Sparse observation wave field reconstruction method and system based on explosion wave dynamics constraint neural operator

Abstract

The application discloses a sparse observation wave field reconstruction method and system based on explosion wave dynamics constraint neural operator, and relates to the field of data processing.The method comprises the following steps: obtaining explosion source parameters, boundary parameters, pressure data of sparse measuring points, measuring point coordinates and sampling time of an explosion shock wave field; constructing a degenerate observation mapping from a continuous wave field to discrete measuring points according to the measuring point coordinates, the sampling time and the explosion source parameters; encoding the pressure data, the measuring point coordinates, the explosion source parameters, the boundary parameters and the time part in the degenerate observation mapping into initial features of the measuring points, obtaining features of the measuring points according to the initial features of the measuring points and the space part in the degenerate observation mapping, inputting the features of the measuring points into a pre-trained neural operator, and obtaining a continuous spatiotemporal distribution result of the explosion shock wave field.Through the above scheme, the accuracy, stability and physical credibility of the reconstruction result of the explosion shock wave field under the condition of sparse observation can be improved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a sparse observation wavefield reconstruction method and system based on explosion wave dynamics constrained neural operators. Background Technology

[0002] Explosion shock waves are typical transient physical phenomena in fields such as explosions, weapon damage assessment, protective structure design, industrial blasting, safety assessment, and special testing. After an explosion, the shock wave rapidly generates a strong, discontinuous, high-gradient, and highly nonlinear pressure disturbance within a very short time, and then propagates, attenuates, reflects, and superimposes in space. Accurately obtaining the spatial distribution and evolution of the explosion shock wave field is crucial for assessing explosion power, optimizing protective structures, delineating hazardous areas, and interpreting test data.

[0003] Currently, explosion shock wave testing mainly relies on pressure sensors, overpressure sensors, or dynamic pressure testing systems deployed at specific locations. These systems record typical parameters such as shock wave arrival time, peak pressure, duration of barotropic action, and impulse through discrete measuring points. With the development of dynamic testing technology, the accuracy and sampling frequency of single-point pressure testing have been significantly improved, enabling better acquisition of transient response information at the measuring points. However, the explosion shock wave field is essentially a continuous spatiotemporal field. Relying on only a limited number of measuring points is insufficient to fully reflect the propagation pattern, peak distribution, and local high-gradient changes of the shock wave in space. Especially in field explosion tests, weapon effect tests, and complex boundary environments, the number of sensors is usually limited due to constraints such as testing cost, safety distance, deployment space, sensor survivability, and synchronous acquisition conditions. The distribution of measuring points often exhibits sparse, irregular, and locally missing characteristics. Therefore, how to reconstruct the continuous explosion shock wave field based on limited discrete observation data has become a key technical problem in explosion testing and shock wave effect analysis.

[0004] Methods for obtaining the shock wave field of an explosion mainly fall into three categories: empirical formula estimation, numerical simulation calculation, and data-driven reconstruction. Empirical formulas or semi-empirical models typically estimate parameters such as overpressure peak, arrival time, and impulse based on the explosion equivalent, distance from the explosion center, propagation medium, and empirical attenuation laws. They offer advantages such as simple calculation and ease of engineering application. However, they are often based on assumptions of an ideal free field, homogeneous medium, and regular propagation, making it difficult to accurately describe phenomena such as shock wave reflection, diffraction, obstruction, local enhancement, and multi-wave superposition under complex boundary conditions. Numerical simulation methods typically employ finite element, finite volume, or computational fluid dynamics methods to model the explosion source term, air medium, boundary conditions, and structural response. They can comprehensively characterize the shock wave propagation process, but they are highly sensitive to mesh quality, time step, source term model, and boundary parameters, resulting in high computational costs. Furthermore, the explosion source state, environmental disturbances, and sensor positions in actual field tests are difficult to model accurately, leading to discrepancies between simulation results and measured data. Therefore, relying solely on empirical formulas or numerical simulations is insufficient to meet the demand for rapid and accurate reconstruction of the explosion shock wave field under limited measured data conditions.

[0005] In recent years, spatial interpolation, compressed sensing, machine learning, deep learning, physical information neural networks, and neural operators have been increasingly used for wavefield reconstruction under sparse measurement conditions. These methods can infer the pressure distribution in unmeasured areas using limited sensor observation data, thus improving field estimation capabilities under discrete observation conditions to some extent. However, traditional interpolation methods typically rely on the assumption of smooth continuity, making it difficult to adapt to the strong discontinuities, high gradients, and abrupt changes in local peaks in explosion shock waves. While pure data-driven models have strong nonlinear fitting capabilities, they usually rely on a large number of high-quality samples and lack explicit constraints on the propagation dynamics, conservation relationships, and physical boundary conditions of explosion waves, easily leading to non-physical pseudo-solutions, peak position shifts, and local structural distortions. Although existing physical information neural networks and neural operators provide new technical paths for continuous wavefield reconstruction, they still suffer from shortcomings in explosion wavefield applications, such as insufficient embedding of dynamic mechanisms, poor adaptability to sparse and irregular observations, and limited generalization ability under different explosion conditions and measurement point layouts. Therefore, it remains difficult to achieve coordinated reconstruction of the peak distribution, propagation time sequence, and spatial evolution structure of explosion shock waves.

