An Online Update Method for an Integrated Model for NOx Concentration Prediction Based on RLS

Abstract

This invention discloses an online update method for an integrated NOx concentration prediction model based on Recurrent Least Signature (RLS), belonging to the field of industrial process pollution control and prediction modeling technology. The method includes a training phase and an online update phase. In the training phase, variable time delay estimation and reconstruction are performed, and the Markov-LHS-MOGA method is used to optimize training samples; three base learners—random forest, gated recurrent unit, and one-dimensional convolutional neural network—are trained in parallel; based on the prediction results of the validation set, the RLS fusion unit parameters are initialized offline. In the online update phase, real-time data is input to the base learners to obtain prediction vectors, which are then processed by the RLS fusion unit to output the final predicted value; when the delayed true value arrives, the fusion unit weights are dynamically updated using the RLS algorithm to achieve online model adaptation. This invention effectively solves the problems of poor adaptability of static models under operating conditions and the decrease in prediction accuracy with drifting operating conditions, significantly improving the real-time performance, accuracy, and long-term stability of NOx concentration prediction, providing a reliable basis for optimizing ammonia injection control.

Description

Technical Field

[0001] This invention belongs to the field of industrial process pollution control and prediction modeling technology, specifically involving an online update method for an integrated NOx concentration prediction model based on RLS. Background Technology

[0002] NOx in flue gas from coal-fired power plants is one of the major air pollutants. Denitrification via SCR systems is currently the mainstream control technology, but its efficiency depends on the precise control of ammonia injection, which in turn requires real-time and accurate detection of inlet NOx concentration. Traditional continuous emission monitoring systems (CEMS) suffer from drawbacks such as prolonged measurement time, high maintenance costs, and susceptibility to interference, making them unsuitable for real-time control requirements.

[0003] Therefore, data-driven soft-measurement models for NOx concentration have been extensively studied. Existing methods often employ machine learning or deep learning models such as Random Forest (RF), Gated Recurrent Unit (GRU), and Convolutional Neural Network (CNN) to construct static prediction models. However, the operating conditions of coal-fired power plants are complex and variable, exhibiting significant dynamic and multimodal characteristics. Once trained, static models have fixed parameters, making it difficult to adapt to changes in operating conditions and data distribution, leading to decreased prediction performance and insufficient generalization ability in long-term online applications.

[0004] Recursive least squares (RLS), a classic online parameter estimation algorithm, can recursively update model parameters as new data arrives, exhibiting good real-time adaptability. However, directly applying it to the online training of complex nonlinear NOx prediction models (such as deep neural networks) presents problems such as computational complexity and the potential to get trapped in local optima.

[0005] Therefore, how to construct a NOx concentration prediction method that can integrate the advantages of multiple models and be updated online adaptively to maintain high prediction accuracy in the long term is a technical problem that urgently needs to be solved. Summary of the Invention

[0006] This invention aims to overcome the shortcomings of existing static prediction models that cannot adapt to changes in operating conditions, leading to performance degradation. It provides an online update method for an integrated NOx concentration prediction model based on recursive least squares (RLS). This method effectively improves the prediction accuracy, stability, and long-term adaptability of the model under dynamic operating conditions by integrating multiple machine learning models and introducing an online recursive update mechanism.

[0007] To achieve the above objectives, the present invention adopts the following technical solution;

[0008] An online update method for an RLS-based ensemble model for NOx concentration prediction includes a training phase and an online ensemble prediction and model update phase; wherein,

[0009] The training phase includes the following steps;

[0010] S1. Data Acquisition;

[0011] Real-time operating data of coal-fired power plants are collected, including multiple auxiliary variables and the target variable NOx concentration;

[0012] S2. Data preprocessing;

[0013] The collected raw data is preprocessed, including time delay estimation and reconstruction of the auxiliary variables based on the maximum information coefficient, and the Markov-LHS-MOGA method is used to optimize the samples of the preprocessed data to obtain the training set and the validation set.

[0014] S3. Base learner model training;

[0015] Three base learner models were trained in parallel using the training set: a random forest model, a gated recurrent unit model, and a one-dimensional convolutional neural network model.

[0016] S4. Model Validation;

[0017] The trained base learner model is validated using the validation set.

