Model training method for predicting one-dimensional combustion characteristics of a porous media burner

Abstract

This disclosure proposes a model training method for predicting the one-dimensional combustion characteristics of porous media burners. The method includes: modeling the combustion process of the porous media burner to obtain a combustion model; performing numerical simulation based on the combustion model to obtain the one-dimensional temperature field distribution at each first sampling point within the spatial distribution range of operating parameter variables; using target interpolation to obtain the one-dimensional temperature field distribution at each second sampling point, where the one-dimensional temperature field distribution conforms to the variation law of the operating parameter variables; and using the one-dimensional temperature field distribution at each sampling point as a training set to train the neural network model, thereby obtaining a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner. This allows for a better approximation of the target physical laws, avoiding deviations from physical laws under small sample size conditions, and achieving more accurate prediction precision.

Description

Technical Field

[0001] This disclosure relates to the field of gas turbine technology, and more particularly to a model training method for predicting one-dimensional combustion characteristics of porous media burners. Background Technology

[0002] Currently, the main applications of porous media combustion technology are concentrated in atmospheric pressure, low temperature, and low flow rate environments. In contrast, the working environment of a gas turbine combustor is characterized by high pressure, high temperature, and high speed. Due to these environmental differences, applying porous media combustion technology to gas turbines faces a series of challenges, such as achieving flame stability under high pressure, resisting the erosion of combustor materials by high-temperature flames, and dealing with high-frequency thermal shock.

[0003] To meet the rapid iterative requirements of gas turbine combustor structural design and to realize the application of porous media combustion technology in this field, the primary task is to conduct numerical simulations of the combustor structure designed in the prior analysis to predict its combustion characteristics. Subsequently, using iterative optimization techniques, based on the numerical simulation results, the equivalence ratio and velocity boundaries for stable combustion are adjusted to achieve multi-dimensional control over a wide range of varying heat loads and power outputs. This process provides the optimal design scheme for subsequent test specimen preparation and combustor performance testing.

[0004] Related technologies can predict burner combustion characteristics using neural network models. However, neural network models typically require a large amount of training data to effectively learn patterns and laws, especially when dealing with complex problems or high-dimensional data. With small sample sizes, insufficient data can lead to overfitting or failure to capture the true physical laws, thus affecting the accuracy of burner combustion characteristic predictions. Summary of the Invention

[0005] This disclosure aims to at least partially address one of the technical problems in the related art.

[0006] Therefore, this disclosure proposes a model training method, a prediction method, apparatus, electronic device, computer-readable storage medium, and computer program product for predicting one-dimensional combustion characteristics of porous media burners, in order to solve the problem in related technologies that, for small sample points, due to insufficient data, neural network models may overfit or fail to capture the real physical laws well, thereby affecting the prediction accuracy of the combustion characteristics of burners.

[0007] The first aspect of this disclosure proposes a model training method for predicting one-dimensional combustion characteristics of a porous media burner, comprising: modeling the combustion process of a porous media burner with a target structure to obtain a combustion model, and determining operating condition parameter variables and the spatial distribution range of the operating condition parameter variables; performing numerical simulation based on the combustion model for multiple first sampling points within the spatial distribution range to obtain a one-dimensional temperature field distribution of the porous media burner at each first sampling point, wherein the one-dimensional temperature field distribution includes the temperature at multiple preset positions of reactors in the axial direction of the porous media burner; and performing numerical simulation for multiple second sampling points within the spatial distribution range. Using a target interpolation method, based on the one-dimensional temperature field distribution of the porous media burner at each of the first sampling points, the one-dimensional temperature field distribution of the porous media burner at each of the second sampling points is obtained. The one-dimensional temperature field distribution of the porous media burner at each of the second sampling points conforms to a target physical law, which is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable. The one-dimensional temperature field distributions of the porous media burner at each of the first and second sampling points are used as a training set to train the neural network model, resulting in a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

[0008] A second aspect of this disclosure provides a method for predicting the one-dimensional combustion characteristics of a porous media burner, comprising: acquiring a target prediction model, wherein the target prediction model is trained based on the method described in the first aspect embodiment; using the target prediction model to predict the one-dimensional combustion characteristics of the porous media burner, obtaining a one-dimensional temperature field distribution of the porous media burner at a target value of the operating condition parameter variable, wherein the one-dimensional temperature field distribution includes the temperatures at preset positions of multiple reactors in the axial direction of the porous media burner; and determining the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target value point based on the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameter variable.

[0009] A third aspect of this disclosure provides a model training device for predicting one-dimensional combustion characteristics of a porous media burner, comprising: a modeling module for modeling the combustion process of a porous media burner of a target structure, obtaining a combustion model, and determining operating condition parameter variables and the spatial distribution range of the operating condition parameter variables; a simulation module for performing numerical simulation based on the combustion model at multiple first sampling points within the spatial distribution range, obtaining a one-dimensional temperature field distribution of the porous media burner at each first sampling point, wherein the one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors along the axial direction of the porous media burner; and an acquisition module for obtaining the temperature at multiple first sampling points within the spatial distribution range. Multiple second sampling points are used, and a target interpolation method is employed. Based on the one-dimensional temperature field distribution of the porous media burner at each of the first sampling points, the one-dimensional temperature field distribution of the porous media burner at each of the second sampling points is obtained. The one-dimensional temperature field distribution of the porous media burner at each of the second sampling points conforms to a target physical law, which is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable. A training module is used to use the one-dimensional temperature field distribution of the porous media burner at each of the first and second sampling points as a training set to train the neural network model, obtaining a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

[0010] A fourth aspect of this disclosure provides a device for predicting the one-dimensional combustion characteristics of a porous media burner, comprising: an acquisition module for acquiring a target prediction model, wherein the target prediction model is trained based on the method described in the first aspect embodiment; a prediction module for using the target prediction model to predict the one-dimensional combustion characteristics of the porous media burner, thereby obtaining a one-dimensional temperature field distribution of the porous media burner at a target value of the operating condition parameter variable, wherein the one-dimensional temperature field distribution includes the temperatures at preset positions of multiple reactors in the axial direction of the porous media burner; and a temperature determination module for determining the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target value based on the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameter variable.

[0011] The electronic device proposed in the fifth aspect of this disclosure includes: a processor and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the model training method for predicting one-dimensional combustion characteristics of a porous media burner as proposed in the first aspect of this disclosure, or to implement the prediction method for one-dimensional combustion characteristics of a porous media burner as proposed in the second aspect of this disclosure.

[0012] A sixth aspect of this disclosure provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement a model training method for predicting one-dimensional combustion characteristics of a porous media burner as proposed in a first aspect of this disclosure, or to implement a method for predicting one-dimensional combustion characteristics of a porous media burner as proposed in a second aspect of this disclosure.

[0013] A seventh aspect of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements a model training method for predicting one-dimensional combustion characteristics of a porous media burner as proposed in a first aspect of this disclosure, or implements a method for predicting one-dimensional combustion characteristics of a porous media burner as proposed in a second aspect of this disclosure.

[0014] The technical solution proposed in this disclosure models the combustion process of a porous media burner with a target structure, obtaining a combustion model. Based on this model, numerical simulation is performed to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. This achieves high-fidelity numerical simulation to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. By employing target interpolation, based on the one-dimensional temperature field distribution of the porous media burner at each first sampling point, the one-dimensional temperature field distribution at each second sampling point is obtained. This effectively increases the number of sampling points, thereby increasing the number of training samples in the training set and improving the generalization ability of the target prediction model. Furthermore, the one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to the target's physical laws. This achieves coupling of physical information based on high-fidelity numerical simulation, enabling the target prediction model trained on the neural network model using the training set to better approximate the target's physical laws when predicting the one-dimensional combustion characteristics of the porous media burner. This avoids deviations from physical laws under small sample conditions, achieving more accurate prediction precision. By employing a target prediction model, the one-dimensional combustion characteristics of a porous media burner are predicted, yielding a one-dimensional temperature field distribution at target values ​​of operating parameters. This one-dimensional temperature field distribution includes the temperatures at preset locations of multiple reactors along the axial direction of the porous media burner. Based on this one-dimensional temperature field distribution at the target values ​​of operating parameters, the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target values ​​are determined. This enables rapid prediction of the one-dimensional combustion characteristics of the porous media burner using a target prediction model, and it better approximates the target physical laws during prediction, avoiding deviations from physical laws under small sample sizes, thus achieving more accurate prediction precision.

