A time-space multi-scale ai reduction method and system for mechatronic co-simulation

Abstract

The application discloses a time-space multi-scale AI reduction method and system for electromechanical simulation, and mainly relates to the technical field of electromechanical multi-physical field coupling simulation. The method comprises the following steps: obtaining full-order simulation snapshot data of an electromechanical simulation system under time-space multi-scale conditions; performing time-space multi-scale feature decomposition on the full-order simulation snapshot data, and extracting cross-scale spatial base functions and time coefficients; constructing an intelligent reduction model with a time-space attention mechanism as the core, and dynamically optimizing the reduction dimension through a reinforcement learning strategy; inputting real-time working condition parameters to output electromechanical coupling response prediction results after reduction; and continuously monitoring prediction residuals and triggering incremental online updating of the model. The application has the beneficial effect that the balance between precision and calculation efficiency of electromechanical simulation is achieved through time-space multi-scale intelligent reduction.

Description

Technical Field

[0001] This invention relates to the field of electromechanical multiphysics coupling simulation technology, specifically a spatiotemporal multiscale AI order reduction method and system for electromechanical co-simulation. Background Technology

[0002] Electromechanical equipment involves strong coupling of multiple physical fields such as electromagnetic field, structural mechanical field, and temperature field during operation. Its high-fidelity full-order simulation usually requires the construction of finite element models with tens of millions of degrees of freedom and the solution at multiple scales in time and space. This results in huge consumption of computing resources and long simulation cycle, making it difficult to meet the high requirements of real-time performance and accuracy in scenarios such as digital twins.

[0003] Traditional model reduction methods, such as intrinsic orthogonal decomposition, establish low-order substitute models by linearly projecting full-order snapshots. While this method can accelerate single simulations, it struggles to effectively capture cross-scale coupling features when dealing with inherent spatial local details and long-term dynamics in electromechanical systems, as well as the wide-ranging time-varying parameters. This leads to a significant decrease in accuracy after model reduction and a lack of adaptive adjustment capabilities. Achieving a dynamic balance between full-order simulation accuracy and computational efficiency across different operating conditions, and realizing model reduction with spatiotemporal multi-scale perception and intelligent adaptive capabilities, has become a pressing technical problem in this field.

[0004] Therefore, there is an urgent need for a spatiotemporal multi-scale AI order reduction method and system for electromechanical co-simulation to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a spatiotemporal multi-scale AI order reduction method and system for electromechanical co-simulation. It achieves a balance between accuracy and computational efficiency in electromechanical simulation through spatiotemporal multi-scale intelligent order reduction.

[0006] To achieve the above objectives, the present invention employs the following technical solution: On the one hand, this invention provides a spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation, comprising the following steps: Step S1: Obtain full-scale simulation snapshot data of the electromechanical co-simulation system at multiple spatiotemporal scales. The full-scale simulation snapshot data includes the physical field distribution and response at different spatial scale levels and time sampling frequencies. Step S2: Perform spatiotemporal multi-scale feature decomposition on the full-order simulation snapshot data obtained in step S1, and extract the cross-scale spatial basis functions and corresponding time coefficients; Step S3: Based on the extracted spatial basis functions and temporal coefficients, construct an intelligent order reduction model with spatiotemporal attention mechanism as its core, and dynamically optimize the order reduction dimension through reinforcement learning strategy; Step S4: Input the real-time operating parameters into the intelligent reduced-order model constructed in step S3, and output the reduced-order electromechanical coupling response prediction results; Step S5: Continuously collect new simulation or sensing data, calculate the prediction residuals, and trigger incremental online updates of the reduced-order model when the residuals exceed the preset threshold.

[0007] Preferably, in step S1, the full-order simulation snapshot data is generated by an electromechanical coupled multiphysics finite element model. The finite element model includes bidirectional coupling of electromagnetic field, structural mechanical field and temperature field. The spatial scale level is determined by an adaptive mesh refinement strategy, and the time sampling frequency is set according to the Nyquist criterion for a preset multiple of the highest frequency component of interest.

[0008] Preferably, step S2 includes: Step S21: Divide the acquired full-scale simulation snapshot data into fine-scale snapshot matrices according to the spatial grid size and time step. With coarse-scale snapshot matrix ; Step S22: For each fine-scale snapshot matrix With coarse-scale snapshot matrix Perform eigenorthogonal decomposition to extract the fine-scale spatial basis function set. Coarse-scale spatial basis function set and their respective time coefficient matrices and ; Step S23: Introduce a multi-scale orthogonal expansion method to expand the fine-scale time coefficients. Projection to coarse-scale spatial basis functions In the envelope space, the cross-scale coupling coefficient matrix is ​​decomposed. With cross-scale compensation terms ; Step S24: Use an adaptive clustering algorithm to analyze the cross-scale coupling coefficient matrix. Clustering of column vectors identifies the dominant spatiotemporal coupling patterns, resulting in a refined set of multi-scale basis functions. With the corresponding multi-scale time coefficient .

