Time-space dual-scale SCR denitration system modeling method based on KAN network

Abstract

The invention provides a time-space dual-scale SCR denitration system modeling method based on a KAN network, and relates to the technical field of SCR denitration system management, and the method comprises the steps: collecting a plurality of input variables and outlet NOx concentrations of an SCR denitration system; a spatial feature extraction module is adopted to analyze the coupling relation among the multiple input variables, and spatial feature vectors are formed; a time feature extraction module is adopted to analyze the change rule of the NOx concentration of the outlet, and a time feature vector is obtained; fusing the spatial feature vector and the time feature vector by using a feature fusion module to obtain a space-time fusion feature; inputting the space-time fusion features into a KAN network based on a spline function for training until the model converges; the trained spatial feature extraction module, the trained time feature extraction module, the trained feature fusion module and the trained KAN network are jointly integrated into a space-time dual-scale KAN model, the outlet NOx concentration of the SCR denitration system is predicted in real time through the model, and the prediction precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of SCR denitration system management, and particularly relates to a time-space double-scale SCR denitration system modeling method based on a KAN network. BACKGROUND

[0002] Nitrogen oxides (NOx) generated by coal-fired power generation are one of the main atmospheric pollutants, and the selective catalytic reduction (SCR) denitration system is the core technology for current coal-fired units to achieve NOx ultra-low emission. The SCR denitration system reduces NOx to harmless nitrogen and water by spraying a reducing agent into the flue gas under the action of a catalyst. However, the SCR denitration system is a typical complex multivariable, nonlinear, large-delay and time-varying dynamic system, and its reaction process is strongly disturbed by many factors such as coal type change, load fluctuation, uneven temperature field distribution, etc., making it extremely difficult to establish a mathematical model that can accurately describe the input-output relationship of the system. Traditional single modeling methods are difficult to accurately capture the dynamic characteristics of the system in the full operating range, seriously affecting the ammonia injection optimization control and emission accurate prediction based on the model.

[0003] To overcome the limitations of single models, existing technologies have proposed various modeling strategies based on multi-model integration and intelligent algorithms. Some research uses an improved Adaboost ensemble learning method, introduces a regularization factor and prior knowledge to optimize the loss function, and automatically generates multiple sample subsets to train different support vector machine (SVM) local models, aiming to improve the modeling accuracy in multiple operating conditions. Another research uses ensemble extreme learning machine (ELM) for modeling, combines multiple extreme learning machines with different activation functions and kernel extreme learning machines as base learners, and uses partial least squares method for result integration to cope with the nonlinear and strong disturbance characteristics of the system. In addition, to address the delay and data distortion problems in the measurement of outlet NOx concentration, another research proposes a prediction model based on improved Harris Hawks Optimization (IHHO) optimization of Long Short-Term Memory (LSTM), which reconstructs the input features through the maximum information coefficient and maximum correlation minimum redundancy algorithm to improve the prediction accuracy.

[0004] While the aforementioned methods have improved the performance of SCR denitrification system models to some extent, they still have significant limitations: First, the models generally rely on complex integrated frameworks or heterogeneous base learner combinations, resulting in complex structures, heavy computational burdens, and difficulties in industrial deployment and debugging. Second, their basis functions or network structures are fixed, lacking the ability to adapt to the inherent physicochemical laws of the SCR process, and failing to fundamentally solve the modeling bottlenecks caused by the system's strong nonlinearity and time-varying characteristics, thus limiting the ability to improve accuracy. Therefore, developing a novel modeling method with a simpler structure and the ability to adapt to the complex characteristics of the system is of great practical significance for achieving precise control of SCR denitrification systems. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a temporal and spatial dual-scale SCR denitrification system modeling method based on KAN networks. By integrating dual-scale information of spatial and temporal data and combining it with KAN networks, high-precision modeling of the outlet NOx concentration of the SCR denitrification system is achieved. The technical solution of this method is as follows: This application provides a time-space dual-scale SCR denitrification system modeling method based on KAN networks, including: Collect historical operating data of the SCR denitrification system, which includes multiple input variables and outlet NOx concentration; A spatial feature extraction module is used to extract the nonlinear coupling relationship between the input variables from the multiple input variables at the same time point, and to form a spatial feature vector. A time feature extraction module is used to extract the dynamic change trend and lag characteristics of the outlet NOx concentration from the historical sequence of the NOx concentration, and to form a time feature vector. The spatial feature vector and the temporal feature vector are fused using a feature fusion module to obtain spatiotemporal fusion features; The spatiotemporal fusion features are input into a KAN network based on spline functions for training. The spline basis functions of the KAN network are adjusted by an optimization algorithm to minimize the error between the predicted NOx concentration at the outlet and the measured NOx concentration at the outlet, until the model converges. The trained spatial feature extraction module, temporal feature extraction module, feature fusion module, and KAN network are integrated into a spatiotemporal dual-scale KAN model, which is used for online real-time prediction of the outlet NOx concentration of the SCR denitrification system.