[0018] S5. RLS merger initialization;

[0019] The blending strategy is adopted to obtain the prediction output results of the three base learner models on the validation set. These results are used as input data, and the corresponding real NOx concentration values ​​are used as output data to train the RLS fusion model and complete the offline initialization of parameters.

[0020] The online integrated prediction and model update phase includes the following steps;

[0021] S6. Real-time prediction;

[0022] The auxiliary variable data collected in real time is input into the three base learner models that have been trained, and the predicted values ​​of each model are obtained and combined into a prediction vector.

[0023] S7. Integrated output;

[0024] The prediction vector is input into the initialized RLS fusion unit to calculate and output the integrated prediction value of NOx concentration at the current time.

[0025] S8. Online updates;

[0026] Once the actual NOx concentration measurement with a time delay arrives, the prediction residual at the current moment is calculated. Based on this residual and the prediction vector, the weight parameters of the fusion unit are updated online using the RLS algorithm to achieve adaptive updating of the model.

[0027] Preferably, the time delay estimation based on the maximum information coefficient (MIC) in step 2 specifically includes:

[0028] S201, given a containing A matrix of auxiliary variables and a target variable matrix , and It is expressed as follows:

[0029] (twenty one);

[0030] (twenty two);

[0031] in, , This is the sampling start time. This is the end time of sampling. The number of selected samples;

[0032] S202, for each auxiliary variable Construct its delayed sequence ,in, ; The maximum delay time for all auxiliary variables;

[0033] S203, calculate the relationship between each column of the delayed sequence and the target variable matrix. The maximum information coefficient between the two values ​​is used to determine the optimal delay time for this auxiliary variable, which is the delay time that maximizes the maximum information coefficient. ;

[0034] S204, based on the optimal delay time of all auxiliary variables. For the original auxiliary variable matrix Reconstruct the matrix to obtain a new input matrix. (twenty three);

[0035] in, The reconstructed auxiliary variable matrix; Indicates the first One auxiliary variable; Indicates the current time; For the first The optimal delay time for each auxiliary variable; Indicates the first The actual time at which each auxiliary variable should take its value; Indicates the first The values ​​of each auxiliary variable at the optimal delay time; This represents the total number of auxiliary variables.

[0036] Preferably, step 2 uses the Markov-LHS-MOGA method for sample selection, specifically including:

[0037] S211, perform density clustering on the reconstructed dataset after time delay to obtain the working condition label sequence for each sample;

[0038] S212, Construct a Markov state transition probability matrix based on the working condition label sequence;

[0039] S213, Based on the state transition probability matrix, simulate and generate a working condition path sequence;

[0040] S214, in each state of the working condition path sequence, extract the sample subset corresponding to the working condition, and perform Latin hypercube sampling on the subset to obtain the initial sample subset;

[0041] S215, based on the initially selected sample subset, a multi-objective genetic algorithm is used for further optimization. The optimization objective function is:

[0042] (28);

[0043] (29);

[0044] in, This represents the total loss function value. The primary objective is to balance model accuracy and sample decimality. Encode the individuals whose states are selected for the sample; This represents the prediction error of the RF model trained on the selected samples across all samples. This is a penalty item; and These are weighting coefficients; Indicates the current individual The number of samples selected; For the initial sample set The total number of samples; Select a proportion for the sample; determine the final optimal sample set by finding the subset of samples that minimizes the objective function.

[0045] Preferably, step S3 further includes a hyperparameter optimization step before training the base learner model:

[0046] The hyperparameters of the gated recurrent unit (GRU) model and the one-dimensional convolutional neural network (1D CNN) model are optimized using the differential evolution algorithm.

[0047] The hyperparameters of the Random Forest (RF) model were optimized using a grid search method.

[0048] Preferably, in step S3, the random forest model is used to evaluate variable importance and perform feature selection; the gated recurrent unit model is used to capture long-term dependencies in time series; and the one-dimensional convolutional neural network model is used to extract local temporal features.

[0049] Preferably, the online adaptive update process in step S8 is as follows:

[0050] Let the prediction vector of the base learner at time t be... The fusion weight vector is The covariance matrix is The forgetting factor is When new data pairs with delays , Upon arrival, update in the following order;

[0051] Calculate the gain vector. (4); Update the weight vector, (5);

[0052] Update the covariance matrix. (6).

[0053] Preferably, the forgetting factor The value range is from 0.8 to 0.99.