[0006] Therefore, it is necessary to propose a wavefield reconstruction method and system that integrates explosion wave dynamics constraints, sparse observation mapping, and the continuous field expression capabilities of neural operators, so as to improve the accuracy, stability, and physical reliability of explosion shock wavefield reconstruction results under sparse observation conditions. Summary of the Invention

[0007] Therefore, it is necessary to provide a sparse observation wavefield reconstruction method and system based on explosion wave dynamics constrained neural operators to address the above-mentioned technical problems, which can improve the accuracy of continuous wavefield recovery under sparse measurement point conditions.

[0008] Firstly, this application provides a sparse observation wavefield reconstruction method based on explosion wave dynamics-constrained neural operators. The method includes:

[0009] Acquire the explosion source parameters, boundary parameters, pressure data, coordinates, and sampling time of sparse measuring points in the explosion shock wave field;

[0010] Based on the coordinates of the measuring points, the sampling time, and the parameters of the explosion source, a degenerate observation map from the continuous wave field to the discrete measuring points is constructed; wherein, the degenerate observation map characterizes the spatiotemporal propagation correlation between the measuring points;

[0011] The pressure data, measuring point coordinates, explosion source parameters, boundary parameters, and the temporal portion of the degradation observation map are encoded as initial features of the measuring point. The measuring point features are obtained based on the initial features of the measuring point and the spatial portion of the degradation observation map. The measuring point features are then input into a pre-trained neural operator to obtain the continuous spatiotemporal distribution results of the explosion shock wave field.

[0012] In one embodiment, constructing a degenerate observation mapping from the continuous wave field to discrete measurement points based on the measurement point coordinates, sampling time, and explosion source parameters includes:

[0013] Obtain the blast center coordinates from the blast source parameters, and then determine the straight-line distance between the blast center and each measuring point based on the blast center coordinates and the measuring point coordinates.

[0014] Based on the equivalent propagation velocity and straight-line distance, the estimated arrival time of the explosion shock wave at each measuring point is obtained;

[0015] Based on the estimated arrival time of each measuring point, the propagation delay characteristics are obtained and used as the time component in the degraded observation mapping.

[0016] Based on the coordinates of the measurement points and the characteristics of the propagation delay, the propagation adjacency weights are obtained and used as the spatial component in the degraded observation map.

[0017] In one embodiment, obtaining the measurement point features based on the initial features of the measurement point and the spatial portion of the degraded observation map includes:

[0018] The propagation neighborhood of each measuring point is obtained from the spatial portion of the degraded observation map;

[0019] For any measurement point, the initial feature of the measurement point is used as the current feature. The current feature corresponding to the measurement point is aggregated with the current feature corresponding to the propagation neighborhood. The aggregation result is then updated as the current feature of the measurement point to enter the next round of feature update.

[0020] In one embodiment, the neural operator introduces explosion wave dynamics constraints during training, which include: arrival time constraints, peak decay constraints, wavefront continuity constraints, governing equation residual constraints, and boundary condition constraints.

[0021] In one embodiment, the loss function of the neural operator during training includes supervision loss, observation loss, and physical residual loss;

[0022] The supervisory loss is constructed based on the error between the predicted stress value output by the neural operator and the actual stress value.

[0023] The observation loss is constructed based on the error between the predicted pressure value and the pressure data;

[0024] The physical residual loss is constructed based on arrival time constraints, peak attenuation constraints, wavefront continuity constraints, governing equation residual constraints, and boundary condition constraints.

[0025] In one embodiment, the continuous spatiotemporal distribution results include: pressure prediction values ​​at any location and at any time within a specified spatial region, as well as overpressure peak distribution, wavefront arrival time distribution, and impulse distribution during the barotropic action phase extracted from the pressure prediction values.

[0026] Secondly, this application also provides a sparse observation wavefield reconstruction system based on explosion wave dynamics-constrained neural operators. The system includes:

[0027] The data acquisition module is used to acquire the explosion source parameters, boundary parameters, pressure data, coordinates, and sampling time of the explosion shock wave field;

[0028] The sparse observation preprocessing module is used to reconstruct the sparse observation explosion shock wave field based on the explosion source parameters, boundary parameter pressure data, and measurement point coordinates;

[0029] The degenerate observation mapping module is used to construct a degenerate observation mapping from the continuous wave field to discrete measurement points based on the measurement point coordinates, sampling time, and explosion source parameters; wherein, the degenerate observation mapping characterizes the spatiotemporal propagation correlation between measurement points;

[0030] The output module encodes pressure data, measuring point coordinates, explosion source parameters, boundary parameters, and the temporal portion of the degraded observation map into initial features of the measuring point. Based on the initial features of the measuring point and the spatial portion of the degraded observation map, the module obtains the measuring point features and inputs them into a pre-trained neural operator to obtain the continuous spatiotemporal distribution results of the explosion shock wave field.