[0006] Optionally, the step of employing a spatial feature extraction module to extract the nonlinear coupling relationship between the input variables from the multiple input variables at the same time point to form a spatial feature vector includes: The multiple input variables are arranged in chronological order of collection time, and a one-dimensional feature vector is constructed for the multiple input variables at the same time point; For each of the one-dimensional feature vectors, a convolution process is performed on the one-dimensional feature vector to obtain an initial feature vector containing the nonlinear coupling relationship of the multiple input variables; Max pooling is performed on the initial feature vector to reduce its dimensionality, resulting in a spatial feature vector.

[0007] Optionally, the initial feature vector is: ; in, This represents the local data of the one-dimensional feature vector. This represents the convolution kernel, which is... The two-dimensional weight matrix, and Define the detector Size.

[0008] Optionally, the spatial feature extraction module employs a convolutional neural network, which consists of an input layer, two convolutional layers, and a global pooling layer connected sequentially.

[0009] Optionally, the time feature extraction module extracts the dynamic trend and lag characteristics of the NOx concentration at the outlet from the historical sequence to form a time feature vector, including: The NOx concentrations at the outlets are arranged in chronological order of output time to form a dataset L = {l(tn),…, l(t-2), l(t-1),l(t)} with a time-series relationship; The dataset L is shifted forward by one time step and then fed into the time feature extraction module. The time feature extraction module uses l(tn),..., l(t-1) to predict the outlet NOx concentration at time t to obtain the time feature vector.

[0010] Optionally, the time feature extraction module employs a long short-term memory network, which consists of a forget gate, an input gate, and an output gate connected in sequence.

[0011] Optionally, the outlet NOx concentration at time t can be predicted using the Long Short-Term Memory network through l(tn),…, l(t-1): ; in, It is the activation value of the output gate at time t, used to control... The amount of information flowing out of the middle, tanh(·) represents the activation function, This represents the cell state of the Long Short-Term Memory network at time t.

[0012] Optionally, the spatiotemporal fusion features can be calculated using the following formula: ; Where X represents the spatial feature vector and Y represents the temporal feature vector. , These represent the feature weights of the spatial feature vector X and the temporal feature vector Y, respectively.

[0013] Optionally, the spatiotemporal fusion features are input into a KAN network based on spline functions for training. The spline basis functions of the KAN network are adjusted through an optimization algorithm to minimize the error between the predicted outlet NOx concentration and the measured outlet NOx concentration, until the model converges. This includes: The spatiotemporal fusion features are passed through spline functions in the KAN network to output the predicted NOx concentration at the outlet. The error between the predicted NOx concentration at the outlet and the measured NOx concentration at the outlet is received through a backpropagation algorithm, and the spline function is adjusted according to the error. The hyperparameters of the KAN network are adjusted through cross-validation, and the optimal combination of hyperparameters is selected as the hyperparameter configuration of the KAN network. Optionally, the predicted NOx concentration at the outlet can be calculated using the following formula: ; in, Let represent the residual activation function, and w is the control factor, b(·) is the basic function, spline(·) is the spline function, and b(U) = spline(U). Let represent the residual activation function of the q-th connected node; The term "main path function" refers to the combination of main path spline functions in the KAN network.

[0014] The technical solutions provided in this application can achieve the following technical effects: (1) This application extracts the nonlinear coupling relationship between multiple input variables at the same time through a spatial feature extraction module, and analyzes the instantaneous static correlation between ammonia injection rate and inlet NOx concentration. At the same time, it extracts the dynamic trend and delay characteristics of outlet NOx concentration from the historical sequence of outlet NOx concentration through a temporal feature extraction module, and captures the inertial law of system response. Finally, feature vectors of different scales containing spatial and temporal information are fused to form a spatiotemporal fusion feature. This feature combines the static correlation and dynamic temporal sequence of the system, providing a more comprehensive and deeper information expression for subsequent models than a single feature, and fundamentally solves the bottleneck problem of model accuracy caused by incomplete feature representation.

