A spatio-temporal adaptive equipment digital twin physical field order reduction reconstruction method
By employing a spatiotemporally adaptive method for reducing the order of the physical field of a digital twin for equipment, and utilizing intrinsic orthogonal decomposition and radial basis functions to construct a global surrogate model, combined with multi-window greedy search and spatial partitioning residual enhancement surrogate model, the problem of real-time high-precision calculation of the physical field in heavy equipment manufacturing by digital twin systems is solved, and real-time high-precision prediction of the physical field of equipment such as forging hydraulic presses is realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-04-22
- Publication Date
- 2026-07-31
AI Technical Summary
In the manufacturing of heavy equipment, existing technologies, such as digital twin systems, cannot meet the real-time high-precision calculation requirements of physical fields under unsteady thermo-mechanical coupling conditions. In particular, during the processing of equipment such as forging hydraulic presses, the computational cost of finite element analysis is high and cannot be adaptively adjusted, resulting in insufficient prediction accuracy.
A spatiotemporally adaptive method for reconstructing the physical field of a digital twin of an equipment by reducing its order is adopted. A global surrogate model is constructed by intrinsic orthogonal decomposition and radial basis functions. Combined with multi-window greedy search and spatial partitioning residual enhancement surrogate model, real-time high-precision prediction of the physical field is achieved.
It enables millisecond-level real-time solution and visualization of physical fields during the processing of equipment such as forging hydraulic presses, improving the prediction accuracy of key time intervals and spatial regions, and meeting the real-time high-precision calculation requirements of digital twin systems.
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Figure CN122088301B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of numerical simulation technology, and in particular to a spatiotemporally adaptive method for reconstructing the physical field of a digital twin of an equipment by reducing its order. Background Technology
[0002] In the field of heavy equipment manufacturing, during the processing of core equipment such as forging hydraulic presses, forgings and other processed objects undergo complex thermo-mechanical coupling deformation, with their physical fields such as temperature, stress, and displacement continuously evolving in time and space. Digital twin technology, by constructing a virtual mirror model of the physical entity and integrating sensor data and simulation data, achieves real-time mapping and feedback of the physical state, and is one of the core technologies for intelligent management and control of heavy equipment.
[0003] To fully characterize the spatial distribution of multiple physical properties of a processed object, the finite element method (FEM) is typically used to simulate and analyze the physical field. However, the computational cost of FEM increases dramatically with model size and coupling complexity, with single solutions taking minutes to hours, failing to meet the real-time requirements of digital twin systems for millisecond-level physical field responses. Furthermore, the internal physical quantities of the object are difficult to measure directly during processing, and only local information can be obtained through a limited number of sensors.
[0004] Existing model order reduction methods based on intrinsic orthogonal decomposition combined with radial basis functions mostly use a single global model to approximate the system. These methods cannot adapt to the spatiotemporal non-uniform evolution characteristics of the physical field under unsteady thermo-coupling conditions. They suffer from insufficient prediction accuracy in key time intervals and spatial regions and cannot adaptively adjust the modeling strategy, making it difficult to meet the real-time high-precision calculation requirements of digital twin systems for physical fields. Summary of the Invention
[0005] The purpose of this application is to provide a spatiotemporally adaptive method for reducing the order of physical field reconstruction in equipment digital twins. This method can improve the prediction accuracy of key time intervals and spatial regions under unsteady thermo-coupling conditions while ensuring the real-time performance of physical field solutions, thus meeting the application requirements of equipment digital twin systems.
[0006] To achieve the above objectives, this application provides the following solution: A spatiotemporally adaptive method for reducing the order of physical field reconstruction of a digital twin of an equipment includes the following steps: Based on the finite element simulation sample dataset of physical fields, the intrinsic orthogonal decomposition method is used to perform order reduction processing on the high-dimensional physical field data, extract the dominant mode basis, and generate low-dimensional coefficient representations.
[0007] Using normalized operating parameters and time as inputs and intrinsic orthogonal decomposition coefficients as outputs, a mapping relationship between inputs and outputs is established using radial basis functions to construct a global proxy model for the physical field.
[0008] The prediction error of the global proxy model of the physical field is analyzed in terms of its time dimension distribution characteristics. A multi-window greedy search strategy is used to identify the high error time intervals, and a time-segmented adaptive proxy model is constructed based on the sample data in the high error time intervals.
[0009] Spatial dimension distribution feature analysis is performed on the prediction error of the global surrogate model of the physical field. Based on the error significance index, the physical field space is divided into multiple sub-regions. Based on the prediction residuals of each sub-region, a spatial partition residual enhanced surrogate model is constructed.
[0010] The time-segmented adaptive proxy model and the spatial partitioned residual enhancement proxy model are cascaded and integrated to generate a spatiotemporal joint adaptive proxy model. This model is used to solve for and output the physical field distribution data of the target equipment processing object based on real-time operating condition parameters.