[0009] Preferably, step S3 includes: Step S31: Construct a deep operator network with an encoder-decoder structure, where the encoder converts the input multi-scale time coefficients... The operating parameters are mapped to a low-dimensional manifold feature space, and the decoder maps the low-dimensional manifold features back to the reconstructed physical field space. Step S32: Embed a spatiotemporal attention module in the bottleneck layer of the encoder and decoder. The spatiotemporal attention module includes a temporal self-attention sub-layer and a spatial cross-attention sub-layer. The temporal self-attention sub-layer is used to capture long-range dependencies in the temporal coefficient sequence, and the spatial cross-attention sub-layer is used to associate information transfer between basis functions of different spatial scales. Step S33: Define the action space of the reduced dimension, take the current reconstruction error, model complexity and prediction latency as the state input of reinforcement learning, and output the optimal reduced dimension through the execution-evaluation network. The evaluation network uses the weighted sum of reconstruction accuracy and computational cost as the reward function. Step S34: Feed the optimized reduced-order dimension back to the encoder-decoder network to adjust the dimension of the low-dimensional manifold features.

[0010] Preferably, in step S32, when training the spatiotemporal attention module, a contrastive learning strategy is adopted to enhance the representation ability of cross-scale features, specifically: Construct positive sample pairs and negative sample pairs. The positive sample pairs consist of the fine-scale spatial basis function coefficients and the coarse-scale spatial basis function coefficients at the same physical time. The negative sample pairs are formed by a random combination of the fine-scale spatial basis function coefficients and the coarse-scale spatial basis function coefficients at different physical times. By using a contrastive loss function to constrain the feature vectors output by the spatiotemporal attention module, positive sample pairs attract each other in the embedding space, while negative sample pairs repel each other. A cross-scale consistency regularization term is added to the contrastive loss function. This consistency regularization term penalizes the differences in the distribution of attention weights for the same physical quantity at different scales, forcing the model to learn intrinsic representations that are independent of scale.

[0011] Preferably, in step S34, after adjusting the dimension of the low-dimensional manifold features, physical constraints are applied to the decoder output, specifically as follows: The residual terms corresponding to the Maxwell equations or structural dynamics equations obeyed by the electromechanical system are used as physical driving loss terms, and are weighted and combined with the data reconstruction loss terms to form the total loss function. When training a deep operator network, the total loss function is minimized.

[0012] Preferably, in step S5, the incremental online update of the triggered order reduction model specifically includes: When the prediction residual exceeds the preset threshold, select the full-order simulation snapshot or high-fidelity data collected by the sensor within the nearest neighbor time window to form an incremental dataset. We fine-tune the weights of the fully connected layer at the decoder end of the encoder-decoder network using an incremental dataset, while keeping the weights of the encoder and spatiotemporal attention modules unchanged. During the fine-tuning process, the elastic weight consolidation algorithm is used to calculate the importance of each weight parameter to the historical task, and the weight update magnitude is constrained based on the importance.

[0013] On the other hand, the present invention provides a spatiotemporal multi-scale AI order reduction system for electromechanical co-simulation, used to implement the spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation as described above, including: Data acquisition module: used to collect or receive full-scale simulation snapshot data and real-time operating parameters of the electromechanical co-simulation system at multiple spatiotemporal scales; The intelligent order reduction module includes an embedded spatiotemporal feature decomposition unit, a reinforcement learning dimensionality optimization unit, and a prediction result output unit. Among them, the spatiotemporal feature decomposition unit is used to extract the spatial basis functions and corresponding time coefficients across scales; the reinforcement learning dimension optimization unit is used to dynamically optimize the reduced dimension; and the prediction result output unit is used to output the reduced electromechanical coupling response prediction result. Online update module: Used to monitor prediction residuals and trigger incremental online updates.

[0014] Preferably, the intelligent reduction module is deployed in an edge computing device or a cloud server, exchanges data with the data acquisition module through an asynchronous communication mechanism, and exports the reduced model in a lightweight inference engine format for the digital twin system to call in real time.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention uses spatiotemporal multi-scale feature decomposition to finely divide the full-order simulation snapshot into different spatial scales and time frequency components, effectively decoupling the inherent large-scale slow-change behavior and small-scale local details in electromechanical systems, overcoming the drawback of losing cross-scale coupling features by single-scale projection, and improving the physical representation fidelity of the reduced-order model from the source. 2. This invention constructs a deep operator network with a spatiotemporal attention mechanism as its core, enabling the reduced-order model to autonomously capture long-range dependencies in time series and information interactions between different spatial scales, significantly enhancing the modeling ability for complex nonlinear electromechanical coupling dynamics; combined with contrastive learning and cross-scale consistency regularization, it further strengthens the model's extraction of scale-independent intrinsic representations and improves generalization performance under unseen conditions. 3. This invention introduces a reinforcement learning strategy to dynamically optimize the order reduction dimension. It adaptively adjusts the model complexity according to the complexity of the current working condition, reconstruction accuracy, and time delay requirements, so that the order reduction model can achieve an intelligent balance between computational efficiency and simulation accuracy across working conditions, avoiding the limitations of manually setting the order reduction in traditional methods. 4. This invention endows the reduced-order model with continuous learning capability through prediction residual monitoring and incremental online update mechanism. It can automatically adapt to the drift of system characteristics during long-term operation, maintain prediction performance without decay, and ensure continuous availability in long-term application scenarios such as digital twins. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a flowchart of the present invention for extracting spatial basis functions and corresponding time coefficients across scales; Figure 3 This is a flowchart of the dynamic optimization process for the reduced-order dimension according to the present invention; Figure 4 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0017] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0018] In this invention, terms such as "upper," "lower," "left," "right," "front," "back," "vertical," "horizontal," "side," and "bottom" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used only to facilitate the description of the structural relationships of the various components or elements of this invention and do not specifically refer to any component or element in this invention. They should not be construed as limiting the invention.