[0015] Additional aspects and advantages of this disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this disclosure. Attached Figure Description

[0016] The above and / or additional aspects and advantages of this disclosure will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, in which:

[0017] Figure 1 A schematic flowchart illustrating a model training method for predicting one-dimensional combustion characteristics of a porous media burner, provided in an embodiment of this disclosure.

[0018] Figure 2 A schematic diagram of the structure and initial structural parameters of a porous media burner provided in an embodiment of this disclosure;

[0019] Figure 3 A schematic flowchart illustrating the method for predicting the one-dimensional combustion characteristics of a porous media burner provided in this embodiment of the present disclosure;

[0020] Figure 4 This is a schematic diagram showing the distribution of the first candidate sampling point, the second candidate sampling point, and the second sampling point within the spatial distribution range of the operating condition parameter variables.

[0021] Figure 5 This is a schematic diagram of the temperature response surface obtained based on physical information;

[0022] Figure 6 This is a schematic diagram of the structure of a deep neural network model;

[0023] Figure 7 This is a schematic diagram showing the average temperature, maximum temperature, and outlet temperature of a porous media burner at multiple values ​​of operating parameter variables.

[0024] Figure 8 This is another schematic diagram of the average temperature, maximum temperature, and outlet temperature of a porous media burner at multiple values ​​of operating parameter variables.

[0025] Figure 9 This is another schematic diagram of the average temperature, maximum temperature, and outlet temperature of a porous media burner at multiple values ​​of operating parameter variables.

[0026] Figure 10 This is another schematic diagram of the average temperature, maximum temperature, and outlet temperature of a porous media burner at multiple values ​​of operating parameter variables.

[0027] Figure 11The image shows the actual variations in the average temperature, maximum temperature, and outlet temperature of the porous media burner with respect to the inlet air velocity and equivalence ratio within the range of 0.3-20 m / s and equivalence ratio of 0.4-0.8.

[0028] Figure 12 This is a schematic diagram of the structure of a model training device for predicting one-dimensional combustion characteristics of a porous media burner, provided in an embodiment of this disclosure.

[0029] Figure 13 A schematic diagram of the structure of a device for predicting the one-dimensional combustion characteristics of a porous media burner provided in an embodiment of this disclosure;

[0030] Figure 14 A block diagram of an exemplary electronic device suitable for implementing embodiments of the present disclosure is shown. Detailed Implementation

[0031] Embodiments of this disclosure are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this disclosure, and should not be construed as limiting this disclosure.

[0032] It should be noted that the information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, data stored, data displayed, etc.) and signals involved in this disclosure are all 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.

[0033] To meet the rapid iterative requirements of gas turbine combustor structural design and to realize the application of porous media combustion technology in this field, the primary task is to conduct numerical simulations of the combustor structure designed in the prior analysis to predict its combustion characteristics. Subsequently, using iterative optimization techniques, based on the numerical simulation results, the equivalence ratio and velocity boundaries for stable combustion are adjusted to achieve multi-dimensional control over a wide range of varying heat loads and power outputs. This process provides the optimal design scheme for subsequent test specimen preparation and combustor performance testing.

[0034] Research on porous media combustion technology typically requires significant computational time and resources for high-fidelity numerical simulations. This is because porous media combustion involves multiple coupled physical and chemical phenomena, including heat, mass transfer, chemical reactions, and momentum transfer. Furthermore, accurately describing the chemical reactions during combustion necessitates detailed chemical mechanisms, potentially encompassing hundreds of chemical species and thousands of reactions. Solving the rate equations for these chemical reactions demands substantial computation. In design optimization problems (under multi-parameter query scenarios), a large design space needs to be explored for parameter optimization, sensitivity analysis, or uncertainty quantification to find the optimal solution. Using high-fidelity numerical simulations to evaluate every design point may be impractical.

[0035] Parametric surrogate models can significantly reduce computational costs and time, but their predictive accuracy needs improvement and they may deviate from the physical laws dominated by the governing equations, lacking physical interpretability. On the other hand, it is crucial to easily embed parametric surrogate models into existing engineering design software, which requires consideration of factors such as software architecture, interface design, performance optimization, stability, and reliability.

[0036] Neural network models, as parameterized surrogate models, typically provide standardized interfaces and APIs (Application Programming Interfaces). These standardized interfaces and APIs make using neural network models in different software environments simpler and more reliable. Furthermore, neural network models have a large developer community, providing abundant open-source tools, libraries, and documentation, accelerating the integration process of neural network models into industrial software. Using neural network models as surrogate models allows for easy embedding into existing engineering design software, accelerating the engineering design process.

[0037] On the other hand, compared to other types of surrogate models, neural network models can capture complex nonlinear relationships, are suitable for simulating and predicting the behavior of various complex systems, and have good generalization ability, meaning they perform well on unseen data. Using neural network models as surrogate models can, to a certain extent, ensure the accuracy of computation and prediction.

[0038] Therefore, related technologies can predict the combustion characteristics of burners using neural network models. However, neural network models typically require a large amount of training data to effectively learn patterns and laws, especially when dealing with complex problems or high-dimensional data. For small sample points, due to insufficient data, neural network models may overfit or fail to capture the true physical laws, thus affecting the accuracy of burner combustion characteristic predictions.

[0039] This application proposes a model training method, a prediction method, apparatus, electronic device, computer-readable storage medium, and computer program product for predicting the one-dimensional combustion characteristics of porous media burners, in order to improve the prediction accuracy of neural network models for one-dimensional combustion characteristics of porous media burners. The one-dimensional combustion characteristics refer to the phenomena such as flame and combustion wave propagation, reaction, and heat transfer during combustion, which mainly occur along one direction. In this embodiment, this direction refers to the axial direction of the porous media burner.

[0040] The following, with reference to the accompanying drawings, explains the model training method for predicting the one-dimensional combustion characteristics of porous media burners, the prediction method, apparatus, electronic equipment, computer-readable storage medium, and computer program product.

[0041] Figure 1 This is a schematic flowchart illustrating a model training method for predicting one-dimensional combustion characteristics of a porous media burner, provided in an embodiment of this disclosure.

[0042] The model training method for predicting the one-dimensional combustion characteristics of porous media burners can be configured to be executed in a model training device for predicting the one-dimensional combustion characteristics of porous media burners. Hereinafter, the model training device for predicting the one-dimensional combustion characteristics of porous media burners will be referred to as the model training device. The model training device can be a server, electronic equipment, or can be configured within a server or electronic equipment; this application does not impose any limitations on this.

[0043] Electronic devices include, for example, hardware devices with data processing capabilities such as computers, tablets, and personal digital assistants.

[0044] It should be noted that the execution entity of the embodiments disclosed herein may be, in hardware, a central processing unit (CPU) in a server or electronic device, and in software, a related service in a server or electronic device, and there are no limitations on this.

[0045] like Figure 1 As shown, the model training method for predicting the one-dimensional combustion characteristics of porous media burners includes:

[0046] S101. Model the combustion process of the porous media burner of the target structure to obtain the combustion model, and determine the operating condition parameter variables and the spatial distribution range of the operating condition parameter variables.

[0047] The target structure, i.e. the structure of the given porous media burner, can be designed as needed, and this disclosure does not impose any restrictions on it.

[0048] In this embodiment of the disclosure, based on the structural design and initial structural parameters of the porous media burner, tools such as Cantera can be used to describe the physical behavior of the porous media burner during the combustion process using control equations, thereby modeling the combustion process of the porous media burner and obtaining a combustion model.