[0011] Optionally, the physical field finite element simulation sample dataset is obtained through the following steps: establishing a thermo-mechanical coupled finite element analysis model based on the process parameters of the target equipment, determining the working condition parameter space and performing sampling operations to generate the physical field finite element simulation sample dataset; the physical field finite element simulation sample dataset includes the working condition parameters and corresponding physical field data of the entire processing of the target equipment.
[0012] The operating parameters include the downward pressure speed of the target equipment and the initial temperature of the workpiece; the operating parameter space is the Cartesian product space of the range of downward pressure speed and the range of the initial temperature of the workpiece; the sampling operation adopts the Latin hypercube sampling method combined with the maximum and minimum distance criterion.
[0013] Optionally, based on the finite element simulation sample dataset of the physical field, the intrinsic orthogonal decomposition method is used to perform order reduction processing on the high-dimensional physical field data, extract the dominant modal basis, and generate a low-dimensional coefficient representation. Specifically, this includes the following steps: The physical field data at each time step in the finite element simulation sample dataset are expanded into column vectors according to the node number, and a snapshot matrix is constructed.
[0014] Perform singular value decomposition on the snapshot matrix, determine the mode cutoff number based on the cumulative energy proportion criterion, and retain the number of dominant modes corresponding to the mode cutoff number to form the eigenorthogonal decomposition basis matrix.
[0015] Physical field data are converted into low-dimensional coefficient representations under the corresponding eigenorthogonal decomposition basis matrix through orthogonal projection.
[0016] Optionally, the physical layer global proxy model is a radial basis function interpolation model; using normalized operating parameters and time as inputs and intrinsic orthogonal decomposition coefficients as outputs, a mapping relationship between inputs and outputs is established using radial basis functions to construct the physical field global proxy model, specifically including the following steps: The normalized operating parameters and time are subjected to minimum-maximum normalization to generate a normalized input vector.
[0017] A mapping model from operating parameters to intrinsic orthogonal decomposition coefficients is established using radial basis functions, resulting in a radial basis function interpolation model.
[0018] A system of linear equations is established based on the interpolation conditions. Solving the system of linear equations yields the interpolation weights of the radial basis function interpolation model. The radial basis function interpolation model is used to calculate the predicted values of the intrinsic orthogonal decomposition coefficients based on the input operating parameters. The physical field prediction data is obtained by reconstructing the intrinsic orthogonal decomposition basis matrix.
[0019] Optionally, a time-dimensional distribution feature analysis is performed on the prediction error of the global proxy model of the physical field. A multi-window greedy search strategy is used to identify high-error time intervals, and a time-segmented adaptive proxy model is constructed based on the sample data within the high-error time intervals. Specifically, this includes the following steps: The error energy of the global proxy model of the physical field at each time step is calculated to obtain the error energy time series and the total error energy in the entire time domain.
[0020] Gaussian smoothing is applied to the error energy time series, and the maximum and minimum points of the smoothed series are detected. The entire time domain is divided into multiple independent time regions with the minimum points as the boundary.
[0021] In each independent time region, a minimum energy coverage window search is performed starting from the peak value of the error energy to determine the set of high error time windows.
[0022] Local snapshot data are extracted within each high-error time window to construct a local intrinsic orthogonal decomposition basis and local radial basis function mapping model. A time decay function is introduced at the end boundary of the high-error time window to achieve a smooth transition of the model prediction results. Each local radial basis function mapping model constitutes a time-segmented adaptive surrogate model.
[0023] Optionally, spatial dimension distribution feature analysis is performed on the prediction error of the global surrogate model of the physical field. Based on the error significance index, the physical field space is divided into multiple sub-regions. Based on the prediction residuals of each sub-region, a spatial partitioned residual enhanced surrogate model is constructed, which specifically includes the following steps: Divide the workpiece into multiple equidistant spatial sub-regions along its height direction, and calculate the average prediction error of nodes within each spatial sub-region.
[0024] Based on the average prediction error of the entire region, the error significance index of each spatial sub-region is calculated.
[0025] Based on the numerical range of the error significance index, the physical field space is divided into a high error region, a transition region, and a low error region.
[0026] The prediction residuals of the high error region and the transition region are extracted separately, and the residual intrinsic orthogonal decomposition basis and residual radial basis function mapping model of the corresponding region are constructed. Each residual radial basis function mapping model constitutes a spatial partition residual enhancement surrogate model. In the prediction stage, the corresponding spatial enhancement coefficient is matched according to the spatial sub-region to which the node belongs, and the residual correction amount is superimposed to generate the final prediction value.
[0027] Optionally, the region with an error significance index greater than 2 is the high error region, the region with an error significance index greater than 1.5 and less than or equal to 2 is the transition region, and the region with an error significance index less than or equal to 1.5 is the low error region; the spatial enhancement coefficient of the high error region is 1.0, the spatial enhancement coefficient of the transition region is 0.5, and the spatial enhancement coefficient of the low error region is 0.