[0054] Preferably, in step S8, considering the measurement delay of the true NOx concentration, in the early stages of the testing phase... At the first time step, only prediction is performed without updating the fusion parameters; from the second time step... Starting at a certain time step, after the true value is reached, the prediction in S7 and the parameter update in S8 are executed synchronously.

[0055] Preferably, the auxiliary variables include at least one of total air volume, total coal volume, main steam pressure, and unit load.

[0056] The beneficial technical effects of this invention are as follows:

[0057] 1. Strong dynamic adaptability, enabling long-term stable prediction;

[0058] Through the online recursive update mechanism of the RLS fusion unit, the model can respond in real time to changes in working conditions and data distribution drift, dynamically adjust the fusion weights of each base learner, effectively overcome the inherent defects of static model parameters being fixed and performance deteriorating over time, and significantly improve the long-term adaptability and predictive stability of the model in dynamic industrial environments.

[0059] 2. High prediction accuracy, fully leveraging the advantages of integration;

[0060] This innovative approach integrates three complementary base learners: Random Forest (RF), Gated Recurrent Unit (GRU), and One-Dimensional Convolutional Neural Network (1D-CNN). RF excels at handling nonlinear relationships and feature selection; GRU focuses on capturing long-term temporal dependencies; and 1D-CNN effectively extracts local temporal features. The prediction results from these three learners are dynamically and optimally weighted and fused using the RLS algorithm, resulting in a comprehensive prediction accuracy significantly superior to any single model.

[0061] 3. Highly efficient sample utilization, improving modeling efficiency and generalization ability;

[0062] A Markov-LHS-MOGA sample optimization strategy is proposed, which integrates the temporal dynamics of Markov chains, the spatial uniformity of Latin hypercube sampling, and the global optimization capability of multi-objective genetic algorithms. This method can automatically select high-representative, low-redundancy, high-quality training samples from massive, redundant industrial data. While ensuring the model's generalization performance, it significantly reduces the amount of training data, improves model training efficiency, and mitigates the risk of overfitting.

[0063] 4. The project has good practicality and clear industrial feasibility;

[0064] The entire method is designed to closely align with industrial realities: the MIC method effectively compensates for measurement lags between variables; the model update mechanism matches the actual field conditions where real values ​​have fixed delays; and it utilizes only existing DCS system data from power plants, eliminating the need for additional hardware costs. This invention provides coal-fired power plants with a high-precision, low-cost, and easy-to-implement real-time soft measurement solution for NOx concentration, offering reliable technical support for optimizing ammonia injection control and achieving ultra-low NOx emissions. Attached Figure Description

[0065] Figure 1 This is a schematic diagram of a one-dimensional convolutional neural network structure, showing the connection relationships and data flow of the input layer, convolutional layer, pooling layer, fully connected layer, and output layer, used to illustrate the network architecture of a 1D CNN base learner.

[0066] Figure 2This diagram illustrates the overall strategy of the NOx concentration prediction method proposed in this invention, outlining the entire process framework from data acquisition, preprocessing, sample selection to integrated modeling and online updates.

[0067] Figure 3 The graph shows the prediction error of the static model GRU with base learners on the test set.

[0068] Figure 4 The graph shows the prediction error of the static model RF with base learners on the test set.

[0069] Figure 5 The prediction error curve of the static 1D-CNN model with base learner on the test set.

[0070] Figure 6 The graph shows the prediction results of the RLS-GRC ensemble model on the test set after adopting the RLS online update strategy, demonstrating its improvement in prediction accuracy and stability compared to the static model.

[0071] Figure 7 This is a scatter plot of the predictions from the RLS-GRC model, used to visually assess the degree of agreement between the predicted and actual values, as well as the concentration of errors. Detailed Implementation

[0072] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0073] 1. Principles of relevant algorithms;

[0074] 1.1 Recursive Least Squares Method;

[0075] Relative Least Squares (RLS) is an online parameter estimation algorithm based on the least squares method. Its basic idea is to continuously update the parameter estimates recursively. With each new observation, the model parameters are adjusted based on the latest data to minimize the error, making it particularly suitable for processing time series data. RLS is based on least squares, a method that estimates model parameters by minimizing the sum of squared errors between the observed values ​​and the model output. Given input data... and output data ,in This represents the dimension of the input, assuming the model is:

[0076] (1);

[0077] in, Let be the parameter vector to be estimated. This is the error term; for Transpose.