[0049] Combustion models, based on certain assumptions, apply single or complex physical and chemical reaction mechanisms, such as those involving the gas phase and condensed phase, to describe the combustion process in a representative way.

[0050] The governing equations (specifically partial differential equations) are mathematical expressions that transform the physical phenomena such as fluid flow, heat transfer, and chemical reactions within the burner. They accurately describe the relationships and changes in various physical quantities (such as temperature, pressure, and component concentration) during combustion. These equations may include the gas-phase mass conservation equation, the gas-phase energy conservation equation, and the gas-solid heat transfer equation. Specifically, the gas-phase mass conservation equation describes the changes in gas-phase mass during combustion in a porous media burner. The gas-phase energy conservation equation describes the changes in internal energy of the gas phase during combustion, including energy changes caused by convection, conduction, radiation, and chemical reactions. The gas-solid heat transfer equation describes the heat transfer between the gas and solid phases due to temperature differences during combustion in a porous media burner.

[0051] refer to Figure 2 The structural design and initial structural parameters of a porous media burner can be, for example, as follows: Figure 2 As shown. The porous media burner can be 9.4 inches in total length and includes: a preheating layer formed by two first reactors, a cavity section formed by two second reactors, a combustion zone formed by two third reactors, two fourth reactors, eight fifth reactors and two sixth reactors, and a heat recirculation zone formed by two seventh reactors. Figure 2In the diagram, 2×R1 represents two first reactors, 2×R2 represents two second reactors, and so on. PPI represents porosity, characterizing the average number of pores per unit inch, and ε represents emissivity. Taking the cavity section as an example, it is assumed to be a ZrO2 ring with a porosity of 0.5 and an emissivity of 0.001; other sections follow the same principle and will not be elaborated further. The combustion process of this porous media burner is modeled using Cantera, resulting in a combustion model that includes governing equations such as the gas phase mass conservation equation, the gas phase energy conservation equation, and the gas-solid heat transfer equation. For example, the TPRC (Thermal Properties Research Center) data series can be used as reference data for material thermal conductivity, based on thermodynamic property data provided in a certain aerospace report. Radiative thermal conductivity is calculated using the Roeesland model. For the chemical reaction mechanism, the GRI 3.0 reaction mechanism is adopted, and a chemical reaction network consisting of 20 reactors is constructed. It is assumed that the system will reach a steady state after a combustion process of 3600 seconds.

[0052] In this embodiment, the Design of Experiments (DOE) method can be used to determine the operating parameter variables and their spatial distribution range based on the lean-burn boundary and the actual operating conditions of the gas turbine. DOE is an experimental design method used to explore and verify the impact of factors on results. This method systematically plans, executes, and analyzes experiments to understand how each variable affects a specific response variable, thereby optimizing product performance, improving production efficiency, or reducing costs.

[0053] Among them, the operating condition parameter variable is a parameter variable used to represent the operating condition.

[0054] As an example, the operating parameters determined by the DOE method may include the inlet air velocity and the inlet chemical equivalence ratio of the porous media burner. The inlet chemical equivalence ratio, or simply equivalence ratio, is the proportion required for reactants to react according to the stoichiometric relationships in a chemical reaction. In combustion, this can be understood as the theoretical ratio between fuel and oxidant (usually oxygen from the air) required for complete combustion. The spatial distribution range of the inlet air velocity can be 0.3–20 m / s, and the spatial distribution range of the inlet chemical equivalence ratio can be 0.4–0.8.

[0055] As an example, the determined operating parameters may also include other operating parameters, such as the porosity of the porous media burner and the structure of the porous media burner.

[0056] S102. For multiple first sampling points in the spatial distribution range, numerical simulation is performed based on the combustion model to obtain the one-dimensional distribution of the temperature field of the porous media burner at each first sampling point. The one-dimensional distribution of the temperature field includes the temperature at the preset positions of multiple reactors in the axial direction of the porous media burner.

[0057] In this context, the axial direction of the porous media burner is parallel to its main axis or centerline. The porous media burner comprises multiple reactors arranged axially, and during combustion, the airflow, including combustion gases, flows along this axial direction. For example, Figure 2 The axial direction of the porous media burner is horizontal.

[0058] The preset position can be set as needed, for example, it can be set to the middle section of the reactor.

[0059] In this context, any sampling point within the spatial distribution range of the operating condition parameter variables corresponds to a value of the operating condition parameter variable. For example, if the operating condition parameter variables include the inlet air velocity and the inlet chemical reaction equivalence ratio of the porous media burner, and the spatial distribution range of the inlet air velocity is 0.3-20 m / s, and the spatial distribution range of the inlet chemical reaction equivalence ratio is 0.4-0.8, then a certain sampling point could correspond to an inlet air velocity of 0.4 and an inlet chemical reaction equivalence ratio of 0.5.

[0060] As an example, multiple first sampling points in the spatial distribution range of the operating condition parameter variables can be obtained in the following ways: At least one of the following sampling methods is used to sample the spatial distribution range of the operating condition parameter variables to obtain multiple first candidate sampling points: Latin hypercube sampling, Sobol sampling, Kronecker sampling, and random sampling; resampling is performed within the boundary region of the spatial distribution range of the operating condition parameter variables to obtain multiple second candidate sampling points; the multiple first candidate sampling points and the multiple second candidate sampling points are used as multiple first sampling points.

[0061] Latin hypercube sampling is a method for approximate random sampling from a multivariate parameter distribution. It divides the range of values ​​for each variable into several intervals with equal probability and randomly selects a value from each interval to ensure the randomness and uniformity of the sample.

[0062] Sobol sampling is a method for generating low-discrepancy sequences that cover the sample space more uniformly than simple random sequences, thus improving convergence speed in Monte Carlo simulations.

[0063] Kronecker sampling is another method for generating low-discrepancy sequences. It is based on the Kronecker product to construct sequences and is also used to improve the efficiency of Monte Carlo simulations.

[0064] Random sampling refers to the uncertainty or unpredictability of data or events occurring in statistics and computer science. In numerical analysis, randomness is often simulated using random number generators (RNGs).

[0065] As an example, the combustion model includes governing equations for describing the physical behavior during combustion. These governing equations include: meteorological mass conservation equation, meteorological energy conservation equation, and gas-solid heat transfer equation. Step S102 can be implemented as follows: for each first sampling point, based on the values ​​of the operating condition parameter variables at that first sampling point, the meteorological mass conservation equation, meteorological energy conservation equation, and gas-solid heat transfer equation are solved to obtain the one-dimensional temperature field distribution of the porous media burner at that first sampling point.

[0066] Specifically, for each first sampling point, the parameters such as the inlet boundary conditions required to solve the governing equations can be determined based on the values ​​of the operating condition variables at that point. Then, the governing equations are solved based on the inlet boundary conditions and other parameters to obtain the one-dimensional temperature field distribution of the porous media burner at that first sampling point. The inlet boundary conditions may include inlet air temperature, inlet mass flow rate, etc.

[0067] The one-dimensional temperature field distribution of the porous media burner at a certain sampling point can be understood as the temperature at a preset position of multiple reactors in the axial direction of the porous media burner when the operating parameter variable takes the value at that sampling point.

[0068] It should be noted that the one-dimensional temperature field distribution in the embodiments of this application is obtained under given operating conditions. For example, the given operating conditions may include: using methane as fuel, maintaining its temperature at room temperature, using ambient pressure, and having an inlet air temperature of 700K (Kelvin), etc. Under these operating conditions, the one-dimensional temperature field distribution is calculated based on the operating condition parameter variables and the temperatures of the air and fuel, taking into account the fuel inlet velocity, premixed fuel temperature, and mass flux.