[0028] Optionally, the cascaded integration process adopts a time-first, spatially nested hierarchical structure, and only enables the spatial partitioning residual enhancement surrogate model within the high-error time interval.
[0029] Optionally, the digital twin system performs a visualization operation of the physical field distribution based on the solved physical field distribution data and the coordinates of the grid model nodes.
[0030] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a spatiotemporally adaptive method for physical field reduction and reconstruction in equipment digital twins. Firstly, based on a finite element simulation sample dataset of the physical field, the intrinsic orthogonal decomposition method is used to reduce the order of the high-dimensional physical field data, extracting the dominant mode basis and generating a low-dimensional coefficient representation. Next, using normalized operating parameters and time as inputs and intrinsic orthogonal decomposition coefficients as outputs, a radial basis function is used to establish a mapping relationship between the input and output, constructing a global proxy model of the physical field. This achieves a rapid mapping from operating parameters to the physical field distribution, replacing time-consuming finite element iterative calculations and initially meeting the real-time requirements of digital twin systems for physical field solving. After obtaining the global proxy model of the physical field, the temporal dimension distribution characteristics of the prediction error of the global proxy model are first analyzed. A multi-window greedy search strategy is used to identify high-error time intervals. Then, the spatial dimension distribution characteristics of the prediction error of the global proxy model are analyzed. Based on the error significance index, the physical field space is divided into multiple sub-regions, and a spatial partitioning residual enhancement proxy model is constructed. Subsequently, the spatiotemporal joint adaptive proxy model balances prediction accuracy and computational overhead through a time-priority, spatially nested hierarchical structure, achieving high-precision spatiotemporal fitting of the physical field under unsteady thermo-coupling conditions. Finally, it is deployed in the digital twin system of the target equipment. Based on the real-time operating condition parameters, the physical field distribution data of the target equipment processing object is solved and output, realizing millisecond-level real-time solution and visualization of the physical field during the processing, meeting the core application requirements of the heavy equipment digital twin system for real-time high-precision mapping of the physical field. Attached Figure Description
[0031] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0032] Figure 1 A flowchart illustrating a spatiotemporally adaptive method for reconstructing the physical field of a digital twin of an equipment using physical field reduction, provided as an embodiment of this application.
[0033] Figure 2 This is a schematic diagram of the multi-window greedy time segmentation process in a spatiotemporally adaptive equipment digital twin physics field order reduction reconstruction method provided in an embodiment of this application.
[0034] Figure 3 This is a schematic diagram illustrating the spatial distribution characteristics analysis and spatial partitioning process of error energy in a spatiotemporally adaptive equipment digital twin physical field order reduction and reconstruction method provided in an embodiment of this application.
[0035] Figure 4This is a schematic diagram of the prediction process of a spatiotemporally adaptive proxy model in a spatiotemporally adaptive equipment digital twin physical field order reduction reconstruction method provided in an embodiment of this application.
[0036] Figure 5 This is a displacement field distribution diagram of a forging at a certain moment under typical working conditions in a spatiotemporally adaptive equipment digital twin physical field order reduction reconstruction method provided in an embodiment of this application. Detailed Implementation
[0037] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0038] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0039] This application provides a spatiotemporally adaptive method for reducing the order of physical field reconstruction in a digital twin of equipment. In an exemplary embodiment, the hot forging process of a forging hydraulic press is used as a specific application scenario. Figure 1 As shown, it includes the following steps: S1. Establish a thermo-mechanical coupled finite element analysis model based on the process parameters of the target equipment, determine the operating condition parameter space, perform sampling operations, and generate a physical field finite element simulation sample dataset. The physical field finite element simulation sample dataset includes the operating condition parameters and corresponding physical field data for the entire processing of the target equipment.
[0040] First, based on the hot forging process parameters of the forging hydraulic press, a thermo-structural coupled finite element analysis model of the forging is established. The mesh generation of the model remains consistent under all subsequent operating conditions to ensure a constant node spatial distribution. The process parameters that play a dominant role in the evolution of the forging's physical field are selected as operating parameters, specifically the downward pressing speed of the forging hydraulic press. With the initial temperature of the forging The working parameter space is defined as the Cartesian product space of the range of downward pressing speed and the range of the initial temperature of the workpiece, i.e. ,in The range of values for the downward pressure speed. This represents the minimum downward pressure speed. This represents the maximum downward pressure speed. The range of values for the initial temperature of the forging. This represents the minimum initial temperature of the forging. This represents the maximum initial temperature of the forging. In this embodiment, the pressing speed... The value range is 1500mm / s~2200mm / s, and the initial temperature of the forging is... The value range is 850℃~950℃.