[0078] The goal of the least squares method is to estimate the parameters by minimizing the sum of squared errors. :

[0079] (2);

[0080] in, This is the sum of squared errors; for Transpose; For parameter estimation.

[0081] The parameter estimates can be obtained by solving for them.

[0082] (3);

[0083] The goal of RLS is to update parameter estimates recursively. Covariance Matrix .

[0084] For new observations , First, the increment vector is calculated using the following formula. :

[0085] (4);

[0086] in, Forgetting factor, usually This is used to control the impact of historical data.

[0087] Update parameter estimates:

[0088] (5).

[0089] Update the covariance matrix:

[0090] (6).

[0091] 1.2 Random Forest Algorithm;

[0092] Random Forest (RF) is a typical ensemble learning algorithm, consisting of multiple decision trees, suitable for nonlinear classification and regression tasks. Its core idea is to integrate multiple weak learners into a strong learner through bagging and feature subspace strategies, thereby improving robustness and generalization ability. Classification and Regression Tree (CART) is a commonly used basic decision tree in RF. In regression tasks, CART uses mean squared error as the splitting criterion.

[0093] (7);

[0094] in, Mean square error; The total number of samples at the current node. , These are the target variables and their means for the current node samples, respectively.

[0095] For variables and cutoff points, the cost function of CART regression... for:

[0096] (8);

[0097] in, , , These represent the number of training samples for the left child node, right child node, and all nodes after the segmentation, respectively. , These are the mean square errors of the left and right child nodes, respectively; As the dividing point, at the th A specific numerical value on a feature is used to divide the sample into a left subset and a right subset; For feature indexing.

[0098] When constructing a CART tree, starting from the root node, the cost function is calculated for each variable and split point, and the optimal partitioning scheme is selected until the termination condition is met. The construction process of an RF regression model includes:

[0099] Step 1: Generate multiple sample subsets from the original training set using the bootstrap sampling method. The samples that are not selected are called out-of-bag (OOB) samples, which are used for validation.

[0100] Step 2: When constructing each tree, randomly select some features for node partitioning, and select the optimal feature from them for partitioning until the termination condition is met.

[0101] Step 3: After all trees have been trained, average the predicted values ​​of all trees for each sample to obtain the final result.

[0102] RF can also be used to assess variable importance, calculated based on changes in OOB sample error:

[0103] (9);

[0104] in, Indicates the importance score of the variable; It is a feature index number, used to distinguish different input variables; It is the total number of decision trees in the random forest. and In the initial set of variables, the variables are... Decision trees before and after random sorting The prediction error of OOB samples; It is the summation index.

[0105] 1.3 Gated Loop Unit;

[0106] A Gated Recurrent Unit (GRU) is a recurrent neural network architecture suitable for modeling long-term dependencies in time series data. GRU controls the flow of information through reset and update gates. The reset gate determines the degree of forgetting of historical information, while the update gate controls the fusion of historical and new information in the current state. At time step... At any given time, the computation process within a single GRU neuron is as follows:

[0107] (1) Reset the door Controls the degree of forgetting of information from the previous moment, with a value ranging from 0 to 1. The calculation method is shown in the following formula;

[0108] (10);

[0109] in, To reset the gate vector; For the sigmoid function, Let the input vector be the input vector at the current time. Let be the hidden state vector from the previous time step. For the input weight matrix (corresponding to the input ), Input weight matrix (corresponding to hidden state) ), This is the bias vector.

[0110] (2) Candidate hidden state Reset the door Compared to the previous hidden state Multiplication determines the amount of information retained from the past by integrating the input from the current moment. Obtain the candidate hidden state at the current time. , The calculation method is shown in the following formula:

[0111] (11);

[0112] in, This represents the candidate hidden state vector at the current time step. It is the hyperbolic tangent activation function; For the current input The weight matrix; The state is hidden from the previous moment. The weight matrix, The symbol for element-wise multiplication. This is the bias vector.

[0113] (3) Update the door Update Gate Control the output at the current moment Retain historical status information and receiving new information proportion, The calculation method is shown in the following formula:

[0114] (12);

[0115] in, For the current input Weight matrix; The state is hidden from the previous moment. The weight matrix, This is the bias vector.

[0116] Finally, the output at the current moment The calculation method is shown in the following formula:

[0117] (13).

