Real-time perception and prediction method for thermal storage system based on hybrid simulation and PINN

Abstract

The application discloses a kind of based on hybrid simulation and PINN's heat storage system real-time perception prediction method, belongs to high temperature heat storage system intelligent monitoring, digital twin and multi-physical field simulation technical field.The method is offline and trains hybrid model, including parameterized coarse grid numerical simulation model and physical information neural network;Wherein the loss function of physical information neural network contains discrete physical residual term, which is calculated using the same discrete format as the coarse grid model.Online stage, use coarse grid model to quickly solve according to real-time data, obtain coarse grid physical field approximate solution;Then the solution is used as physical prior input to train the physical information neural network, and the high-precision full-field physical state at future time is inferred in parallel.The application realizes the millisecond to second level real-time high-precision perception and prediction of the internal multi-physical field state of heat storage system through two-level collaborative architecture, and provides core driving for system intelligent control and digital twin.

Description

Technical Field

[0001] This invention belongs to the field of intelligent monitoring, digital twin and multiphysics simulation technology of high temperature thermal storage systems. Specifically, it relates to a real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN, which is used to achieve high-precision, real-time status sensing and short-term prediction of multiphysics fields inside the thermal storage system. Background Technology

[0002] In the intelligent operation and advanced control of high-temperature thermal storage systems (such as electromagnetic induction heating fluidized particulate thermal storage systems), it is crucial to obtain in real time and accurately the three-dimensional distribution and evolution of multiple physical fields such as electromagnetic field, temperature field, and flow field within the system. This is a prerequisite for conducting system safety monitoring, efficiency optimization, and implementing advanced control strategies such as model predictive control.

[0003] Currently, the main technical approaches have inherent limitations:

[0004] Firstly, high-precision computational fluid dynamics or finite element simulation uses fine mesh to discretize and solve the control equations. Although the accuracy is high, the computational resources are huge and the time consumption is extremely long (usually several hours to several days). It cannot meet the real-time decision-making requirements of control systems at the millisecond to second level. Moreover, it requires recalculation every time the parameters change, resulting in poor flexibility.

[0005] Secondly, while purely data-driven neural network models are trained on historical data and have fast inference speeds, they are essentially "black boxes," heavily reliant on the coverage of training data and lack constraints from physical laws. When operating conditions not covered by training data or when system states drift, prediction results may deviate significantly from physical reality, resulting in low reliability and failing to guarantee that solutions satisfy fundamental physical laws such as mass and energy conservation.

[0006] Third, traditional reduced-order models are computationally fast, but they are usually linearized or simplified for specific design conditions. When the system operating state deviates significantly from the design point, the model accuracy drops sharply and the generalization ability is insufficient.

[0007] Fourth, although conventional physical information neural networks embed physical laws into the network by automatically differentiating and calculating the residuals of continuous partial differential equations, they suffer from problems such as unstable training, large memory consumption, and fundamental incompatibility with the discrete format used by industrial standard numerical solvers. This makes it difficult to directly compare their results with high-confidence simulations, thus limiting their engineering credibility.

[0008] Therefore, existing technologies cannot achieve a good balance between computational efficiency, physical accuracy, generalization ability under operating conditions, and consistency with industrial standards. This has become a key technological bottleneck restricting the real-time intelligent and autonomous operation of thermal storage systems. Summary of the Invention

[0009] To address the aforementioned technical challenges, this invention provides a real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN. It creatively employs a two-tiered collaborative hybrid architecture of "physical skeleton generation" and "intelligent fine-tuning prediction," deeply integrating rapid coarse-grid numerical simulation with a physical information neural network based on discrete format residuals. Furthermore, it introduces a key mechanism of "using the coarse-grid solution as a priori physical input." This enables rapid, high-precision sensing and short-term prediction of the multi-physics states within complex thermal storage systems at millisecond to second levels, while ensuring consistency with industrial numerical solver formats and compliance with fundamental physical conservation laws. This provides a core driver for real-time optimization control, safety early warning, and high-fidelity digital twins of the system.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN includes:

[0012] Step S1, offline stage: Construct and train a hybrid simulation model of the corresponding thermal storage system. The hybrid simulation model includes a parameterized coarse-grid numerical simulation model and a physical information neural network model. The coarse-grid physical field approximation solution output by the coarse-grid numerical simulation model is used as the input of the physical information neural network model. The loss function of the physical information neural network model includes a discrete physical residual term. The discrete physical residual term refers to the sum of squared residuals calculated by substituting the predicted values ​​of the physical information neural network into the discrete control equations using a discrete format completely consistent with the coarse-grid numerical simulation model.

[0013] Step S2, the online stage, inputs the real-time collected thermal storage system operation data into the parameterized coarse-grid numerical simulation model to obtain the approximate solution of the coarse-grid physical field at the current moment; then inputs the coarse-grid physical field approximate solution and the spatiotemporal coordinates of the future moment into the trained physical information neural network model to infer and output a high-precision full-field physical state prediction for the future moment.

[0014] Furthermore, in step S1, the coarse-grid numerical simulation model is based on a fixed computational grid, and the conserved governing equations are discretized using the finite volume method, finite difference method, or finite element method; the fixed computational grid is a non-uniform grid, and local refinement is performed in key regions with large physical field gradients.