[0019] Example: This embodiment uses a certain type of permanent magnet synchronous motor as the research object. During operation, this motor involves strong bidirectional coupling of electromagnetic fields, structural mechanical fields, and temperature fields. Its finite element full-order model contains approximately eight million mesh nodes, and a single transient simulation takes about forty minutes, which is insufficient to meet the real-time state extrapolation requirements of a digital twin system. This embodiment employs a spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation to reduce the order of the motor model, as provided in this embodiment. Figure 1 As shown, the implementation steps are as follows: Step S1: Obtain full-scale simulation snapshot data of the electromechanical co-simulation system across multiple spatiotemporal scales: A multi-physics coupled finite element model of a permanent magnet synchronous motor is constructed. The governing equations of this model include: The electromagnetic field adopts the magnetic vector potential form of Maxwell's equations. The air gap magnetic flux density distribution and the magnetic field generated by the winding current are solved by the finite element method. At the same time, considering the nonlinear magnetic saturation characteristics of ferromagnetic materials, the Newton-Raphson iteration method is used for nonlinear solution. The structural mechanics field is based on the equations of elasticity, taking into account the stator vibration and rotor dynamic response caused by electromagnetic force. The displacement field is solved in the frequency domain using the modal superposition method, and the Rayleigh damping model is introduced to characterize the energy dissipation characteristics of the structure. The temperature field is based on the Fourier heat conduction equation and surface convection heat transfer boundary conditions, coupled with electromagnetic loss and mechanical friction loss as internal heat sources, and the temperature gradient distribution from the winding end to the outer surface of the casing is calculated using transient thermal analysis method. There is a two-way coupling relationship between the three physical fields mentioned above: The electromagnetic force obtained from electromagnetic field calculations serves as the excitation load of the structural mechanical field, while the copper and iron losses in the electromagnetic losses serve as the internal heat source input for the temperature field. The displacement and strain obtained from the structural mechanics field solution affect the air gap size of the electromagnetic field, thereby changing the magnetic flux distribution; The temperature distribution obtained from the temperature field calculation affects the material's physical properties such as electrical conductivity, magnetic permeability, and mechanical elastic modulus, which in turn feeds back into the calculation process of the electromagnetic field and structural mechanical field. This coupling relationship is exchanged multiple times in each time step through an iterative coupling method until convergence. To generate full-scale simulation snapshot data covering the complete operating condition space, the parameter scanning scheme is set as follows: (1) The speed range is from 10% to 150% of the rated speed, with 15 speed gears in 10% increments; (2) The load torque range is from no-load to rated load, with five load levels in 25% increments; (3) The initial winding temperature is set to three levels: ambient temperature 25 degrees Celsius, rated operating temperature 80 degrees Celsius, and extreme temperature 120 degrees Celsius. The parameter combinations generated a total of 225 sets of simulation conditions. Under each set of conditions, a full-order transient simulation was performed once, with a simulation duration of 0.5 seconds, which was sufficient to cover the electromechanical transient process of the motor. Regarding the setting of spatial scale levels, based on the adaptive mesh refinement strategy, mesh refinement is performed in locations with large physical quantity gradients, such as the air gap region and the winding ends. The feature size of the fine-scale mesh is approximately 0.05 mm, which is used to capture local spatial harmonic components of the electromagnetic field and local hot spots of the temperature field. In regions with gentle changes in physical quantities, such as the stator yoke and the casing, a coarse-scale mesh with a feature size of approximately 2 mm is used to characterize the overall structural deformation and macroscopic temperature distribution. The two spatial scale levels of mesh achieve displacement continuity and heat flow continuity conditions at the interface through a multi-point constraint method. Regarding the setting of the time sampling frequency, based on the Nyquist criterion, considering that the highest frequency component of interest for this motor is the high-order harmonic near the switching frequency, which is about 10 kHz, full-order snapshots are collected at a sampling rate of 20 times the highest frequency, i.e., 200 kHz, with a corresponding time step of 5 microseconds. A total of 100,000 time step snapshot data are collected in a simulation duration of 0.5 seconds. For slowly varying physical processes with lower interest, a coarse time-scale snapshot with a sampling rate of 2 kHz is generated by downsampling, with a corresponding time step of 0.5 milliseconds. The snapshots of the two time scales constitute complete time-level data. The final full-order simulation snapshot data is organized in tensor form, denoted as ,in This represents the total number of spatial degrees of freedom, which is 8 million in this embodiment; This represents the total number of time steps, which is 100,000 in this embodiment. The number of operating condition parameter combinations is 225 in this embodiment. Each snapshot contains three physical quantities: magnetic flux density distribution, displacement field distribution, and temperature field distribution at that moment. At the same time, each snapshot corresponds to one operating condition parameter vector, which contains the rotational speed value, load torque value, initial winding temperature value, and corresponding physical property parameter correction coefficient.