[0041] The Latin hypercube sampling method was used for initial sampling in the aforementioned working condition parameter space. The initial samples were augmented using the maximum-minimum distance criterion to improve the uniformity of parameter space coverage under finite sample conditions, ultimately obtaining 25 sets of working condition samples. Of these, 20 sets were used as the training set for model construction, and 5 sets were used as the test set for verifying the model's generalization ability. Thermal-structural coupled parametric simulations were performed on the 25 sets of working condition sampling points in finite element analysis software to obtain the displacement and temperature field data of the forging at each time step throughout the entire processing process under each working condition. All data were aligned by node number and time step to form a physical field finite element simulation sample dataset.
[0042] S2. Based on the finite element simulation sample dataset of the physical field, the intrinsic orthogonal decomposition method is used to perform order reduction processing on the high-dimensional physical field data, extract the dominant mode basis, and generate a low-dimensional coefficient representation. Step S2 specifically includes the following steps: S21. Expand the physical field data of each time step in the physical field finite element simulation sample dataset into column vectors according to the node number, and construct a snapshot matrix.
[0043] Given a finite element model containing There are nodes, with a total of Each working condition sample contains [number] working conditions. If there are 1 time step, then the total number of snapshots is 1. For vector fields such as displacement fields, the dimension of each snapshot is... For scalar fields such as temperature fields, the dimension of each snapshot is... The physical fields at each time step are expanded into column vectors according to the node number, and all snapshots are organized into a snapshot matrix. , R It is the field of real numbers.
[0044] S22. Perform singular value decomposition on the snapshot matrix, determine the mode cutoff number based on the cumulative energy proportion criterion, and retain the number of dominant modes corresponding to the mode cutoff number to form the eigenorthogonal decomposition basis matrix. Then, perform the snapshot matrix according to the following formula... S Perform singular value decomposition: in, The column vectors are left singular vectors, forming an orthogonal basis of the physical field, namely the eigenorthogonal decomposition modes; It is a diagonal matrix, and the diagonal elements are singular values arranged in descending order, reflecting the magnitude of the physical field energy captured by each mode; The column vectors are right singular vectors. The modal cutoff number is determined according to the cumulative energy percentage criterion shown below. K : .
[0045] in, This is a function of cumulative energy percentage. Let be the rank of the snapshot matrix. The first one after singular value decomposition, sorted in descending order i A singular value, Reflecting the i The physical field energy captured by each mode, The set energy threshold.
[0046] Before keeping K The dominant modes constitute the eigenorthogonal decomposition basis matrix. The truncated eigenorthogonal decomposition basis matrix is: .
[0047] Among them, modal truncation number K much smaller N This achieves dimensionality reduction of high-dimensional physical fields, where Φ is the eigenorthogonal decomposition (POD) basis matrix. For length is N The column vectors are the dominant mode basis vectors.
[0048] S23. Convert the physical field data into a low-dimensional coefficient representation under the corresponding eigenorthogonal decomposition basis matrix through orthogonal projection.
[0049] An arbitrary physical field snapshot can be approximated as: , This is the POD coefficient vector corresponding to this snapshot. a i The first of the POD coefficient vectors i Each component can be obtained through orthogonal projection: .
[0050] in, For the transpose of the basis matrix Φ, S This is a snapshot of the physical field. The equation projects the original physical field snapshot S onto a low-dimensional space defined by basis vectors, thus requiring only a very small number of coefficient vectors to be processed. a The eigenorthogonal decomposition basis matrix Φ and the low-dimensional coefficient vector obtained in this step a This will serve as input for subsequent steps.
[0051] S3. Using the normalized operating parameters and time as input and the intrinsic orthogonal decomposition coefficients as output, a mapping relationship between the input and output is established using radial basis functions to construct a global proxy model of the physical field. Step S3 specifically includes the following steps: S31. Perform minimum-maximum normalization on the normalized operating parameters and time to generate a normalized input vector. For each input parameter (time... t Downward pressure speed With the initial temperature of the forging The input vector is then normalized, and the normalized input vector is... . For normalized time, The initial temperature of the forging after normalization. This represents the normalized downward pressure velocity.
[0052] S32. A mapping model from the operating parameters to the intrinsic orthogonal decomposition coefficients is established using radial basis functions (RBFs), resulting in a radial basis function interpolation model. In this embodiment, the radial basis function interpolation model is the global proxy model for the physical field. The basic idea of using radial basis functions (RBFs) to establish the mapping model from the operating parameters to the intrinsic orthogonal decomposition coefficients is to represent the objective function as a weighted superposition of a set of radial basis functions centered at the sample points. For the... i Each POD coefficient component Its interpolation model is ,in, N S The number of working condition samples in the training set. P j For the first j The vector of operating parameters for each sample, and the vector of POD coefficients corresponding to a certain time step are: ; Operating parameters P The corresponding number i One predicted value for the POD coefficient, The interpolation weights to be solved are... Let || be the radial basis function and || be the Euclidean distance. In this embodiment, the radial basis function is selected as the thin plate spline kernel function, which does not require manual setting of shape parameters and has optimal smoothness properties.
