A method and system for identifying parameters of a numerical model of a pellet belt induration machine

Abstract

This invention discloses a method and system for parameter identification of a numerical model of a pellet belt roaster, belonging to the field of parameter identification for pellet belt roaster models. The method includes: acquiring operational data and determining the parameters to be identified and their feasible regions, constructing a training dataset; dividing the process into multiple process regions along its length, constructing PINN sub-models for each region, and organizing them into a PINN surrogate model; substituting the sub-model outputs into the heat transfer control equation to construct physical residuals, constructing a joint loss function by combining data loss and boundary constraints, and training the surrogate model; using the measured temperature of the bellows as the target, employing an optimization algorithm to search for the optimal combination of model parameters within the feasible region that minimizes the deviation between the predicted and measured temperatures. This invention significantly improves parameter identification efficiency by constructing a PINN surrogate model to replace the numerical model for forward prediction, while introducing physical constraints to ensure prediction accuracy, effectively solving the problems of model parameters relying on empirical settings and low identification efficiency.

Description

Technical Field

[0001] This invention relates to the field of parameter identification for pellet belt roaster models, and particularly to a method and system for parameter identification of numerical models of pellet belt roasters. Background Technology

[0002] As one of the main raw materials for blast furnace ironmaking, iron ore pellets possess high grade, uniform particle size, and excellent metallurgical properties. Their quality directly affects the smooth operation of the blast furnace and the quality of crude steel products. The belt pellet roaster is the core thermal equipment in pellet production. Green pellets sequentially pass through drying, preheating, roasting, and homogenization zones on the trolley to complete consolidation. The internal gas-solid temperature field and other physical field states directly determine the roasting quality of the pellets. However, because the belt roaster is a closed structure, thermocouples and pressure gauges can only be arranged in the wind box and fume hood, making it difficult to directly measure the temperature distribution inside the feed layer.

[0003] To obtain the internal temperature field of a belt pellet roaster, researchers typically establish a gas-solid coupled heat transfer numerical simulation model, solving the mass, momentum, and energy conservation equations to obtain the temperature field distribution. However, some model parameters cannot be directly measured in industrial settings and are often determined based on human experience or empirical correlations, making it difficult to fully adapt to industrial conditions. This limits the predictive accuracy of the mechanistic model, necessitating parameter identification and correction. However, parameter identification requires repeated forward solving of the model, but the mechanistic model involves a system of nonlinear partial differential equations coupled with multiple physics fields, requiring discrete iterations in both the spatial and temporal domains. This results in lengthy solutions and numerous identification iterations, leading to low identification efficiency.

[0004] Therefore, there is an urgent need for a computationally efficient method for identifying model parameters to quickly predict temperature fields and invert model parameters, thereby improving the accuracy of numerical simulation models. Summary of the Invention

[0005] To address the shortcomings in the background technology, this invention provides a method and system for parameter identification of a numerical model of a pellet belt roaster, which solves the problems that some parameters in the numerical model rely on empirical settings and are difficult to adapt to actual operating conditions, as well as the problems that traditional parameter identification repeatedly calls the gas-solid coupling heat transfer numerical model, resulting in long calculation time and low identification efficiency.

[0006] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for parameter identification of a numerical model of a pellet belt roaster, the method comprising: S1: Obtain process data of the pellet belt calciner and determine the parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model; generate parameter samples within the feasible regions of the parameters to be identified, combine the process data and parameter samples and input them into the gas-solid coupled heat transfer numerical model to obtain the corresponding gas phase temperature field and solid phase temperature field, and construct a training dataset. S2: Divide the pellet belt calciner into multiple sequentially connected process areas, construct PINN sub-models for each area, and organize them in sequence to form a PINN proxy model; S3: Substitute the outputs of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals. Construct data loss based on the deviation between the gas phase temperature field and solid phase temperature field predicted by the PINN surrogate model and the corresponding gas phase temperature field and solid phase temperature field calculated by the numerical model. Set boundary constraints according to the gas flow direction of each process region. Combine physical residuals, data loss and boundary constraints to construct a joint loss function. Use the training dataset to train the PINN surrogate model. S4: Obtain process data for parameter identification, use optimization algorithms to generate candidate parameter combinations within the feasible region, input them into the trained PINN surrogate model to obtain the predicted temperature field, extract the predicted temperature corresponding to the measured position of the bellows, use the deviation between the predicted temperature and the measured temperature of the bellows as the objective function value, update the candidate parameter combinations until convergence, and output the candidate parameter combination with the smallest objective function value as the optimal model parameter combination.

[0007] Furthermore, in S1, the process of constructing the training dataset is as follows: Process data of the pellet belt roaster during operation were collected and cleaned to remove abnormal data, resulting in an operating condition sample. The operating process data included the trolley speed, inlet gas temperature of each process zone, fume hood pressure, wind box pressure, and measured wind box temperature. The parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model are determined; the parameters to be identified include bed porosity, moisture evaporation rate correction coefficient and convective heat transfer correction coefficient. Within the feasible domain of the parameters to be identified, parameter samples are generated using the Latin hypercube sampling method. The parameter samples are then combined with the operating condition samples to generate input samples for the calculation of the gas-solid coupling heat transfer numerical model. Input the samples into the gas-solid coupled heat transfer numerical model, calculate the gas phase temperature field and solid phase temperature field of each process region, and construct a training dataset.

[0008] Furthermore, in S2, the specific construction process of the PINN proxy model is as follows: The roasting process is divided into multiple sequentially connected process zones along the length of the pellet belt roaster; among them, the process zones include a blower zone where gas flows from bottom to top and an exhaust zone where gas flows from top to bottom. For each process area, a spatial coordinate system based on the material layer height direction is constructed. Regional time variables The process data and the parameters to be identified are used as inputs, with the gas phase temperature of the corresponding process region as the reference. and solid phase temperature The output is the PINN sub-model; The PINN sub-models are organized according to the order of each process area along the direction of the trolley to obtain the PINN proxy model for predicting the gas phase temperature field and solid phase temperature field of each process area of ​​the pellet belt roaster. Among them, the Time variables for each process area With physical time The mapping relationship between them is as follows: ; in, For the first The physical length of each region, in meters. The speed of the trolley is expressed in m / s. For the first The starting physical time of each region is expressed in seconds.