[0020] Step S2: Perform spatiotemporal multi-scale feature decomposition on the full-order simulation snapshot data obtained in Step S1, and extract the cross-scale spatial basis functions and corresponding time coefficients: like Figure 2 As shown, this step uses a combination of multi-scale intrinsic orthogonal decomposition and multi-scale orthogonal expansion to compress high-dimensional full-order snapshot data into low-dimensional cross-scale feature representations. First, the full-scale simulation snapshot data obtained in step S1 is divided into two types of snapshot matrices according to the spatial grid size and time step: the node data belonging to the fine-scale region in all grid nodes are combined with the fine-time step sampling data to form a fine-scale snapshot matrix. ,in For fine-scale spatial degrees of freedom, The total number of snapshot columns is calculated by stitching together all time steps and all operating condition parameter groups after expansion; all coarse-scale grid node data are combined with coarse-scale time step sampled data to form a coarse-scale snapshot matrix. ,in For coarse-scale spatial degrees of freedom, This corresponds to the total number of snapshot columns. Much larger This reflects the higher requirements for spatial resolution in fine-scale regions; Secondly, perform eigenorthogonal decomposition on the two snapshot matrices respectively to obtain a fine-scale snapshot matrix. For example, first subtract the time mean from each snapshot to obtain the zero-mean snapshot matrix. Then construct the covariance matrix. ,right Perform eigenvalue decomposition, arrange the eigenvalues ​​from largest to smallest, and take the top [values]. The eigenvectors corresponding to each eigenvalue constitute a set of fine-scale spatial basis functions. ,in For the first The fine-scale spatial basis function vectors correspond to the fine-scale time coefficient matrix as follows: , Similarly, for the coarse-scale snapshot matrix... Perform eigenorthogonal decomposition to obtain a coarse-scale spatial basis function set. and coarse-scale time coefficient matrix , In this embodiment, A value of 120 represents 99.5% of the energy used to capture fine-scale snapshots. The value is 30, and the energy ratio of capturing coarse-scale snapshots is 99.8%. It should be noted that in this embodiment, the fine-scale snapshots correspond to 100,000 time steps, and the coarse-scale snapshots correspond to 1,000 time steps after downsampling. The time step numbers of the two types of snapshots are aligned according to the time step size during subsequent multi-scale orthogonal unfolding. Then, a multi-scale orthogonal expansion method is introduced to explicitly extract cross-scale coupling information, and the fine-scale time coefficient matrix is ​​transformed. To coarse-scale space basis functions The spanned envelope space is orthogonally projected, and the projection operator is defined as follows: The projection coefficient matrix of the fine-scale snapshot in the coarse-scale envelope space is denoted as... The matrix This describes how fine-scale dynamic behavior maps to coarse-scale spatial patterns, i.e., the cross-scale coupling coefficient matrix. The cross-scale compensation term is obtained by subtracting the coarse-scale projection reconstruction from the fine-scale snapshot. , This compensation term contains local detail information unique to the fine scale and that cannot be expressed by coarse-scale spatial basis functions. Perform the intrinsic orthogonal decomposition again to extract the eigenvalues. Compensation basis functions In this embodiment With a value of 20, this set of compensation basis functions is only used for the local detail superposition during the final physical field reconstruction and does not participate in the time coefficient propagation process of the reduced-order model in step S3. Therefore, it will not increase the input dimension of the reduced-order model and avoids the dimensional conflict with the global multi-scale basis functions. Finally, an adaptive clustering algorithm was used to analyze the cross-scale coupling coefficient matrix. Perform pattern recognition on the column vectors, and... Each column is considered a sample point, and the sample space dimension is... The algorithm based on density peak clustering is used to automatically determine the number of cluster centers. The basis functions corresponding to each cluster center are combined to form a dominant spatiotemporal coupling mode. The spatial basis functions corresponding to each cluster center and its neighborhood samples are selected, along with the fine-scale basis functions. Coarse-scale basis functions and compensation basis functions Take the union to form a refined set of multi-scale basis functions. Its dimension is denoted as In this embodiment The value is 85, corresponding to the multi-scale time coefficient matrix. ,in This is the total zero-mean snapshot matrix obtained by concatenating the fine-scale and coarse-scale snapshots in spatial dimensions; Thus, the spatiotemporal multiscale feature decomposition, from the original full-order snapshot with tens of millions of degrees of freedom to the 85-dimensional time coefficient, has been completed.