[0015] (2) This application also employs the KAN network, which replaces the linear weights in the network with learnable spline functions. The parameters of the spline functions are optimized during training through gradient descent, enabling the entire KAN network to adaptively adjust the shape of each spline function within it. This mechanism allows the KAN network to directly approximate the complex nonlinear mapping relationship between spatiotemporal fusion features and outlet NOx concentration, which is difficult to describe with explicit mathematical formulas, with extremely high flexibility and accuracy. This results in a significant improvement in prediction accuracy and provides technical support for building high-precision prediction models. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. In the drawings: Figure 1 This is a flowchart of the time-space dual-scale SCR denitrification system modeling method based on KAN network according to an embodiment of this application; Figure 2 This is a structural diagram of the spatiotemporal dual-scale KAN model in the embodiments of the method of this application; Figure 3 This is a flowchart illustrating the training process of the KAN network in the method embodiments of this application; Figure 4 This is a comparison chart of the prediction results of the spatiotemporal dual-scale KAN model and the traditional modeling method for predicting the outlet NOx concentration of the same SCR denitrification system in the embodiments of the method of this application; Figure 5 This is a structural diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0017] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0018] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such use can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the term "comprising" and its variations should be interpreted as open-ended terms meaning "including but not limited to."

[0019] This application provides a time-space dual-scale SCR denitrification system modeling method based on KAN networks, such as... Figure 1 As shown, the method mainly includes the following steps S101 to S106: Step S101: Collect historical operating data of the SCR denitrification system. The historical operating data includes multiple input variables and the outlet NOx concentration.

[0020] SCR (Selective Catalytic Reduction) denitrification systems are typically located between the economizer and air preheater in coal-fired power plants. Their core structure includes an ammonia injection grid, a catalyst bed, and related monitoring and control systems. To achieve accurate modeling of the SCR denitrification system, historical operational data comprehensively reflecting the SCR process needs to be collected from the power plant's Distributed Control System (DCS). Specifically, data collected covers a continuous operating period (e.g., several months) of the SCR system. This data is directly obtained from field measuring instruments and sensors connected to the DCS, ensuring the accuracy of the data source.

[0021] The historical operating data collected in this embodiment includes multiple input variables, such as generator active power, inlet NOx concentration of the SCR denitrification system, inlet flue gas flow rate, inlet flue gas oxygen content, and ammonia injection rate, all of which affect the SCR reaction process. Specifically, generator active power reflects the overall load of the unit; inlet NOx concentration characterizes the pollutant level of the flue gas to be treated; inlet flue gas flow rate affects the residence time of reactants in the catalyst; inlet flue gas oxygen content affects the chemical environment of the NOx reduction reaction; and ammonia injection rate is the main control variable of the SCR denitrification system, directly determining the amount of reductant supplied. The historical operating data also includes the outlet NOx concentration of the SCR denitrification system, which serves as the prediction target after modeling.

[0022] Because historical operational data collected on-site often contains noise, missing values ​​due to communication failures, and outliers caused by instrument malfunctions, direct use would severely impact the performance of subsequently trained models. Therefore, preprocessing operations such as data cleaning, outlier removal, and normalization are necessary. Data cleaning involves identifying and removing obvious erroneous records and null values. Outlier removal uses statistical methods or thresholding methods based on field experience to identify and remove anomalous data points that significantly deviate from normal operating conditions. Normalization maps data with different dimensions and orders of magnitude to the same interval through methods such as linear transformations to eliminate scale differences between different data.

[0023] For the historical running data after preprocessing, this embodiment divides it into two parts, a training set and a test set, in a 6:4 ratio. The training set contains 6,000 sets of data, and the test set contains 4,000 sets of data. The training set is input into steps S102 and S103, respectively, and is used as input for the spatial feature extraction module and the temporal feature extraction module. The test set is input into step S105 and is used to verify the deviation between the predicted NOx concentration at the outlet output by the KAN network and the measured NOx concentration at the outlet.

[0024] Step S102: Using a spatial feature extraction module, the nonlinear coupling relationship between multiple input variables at the same time point is extracted to form a spatial feature vector.