[0009] Furthermore, in S3, the construction of the physical residual includes: The gas phase temperature output by each PINN sub-model and solid phase temperature Substituting the gas-solid coupling heat transfer control equations, the spatial coordinates of the gas phase temperature and solid phase temperature relative to the height of the material layer are calculated using automatic differentiation. Regional time variables The partial derivatives are used to construct the physical residuals of the gas-phase energy equation. Physical residuals of the solid-state energy equation : ; ; in, The apparent mass flow rate of the gas; This is the specific heat capacity of the gas at constant pressure. The spatial coordinates are in the direction of the material layer height; The convective heat transfer coefficient between the gas and solid phases; Specific surface area; For the first The chemical reaction in each region is exothermic; For the first The chemical reaction endothermic term in each region; The bulk density of the solid phase; The specific heat capacity at constant pressure for a solid phase; It represents the effective thermal conductivity of the solid phase.

[0010] Furthermore, in S3, setting boundary constraints includes: Gas phase boundary constraints are set according to the gas flow direction and inlet / outlet thermal state of each process zone; among them, gas phase boundary constraints include hard boundary constraints at the gas inlet and soft boundary constraints at the gas outlet. For the blower zone where gas flows from bottom to top, the bottom of the material layer... As the gas phase inlet boundary, the top of the material layer As the gas phase outlet boundary; for the exhaust area where gas flows from top to bottom, the top of the material layer As the gas phase inlet boundary, the bottom of the material layer As the gas phase exit boundary; among which... This refers to the height of the material layer. The hard boundary constraint at the gas inlet uses a trainable attenuation parameter. The decay function ensures that the gas phase temperature output by the PINN submodel at the gas phase inlet boundary is equal to the inlet gas temperature of the corresponding process region. : ; For the blower region, the attenuation function : ; For the exhaust area, the attenuation function : ; in, For the first The change in gas phase temperature output by the PINN submodel for each region; For network trainable parameters that are greater than 0; The gas phase outlet soft boundary constraint is constructed based on the temperature gradient of the gas phase temperature at the gas outlet boundary, thus creating the gas phase outlet boundary loss. for: ; in, For the first The gas outlet boundary location of each region, for the blower area For ventilation areas ; For regional time variables Expectations.

[0011] Furthermore, in step S3, setting boundary constraints also includes setting solid-phase boundary constraints: Solid-phase boundary constraints include adiabatic boundary constraints on both sides of the material layer height and initial solid-phase temperature constraints in each process zone; the boundary loss corresponding to solid-phase boundary constraints. for: ; in, For the first The initial solid-phase temperature of each region; To the height of the material layer Expectations; The initial solid phase temperature is transferred via a chain-like method between adjacent process zones, specifically as follows: ; in, The initial solid temperature is given for the first process region; For the first The solid phase temperature of each process region when the region time variable equals 1, and used as the first... The initial solid phase temperature of a process zone when the zone time variable is equal to 0.

[0012] Furthermore, in S3, the data loss is constructed by comparing the gas-phase temperature and solid-phase temperature predicted by the PINN surrogate model with the gas-phase temperature and solid-phase temperature calculated by the gas-solid coupling heat transfer numerical model. : ; in, For the first Number of training data points in each process area; , The first number obtained based on the PINN model prediction The gas phase temperature and solid phase temperature corresponding to each training data point; , The results obtained from the numerical model of gas-solid coupled heat transfer are respectively the first... The gas phase temperature and solid phase temperature corresponding to each training data point.

[0013] Furthermore, in step S3, the training dataset is used to iteratively train each PINN sub-model and update the parameters of each PINN sub-model until the preset convergence condition is met. Among them, the Joint loss function of PINN sub-models for each process region It is the physical residual based on the gas phase energy equation. Physical residuals of the solid-state energy equation Boundary loss corresponding to gas phase boundary constraints Boundary loss corresponding to solid boundary constraints and data loss The constructed result is represented as: ; in, , , , and The first Weighting coefficients for physical residuals of gas phase energy equations, physical residuals of solid phase energy equations, gas phase boundary loss, solid phase boundary loss, and data loss in each process region; To calculate the expectation within the computational domain.

[0014] Furthermore, in step S4, the objective function value is specifically the deviation between the predicted temperature and the measured temperature of the bellows. Specifically, the objective function value is the mean square error between the predicted and measured temperatures of the bellows. : ; in, It is a candidate parameter vector composed of each parameter to be identified; This refers to the number of measured bellows temperatures, i.e., the number of process sections. Candidate parameter vector The corresponding number Each bellows predicts the temperature; In order to be with the first The actual measured temperature corresponds to the predicted temperature of each bellows.

[0015] Secondly, the present invention provides a parameter identification system for a numerical model of a pellet belt roaster, the system being used to perform the steps of the method described above, including: The dataset construction module is used to acquire process data of the pellet belt calciner and determine the parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model. Parameter samples are generated within the feasible regions of the parameters to be identified. The process data and parameter samples are combined and input into the gas-solid coupled heat transfer numerical model to obtain the corresponding gas phase temperature field and solid phase temperature field, and to construct the training dataset. The PINN proxy model construction module is used to divide multiple sequentially connected process regions along the length of the pellet belt calciner, construct PINN sub-models for each region, and organize them in sequence to form a PINN proxy model. The PINN surrogate model training module is used to substitute the output of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals, construct data loss based on the deviation between the predicted temperature and the temperature calculated by the numerical model, and set boundary constraints according to the gas flow direction of each process region. The physical residuals, data loss and boundary constraints are combined to construct a joint loss function, and the PINN surrogate model is trained using the training dataset. The model parameter identification module is used to acquire process data of parameter identification working conditions, generate candidate parameter combinations in the feasible region using optimization algorithms, input them into the trained PINN surrogate model to obtain the predicted temperature field, extract the predicted temperature corresponding to the measured position of the bellows, use the deviation between the predicted temperature and the measured temperature of the bellows as the objective function value, update the candidate parameter combinations until convergence, and output the candidate parameter combination with the smallest objective function value as the optimal model parameter combination.