[0118] 1.4 One-dimensional convolutional neural networks;

[0119] A one-dimensional convolutional neural network (1DCNN) is a type of neural network used to process one-dimensional sequential data, widely applied in time series analysis, text classification, audio processing, and other fields. Its principle is similar to that of a two-dimensional convolutional network, but the convolution operation only slides in one direction. The structure is as follows: Figure 1 As shown.

[0120] A typical 1D CNN consists of an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. The input layer receives one-dimensional sequence data. The convolutional layer is the core layer of the network, using convolutional kernels to extract local features. The convolutional kernel slides across the input data with a fixed stride, calculates the dot product, and adds a bias term; each convolutional kernel generates a feature map. The formula for calculating the elements generated by the k-th convolutional kernel in the feature map F is as follows:

[0121] (14);

[0122] in, This represents the element value of the output feature map, indicating the th element. The convolutional kernel (i.e., the nth kernel) The position of each feature map in the output sequence The value at that location; This indicates the location of the input data (or the feature map from the previous layer). The value at; Represents the weight values ​​of the convolution kernel; , The size of the convolution kernel. This is a bias term.

[0123] Pooling layers: Located after convolutional layers, they downsample the feature maps, reducing dimensionality, computation, and preventing overfitting. Common operations include max pooling and average pooling. The formula for max pooling is as follows:

[0124] (15);

[0125] in, The output feature map after pooling is located at... The value at; Indicates the feature map index. Indicates the position of the output sequence; This represents a local rectangular region of the input feature map. The average pooling calculation formula is as follows:

[0126] (16);

[0127] in, For local areas The number of elements in the middle.

[0128] Fully connected layer: Located at the end of the network, it transforms the feature map into a one-dimensional vector and maps it to the output space. Non-linear transformations are often achieved through activation functions (such as ReLU, Sigmoid, or Softmax). Its calculation is as follows:

[0129] (17);

[0130] in, The input vector of the fully connected layer. This is the weight matrix. For bias vectors, For activation function, This is the output vector.

[0131] 2. Predictive modeling strategies and implementation;

[0132] The basic idea of ​​the proposed algorithm is as follows: Figure 2 As shown, it mainly consists of three parts: data acquisition, data preprocessing, and an integrated prediction framework.

[0133] 2.1 Data Acquisition;

[0134] Process data is collected through a distributed control system (DCS). However, fluctuations in unit load, differences in fuel quality, and changes in external environmental conditions lead to highly dynamic and complex actual operating conditions of power plants; these variable operating characteristics result in nonlinear and non-stationary characteristics in both time and space for the process data. Furthermore, measurement delays exist for each process variable; for example, the delay in CEMS measurement of NOx concentration can reach tens of seconds to several minutes, causing DCS data asynchrony and weakening the true correlation between variables. In long-term, continuous, and high-frequency sampling processes, the initial samples also exhibit significant redundancy. To address these data characteristics, this application first uses the Maximum Information Coefficient (MIC) method to estimate the time lag relationship between each auxiliary variable and NOx, and reconstructs the data to eliminate time-series mismatches. Then, the correlation between each auxiliary variable and NOx concentration is calculated, and highly correlated variables are selected to improve model training accuracy. Finally, the sample optimization method proposed in this application alleviates the problems of data redundancy and uneven distribution, improving model training efficiency and generalization.

[0135] 2.2 Data preprocessing;

[0136] 2.2.1 Time Delay Estimation Based on MIC;

[0137] This application uses MIC to estimate the time delay between each auxiliary variable and the NOx concentration. By reconstructing the sequence of auxiliary variables with different lag steps (such as t-1, t-2, t-3), the MIC value between the auxiliary variables and the NOx concentration is calculated, and the lag time corresponding to the largest MIC is selected as the optimal delay.

[0138] In calculating the MIC, we first need to calculate the MI, which represents the amount of information about one random variable contained in another. Consider two discrete random variables. and , and The MI can be calculated by the following formula:

[0139] (18);

[0140] in, and They represent and The marginal probability density function, express and The joint probability density function.

[0141] When both sets of variables are continuous random variables, the MI is calculated as follows:

[0142] (19).

[0143] random variable and The maximum information coefficient between them is calculated as follows:

[0144] (20).

[0145] in, and Represents respectively in shaft and The number of grids divided along the axis, Set an upper limit for the number of grid cells. This represents the number of samples.