[0025] The core function of the spatial feature extraction module is to learn the relationships between multiple input variables. Therefore, the available neural network structures include, but are not limited to, Convolutional Neural Networks (CNNs), Deep Neural Networks (DNNs), Graph Neural Networks (GNNs), and Transformer networks. CNNs use a locally connected convolutional kernel that slides across the input data to extract local features through convolution operations. Each neuron in a DNN is connected to all neurons in the previous layer. This structure theoretically allows it to approximate any complex nonlinear function, thus globally and densely learning various high-order interactions that may exist between all input variables. However, it has a large number of parameters and lacks inductive bias for the local relationships between variables. GNNs, based on the abstraction of input variables as nodes in a graph structure, aggregate information from neighboring nodes, allowing the representation of each variable node to incorporate information from its associated variables. Transformer networks have a self-attention mechanism, enabling them to dynamically calculate the association weights between each variable and all other variables, and automatically identify which variable relationships are more important in a specific context, thus efficiently capturing global dependencies without prior knowledge.

[0026] In this embodiment, CNN is preferably used as the spatial feature extraction module. Although there is no two-dimensional spatial adjacency relationship between the various input variables of the SCR denitrification system like that in image pixels, the inherent coupling relationship between the different physical quantities describing the same SCR denitrification system is often more significant and stable in the local variable group. Therefore, by utilizing the local connectivity and weight sharing characteristics of CNN, it is not only suitable for learning the complex correlation between multiple input variables, but also has the advantage of high computational efficiency compared to other networks due to the small number of network parameters of CNN.

[0027] like Figure 2As shown, the CNN constructed in this embodiment consists of an input layer, two convolutional layers, and a global pooling layer connected sequentially. Before inputting multiple input variables from the training set into the CNN, the input variables in the training set are arranged in chronological order of acquisition time. For each independent time point t, its corresponding multiple input variables (such as the generator active power, the inlet NOx concentration of the SCR denitrification system, the inlet flue gas flow rate, the inlet flue gas oxygen content, and the ammonia injection rate at time t) are constructed into a one-dimensional feature vector s_t, where s_t∈R^N, and N is the number of input variables. Therefore, all input variables contained in the training set can be represented as a series of time-ordered one-dimensional feature vector sequences S={s_1, s_2, ...,s_T}, t∈T. The input layer in the CNN then sequentially feeds the one-dimensional feature vector s_t from the one-dimensional feature vector sequence S into the convolutional layer in chronological order.

[0028] The convolutional layer analyzes multiple input variables in the one-dimensional feature vector s_t to obtain an initial feature vector X that contains the non-linear coupling relationships between the multiple input variables. * for: ; in, This represents the local data of the current one-dimensional feature vector s_t. This represents the convolution kernel, which is... The two-dimensional weight matrix, and Define the detector Size.

[0029] In this embodiment, after the first convolutional layer parses the nonlinear coupling relationships between multiple input variables to obtain an initial feature vector, the second convolutional layer further parses the nonlinear coupling relationships to obtain an initial feature vector with higher accuracy. In other words, through the cascaded processing of two convolutional layers, the nonlinear coupling relationships between the input variables are gradually parsed and refined, generating an initial feature vector X containing rich spatial information. * Next, the second convolutional layer inputs the output initial feature vector into the global pooling layer for max pooling dimensionality reduction, thereby obtaining the spatial feature vector X: ; in, This represents the global max pooling function.

[0030] Step S103: Using the time feature extraction module, the dynamic change trend and delay characteristics of the NOx concentration at the outlet are extracted from the historical sequence to form a time feature vector.

[0031] The core function of the temporal feature extraction module is to learn the temporal dependencies in sequential data. Therefore, the available neural network structures include, but are not limited to, Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and Temporal Convolutional Networks (TCNs). RNNs process sequential data through their recurrent connection structure, but they suffer from vanishing or exploding gradients, making it difficult to learn long-term dependencies. GRUs, a variant of LSTMs, have a simpler structure, controlling information flow through reset and update gates. However, their memory capacity is generally weaker than LSTMs when processing industrial process data with complex long-term memory and significant latency characteristics. TCNs use causal convolutions to ensure temporal order and can expand the receptive field through dilated convolutions, but their relatively fixed structural design lacks flexibility in adaptively capturing dynamics at different time scales.

[0032] This embodiment preferably uses LSTM as the time feature extraction module because the change in NOx concentration at the outlet of an SCR denitrification system is a typical nonlinear, long-delayed dynamic process, and its current state is heavily dependent on the system state at multiple historical time points. LSTM networks have a unique gating mechanism that can selectively remember, forget, and output information, thereby effectively capturing long-term dependencies and dynamic evolution patterns in time series, making them suitable for modeling the delayed and dynamic characteristics of NOx concentration at the outlet of an SCR denitrification system.