[0031] Thirdly, this application also provides a computer device. The computer device includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the sparse observation wavefield reconstruction method based on explosion wave dynamics constrained neural operators described above.

[0032] Fourthly, this application also provides a computer-readable storage medium. This computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps in the sparse observation wavefield reconstruction method based on explosion wave dynamics constrained neural operators described above.

[0033] Fifthly, this application also provides a computer program product. The computer program product includes a computer program that, when executed by a processor, implements the steps in the sparse observation wavefield reconstruction method based on explosion wave dynamics-constrained neural operators described above.

[0034] The aforementioned sparse observation wavefield reconstruction method and system based on explosion wave dynamics-constrained neural operators includes the following steps: acquiring the explosion source parameters and boundary parameters of the explosion shock wave field, as well as the pressure data, coordinates, and sampling time of sparse measuring points; constructing a degenerate observation mapping from the continuous wavefield to discrete measuring points based on the measuring point coordinates, sampling time, and explosion source parameters; wherein, the degenerate observation mapping characterizes the spatiotemporal propagation correlation between measuring points; encoding the pressure data, measuring point coordinates, explosion source parameters, boundary parameters, and the temporal component of the degenerate observation mapping as initial features of the measuring points; obtaining measuring point features based on the initial features and the spatial component of the degenerate observation mapping; and inputting the measuring point features into a pre-trained neural operator to obtain the continuous spatiotemporal distribution results of the explosion shock wave field. This approach improves the accuracy, stability, and physical reliability of the explosion shock wave field reconstruction results under sparse observation conditions. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating a sparse observation wavefield reconstruction method based on explosion wave dynamics constrained neural operators in one embodiment.

[0036] Figure 2 This is a schematic diagram of the degenerate observation mapping of sparse irregular measurement points in one embodiment;

[0037] Figure 3 A block diagram of a neural operator structure that incorporates explosion wave dynamics constraints in one embodiment;

[0038] Figure 4 Here is a flowchart of the training process for an explosion wave dynamics-constrained neural operator in one embodiment;

[0039] Figure 5 This is a block diagram of a sparse observation wavefield reconstruction system based on explosion wave dynamics constrained neural operators in one embodiment. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0041] Existing explosion shock wave field reconstruction technology still has many limitations and cannot meet the requirements for accurate recovery of continuous wave fields under sparse measurement point conditions. Traditional empirical formulas and semi-empirical models typically rely on proportional distance, explosive yield, and ideal free-field propagation assumptions. They are suitable for estimating parameters such as peak overpressure, arrival time, and impulse at a single point, but struggle to describe the real wave field evolution under complex boundaries, non-uniform media, reflection superposition, and local high gradient abrupt changes. While numerical simulation methods can comprehensively characterize the propagation process of explosive waves, they are highly sensitive to grid scale, time step, explosive source model, boundary conditions, and environmental parameters, resulting in high computational costs and difficulty in real-time fusion with limited measurement data from actual external fields. Traditional interpolation, regression, and compressed sensing methods often rely on assumptions of smooth, continuous, or sparse representations. When faced with the strong discontinuities, strong nonlinearities, peak abrupt changes, and propagation temporal coupling characteristics of explosive shock wave fields, they are prone to peak attenuation, wavefront position shifts, and local structural distortions. Although pure data-driven deep learning models possess nonlinear fitting capabilities, they typically rely on a large number of high-quality training samples and lack mechanisms for explosive wave dynamics, propagation constraints, and physical consistency discrimination. They are prone to generating non-physical pseudo-solutions in unmeasured regions and have insufficient generalization ability when faced with different explosive yields, different measurement point layouts, and different boundary conditions.

[0042] To address the aforementioned problems, this application provides a sparse observation wavefield reconstruction method based on explosion wave dynamics-constrained neural operators, such as... Figure 1 As shown, it includes the following steps:

[0043] S1. Obtain the explosion source parameters, boundary parameters, pressure data, coordinates, and sampling time of the sparse measuring points in the explosion shock wave field.

[0044] Among them, the explosion source parameters characterize the initial excitation conditions of the explosion wave, including the explosion yield, explosion center coordinates, detonation time, and charge type.

[0045] Boundary parameters are used to constrain the wave field propagation path, including ground boundaries, obstacle boundaries, and reflection boundaries.

[0046] Pressure data from sparsely spaced measuring points is acquired by sensors deployed at these points. This data includes the pressure time history, sampling frequency, and time window for each measuring point. The sampling time can be determined based on the sampling frequency and time window. Each measuring point has unique coordinates, a measuring point number, and other parameters.

[0047] In addition, this embodiment will collect environmental parameters, including temperature, air pressure, medium parameters, and sound speed correction parameters, to correct the propagation attenuation law of the shock wave, thereby reconstructing the explosion shock wave field more accurately.

[0048] S2. Denoise, normalize, synchronize time, and remove outliers from the pressure signals at each measuring point to form a sparse observation dataset.