[0016] This invention proposes a parameter identification method and system for a numerical model of a pellet belt roaster. The method replaces the traditional high-precision gas-solid coupled heat transfer numerical model with a PINN surrogate model, transforming the repeated numerical solution of partial differential equations required in the parameter identification process into fast forward inference via a neural network. This effectively solves the technical problems of long computation time and low identification efficiency caused by repeated calls to the mechanistic model in traditional parameter identification methods. The physical residuals of the gas-solid coupled heat transfer control equations, the hard boundary constraints at the gas inlet, the soft boundary constraints at the gas outlet, and the adiabatic boundary constraints of the solid phase, along with the chain-like initial temperature transfer conditions and data loss, are used to construct a joint loss function. This ensures that the surrogate model strictly follows the physical laws of heat transfer while fitting the numerical simulation data. Using the bellows temperature measurement data as the target, an optimization algorithm automatically searches for the optimal combination of parameters to be identified, overcoming the shortcomings of traditional methods that rely on manual experience or general correlation formulas to determine parameters, making it difficult to adapt to actual working conditions. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the parameter identification method for a numerical model of a pellet belt roaster provided in an embodiment of the present invention. Figure 2 These are FDM gas phase temperature fields and absolute temperature error cloud maps of different models provided in embodiments of the present invention; wherein, Figure 2 (a) is a schematic diagram of the gas phase temperature field of FDM. Figure 2(b) is a graph showing the absolute error between the PINN model's predicted vapor phase temperature field and the FDM vapor phase temperature field. Figure 2 (c) is a graph showing the absolute error between the gas phase temperature field predictions from the MLP model and the gas phase temperature field from the FDM model. Figure 3 These are FDM solid-state temperature field and absolute temperature error cloud maps of different models provided in embodiments of the present invention; wherein, Figure 3 (a) is a schematic diagram of the temperature field of the solid phase in FDM. Figure 3 (b) is a graph showing the absolute error between the solid-state temperature field predictions from the PINN model and the solid-state temperature field from the FDM model. Figure 3 (c) is a graph showing the absolute error between the solid-phase temperature field predictions of the MLP model and the solid-phase temperature field of the FDM model; Figure 4 This is a comparison chart of the predicted and measured values ​​of the windbox temperature before and after parameter identification, provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] Example 1

[0021] like Figure 1 As shown, this embodiment provides a method for parameter identification of a numerical model of a pellet belt roaster, specifically including: S1. Constructing a training dataset: Obtain process data from the pellet belt calciner and determine the parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model; generate parameter samples within the feasible regions of the parameters to be identified, combine the process data and parameter samples, input them into the gas-solid coupled heat transfer numerical model, obtain the corresponding gas phase temperature field and solid phase temperature field, and construct a training dataset.

[0022] S101. Acquire process data. Obtain the trolley running speed from the field data acquisition system of the pellet belt roaster. (Unit: m / s) Inlet gas temperature of each process zone (Unit: K) Fume Hood Pressure (Unit: Pa) Bellows pressure (Unit: Pa) and measured temperature of the bellows in each process area (Unit: K). The collected raw process data was cleaned to remove abnormal process data caused by downtime, material change, equipment malfunction, and data storage anomalies, resulting in 175 sets of normal process data. Then, five representative operating conditions covering the boundaries and central area of ​​the operating range were selected from the normal process data to form operating condition samples for constructing the PINN proxy model training dataset.

[0023] S102. Determine the parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model. In this specific implementation, the parameters to be identified include the bed porosity. Correction factor for water evaporation rate and convective heat transfer correction factor The feasible region for each parameter to be identified is determined based on its physical meaning, historical process data, and empirical range. In this specific implementation, the bed porosity... The feasible region is [0.3, 0.42], and the water evaporation rate correction coefficient is... The feasible region is [0.5, 2.5], and the convective heat transfer correction coefficient is... The feasible region is [0.8, 2].

[0024] S103. Generate parameter samples. Within the feasible region formed by the three parameters to be identified, 25 representative parameter samples are generated using the Latin hypercube sampling method, ensuring a relatively uniform projection distribution of each parameter sample across all dimensions. These 25 parameter samples are then combined with the 5 operating condition samples obtained in S102 to generate 5 × 25 = 125 input samples for the gas-solid coupled heat transfer numerical model calculation.

[0025] S104. Construct the training dataset. Input 125 sets of input samples into the gas-solid coupled heat transfer numerical model of the pellet belt calciner. Use the explicit finite difference method to discretize the computational domain into a grid, and determine the numerical solution direction according to the gas flow direction of each process zone to obtain the gas phase temperature field corresponding to each set of input samples. and solid phase temperature field , construct the training dataset for the PINN agent model.

[0026] S2. Constructing the PINN proxy model: Divide the process area into multiple sequentially connected areas along the length of the pellet belt roaster, construct a PINN sub-model for each area, and organize them in sequence to form the PINN proxy model.

[0027] S201. Dividing the process zones. In this specific implementation, the roasting process is divided into 14 sequentially connected process zones along the length of the pellet belt roaster. Zones 1 to 2 are the blower zones where gas flows from bottom to top (airflow direction from the bottom of the material layer to the top), and zones 3 to 14 are the exhaust zones where gas flows from top to bottom (airflow direction from the top of the material layer to the bottom). The trolley carries the green pellets at a speed... (Unit: m / s) Passing through the above 14 process zones in sequence, the physical length of each process zone is... (Unit: m) .