[0015] Furthermore, the conservation-type governing equations include mass conservation equations, momentum conservation equations, and energy conservation equations; the energy conservation equations include eddy current Joule heat source terms generated by electromagnetic induction, and the momentum conservation equations include electromagnetic volume force terms generated by electromagnetic fields acting on the conductive medium; the discrete physical residual terms of the parameterized coarse-grid numerical simulation model and the physical information neural network model both include the eddy current Joule heat source terms and the electromagnetic volume force terms.

[0016] Furthermore, in step S1, the input of the physical information neural network model includes spatiotemporal coordinate points and the coarse-grid physical field approximation solution output by the coarse-grid numerical simulation model at the spatiotemporal coordinate points. The coarse-grid physical field approximation solution includes coarse-grid numerical solutions for the temperature field, velocity field, pressure field, magnetic induction field, and electric field intensity field. The output of the physical information neural network model is the corresponding high-precision physical field prediction variables, including high-precision prediction values ​​for the temperature field, velocity field, pressure field, magnetic induction field, and electric field intensity field.

[0017] Furthermore, in step S1, the loss function of the physical information neural network model is composed of a weighted average of a data loss term, a discrete physical residual loss term, and a boundary condition loss term; wherein, when calculating the data loss term and the boundary condition loss term, a 0-1 binary mask is used for identification and filtering.

[0018] Furthermore, the discrete physical residual loss term is calculated as follows: on all nodes of the fixed computational grid, using a discretization format completely consistent with the coarse grid numerical simulation model, the spatial discrete derivative and time discrete derivative of the predicted value output by the physical information neural network model are calculated, substituted into the discretized conservation control equations, to obtain the residual of each grid node, and then the sum of squares or mean square of the residuals of all grid nodes are calculated.

[0019] Furthermore, in step S1, the loss function adopts a hierarchical standardization and balancing design, including: when calculating the data residual term, discrete physical residual term, and boundary condition residual term, standardizing each type of residual on all corresponding calculation nodes, calculating the mean square value of each type of node residual after standardization, dividing it by the total number of nodes of the corresponding category to obtain the average loss term that is independent of the number of nodes, and applying weighting coefficients to each average loss term after processing to form the total loss function.

[0020] Furthermore, in step S1, a physical information neural network training method based on physical prior initialization is adopted, including: setting the weight matrix of the output layer of the physical information neural network model to zero, and simultaneously initializing its bias vector to a function associated with the input spatiotemporal coordinates, directly returning the coarse-grid physical field approximation solution calculated by the coarse-grid numerical simulation model at the corresponding coordinate point; so that at the initial moment of training, the predicted output value of the physical information neural network model for any input coordinate is always equal to the coarse-grid physical field approximation solution at the corresponding coordinate point, forming an explicit residual learning framework.

[0021] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN.

[0022] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN.

[0023] The beneficial effects of this invention are as follows:

[0024] First, it achieves a balance between efficiency, accuracy, and reliability. By combining the collaborative efforts of "fast coarse-grid solving to provide the physical framework" and "millisecond-level fine-tuning prediction using a neural network based on physical information," the contradiction between real-time performance and high accuracy is overcome at the system level. Coarse-grid solving ensures the physical foundation, while neural network inference achieves a leap in speed, enabling a single full-field prediction to be completed within milliseconds.

[0025] Second, it boasts high physical consistency and engineering reliability. It innovatively employs discrete format residuals, identical to those of coarse-grid solvers, as the physical constraints of the physical information neural network. This aligns the neural network's predictions mathematically with industry-standard numerical solvers, allowing the results to be directly compared with high-fidelity simulations. This solves the problem of the disconnect between conventional physical information neural networks and engineering practice.

[0026] Third, it exhibits stable training and strong generalization ability. Discrete-format residual calculation is insensitive to noise, resulting in more stable training. The coarse-grid solution provides strong physical priors as input, guiding the network's learning and enabling it to provide predictions that conform to physical laws even in sparse sensor regions or under conditions of slight extrapolation, thus enhancing its generalization ability.

[0027] Fourth, it provides core sensing capabilities for real-time intelligent control. The real-time, full-field, and high-precision physical state output by this invention serves as the "eyes" driving advanced algorithms such as model predictive control and reinforcement learning to make optimal decisions, forming the "real-time state-driven engine" of the high-fidelity digital twin of the thermal storage system. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN, as presented in this invention.

[0029] Figure 2 A flowchart for numerically solving the coarse-grid downflow-thermal-electromagnetic coupled multiphysics solution;

[0030] Figure 3 A flowchart illustrating the offline modeling and training phases;

[0031] Figure 4 This is a flowchart illustrating the online real-time state perception and prediction phase.

[0032] Figure 5 This is a diagram of the neural network topology. Detailed Implementation

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0034] like Figure 1 As shown, this invention provides a real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN, specifically including the following steps:

[0035] Step S1: In the offline stage, a hybrid simulation model of the corresponding thermal storage system is constructed and trained. The hybrid simulation model includes a parameterized coarse-grid numerical simulation model and a physical information neural network model. The coarse-grid physical field approximation solution output by the coarse-grid numerical simulation model is used as the input to the physical information neural network model. The loss function of the physical information neural network model includes a discrete physical residual term. The discrete physical residual term refers to the sum of squared residuals calculated by substituting the predicted values ​​of the physical information neural network into the discrete control equations using a discrete format completely consistent with the coarse-grid numerical simulation model. Specifically:

[0036] Step S1.1: Based on the physical structure of the target thermal storage system, generate a fixed computational grid covering the entire computational domain. This grid is preferably a non-uniform grid, with localized refinement in critical areas where the physical field changes drastically (such as near the electromagnetic heating coil, the heat exchange pipe wall, and the fluidized bed inlet area), and coarser grids used in other areas to balance accuracy and computational burden.