[0053] S33. Establish a system of linear equations based on the interpolation conditions, solve the system of linear equations to obtain the interpolation weights of the radial basis function interpolation model; the radial basis function interpolation model is used to calculate the predicted values of the intrinsic orthogonal decomposition coefficients based on the input working parameters, and the physical field prediction data is obtained by reconstructing the intrinsic orthogonal decomposition basis matrix.
[0054] A system of linear equations is established using interpolation conditions, and all interpolation weights are obtained by solving it. Complete the construction of the global proxy model.
[0055] During the operating condition response inference phase, for the new operating condition parameters First, calculate the predicted values of the intrinsic orthogonal decomposition coefficients. The physical field is then reconstructed by decomposing the basis matrices using eigenorthogonal decomposition. .
[0056] S4. Perform time dimension distribution characteristic analysis on the prediction error of the global proxy model of the physical field, adopt a multi-window greedy search strategy to identify the high error time interval, and construct a time segmented adaptive proxy model based on the sample data in the high error time interval.
[0057] like Figure 2 As shown, due to the unsteady-state characteristics of the forging process, the prediction error of the global surrogate model exhibits a significant non-uniform distribution over time. The error is higher in the initial stage when the anvil establishes contact with the high-temperature forging, lower in the middle stage when the forging is stable, and rises again in the final stage, exhibiting a multi-peak distribution. In this embodiment, step S4 specifically includes the following steps: S41. Calculate the error energy of the global proxy model of the physical field at each time step to obtain the error energy time series and the total error energy in the entire time domain.
[0058] The global proxy model constructed in step S3 is used to predict all working condition samples in the training set, and the prediction error at each time step t is calculated. The error energy at time step t is defined. Calculate the total error energy over the entire time domain by summing the squares of the prediction errors for all nodes at that time step. .
[0059] S42. Perform Gaussian smoothing on the error energy time series, detect the maxima and minima of the smoothed series, and divide the entire time domain into multiple independent time regions using the minima as boundaries. Each region contains a major error peak. The set of maxima is... , For the first p The set of local maxima and minima is . , For the first p A minimum point, p =1,2,…, P The time domain is divided into sections with the minimum point as the boundary. P Each is a separate region. (Denotes as follows) ,in, R p For the first p Each independent time zone.
[0060] S43. Within each independent time region, perform a minimum energy coverage window search starting from the peak error energy to determine the set of high-error time windows. The minimum energy coverage window search algorithm is as follows: Calculate the region... R p energy E p and target energy , q Given an energy coverage threshold, initialize the window boundaries. , The current search term is p The left boundary (starting time) of a high-error time window. The current search term is p The right boundary (end time) of a high-error time window. For the first p Each maximum point (error peak), cumulative energy ;when Calculate the left extension gain. and right extension gain The direction with the largest gain is selected for expansion, and the accumulated energy is updated until the energy coverage condition is met. The obtained window Add to high error time window set .
[0061] The goal of the minimum energy coverage window algorithm is to achieve the minimum energy coverage window given a minimum energy coverage threshold. q Under the premise of finding the time range Make the window length The smallest and satisfying the following formula: .
[0062] In the formula, The proportion of window error energy. For a moment t The error signal, t a and t b These are the start and end points of the window, respectively. The total energy of the error over the entire time range. q This is the preset energy coverage threshold.
[0063] S44. Extract corresponding local snapshot data within each high-error time window and construct a local intrinsic orthogonal decomposition basis and local radial basis function mapping model. Within each high-error time window, extract physical field snapshots of all operating conditions in the training set within that time window to form a local snapshot matrix. Perform singular value decomposition on the local snapshot matrix to extract the local intrinsic orthogonal decomposition basis and increase the number of modes to capture more details of physical field changes. Using operating condition parameters and time as inputs and local coefficients as outputs, establish a local radial basis function mapping model. Each local radial basis function mapping model constitutes a time-segmented adaptive surrogate model.
[0064] In each high error time window Within this time window, physical field snapshots of all operating conditions in the training set are extracted to form a local snapshot matrix. Singular value decomposition is performed on the local snapshot matrix to extract the local eigenorthogonal decomposition basis. A local radial basis function mapping model is established using operating parameters and time as inputs and local coefficients as outputs.
[0065] Furthermore, a time decay function is introduced at the end boundary of the high-error time window to achieve a smooth transition of the model's prediction results. The time decay function is as follows: .
[0066] In the formula, Let be the time decay function. For high error window The right boundary, The length of the decay interval, i.e., if it exists , making Then take A time decay function is introduced to achieve a smooth transition, so that the effect of the piecewise model gradually weakens after the high error window ends, avoiding abrupt changes in the prediction results at the time boundary.