[0028] S202. Construct PINN sub-models for each process region. In this specific implementation, a PINN sub-model is constructed for each process region. Introduce dimensionless time variables within each process region. and establish With physical time Mapping relationship between (unit: s): ; in, For the first The physical length of each region (unit: m). The speed of the trolley (unit: m / s). For the first The starting physical time of each region (unit: s).

[0029] No. The PINN sub-model corresponding to each process area uses spatial coordinates in the direction of material layer height. (Unit: m) (Total height of material layer), dimensionless region time variable Process data (i.e., operating condition data) and parameters to be identified As input, the gas phase temperature of the corresponding process zone. and solid phase temperature For output. In this specific implementation, each PINN sub-model adopts a multi-layer fully connected feedforward neural network structure, which consists of an input layer, a shared hidden layer, and an output branch. The shared part contains 3 hidden layers, and each output branch further has 1 hidden layer. Each layer contains 128 neurons. The Tanh function is used as the activation function for the hidden layers, and the network weights adopt the Xavier normal initialization strategy to improve the stability of network training.

[0030] S203. Forming the PINN surrogate model. Following the sequential order of each process region along the trolley's direction of travel, the 14 PINN sub-models are organized sequentially, allowing each PINN sub-model to predict the gas phase temperature field and solid phase temperature field of its corresponding process region. Adjacent process regions are connected through a solid phase temperature chain, forming a complete PINN surrogate model.

[0031] S3. Training the PINN surrogate model: Substitute the outputs of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals, construct data loss based on the deviation between the predicted temperature and the temperature calculated by the numerical model, and set boundary constraints according to the gas flow direction of each process region. Combine the physical residuals, data loss and boundary constraints to construct a joint loss function, and use the training dataset to train the PINN surrogate model.

[0032] S301. Data Partitioning. Specifically, the 125 sets of training data constructed in S104 are randomly divided into a training set and a test set in an 8:2 ratio. The training set contains 100 samples for learning the network parameters of the PINN surrogate model; the test set contains 25 samples for evaluating the temperature field prediction accuracy and generalization ability of the trained model.

[0033] S302, Construct the physical residual. (Based on the...) Taking a process region as an example, based on the dimensionless regional time variable introduced in S202... , will the The gas phase temperature output by each PINN sub-model and solid phase temperature Substituting the gas-solid coupling heat transfer control equations, the spatial coordinates of the gas phase temperature and solid phase temperature relative to the height of the material layer are calculated using automatic differentiation. Regional time variables The partial derivatives are used to construct the physical residuals of the gas-phase energy equation. Physical residuals of the solid-state energy equation : ; ; in, The apparent mass flow rate of the gas is expressed in kg / (m²·s); This is the specific heat capacity of a gas at constant pressure, expressed in J / (kg·K). These are the spatial coordinates along the height of the material layer, in meters (m). is the convective heat transfer coefficient between the gas and solid phases, with units of W / (m²·K); Specific surface area, in m² / m³; For the first The exothermic terms of chemical reactions in each region are expressed in W / m³. For the first The endothermic terms of chemical reactions in each region are expressed in W / m³. This represents the bulk density of the solid phase, expressed in kg / m³. This is the isobaric specific heat capacity of the solid phase, expressed in J / (kg·K). The effective thermal conductivity of the solid phase is expressed in W / (m·K).

[0034] S303. Set gas phase boundary constraints. Set gas phase boundary constraints according to the gas flow direction and inlet / outlet thermal conditions of each process zone, including hard boundary constraints at the gas phase inlet and soft boundary constraints at the gas phase outlet.

[0035] For the blower zones (zones 1 to 2) where gas flows from bottom to top, the bottom of the material layer... As the gas phase inlet boundary, the top of the material layer As the gas phase outlet boundary; for the exhaust areas (regions 3 to 14) where gas flows from top to bottom, the top of the material layer As the gas phase inlet boundary, the bottom of the material layer As the gas phase exit boundary; among which... This refers to the height of the material layer.

[0036] Specifically, the hard boundary constraint at the gas inlet employs a trainable attenuation parameter. ( The decay function of ) ensures that the gas phase temperature output by the PINN submodel at the gas phase inlet boundary is equal to the inlet gas temperature of the corresponding process region. : ; in, For the first The change in gas phase temperature output by the PINN sub-model for each region is directly predicted by the network; For network trainable parameters that are greater than 0; This is the decay function.

[0037] For the blower region, the attenuation function : ; For the exhaust area, the attenuation function : ; The aforementioned attenuation function results in the blower region at the gas phase inlet boundary. or ventilation area , ,thereby Being precisely satisfied; as one moves away from the entrance boundary, As the value gradually approaches 1, the temperature change in the network output is fully released. (Attenuation parameter) As a trainable parameter of the network, it adaptively adjusts the attenuation pattern of the inlet temperature transitioning into the material layer during the training process.

[0038] Specifically, the gas phase outlet soft boundary constraint constructs the gas phase outlet boundary loss based on the temperature gradient of the gas phase temperature at the gas outlet boundary. for: ; in, For the first The gas outlet boundary location of each region, for the blower area For ventilation areas ; For regional time variables The expectation is that the average is taken over all time sampling points. By using the soft boundary constraint at the gas exit, the temperature gradient of the gas phase along the height of the material layer should be zero at the gas exit boundary, that is, the temperature distribution has reached a fully developed state.

[0039] S304. Set solid phase boundary constraints. Solid phase boundary constraints include the adiabatic boundary constraints on both sides of the material layer height direction and the initial solid phase temperature constraints of each process zone.