[0037] Step S1.2: Establish a parameterized coarse-grid numerical simulation model of the thermal storage system. For example... Figure 2 As shown, this model, based on the fixed computational grid, employs discretization methods such as the finite volume method to spatially discretize the conservation-type governing equations (including mass, momentum, and energy conservation equations) describing the system's physical processes (electromagnetic induction, fluid flow, heat and mass transfer), forming a set of algebraic equations that can be solved quickly. The core objective of this model is to provide, rapidly (within seconds), approximate solutions to the physical fields that satisfy global physical conservation laws and meet the current boundary conditions, serving as the "physical framework" for subsequent processing.

[0038] Furthermore, the coupling of the conservation-type governing equations is manifested in the following ways: the energy conservation equation includes a Joule heat source term generated by electromagnetic induction; the momentum conservation equation includes an electromagnetic volume force term generated by the electromagnetic field acting on the conductive medium. The parameterized coarse-grid numerical simulation model and the physical loss term of the physical information neural network must both include the aforementioned source terms to accurately describe the electromagnetic-fluid-thermal multiphysics coupling effect. Specifically:

[0039] During electromagnetic induction heating, an alternating electromagnetic field induces eddy currents within the conductive heat storage particles, generating Joule heating; this is the core internal heat source of the system. In the energy conservation equation, a volumetric heat source term S needs to be added. h The calculation formula is as follows:

[0040] ;

[0041] Where J is the induced current density vector, and σ is the conductivity of the particle. The induced current density J can be obtained by solving the simplified electromagnetic field equations (such as the quasi-static approximation that neglects displacement current in the industrial frequency range):

[0042] ;

[0043] Where A is the magnetic vector potential and μ is the magnetic permeability. The source current density (coil current density). For time variables, To obtain the partial derivative with respect to time, For Hamiltonian operators; where, To calculate the curl of the spatial coordinates of the vector field X, To calculate the divergence of the vector field X, The gradient of the scalar field Ψ is calculated using a mathematical operator commonly used in this field, which will not be elaborated upon separately below.

[0044] For a time-varying electromagnetic field, the fundamental relationship between the magnetic vector potential A and the magnetic induction intensity B and electric field intensity E can be obtained as follows:

[0045] ;

[0046] in, This is a scalar potential. Under sinusoidal AC steady-state conditions (the coil current has a single frequency), angular frequency All field quantities are adjusted over time. Regular changes. Represented using complex phasors (denoted as...). Time derivative Transform into a multiplier If the Coulomb specification is chosen... Furthermore, since there is no external charge source, the potential gradient term can be ignored, thus yielding the frequency domain relationship:

[0047] ;

[0048] Let A, E, and B be the phasors in the frequency domain corresponding to the time-harmonic electromagnetic quantities A, E, and B, respectively. j is the imaginary unit. ω is the angular frequency.

[0049] By generalized Ohm's law: .

[0050] Where v is the velocity of the conductive particles.

[0051] Finally, the heat source S was obtained. h The spatiotemporal distribution function of J is determined by the electromagnetic field distribution (B, E) and the particulate properties.

[0052] Besides generating heat, the electromagnetic field also exerts volume forces (electromagnetic forces) on conductive / magnetic particles, affecting particle motion and flow field distribution within the fluidized bed. An electromagnetic volume force term F needs to be added to the fluid momentum conservation equation. em For this system, the electromagnetic force is the Lorentz force. The expression for the Lorentz force is (primarily considering the magnetic force):

[0053] F em = J×B, where J is the aforementioned induced current density and B is the magnetic flux density. This force is perpendicular to the directions of the current and magnetic field, and may affect the fluidization state of local particles.

[0054] The aforementioned source terms tightly couple the electromagnetic field, temperature field, and flow field, forming a closed multiphysics problem. A sequential coupling strategy can be employed to improve online solution efficiency. The specific steps are as follows:

[0055] To handle sinusoidal alternating current from a coil, the time-domain problem is usually transformed into the frequency domain, at which point the equation can be expressed as:

[0056] ;

[0057] in, , Let A be the time-harmonic magnetic vector and J be the source current density vector. s The corresponding frequency domain complex phasor.

[0058] The magnetic vector potential A can be obtained by numerically discretizing the electromagnetic field control equations based on the coil current and frequency, and by solving the equations numerically. Furthermore, the approximate distributions of the fields B, E, and J can be obtained by solving the fundamental relationships between physical quantities.

[0059] Based on the approximate solutions for B, E, and J, and the corresponding formulas, the eddy current heat source distribution S can be calculated. h and electromagnetic force distribution F em .

[0060] S h and F em As the heat source and force source terms of the fluid dynamics governing equations (mass, momentum, and energy equations), approximate solutions to the temperature field, fluid velocity field, and pressure field are obtained by numerically discretizing the governing equations to solve the fluid-thermal-electromagnetic coupling problem.