[0146] The algorithm is given a set of... A matrix of auxiliary variables and a target variable matrix ,in , This is the sampling start time. This is the end time of sampling. This represents the number of samples. and It can be represented as follows:

[0147] (twenty one);

[0148] (twenty two);

[0149] Auxiliary variables with different delay times will be embedded. Reconstructed into a new sequence ,in , This represents the maximum delay time for all auxiliary variables. Calculate sequentially. Each column in the target variable The MIC is determined when the MIC reaches its maximum value. The optimal delay time is .

[0150] Based on the optimal delay time of each auxiliary variable For the auxiliary variable matrix The reconstructed matrix is ​​shown below.

[0151] (twenty three);

[0152] in, The reconstructed auxiliary variable matrix; Indicates the first One auxiliary variable; Indicates the current time; For the first The optimal delay time for each auxiliary variable; Indicates the first The actual time at which each auxiliary variable should take its value; Indicates the first The values ​​of each auxiliary variable at the optimal delay time; This represents the total number of auxiliary variables.

[0153] 2.2.2 Sample optimization method based on Markov-LHS-MOGA;

[0154] Industrial data often exhibits significant sequential characteristics and multi-condition distribution. To simultaneously consider the temporal representativeness of the samples, the balance of operating conditions, and the modeling efficiency, a sample optimization method based on a combination of Markov-LHS and MOGA is proposed.

[0155] The basic idea of ​​Markov-LHS is to ensure the temporal continuity and balanced distribution of operating conditions of samples through Markov transition constraints, thus preserving the dynamic characteristics of industrial processes. The algorithm first uses density clustering to cluster the dataset after time reconstruction and variable selection. , This represents the working condition label obtained from density clustering. It is the total number of samples. The purpose of sampling is to select from... Select a subset This allows the prediction model to maximize its generalization ability while maintaining the representativeness of the original data distribution, thus reducing the number of samples.

[0156] First, the operating condition label sequence Construct the state transition probability matrix The definition is as follows:

[0157] (twenty four);

[0158] in, Let be the transition probability from state i to state j in a Markov chain; This is the symbol for conditional probability; For the first Operating condition labels for each sample; For the first Operating condition labels for each sample; , For operating condition status index; This represents the total number of operating condition categories; This is the probability normalization condition.

[0159] Subsequently, estimates were obtained from the actual operating condition sequence. And based on the Markov chain model, simulate the generation of a chain of length. Working condition path sequence:

[0160] (25);

[0161] in, This is a simulated sequence of operating conditions; For the first in the path The operating status at each location (time); This represents the length of the simulated path (i.e., the number of states).

[0162] In each path state Next, extract the corresponding working condition sample set:

[0163] (26);

[0164] in, The working condition label is The sample set; For the first The input feature vector of each sample (i.e., the vector reconstructed by auxiliary variables); For the first The target variable value (NOx concentration) for each sample; For the first The true working condition labels of each sample (from historical data clustering results).

[0165] LHS sampling is then performed on this set to maintain good uniformity in the feature space. The final initial sample subset is represented as:

[0166] (27);

[0167] in, For the initial selection of a subset of samples; set union operator; For the Latin hypercube sampling function, for the set Perform sampling; The source sample set to be sampled; In the first Path status (operating condition) The number of samples to be drawn under the plan can be set uniformly or allocated according to the state transition probability.

[0168] To further optimize the structure of the selected samples, the MOGA algorithm is introduced to optimize the structure of the samples initially selected by Markov-LHS, and finally the Markov-LHS-MOGA sample optimization algorithm is realized.

[0169] MOGA, based on the genetic algorithm framework, incorporates the predictive metrics of a regression model into the optimization objective, constructing a regression model by selecting appropriate samples to optimize the objective function. This is applied to the sample set after initial selection using Markov-LHS. Given an individual Represents the initial sample set For each sample, determine its selection state and define the following objective function:

[0170] (28);

[0171] (29);

[0172] in, This is the total loss function value; the smaller the value, the smaller the corresponding sample subset. The better, the goal of the multi-objective genetic algorithm (MOGA) is to find the optimal solution. Minimize the sample subset; The primary objective term is composed of a weighted average of prediction error and sample proportion, used to balance model accuracy and sample decimality. Encode the individuals whose states are selected for the sample; This is a penalty term, a constraint mechanism, normally set to 0; when the selected sample set... When the quality is extremely poor, its value is set to... This completely eliminates the candidate solution in the optimization algorithm; and These are weighting coefficients (component coefficients) used to adjust the prediction error term. and sample proportion Its relative importance in the overall objective; Indicates the current individual The number of samples selected; For the initial sample set The total number of samples; Select a proportion for the sample.