[0040] Boundary loss corresponding to solid boundary constraints for: ; in, For the first The initial solid-phase temperature of each region; To the height of the material layer The expected value (i.e., the average over all spatial sampling points). According to the above formula, the boundary loss corresponding to the solid-phase boundary constraint consists of three terms: the first two terms constrain the bottom of the material layer. and top The adiabatic boundary conditions are determined by calculating the solid phase temperature. At these two locations, the height coordinates Take the partial derivative and square it, then apply the time variable to the region. The expectation term is used to penalize the temperature gradient that occurs at these two boundaries at any time, thereby forcing a zero heat flow boundary, i.e., no heat exchange with the outside through the upper and lower boundaries; the third term constrains each process region at the initial time. The initial solid phase temperature distribution, which is the solid phase temperature predicted by the model over the entire height of the material layer at that moment. Compared with the initial temperature reference distribution of this region The square of the difference, for The expected value is calculated to ensure that the first region uses a known starting temperature, and subsequent regions seamlessly inherit the ending temperature of the previous region, thus achieving a chain-like transfer of solid-state temperature between regions. These three factors together guarantee the rationality of the solid-state temperature field in terms of spatial boundaries and temporal connections.

[0041] The initial solid phase temperature is transferred via a chain-like method between adjacent process zones, specifically as follows: ; in, The initial solid phase temperature of the first process zone (zone 1) is determined by the measured temperature data of the pellets at the feed inlet on site. For the first The solid phase temperature of each process region when the region time variable equals 1, and used as the first... The initial solid temperature of a process region when the region time variable is equal to 0, i.e., for The process region, where the initial solid-phase temperature distribution of the current region is equal to that of the previous process region at the end of the region's time. The solid phase temperature distribution at the location is used to achieve seamless connection of the solid phase temperature field between adjacent process regions.

[0042] S305, Constructing Data Loss. Based on the gas phase temperature predicted by the PINN surrogate model. and solid phase temperature The gas phase temperature calculated using the gas-solid coupled heat transfer numerical model in S104 and solid phase temperature The deviation between them is used to construct the data loss as : ; in, For the first Number of training data points in each process area; , The first number obtained based on the PINN model prediction The gas phase temperature and solid phase temperature corresponding to each training data point; , The results obtained from the numerical model of gas-solid coupled heat transfer are respectively the first... The training data points correspond to the gas phase temperature and solid phase temperature. By constructing a data loss, the PINN surrogate model learns and fits the temperature field data generated by the high-precision gas-solid coupled heat transfer numerical model, thereby ensuring that the surrogate model has sufficient prediction accuracy.

[0043] S306. Construct and train the joint loss function. Iteratively train each PINN sub-model using the training dataset, updating the parameters of each PINN sub-model until the preset convergence condition is met; Among them, the Joint loss function of PINN sub-models for each process region It is the physical residual based on the gas phase energy equation. Physical residuals of the solid-state energy equation Boundary loss corresponding to gas phase boundary constraints Boundary loss corresponding to solid boundary constraints and data loss The constructed result is represented as: ; in, , , , and The first The weighting coefficients of the physical residuals of the gas phase energy equation, the physical residuals of the solid phase energy equation, the gas phase boundary loss, the solid phase boundary loss, and the data loss in each process region are used to balance the relative importance of different loss terms in joint training. In the computational domain (i.e., for the height of the material layer) and regional time variables Calculate the expectation within all sampling points.

[0044] In this embodiment, the AdamW optimizer and adaptive learning rate strategy are used to iteratively update the parameters of each PINN sub-model. Training is terminated when the loss does not decrease for a preset number of consecutive training epochs or when the training epochs reach a preset maximum value. In this embodiment, the PINN sub-models corresponding to regions 1-2 are trained for 3000 epochs, the PINN sub-models corresponding to regions 3-5 are trained for 3500 epochs, and the PINN sub-models corresponding to regions 6-14 are trained for 4000 epochs; the initial learning rate is set to 5 × 10⁻⁶. -4 The gradient clipping threshold is set to 0.7.

[0045] S307. Model Testing and Evaluation. Input the process data and parameters to be identified from the test set into the trained PINN surrogate model to obtain the corresponding gas phase temperature field and solid phase temperature field. Calculate the root mean square error and coefficient of determination between the temperature predicted by the PINN surrogate model and the temperature calculated by the gas-solid coupled heat transfer numerical model to evaluate the temperature field prediction accuracy of the PINN surrogate model and its generalization ability to samples not involved in the training.

[0046] To further verify the predictive ability of the constructed PINN surrogate model, a pure data-driven multilayer perceptron model with the same input and output was constructed as a control model. The root mean square error (RMSE) was used to evaluate the quantitative prediction error of the temperature field, and the coefficient of determination (R²) was used to evaluate the ability to restore the temperature distribution pattern of the entire field. The comparison results of the two models on the training set and the test set are shown in Table 1 and Table 2, respectively.

[0047] Table 1. Performance Comparison of PINN and MLP Training Set Models

[0048] Table 2 Performance Comparison of PINN and MLP Test Set Models

[0049] From Table 1, Table 2, Figure 2 and Figure 3 It can be seen that the PINN proxy model constructed in this invention has lower RMSE values ​​for both the gas and solid phase temperature fields on the training and test sets than the MLP model. 2 All of these results are higher than those of the MLP model, indicating that the PINN surrogate model outperforms the MLP model in both quantitative prediction accuracy of the temperature field and ability to reproduce the overall temperature distribution pattern, and also exhibits good generalization ability. Figure 2 (a) is a schematic diagram of the gas phase temperature field of FDM. Figure 2 (b) is a graph showing the absolute error between the PINN model's predicted vapor phase temperature field and the FDM vapor phase temperature field. Figure 2 (c) is a graph showing the absolute error between the gas phase temperature field predictions from the MLP model and the gas phase temperature field from the FDM model. Figure 3 (a) is a schematic diagram of the temperature field of the solid phase in FDM. Figure 3 (b) is a graph showing the absolute error between the solid-state temperature field predictions from the PINN model and the solid-state temperature field from the FDM model. Figure 3 (c) is a graph showing the absolute error between the solid temperature field predictions from the MLP model and the solid temperature field predictions from the FDM model.