[0069] S103. For multiple second sampling points in the spatial distribution range, a target interpolation method is adopted. Based on the one-dimensional temperature field distribution of the porous media burner at each first sampling point, the one-dimensional temperature field distribution of the porous media burner at each second sampling point is obtained. The one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to the target physical law, which is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable.

[0070] As an example, S103 can be implemented as follows: For each second sampling point within the spatial distribution range, using a target interpolation method, the one-dimensional distribution of the temperature field at at least one first sampling point surrounding that second sampling point is calculated to obtain the one-dimensional distribution of the temperature field of the porous media burner at that second sampling point, ensuring that the one-dimensional distribution of the temperature field of the porous media burner at each second sampling point conforms to the target physical law. Therefore, based on the one-dimensional distribution of the temperature field of the porous media burner at each first sampling point, the one-dimensional distribution of the temperature field of the porous media burner at more sampling points can be amplified based on the target interpolation method and physical information, rather than high-fidelity numerical simulation.

[0071] This method involves sampling the spatial distribution range of operating condition parameter variables at preset intervals to obtain multiple second sampling points. The preset interval can be set as needed, and this disclosure does not impose any restrictions on it. The multiple first sampling points may be partially or completely different from the multiple second sampling points.

[0072] Interpolation is a method of estimating unknown data points using known data points. It estimates the approximate value of a function at other points based on the function's values ​​at a finite number of points. The interpolation process constructs a specific function (called the interpolation function) that is equal to the original function at the known data points and provides an approximation of the original function at other points.

[0073] The interpolation methods can include, but are not limited to, the following:

[0074] Polynomial interpolation: such as Lagrange interpolation, which constructs a polynomial function that is equal to the original function at known data points;

[0075] Radial basis function interpolation: This method uses radial basis functions (such as Gaussian functions) as basis functions and constructs an interpolation function by linearly combining these basis functions. It is commonly used in machine learning to handle high-dimensional data and complex functions.

[0076] Spline interpolation: In particular, cubic spline interpolation constructs a piecewise polynomial function between data points, which is a cubic polynomial in each subinterval and smooth over the entire interval.

[0077] Among them, the operating parameters include the inlet air velocity and the inlet chemical reaction equivalence ratio of the porous media burner. Taking the outlet temperature of the porous media burner (i.e., the temperature at the preset position of the last reactor of the porous media burner) as an example, the target physical law may include: given the inlet chemical reaction equivalence ratio, as the inlet air velocity increases, the outlet temperature of the porous media burner shows a trend of first rising and then leveling off; given the inlet air velocity, as the inlet chemical reaction equivalence ratio increases, the outlet temperature of the porous media burner shows an upward trend.

[0078] The target interpolation method in this embodiment is one of a variety of candidate interpolation methods. The variety of candidate interpolation methods may include the above-mentioned interpolation methods. The one-dimensional temperature field distribution of the porous medium burner at each second sampling point obtained by using the target interpolation method conforms to the target physical law.

[0079] As an example, prior to S103, the target interpolation method can be determined from multiple candidate interpolation methods in the following way:

[0080] For any candidate interpolation method and multiple fourth sampling points in the spatial distribution range, the candidate interpolation method is adopted to obtain the one-dimensional temperature field distribution of the porous medium burner at each fourth sampling point based on the one-dimensional temperature field distribution of the porous medium burner at each first sampling point.

[0081] Determine whether the one-dimensional temperature field distribution of the porous media burner at each fourth sampling point conforms to the target physical law. If so, then determine the candidate interpolation method as the target interpolation method.

[0082] Among them, the fourth sampling point is any sampling point in the spatial distribution range of the working condition parameter variable. Multiple fourth sampling points are partially or completely different from multiple first sampling points, and multiple fourth sampling points can be the same as, partially different from or completely different from multiple second sampling points.

[0083] Specifically, for each candidate interpolation method and each fourth sampling point within the spatial distribution range, the candidate interpolation method can be used to calculate the one-dimensional temperature field distribution at at least one first sampling point surrounding the fourth sampling point, thus obtaining the one-dimensional temperature field distribution of the porous media burner at that fourth sampling point. The candidate interpolation method that ensures the obtained one-dimensional temperature field distribution of the porous media burner at each fourth sampling point conforms to the target physical law is then determined as the target interpolation method. After determining the target interpolation method from multiple candidate interpolation methods, the target interpolation method can be used to obtain the one-dimensional temperature field distribution of the porous media burner at each second sampling point, where this one-dimensional temperature field distribution conforms to the target physical law.

[0084] As an example, to ensure the accuracy of the one-dimensional temperature field distribution of the porous medium burner at each second sampling point obtained by the target interpolation method, the accuracy of the target interpolation method can also be judged. That is, the method can also include:

[0085] For multiple third sampling points in the spatial distribution range, a target interpolation method is adopted to obtain the one-dimensional temperature field distribution of the porous medium burner at each third sampling point based on the one-dimensional temperature field distribution of the porous medium burner at each first sampling point.

[0086] It is determined that the one-dimensional temperature field distribution of the porous media burner at each third sampling point conforms to the target physical law, and the difference between it and the one-dimensional temperature field distribution of the porous media burner at the corresponding third sampling point is less than a preset value; wherein, the one-dimensional temperature field distribution of the reference temperature field is obtained by numerical simulation based on the combustion model, which is the one-dimensional temperature field distribution of the porous media burner at the corresponding third sampling point.

[0087] Among them, the third sampling point is any sampling point in the spatial distribution range of the working condition parameter variable. Multiple third sampling points are partially or completely different from multiple first sampling points. Multiple third sampling points can be partially or completely different from multiple second sampling points. Multiple third sampling points can be the same as, partially different from, or completely different from multiple fourth sampling points.

[0088] The preset values ​​can be set as needed.

[0089] Understandably, for each third sampling point within the spatial distribution range, the governing equations can be solved based on the values ​​of the operating parameters at that third sampling point to obtain the one-dimensional temperature field distribution of the porous media burner at that third sampling point. Since this is obtained through numerical simulation, the one-dimensional temperature field distribution can be considered high-fidelity numerical simulation data and referred to as the reference one-dimensional temperature field distribution. Alternatively, a target interpolation method can be used to obtain the one-dimensional temperature field distribution of the porous media burner at each third sampling point based on the one-dimensional temperature field distribution at each first sampling point. Then, it can be determined whether the one-dimensional temperature field distribution of the porous media burner at each third sampling point conforms to the target physical laws, and whether the difference between this distribution and the reference one-dimensional temperature field distribution at the corresponding third sampling point is less than a preset value. If both are true, the accuracy of the target interpolation method is high, thus the accuracy of the one-dimensional temperature field distribution of the porous media burner at each second sampling point obtained through the target interpolation method is high.

[0090] S104. Using the one-dimensional temperature field distribution of the porous media burner at each first sampling point and each second sampling point as the training set, the neural network model is trained to obtain a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

[0091] The prediction of the one-dimensional combustion characteristics of the porous media burner can include predicting the one-dimensional temperature field distribution of the porous media burner at a certain value of the operating parameter variable. Specifically, it involves predicting the temperature at preset positions of multiple reactors along the axial direction of the porous media burner when the operating parameter variable is a certain value. Based on the one-dimensional temperature field distribution, it also involves determining the average temperature, maximum temperature, and outlet temperature of the porous media burner at that value of the operating parameter variable. The average temperature is the average temperature at preset positions of several reactors in the porous media burner; the maximum temperature is the highest temperature among the preset positions of several reactors in the porous media burner; and the outlet temperature is the temperature at the preset position of the last reactor in the porous media burner. For example, using... Figure 2 For example, the average temperature can be the average of the temperatures in the middle section of the 11th reactor to the middle section of the 20th reactor; the maximum temperature can be the highest value of the temperatures in the middle section of the 11th reactor to the middle section of the 20th reactor; and the outlet temperature can be the temperature in the middle section of the 20th reactor.

[0092] The temperature field of the porous media burner at each first sampling point or each second sampling point is a one-dimensional distribution, which is a training sample in the training set.

[0093] Among them, the neural network model can be any type of neural network model, such as deep neural network or convolutional neural network.

[0094] In this embodiment of the disclosure, the sampling point corresponding to each training sample, i.e., the value of the operating condition parameter variable at the sampling point, can be used as the input of the neural network model. The neural network model predicts the one-dimensional temperature field distribution of the porous media burner at the sampling point. The predicted one-dimensional temperature field distribution is then compared with the known one-dimensional temperature field distribution corresponding to the training sample. Based on the degree of deviation between the predicted one-dimensional temperature field distribution of all training samples in the training set and the known one-dimensional temperature field distribution, the model parameters of the neural network model are adjusted, thereby achieving the training of the neural network model and obtaining a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

[0095] Taking a deep feedforward neural network as an example, "feedforward" refers to the flow of physical information from the input x, through an intermediate function defining f, and finally to the output y, without any feedback connections from the output to the various connection layers. A deep feedforward neural network defines a mapping function y = f(x; θ) and learns the values ​​of the parameters θ, including the weights W, from the training set. (i) and deviation b (i) That is, {W (i) and b (i) Let i = 1, 2, ..., l}, and select an appropriate loss function to make the predicted result as close as possible to the actual value. The function f is expressed as follows:

[0096] y = f(x; θ) = f (l) (f l- 1(...f 2 (f 1 )))(1)

[0097] Among them, f 1 The input layer of a neural network model, f l The output layer of a neural network model is called the output layer. The total length l of the chain represents the depth of the neural network model, i.e., the number of layers in the neural network model.

[0098] i-th th Layer weight matrix W (i) It can be represented as follows:

[0099]

[0100] in, Represents (i-1) th layer (n) (i-1) ) th Neuron to i th layer (n) (i) ) th The connection weights between neurons, n (i) Representing i th The number of neurons in a layer.

[0101] i-th th deviation vector b (i) The expression is as follows:

[0102]

[0103] in, Representing the i-th th layer (n) (i) ) th Neuronal deviation.

[0104] i thThe intermediate information carried by layer neurons, i.e., the output h (i) It can be defined as:

[0105] h (i) =σ i (W (i) h (i-1) +b (i) (4)

[0106] Where, σ i Indicate i th The activation function of the layer is key to simulating the nonlinearity of the neural network, and the ReLU activation function can be selected.

[0107] Given a training set N train Therefore, the loss function J(θ) can be used to evaluate the degree of deviation between the predicted values ​​(i.e., the predicted one-dimensional temperature field distribution in the aforementioned example) and the actual values ​​(i.e., the known one-dimensional temperature field distribution in the aforementioned example) on the entire training set.

[0108]

[0109] In the formula, N train y is the number of training samples included in the training set. train Represents the actual value, y * This represents the predicted value of the neural network model.

[0110] The model training method for predicting the one-dimensional combustion characteristics of porous media burners disclosed herein involves modeling the combustion process of a porous media burner with a target structure to obtain a combustion model. Numerical simulation is then performed based on this model to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. This achieves high-fidelity numerical simulation to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. Furthermore, by employing target interpolation, the one-dimensional temperature field distribution of the porous media burner at each second sampling point is obtained based on the one-dimensional temperature field distribution at each first sampling point, effectively amplifying the sampling... The number of sampling points is increased, thereby expanding the number of training samples in the training set and improving the generalization ability of the target prediction model. Furthermore, the one-dimensional distribution of the temperature field at each second sampling point of the porous media burner conforms to the target physical law. This realizes the coupling of physical information on the basis of high-fidelity numerical simulation, so that the target prediction model obtained by training the neural network model based on the training set can better approximate the target physical law when predicting the one-dimensional combustion characteristics of the porous media burner. This avoids the situation of deviating from the physical law under the condition of a small number of samples, and achieves more accurate prediction accuracy, thus achieving the same function as PINN (Physics-informed neural network).

[0111] It should be noted that, since the target prediction model obtained by training the neural network based on the training set in this embodiment has the same function as PINN, the target prediction model in this embodiment can also be called PINN. Furthermore, in this embodiment, after obtaining the one-dimensional temperature field distribution of the porous media burner at each first sampling point and each second sampling point, the one-dimensional temperature field distribution can be corrected based on high-precision experimental data and additional high-fidelity numerical simulations to generate a higher-quality training set. This ensures that the target prediction model trained based on the training set can follow relevant physical laws and has stronger generalization ability.

[0112] Based on the model training method for predicting the one-dimensional combustion characteristics of porous media burners provided in the above embodiments, this disclosure also provides a method for predicting the one-dimensional combustion characteristics of porous media burners.

[0113] The following is combined Figure 3 The method for predicting the one-dimensional combustion characteristics of the porous media burner provided in the embodiments of this application is further explained.

[0114] Figure 3 This is a schematic flowchart illustrating a method for predicting the one-dimensional combustion characteristics of a porous media burner, as provided in an embodiment of this disclosure.

[0115] like Figure 3 As shown, the method for predicting the one-dimensional combustion characteristics of the porous media burner includes:

[0116] S301. Obtain the target prediction model.

[0117] The target prediction model can be trained based on the method described in the above embodiments.

[0118] S302. Using a target prediction model, the one-dimensional combustion characteristics of the porous media burner are predicted to obtain the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating condition parameter variables. The one-dimensional temperature field distribution includes the temperatures at preset positions of multiple reactors in the axial direction of the porous media burner.

[0119] The target value can be any value of the operating condition parameter variable.

[0120] The one-dimensional temperature field distribution of the porous media burner at the target value of the operating parameter variable can be understood as the temperature at the preset position of multiple reactors in the axial direction of the porous media burner when the operating parameter variable is the target value.

[0121] In the embodiments of this disclosure, by inputting the target value of the operating condition parameter variable into the target prediction model, the one-dimensional distribution of the temperature field of the porous media burner at the target value of the operating condition parameter variable can be obtained.

[0122] It should be noted that the one-dimensional combustion characteristics of the porous media burner predicted in the embodiments of this disclosure can be the one-dimensional combustion characteristics of the porous media burner under any operating conditions. These operating conditions can be the same as or different from the operating conditions in the training process of the target prediction model.

[0123] S303. Based on the one-dimensional distribution of the temperature field at the target value of the operating condition parameter variables of the porous media burner, determine the average temperature, maximum temperature and outlet temperature of the porous media burner at the target value.

[0124] Wherein, the average temperature is the average temperature at preset locations of several reactors in the porous media burner; the maximum temperature is the highest temperature among the preset locations of several reactors in the porous media burner; and the outlet temperature is the temperature at the preset location of the last reactor in the porous media burner. For example, with... Figure 2 For example, the average temperature can be the average of the temperatures in the middle section of the 11th reactor to the middle section of the 20th reactor; the maximum temperature can be the highest value of the temperatures in the middle section of the 11th reactor to the middle section of the 20th reactor; and the outlet temperature can be the temperature in the middle section of the 20th reactor.

[0125] It should be noted that, in this embodiment of the disclosure, a response surface model can be constructed based on the target prediction model to relate the operating condition parameters to the average temperature, maximum temperature, and outlet temperature of the porous media burner. Such a model can quickly and accurately predict the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target value given the operating condition parameters, thereby supporting iterative optimization of the structure and operating condition parameters of the porous media burner. Specifically, the response surface model can consist of a target prediction model and a temperature calculation module. The target prediction model can quickly and accurately predict the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameters, and the temperature calculation module can determine the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target value based on this one-dimensional temperature distribution.

[0126] In summary, the method for predicting the one-dimensional combustion characteristics of a porous media burner provided in this disclosure uses a target prediction model to predict the one-dimensional combustion characteristics of the porous media burner, obtaining the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating parameter variables. The one-dimensional temperature field distribution includes the temperatures at preset positions of multiple reactors along the axial direction of the porous media burner. Based on the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating parameter variables, the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target values ​​are determined. This achieves rapid prediction of the one-dimensional combustion characteristics of the porous media burner based on the target prediction model, and it can better approximate the target physical laws during prediction, avoiding deviations from physical laws under small sample size conditions, thus achieving more accurate prediction precision.