[0033] like Figure 2 As shown, the LSTM constructed in this embodiment consists of a forget gate, an input gate, and an output gate connected sequentially. Before inputting the outlet NOx concentrations from the training set into the LSTM, the outlet NOx concentrations are first arranged in chronological order of output time to form a dataset L = {l(tn),…, l(t-2), l(t-1),l(t)} with a temporal relationship. This dataset is shifted forward by one time step and then fed into the LSTM to predict the outlet NOx concentration at time t using l(tn),…, l(t-1).

[0034] Specifically, the prediction results of LSTM at each time point t are as follows: ; in, Indicates the activation value of the forget gate. Refers to the Sigmod function in the activation function. The weight coefficient matrix is ​​represented by W+. The weight coefficient matrix differs depending on the node of the LSTM where the outlet NOx concentration is located, hence the use of W+subscripts. This represents the weight coefficient matrix assigned to different nodes. Indicates the NOx concentration at the export site. Both represent bias. This represents the activation value of the input gate. to The straight lines between them represent the memory cells of the LSTM. This represents the output value of the memory unit at time t. Represents the temporary state of a memory cell; to The straight lines between them represent the cellular units of the LSTM. tanh(·) represents the output value of the cell unit at time t, and is different from the output value of the cell unit at time t. Activation function, It is the activation value of the output gate at time t, used to control... The amount of information flowing out. In this embodiment, the information obtained from LSTM... The output is a time feature vector Y.

[0035] Therefore, by using LSTM to model the historical sequence of outlet NOx concentration, and through its internal gating mechanism to adaptively learn the influence of past outlet NOx concentration on the current outlet NOx concentration, a time feature vector Y that can characterize the dynamic trend and delay characteristics of the outlet NOx concentration of the SCR denitrification system can be obtained.

[0036] Step S104: The spatial feature vector and the temporal feature vector are fused using the feature fusion module to obtain the spatiotemporal fused feature.

[0037] The core function of the feature fusion module is to integrate feature vectors from different feature extractors, representing different physical meanings, into a unified, more informative fused feature. Therefore, the fusion strategies that can be used include, but are not limited to, vector concatenation, weighted summation, attention fusion, and fusion based on fully connected networks. In this embodiment, the feature fusion module adopts a weighted summation fusion strategy to fuse the spatial feature vector X and the temporal feature vector Y to obtain the spatiotemporal fused feature U. The fusion formula is: ; in, , These represent the feature weights of the spatial feature vector X and the temporal feature vector Y, respectively. The two feature weights are typically set to be equal initially, each accounting for 50% of the weight, and then further adjusted based on the validation results of the test set, as in this embodiment. , B is the bias term.

[0038] Therefore, by fusing the spatial feature vector X and the temporal feature vector Y, dual-scale information integration of spatial and temporal information is achieved, generating a spatiotemporal fusion feature U that combines temporal dynamics and variable correlation.

[0039] Step S105: Input the spatiotemporal fusion features into the KAN network based on spline functions for training. Adjust the spline basis functions of the KAN network through optimization algorithm to minimize the error between the predicted NOx concentration at the outlet and the measured NOx concentration at the outlet until the model converges.

[0040] KAN (Kolmogorov–Arnold Network) is an emerging neural network architecture. In this embodiment, learnable spline functions are used to replace the fixed linear weights and nonlinear activation function combinations in traditional multilayer perceptrons. By using spline functions (such as B-splines) as basic operators, KAN networks have the ability to directly approximate complex function combinations, thereby more accurately capturing the potential nonlinear mapping relationship between the spatiotemporal fusion features of the input and the prediction target.

[0041] like Figure 2 and Figure 3 As shown, the training of the KAN network using the spatiotemporal fusion feature U in this embodiment is mainly divided into three parts.

[0042] The first part is the forward propagation, which refers to passing the spatiotemporal fusion feature U through the spline function spline(·) in the KAN network, ultimately outputting the predicted NOx concentration at the exit. Specifically, the spline function spline(·) of the KAN network is expressed as: ; Among them, c i It is the optimization coefficient, coefficient c i Optimization is performed during training using gradient descent, B i It refers to the i-th B-spline basis function. spline(·) replaces the fixed activation function in the traditional neural network. spline(·) can also be represented by the basic function b(·), that is, b(U)=spline(U).