[0050] S4. Identify numerical model parameters: Obtain process data and measured temperature for parameter identification conditions, use optimization algorithms to generate candidate parameter combinations within the feasible region, input them into the trained PINN surrogate model to obtain the predicted temperature field, extract the predicted temperature corresponding to the measured position of the bellows, use the deviation between the predicted temperature and the measured temperature of the bellows as the objective function value, update the candidate parameter combinations until convergence, and output the candidate parameter combination with the smallest objective function value as the optimal model parameter combination.

[0051] S401. Obtain parameter identification condition data. Select one or more sets of parameter identification conditions from the 175 sets of normal process data after S101 cleaning, and obtain the corresponding process data, including the trolley running speed. Inlet gas temperature of each process zone Fume hood pressure Bellows pressure ) and the measured temperature of the gas outlet of each air box ,in, , This represents the total number of temperature measurement points at the bellows.

[0052] S402. Generate candidate parameter combinations and predict the temperature field. The type of optimization algorithm can be selected according to actual needs and is not limited. In this embodiment, a particle swarm optimization algorithm is used to generate candidate parameter combinations within the feasible region of the parameters to be identified. Specifically, the particle swarm size is set to 70, the maximum number of iterations is set to 500, the inertia weight is set to 0.9, and both the individual learning factor and the swarm learning factor are set to 2.0. The position of each particle is represented as a candidate parameter vector. And initialize the velocity of each particle.

[0053] The operational process data corresponding to the parameter identification condition are compared with the candidate parameter vectors corresponding to each particle. By inputting the trained PINN surrogate model into the input, the gas phase temperature field corresponding to each candidate parameter combination is obtained. and solid phase temperature field .

[0054] S403. Calculate the objective function value. Extract the predicted temperature corresponding to the gas outlet temperature measurement position of each wind box from the gas phase temperature field output by the PINN surrogate model. The mean square error between the predicted temperature and the measured temperature is calculated as the objective function value. : ; in, It is a candidate parameter vector composed of each parameter to be identified; The quantity of actual measured temperatures of the bellows; Candidate parameter vector The corresponding number Each bellows predicts the temperature; In order to be with the first The predicted temperature of each bellows corresponds to the actual measured temperature of that bellows. Objective function value. The smaller the value, the better the model-predicted temperature matches the actual measured temperature of the bellows under the candidate parameter combination.

[0055] S404. Parameter Optimization and Convergence. The optimal position of each individual particle and the global optimal position of the particle swarm are updated based on the objective function value (fitness value) of each particle. The velocity and position of each particle are iteratively updated according to the velocity and position update rules of the particle swarm optimization algorithm. Boundary correction is performed on particle positions that exceed the feasible region of the parameters to be identified after the update.

[0056] When the change in the global optimal objective function value of the particle swarm is less than Alternatively, the iteration of the particle swarm optimization algorithm can be stopped when the maximum number of iterations reaches 500. Output the global optimum position of the particle swarm corresponding to the minimum objective function value: ; Will Bed porosity Correction factor for water evaporation rate and convective heat transfer correction factor This is the optimal combination of model parameters for a gas-solid coupled heat transfer numerical model.

[0057] This invention constructs a PINN surrogate model and automatically optimizes parameters using on-site temperature measurement data, achieving adaptive calibration of model parameters to actual operating conditions. It solves the technical problem that some parameters in numerical models rely on manual experience and are difficult to adapt to actual operating conditions, effectively improving the prediction accuracy of gas-solid coupled heat transfer numerical models under actual industrial operating conditions. This invention uses a PINN surrogate model to replace the traditional high-precision numerical model for forward temperature field prediction in parameter identification, transforming the iterative solution of partial differential equations into rapid inference by neural networks. This solves the technical problem of long computation time and low identification efficiency caused by repeated calls to the gas-solid coupled heat transfer numerical model in traditional parameter identification methods. While ensuring prediction accuracy, it significantly reduces the computational cost of a single evaluation and greatly improves the overall efficiency of parameter identification. This invention combines the physical residuals of the gas-solid coupled heat transfer control equations, the hard boundary constraints at the gas inlet and the soft boundary constraints at the outlet, the adiabatic boundary constraints of the solid phase, and the chain-like initial temperature transfer conditions between regions with the data loss to construct a joint loss function. This solves the technical problems that the internal temperature field of the material layer in a belt roaster is difficult to measure directly and that a purely data-driven surrogate model is prone to deviating from physical laws. This allows the PINN surrogate model to simultaneously fit numerical simulation data and strictly follow the physical laws of heat transfer during the training process.

[0058] After parameter identification, the optimal model parameters were combined and substituted back into the gas-solid coupled heat transfer numerical model. Temperature field calculations were performed on 175 sets of normal operating conditions. The relative and absolute errors between the numerical model-predicted and measured temperatures at each temperature measurement location before and after parameter identification were compared. The error comparison results before and after parameter identification are shown in Tables 3 and 4, respectively. Figure 4 As shown.

[0059] Table 3 Comparison of absolute errors before and after parameter identification

[0060] From Table 3 and Figure 4 It can be seen that after substituting the optimal model parameters obtained from the identification back into the gas-solid coupled heat transfer numerical simulation model, the average relative error of the gas outlet temperature of each wind box decreased from 12.76% to 7.06%, an overall improvement of 44.67%; the average absolute error decreased from 35.92℃ to 16.01℃, an overall improvement of 55.43%. The improvement was particularly significant for the wind boxes corresponding to the calcination and soaking sections, with relative errors decreasing from 19.20% and 18.13% to 5.58% and 4.75%, respectively, an improvement of over 70%; the absolute errors also decreased from 82.10℃ and 92.51℃ to 23.83℃ and 24.22℃, respectively, a reduction of 58.27℃ and 68.29℃. In summary, the method of this invention effectively improves the calculation accuracy of the numerical simulation model and verifies the effectiveness of model parameter identification based on the PINN surrogate model.