[0173] The prediction error of the RF model trained on the selected samples over the entire dataset is defined as follows:

[0174] (30);

[0175] in, Indicates the selected sample The model's predicted values, Indicates no sample was selected. The model's predicted values; This indicates the selected subset of samples (training subset). This indicates the subset of samples that were not selected (validation / test subset). Selected sample The true value of the target variable; Unselected samples The true value of the target variable; The sum of squared prediction errors over the selected sample set; This is the sum of squared prediction errors on the unselected sample set. Under normal circumstances, The value is 0; when the selected sample Value greater than 1.25 times the unsampled data When the value is zero, it is considered that the selected samples have lost their function in model training. The value is ∞.

[0176] The optimal sample set is determined by finding the subset of samples that minimizes the objective function. .

[0177] 2.3 Integrated Prediction Framework;

[0178] The operation exhibits typical multi-condition characteristics, with NOx emission concentrations significantly affected by factors such as load level, fuel type, and combustion method, showing marked fluctuations. Most current studies construct static NOx prediction models based on specific operating conditions; however, these models lack adaptability and struggle to cope with changes in operating conditions, leading to decreased online prediction accuracy and limiting their long-term stable application. To address these issues, this application proposes an integrated online NOx concentration prediction model based on Relative Stress Law (RLS-GRC).

[0179] Considering the obvious time-series characteristics of actual industrial data, a GRU is introduced to construct a time-series prediction sub-model to enhance the ability of the integrated strategy to handle long-term time-series predictions. Furthermore, coal-fired power generation processes exhibit certain periodicity, thus NOx concentration has an inherent correlation with historical spatial data. Therefore, this application introduces a CNN to establish a spatial prediction sub-model. Simultaneously, when constructing prediction models for actual industrial processes, the impact of the randomness and uncertainties of complex processes on prediction robustness must be considered. To address this issue, this application also introduces a RF to construct a prediction sub-model. In summary, the proposed method uses GRU, RF, and 1D CNN as base learners, which complement each other to enhance prediction capabilities. Since the output of all sub-models is the predicted value of NOx concentration, the sub-model outputs only differ in accuracy, without any output conflict. Considering that RLS can recursively update the fusion parameters, achieving rapid response to data drift and possessing good online adaptability, this application uses RLS as a meta-learner to dynamically fuse the sub-model prediction results.

[0180] like Figure 2 As shown, GRU, RF, and 1D CNN serve as base learners, modeling and computing independently in parallel. Meanwhile, RLS, as a meta-learner, does not directly model the original data but instead receives the predictions from the three base learners as input, fusing them through a recursive least squares update mechanism. If the prediction performance of a particular model degrades under specific conditions, the RLS fusion unit dynamically adjusts its weights based on residual feedback, achieving complementary advantages among multiple models and improving overall prediction accuracy through a "dynamic weighted fusion" mechanism.

[0181] During the training phase, firstly, kernel density estimation is performed on the training set data to identify and remove outlier samples; secondly, hyperparameter optimization is performed on the base learner model, with differential evolution algorithm used to optimize the hyperparameters of GRU and 1D-CNN, and grid search used for RF; then, the base learner model is trained using the training set data, and the training effect is verified by the validation set; finally, the blending strategy is used to use the predictions of the base learner on the validation set as input to the RLS fusion machine for offline initialization of the RLS fusion machine model.

[0182] During the testing phase, to conform to the measurement characteristics of industrial environments, the test set data was progressively input into the prediction vectors obtained from the three-based learner. These prediction vectors were then input into an offline-trained RLS fusion unit to calculate the final ensemble prediction output. Simultaneously, the actual feedback of NOx at the SCR inlet was considered. The delay of one sampling step, before The first test sample is used only for prediction and is not used to update the RLS fusion model; from the second... Starting with a sample, when the true value is reached, the base learner prediction vector at the corresponding true value time is used to construct a residual with the true value. The fusion parameters are updated online according to the RLS recursive formula, and the prediction output is performed, thereby realizing an online iterative mechanism that synchronizes prediction and parameter update.