[0021] Step S3: Based on the extracted spatial basis functions and temporal coefficients, construct an intelligent order reduction model with spatiotemporal attention mechanism at its core, and dynamically optimize the order reduction dimension through reinforcement learning strategy: like Figure 3 As shown, this step constructs a deep operator network model that can adaptively adjust the reduced-order dimensionality, and uses the multi-scale time coefficients extracted in step S2. As training data, the reduced-order model can directly predict the time evolution trajectory of the electromechanical coupling response based on the input operating parameters: First, a deep operator network with an encoder-decoder structure is constructed, where the encoder... It consists of three fully connected layers and one-dimensional convolutional layers, and its input is a multi-scale temporal coefficient segment within the current time window. With operating condition parameter vector The concatenated vector has dimensions of ,in This represents the number of time steps within the time window, with a value of 20. The dimension of the operating condition parameter vector is 3 in this embodiment. The encoder maps the input to a low-dimensional manifold feature space through a nonlinear transformation, and outputs a feature vector. , , This refers to the current reduced-order dimension, the decoder. It consists of another set of one-dimensional convolutional layers and fully connected layers, with low-dimensional manifold features. query vectors for future time steps As input, the output is the predicted multi-scale time coefficients. ,in To predict lookahead steps, this encoder-decoder architecture enables the model to recover high-fidelity temporal evolution sequences from compressed low-dimensional representations, with an initial reduced dimensionality. The value was set to 64 during the training phase; it should be noted that... The setting of 64 during the training phase was not arbitrary: Although the 85-dimensional multi-scale basis function extracted in step S2 has captured more than 99% of the energy of the full-order snapshot, it contains some redundant weakly coupled modes and noise components. According to the reinforcement learning optimization experiment, under the premise of maintaining the reconstructed energy ratio of not less than 99%, the 85-dimensional basis can be further compressed in the range of 32 to 64 dimensions with almost no loss of accuracy. In this embodiment, the upper limit of this range of 64 dimensions is taken as the initial reduction dimension to retain sufficient feature capacity in the initial training stage, and then dynamically simplified according to the actual working conditions through reinforcement learning strategy. Secondly, a spatiotemporal attention module is embedded in the bottleneck layer of the encoder and decoder. This spatiotemporal attention module consists of two parallel sub-layers: a temporal self-attention sub-layer takes the temporal coefficient feature sequence extracted by the encoder as input and calculates the attention weight between any two time positions in the sequence. This weight is obtained through a query vector. With key vector The dot product is obtained after scaling and Softmax normalization for the value vector. The weighted summation is calculated using the following formula: ,in The dimension of the key vector, and the scaling factor. To prevent gradient vanishing due to excessively large dot products, this self-attention mechanism effectively captures the long-range time dependency between long-period oscillations caused by current harmonics and the cumulative effect of the temperature field in electromechanical systems. The spatial cross-attention sublayer uses fine-scale basis function coefficients and coarse-scale basis function coefficients as two sets of inputs to calculate the fine-scale query vector. With coarse-scale key vector The cross-attention weights between different spatial scales enable information transfer and fusion, and their calculation formula is as follows: This cross-scale attention mechanism enables the model to automatically learn the relationship between local magnetic saturation details in the air gap and overall stator deformation without the need for manual pre-setting of coupling functions; When training the spatiotemporal attention module, a contrastive learning strategy is used to enhance its discriminative representation ability of cross-scale features, constructing positive and negative sample pairs from the training dataset: Positive sample pairs From the same physical moment The feature vector after encoding and mapping of the coefficients of the fine-scale spatial basis functions The feature vector obtained by encoding and mapping the coefficients of the coarse-scale spatial basis functions The components describe the representation of the same physical state from different scale perspectives; negative sample pairs From time The fine-scale eigenvectors and another different time point The coarse-scale feature vectors are randomly combined, and the contrast loss function adopts the normalized temperature cross-entropy loss, the expression of which is: ; in This represents the batch size, with a value of 64. This represents the cosine similarity between two feature vectors. The temperature hyperparameter, with a value of 0.1, is used to control the concentration of the similarity distribution; the denominator contains... The summation iterates through all positive and negative sample pairs within the batch, minimizing the contrastive loss function so that positive sample pairs are close to each other in the embedding space and negative sample pairs are far apart, thereby learning a discriminative and consistent cross-scale intrinsic representation. Based on the comparative loss function, a cross-scale consistency regularization term is added, which is defined as the consistency between the spatiotemporal attention weight distributions of the same physical quantity at different scales. Divergence: ; in and They represent the first The probability distribution of attention weights at fine and coarse scales in each attention head. for divergence operator, The total number of attention heads is 8. This regularization term penalizes the problem of inconsistent attention to the same physical phenomenon at different scales, forces the model to learn physical intrinsic representations that are independent of the observation scale, and effectively improves the model's generalization ability under different operating parameters. Introducing reinforcement learning strategies to reduce dimensionality Dynamic optimization is performed to achieve an intelligent balance between computational efficiency and reconstruction accuracy across operating conditions, defining an action space with reduced order dimensions. For several discrete candidate dimension values, in this embodiment, we take... Reinforcement learning state input It consists of three parts: (1) Reconstruction error of the current model , defined as the root mean square error between the predicted value and the actual value within the most recent ten time steps; (2) Model complexity With the current reduced dimension With the largest dimension It is measured by the ratio; (3) Predicting delay , which is the time interval from input to output response; Execution Network Output in motion space Based on the probability distribution above, the agent samples and selects actions of reduced dimensionality. Evaluation network Estimate the expected cumulative reward starting from the current state to evaluate the merits of the action; The reward function is designed as a weighted trade-off between reconstruction accuracy and computational cost: ; in , , The weights are 1.0, 0.5, and 0.3, respectively, reflecting different emphases on accuracy, complexity, and real-time performance. The execution-evaluation network is trained using a proximal policy optimization algorithm, updating the network parameters by maximizing the expected cumulative reward. The evaluation network parameters are updated by minimizing the temporal difference error. ; Finally, the optimal reduced dimensionality of the reinforcement learning strategy output is determined. Feedback is sent to the encoder-decoder network to adjust the dimension of the low-dimensional manifold features in the bottleneck layer, enabling the deep operator network to operate at the optimal dimension under the current conditions. When fine-tuning the deep operator network to adapt to the new reduced-order dimension, physical constraints are applied to the decoder output. Specifically, the residual terms of Maxwell's equations obeyed by the electromechanical system are used as the physical driving loss term. Specifically, for each time step of the reduced-order model's predicted magnetic vector potential... (Obtained through linear reconstruction of multi-scale basis functions), its curl is calculated to obtain the magnetic flux density. Combined with the material's magnetic reluctance (Obtained by interpolation from the current temperature field) and known source current density Numerical calculation of residuals of Norm square, i.e. ,in Resistivity The magnetic vector potential, The source current density is used as the residual, which directly measures the degree to which the electromagnetic field quantity after order reduction and reconstruction violates the governing equations of Maxwell's equations. The total loss function is composed of a weighted combination of data reconstruction loss term, comparison loss term, consistency regularization term, and physics-driven loss term. ; in The mean square error between the predicted time coefficient and the actual time coefficient; , , The weights for each loss term are set to 0.1, 0.05, and 0.02 in this embodiment (these values ​​were determined using a grid search on the validation set to maintain a balanced magnitude across the loss terms and prevent any single term from dominating the training process). The AdamW optimizer is used during training, with an initial learning rate set to... And a cosine annealing strategy is used to gradually decay the learning rate over 500 training cycles. With the batch size set to 64, after training, an intelligent reduced-order model with spatiotemporal multi-scale perception and dimensional adaptive adjustment capabilities is obtained.

[0022] Step S4: Input the real-time operating parameters into the intelligent reduced-order model constructed in step S3, and output the reduced-order electromechanical coupling response prediction results: During the actual deployment phase, the digital twin system collects the current speed, load torque, and winding temperature of the permanent magnet synchronous motor in real time as a vector of operating parameters. The input is fed into the intelligent reduction model trained in step S3. Simultaneously, the system maintains a length of... The sliding time window stores the most recent data in the buffer. The encoder reads historical time coefficients within a time window, based on a multi-scale time coefficient sequence that has been verified by full-order simulation or sensor measurements. and real-time operating parameters Output the low-dimensional manifold features at the current time. decoder with Given the condition, the multi-scale time coefficients are predicted forward in an autoregressive manner for multiple future time steps. ; To further improve computational efficiency, this embodiment performs lightweight optimization on the spatiotemporal attention module during the inference phase, using structured pruning techniques to remove attention weights below a preset threshold. In this embodiment, the 8 attention heads in the temporal attention sublayer are reduced to 5, and the 8 attention heads in the spatial cross attention sublayer are reduced to 4. The total number of model parameters is reduced from about 3.8 million to about 2.1 million, and the time taken for a single inference is reduced from about 12 milliseconds to about 3.5 milliseconds. Multi-scale time coefficient prediction values ​​from decoder output Through spatial basis functions Linear reconstruction yields the physical field distribution: ; in Indicates spatial location Place, No. Reconstructed physical field values ​​for a future time step, including magnetic flux density, displacement field, and temperature field; The spatial mean field of the full-order snapshot data has been calculated and saved in the zero-mean preprocessing stage of step S2. It must be added back during reconstruction; otherwise, the temperature field and magnetic flux density distribution will show negative shifts. For the first Multi-scale time coefficients in The predicted value at any given time; For the first Multiscale spatial basis functions at position The value at; The total dimension of the multi-scale basis functions is used. After reconstruction, the prediction results are pushed to the digital twin visualization interface in the form of a three-dimensional cloud map for operation and maintenance personnel to perform status monitoring and fault early warning.

[0023] Step S5: Continuously collect new simulation or sensing data, calculate the prediction residuals, and trigger incremental online updates of the reduced-order model when the residuals exceed a preset threshold. During long-term operation, the motor in a digital twin system may experience system characteristic drift due to factors such as winding aging, bearing wear, and gradual demagnetization of permanent magnets. This leads to a slow decline in the prediction accuracy of the offline-trained reduced-order model. To address this issue, this embodiment establishes a complete set of prediction residual monitoring and incremental online update mechanisms: Continuously collecting new data sources includes two categories: One type is full-level simulation verification snapshots that are periodically executed through a high-performance computing cluster in the cloud, generated every 24 hours, covering the range of major operating conditions experienced by the motor in the past day; Another type is high-fidelity real-time measurement data deployed in motor housing vibration sensors and winding temperature sensors, with a sampling frequency of 1000 Hz, continuously monitoring two key physical quantities: stator vibration displacement and winding hot spot temperature. The predicted residuals are calculated using the sliding window normalized root mean square error index. ; in The true physical field values ​​are obtained through full-order simulation or sensor acquisition. These are the corresponding physical field values ​​predicted by the reduced-order model. This is the length of the sliding window; in this embodiment, the value is 100. The sampling time interval; Let be a small positive number, taking the value of To avoid numerical instability when the denominator is zero, the preset threshold is set to 5%. When the accuracy of the downgraded model has degraded to an unacceptable level, an incremental online update process is automatically triggered. The specific process of incremental online updates is as follows: Select one hundred sets of full-order simulation verification snapshots and measured high-fidelity sensor data from the nearest neighbor time window to form an incremental dataset. To avoid forgetting, this embodiment employs an update strategy that combines parameter-level knowledge distillation with elastic weight consolidation for encoder network parameters. And spatiotemporal attention module parameters The reason for keeping its weight unchanged is: The degradation effects of winding aging and permanent magnet demagnetization in permanent magnet synchronous motors during long-term operation are mainly manifested as gradual changes in steady-state output characteristics, such as electromagnetic loss distribution shift, increased winding resistance, and reduced back electromotive force amplitude. However, the intrinsic characteristics of the electromagnetic-structure-temperature spatiotemporal coupling mode inside the motor, including the spatial harmonic order distribution caused by stator cogging effect, modal structure, and heat diffusion path, are determined by the motor's geometric topology and physical laws, and remain structurally unchanged during the aging process. Therefore, the multi-scale time coefficient mapping relationship extracted by the encoder and the long-range dependency mode captured by the spatiotemporal attention module have cross-stage universality and do not need to be modified in each incremental update. Only the fully connected layer at the end of the decoder is responsible for mapping low-dimensional manifold features back to specific physical quantity values. It is most directly affected by the shift in material property parameters, so it is selected as the only object for fine-tuning. For the weights of the fully connected layers at the end of the decoder network Using incremental datasets Fine-tuning is performed, with the optimization objective being the reconstruction loss on the incremental dataset; During fine-tuning, each weight parameter of the fully connected layer of the decoder is adjusted. The importance metric to historical tasks is calculated using the elastic weight consolidation algorithm, which is approximated by the diagonal elements of the Fisher information matrix. ; in Represents weight parameters Fisher information value, The first fully connected layer at the end of the decoder represents the... One weight parameter, For partial derivative operators, For the model to perform on a given input Time output The conditional probability and gradient are calculated through backpropagation. During fine-tuning, an elastic regularization constraint term is added to the original loss function. ,in The weight values ​​before the update. The strength hyperparameter for elastic weight consolidation is set to 100. This constraint restricts excessive modification of important weight parameters from historical tasks, allowing the model to retain as much learned knowledge as possible while adapting to new data distributions. After the update, re-evaluate the prediction residuals of the reduced-order model on the validation set to confirm. Once the error rate falls below 5%, the updated model parameters are pushed to the online inference engine to replace the old model. The entire incremental update process is fully automated, requiring no manual intervention or retraining of the entire history. Each update takes less than five minutes, ensuring the continuous availability and real-time performance of the digital twin system during long-term operation. It should be noted that in this embodiment, a full-order simulation verification snapshot every 24 hours is used as the benchmark for residual evaluation and incremental updates. This frequency is a preferred value and is suitable for industrial scenarios with high-performance cloud computing clusters and regular offline simulation conditions. For on-site deployment scenarios with limited computing resources, residual monitoring and update triggering can be performed solely based on high-fidelity measured data from vibration and temperature sensors. There is no need to force regular full-order simulations. The update triggering condition can be adjusted to require the average residual value to exceed a threshold for 10 consecutive monitoring cycles, thereby covering different levels of computing power conditions in industrial sites.