[0061] Implementation in PINNs: such as Figure 5 As shown, in the loss function L of the physical information neural network, when calculating the discrete residuals of the momentum equation and energy equation, the aforementioned F must be included. em and S h Both can directly use known values ​​in the corresponding spatiotemporal coordinates calculated by the coarse-grid numerical simulation model.

[0062] Step S1.3: Construct a physical information neural network model. The input to this network includes the spatiotemporal coordinates (x, y, z, t) and the coarse-grid approximate solution of the physical field at that spatiotemporal coordinate point (e.g., T) output by the coarse-grid numerical simulation model. coarse U coarse , p coarse B coarse E coarse This refers to the coarse-grid numerical solution corresponding to the temperature field, velocity field, pressure field, magnetic field strength, and electric field strength. Its output is the corresponding high-precision prediction of the physical field variables (such as T). pred U pred , p pred B pred E pred This refers to high-precision predictions of the temperature field, velocity field, pressure field, magnetic field strength field, and electric field strength field. The loss function L of this physical information neural network model consists of the following three weighted terms:

[0063] ,

[0064] in:

[0065] L represents the total loss function.

[0066] λ data , λ pde , λ bc This represents the weighting coefficient, used to balance the importance of data loss, physical residual loss, and boundary condition loss.

[0067] L data This represents the data loss term, used to constrain the network output to approximate the measured value on a small number of grid nodes with sensor data.

[0068] L pde The discrete physical residual loss term is one of the core innovations of this invention. At the nodes of the fixed computational grid, using a discrete format completely consistent with the coarse-grid numerical model in S1.2 (such as the central difference format of the finite volume method), the spatial / temporal discrete derivatives of the predicted values ​​output by the network are calculated and substituted into the discrete algebraic form of the governing equations to calculate the sum of squared residuals. This forces the physical information neural network prediction to approximately satisfy the same discrete conservation equations as industrial numerical solvers at any location.

[0069] L bc This represents the boundary condition loss term, which constrains the network output at the boundary nodes, forcing the network output to satisfy the known boundary conditions.

[0070] In computational physical information neural networks (PINNs), data and boundary loss terms (L) are used. data L bc To accurately match the physical reality and known boundary conditions of "sparse sensors," a 0-1 binary mask is needed for identification and filtering. The specific method is as follows:

[0071] Construct the mask vector: Generate a binary (0-1) vector with the same number of computation grid nodes. This vector is set to 1 at the node location where the sensor is located / at the node location of the grid that is determined to be a boundary, and set to 0 at all node locations without sensors / at the node locations of the grid that are determined to be non-boundary.

[0072] Loss calculation using a mask: When calculating the mean squared error loss, the mask vector is multiplied element-wise by the point-by-point prediction error. This operation is equivalent to: retaining the error value only on sensor nodes / boundary nodes with a mask of 1, and zeroing the error on non-sensor nodes / non-boundary nodes with a mask of 0. Alternatively, the predicted and measured values ​​of the corresponding nodes can be directly extracted in the code implementation based on the grid index corresponding to the sensor installation location / boundary location. To facilitate vectorized parallel computation and improve training efficiency, the mask vector method is preferred.

[0073] To ensure the stability and convergence efficiency of the physical information neural network training, the loss function adopts a hierarchical standardization and balancing design:

[0074] Node residual standardization: When calculating data residual terms, discrete residual terms of physical equations, and boundary condition residual terms, the residuals of each type are first standardized on all corresponding calculation nodes (e.g., converted to zero mean or unit variance) to eliminate the influence of different physical dimensions and initial distributions on the residual values.

[0075] For the standardized node residuals, calculate their mean square values ​​separately, i.e., sum them up and divide by the total number of nodes in the corresponding category, thus obtaining the average loss term L, which is independent of the number of nodes. data , L pde , L bc .

[0076] Weighting coefficients are applied to each of the average loss terms after the above processing to form the total loss function. Weights can be used to balance the ultimate importance of different optimization objectives, or dynamically adjusted through adaptive strategies to optimize the training process.

[0077] This three-level processing system systematically solves the optimization deviation problem caused by differences in dimensions and sample size, providing a solid foundation for collaborative optimization of multi-objective physical constraints.

[0078] Step S1.4: Using high-fidelity simulation data, historical operating data, or a combination of both, perform offline training on the physical information neural network until its total loss function converges. The trained physical information neural network has the ability to quickly infer high-precision full-field states based on the input (coordinates + coarse mesh solution).

[0079] like Figure 3 As shown, a physical information neural network training method based on physical prior initialization is applied to the real-time state perception and prediction of a thermal storage system. This method aims to address the problems of lack of physical meaning in the output, slow convergence speed, and training instability in physical information neural networks caused by random parameter initialization in the early stages of training. The core of the method lies in performing specific initialization operations on the output layer parameters of the physical information neural network used for state perception during initialization. This uses the approximate solution of the physical field provided by coarse-grid numerical simulation as the initial state of the strongly physical prior embedded model, thereby achieving robust optimization starting from this physical framework and using residual learning as the mode. Specifically, the initialization method includes:

[0080] The weight matrix of the output layer of the physical information neural network is set to zero, and its bias vector is initialized to a function associated with the input spatiotemporal coordinates. This function directly returns the coarse-grid physical field approximation solution (such as temperature T) obtained from coarse-grid numerical simulation at the corresponding coordinate point.coarse Speed ​​U coarse Pressure p coarse (etc.). Through this operation, at the initial moment of training, the predicted output value of the physical information neural network for any input coordinate is always equal to the coarse-grid physical field approximation solution at that point, thus providing a globally consistent and physically reliable starting point for the optimization process.

