thereby generating a dynamic topological state matrix. The topology-parameter bidirectional transient coupling engine, as the core unit for real-time interlocking of geometric configuration and physical properties, is configured to receive the dynamic topology state matrix, run geometry-driven physical logic, update the system stiffness and damping matrices based on the deformation degree of the geometric configuration through nonlinear constitutive mapping, and generate a transient stiffness / damping field matrix characterizing parasitic stiffness effects; then, it runs physical-locked geometry logic, solves for the transient internal force vectors of the connection points based on the transient stiffness / damping field matrix, compares the magnitude of the vector with the local locking threshold of the connection points, performs degree-of-freedom locking on over-limit nodes to modify the topology connection matrix, and generates reduced-order topology state data; The adaptive reduced-order manifold solving unit is configured to receive the reduced-order topology state data, identify the regions marked as locked and merge rigid node variables to dynamically reduce the dimension of the computation matrix, solve the system state response solution including displacement, velocity and acceleration, and transmit the solution back to the excitation sensing and manifold initialization unit as a feedback signal. The geometry-driven physical logic in the topology-parameter bidirectional transient coupling engine specifically includes: The system receives node displacement and rotation data in real time and calculates the rate of change of geometric coordinates. When the rate of change exceeds the preset linear range, it determines that the configuration has undergone minor deformation or large-angle folding. Based on the current degree of geometric distortion, the element values ​​in the system stiffness matrix and damping matrix are updated instantaneously to reshape the energy dissipation path, thereby obtaining the transient stiffness / damping field matrix. The physical locking geometry logic in the topology-parameter bidirectional transient coupling engine specifically includes: The magnitude of the transient internal force vector of each connection point, obtained based on dynamic calculations, is compared with the local locking threshold of the connection point, which serves as the critical force value for maintaining the flexible motion state of the connection structure. When the magnitude of the transient internal force vector exceeds the local locking threshold of the connection point, the connection point is determined to enter a near-rigid state and a degree-of-freedom locking command is triggered.

2. The spring damping parametric modeling system according to claim 1, characterized in that, The specific logic for determining spectral centroid mutations by the excitation sensing and manifold initialization unit is as follows: The change in the centroid of the external excitation signal's spectrum per unit time is calculated. If the change exceeds a preset threshold, it is determined that the system has entered a non-stationary operating condition. At this point, the preset static stiffness matrix is ​​stopped, and the process of constructing the dynamic state space equation is started instead.

3. The spring damping parametric modeling system according to claim 1, characterized in that, The construction of the dynamic state-space equations is characterized by: The spring stiffness coefficient and damping coefficient are defined as intrinsic state variables that evolve in real time with the geometric topology state variables, rather than preset constants, thereby establishing a three-dimensional dynamic mapping relationship between generalized coordinates, topological adjacency and physical parameters.

4. The spring damping parametric modeling system according to claim 1, characterized in that, The specific execution method of the degree-of-freedom locking instruction is as follows: By adding Lagrange multiplier constraints or directly performing matrix row and column reduction operations based on Gaussian elimination, the topological connection matrix of the system is forcibly modified, so that the associated nodes are merged into the same moving rigid body in the current time step, thereby temporarily freezing the relative motion degrees of freedom between the nodes.

5. The spring damping parametric modeling system according to claim 1, characterized in that, The order reduction processing logic of the adaptive order reduction manifold solving unit is as follows: Based on the geometric degrees of freedom locked by physical and mechanical states, an adaptive order reduction operation is performed at the mathematical solution level. By merging nodal variables that are temporarily made rigid, the number of equations to be solved and the condition number of the stiffness matrix are dynamically reduced without sacrificing flexibility accuracy.

6. The spring damping parametric modeling system according to claim 1, characterized in that, It also includes a virtual sensing and state reconstruction unit, which is used to mine data value by utilizing intermediate computational variables, and is configured to simultaneously receive topological distortion data and parameter evolution history generated by the topology-parameter bidirectional transient coupling engine. Using the topological distortion data generated during the calculation process as a virtual sensing source, the stress distribution state inside the physical system is calculated by performing inverse deduction based on the physical mapping relationship between the distortion degree of the parameterized topology and the internal stress. The output includes an enhanced simulation report containing the conventional dynamic response and the derived internal stress contour plot.

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