[0067] S5. Perform spatial dimension distribution characteristic analysis on the prediction error of the global surrogate model of the physical field. Based on the error significance index, divide the physical field space into multiple sub-regions, and construct a spatial partitioned residual enhanced surrogate model based on the prediction residuals of each sub-region. Step S5 specifically includes the following steps: S51. Divide the workpiece into multiple equidistant spatial sub-regions along its height direction, and calculate the average prediction error of nodes within each spatial sub-region. .like Figure 3 As shown, the forging is divided into several spatial regions along the height direction. A surrogate model is used for training, and the average prediction error of the nodes in each region is statistically analyzed.
[0068] S52. Using the global average prediction error as a benchmark, calculate the error significance index for each spatial sub-region. Based on this, define the significance index of error for each region. .
[0069] S53. Based on the numerical range of the error significance index, the physical field space is divided into a high-error region, a transition region, and a low-error region. The space is divided into three types of regions based on the error significance index: High error region , Transition zone , Low error zone .
[0070] S54. Extract the prediction residuals of the high error region and the transition region respectively, and construct the residual intrinsic orthogonal decomposition basis and residual radial basis function mapping model of the corresponding region; each residual radial basis function mapping model constitutes a spatial partition residual enhancement surrogate model.
[0071] This embodiment employs a spatial partitioning proxy modeling method based on residual enhancement, rather than constructing independent partitioning models for different spatial regions. This is because independent partitioning modeling would result in independent eigenorthogonal decomposition bases for each region, lacking coupling relationships and disrupting the spatial continuity of the physical field. The core idea of residual enhancement is to construct a secondary correction model for prediction bias in high-error regions within a unified order reduction framework. This model achieves local accuracy improvement through residual superposition while maintaining the overall consistency of the physical field.
[0072] Extracting surrogate models in the high error region The prediction residuals of all nodes constitute the residual snapshot matrix in the high error region. The intrinsic orthogonal decomposition is performed to extract the dominant modes of the residuals and construct the residual basis. Calculate the projection coefficients of each residual snapshot under this basis, and establish a residual radial basis function mapping model for the high error region. For the transition region... Construct the transition region residual basis using the same method. The number of modes retained in the transition region is less than that in the high error region when mapped to the residual radial basis function model.
[0073] Specifically, the predicted residuals are calculated according to the following formula. : .
[0074] In the formula, For the proxy model to the first s Group working conditions, first t The predicted physical field values at the time step; These are the corresponding finite element simulation values.
[0075] For the high error region Extract the residual components corresponding to all degrees of freedom within this region to form a local residual vector. Arrange the local residual vectors of all operating conditions in the training set at each time step within the target time window in columns to form a residual snapshot matrix for the high error region. : .
[0076] In the formula, For the degrees of freedom in the high error region, This represents the total number of snapshots in the high-error region.
[0077] For the transition region Constructing the residual snapshot matrix : .
[0078] in, The number of degrees of freedom in the transition region. This represents the total number of snapshots in the transition region.
[0079] For the residual matrix in the high error region Perform singular value decomposition and retain the first... The dominant modes constitute the residual basis. The projection coefficients of each residual snapshot under this basis are calculated, and a residual RBF interpolation model for the high error region is established. This represents the number of residual modes to be truncated in the high error region. This is the residual basis matrix in the high error region.
[0080] During the prediction phase, spatial enhancement coefficients are matched according to the spatial sub-region to which a node belongs, and residual corrections are added to generate the final predicted value. For nodes in high error regions... The final predicted value is ,in For high error region enhancement coefficients; for transition region nodes The final predicted value is ,in For the transition region enhancement coefficient; for nodes in the low error region Direct output . In order to be in t The time-based proxy model for nodes i The predicted values of the physical field.
[0081] Specifically, in this embodiment, the region with an error significance index greater than 2 is the high error region, the region with an error significance index greater than 1.5 and less than or equal to 2 is the transition region, and the region with an error significance index less than or equal to 1.5 is the low error region; the spatial enhancement coefficient of the high error region is 1.0, the spatial enhancement coefficient of the transition region is 0.5, and the spatial enhancement coefficient of the low error region is 0.
[0082] S6. The time-segmented adaptive proxy model and the spatial partitioned residual enhancement proxy model are cascaded and integrated to generate a spatiotemporal joint adaptive proxy model. This framework adopts a hierarchical structure of time priority and spatial nesting. First, it divides the time period into high-error and low-error time periods according to the time dimension; then, a spatial adaptive mechanism is introduced only in the high-error time period, determining whether to superimpose residual correction based on the spatial region to which the node belongs. That is, the spatial partitioned residual enhancement proxy model is only activated in the high-error time interval.