[0049] Let the continuous pressure field of the explosion shock wave be represented as:

[0050]

[0051] in, Indicates spatial location, Indicates the spatial region to be reconstructed. Indicates time, This represents the observation time window. In actual testing, pressure time history data can only be obtained at a limited number of measuring points. Let the first point be... The coordinates of the measuring points are The corresponding observed pressure is:

[0052]

[0053] in, For the first Each measuring point is at The measured pressure value at any given time. For measuring noise.

[0054] For all Each measuring point and At each sampling time, sparse observations can be represented as:

[0055]

[0056] in, This represents the sampling operator from a continuous pressure field to observations at sparse measuring points. Represents the set of coordinates of the measuring points. This represents the set of sampling times.

[0057] The objective of this invention is based on observation from finite measurement points. Coordinates of measuring points Explosion source parameters and boundary conditions Reconstruct the shock wave field of an explosion at any location and at any time within the entire space region:

[0058]

[0059] in, The explosion wave dynamics constrained neural operator constructed in this invention, For network parameters, To reconstruct the pressure field.

[0060] S3. Based on the coordinates of the measuring points, the sampling time, and the parameters of the explosion source, construct a degenerate observation map from the continuous wave field to the discrete measuring points; whereby the degenerate observation map characterizes the spatiotemporal propagation correlation between the measuring points.

[0061] In actual explosion tests, the distribution of measurement points is usually not a regular grid, but rather an irregular sparse topology formed by limitations such as safety distance, site space, deployment conditions, and sensor survivability. To avoid peak attenuation and wavefront shift caused by direct interpolation, this embodiment first constructs a degenerate observation mapping from the continuous wavefield to the discrete measurement point response.

[0062] like Figure 2 As shown, the degradation observation mapping module uses the explosion center coordinates, measuring point coordinates, sampling time series, and measuring point pressure data as inputs to construct the propagation correlation between measuring points and explosion sources, and between measuring points.

[0063] For the first The linear distance between each measuring point and the explosion center is:

[0064]

[0065] in, Let be the coordinates of the explosion center. Based on the sound velocity of the medium and the equivalent propagation velocity of the explosion shock wave, the first... Theoretical arrival time estimates for each measuring point:

[0066]

[0067] in, For the detonation moment, To account for the equivalent propagation velocity after environmental parameter correction, the propagation delay characteristics at the measurement points are further constructed:

[0068]

[0069] in, Indicates the first The measuring point and the first The propagation time difference between measurement points is caused by the difference in spatial distance.

[0070] To characterize the spatial propagation association between irregular measurement points, this invention constructs a propagation adjacency weight:

[0071]

[0072] in, For measuring points With measuring points Propagation correlation weight between them and These are spatial scale parameters and time scale parameters, respectively. This method establishes connections between measuring points not only based on spatial distance but also on the dynamic correlation based on the shock wave propagation delay, thus avoiding erroneous propagation relationships caused by mere spatial proximity.

[0073] S4. Construct dynamic constraints for the explosion wave, including propagation arrival time constraints, peak attenuation constraints, wavefront continuity constraints, boundary condition constraints, and residual constraints of the governing equations.

[0074] First, the arrival time constraint is based on the fact that when the blast shock wave propagates outward from the blast center, the arrival time at different locations should have a consistent relationship with the propagation distance.

[0075] Suppose the reconstructed pressure field is at location The arrival time at:

[0076]

[0077] in, The pressure reaches the threshold for judgment. The arrival time constraint can be expressed as:

[0078]

[0079] Where M represents the number of sampling points.

[0080] Second, the peak attenuation constraint is based on the fact that the peak overpressure of the explosion shock wave generally decreases with the propagation distance.

[0081] Let the peak reconfiguration pressure be:

[0082]

[0083] The peak attenuation constraint can then be expressed as:

[0084]

[0085] in, Let be the empirical or semi-empirical decay function determined by the explosive yield and propagation distance. This constraint does not require the model to be completely equivalent to the empirical formula, but rather treats it as a physical prior to prevent the reconstructed peak from exhibiting anomalies that significantly violate the decay law.

[0086] Third, the wavefront continuity constraint is based on the following fact: the wavefront of an explosion shock wave should have a continuous propagation characteristic in an unobstructed area, and should not exhibit unfounded breaks or reverse propagation in unmeasured areas.

[0087] The wavefront continuity constraint can be expressed as:

[0088]

[0089] This constraint can suppress local mutations and non-physical propagation paths in the arrival time field.

[0090] Fourth, residual constraints of the governing equations. Within a locally continuous region, the propagation of pressure disturbances can be approximately constrained by the wave equation or the equivalent fluid dynamics equation.

[0091] To reduce computational complexity, this invention constructs a pressure field residual at the output of the neural operator:

[0092]

[0093] The corresponding physical residual loss is:

[0094]

[0095] In regions with strong discontinuities in the wavefront, the peak value of the shock wave can be avoided by increasing the wavefront weight or introducing piecewise residual weights.

[0096] Fifth, boundary condition constraints. For ground, wall, obstacle, or other reflective boundaries, the reconstructed pressure field should satisfy the corresponding boundary conditions. For rigid reflective boundaries, normal gradient constraints can be used:

[0097]

[0098] in, For the boundary normal vector, This represents the number of boundary sampling points.