[0081] This initialization strategy works in conjunction with the feature of "using the coarse-grid physical field approximation solution as the neural network input," forcing the network to be trained in an explicit residual learning manner: the initial output of the physical information neural network is the physical skeleton (the coarse-grid physical field approximation solution), and then by minimizing the loss function that includes data fitting, physical equation constraints, and boundary condition constraints, the physical information neural network parameters only need to learn a fine-tuning amount superimposed on this skeleton. This greatly reduces the learning difficulty, ensures rapid convergence and stability of the training process, and is one of the key enabling technologies for achieving high-precision, reliable, real-time state awareness.

[0082] Step S2: In the online phase, the real-time collected operating data of the thermal storage system is input into the parameterized coarse-grid numerical simulation model to obtain the approximate solution of the coarse-grid physical field at the current moment; then, the approximate solution of the coarse-grid physical field and the spatiotemporal coordinates of future moments are input into the trained physical information neural network model to infer and output a high-precision prediction of the overall physical state at future moments. Figure 4 As shown, specifically:

[0083] Step S2.1: Collect real-time operating data of the thermal storage system, including boundary conditions, control commands, and sparsely distributed sensor data.

[0084] Step S2.2: Input the current running data into the parameterized coarse-grid numerical simulation model, solve it within a second, and obtain the coarse-grid physical field approximation solution of the entire computational domain at the current time.

[0085] Step S2.3: The coarse-grid approximate solution of the physical field at the current moment, sensor data, and predicted coordinates at future moments are used as conditional inputs to the trained physical information neural network model. The coarse-grid approximate solution of the physical field serves as crucial prior physical information input, greatly constraining the network's solution space and enabling it to focus on learning fine-scale features.

[0086] Step S2.4: The physical information neural network uses a forward propagation method to infer high-precision physical field predictions on all grid nodes of the entire computational domain at a specified future time (next second) in parallel and rapidly on the GPU. This process can be completed within milliseconds.

[0087] Step S2.5: Output high-precision full-field physical state prediction results for system state monitoring and visualization, or as real-time state input for advanced control algorithms such as model predictive control and reinforcement learning.

[0088] Example:

[0089] This invention uses a modular electromagnetic induction heating fluidized bed particle thermal storage unit as an example. This embodiment details the specific implementation steps of the method, including the establishment of a coarse mesh model, construction of a physical information neural network (including residual initialization, mask design, loss function standardization and balancing), offline training, and online real-time prediction.

[0090] 1. Offline preparation

[0091] 1.1 Geometric modeling and mesh generation;

[0092] A three-dimensional geometric model of the thermal storage unit was established, with dimensions of 1.2 m in diameter and 2.5 m in height. The interior includes electromagnetic induction coils (encircling the container wall) and serpentine heat exchange pipes (arranged between the outer wall and the insulation layer). A fixed unstructured tetrahedral computational mesh of approximately 500,000 nodes was generated. Local refinement (minimum mesh size 5 mm) was applied near the electromagnetic coils, on the heat exchange pipe walls, and in the fluidized bed inlet region, while a coarser mesh (maximum 20 mm) was used in other areas. This mesh was used simultaneously for the discrete residual calculation of the coarse-grid numerical simulation model and the physical information neural network.

[0093] 1.2 Parametric coarse-grid numerical simulation model;

[0094] Based on the above mesh, a parameterized coarse-grid simulation model of fluid-thermal-electromagnetic coupling was established in OpenFOAM. The finite volume method was employed, with a central difference scheme for spatial discretization and implicit Euler time progression. The model accepts the following input parameters: coil current amplitude and frequency (20 kHz), inlet fluidizing gas velocity (2–5 times the minimum fluidizing velocity), inlet temperature (room temperature), and heating power command (0–500 kW). Outputs include: temperature field T. coarse Velocity field U coarse Pressure field p coarse Magnetic induction intensity B coarse Electric field strength E coarse The time for a single solution is approximately 8–10 seconds.

[0095] 1.3 Construction and initialization of physical information neural network;

[0096] Construct a fully connected Physical Information Neural Network (PINN) with the following structure:

[0097] Input layer: 15 nodes, corresponding to (x, y, z, t, T) coarse , u coarse , v coarse , w coarse , p coarse B x,coarse B y,coarse B z,coarse E x,coarse E y,coarse E z,coarse );

[0098] Among them, B x,coarse B y,coarse B z,coarse E represents the magnetic flux density components in the x, y, and z directions obtained from numerical solutions under a coarse grid. x,coarse E y,coarse E z,coarse The electric field intensity components in the x, y, and z directions obtained by numerical solution under coarse mesh. u coarse , v coarse , w coarse These represent the velocity fields output by the coarse-grid numerical simulation model at... x, y, z Components in three directions.

[0099] Hidden layers: 6 layers, 128 neurons per layer, activation function is Swish.

[0100] Output layer: 11 nodes, corresponding to high-precision predicted values:

[0101] (T pred , u pred , v pred , w pred , p pred B x,pred B y,pred B z,pred E x,pred E y,pred E z,pred );

[0102] Among them, B x,pred B y,pred B z,pred E is used to predict the magnetic flux density components in the x, y, and z directions of the output of a neural network model. x,pred E y,pred E z,pred The electric field intensity components in the x, y, and z directions are predicted for the output of the neural network model. Tpred , u pred , v pred , w pred , p pred These represent the temperature field and velocity field predicted by the neural network model, respectively. x, y, z Components in three directions, pressure field.

[0103] Initialization strategy (residual learning):

[0104] Set all weights in the output layer to zero;

[0105] The bias vector of the output layer is initialized as a function that returns the approximate physical field value (i.e., T) pre-calculated and stored by the coarse-grid numerical simulation model at the corresponding input coordinate point. coarse U coarse , p coarse B coarse E coarse ).

[0106] At the start of training, the network prediction is always equal to the coarse grid solution. Subsequent optimization only requires learning the fine correction, forming an explicit residual learning framework.

[0107] 1.4 Loss function design and standardization;

[0108] The loss function consists of three parts: data loss L data Discrete physical residual loss L pde Boundary condition loss L bc .

[0109] (1) Data loss and mask design

[0110] Assume there are only Ns sparse sensors in the computational domain (5 temperature sensors and 2 pressure sensors in this embodiment). Construct a binary mask vector M with the same number of mesh nodes, where M... data,i =1 indicates that there is a sensor reading at the i-th node; otherwise, it is 0. Data loss is calculated as follows:

[0111] ;

[0112] in:

[0113] Let be the spatial coordinates of the i-th grid node, representing the position of the node in the three-dimensional computational domain.

[0114] Let be the time coordinate corresponding to the i-th grid node, representing the time at which the data sample is located.

[0115] The data residual corresponding to each grid point;

[0116] Y pred Y is a physical quantity output by the network (such as temperature). sensor represents the sensor measurement. ⊙ represents element-wise multiplication. ||·||2 represents the L2 norm.

[0117] It should be noted that since vector calculations are typically used in actual computations, element-wise multiplication (⊙) is used here. The expression operates on the variables related to the i-th element node, i.e., it operates on a scalar element of the vector; in practice, ⊙ represents scalar multiplication.

[0118] (2) Discrete physical residual loss

[0119] In this embodiment, the coarse-grid numerical simulation model uses the finite volume method, the spatial discretization scheme is the central difference scheme, and the time progression is implicit Euler.

[0120] At all nodes of the fixed computational grid, using a discretization scheme identical to the coarse-grid numerical model (finite volume method, central difference scheme), the spatial / temporal discrete derivatives of the network output predictions are calculated. These are then substituted into the discretized conserved Navier-Stokes equations, energy equations, and electromagnetic field equations to obtain the residual vector. Taking the energy equation as an example, for a grid cell P, the volume V... P The time step Δt adopts implicit Euler time propagation, and its discrete residual expression is:

[0121] ;

[0122] in:

[0123] The energy equation discrete residual for grid cell P.

[0124] The fluid density is given.

[0125] This is the specific heat capacity at constant pressure.

[0126] Let f be the volume flux through the boundary surface f of the grid cell.

[0127] This is the predicted temperature value at the center of unit P at time step n+1 (time layer n+1).

[0128] This is the predicted temperature value at the center of unit P at the nth time step (nth time layer).

[0129] The predicted temperature value on the unit surface f at the (n+1)th time step (n+1th time layer) is obtained by central difference interpolation.

[0130] is the thermal conductivity.

[0131] This represents the temperature gradient on the unit surface f at the (n+1)th time step (n+1th time layer).

[0132] Let f be the outward normal unit vector of the element surface f.

[0133] Let f be the area of ​​the unit surface.

[0134] J is the eddy current heat source term at the center of unit P, and is calculated synchronously through the electromagnetic field equation.

[0135] Spatial discretization uses a central difference scheme:

[0136] Among them, the physical quantities on the element surface f are interpolated using central difference interpolation:

[0137] ;

[0138] in,

[0139] This is the predicted temperature value at the center of unit P.

[0140] This is the predicted temperature value at the center of the adjacent unit N.

[0141] The gradient on the unit surface f is approximated using the central difference method (orthogonal mesh):

[0142] ;

[0143] N is the neighboring grid cell of grid cell P, and the interface f is located between grid cells P and N;

[0144] It represents the distance from the center of unit P to the center of the adjacent unit N. Let f be the temperature gradient on the unit interface.

[0145] For non-orthogonal meshes, a cross-diffusion correction term needs to be added, with the specific form consistent with the coarse mesh model. The final discrete physical residual loss term is the sum of the squares of the residuals of all mesh elements.

[0146] Similarly, the residuals for each node can be calculated. Momentum residual and electromagnetic field residuals Then, the mean square value is calculated. The expression for the discrete equation loss is:

[0147] ;

[0148] This represents the total number of grid cells.

[0149] (3) Boundary condition residual loss

[0150] Assume there are N in the computational domain bc A boundary grid, M bc,i This is the boundary mesh mask vector; it is set to 1 if the mesh it belongs to is a boundary mesh, and 0 otherwise. The expression for the boundary loss is:

[0151] ;

[0152] in:

[0153] The boundary condition residuals for each grid point.

[0154] Y pred Y is a physical quantity output by the network (such as temperature). bc Given the boundary mesh conditions. ⊙ represents element-wise multiplication. ||·||2 represents the L2 norm.

[0155] It should be noted that since vector calculations are typically used in actual computations, element-wise multiplication (⊙) is used here. The expression operates on the variables related to the i-th element node, i.e., it operates on a scalar element of the vector; in practice, ⊙ represents scalar multiplication.

[0156] (4) Loss function standardization and balancing

[0157] Node residual standardization: for L respectively data L pde L bc The residuals (or errors) of each node involved in the calculation process are standardized, for example:

[0158] ;

[0159] in, μ is the original residual (data residual, physical residual, or boundary residual) of the i-th node (or cell). R σ R This represents the mean and standard deviation of the residual across all nodes involved (e.g., the mean and standard deviation of the data residual are sampled from sparse nodes where the sensor is located). The standardized residual for the i-th node (or cell).

[0160] Internal average of loss terms: After standardization, calculate the mean square value of each type of residual.

[0161] ,

[0162] Among them, M data,i M is a binary mask for the data loss term, with the same dimension as the number of grid nodes. When there is a sensor measurement at the i-th node, M... data,i =1 otherwise 0. This mask is used to retain only the error contribution of the sensor nodes.

[0163] Let the standardized data residual at the i-th node be defined as... ,in This represents the residual of the original data. These are the mean and standard deviation of the data residuals at all sensor nodes, respectively.

[0164] The standardized physical residual at the i-th node. Its original residual. It is obtained by substituting the neural network predictions into the discrete control equations (e.g., the residuals of the energy equation). (momentum residuals, etc.), and then standardized: ,in The mean and standard deviation of the physical residual across all nodes.

[0165] M bc,i M is the binary mask for the boundary condition loss term. When the i-th node is located on the boundary and the boundary conditions at that location are known, M bc,i =1 otherwise 0. This mask is used to preserve only the error of the boundary nodes.

[0166] Let the standardized boundary condition residual at the i-th node be defined as... ,in This represents the original boundary residual. These are the mean and standard deviation of the boundary residuals at all boundary nodes, respectively.

[0167] It should be noted that since vector calculations are typically used in actual computations, element-wise multiplication (⊙) is used here. The expression operates on the variables related to the i-th element node, i.e., it operates on a scalar element of the vector; in practice, ⊙ represents scalar multiplication.

[0168] Weighted balance among loss items: The final total loss is:

[0169] The weight coefficients are dynamically adjusted through an adaptive strategy: increasing λ during the initial training phase. pde To strengthen physical constraints, appropriately reduce λ in the mid-to-late game. pde This improves data fitting accuracy. In this embodiment, an automatic weight adjustment algorithm based on gradient variance is used.

[0170] 1.5 Offline training;

[0171] One hundred sets of fluid-thermal-electromagnetic coupled solutions under different operating conditions (combinations of heating power, fluidizing gas velocity, and inlet temperature) were generated using high-fidelity CFD simulations as a training dataset. The Adam optimizer was employed with an initial learning rate of 1e-3, decreasing by 0.9 every 500 steps. The training process lasted approximately 24 hours until the loss function converged (total loss below 1e-4). During training, the convergence speed was significantly improved due to the use of residual initialization and standardization, and no gradient explosion or convergence oscillations were observed.

[0172] 2. Online real-time status awareness and prediction

[0173] 2.1 Data Acquisition and Coarse Mesh Solution;

[0174] During system operation, real-time data is collected every 5 seconds: coil current (reflecting heating power), inlet fluidizing gas velocity, 5 temperature measuring points, and 2 pressure measuring points. The data at the current moment is input into the coarse-grid numerical simulation model, and the approximate solution of the coarse-grid physical field (temperature, velocity, pressure, and electromagnetic field distribution) for the entire field at the current moment is obtained within 8 seconds.

[0175] 2.2 Physical information neural network reasoning;

[0176] The coarse mesh solution at the current moment (T at each mesh node) coarse U coarse , p coarse B coarse E coarse The system inputs sparse sensor measurements and spatiotemporal coordinates for the next 3 seconds (each time step is 0.1 seconds) into a pre-trained physical information neural network. Utilizing GPU parallel inference, it outputs a high-precision full-field physical field (temperature, velocity, pressure, electromagnetic field) for each moment within the next 3 seconds within 50 milliseconds.

[0177] During a certain operation, the system predicted that due to the power increase, the temperature in the upper right corner of the bed would exceed the safety threshold of 900°C after 2 seconds. This prediction was immediately sent to the control system, which proactively reduced the heating power of the corresponding electromagnetic coil in that area within 0.1 seconds and fine-tuned the fluidizing gas velocity, successfully preventing localized overheating. The entire process, from state awareness to control response, was completed within 0.2 seconds, verifying the real-time performance and reliability of the method of this invention.

[0178] Compared to traditional PINN (continuous residual, unstandardized), the discrete PINN format of this invention (also known as D-PINN) reduces the overall average temperature prediction error by 32% (from 2.3℃ to 1.5℃) and the relative error of the velocity field by 28% on the same test set. Furthermore, the prediction accuracy remains within a reasonable range (error ≤ 5%) under extrapolation conditions (untrained heating power combinations). In terms of inference speed, due to GPU parallelism and a lightweight network structure, the entire field prediction for the next 3 seconds can be completed within 50 milliseconds, fully meeting real-time control requirements.