[0083] like Figure 4 As shown, for given operating parameters and time steps, the model first determines whether the current time step belongs to a high-error period. If not, it directly calls the global model to output the prediction result; if it belongs to a high-error period, it calls the time-segmented local model for prediction and further determines the spatial region to which each node belongs. For nodes in low-error spatial regions, the segmented model prediction value is directly output; for nodes in high-error spatial regions, the residual correction is superimposed on the segmented model prediction. Within the decay interval after the high-error time window ends, the effects of the segmented model and residual correction are gradually transitioned to the global model through a time decay function.
[0084] Spatiotemporal joint adaptive proxy model for nodes i At time step t The final predicted value is: when hour, ;when hour, ;when hour, ;when hour, In the formula and These are the global model and piecewise model predictions for node i at time step t, respectively. This is the correction amount for spatial residual prediction; It is a time decay function; For nodes i Spatial enhancement coefficient.
[0085] S7. Deploy the spatiotemporal joint adaptive proxy model on the digital twin system of the target equipment. Based on the input of real-time operating parameters, solve and output the physical field distribution data of the target equipment's processing object. The digital twin system performs a visualization operation of the physical field distribution based on the solved physical field distribution data and the coordinates of the grid model nodes.
[0086] In this embodiment, during the online operation phase, real-time operating parameters (pressing speed and initial temperature of the forging) are input into the surrogate model. The surrogate model solves in real time to obtain the displacement field distribution of the forging at each time step under the current operating conditions, such as... Figure 5 As shown, the digital twin system records the spatial coordinates of each node in the mesh model. Based on the solved physical field distribution and the spatial coordinates of the corresponding nodes, the physical field is fitted in real time, and the physical quantities are mapped to color vectors to achieve visualization output, thereby realizing real-time simulation and visualization of the physical field of the forging during the forging process.
[0087] The spatiotemporally adaptive physical field reduction and reconstruction method for equipment digital twins provided in the above embodiments of this application achieves rapid low-dimensional solution of high-dimensional physical fields by constructing a global proxy model through intrinsic orthogonal decomposition combined with radial basis functions, ensuring the real-time requirements of the digital twin system. It solves the problem of insufficient representation of unsteady transient features by the global model through a multi-window greedy search strategy to adaptively identify high-error time intervals and construct local segmented models, significantly improving the prediction accuracy of key time stages. Through error saliency partitioning and residual enhancement methods, it achieves accuracy correction in local high-error regions within a unified reduction framework, avoiding the problem of physical field continuity disruption caused by independent partitioning modeling. It adopts a time-first, spatially nested cascaded framework, introducing a spatial adaptive mechanism only during high-error time periods, controlling computational overhead while ensuring accuracy improvement, achieving a balance between accuracy and efficiency, and fully meeting the real-time high-precision calculation requirements of heavy equipment digital twin systems.
[0088] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0089] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A spatiotemporally adaptive method for reconstructing the physical field of a digital twin of equipment by reducing its order, characterized in that, include: Based on the finite element simulation sample dataset of physical fields, the intrinsic orthogonal decomposition method is used to perform order reduction processing on the high-dimensional physical field data, extract the dominant mode basis and generate a low-dimensional coefficient representation; Using the normalized operating parameters and time as inputs and the intrinsic orthogonal decomposition coefficients as outputs, a mapping relationship between the input and output is established using radial basis functions to construct a global proxy model for the physical field. The prediction error of the global proxy model of the physical field is analyzed in terms of its temporal dimension distribution characteristics. A multi-window greedy search strategy is used to identify high error time intervals, and a time-segmented adaptive proxy model is constructed based on the sample data in the high error time intervals. Spatial dimension distribution feature analysis is performed on the prediction error of the global proxy model of the physical field. Based on the error significance index, the physical field space is divided into multiple sub-regions. Based on the prediction residuals of each sub-region, a spatial partition residual enhanced proxy model is constructed. The time-segmented adaptive proxy model and the spatial partitioned residual enhancement proxy model are cascaded and integrated to generate a spatiotemporal joint adaptive proxy model. The spatiotemporal joint adaptive proxy model is used to solve and output the physical field distribution data of the target equipment processing object based on the real-time working condition parameters. The cascaded integration process adopts a time-first, spatially nested hierarchical structure, and the spatial partitioned residual enhancement proxy model is only activated in the high-error time interval. The prediction error of the global proxy model of the physical field is analyzed for its temporal distribution characteristics. A multi-window greedy search strategy is used to identify high-error time intervals, and a time-segmented adaptive proxy model is constructed based on the sample data within the high-error time intervals. Specifically, this includes: Calculate the error energy of the global proxy model of the physical field at each time step to obtain the error energy time series and the total error energy in the entire time domain; Gaussian smoothing is applied to the error energy time series, and the maximum and minimum points of the smoothed series are detected. The entire time domain is divided into multiple independent time regions with the minimum points as the boundary. In each independent time region, a minimum energy coverage window search is performed starting from the error energy peak to determine the set of high error time windows; Local snapshot data are extracted within each high-error time window to construct a local intrinsic orthogonal decomposition basis and local radial basis function mapping model. A time decay function is introduced at the end boundary of the high-error time window to achieve a smooth transition of the model prediction results. Each local radial basis function mapping model constitutes a time-segmented adaptive surrogate model.