[0099] S5. Input the pressure data, explosion source parameters, measurement point coordinates and boundary conditions into the neural operator reconstruction network to obtain the continuous pressure field prediction results.

[0100] This invention employs a neural operator as the core model for continuous wavefield reconstruction. Unlike the point-to-point mapping of traditional neural networks, the neural operator learns function-to-function mapping relationships, enabling it to map the pressure response of sparse measurement points into a continuous pressure field function. Therefore, it is suitable for wavefield reconstruction under different numbers of measurement points, different measurement point layouts, and different reconstruction regions.

[0101] like Figure 3 As shown, the neural operator reconstruction network of the present invention includes an input encoding layer, a propagation feature extraction layer, a neural operator mapping layer, a physical constraint fusion layer, and a continuous field output layer.

[0102] The input encoding layer encodes the pressure sequence at the measuring point, the coordinates of the measuring point, the explosion source parameters, and the boundary parameters into a unified feature:

[0103]

[0104] in, For the input encoding function, For the first Initial characteristics of each measurement point.

[0105] The feature extraction layer propagates the adjacency matrix using measurement points. Aggregate sparse measurement point features:

[0106]

[0107] in, For the first Layer measurement point characteristics, and For trainable parameters, It is a non-linear activation function. For measuring points The propagation neighborhood.

[0108] The neural operator mapping layer further maps sparse measurement point features to arbitrary query points in a continuous space. Its basic form is:

[0109]

[0110] in, For the first Layered continuous latent variable field, This is a learnable kernel function. The target query point (output location). This represents a historical point (input location) in the integration domain. Through this operator mapping, the model can output pressure values ​​at any location and time within a continuous region.

[0111]

[0112] in, To output the mapping function, This represents the number of network layers.

[0113] S6: Combined training of neural operator models.

[0114] like Figure 4 As shown, firstly, a training sample set is constructed. The training samples can consist of numerical simulation data, historical experimental data, and field measured data. For simulation data, a relatively complete pressure field distribution can be obtained, which is used to supervise the model's learning of the continuous wave field structure; for measured data, only the pressure response at sparse measuring points is obtained, which is used to constrain the model to closely approximate the real test results.

[0115] Secondly, sparse observation samples are constructed. For a complete simulated pressure field, sparse sampling can be performed according to the actual sensor deployment to generate simulated sparse observation data:

[0116]

[0117] in, To simulate the pressure field, the model's adaptability to different layout topologies can be enhanced by changing the number, location, and missing measurement points.

[0118] Then, the sparse observation data, measurement point coordinates, explosion source parameters, and boundary conditions are input into the neural operator model to obtain the predicted pressure field. For data with true pressure field labels, a supervised reconstruction loss is used:

[0119]

[0120] in, Indicates the number of supervised sample points; This indicates that the neural operator predicts the stress value; This represents the actual pressure value at the corresponding location and time.

[0121] In one embodiment, for a real-world explosion test scenario with only sparse measurement point observation data, a neural operator model is jointly trained using observation loss and physical constraint loss, and its total loss function is expressed as follows:

[0122]

[0123] in, The observation loss weight.

[0124] The observation loss is defined as:

[0125]

[0126] in, Indicates the number of measuring points; This indicates the number of time sampling points corresponding to each measurement point; Indicates the first Each measuring point at time [time] The measured pressure value.

[0127] Physical constraint loss is defined as:

[0128]

[0129] in: Loss due to arrival time constraints; This is the peak decay constraint loss; For wavefront continuity constraint loss; To control the residual loss of the equation; Loss is due to boundary condition constraints; , , , , These are the weight coefficients for the corresponding loss terms.

[0130] The physical constraint loss embeds the dynamic mechanism of the explosion wave into the training process of the neural operator, which can avoid the generation of non-physical pseudo-solutions in the unobserved area by the pure data-driven model, and make the reconstruction result satisfy both the observation data of the measurement point and the propagation law of the explosion wave.

[0131] The joint loss function ensures that the model can fit the measured data of sparse measurement points while satisfying the dynamic laws of explosion wave propagation and boundary condition constraints, thereby improving the physical reliability and generalization ability of the reconstruction results.

[0132] In another embodiment, for training samples that simultaneously have complete pressure field labels and sparse observation data, the neural operator parameters are optimized by comprehensively considering the supervised reconstruction loss, observation loss, and physical constraint loss:

[0133]

[0134] The optimization objective for the neural operator model parameters is:

[0135]

[0136] in, Represents the parameters of the neural operator model. This represents the optimal model parameters after training.

[0137] After training, when new sparse measurement point data from an explosion experiment are input, the trained neural operator can quickly output the continuous wave field reconstruction results without re-performing a complete simulation calculation.

[0138] S7: Perform physical residual verification on the reconstruction results to suppress non-physical pseudo-solutions that do not satisfy the propagation law of explosion waves.