[0127] The following description, with reference to the accompanying drawings, illustrates the model training method for predicting the one-dimensional combustion characteristics of a porous media burner, the prediction method for the one-dimensional combustion characteristics of a porous media burner, and the prediction accuracy of the prediction method provided in this disclosure. Figure 11 The image shows the actual variations in the average temperature, maximum temperature, and outlet temperature of a porous media burner with respect to the inlet air velocity and equivalence ratio within the range of 0.3-20 m / s and equivalence ratio of 0.4-0.8.

[0128] First, the combustion process of the porous media burner with the target structure can be modeled to obtain a combustion model, and the operating parameters and their spatial distribution range can be determined. The structural design and initial structural parameters of the porous media burner can be, for example, as follows: Figure 2 As shown. Operating parameters include the inlet air velocity *u* and the inlet chemical reaction equivalence ratio of the porous media burner. The spatial distribution range of the inlet air velocity is 0.3-20 m / s, and the spatial distribution range of the inlet chemical reaction equivalence ratio is 0.4-0.8.

[0129] Then, Latin hypercube sampling can be used to sample the spatial distribution range of the operating condition parameter variables, obtaining multiple first candidate sampling points. Resampling is then performed within the boundary regions of the spatial distribution range of the operating condition parameter variables to obtain multiple second candidate sampling points. These multiple first candidate sampling points and multiple second candidate sampling points are then used as multiple first sampling points. The distribution of the first candidate sampling points within the spatial distribution range of the operating condition parameter variables is as follows: Figure 4 As shown in Figure (a), the distribution of multiple first candidate sampling points and multiple second candidate sampling points within the spatial distribution range of the operating condition parameter variables is as follows. Figure 4 As shown in Figure (b), Figure 4In Figure (b), the red circle represents the first candidate sampling point, and the blue circle represents the second candidate sampling point.

[0130] Next, for multiple first sampling points in the spatial distribution range, numerical simulation can be performed based on the combustion model to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. The one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors in the axial direction of the porous media burner.

[0131] Furthermore, the spatial distribution range of the operating condition parameter variables can be sampled at preset intervals to obtain multiple second sampling points. The distribution of these multiple second sampling points within the spatial distribution range of the operating condition parameter variables is as follows: Figure 4 As shown in Figure (c), Figure 4 In Figure (c), the red circle represents the first sampling point, and the blue box represents the second sampling point.

[0132] Furthermore, for multiple second sampling points within the spatial distribution range, a target interpolation method can be employed. Based on the one-dimensional temperature field distribution of the porous media burner at each first sampling point, the one-dimensional temperature field distribution of the porous media burner at each second sampling point can be obtained. The one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to a target physical law, which is the variation law of the one-dimensional temperature field distribution with operating parameter variables. That is, the one-dimensional temperature field distribution of the porous media burner at each second sampling point is obtained by appropriately selecting an interpolation method and combining it with physical information, rather than through high-fidelity numerical simulation. Figure 5 This is a schematic diagram of the temperature response surface obtained based on physical information, including the outlet temperature of the porous media burner at each first sampling point and each second sampling point. Figure 5 The z-axis represents the outlet temperature (T) of the porous media burner, in Kelvin (K). According to... Figure 5 It can be seen that, given the equivalence ratio θ, as the inlet air velocity u increases, the outlet temperature T shows a trend of first rising and then leveling off. This trend of increasing outlet temperature T with a given inlet air velocity u and equivalence ratio θ is consistent with the target physical laws. Figure 5 The outlet temperatures corresponding to sampling points other than the second and first sampling points are compared with the outlet temperatures corresponding to the sampling points obtained based on numerical simulation. The results are similar, which proves that this target interpolation method can effectively increase the number of sampling points while ensuring that the outlet temperatures at each second sampling point conform to the target physical laws, thereby increasing the number of training samples in the training set and ensuring the generalization ability of the deep neural network.

[0133] In this embodiment, a deep neural network and a Gaussian process can be used as surrogate models, respectively. The one-dimensional distribution of the temperature field at each first candidate sampling point of the porous media burner is used as the training set to train the surrogate models of the deep neural network and the Gaussian process, respectively, to obtain trained surrogate models. Based on the trained surrogate models, the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of the operating parameter variables are predicted. Figure 6 This is a schematic diagram of the structure of a deep neural network model. Figure 6 x1, x2, ..., x Din Representing different features of the input data, Figure 6 in y1, y2, y3, y4,…,y Dout These represent the temperatures at preset positions of each reactor in the axial direction of the output porous media burner. Figure 7 Figures (a), (b), and (c) in the figure represent the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of the operating parameter variables when the deep neural network is used as the surrogate model and the one-dimensional distribution of the temperature field of the porous media burner at each first candidate sampling point is used as the training set. Figure 8 Figures (a), (b), and (c) in the figure represent the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of the operating parameter variables, respectively, when the Gaussian process is used as a surrogate model and the one-dimensional distribution of the temperature field at each first candidate sampling point of the porous media burner is used as the training set. The results show that the prediction law of the surrogate model using the Gaussian process does not conform to the target physical law, and only captures the temperature field distribution in a small area near the training sample points. The surrogate model using the deep neural network can capture the spatial distribution of the temperature field better and conforms to the target physical law to a certain extent, but there is still a large predicted temperature difference near the boundary, which does not conform to the theoretical results.

[0134] In this embodiment of the disclosure, a deep neural network can also be used as a surrogate model. The one-dimensional distribution of the temperature field of the porous medium burner at each first candidate sampling point and each second candidate sampling point is used as the training set to train the surrogate model of the deep neural network, thereby obtaining the trained surrogate model. Based on the trained surrogate model, predictions are made respectively. Figure 9 The diagram shows the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of operating parameter variables. Among these... Figure 9 Figures (a), (b), and (c) in the figure represent the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of the operating parameter variables, respectively. According to... Figure 9It can be seen that, compared with using only the one-dimensional distribution of the temperature field of the porous media burner at each first candidate sampling point as the training set, using the one-dimensional distribution of the temperature field of the porous media burner at each first candidate sampling point and each second candidate sampling point as the training set effectively improves the prediction accuracy of the deep neural network near the boundary. The overall trend is consistent with existing physical information, but in some regions (e.g., for the highest temperature, in regions with low inlet air velocity and equivalence ratios of 0.4-0.5 and 0.7-0.8, the development trend of the highest temperature with changes in inlet air velocity does not conform to the target physical law). On the other hand, compared with... Figure 11 Compared with the existing high-fidelity numerical simulation results, there is still a certain prediction error.

[0135] In this embodiment, a deep neural network can be used as a surrogate model. The one-dimensional distribution of the temperature field at each first sampling point and each second sampling point of the porous medium burner is used as the training set to train the surrogate model of the deep neural network, thereby obtaining the trained surrogate model (i.e., the target prediction model in this embodiment). Based on the trained surrogate model, predictions are made respectively. Figure 10 The diagram shows the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of operating parameter variables. Among these... Figure 10 Figures (a), (b), and (c) in the figure represent the average temperature, maximum temperature, and outlet temperature of the porous media burner at multiple values ​​of the operating parameter variables, respectively. Figure 11 In comparison, the results show that the target prediction model can capture the temperature field distribution in the design space better and conforms to relevant physical laws. Therefore, it can be proven that the target prediction model does not deviate from the fundamental physical laws controlled by the governing equations even with a small sample size, and has high prediction accuracy and generalization ability.

[0136] In summary, regardless of the training set used, using a deep neural network as a surrogate model, compared to other surrogate models, can achieve rapid and accurate prediction of the corresponding average temperature, maximum temperature, and outlet temperature given new operating condition parameter variables. This supports the iterative optimization of the porous media burner structure and operating condition parameter variables. On the other hand, using the one-dimensional temperature field distribution of the porous media burner at each first sampling point and each second sampling point as the training set, and employing a deep neural network as a surrogate model, introduces additional physical constraints by considering the physical meaning of the data and using data augmentation methods such as interpolation. This ensures that the deep neural network more accurately fits physical laws in these key areas, effectively improving the model's generalization ability and prediction accuracy.

[0137] Figure 12This is a schematic diagram of the structure of a model training device for predicting one-dimensional combustion characteristics of a porous media burner, provided in an embodiment of this disclosure.

[0138] like Figure 12 As shown, the model training device 1200 for predicting the one-dimensional combustion characteristics of porous media burners includes:

[0139] Modeling module 1210 is used to model the combustion process of the porous media burner of the target structure, obtain the combustion model, and determine the operating condition parameter variables and the spatial distribution range of the operating condition parameter variables.

[0140] The simulation module 1220 is used to perform numerical simulation based on the combustion model for multiple first sampling points in the spatial distribution range, and obtain the one-dimensional distribution of the temperature field of the porous media burner at each first sampling point. The one-dimensional distribution of the temperature field includes the temperature at the preset positions of multiple reactors in the axial direction of the porous media burner.

[0141] The acquisition module 1230 is used to acquire the one-dimensional temperature field distribution of the porous media burner at each second sampling point by using a target interpolation method for multiple second sampling points in the spatial distribution range, based on the one-dimensional temperature field distribution of the porous media burner at each first sampling point. The one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to the target physical law, which is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable.

[0142] The training module 1240 is used to train the neural network model by using the one-dimensional distribution of the temperature field of the porous media burner at each first sampling point and each second sampling point as the training set, so as to obtain a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

[0143] It should be noted that the foregoing explanation of the model training method for predicting the one-dimensional combustion characteristics of porous media burners also applies to the model training device for predicting the one-dimensional combustion characteristics of porous media burners in this embodiment, and will not be repeated here.

[0144] In some embodiments, the model training device 1200 for predicting the one-dimensional combustion characteristics of a porous media burner further includes:

[0145] The first sampling module is used to sample the spatial distribution range of the operating condition parameter variables using at least one of the following sampling methods to obtain multiple first candidate sampling points: Latin hypercube sampling, Sobol sampling, Kronecker sampling, and random sampling.

[0146] The second sampling module is used to resample within the boundary region of the spatial distribution range of the operating condition parameter variables to obtain multiple second candidate sampling points.

[0147] The sampling point determination module is used to determine multiple first candidate sampling points and multiple second candidate sampling points as multiple first sampling points.

[0148] In some embodiments, the combustion model includes governing equations for describing the physical behavior during combustion, the governing equations including: a meteorological mass conservation equation, a meteorological energy conservation equation, and a gas-solid heat transfer equation; simulation module 1220 is used for:

[0149] For each first sampling point, based on the values ​​of the operating condition parameter variables at the first sampling point, the meteorological mass conservation equation, the meteorological energy conservation equation, and the gas-solid heat transfer equation are solved to obtain the one-dimensional temperature field distribution of the porous media burner at the first sampling point.

[0150] In some embodiments, the acquisition module is further configured to, for multiple third sampling points in the spatial distribution range, use a target interpolation method to acquire the one-dimensional temperature field distribution of the porous medium burner at each third sampling point based on the one-dimensional temperature field distribution of the porous medium burner at each first sampling point.

[0151] The model training device 1200 for predicting one-dimensional combustion characteristics of porous media burners also includes:

[0152] The accuracy determination module is used to determine whether the one-dimensional temperature field distribution of the porous media burner at each third sampling point conforms to the target physical law and whether the difference between the one-dimensional temperature field distribution of the porous media burner at the corresponding third sampling point and the reference one-dimensional temperature field distribution at the corresponding third sampling point is less than a preset value. The reference one-dimensional temperature field distribution is obtained by numerical simulation based on the combustion model.

[0153] In this embodiment, a combustion model is obtained by modeling the combustion process of the porous media burner of the target structure. Numerical simulation is then performed based on this model to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. This achieves high-fidelity numerical simulation to obtain the one-dimensional temperature field distribution of the porous media burner at each first sampling point. By employing target interpolation, the one-dimensional temperature field distribution of the porous media burner at each second sampling point is obtained based on the one-dimensional temperature field distribution at each first sampling point. This effectively increases the number of sampling points, thereby increasing the number of training samples in the training set and improving the generalization ability of the target prediction model. Furthermore, the one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to the target physical laws. This achieves coupling of physical information based on high-fidelity numerical simulation, enabling the target prediction model obtained by training the neural network model based on the training set to better approximate the target physical laws when predicting the one-dimensional combustion characteristics of the porous media burner. This avoids deviations from physical laws under small sample conditions, achieving more accurate prediction precision. This aligns with PINN (Physics-informed neural network) and... The network (physically informed neural network model) has the same function.

[0154] Figure 13 This is a schematic diagram of the structure of a device for predicting the one-dimensional combustion characteristics of a porous media burner, provided in an embodiment of this disclosure.

[0155] like Figure 13 As shown, the one-dimensional combustion characteristic prediction device 1300 for the porous media burner includes:

[0156] The acquisition module 1310 is used to acquire the target prediction model, wherein the target prediction model is trained based on the model training method for predicting the one-dimensional combustion characteristics of porous media burners in the foregoing embodiment;

[0157] The prediction module 1320 is used to predict the one-dimensional combustion characteristics of the porous media burner using a target prediction model, and obtain the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameter variable. The one-dimensional temperature field distribution includes the temperature at the preset position of multiple reactors in the axial direction of the porous media burner.

[0158] The temperature determination module 1330 is used to determine the average temperature, maximum temperature and outlet temperature of the porous media burner at the target value based on the one-dimensional distribution of the temperature field at the target value of the operating condition parameter variable of the porous media burner.

[0159] It should be noted that the aforementioned explanation of the method for predicting the one-dimensional combustion characteristics of porous media burners also applies to the device for predicting the one-dimensional combustion characteristics of porous media burners in this embodiment, and will not be repeated here.

[0160] In this embodiment, a target prediction model is used to predict the one-dimensional combustion characteristics of a porous media burner, obtaining the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating parameter variables. The one-dimensional temperature field distribution includes the temperatures at preset positions of multiple reactors along the axial direction of the porous media burner. Based on the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating parameter variables, the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target values ​​are determined. This enables rapid prediction of the one-dimensional combustion characteristics of the porous media burner based on the target prediction model, and it can better approximate the target physical law during prediction, avoiding deviations from the physical law under small sample size conditions, thus achieving more accurate prediction precision.

[0161] Figure 14 A block diagram of an exemplary electronic device suitable for implementing embodiments of the present disclosure is shown. Figure 14 The electronic device 12 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0162] like Figure 14 As shown, the electronic device 12 is represented in the form of a general-purpose computing device. The components of the electronic device 12 may include, but are not limited to: one or more processors or processing units 16, memory 28, and bus 18 connecting different system components (including memory 28 and processing unit 16).

[0163] Bus 18 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. Examples of these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0164] Electronic device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by electronic device 12, including volatile and non-volatile media, removable and non-removable media.

[0165] Memory 28 may include computer system readable media in the form of volatile memory, such as Random Access Memory (RAM) 30 and / or cache 32. Electronic device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be used to read and write non-removable, non-volatile magnetic media (… Figure 14 Not shown; usually referred to as a "hard drive".

[0166] although Figure 14 Not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disc drive for reading and writing to a removable non-volatile optical disc (e.g., a compact disc read-only memory (CD-ROM), a digital video disc read-only memory (DVD-ROM), or other optical media) may be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of this disclosure.

[0167] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 typically perform the functions and / or methods described in the embodiments of this disclosure.