[0179] On the other hand, the present invention provides a real-time sensing and prediction system for thermal storage systems based on hybrid simulation and PINN, which includes various modules capable of implementing the steps of the aforementioned method, specifically including:

[0180] Offline modeling and training module: used to generate fixed meshes, build and train coarse-mesh numerical simulation models and physical information neural network models.

[0181] Data acquisition and interface module: used to acquire sensor data, control signals and boundary conditions of the thermal storage system in real time.

[0182] Online hybrid simulation engine: This is the core module, including:

[0183] Coarse-mesh fast-solver element: Receives real-time data and drives the rapid solution of the parametric model.

[0184] Physical information neural network inference unit: Loads the trained network model, receives coarse grid solutions and real-time data, and performs parallel inference of high-precision full-field state.

[0185] Status output and application module: Outputs the predicted high-precision full-field physical state to the monitoring interface, database or advanced control system.

[0186] Thirdly, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN.

[0187] Fourthly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN.

[0188] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN, characterized in that, include: Step S1, Offline Stage: Construct and train a hybrid simulation model for the corresponding thermal storage system. The hybrid simulation model includes a parameterized coarse-grid numerical simulation model and a physical information neural network model. The coarse-grid physical field approximation solution output by the coarse-grid numerical simulation model is used as the input of the physical information neural network model. The loss function of the physical information neural network model includes a discrete physical residual term. The discrete physical residual term is calculated as follows: On all nodes of a fixed computational grid, using a discretization format completely consistent with the coarse-grid numerical simulation model, calculate the spatial and temporal discrete derivatives of the predicted values ​​output by the physical information neural network model. Substitute these derivatives into the discretized conservatism control equations to obtain the residuals of each grid node. Then, calculate the sum of squares or mean square of the residuals of all grid nodes. Step S2, Online Stage: The real-time collected operating data of the thermal storage system is input into the parameterized coarse-grid numerical simulation model to obtain the approximate solution of the coarse-grid physical field at the current moment; then the approximate solution of the coarse-grid physical field and the spatiotemporal coordinates of the future moment are input into the trained physical information neural network model to infer and output a high-precision full-field physical state prediction for the future moment. In step S1, a physical information neural network training method based on physical prior initialization is adopted, which includes: setting the weight matrix of the output layer of the physical information neural network model to zero, and simultaneously initializing its bias vector to a function associated with the input spatiotemporal coordinates, directly returning the coarse-grid physical field approximation solution calculated by the coarse-grid numerical simulation model at the corresponding coordinate point; so that at the initial moment of training, the predicted output value of the physical information neural network model for any input coordinate is always equal to the coarse-grid physical field approximation solution at the corresponding coordinate point, forming an explicit residual learning framework.

2. The real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in claim 1, characterized in that, In step S1, the coarse-grid numerical simulation model is based on a fixed computational grid, and the conserved control equations are discretized using the finite volume method, finite difference method, or finite element method. The fixed computational grid is a non-uniform grid, and local refinement is performed in a preset key region with a large physical field gradient.

3. The real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in claim 2, characterized in that, The conservation-type governing equations include mass conservation equations, momentum conservation equations, and energy conservation equations; the energy conservation equations include eddy current Joule heat source terms generated by electromagnetic induction, and the momentum conservation equations include electromagnetic volume force terms generated by electromagnetic fields acting on conductive media; the discrete physical residual terms of the parameterized coarse-grid numerical simulation model and the physical information neural network model both include the eddy current Joule heat source terms and the electromagnetic volume force terms.

4. The real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in claim 1, characterized in that, In step S1, the input of the physical information neural network model includes spatiotemporal coordinate points and the coarse-grid physical field approximation solution output by the coarse-grid numerical simulation model at the spatiotemporal coordinate points. The coarse-grid physical field approximation solution includes coarse-grid numerical solutions for temperature field, velocity field, pressure field, magnetic induction field, and electric field intensity field. The output of the physical information neural network model is the corresponding high-precision physical field prediction variables, including high-precision prediction values ​​for temperature field, velocity field, pressure field, magnetic induction field, and electric field intensity field.

5. The real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in claim 1, characterized in that, In step S1, the loss function of the physical information neural network model is composed of a weighted sum of data residual terms, discrete physical residual terms, and boundary condition residual terms; wherein, when calculating the data residual terms and the boundary condition residual terms, a 0-1 binary mask is used for identification and filtering.

6. The real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in claim 1, characterized in that, In step S1, the loss function adopts a hierarchical standardization and balancing design, including: when calculating the data residual term, discrete physical residual term, and boundary condition residual term, standardizing each type of residual on all corresponding calculation nodes, calculating the mean square value of each type of node residual after standardization, dividing it by the total number of nodes of the corresponding category to obtain the average loss term that is independent of the number of nodes, and applying weighting coefficients to each average loss term after processing to form the total loss function.

7. An electronic device, characterized in that, include: One or more processors; Memory, which stores one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the real-time sensing and prediction method for thermal storage systems based on hybrid simulation and PINN as described in any one of claims 1-6.

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