[0024] like Figure 4 As shown, this embodiment also provides a spatiotemporal multi-scale AI order reduction system for electromechanical co-simulation. This system comprises three parts: a data acquisition module, an intelligent order reduction module, and an online update module. The data acquisition module is deployed on the industrial IoT edge gateway. It establishes communication connections with the finite element simulation workstation and the field sensor network through the OPC UA protocol. It is responsible for collecting and receiving full-level simulation snapshot data and real-time operating parameters, and preprocessing and cleaning the data according to a unified timestamp alignment format to remove abnormal jump data points caused by instantaneous sensor disconnection or electromagnetic interference. The intelligent order reduction module is deployed on a cloud server equipped with an NVIDIA A10 GPU and runs as a containerized microservice. This module has three embedded functional units: a spatiotemporal feature decomposition unit that performs multi-scale intrinsic orthogonal decomposition and cross-scale orthogonal expansion on the full-order snapshot data transmitted by the data acquisition module, and outputs a refined set of multi-scale basis functions and corresponding time coefficients; a reinforcement learning dimensionality optimization unit that inputs the current reconstruction error, model complexity and prediction latency into the execution-evaluation network, and outputs the optimal reduced dimension; and a prediction result output unit that inputs real-time operating parameters into the intelligent order reduction model after dimensionality optimization, and outputs the prediction results of magnetic flux density distribution, displacement field distribution and temperature field distribution for display on the digital twin visualization platform. The online update module continuously monitors the prediction residuals. When the residuals exceed a preset threshold, it automatically triggers an incremental online update process. Incremental data is selected from the nearest neighbor time window, and the fully connected layer at the end of the decoder is fine-tuned under the elastic weight consolidation constraint to complete the online iteration of the model parameters. The intelligent order reduction module exchanges data with the data acquisition module through an asynchronous message queue and exports a lightweight order reduction model after pruning optimization in an open neural network exchange format for the digital twin system to call in real time. The single inference latency meets the hard real-time requirement of less than ten milliseconds for the digital twin system.

[0025] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation, characterized in that, Includes the following steps: Step S1: Obtain full-scale simulation snapshot data of the electromechanical co-simulation system at multiple spatiotemporal scales. The full-scale simulation snapshot data includes the physical field distribution and response at different spatial scale levels and time sampling frequencies. Step S2: Perform spatiotemporal multi-scale feature decomposition on the full-order simulation snapshot data obtained in step S1, and extract the cross-scale spatial basis functions and corresponding time coefficients; Step S3: Based on the extracted spatial basis functions and temporal coefficients, construct an intelligent order reduction model with spatiotemporal attention mechanism as its core, and dynamically optimize the order reduction dimension through reinforcement learning strategy; Step S4: Input the real-time operating parameters into the intelligent reduced-order model constructed in step S3, and output the reduced-order electromechanical coupling response prediction results; Step S5: Continuously collect new simulation or sensing data, calculate the prediction residuals, and trigger incremental online updates of the reduced-order model when the residuals exceed a preset threshold. Step S2 includes: Step S21: Divide the acquired full-scale simulation snapshot data into fine-scale snapshot matrices according to the spatial grid size and time step. With coarse-scale snapshot matrix ; Step S22: For each fine-scale snapshot matrix With coarse-scale snapshot matrix Perform eigenorthogonal decomposition to extract the fine-scale spatial basis function set. and the corresponding fine-scale time coefficient matrix Coarse-scale spatial basis function set and the corresponding coarse-scale time coefficient matrix ; Step S23: Introduce a multi-scale orthogonal expansion method to expand the fine-scale time coefficient matrix. Projection to coarse-scale spatial basis functions In the envelope space, the cross-scale coupling coefficient matrix is ​​decomposed. With cross-scale compensation terms Regarding compensation items Perform eigenorthogonal decomposition again to extract the compensation basis functions. ; Step S24: Use an adaptive clustering algorithm to analyze the cross-scale coupling coefficient matrix. Clustering of column vectors identifies dominant spatiotemporal coupling patterns. The basis functions corresponding to each cluster center are combined to form a dominant spatiotemporal coupling pattern. Spatial basis functions corresponding to each cluster center and its neighborhood samples are selected, along with fine-scale basis functions. Coarse-scale basis functions and compensation basis functions Take the union to form a refined set of multi-scale basis functions. With the corresponding multi-scale time coefficient ; Step S3 includes: Step S31: Construct a deep operator network with an encoder-decoder structure, where the encoder converts the input multi-scale time coefficients... The operating parameters are mapped to a low-dimensional manifold feature space, and the decoder maps the low-dimensional manifold features back to the reconstructed physical field space. Step S32: Embed a spatiotemporal attention module in the bottleneck layer of the encoder and decoder. The spatiotemporal attention module includes a temporal self-attention sub-layer and a spatial cross-attention sub-layer. The temporal self-attention sub-layer is used to capture long-range dependencies in multi-scale temporal coefficient sequences, and the spatial cross-attention sub-layer is used to associate information transfer between spatial basis functions of different scales. Step S33: Define the action space of the reduced dimension, take the current reconstruction error, model complexity and prediction latency as the state input of reinforcement learning, and output the optimal reduced dimension through the execution-evaluation network. The evaluation network uses the weighted sum of reconstruction accuracy and computational cost as the reward function. Step S34: Feed the optimized reduced-order dimension back to the encoder-decoder network to adjust the dimension of the low-dimensional manifold features.

2. The spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation according to claim 1, characterized in that, In step S1, the full-order simulation snapshot data is generated by the electromechanical coupled multiphysics finite element model. The finite element model includes bidirectional coupling of electromagnetic field, structural mechanical field and temperature field. The spatial scale level is determined by an adaptive mesh refinement strategy, and the time sampling frequency is set according to the Nyquist criterion for a preset multiple of the highest frequency component of interest.

3. The spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation according to claim 1, characterized in that, In step S32, when training the spatiotemporal attention module, a contrastive learning strategy is adopted to enhance the representation ability of cross-scale features, specifically: Construct positive sample pairs and negative sample pairs. The positive sample pairs consist of the fine-scale spatial basis function coefficients and the coarse-scale spatial basis function coefficients at the same physical time. The negative sample pairs are formed by a random combination of the fine-scale spatial basis function coefficients and the coarse-scale spatial basis function coefficients at different physical times. By using a contrastive loss function to constrain the feature vectors output by the spatiotemporal attention module, positive sample pairs attract each other in the embedding space, while negative sample pairs repel each other. A cross-scale consistency regularization term is added to the contrastive loss function. This consistency regularization term penalizes the differences in the distribution of attention weights for the same physical quantity at different scales, forcing the model to learn intrinsic representations that are independent of scale.

4. The spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation according to claim 1, characterized in that, In step S34, after adjusting the dimension of the low-dimensional manifold features, physical constraints are applied to the decoder output, specifically: The residual terms corresponding to the Maxwell equations or structural dynamics equations obeyed by the electromechanical system are used as physical driving loss terms, and are weighted and combined with the data reconstruction loss terms to form the total loss function. When training a deep operator network, the total loss function is minimized.

5. The spatiotemporal multi-scale AI order reduction method for electromechanical co-simulation according to claim 1, characterized in that, In step S5, the incremental online update of the triggered order reduction model specifically includes: When the prediction residual exceeds the preset threshold, select the full-order simulation snapshot or high-fidelity data collected by the sensor within the nearest neighbor time window to form an incremental dataset. We fine-tune the weights of the fully connected layer at the decoder end of the encoder-decoder network using an incremental dataset, while keeping the weights of the encoder and spatiotemporal attention modules unchanged. During the fine-tuning process, the elastic weight consolidation algorithm is used to calculate the importance of each weight parameter to the historical task, and the weight update magnitude is constrained based on the importance.

6. A spatiotemporal multi-scale AI order reduction system for mechatronics co-simulation, used to implement the spatiotemporal multi-scale AI order reduction method for mechatronics co-simulation as described in any one of claims 1-5, characterized in that, include: Data acquisition module: used to collect or receive full-scale simulation snapshot data and real-time operating parameters of the electromechanical co-simulation system at multiple spatiotemporal scales; The intelligent order reduction module includes an embedded spatiotemporal feature decomposition unit, a reinforcement learning dimensionality optimization unit, and a prediction result output unit. Among them, the spatiotemporal feature decomposition unit is used to extract the spatial basis functions and corresponding time coefficients across scales; the reinforcement learning dimension optimization unit is used to dynamically optimize the reduced dimension; and the prediction result output unit is used to output the reduced electromechanical coupling response prediction result. Online update module: Used to monitor prediction residuals and trigger incremental online updates.

7. The spatiotemporal multi-scale AI order reduction system for electromechanical co-simulation according to claim 6, characterized in that, The intelligent model reduction module is deployed on an edge computing device or a cloud server. It exchanges data with the data acquisition module through an asynchronous communication mechanism and exports the model reduction in a lightweight inference engine format for the digital twin system to call in real time.

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