[0168] Electronic device 12 can also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), and with one or more devices that enable human interaction with the electronic device 12, and / or with any device that enables the electronic device 12 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed via input / output (I / O) interface 22. Furthermore, electronic device 12 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 20. Figure 14 As shown, network adapter 20 communicates with other modules of electronic device 12 via bus 18. It should be understood that, although... Figure 14 As not shown, other hardware and / or software modules may be used in conjunction with electronic device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0169] The processing unit 16 executes various functional applications and data processing by running programs stored in the memory 28, such as implementing the model training method for predicting one-dimensional combustion characteristics of porous media burners mentioned in the foregoing embodiments.

[0170] To implement the above embodiments, this disclosure also proposes a non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements a model training method for predicting one-dimensional combustion characteristics of porous media burners as proposed in the foregoing embodiments of this disclosure.

[0171] To implement the above embodiments, this disclosure also proposes a computer program product that, when the instructions in the computer program product are executed by a processor, performs a model training method for predicting one-dimensional combustion characteristics of porous media burners as proposed in the foregoing embodiments of this disclosure.

[0172] The collection, storage, use, processing, transmission, provision, and disclosure of user personal information involved in this disclosure all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0173] It should be noted that personal information collected from users should be used for legitimate and reasonable purposes and should not be shared or sold outside of these legitimate uses. Furthermore, such collection / sharing should only be conducted after receiving the user's informed consent, including but not limited to notifying the user to read the user agreement / user notice and sign an agreement / authorization that includes authorization of relevant user information before the user uses the function. In addition, any necessary steps must be taken to protect and safeguard access to such personal information data and ensure that others with access to personal information data comply with their privacy policies and procedures.

[0174] This disclosure is intended to provide implementation schemes for users to selectively prevent the use or access to their personal information data. Specifically, this disclosure is intended to provide hardware and / or software to prevent or block access to such personal information data. Once personal information data is no longer needed, risks can be minimized by restricting data collection and deleting data. Furthermore, where applicable, such personal information is de-identified to protect user privacy.

[0175] In the foregoing descriptions of the embodiments, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0176] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this disclosure, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0177] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of this disclosure includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of this disclosure pertain.

[0178] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0179] It should be understood that various parts of this disclosure can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0180] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0181] Furthermore, the functional units in the various embodiments of this disclosure can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0182] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present disclosure have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present disclosure. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present disclosure.

Claims

1. A model training method for predicting one-dimensional combustion characteristics of porous media burners, characterized in that, The method includes: The combustion process of the porous media burner with the target structure is modeled to obtain a combustion model, and the operating condition parameter variables and the spatial distribution range of the operating condition parameter variables are determined. For multiple first sampling points in the spatial distribution range, numerical simulation is performed based on the combustion model to obtain a one-dimensional temperature field distribution of the porous media burner at each first sampling point. The one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors in the axial direction of the porous media burner. For multiple second sampling points within the spatial distribution range, a target interpolation method is adopted. Based on the one-dimensional temperature field distribution of the porous media burner at each of the first sampling points, the one-dimensional temperature field distribution of the porous media burner at each of the second sampling points is obtained. The one-dimensional temperature field distribution of the porous media burner at each of the second sampling points conforms to the target physical law, which is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable. The one-dimensional temperature field distribution of the porous media burner at each of the first sampling points and each of the second sampling points is used as the training set to train the neural network model, thereby obtaining a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

2. The method according to claim 1, characterized in that, The method further includes: At least one of the following sampling methods is used to sample the spatial distribution range of the operating condition parameter variables to obtain multiple first candidate sampling points: Latin hypercube sampling, Sobol sampling, Kronecker sampling, and random sampling. Resampling is performed within the boundary region of the spatial distribution range of the operating condition parameter variables to obtain multiple second candidate sampling points; The plurality of first candidate sampling points and the plurality of second candidate sampling points are used as the plurality of first sampling points.

3. The method according to claim 1, characterized in that, The combustion model includes control equations for describing the physical behavior during the combustion process, including: meteorological mass conservation equation, meteorological energy conservation equation, and gas-solid heat transfer equation; The step of performing numerical simulation based on the combustion model for multiple first sampling points within the spatial distribution range to obtain a one-dimensional temperature field distribution of the porous media burner at each first sampling point includes: For each of the first sampling points, based on the values ​​of the operating condition parameter variables at the first sampling point, the meteorological mass conservation equation, the meteorological energy conservation equation, and the gas-solid heat transfer equation are solved to obtain the one-dimensional temperature field distribution of the porous media burner at the first sampling point.

4. The method according to any one of claims 1-3, characterized in that, The method further includes: For multiple third sampling points in the spatial distribution range, the target interpolation method is used to obtain the one-dimensional temperature field distribution of the porous medium burner at each third sampling point based on the one-dimensional temperature field distribution of the porous medium burner at each first sampling point. It is determined that the one-dimensional temperature field distribution of the porous media burner at each of the third sampling points conforms to the target physical law, and the difference between the one-dimensional temperature field distribution of the porous media burner at the corresponding third sampling point and the reference one-dimensional temperature field distribution at the corresponding third sampling point is less than a preset value; wherein, the reference one-dimensional temperature field distribution is obtained by numerical simulation based on the combustion model, which is the one-dimensional temperature field distribution of the porous media burner at the corresponding third sampling point.

5. A method for predicting the one-dimensional combustion characteristics of a porous media burner, characterized in that, include: Obtain a target prediction model, wherein the target prediction model is trained based on the method of any one of claims 1-4; Using the target prediction model, the one-dimensional combustion characteristics of the porous media burner are predicted to obtain the one-dimensional temperature field distribution of the porous media burner at the target values ​​of the operating condition parameter variables. The one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors in the axial direction of the porous media burner. Based on the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameter variable, the average temperature, maximum temperature and outlet temperature of the porous media burner at the target value point are determined.

6. A model training device for predicting one-dimensional combustion characteristics of porous media burners, characterized in that, include: The modeling module is used to model the combustion process of the porous media burner of the target structure, obtain the combustion model, and determine the operating condition parameter variables and the spatial distribution range of the operating condition parameter variables. The simulation module is used to perform numerical simulation based on the combustion model for multiple first sampling points in the spatial distribution range to obtain a one-dimensional temperature field distribution of the porous media burner at each first sampling point, wherein the one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors in the axial direction of the porous media burner. The acquisition module is used to acquire, for multiple second sampling points in the spatial distribution range, the one-dimensional temperature field distribution of the porous media burner at each second sampling point using a target interpolation method, based on the one-dimensional temperature field distribution of the porous media burner at each first sampling point, wherein the one-dimensional temperature field distribution of the porous media burner at each second sampling point conforms to a target physical law, and the target physical law is the variation law of the one-dimensional temperature field distribution with the operating condition parameter variable; The training module is used to train the neural network model by using the one-dimensional distribution of the temperature field of the porous media burner at each of the first sampling points and each of the second sampling points as the training set, so as to obtain a target prediction model for predicting the one-dimensional combustion characteristics of the porous media burner.

7. A device for predicting the one-dimensional combustion characteristics of a porous media burner, characterized in that, include: An acquisition module is used to acquire a target prediction model, wherein the target prediction model is trained based on the method of any one of claims 1-4; The prediction module is used to predict the one-dimensional combustion characteristics of the porous media burner using the target prediction model, and obtain the one-dimensional temperature field distribution of the porous media burner at the target value of the operating condition parameter variable, wherein the one-dimensional temperature field distribution includes the temperature at preset positions of multiple reactors in the axial direction of the porous media burner. The temperature determination module is used to determine the average temperature, maximum temperature, and outlet temperature of the porous media burner at the target value based on the one-dimensional distribution of the temperature field of the porous media burner at the target value of the operating condition parameter variable.

8. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the method as described in any one of claims 1-4, or to implement the method as described in claim 5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-4, or to implement the method as described in claim 5.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the method of any one of claims 1-4, or the method of claim 5.

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