[0183] Figure 3 , Figure 4 , Figure 5 The graphs show the prediction error curves of three base learner static models (GRU, RF, and 1D-CNN) on the test set, which are used to compare and analyze the performance fluctuations of static models in specific operating conditions.

[0184] Example 1: Validation of the sample optimization method based on the Tennessee (TE) benchmark dataset;

[0185] 1. Experimental Objective and Dataset Description: This embodiment aims to verify the effectiveness of the Markov-LHS-MOGA sample optimization method proposed in this invention. The Tennessee Eastman (TE) chemical process simulation dataset, widely recognized in the field of process monitoring, is selected as the test platform. This dataset simulates the dynamics of multi-unit chemical processes and provides a variety of preset failure modes, facilitating labeled, multi-condition comparative analysis.

[0186] 2. Data preparation and experimental setup;

[0187] Features and Objectives: Twenty continuously measurable process variables from the TE dataset are selected as auxiliary variables (features), and the process state is used as the prediction objective. A multi-class classification (operating condition identification) or key variable regression prediction task is constructed to evaluate sample quality. This embodiment takes the early identification of fault conditions as an example.

[0188] Operating condition classification: Three typical preset fault modes are selected to form a training set;

[0189] Condition 1: Abnormal A / C feed flow ratio;

[0190] Condition 2: Abnormal content of component B;

[0191] Condition 3: Material D has an abnormal temperature.

[0192] Data scale: In the original training set, each working condition contains 960 samples, for a total of 2880 samples.

[0193] Preferred parameters: When applying the method of this invention, the weight coefficients of the objective function of the multi-objective genetic algorithm (MOGA) are set as follows: , .

[0194] 3. Sample selection process and results;

[0195] The optimization process employs the Markov–LHS–MOGA algorithm for iterative optimization, compressing the training set size while maintaining sample representativeness through a multi-objective evolutionary mechanism. During optimization, the number of samples adaptively adjusts with iterations under different conditions, and the objective function value gradually converges with increasing generations, indicating that the algorithm possesses good optimization stability and convergence.

[0196] The final sample set, after optimization, is a new training set that is highly representative and small in size, selected from the original 2880 samples.

[0197] 303 sets of samples were selected for working condition 1;

[0198] 385 samples were selected for working condition 2;

[0199] 318 samples were selected for operating condition 3;

[0200] A total of 1006 groups were included, a reduction of approximately 65% ​​in sample size.

[0201] 4. Optimization effect verification and analysis;

[0202] To quantify the effectiveness of sample optimization, the same GRU, RF, and 1DCNN prediction models were trained using the training sets before and after optimization, respectively, and their performance was compared on a unified test set. Evaluation metrics included mean squared error (MSE), mean absolute error (MAE), and model training time. The results are shown in Table 1.

[0203] Table 1: Comparison of Sample Optimization Algorithms Based on TE Dataset;

[0204] .

[0205] For the GRU and RF models: training with a sample set optimized by Markov-LHS-MOGA achieved the lowest MSE and MAE on the test set, and the shortest training time. This indicates that optimizing the sample set significantly improves training efficiency while enhancing the model's generalization ability and mitigating overfitting.

[0206] For 1D CNN models: the prediction accuracy (MSE, MAE) of models trained with optimized samples is roughly equivalent to or slightly lower than that of models trained using the full set, but the training time is significantly reduced (approximately 18%). This is likely due to the strong feature extraction and anti-overfitting capabilities of CNNs, making them insensitive to sample redundancy. Optimizing samples significantly improves training efficiency with almost no loss of accuracy.

[0207] In conclusion, this embodiment validates the effectiveness of the Markov-LHS-MOGA sample selection method on the standard TE dataset. This method can intelligently filter out high-value core samples from massive and redundant industrial data, significantly reducing model training time (13%-40%) while maintaining or even improving the model's prediction accuracy, thus laying a high-quality data foundation for the subsequent construction of efficient and accurate ensemble prediction models.

[0208] Example 2: Construction and online updating of NOx concentration prediction model based on actual operating data of coal-fired power plants.

[0209] This embodiment uses the actual historical operating data of a 600MW coal-fired unit as an example to illustrate in detail the implementation steps of the method described in this invention.

[0210] 1. