A method for monitoring the global performance of complex equipment driven by sparse measurement points

Abstract

This invention discloses a sparse measurement point-driven global performance monitoring method for complex equipment, belonging to the field of complex equipment monitoring technology. The invention first establishes a physical field simulation analysis model of the complex equipment, and constructs a training dataset through simulation calculations with multiple sets of different excitation parameters. Based on the dataset, a reduced-order surrogate model containing Fourier neural operators is trained. Measured state data of sparse measurement points in the target area are collected. Using the sparse measurement point data as constraints, an adaptive evolutionary strategy optimization algorithm based on the covariance matrix is ​​employed to solve for the optimal state parameters. The optimal parameters are input into the reduced-order surrogate model to obtain the global state distribution results, thus completing the equipment performance monitoring. This invention can achieve rapid reconstruction of the global physical field under conditions of a small number of measurement points, reducing measurement and calculation costs and improving the stability and engineering adaptability of the reconstruction results.

Description

Technical Field

[0001] This invention relates to the field of complex equipment monitoring technology, and in particular to a sparse measurement point-driven method for global performance monitoring of complex equipment. Background Technology

[0002] In complex equipment and related physical systems, the overall distribution of temperature, pressure, vibration, and electromagnetic fields within the target area is crucial for evaluating equipment performance. To analyze the equipment's response under different excitation conditions, it is typically necessary to acquire state data from multiple locations within the target area and use this data to determine the overall operating state and performance level of the equipment. Therefore, various existing technological approaches have emerged regarding the acquisition, prediction, and analysis of the physical field distribution within the target area.

[0003] Physics-based analysis methods using numerical simulation typically begin by establishing a physical model of the complex equipment, determining its geometry, material parameters, boundary conditions, and excitation conditions. Then, numerical calculation methods are used to solve for the state distribution within the target region, ultimately obtaining the state values ​​at each location and the overall distribution. The main process generally includes: model building, parameter setting, numerical solution calculation, outputting the overall state distribution of the target region, and repeating the calculation as needed by changing parameters or operating conditions. This type of method is characterized by clear physical meaning and strong interpretability of results, and is therefore widely used in the design analysis, performance evaluation, and scheme verification of complex equipment.

[0004] Data-driven physics prediction methods typically utilize existing sample data to train prediction models and establish a mapping relationship between input conditions and the overall state distribution of the target region, thereby reducing the workload of repetitive numerical calculations. The main process generally includes: constructing a sample dataset, organizing and preprocessing the sample data, training the prediction model, and quickly outputting the corresponding prediction results after inputting new conditional information. The basic idea of ​​this type of method is to learn the system response patterns using existing data to improve analysis efficiency. Some existing methods also attempt to recover field distributions or identify parameters under limited observation conditions to adapt to application scenarios where measurement points are limited or direct global acquisition is difficult. Some methods also employ generative models to recover a global field distribution consistent with observations under constraints of limited observation information, thereby improving the expressive power and adaptability in complex physics reconstruction tasks. While these existing technologies have certain advantages in physics analysis and prediction, they still have some problems and shortcomings.

[0005] Numerical simulation-based physics field analysis methods typically require repeated full solutions under different parameter conditions, resulting in significant computational load and time. When analyzing numerous operating conditions or needing rapid results, these methods often struggle to balance efficiency and cost. This is because these methods fundamentally rely on a complete numerical computation process, where each parameter change may correspond to a new global solution.

[0006] While data-driven physics prediction methods can improve computational speed to some extent, their performance typically depends on the coverage of training samples and the consistency between input and training data. When input conditions change significantly, or when the data format in the actual application differs from that in the training phase, the stability and accuracy of the prediction results are easily affected. This problem arises because these methods primarily rely on samples to learn the relationship between input and output, and the model's generalization ability is limited by the distribution of the training data.

[0007] In practical applications, the overall state information within a target area is often difficult to obtain directly from a large number of measurement points, due to limitations in the number and deployment of these points, as well as high testing costs. Under these conditions, inferring the overall distribution state from limited observation results often leads to insufficient information, resulting in biased or unstable results. This problem arises because local observations can only reflect the state at a limited number of locations, while the overall physical field distribution has spatial correlation and parameter dependence characteristics, making it difficult to fully characterize the global state based on only a small amount of local information.

[0008] Furthermore, some existing technologies focus more on the predictive power of the algorithm model itself, while not giving sufficient consideration to the completeness of the process, ease of implementation, and output format in engineering applications. For specific equipment performance monitoring tasks, a single numerical solution or a single prediction model often fails to directly form a clear, complete, and easily implementable technical process. This problem arises because existing research focuses more on model effectiveness verification, while engineering applications emphasize a holistic technical solution from data acquisition and processing to result output.

[0009] In summary, although existing technologies have formed the main technical routes represented by numerical simulation analysis and data-driven prediction, they still generally suffer from problems such as low computational efficiency, sensitivity to data conditions, insufficient overall state characterization ability under limited observation conditions, and imperfect adaptability to engineering applications, and there is still a need for further improvement. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of the prior art and provide a global performance monitoring method for complex equipment driven by sparse measurement points. This method solves the problems of high measurement cost, high cost of repeated simulation calculation, difficulty in effectively representing the overall physical field distribution under limited measurement point conditions, insufficient stability of direct inversion, and inconvenience in engineering application in the prior art. Thus, it enables the rapid acquisition of key state parameters of complex equipment and the efficient reconstruction and performance monitoring of the overall physical field distribution of the target area by relying only on a small number of measurement point data.

[0011] This invention provides a sparse measurement point-driven global performance monitoring method for complex equipment, used for physical field distribution reconstruction and performance monitoring of a target area of ​​complex equipment, comprising the following steps: A physical field simulation analysis model of the complex device is established. Simulation points are preset in the target area. Through simulation calculations of multiple sets of different excitation parameters, the state value data of each simulation point in the target area corresponding to each set of excitation parameters is obtained. After preprocessing, a training dataset is constructed. Train a reduced-order proxy model based on the aforementioned training dataset; Collect measured state data of preset sparse measuring points within the target area of ​​the complex equipment, and obtain sparse measuring point observation data after preprocessing; Using the excitation parameters or equivalent state parameters as variables to be optimized, and the sparse measurement point observation data as constraints, an objective function is constructed, and the optimal state parameters are obtained by iteratively solving the optimization algorithm. The optimal state parameters are input into the trained reduced-order proxy model to obtain the global state distribution results of the target area, thereby completing the global performance monitoring of the complex device.

[0012] Therefore, through a complete technical process of offline simulation modeling and dataset construction, reduced-order surrogate model training, online sparse measurement point data acquisition, parameter inversion, and global state distribution reconstruction, the overall physical field distribution of the target area of ​​complex equipment can be rapidly recovered under the condition of a small number of sparse measurement points. This eliminates the need for repeated high-cost numerical simulation calculations, significantly reducing measurement costs and computational overhead. The technical path of parameter inversion superimposed with a reduced-order surrogate model first obtains the matching state parameters based on sparse measurement point data, and then recovers the global distribution through the model. This avoids the instability of directly extrapolating the global results based on local measurement points, improving the stability and rationality of the reconstruction results. At the same time, a complete and clear engineering implementation process is formed, reducing the difficulty of on-site implementation and improving the engineering adaptability of the method.

[0013] The reduced-order surrogate model is a one-dimensional Fourier neural operator model. It takes the activation parameters as conditional inputs and the spatial coordinates of the target region as position inputs, and outputs the state prediction value of the corresponding spatial point. The spatial position encoding branch performs geometric enhancement on the input spatial point coordinates through an integrated polar-Cartesian (IPHI) coordinate encoding module, and then processes it through Fourier position encoding and a fully connected layer to output the position embedding feature. The geometric enhancement representation includes the original coordinate information of the spatial point, as well as the angle features and distance features related to the central reference position.

[0014] Therefore, by using the IPHI coordinate encoding module to geometrically enhance the representation of spatial point coordinates, angle and distance features related to the central reference position are added to the original coordinate information. Combined with Fourier position encoding and fully connected layer processing, the model's ability to express spatial geometric position and global state distribution is effectively enhanced, enabling the model to accurately learn the physical field response characteristics of different spatial positions and significantly improving the accuracy of physical field prediction results.

[0015] The reduced-order surrogate model includes a parameter feature extraction branch, a spatial location encoding branch, a feature fusion layer, a Fourier neural operator backbone network, and a fully connected output layer. The parameter feature extraction branch performs dimensionality upscaling and feature extraction on the input activation parameters through a fully connected mapping layer, and outputs high-dimensional parameter features. The fully connected mapping layer includes at least two fully connected layers and uses the modified linear unit (ReLU) nonlinear activation function.

[0016] Therefore, by using multi-layer fully connected mapping layers to increase the dimensionality and extract features of the activation parameters, the original low-dimensional activation parameters can be transformed into high-dimensional parameter features suitable for subsequent network computation. This fully explores the influence of activation parameters on the physical field distribution. Combined with the ReLU nonlinear activation function, it effectively improves the model's ability to learn the nonlinear mapping relationship between activation parameters and physical field distribution.

[0017] The feature fusion layer performs dot product fusion on high-dimensional parameter features and location embedding features, and outputs a fused feature that simultaneously contains excitation parameter information and spatial location information; the dot product fusion is the multiplication of corresponding dimension elements, and the fused feature is then subjected to batch normalization.

[0018] Therefore, by using the dot product fusion method, the fusion feature of each spatial point simultaneously contains the current excitation parameter conditions and the spatial location information of that point, establishing a joint representation of the same set of excitation parameters producing different physical field responses at different spatial locations, providing a reliable foundation for the subsequent model to learn the mapping relationship between parameters and response fields; after fusion, batch normalization processing further improves the stability and convergence speed of the model training process.

[0019] The Fourier neural operator backbone network is composed of multiple layers of stacked spectral convolutional units and pointwise convolutional units. The spectral convolutional units transform the input features to the frequency domain through fast Fourier transform, perform complex weight mapping on the low-frequency modes, and then transform them back to the spatial domain through inverse fast Fourier transform to extract global coupled features. The pointwise convolutional units use 1×1 convolutional kernels to extract local linear features. The outputs of the spectral convolutional units and the outputs of the pointwise convolutional units in each layer are superimposed and then processed by a nonlinear activation function.

[0020] Therefore, by extracting the global coupling features of the physical field distribution in the frequency domain through spectral convolution units, the spatial global correlation characteristics of the physical field distribution can be effectively captured, adapting to the long-range dependence characteristics of the physical field distribution; by supplementing the local linear feature expression capability through pointwise convolution units, both the global distribution law and local change features are extracted; the multi-layer stacked structure enables the model to enhance the influence of excitation parameter changes on the overall physical field distribution layer by layer, further improving the model's prediction accuracy and generalization ability for complex physical field distributions.

[0021] The objective function is a robust error function that combines prior constraints and bias compensation terms; the prior constraints are reasonable range constraints on the excitation parameters, and the bias compensation terms are used to correct deviations caused by measurement noise.

[0022] Therefore, by adopting a robust error function that combines prior constraint terms and bias compensation terms, the inversion parameters are ensured to be within a reasonable range through the prior constraint terms, avoiding parameter results that do not conform to physical meaning. At the same time, the bias compensation terms effectively reduce the impact of measurement noise and abnormal deviations on the parameter solution results, significantly improving the robustness and accuracy of the parameter inversion process.

[0023] The optimization algorithm is a covariance matrix adaptive evolution strategy optimization algorithm, and its iteration termination condition is that the number of iterations reaches a preset threshold, or the objective function value is less than a preset error threshold.

[0024] Therefore, by setting dual iteration termination conditions, the algorithm can avoid infinite iteration by setting a preset iteration number threshold, thus ensuring the efficiency of parameter inversion. At the same time, the parameter inversion results can be ensured to meet the accuracy requirements by setting a preset error threshold. This balances the efficiency and accuracy of parameter solving and is suitable for the application needs of rapid monitoring in engineering sites.

[0025] The preprocessing of the sparse measurement point observation data includes superimposing Gaussian distributed noise on the measured state data to simulate measurement disturbances, and then performing standardization processing; the mean of the Gaussian distributed noise is 0, and the variance is a preset value.

[0026] Therefore, by superimposing Gaussian distributed noise to simulate the random errors and disturbances in the actual measurement process, the preprocessed observation data is closer to the real engineering measurement conditions, which improves the adaptability of the method to the actual measurement scenario. Through standardization processing, the observation data meets the input requirements of subsequent parameter inversion calculation, which further improves the stability of the parameter solution process.

[0027] The training dataset consists of multiple sets of one-to-one corresponding excitation parameters and global state distribution samples of the target region. Each set of samples contains the position coordinates and state values ​​of all simulation points in the target region under the corresponding excitation parameters. The preprocessing includes data normalization and outlier removal.

[0028] Therefore, by constructing a training dataset containing multiple sets of excitation parameters and corresponding global state distributions, comprehensive supervised learning samples are provided for the reduced-order surrogate model, enabling the model to fully learn the mapping relationship between excitation parameters and the physical field distribution of the target region. Through data normalization and outlier removal preprocessing, the stability and convergence of the model training process are effectively improved, ensuring the prediction accuracy of the model.

[0029] The number of sparse measuring points is 9, and they are arranged in a 3×3 equidistant pattern in the central area of ​​the complex equipment target area. The spacing between adjacent measuring points is a preset fixed value; the preset fixed value is determined according to the size of the complex equipment target area.

[0030] Therefore, by using nine sparse measuring points arranged in a 3×3 equidistant pattern, the physical field distribution characteristics of the central region of the target area can be fully obtained while controlling the number of measuring points and reducing measurement costs. This provides reliable local observation constraints for parameter inversion, balances measurement costs with the accuracy of inversion results, and is suitable for practical application scenarios where the layout of measuring points is limited in engineering projects. Attached Figure Description

[0031] Figure 1 A schematic diagram of the parameter inversion process involved in an embodiment of the present invention is shown. Detailed Implementation

[0032] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, the same reference numerals are used for the same parts, and repeated descriptions are omitted. Furthermore, the drawings are merely schematic diagrams, and the proportions of the parts or the shapes of the parts may differ from the actual figures.

[0033] This embodiment provides a sparse measurement point-driven global performance monitoring method for complex equipment, used for reconstructing the physical field distribution and monitoring the global performance of the target area of ​​complex equipment. The method employs a core technical approach of offline sample construction and model training, followed by sparse measurement point-driven inversion and reconstruction during online monitoring. The offline stage provides basic data and a core prediction model for online monitoring, while the online stage, based on the results of the offline stage, uses a small amount of sparse measurement point data to complete global state recovery. These two stages form a complete technical loop, jointly addressing the common technical problems in existing technologies, such as difficulty in effectively representing the global state distribution of complex equipment under limited measurement point conditions, low computational efficiency, and poor engineering adaptability.

[0034] In this embodiment, the complex device refers to an electromagnetically sensitive or electromagnetically responsive system with multi-physics coupling characteristics, nonlinear material properties, or complex geometric topology. Its core characteristic is that during operation or disturbance, the internal electromagnetic field distribution follows complex partial differential equation constraints, and it is difficult to obtain an accurate solution using simple analytical methods.

[0035] In this embodiment, the core steps of the method of the present invention include simulation modeling and dataset construction and reduced-order proxy model training in the offline stage, as well as sparse measurement point data acquisition, parameter inversion, global state distribution reconstruction and performance monitoring in the online stage, which constitute the overall technical framework of the present invention.

[0036] In this implementation, the preparatory work for the offline phase is performed first to provide basic support for online monitoring: The first step involves establishing a physical field simulation analysis model for the complex equipment. Simulation points are preset within the target area. Through simulation calculations using multiple sets of different excitation parameters, the state value data of each simulation point within the target area corresponding to each set of excitation parameters is obtained. After preprocessing, a training dataset is constructed. This step forms the basis for subsequent training of the reduced-order surrogate model, providing sample data for supervised learning. In this embodiment, 729 simulation points are set within the target area. 800 different excitation parameter settings are selected within the preset excitation parameter range, and simulation calculations are performed separately to obtain 800 sets of corresponding physical field distribution results for the target area. Each set of results includes the state values ​​of the 729 simulation points under the corresponding excitation parameter conditions. By sampling multiple sets of excitation parameters in the parameter space and solving for the corresponding physical field distribution, a corresponding sample relationship between the excitation parameters and the overall physical field distribution is established, enabling the subsequent model to learn the influence of parameter changes on the global state distribution.

[0037] The second step is to train a reduced-order surrogate model based on the training dataset. The trained reduced-order surrogate model is a one-dimensional Fourier neural operator model. Its core essence is to establish a fast mapping relationship between the excitation parameters and the spatial coordinates of the target area spatial points through offline learning, thereby replacing the traditional high-cost electromagnetic field numerical simulation calculation and providing core forward computing capabilities for parameter inversion and global magnetic field reconstruction in the online stage.

[0038] 1. This reduced-order surrogate model consists of five sequentially connected modules: a parameter feature extraction branch, a spatial location encoding branch, a feature fusion layer, a Fourier neural operator backbone network, and a fully connected output layer. The specific implementation mechanisms of each module are as follows: 2. Parameter feature extraction branch: Taking the excitation parameters as input, the original low-dimensional excitation parameters are upgraded and features are extracted through at least two fully connected layers to output high-dimensional parameter features; all fully connected layers use the modified linear unit (ReLU) as a nonlinear activation function to explore the nonlinear correlation between the excitation parameters and the magnetic field distribution.

[0039] 3. Spatial Position Encoding Branch: Taking the spatial coordinates of the target area as input, the original coordinates are first geometrically enhanced by an integrated polar-Cartesian (IPHI) coordinate encoding module. The geometrically enhanced representation not only includes the original xyz coordinate information of the spatial point, but also constructs the pitch angle, azimuth angle, and distance features of the point relative to the reference position of the center of the target area. Subsequently, the geometrically enhanced coordinate information is processed by Fourier position encoding and a fully connected layer to output position embedding features, which are used to enhance the model's ability to express spatial geometric position and global magnetic field distribution.

[0040] 4. Feature Fusion Layer: Receives high-dimensional parameter features from the parameter feature extraction branch and location embedding features from the spatial location encoding branch. Performs element-wise multiplication of the two features to fuse them, so that the fused feature of each spatial point simultaneously contains the current activation parameter information and the spatial location information of that point. The fused features are then processed by batch normalization and input into the subsequent backbone network to improve the stability of model training.

[0041] 5. Fourier Neural Operator Backbone Network: Composed of multiple layers of stacked spectral convolutional units and pointwise convolutional units; the spectral convolutional units transform the input features to the frequency domain through fast Fourier transform, perform complex weight mapping on the main low-frequency modes, and then transform them back to the spatial domain through inverse fast Fourier transform to extract the global coupling features of the magnetic field distribution; the pointwise convolutional units use 1×1 convolutional kernels to supplement the extraction of local linear features of the magnetic field distribution; the outputs of the spectral convolutional units and the pointwise convolutional units in each layer are superimposed and processed by a nonlinear activation function to enhance the influence of the excitation parameter changes on the overall magnetic field distribution layer by layer.

[0042] 6. Fully connected output layer: Receives the high-dimensional features output by the Fourier neural operator backbone network, maps them to the magnetic field prediction values ​​of the corresponding spatial points, and completes the final forward computation.

[0043] Furthermore, the training process of this reduced-order surrogate model is as follows: using the excitation parameters and spatial coordinates of simulation points in the training dataset as inputs, and the simulation magnetic field value of the corresponding simulation point as the supervision signal, the parameters of each module of the model are iteratively updated using conventional optimization algorithms in this field until the prediction error of the model on the validation set converges to a preset range; the trained model can support two calling methods simultaneously: one is to input candidate parameters and sparse measurement point coordinates, and directly output the magnetic field prediction value of the corresponding measurement point (used in the parameter inversion stage); the other is to input the optimal state parameters and the coordinates of all simulation points in the target area, and output the magnetic field prediction value of all simulation points (used in the global magnetic field reconstruction stage).

[0044] The third step involves collecting measured state data from pre-defined sparse measuring points within the target area of ​​the complex equipment. After preprocessing, the sparse measuring point observation data is obtained. This step provides observational constraints for parameter inversion and serves as a bridge connecting the offline model and the actual equipment state. In this embodiment, nine sparse measuring points are arranged in a 3×3 equidistant pattern in the central region of the target area. This allows for the acquisition of the core physical field characteristics of the target area while controlling the number of measuring points, providing reliable constraints for subsequent parameter inversion.

[0045] The fourth step involves constructing an objective function using excitation parameters or equivalent state parameters as variables to be optimized and sparse measurement point observation data as constraints. The optimal state parameters are then obtained through iterative solving using the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) optimization algorithm. The variables to be optimized are excitation parameters that directly characterize the working state of the magnetic shielding equipment, or equivalent state parameters that have a one-to-one mapping relationship with the excitation parameters. The objective function measures the consistency between the current candidate parameters and the actual state. Mean squared error loss is used to calculate the difference between the predicted and measured values ​​of the reduced-order surrogate model at the sparse measurement point locations. If necessary, prior constraint terms and bias compensation terms can be combined to improve robustness against noise and abnormal deviations. The prior constraint terms are used to limit the parameters to be optimized within a physically reasonable range, and the bias compensation terms are used to correct systemic deviations caused by measurement noise.

[0046] In this implementation, the Covariance Matrix Adaptive Evolutionary Strategy Optimization (CMA-ES) algorithm is used to solve the problem. The search variable is the unit parameter u, and the boundary conditions are... In each iteration, the algorithm generates a set of candidate parameters based on the current mean and covariance matrix; for each candidate parameter, it calls a reduced-order surrogate model to calculate the predicted value of the measurement point and calculates the objective function. The search distribution is then updated based on the objective function value until the maximum number of evaluations or the error threshold is reached. The complete process of inverting the optimal state parameters using sparse measurement point observations is as follows: Step 1: Input observation data Input sparse measurement point observations

[0047] Step 2: Generate candidate parameters Generate candidate state parameter vectors:

[0048] Step 3: Invoke the downgraded proxy model Invoke the trained downgraded proxy model:

[0049] Step 4: Extract predicted values ​​of measuring points Extract the predicted values ​​of sparse measurement point locations from the model output:

[0050] Step 5: Construct the objective function Construct an objective function that includes Huber loss, parameter priors, and bias regularization. The complete expression is as follows:

[0051] Huber's loss function is a piecewise function: When |r| ≤ δ, ρ(r) = (1 / 2) * r² When |r|>δ, ρ(r) = δ * (|r| - (1 / 2)δ) Parameter normalization formula (maps the true parameters to a [0,1] unit space): u (θ) = (θ - LB) / (UB - LB) In the formula: Number of sparse measurement points Candidate parameters In the Predicted values ​​for each measuring point Overall zero-point offset compensation amount : No. Observations at each measuring point : Parameter prior constraint weights, : Weight of the bias regularization term : The normalized parameter corresponding to the prior center, δ: Huber loss threshold, r: The residual between the predicted value and the measured value after global zero-point bias compensation at the i-th sparse measurement point.

[0052] Step 6: Update candidate parameters The covariance matrix adaptive evolution strategy (CMA-ES) is adopted to update the search distribution based on the objective function value and generate new candidate parameters.

[0053] Step 7: Termination Condition Determination Determine if the termination condition is met: Termination condition: Reaching the maximum number of iterations or the objective function converges (using sparse measurement point error constraint parameter inversion). If the condition is not met: Return to step 2 and proceed to the next iteration. If satisfied: Proceed to step 8 Step 8: Output optimal parameters Output optimal state parameters:

[0054] The execution flow of the covariance matrix adaptive evolution strategy optimization algorithm is as follows: using the rated operating parameters of the magnetic shielding device as the initial parameter center, multiple sets of candidate parameters are generated in the parameter space; each set of candidate parameters and the coordinates of the sparse measurement points are input into the trained reduced-order surrogate model, and the reduced-order surrogate model directly outputs the magnetic field prediction value of the corresponding measurement point position; the fitness value corresponding to each set of candidate parameters is calculated according to the objective function, and the smaller the fitness value, the higher the matching degree between the candidate parameter and the actual state; the candidate parameters are sorted according to the fitness value from smallest to largest, and the candidate parameters with the best fitness are selected to adaptively update the mean and covariance matrix of the parameter search distribution; the above sampling, calculation and update process is repeated until the preset convergence condition or the maximum number of iterations is reached, and the candidate parameter with the smallest fitness value is output as the optimal state parameter.

[0055] The core of this step is to transform the inverse problem of recovering the global state from local measurement points into an optimization problem of finding the parameters that best match the observed data. The principle of parameter inversion is as follows: Figure 1 As shown in the figure. In this step, the trained reduced-order surrogate model provides fast forward computation capability for the optimization process. Each set of candidate parameters can quickly obtain the predicted value of the corresponding measurement point through the reduced-order surrogate model, without the need for repeated numerical simulation, which significantly improves the efficiency of parameter solution. Meanwhile, the covariance matrix adaptive evolution strategy optimization algorithm, as a well-known high-dimensional nonlinear optimization algorithm in this field, can efficiently find the optimum in the high-dimensional parameter space, avoid getting trapped in local optima, and ensure the accuracy and stability of the parameter inversion results.

[0056] The fifth step involves inputting the optimal state parameters into the trained reduced-order surrogate model to obtain the global state distribution results of the target area, thus completing the global performance monitoring of the complex equipment. Specifically, the optimal state parameters obtained in the previous steps, along with the spatial coordinates of all 729 simulation points within the target area, are input into the reduced-order surrogate model. The reduced-order surrogate model first performs dimensionality enhancement and feature extraction on the optimal state parameters through a parameter feature extraction branch to obtain high-dimensional parameter features. Simultaneously, it performs geometric enhancement and position encoding on the coordinates of each simulation point through a spatial position encoding branch to obtain the position embedding features corresponding to each simulation point. Subsequently, the high-dimensional parameter features and the position embedding features of each simulation point are multiplied and fused. After the fused features are processed by the Fourier neural operator backbone network to extract global and local features, the magnetic field prediction value of the corresponding simulation point is output by the fully connected output layer. After traversing all simulation points within the target area and completing the calculation, the prediction values ​​of each simulation point are inversely normalized (restoring to the actual magnetic field value) and arranged according to spatial position to obtain the global magnetic field distribution results of the target area.

[0057] In this embodiment, the overall architecture of the reduced-order proxy model consists of five parts: a parameter feature extraction branch, a spatial location encoding branch, a feature fusion layer, an FNO backbone network, and an output layer. 1. Parameter Feature Extraction Branch Input: Excitation / state parameter vector (4-dimensional).

[0058] First layer: Fully connected mapping layer FC0.

[0059] Output: High-dimensional parametric features ( (For parameter feature dimensions).

[0060] 2. Spatial location coding branch Input: Spatial point coordinates (3-dimensional).

[0061] First layer: Geometric enhancement representation, generating feature vectors: .

[0062] Second layer: Fourier positional encoding / IPHI.

[0063] Output: Location embedding features ( (Location feature dimension).

[0064] 3. Feature Fusion Layer Fusion method: point-by-point (Hadamard) fusion, that is, the parametric features and the location features are multiplied element by element.

[0065] Output: Fusion features, input into the FNO backbone network.

[0066] 4. FNO Backbone Network It consists of four identical series-connected units, each with the following structure: The system consists of four layers: a spectral convolutional layer, a 1×1 pointwise convolutional layer, and a GELU nonlinear activation function, connected sequentially.

[0067] 5. Output Layer First layer: Fully connected layer FC1.

[0068] Second layer: Fully connected layer FC2.

[0069] Output: Predicted state values ​​of spatial points ( (For output dimensions).

[0070] Core expression of the model:

[0071] Note: Input is a parameter. Coordinates of 729 spatial points The output is the state value of the corresponding spatial point.

[0072] in, : Excitation / state parameter vector ,in (Total number of spatial points in the target area) : Parameter characteristics, Location features Hadamard fusion operation (point-by-point fusion) These are the parameter feature dimension, the location feature dimension, and the output dimension, respectively.

[0073] In this embodiment, the complete process of generating the global state distribution of the target region from the optimal state parameters includes 5 core steps: Step 1: Input optimal parameters Input the optimal state parameters obtained from the inversion:

[0074] Step 2: Input the set of spatial coordinates Input the set of coordinates of all spatial points in the target region:

[0075] Step 3: Call the proxy model for global inference Invoke the trained and fixed-weights reduced-order surrogate model:

[0076] Core formula: Predict each of the 729 simulation points one by one to form a global distribution vector. Key advantage: No need to repeatedly perform costly numerical simulations. Step 4: Output the global state vector Output the global state value vector:

[0077] Step 5: Reconstruct the global distribution results The global state distribution of the target region is reconstructed, and the output format is a global magnetic field / global state distribution map.

[0078] This embodiment illustrates the actual execution process of the above three technical features. The target region is set with N=729 spatial points. In the offline phase, 800 sets of samples are constructed, each set containing 4-dimensional state parameters and the magnetic flux density modulus of 729 spatial points. After training, a fixed-weight FNO1d reduced-order surrogate model is obtained. In the online phase, nine sparse measurement points (3×3) at the center section of the target region are used as observation constraints. The state parameters are inverted using CMA-ES and then input into the surrogate model to obtain the global state distribution of 729 points.

[0079] The specific implementation method is as follows: 1. Parameters for the embodiment are detailed in Table 1. Table 1 Parameter Setting Table

[0080] 2. Sparse measurement point observation data This embodiment uses 3×3 measuring points at the center section of the target area. The observed values ​​in Table 2 are the measured values ​​of the measuring points after superimposing a 1% Gaussian perturbation on the reference state output; in actual engineering implementation, this column can be replaced with the actual measured values ​​of the sensor, and the objective function and solution process remain unchanged.

[0081] Table 2 Observation data of sparse measuring points

[0082] 3. The inversion results and global state distribution output are detailed in Table 3. Table 3 Inversion Results and Global State Distribution Output Results

[0083] As can be seen from the above embodiments, only nine measurement point observations are required in the online phase to obtain the optimal state parameters through objective function constraints and CMA-ES. Then The FNO1d reduced-order surrogate model, trained with the coordinates of 729 target area spatial points, can output a 729-dimensional global state distribution in one go. This process does not require re-calling the full numerical simulation solver, and the output format is a [X,Y,Z,yhat] data table, contour plot, or performance monitoring index.

[0084] This step is the ultimate goal of the invention. The optimal state parameters obtained through the previous steps can characterize the current working state of the complex device. By inputting them into the reduced-order proxy model, the overall physical field distribution of the target area can be quickly recovered through the fast mapping relationship between the learned parameters and the global field distribution. There is no need to perform a complete numerical simulation again. This achieves efficient reconstruction from a small amount of local measurement point data to the global state distribution, providing a complete basis for the performance evaluation of complex devices.

[0085] The above five steps form a complete technical closed loop. The offline stage of dataset construction provides a data foundation for model training. The trained reduced-order surrogate model provides core computing power for parameter inversion and global reconstruction in the online stage. The parameter inversion process transforms the local observations of sparse measurement points into parameter representations of the global state of the equipment. Finally, the global state distribution is reconstructed through the reduced-order surrogate model. Each step supports and works synergistically to jointly realize the global performance monitoring of complex equipment under sparse measurement point conditions.

[0086] In this embodiment, the specific implementation of the spatial location encoding branch is a core component of the reduced-order proxy model, providing the model with enhanced expressive power of spatial location information.

[0087] In this embodiment, the spatial location encoding branch uses the IPHI coordinate encoding module to geometrically enhance the coordinates of the input spatial point. This enhanced representation is then processed by Fourier location encoding and a fully connected layer to output the location embedding features. The geometrically enhanced representation not only includes the original xyz coordinates of the spatial point but also constructs angular features (pitch angle theta, azimuth angle fi) and distance features (radius) related to the central reference position, enabling a more comprehensive characterization of the relative positional relationship of the spatial point within the target region. Subsequently, the location information is mapped to a high dimension using Fourier location encoding and then processed by a fully connected layer to finally obtain the location embedding features.

[0088] In this context, the location embedding features output by the spatial location encoding branch can be fused with the high-dimensional parameter features output by the parameter feature extraction branch. This enables the model to distinguish the differences in physical field responses at different spatial locations under the same excitation parameters, effectively enhancing the model's ability to express spatial geometric locations and global state distribution patterns. This provides accurate location information support for the subsequent feature extraction of the Fourier neural operator backbone network and significantly improves the model's prediction accuracy for state values ​​at different spatial locations.

[0089] In this embodiment, the specific implementation of the parameter feature extraction branch is a core component of the reduced-order surrogate model, used to extract effective features from the excitation parameters.

[0090] In this embodiment, the parameter feature extraction branch performs dimensionality upscaling and feature extraction on the input activation parameters through a fully connected mapping layer, outputting high-dimensional parameter features. The fully connected mapping layer contains at least two fully connected layers and employs the ReLU nonlinear activation function. The original input activation parameters are typically low-dimensional vectors. The first fully connected layer upscales them, mapping them to a high-dimensional feature space. Subsequent fully connected layers then perform feature transformation and extraction, utilizing the ReLU nonlinear activation function to uncover the nonlinear correlation between the activation parameters and the physical field distribution, ultimately outputting high-dimensional parameter features suitable for subsequent network computation.

[0091] In this context, the high-dimensional parameter features output by the parameter feature extraction branch contain the core information about the influence of excitation parameters on the physical field distribution. This information can be fused with the location embedding features output by the spatial location encoding branch, enabling the model to establish the correlation between changes in excitation parameters and the global state distribution. This provides the core information of parameter conditions for the subsequent feature extraction of the Fourier neural operator backbone network, ensuring that the model can accurately learn the physical field distribution patterns under different excitation parameters.

[0092] In this embodiment, the feature fusion layer is a core component that connects the parameter feature extraction branch, the spatial location coding branch, and the subsequent backbone network, and is used to achieve the joint representation of parameter information and location information.

[0093] In this implementation, the feature fusion layer performs dot product fusion on high-dimensional parametric features and location embedding features, outputting fused features that simultaneously contain both excitation parameter information and spatial location information. Specifically, dot product fusion involves multiplying corresponding dimensions, ensuring that each spatial location's feature incorporates both the current excitation parameter conditions and the spatial information of that location, establishing a correspondence between "parameters-location-physical response." The fused features are further processed through batch normalization to adjust the feature distribution range and improve the stability of model training.

[0094] This technical feature plays a crucial role in the reduced-order surrogate model: it connects the parameter feature extraction branch and the spatial location encoding branch, effectively fusing the two independent features to provide the subsequent Fourier neural operator backbone network with fused features that simultaneously contain parameter conditions and location information. This enables the backbone network to learn the global influence of the excitation parameters and the local differences in spatial location at the same time, which is the core foundation for the model to accurately predict state values ​​of different parameters and different locations.

[0095] In this embodiment, the specific structure of the Fourier neural operator backbone network is the core of the reduced-order surrogate model, used to extract global and local features of the physical field distribution to achieve accurate physical field prediction.

[0096] In this embodiment, the Fourier neural operator backbone network is composed of multiple layers of stacked spectral convolutional units and pointwise convolutional units. The spectral convolutional units first transform the input features to the frequency domain using a Fast Fourier Transform (FFT), then perform complex weight mapping on the main low-frequency modes in the frequency domain, and finally transform them back to the spatial domain using an Inverse Fast Fourier Transform (IFT). This effectively captures the global coupling features in the physical field distribution and adapts to the long-range spatial dependence characteristics of the physical field distribution. The pointwise convolutional units use 1×1 convolutional kernels to supplement the expressive power of local linear features and capture the details of local changes in the physical field distribution. In each layer, the outputs of the spectral convolutional units and the pointwise convolutional units are superimposed, and then processed by a nonlinear activation function to extract and enhance the influence of changes in excitation parameters on the overall physical field distribution layer by layer.

[0097] In this configuration, it works synergistically with the preceding feature fusion layer and the subsequent fully connected output layer. The fused features output from the feature fusion layer are input into the backbone network, and through stacked multi-layer spectral convolutions and pointwise convolutions, both the global coupling relationships and local variation features of the physical field distribution are captured. The final high-dimensional features are then input into the fully connected output layer to obtain the state prediction values ​​for the corresponding spatial points. This structure fully leverages the advantages of Fourier neural operators in function space mapping learning, accurately fitting the nonlinear mapping relationship from activation parameters to the global state distribution, while also possessing excellent generalization ability, ensuring the prediction accuracy of the model under different activation parameters.

[0098] In this embodiment, the specific form of the objective function during the parameter inversion process is the core design to ensure the robustness and accuracy of the parameter inversion results.

[0099] In this embodiment, the objective function employs a robust error function that combines prior constraint terms and bias compensation terms. The main error component characterizes the difference between the predicted values ​​of the reduced-order surrogate model at the measurement point locations and the observed values ​​at sparse measurement points, preferentially using mean squared error loss. The prior constraint term constrains the reasonable range of the excitation parameters, preventing the inverted parameters from exceeding the physically reasonable range and avoiding unrealistic parameter results. The bias compensation term corrects for deviations caused by measurement noise, effectively reducing the impact of random measurement errors and outliers on the parameter solution results.

[0100] In this context, it works in synergy with other aspects of parameter inversion. The objective function is the optimization target of the covariance matrix adaptive evolution strategy optimization algorithm. A robust objective function can guide the optimization algorithm to seek parameters that conform to the actual physical meaning and have a higher degree of matching with the observation data, avoiding the algorithm from getting trapped in local optima or outputting parameter results that do not meet the requirements. At the same time, it improves the anti-interference ability of the parameter inversion process against measurement noise, ensuring the stability and accuracy of the parameter inversion results under actual engineering measurement conditions.

[0101] In this embodiment, the iteration termination condition of the covariance matrix adaptive evolution strategy optimization algorithm is a key design that balances the efficiency and accuracy of parameter inversion.

[0102] In this embodiment, the iteration termination condition of the covariance matrix adaptive evolutionary strategy optimization algorithm is set as two conditions: first, the number of iterations reaches a preset threshold; second, the objective function value is less than a preset error threshold. Iteration terminates when either condition is met. In actual execution, the algorithm starts from the initial parameter center, generates multiple sets of candidate parameters in the parameter space, calculates the objective function value corresponding to each candidate parameter, updates the search distribution based on the fitness results, and repeats the iteration process. Iteration terminates when the number of iterations reaches the preset maximum number of iterations, or when the objective function value drops below the preset error threshold, and the optimal parameter result is output.

[0103] In this context, it works in synergy with the overall parameter inversion process. By presetting the maximum number of iterations, it avoids infinite iterations of the algorithm, ensuring that the parameter inversion process can be completed within a limited time, adapting to the needs of rapid monitoring in engineering sites. By presetting an error threshold, it ensures that the parameter inversion results meet the preset accuracy requirements, avoiding parameter result deviations caused by insufficient iterations. The setting of dual termination conditions effectively balances the efficiency and accuracy of parameter inversion, enabling this method to achieve fast and accurate parameter solutions in engineering applications.

[0104] In this embodiment, the preprocessing of sparse measurement point observation data is a crucial step in ensuring that the parameter inversion process is adapted to the actual engineering scenario.

[0105] In this embodiment, the preprocessing of sparse measurement point observation data includes superimposing Gaussian distributed noise on the measured state data to simulate measurement disturbances, followed by standardization. The Gaussian distributed noise has a mean of 0 and a preset variance, which can be adjusted according to the measurement accuracy of the actual sensor to simulate random errors and disturbances present in real sensor measurements. Standardization adjusts the measurement point data to a numerical range consistent with the model training data, ensuring it meets the input requirements for subsequent parameter inversion calculations.

[0106] In this context, it works in synergy with the parameter inversion process. By superimposing Gaussian noise to simulate measurement disturbances, the preprocessed observation data is made closer to real engineering measurement conditions. The parameter inversion process based on this data can effectively verify the robustness of the method in actual measurement scenarios. Through standardization, the distribution consistency between the observation data and the model training data is ensured, avoiding model prediction bias caused by differences in data scale, and further improving the stability and accuracy of the parameter inversion process.

[0107] In this embodiment, the composition and preprocessing of the training dataset are fundamental to ensuring the training effect of the downgraded proxy model.

[0108] In this embodiment, the training dataset consists of 800 sets of one-to-one corresponding samples of the global state distribution of the target region, with each set containing the location coordinates and state values ​​of 729 simulation points within the target region under the corresponding excitation parameters. Data preprocessing includes data normalization and outlier removal. Data normalization scales the state values ​​to a uniform numerical range, and the normalized results are then restored to the actual state values ​​during model output, improving the stability of model training. Outlier removal removes abnormal data that may occur during simulation calculations, preventing interference with model training. The dataset is further divided into a training set, a validation set, and a test set, used for model training, parameter tuning, and performance verification, respectively.

[0109] In this context, it collaborates with the training phase of the reduced-order surrogate model. A comprehensive and standardized training dataset provides ample supervised learning samples for the reduced-order surrogate model, enabling it to fully learn the physical field distribution patterns of the target region under different excitation parameters. The standardized preprocessing effectively improves the convergence speed and stability of the model training process, ensuring that the trained model possesses excellent prediction accuracy and generalization ability, providing a reliable model foundation for subsequent online parameter inversion and global state distribution reconstruction.

[0110] In this embodiment, the number and arrangement of sparse measurement points are the core design considerations that balance measurement cost and inversion accuracy.

[0111] In this embodiment, there are nine sparse measurement points, arranged in a 3×3 equidistant pattern in the central region of the complex equipment target area. The spacing between adjacent measurement points is a preset fixed value, which is determined according to the size of the complex equipment target area. The 3×3 equidistant arrangement can form a uniform distribution of observation points in the central region of the target area, fully acquiring the physical field distribution characteristics of the core area of ​​the target area, and providing uniform and reliable local observation constraints for parameter inversion.

[0112] In this context, it works synergistically with the parameter inversion process: the setting of 9 sparse measurement points significantly reduces the reliance on high-density measurement point deployment, lowers measurement costs and reduces the difficulty of on-site deployment, and is suitable for practical scenarios in engineering where measurement point deployment space is limited and testing costs are high; at the same time, the 3×3 equidistant arrangement can provide sufficient local observation constraints for parameter inversion, avoid deviations in inversion results caused by uneven distribution of measurement points, ensure the accuracy of parameter inversion results under conditions of a small number of measurement points, and thus ensure the accuracy of global state distribution reconstruction.

[0113] In summary, this embodiment, through the synergistic combination of the above-mentioned technical features, forms a complete method for global performance monitoring of complex equipment driven by sparse measurement points. It can achieve rapid recovery of the overall physical field distribution of the target area using only a small amount of sparse measurement point data. It effectively solves the problems of high measurement cost, high cost of repeated simulation calculation, difficulty in effectively representing the overall physical field distribution under limited measurement point conditions, insufficient stability of direct inversion, and inconvenience in engineering application in the prior art, and has excellent engineering application value.

[0114] The embodiments described above do not constitute a limitation on the scope of protection of this technical solution. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the above embodiments should be included within the scope of protection of this technical solution.

Claims

1. A sparse measurement point-driven global performance monitoring method for complex equipment, used for target area state distribution reconstruction and performance monitoring of magnetically shielded complex equipment, characterized in that, Includes the following steps: A physical field simulation analysis model of the complex device is established. Simulation points are preset in the target area. Through simulation calculations of multiple sets of different excitation parameters, the state value data of each simulation point in the target area corresponding to each set of excitation parameters is obtained. After preprocessing, a training dataset is constructed. Train a reduced-order proxy model based on the aforementioned training dataset; Collect measured state data of preset sparse measuring points within the target area of ​​complex equipment, and obtain sparse measuring point observation data after preprocessing; Using the excitation parameters or equivalent state parameters as variables to be optimized, and the sparse measurement point observation data as constraints, an objective function is constructed, and the optimal state parameters are obtained by iteratively solving the optimization algorithm. The optimal state parameters are input into the trained reduced-order proxy model to obtain the global state distribution results of the target area, thereby completing the global performance monitoring of the complex device.

2. The method according to claim 1, characterized in that, The reduced-order proxy model is a one-dimensional Fourier neural operator model. It takes the activation parameters as conditional input and the spatial coordinates of the target region as position input, and outputs the state prediction value of the corresponding spatial point. The spatial position encoding branch performs geometric enhancement on the input spatial point coordinates through an integrated polar-Cartesian (IPHI) coordinate encoding module, and then processes it through Fourier position encoding and a fully connected layer to output the position embedding feature. The geometrically enhanced representation includes the original coordinate information of the spatial point, as well as the angular and distance features related to the central reference position.

3. The method according to claim 2, characterized in that, The reduced-order surrogate model includes a parameter feature extraction branch, a spatial location encoding branch, a feature fusion layer, a Fourier neural operator backbone network, and a fully connected output layer. The parameter feature extraction branch performs dimensionality upscaling and feature extraction on the input activation parameters through a fully connected mapping layer, and outputs high-dimensional parameter features. The fully connected mapping layer includes at least two fully connected layers and uses the modified linear unit (ReLU) nonlinear activation function.

4. The method according to claim 3, characterized in that, The feature fusion layer performs dot product fusion on high-dimensional parameter features and location embedding features, and outputs a fused feature that simultaneously contains excitation parameter information and spatial location information; the dot product fusion is the multiplication of corresponding dimension elements, and the fused feature is then subjected to batch normalization.

5. The method according to claim 3, characterized in that, The Fourier neural operator backbone network is composed of multiple layers of stacked spectral convolutional units and pointwise convolutional units. The spectral convolutional units transform the input features to the frequency domain through fast Fourier transform, perform complex weight mapping on the low-frequency modes, and then transform them back to the spatial domain through inverse fast Fourier transform to extract global coupled features. The pointwise convolutional units use 1×1 convolutional kernels to extract local linear features. The outputs of the spectral convolutional units and the outputs of the pointwise convolutional units in each layer are superimposed and then processed by a nonlinear activation function.

6. The method according to claim 1, characterized in that, The objective function is a robust error function that combines prior constraints and bias compensation terms; the prior constraints are reasonable range constraints on the excitation parameters, and the bias compensation terms are used to correct deviations caused by measurement noise.

7. The method according to claim 1, characterized in that, The optimization algorithm is a covariance matrix adaptive evolution strategy optimization algorithm, and its iteration termination condition is that the number of iterations reaches a preset threshold, or the objective function value is less than a preset error threshold.

8. The method according to claim 1, characterized in that, The preprocessing of the sparse measurement point observation data includes superimposing Gaussian distributed noise on the measured state data to simulate measurement disturbances, and then performing standardization processing; the mean of the Gaussian distributed noise is 0, and the variance is a preset value.

9. The method according to claim 1, characterized in that, The training dataset consists of multiple sets of one-to-one corresponding samples of the excitation parameters and the global state distribution of the target region. Each set of samples contains the position coordinates and state values ​​of all simulation points in the target region under the corresponding excitation parameters. The preprocessing includes data normalization and outlier removal.

10. The method according to claim 1, characterized in that, The number of sparse measuring points is 9, and they are arranged in a 3×3 equidistant pattern in the center of the target area of ​​the complex equipment. The spacing between adjacent measuring points is a preset fixed value; the preset fixed value is determined according to the size of the target area of ​​the complex equipment.

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