[0139] After completing the input of sparse observation data, the construction of degenerate observation maps, and the reconstruction by neural operators, the continuous spatiotemporal distribution results of the explosion shock wave field are output. The output results include the pressure prediction value at any location and time within the specified spatial region, as well as the characteristic fields such as the overpressure peak distribution, wavefront arrival time distribution, and impulse distribution during the barotropic action phase, which are further extracted based on the pressure time history composed of the pressure prediction value.

[0140] Among them, the pressure prediction value, i.e. the transient pressure spacetime field, is:

[0141]

[0142] The peak overpressure field is:

[0143]

[0144] The arrival time field is:

[0145]

[0146] The positive pressure impulse field is:

[0147]

[0148] in, and These represent the start and end times of the positive pressure phase.

[0149] To improve the reliability of the reconstruction results, this invention does not simply output the neural network prediction results, but further introduces a physical consistency feedback mechanism in the output stage. This mechanism, based on the propagation law of explosion waves, detects and constrains abnormal peaks, discontinuous wavefronts, unreasonable arrival times, and local results that violate boundary conditions in the reconstructed pressure field. Specifically, the physical consistency feedback module performs a consistency judgment on the pressure field output by the neural operator based on the constructed propagation arrival time constraints, peak attenuation constraints, wavefront continuity constraints, and residual constraints of the governing equations.

[0150] For local regions in the reconstructed pressure field that do not satisfy the propagation law, the system feeds back the corresponding physical residual information to the neural operator reconstruction module. The prediction results for these regions are then adjusted through loss function constraints or post-processing corrections. This process can be represented as:

[0151]

[0152] in, This represents the pressure field after physical consistency feedback correction. This represents the consistency correction operator. Represents the residuals of the governing equations. Indicates the arrival time residual. This represents the peak attenuation residual.

[0153] Through the above methods, this invention can jointly output the amplitude distribution, propagation time sequence, and spatial structure of an explosion shock wave field without relying on dense measurement points. Unlike methods that only output single-point pressure prediction values ​​or two-dimensional interpolated cloud maps, this invention outputs a spatiotemporal pressure field function with continuous spatial representation capabilities, which can be further used for subsequent applications such as hazardous area delineation, impact load analysis, protective structure design, and explosion effect assessment.

[0154] S8: Outputs the continuous spatiotemporal pressure field, overpressure peak distribution, arrival time distribution, and impulse distribution of the explosion shock wave.

[0155] In one embodiment, a system deployment method for implementing the above-described wavefield reconstruction method is provided. This system can be deployed in an experimental data processing server, an edge computing terminal, or a dedicated test analysis workstation to receive sparse measurement point data from explosion shock wave tests and to complete continuous wavefield reconstruction, physical consistency feedback, and result output.

[0156] In terms of hardware composition, the system includes a data acquisition interface, a storage unit, a computing and processing unit, and a display and output unit. The data acquisition interface receives pressure time-history data, measurement point coordinate files, explosion source parameters, and boundary condition information collected by pressure sensors. The storage unit stores historical experimental data, simulation samples, trained neural operator model parameters, and reconstruction results. The computing and processing unit performs data preprocessing, degenerate observation mapping, neural operator inference, dynamic constraint calculation, and physical consistency feedback. The display and output unit generates visualizations of the continuous pressure field, overpressure peak field, arrival time field, and barotropic impulse field.

[0157] In terms of software composition, the system includes a data management program, a preprocessing program, a reconstruction inference program, a physical constraint calculation program, and a result visualization program. The data management program is used to uniformly read pressure time history data and measuring point layout data in different formats; the preprocessing program is used to complete noise reduction, time synchronization, normalization, and outlier removal; the reconstruction inference program is used to call the trained explosion wave dynamics constraint neural operator model and output a continuous spatiotemporal pressure field; the physical constraint calculation program is used to calculate the arrival time residual, peak attenuation residual, governing equation residual, and boundary constraint residual, and feed the residual information back to the reconstruction inference process; the result visualization program is used to output pressure contour maps, peak distribution maps, arrival time distribution maps, impulse distribution maps, and corresponding data files.

[0158] During system operation, the system first imports pressure data and related parameters from sparse measuring points of the explosion test via the data acquisition interface; then, the computational processing unit completes data preprocessing and degenerate observation mapping construction; next, the trained neural operator model is called to predict the continuous pressure field; then, the physical constraint calculation program performs consistency checks and feedback corrections on the prediction results; finally, the display output unit generates the reconstructed results and visualization graphics. Through the above deployment method, this invention can form a complete system implementation path from experimental data access, continuous wave field reconstruction, physical consistency correction to result output.

[0159] To address the shortcomings of existing technologies, such as insufficient accuracy, poor physical consistency, weak generalization ability under complex conditions, and limited continuous field representation capability in the reconstruction of explosive shock wave fields under sparse and irregular measurement point conditions, this invention provides a sparse observation wave field reconstruction method and system based on explosive wave dynamics-constrained neural operators. This invention constructs a degenerate observation mapping from a continuous wave field to discrete measurement point responses, using explosive equivalent, measurement point coordinates, sampling time sequence, boundary conditions, and sparse pressure observations as input information. A neural operator is used to learn the functional mapping relationship from finite discrete observations to a continuous shock wave field. Simultaneously, explosive wave propagation velocity, arrival time, peak attenuation, wavefront continuity, governing equation residuals, and boundary condition constraints are introduced into the model training and reconstruction process. This ensures that the reconstruction results not only match the observation data but also satisfy the explosive wave dynamics propagation mechanism, thereby achieving the coordinated reconstruction of the peak distribution, propagation time sequence, and spatial evolution structure of the explosive shock wave field under sparse measurement point conditions.

[0160] The core improvements and innovations of this invention are as follows:

[0161] 1. Neural operator reconstruction architecture constrained by explosion wave dynamics.

[0162] This invention introduces a neural operator as the core mapping model for continuous wave field reconstruction, establishing a mapping relationship from sparse measuring point pressure response, measuring point spatial coordinates, explosion source parameters, and boundary conditions to the continuous wave field function. Unlike traditional neural networks, which can only predict point values ​​under fixed grids or fixed input dimensions, the neural operator can directly learn the mapping relationship between function spaces, enabling the model to adapt to different numbers of measuring points, different measuring point layouts, and different reconstruction regions. This architecture can overcome the dependence of traditional interpolation methods on the assumptions of regular grids and smooth fields, improving the expressive power of the continuous field of explosion shock waves under sparse and irregular observation conditions.

[0163] 2. Degenerate observation mapping mechanism for sparse and irregular measurement points.

[0164] To address the challenges of limited measurement points, irregular placement, and missing observations in localized areas during field explosion testing, this invention constructs a degenerate observation mapping model from the continuous explosion shock wave field to the discrete sensor response. This model uniformly encodes measurement point coordinates, sampling frequency, observation time window, sensor response location, and spatial topological relationships, enabling the reconstruction network to identify the missing information between discrete observation data and the true continuous wave field. By explicitly describing the degradation process of "continuous field—discrete measurement points—sparse observations," this invention reduces spatial mapping errors caused by irregular measurement points and enhances the model's ability to recover pressure distribution and wavefront structure in unmeasured areas.

[0165] 3. A physical consistency constraint system for the integration of propagation laws.

[0166] This invention embeds the dynamics mechanism of explosion waves into the training and reconstruction process of neural operators, constructing a physical consistency constraint system composed of control equation residuals, initial conditions, boundary conditions, propagation velocity constraints, arrival time constraints, and peak attenuation constraints. This system ensures that the model reconstruction results conform to the basic laws of shock wave propagation, preventing spurious peaks, non-physical oscillations, and unreasonable propagation paths generated by purely data-driven models in sparse observation regions. Through physical residual feedback, this invention can improve the reliability and stability of reconstruction results even when observational data is insufficient.

[0167] 4. A mechanism for the coordinated reconstruction of peak distribution, propagation timing, and spatial structure.

[0168] Existing methods often focus on single-point overpressure peak prediction or local interpolation, making it difficult to simultaneously maintain the amplitude, propagation time, and spatial structure characteristics of the explosion shock wave field. This invention addresses the strong transient evolution of the explosion shock wave field by establishing joint constraints on multiple features, including peak pressure, arrival time, barotropic duration, impulse, and wavefront spatial gradient. This allows the model to reconstruct a continuous pressure field while preserving the wavefront propagation direction, local high-gradient regions, and spatial attenuation patterns. This mechanism effectively reduces problems such as peak attenuation, wavefront misalignment, and local structural ambiguity, improving the overall reconstruction quality of the explosion shock wave field.

[0169] 5. A generalized reconstruction mechanism for different explosion conditions and measurement point layouts.

[0170] This invention uses explosion source parameters, boundary conditions, and measurement point layout parameters as input conditions, enabling the reconstruction model to adaptively reconstruct under different explosion yields, measurement point topologies, and test areas. Compared to traditional deep learning models that require retraining for fixed conditions, this invention leverages the function mapping capabilities of neural operators and physical constraint mechanisms to improve the model's generalization ability to new measurement point layouts and limited sample scenarios, reducing the dependence of explosion shock wave field reconstruction on large-scale labeled samples and repeated field experiments.

[0171] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0172] Based on the same inventive concept, this application also provides a sparse observation wavefield reconstruction system based on explosion wave dynamics constrained neural operators. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the sparse observation wavefield reconstruction system based on explosion wave dynamics constrained neural operators provided below can be found in the limitations of the sparse observation wavefield reconstruction method based on explosion wave dynamics constrained neural operators described above, and will not be repeated here.

[0173] In one embodiment, such as Figure 5 As shown, a sparse observation wavefield reconstruction system based on explosion wave dynamics-constrained neural operators is provided, including: a data acquisition module, a sparse observation preprocessing module, a degenerate observation mapping module, an explosion wave dynamics constraint module, a neural operator reconstruction module, a physical consistency evaluation module, and a result output module. Wherein:

[0174] The data acquisition module is used to acquire the pressure time history and corresponding spatial coordinates of sparse measuring points in the explosion shock wave test; the sparse observation preprocessing module is used to complete signal denoising, time sequence alignment, coordinate normalization and feature extraction; the degenerate observation mapping module is used to establish the mapping relationship between the continuous pressure field and the discrete measuring point response; the explosion wave dynamics constraint module is used to construct physical constraints such as propagation speed, arrival time, peak attenuation, boundary reflection and control equation residuals; the neural operator reconstruction module is used to learn the mapping from sparse observations to the continuous wave field function; the physical consistency evaluation module is used to perform residual testing and non-physical pseudo-solution suppression on the reconstruction results; the result output module is used to output the results such as the continuous wave field, overpressure peak field, arrival time field and impulse field.

[0175] Specifically, each module in the sparse observation wavefield reconstruction system based on explosion wave dynamics constrained neural operators can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0176] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in all of the above method embodiments.

[0177] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in all of the above method embodiments.

[0178] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in all of the above method embodiments.

[0179] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0180] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0181] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0182] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A sparse observation wavefield reconstruction method based on explosion wave dynamics constrained neural operators, characterized in that, The method includes: Acquire the explosion source parameters, boundary parameters, pressure data, coordinates, and sampling time of sparse measuring points in the explosion shock wave field; Based on the coordinates of the measuring points, the sampling time, and the explosion source parameters, a degenerate observation mapping from the continuous wave field to discrete measuring points is constructed; wherein, the degenerate observation mapping characterizes the spatiotemporal propagation correlation between measuring points; The pressure data, the coordinates of the measuring point, the explosion source parameters, the boundary parameters, and the temporal portion of the degradation observation map are encoded as initial features of the measuring point. The measuring point features are obtained based on the initial features of the measuring point and the spatial portion of the degradation observation map. The measuring point features are input into a pre-trained neural operator to obtain the continuous spatiotemporal distribution results of the explosion shock wave field.

2. The method according to claim 1, characterized in that, The process of constructing a degenerate observation mapping from the continuous wave field to the discrete measurement point based on the measurement point coordinates, the sampling time, and the explosion source parameters includes: Obtain the blast center coordinates from the blast source parameters, and obtain the straight-line distance between the blast center and each measuring point based on the blast center coordinates and the measuring point coordinates; Based on the equivalent propagation velocity and the straight-line distance, the estimated arrival time of the explosion shock wave at each measuring point is obtained; Based on the estimated arrival time for each measuring point, the propagation delay characteristics are obtained and used as the time component in the degraded observation map. Based on the coordinates of the measurement points and the propagation delay characteristics, the propagation adjacency weight is obtained and used as the spatial part of the degraded observation map.

3. The method according to claim 1, characterized in that, The step of obtaining the measurement point features based on the initial features of the measurement point and the spatial portion of the degraded observation map includes: The propagation neighborhood of each measurement point is obtained based on the spatial portion of the degraded observation map. For any measurement point, the initial feature of the measurement point is used as the current feature. The current feature corresponding to the measurement point is aggregated with the current feature corresponding to the propagation neighborhood. The aggregation result is then updated to the current feature of the measurement point to enter the next round of feature update.

4. The method according to claim 1, characterized in that, The neural operator incorporates explosion wave dynamics constraints during training, which include: arrival time constraints, peak decay constraints, wavefront continuity constraints, governing equation residual constraints, and boundary condition constraints.

5. The method according to claim 4, characterized in that: The loss function of the neural operator during training includes supervision loss, observation loss, and physical residual loss; The supervision loss is constructed based on the error between the predicted stress value output by the neural operator and the actual stress value. The observation loss is constructed based on the error between the predicted pressure value and the pressure data; The physical residual loss is constructed based on the arrival time constraint, the peak attenuation constraint, the wavefront continuity constraint, the governing equation residual constraint, and the boundary condition constraint.

6. The method according to claim 1, characterized in that, The continuous spatiotemporal distribution results include: pressure prediction values ​​at any location and at any time within a specified spatial region, as well as overpressure peak distribution, wavefront arrival time distribution, and impulse distribution during the barotropic action phase extracted from the pressure prediction values.

7. A sparse observation wavefield reconstruction system based on explosion wave dynamics constrained neural operators, characterized in that, The system includes: The data acquisition module is used to acquire the explosion source parameters, boundary parameters, pressure data, coordinates, and sampling time of the explosion shock wave field; A sparse observation preprocessing module is used to reconstruct the sparse observation explosion shock wave field based on the explosion source parameters, the boundary parameters, the pressure data, and the measurement point coordinates. The degenerate observation mapping module is used to construct a degenerate observation mapping from the continuous wave field to discrete measurement points based on the measurement point coordinates, the sampling time, and the explosion source parameters; wherein, the degenerate observation mapping characterizes the spatiotemporal propagation correlation between measurement points; The result output module is used to encode the pressure data, the measurement point coordinates, the explosion source parameters, the boundary parameters, and the time portion of the degradation observation map into initial features of the measurement point, obtain the measurement point features based on the initial features of the measurement point and the spatial portion of the degradation observation map, input the measurement point features into a pre-trained neural operator, and obtain the continuous spatiotemporal distribution results of the explosion shock wave field.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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