[0043] In other words, the b(·) at the connection point of the KAN network is the learned spline(·). The spatiotemporal fusion feature U flows through all learnable b(·) functions, ultimately outputting the predicted NOx concentration at the outlet. Specifically, the calculation process when the spatiotemporal fusion feature U flows through this KAN network is as follows: ; Here, the f(·) function represents the final output obtained by superimposing multiple learnable b(·) functions, which represents the predicted NOx concentration at the outlet. Let represent the residual activation function, and w is a control factor, which is set in advance based on experience. Its size can be customized and adjusted when training the KAN network. Let represent the residual activation function of the q-th connected node; This represents the master path function, which is a combination of master path spline functions in a KAN network. It also represents the output of a standard KAN network without considering residual connections. The second part utilizes the adaptive function approximation mechanism of the KAN network to optimize network parameters during training to minimize prediction errors. During training, the KAN network receives the error between the predicted and measured NOx concentrations at the outlet via backpropagation, and dynamically adjusts the shape of each spline function based on this error feedback. For example, to address the complex saturation curves or threshold effects that may exist between the ammonia injection rate and the outlet NOx concentration in an SCR denitrification system, the corresponding spline function automatically learns and fits this specific nonlinear relationship. Through iterative optimization, all spline functions distributed across the connection nodes are collaboratively adjusted, enabling the complex function represented by the entire KAN network to approximate the actual physicochemical processes behind the SCR denitrification system with extremely high accuracy, thereby minimizing prediction errors.

[0044] The third part involves adjusting the hyperparameters of the KAN network through cross-validation. Specifically, the network parameters are adjusted in turn using multiple sets of data from the training set, while the test set is used to evaluate the performance of the KAN network on "unseen" data. After training, different combinations of hyperparameters are iterated and their average performance on the test set is observed to select the hyperparameter configuration that best summarizes the inherent laws of the SCR denitrification system rather than random characteristics. This hyperparameter configuration is the final hyperparameter configuration of the KAN network, providing technical assurance that the KAN network can accurately fit the dynamic characteristics of the SCR denitrification system under various operating conditions.

[0045] Therefore, by inputting spatiotemporal fusion features containing spatiotemporal information into the KAN network, minimizing the prediction error using an optimization algorithm, and selecting the optimal hyperparameter configuration of the KAN network through cross-validation, a mathematical model that can accurately describe the dynamic characteristics of the SCR denitrification system can be obtained. This convergent model can then be used to achieve high-precision, adaptive prediction of the outlet NOx concentration of the SCR denitrification system based on new operating data.

[0046] Step S106: The trained spatial feature extraction module, temporal feature extraction module, feature fusion module, and KAN network are integrated into a spatiotemporal dual-scale KAN model, which is used to predict the NOx concentration at the outlet of the SCR denitrification system in real time online.

[0047] Based on the converged KAN network trained in step S105, the spatial feature extraction module trained in step S102, the temporal feature extraction module trained in step S103, and the feature fusion module trained in step S104 are combined to form a complete spatiotemporal dual-scale KAN model. This integrated model encapsulates a fixed and automated data processing and prediction workflow.

[0048] In practical application, after the spatiotemporal dual-scale KAN model receives real-time operational data from the DCS, the spatial feature extraction module first generates a spatial feature vector representing the nonlinear coupling relationship between multiple input variables based on the current time. Simultaneously, the temporal feature extraction module generates a temporal feature vector representing the dynamic evolution of the outlet NOx concentration over time based on the recent historical sequence of the SCR denitrification system's outlet NOx concentration. The feature fusion module then fuses the spatial and temporal feature vectors to form a spatiotemporal fused feature. Finally, this spatiotemporal fused feature is input into the trained KAN network, which uses the learned complex nonlinear mapping relationship to calculate the outlet NOx concentration of the SCR denitrification system at the next time step. Therefore, the spatiotemporal dual-scale KAN model in this embodiment can continuously and continuously predict the outlet NOx concentration of the SCR denitrification system. This prediction result provides crucial decision-making support for operators or advanced control systems, enabling timely and accurate adjustment of ammonia injection volume, ensuring environmental compliance while optimizing ammonia injection costs.

[0049] To verify the accuracy of the spatiotemporal dual-scale KAN model in predicting outlet NOx concentration compared to traditional modeling methods, this embodiment uses the spatiotemporal dual-scale KAN model, CNN, and Ensemble Extreme Learning Machine (EELM) to predict the outlet NOx concentration of the same SCR denitrification system, respectively, and obtains the following results: Figure 4 The prediction results are shown. Figure 4 As can be seen from the curve fit, the predicted curve of the spatiotemporal dual-scale KAN model almost completely overlaps with the actual value curve, especially in the concentration peak segment of the 2000-3000 sampling sequence, where the red dashed line accurately tracks the rise and sharp drop of the actual value; while the predicted curves of CNN and EELM show obvious lag and fluctuation bias, such as Figure 4As shown in the blue and green curves, at the concentration trough near 1000 sampling points, the predicted values ​​of the blue and green curves deviate significantly from the actual values.

[0050] Furthermore, by comparing the prediction deviations of the three models, the prediction deviation table is shown in Table 1:

[0051] Table 1 As shown in Table 1, the spatiotemporal dual-scale KAN model exhibits a root mean square error (RMSE) of only 0.7099 mg / m³, a mean absolute percentage error (MAPE) as low as 2.0293%, and a coefficient of determination (R²) as high as 0.9941 (approaching the ideal value of 1), significantly outperforming other models in all three core indicators. This superior performance stems from the deep adaptation of the modeling method in this application to the data characteristics of the SCR denitrification system. By extracting output autoregressive information at the time scale to capture dynamic temporal patterns, mining the correlation of input variables at the spatial scale to construct interactive logic, and relying on the approximation mechanism of dual-scale feature fusion and KAN network spline functions, high-precision modeling of the complex dynamics of the system is ultimately achieved.

[0052] Therefore, traditional modeling methods struggle to effectively handle the complex spatiotemporal characteristics of SCR denitrification systems, resulting in insufficient accuracy in predicting outlet NOx concentrations. This application utilizes LSTM to capture the temporal information of outlet NOx concentrations, CNN to extract spatial information between different input variables, and combines the nonlinear fitting capability of the spline function of the KAN network. For operating conditions such as load fluctuations in coal-fired units and uneven reductant injection, the nodes are adaptively adjusted for accurate modeling. Actual engineering verification shows that under typical operating conditions, the mean absolute error of the outlet NOx concentration predicted using the spatiotemporal dual-scale KAN model of this application is reduced from 15.2833% of the traditional modeling method to 2.0293%, significantly improving prediction accuracy. The root mean square error is reduced from 4.0602 mg / m³ to 0.7099 mg / m³, substantially improving the accuracy of predicting changes in outlet NOx concentrations in SCR denitrification systems.

[0053] It should be noted that the sequence numbers of the steps in the above embodiments do not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. In practical applications, all the above possible implementation methods can be arbitrarily combined in a combined manner to form possible embodiments of this application, which will not be described in detail here.

[0054] Based on the same inventive concept, this application also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute a time-space dual-scale SCR denitrification system modeling method based on KAN network according to any of the above embodiments.

[0055] In an exemplary embodiment, an electronic device is provided, such as Figure 5 As shown, Figure 5 The illustrated electronic device 500 includes a processor 501 and a memory 503. The processor 501 and the memory 503 are connected, for example, via a bus 502. Optionally, the electronic device 500 may also include a transceiver 504. It should be noted that in practical applications, the transceiver 504 is not limited to one type, and the structure of this electronic device 500 does not constitute a limitation on the embodiments of this application.

[0056] Processor 501 may be a CPU (Central Processing Unit), a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It may implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 501 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0057] Bus 502 may include a pathway for transmitting information between the aforementioned components. Bus 502 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 502 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 5 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0058] The memory 503 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0059] The memory 503 stores computer program code that executes the scheme of this application, and its execution is controlled by the processor 501. The processor 501 executes the computer program code stored in the memory 503 to implement the content shown in the foregoing method embodiments.

[0060] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 5 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0061] Based on the same inventive concept, this application also provides a storage medium storing a computer program, wherein the computer program is configured to execute, at runtime, a time-space dual-scale SCR denitrification system modeling method based on KAN network of any of the above embodiments.

[0062] Those skilled in the art will clearly understand that the specific working process of the systems, devices, and modules described above can be referred to the corresponding process in the foregoing method embodiments. For the sake of brevity, it will not be repeated here.

[0063] Those skilled in the art will understand that the technical solution of this application, or all or part of it, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several program instructions to cause an electronic device (e.g., a personal computer, server, or network device) to execute all or part of the steps of the methods described in the embodiments of this application when running the program instructions. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0064] Alternatively, all or part of the steps of the foregoing method embodiments can be implemented by hardware (such as electronic devices like personal computers, servers, or network devices) associated with program instructions. The program instructions can be stored in a computer-readable storage medium. When the program instructions are executed by the processor of the electronic device, the electronic device executes all or part of the steps of the methods described in the embodiments of this application.

[0065] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that within the spirit and principles of this application, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the corresponding technical solutions to leave the protection scope of this application.

Claims

1. A method for modeling a temporal and spatial dual-scale SCR denitrification system based on KAN networks, characterized in that, include: Collect historical operating data of the SCR denitrification system, which includes multiple input variables and outlet NOx concentration; A spatial feature extraction module is used to extract the nonlinear coupling relationship between the input variables from the multiple input variables at the same time point, and to form a spatial feature vector. A time feature extraction module is used to extract the dynamic change trend and lag characteristics of the outlet NOx concentration from the historical sequence of the NOx concentration, and to form a time feature vector. The spatial feature vector and the temporal feature vector are fused using a feature fusion module to obtain spatiotemporal fusion features; The spatiotemporal fusion features are input into a KAN network based on spline functions for training. The spline basis functions of the KAN network are adjusted by an optimization algorithm to minimize the error between the predicted NOx concentration at the outlet and the measured NOx concentration at the outlet, until the model converges. The trained spatial feature extraction module, temporal feature extraction module, feature fusion module, and KAN network are integrated into a spatiotemporal dual-scale KAN model, which is used for online real-time prediction of the outlet NOx concentration of the SCR denitrification system.

2. The method according to claim 1, characterized in that, The spatial feature extraction module extracts the nonlinear coupling relationship between the input variables from the multiple input variables at the same time point to form a spatial feature vector, including: The multiple input variables are arranged in chronological order of collection time, and a one-dimensional feature vector is constructed for the multiple input variables at the same time point; For each of the one-dimensional feature vectors, a convolution process is performed on the one-dimensional feature vector to obtain an initial feature vector containing the nonlinear coupling relationship of the multiple input variables; Max pooling is performed on the initial feature vector to reduce its dimensionality, resulting in a spatial feature vector.

3. The method according to claim 2, characterized in that, The initial feature vector is: ； in, This represents the local data of the one-dimensional feature vector. This represents the convolution kernel, which is... The two-dimensional weight matrix, and Define the detector Size.

4. The method according to claim 2, characterized in that, The spatial feature extraction module employs a convolutional neural network, which consists of an input layer, two convolutional layers, and a global pooling layer connected sequentially.

5. The method according to claim 1, characterized in that, The time feature extraction module extracts the dynamic trend and lag characteristics of the NOx concentration at the outlet from the historical sequence, forming a time feature vector, including: The NOx concentrations at the outlets are arranged in chronological order of output time to form a dataset L = {l(tn),…, l(t-2), l(t-1),l(t)} with a time-series relationship; The dataset L is shifted forward by one time step and then fed into the time feature extraction module. The time feature extraction module uses l(tn),..., l(t-1) to predict the outlet NOx concentration at time t to obtain the time feature vector.

6. The method according to claim 5, characterized in that, The time feature extraction module uses a long short-term memory network, which consists of a forget gate, an input gate, and an output gate connected in sequence.

7. The method according to claim 6, characterized in that, The exit NOx concentration at time t is predicted using the Long Short-Term Memory network through l(tn),…,l(t-1): ； in, It is the activation value of the output gate at time t, used to control... The amount of information flowing out of the middle, tanh(·) represents the activation function, This represents the cell state of the Long Short-Term Memory network at time t.

8. The method according to claim 1, characterized in that, The spatiotemporal fusion features are calculated using the following formula: ； Where X represents the spatial feature vector and Y represents the temporal feature vector. , These represent the feature weights of the spatial feature vector X and the temporal feature vector Y, respectively.

9. The method according to claim 1, characterized in that, The spatiotemporal fusion features are input into a KAN network based on spline functions for training. The spline basis functions of the KAN network are adjusted through an optimization algorithm to minimize the error between the predicted and measured NOx concentrations at the outlet, until the model converges. This includes: The spatiotemporal fusion features are passed through spline functions in the KAN network to output the predicted NOx concentration at the outlet. The error between the predicted NOx concentration at the outlet and the measured NOx concentration at the outlet is received through a backpropagation algorithm, and the spline function is adjusted according to the error. The hyperparameters of the KAN network are adjusted through cross-validation, and the optimal combination of hyperparameters is selected as the hyperparameter configuration of the KAN network.

10. The method according to claim 9, characterized in that, The predicted NOx concentration at the outlet is calculated using the following formula: ； in, Let represent the residual activation function, and w is the control factor, b(·) is the basic function, spline(·) is the spline function, and b(U) = spline(U). Let represent the residual activation function of the q-th connected node; The term "main path function" refers to the combination of main path spline functions in the KAN network.

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