2. The spatio-temporally adaptive equipment digital twin physics field order reduction reconstruction method of claim 1, wherein, The physical field finite element simulation sample dataset is obtained through the following steps: establishing a thermo-mechanical coupled finite element analysis model based on the process parameters of the target equipment, determining the working condition parameter space and performing sampling operations to generate the physical field finite element simulation sample dataset; the physical field finite element simulation sample dataset includes the working condition parameters and corresponding physical field data of the entire processing of the target equipment; The operating parameters include the downward pressure speed of the target equipment and the initial temperature of the workpiece; the operating parameter space is the Cartesian product space of the range of downward pressure speed and the range of the initial temperature of the workpiece; the sampling operation is performed using the Latin hypercube sampling method combined with the maximum-minimum distance criterion.
3. The spatio-temporally adaptive equipment digital twin physics field order reduction reconstruction method of claim 1, wherein, Based on the finite element simulation sample dataset of physical fields, the intrinsic orthogonal decomposition method is used to reduce the order of high-dimensional physical field data, extract the dominant modal basis, and generate low-dimensional coefficient representations. Specifically, this includes: Expand the physical field data of each time step in the physical field finite element simulation sample dataset into column vectors according to the node number, and construct a snapshot matrix; Perform singular value decomposition on the snapshot matrix, determine the mode cutoff number according to the cumulative energy ratio criterion, and retain the number of dominant modes corresponding to the mode cutoff number to form the intrinsic orthogonal decomposition basis matrix; Physical field data are converted into low-dimensional coefficient representations under the corresponding eigenorthogonal decomposition basis matrix by orthogonal projection.
4. The spatio-temporally adaptive equipment digital twin physics field order reduction reconstruction method of claim 1, wherein, The global proxy model for the physical field is a radial basis function interpolation model. Using normalized operating parameters and time as inputs and intrinsic orthogonal decomposition coefficients as outputs, a mapping relationship between the input and output is established using radial basis functions to construct the global proxy model for the physical field. Specifically, it includes: The normalized operating parameters and time are subjected to minimum-maximum normalization to generate a normalized input vector; A mapping model from operating parameters to intrinsic orthogonal decomposition coefficients is established using radial basis functions, resulting in a radial basis function interpolation model. A system of linear equations is established based on the interpolation conditions. The interpolation weights of the radial basis function interpolation model are obtained by solving the system of linear equations. The radial basis function interpolation model is used to calculate the predicted values of the intrinsic orthogonal decomposition coefficients based on the input operating parameters. The physical field prediction data is obtained by reconstructing the intrinsic orthogonal decomposition basis matrix.
5. The spatio-temporally adaptive equipment digital twin physics field order reduction reconstruction method of claim 1, wherein, Spatial dimension distribution feature analysis is performed on the prediction error of the global surrogate model of the physical field. Based on the error significance index, the physical field space is divided into multiple sub-regions. Based on the prediction residuals of each sub-region, a spatial partitioned residual enhanced surrogate model is constructed, specifically including: Divide the workpiece into multiple equidistant spatial sub-regions along its height direction, and calculate the average prediction error of nodes within each spatial sub-region. Based on the average prediction error of the entire region, the error significance index of each spatial sub-region is calculated; Based on the numerical range of the error significance index, the physical field space is divided into a high error region, a transition region, and a low error region. The prediction residuals of the high error region and the transition region are extracted separately, and the residual intrinsic orthogonal decomposition basis and residual radial basis function mapping model of the corresponding region are constructed. Each residual radial basis function mapping model constitutes a spatial partition residual enhancement surrogate model. In the prediction stage, the corresponding spatial enhancement coefficient is matched according to the spatial sub-region to which the node belongs, and the residual correction amount is superimposed to generate the final prediction value.
6. The spatiotemporally adaptive equipment digital twin physics field order reduction reconstruction method according to claim 5, characterized in that, The region with an error significance index greater than 2 is the high error region, the region with an error significance index greater than 1.5 and less than or equal to 2 is the transition region, and the region with an error significance index less than or equal to 1.5 is the low error region. The spatial enhancement factor is 1.0 in the high error region, 0.5 in the transition region, and 0 in the low error region.
7. The spatiotemporally adaptive equipment digital twin physics field reduction and reconstruction method according to claim 1, characterized in that, The digital twin system performs a visualization operation of the physical field distribution based on the solved physical field distribution data and the coordinates of the grid model nodes.