[0061] Example 2

[0062] This embodiment provides a parameter identification system for a numerical model of a pellet belt roaster. The system is used to perform the steps of the method described above, including: The dataset construction module is used to acquire the operation process data of the pellet belt roaster and determine the parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model; generate parameter samples within the feasible regions of the parameters to be identified, and input the operation process data and parameter samples into the gas-solid coupled heat transfer numerical model to obtain the corresponding gas phase temperature field and solid phase temperature field, and construct the training dataset. The PINN proxy model construction module is used to divide multiple sequentially connected process regions along the length of the pellet belt calciner, construct PINN sub-models for each region, and organize them in sequence to form a PINN proxy model. The PINN surrogate model training module is used to substitute the output of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals, construct data loss based on the deviation between the predicted temperature and the temperature calculated by the numerical model, and set boundary constraints according to the gas flow direction of each process region. The physical residuals, data loss and boundary constraints are combined to construct a joint loss function, and the PINN surrogate model is trained using the training dataset. The model parameter identification module is used to acquire the running process data and measured temperature of the parameter identification working condition. It uses an optimization algorithm to generate candidate parameter combinations within the feasible region, inputs them into the trained PINN surrogate model to obtain the predicted temperature field, extracts the predicted temperature corresponding to the measured location, uses the deviation between the predicted temperature and the measured temperature as the objective function value, updates the candidate parameter combinations until convergence, and outputs the candidate parameter combination with the smallest objective function value as the optimal model parameter combination.

[0063] Example 3

[0064] This embodiment provides a computer device, which includes a processor and a memory. The memory stores a computer program. When the processor executes the computer program, it implements the steps of the method described above. The processor may be a central processing unit, a graphics processing unit, or other processing unit with data processing capabilities. The memory may include volatile memory and non-volatile memory.

[0065] Example 4

[0066] This embodiment provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the steps of the method described above. The computer-readable storage medium includes, but is not limited to, a magnetic disk, an optical disk, a read-only memory, a random access memory, flash memory, and other media capable of storing computer programs.

[0067] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

[0068] The readable storage medium is a computer-readable storage medium, which can be an internal storage unit of the controller described in any of the foregoing embodiments, such as the controller's hard drive or memory. The readable storage medium can also be an external storage device of the controller, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the controller. Further, the readable storage medium can include both the controller's internal storage unit and external storage devices. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium can also be used to temporarily store data that has been output or will be output.

[0069] Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned readable storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0070] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0071] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for parameter identification of a numerical model of a pellet belt roaster, characterized in that, include: S1: Obtain process data from the pellet belt calciner and determine the parameters to be identified and their feasible domain in the gas-solid coupled heat transfer numerical model. Parameter samples are generated within the feasible domain of the parameters to be identified. The process data and parameter samples are combined and input into the gas-solid coupled heat transfer numerical model to obtain the corresponding gas phase temperature field and solid phase temperature field, and a training dataset is constructed. S2: Divide the pellet belt calciner into multiple sequentially connected process areas, construct PINN sub-models for each area, and organize them in sequence to form a PINN proxy model; S3: Substitute the outputs of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals. Construct data loss based on the deviation between the gas phase temperature field and solid phase temperature field predicted by the PINN surrogate model and the corresponding gas phase temperature field and solid phase temperature field calculated by the gas-solid coupling heat transfer numerical model. Set boundary constraints according to the gas flow direction of each process region. Combine physical residuals, data loss and boundary constraints to construct a joint loss function. Use the training dataset to train the PINN surrogate model. S4: Obtain process data under one or more parameter identification conditions, use an optimization algorithm to generate candidate parameter combinations within the feasible region, input them into the trained PINN surrogate model to obtain the predicted temperature field, extract the predicted temperature corresponding to the measured position of the bellows, use the deviation between the predicted temperature and the measured temperature of the bellows as the objective function value, update the candidate parameter combinations until convergence, and output the candidate parameter combination with the minimum objective function value as the optimal model parameter combination; In S2, the specific construction process of the PINN proxy model is as follows: The roasting process is divided into multiple sequentially connected process zones along the length of the pellet belt roaster; among them, the process zones include a blower zone where gas flows from bottom to top and an exhaust zone where gas flows from top to bottom. For each process area, a spatial coordinate system based on the material layer height direction is constructed. Regional time variables The process data and the parameters to be identified are used as inputs, with the gas phase temperature of the corresponding process region as the reference. and solid phase temperature The output is the PINN sub-model; The PINN sub-models are organized according to the order of each process area along the direction of the trolley to obtain the PINN proxy model for predicting the gas phase temperature field and solid phase temperature field of each process area of ​​the pellet belt roaster. Among them, the Time variables for each process area With physical time The mapping relationship between them is as follows: ； in, For the first The physical length of each region For the speed of the trolley, For the first The initial physical time of each region; In step S3, setting boundary constraints includes: Gas phase boundary constraints are set according to the gas flow direction and inlet / outlet thermal state of each process zone; among them, gas phase boundary constraints include hard boundary constraints at the gas inlet and soft boundary constraints at the gas outlet. For the blower zone where gas flows from bottom to top, the bottom of the material layer... As the gas phase inlet boundary, the top of the material layer As the gas phase outlet boundary; for the exhaust area where gas flows from top to bottom, the top of the material layer As the gas phase inlet boundary, the bottom of the material layer As the gas phase exit boundary; among which... This refers to the height of the material layer. The hard boundary constraint at the gas inlet uses a trainable attenuation parameter. The decay function ensures that the gas phase temperature output by the PINN submodel at the gas phase inlet boundary is equal to the inlet gas temperature of the corresponding process region. : ； For the blower region, the attenuation function : ； For the exhaust area, the attenuation function : ； in, For the first The change in gas phase temperature output by the PINN submodel for each region; For network trainable parameters that are greater than 0; The gas phase outlet soft boundary constraint is constructed based on the temperature gradient of the gas phase temperature at the gas outlet boundary, thus creating the gas phase outlet boundary loss. for: ； in, For the first The gas outlet boundary location of each region, for the blower area For ventilation areas ; For regional time variables Expectations on; In step S3, setting boundary constraints also includes setting solid-phase boundary constraints: Solid-phase boundary constraints include adiabatic boundary constraints on both sides of the material layer height and initial solid-phase temperature constraints in each process zone; the boundary loss corresponding to solid-phase boundary constraints. for: ； in, For the first The initial solid-phase temperature of each region; To the height of the material layer Expectations; The initial solid phase temperature is transferred via a chain-like method between adjacent process zones, specifically as follows: ； in, The initial solid temperature is given for the first process region; For the first The solid phase temperature of each process region when the region time variable equals 1, and used as the first... The initial solid phase temperature of a process zone when the zone time variable is equal to 0.

2. The method according to claim 1, characterized in that, In S1, the process of constructing the training dataset is as follows: Process data was collected during the operation of the pellet belt roaster, and the process data was cleaned to remove abnormal operation data to obtain an operating condition sample. The process data included the trolley running speed, inlet gas temperature of each process zone, fume hood pressure, wind box pressure and wind box temperature. The parameters to be identified and their feasible regions in the gas-solid coupled heat transfer numerical model are determined; the parameters to be identified include bed porosity, moisture evaporation rate correction coefficient and convective heat transfer correction coefficient. Within the feasible domain of the parameters to be identified, parameter samples are generated using the Latin hypercube sampling method. The parameter samples are then combined with the operating condition samples to generate input samples for the calculation of the gas-solid coupling heat transfer numerical model. Input the samples into the gas-solid coupled heat transfer numerical model, calculate the gas phase temperature field and solid phase temperature field of each process region, and construct a training dataset.

3. The method according to claim 1, characterized in that, In S3, the construction of the physical residual includes: The gas phase temperature output by each PINN sub-model and solid phase temperature Substituting the gas-solid coupling heat transfer control equations, the spatial coordinates of the gas phase temperature and solid phase temperature relative to the height of the material layer are calculated using automatic differentiation. Regional time variables The partial derivatives are used to construct the physical residuals of the gas-phase energy equation. Physical residuals of the solid-state energy equation : ； ； in, The apparent mass flow rate of the gas; This is the specific heat capacity of the gas at constant pressure. The spatial coordinates are in the direction of the material layer height; The convective heat transfer coefficient between the gas and solid phases; Specific surface area; For the first The chemical reaction in each region is exothermic; For the first The chemical reaction endothermic term in each region; The bulk density of the solid phase; The specific heat capacity at constant pressure for a solid phase; It represents the effective thermal conductivity of the solid phase.

4. The method according to claim 1, characterized in that, In step S3, the data loss is constructed by comparing the gas-phase and solid-phase temperatures predicted by the PINN proxy model with the gas-solid coupling heat transfer numerical model. : ； in, For the first Number of training data points for each process area; , The first number obtained based on the PINN model prediction The gas phase temperature and solid phase temperature corresponding to each training data point; , The results obtained from the numerical model of gas-solid coupled heat transfer are respectively the first... The gas phase temperature and solid phase temperature corresponding to each training data point.

5. The method according to claim 1, characterized in that, In step S3, the training dataset is used to iteratively train each PINN sub-model and update the parameters of each PINN sub-model until the preset convergence condition is met. Among them, the Joint loss function of PINN sub-models for each process region It is the physical residual based on the gas phase energy equation. Physical residuals of the solid-state energy equation Boundary loss corresponding to gas phase boundary constraints Boundary loss corresponding to solid boundary constraints and data loss The constructed result is represented as: ； in, , , , and The first Weighting coefficients for physical residuals of gas phase energy equations, physical residuals of solid phase energy equations, gas phase boundary loss, solid phase boundary loss, and data loss in each process region; To calculate the expectation within the computational domain.

6. The method according to claim 1, characterized in that, In step S4, the objective function value is specifically the deviation between the predicted temperature and the measured temperature of the bellows. : ； in, It is a candidate parameter vector composed of each parameter to be identified; This refers to the number of measured bellows temperatures, i.e., the number of process sections. Candidate parameter vector The corresponding number Each bellows predicts the temperature; In order to be with the first The predicted temperature of each bellows corresponds to the actual measured temperature of that bellows.

7. A parameter identification system for a numerical model of a pellet belt roaster, the system being used to perform the steps of the method as described in any one of claims 1-6, characterized in that, include: The dataset construction module is used to acquire process data from the pellet belt calciner and determine the parameters to be identified and their feasible domains in the gas-solid coupled heat transfer numerical model. Parameter samples are generated within the feasible domain of the parameters to be identified. The process data and parameter samples are combined and input into the gas-solid coupled heat transfer numerical model to obtain the corresponding gas phase temperature field and solid phase temperature field, and a training dataset is constructed. The PINN proxy model construction module is used to divide multiple sequentially connected process regions along the length of the pellet belt calciner, construct PINN sub-models for each region, and organize them in sequence to form a PINN proxy model. The PINN surrogate model training module is used to substitute the output of each PINN sub-model into the gas-solid coupling heat transfer control equation to construct physical residuals, construct data loss based on the deviation between the predicted temperature and the temperature calculated by the numerical model, and set boundary constraints according to the gas flow direction of each process region. The physical residuals, data loss and boundary constraints are combined to construct a joint loss function, and the PINN surrogate model is trained using the training dataset. The model parameter identification module is used to acquire process data and measured temperature of the bellows under the parameter identification working condition. It uses an optimization algorithm to generate candidate parameter combinations within the feasible region and inputs them into the trained PINN surrogate model to obtain the predicted temperature field. It extracts the predicted temperature of the bellows corresponding to the measured position of the bellows and uses the deviation between the predicted temperature and the measured temperature of the bellows as the objective function value. The candidate parameter combinations are updated until convergence, and the candidate parameter combination with the smallest objective function value is output as the optimal model parameter combination.

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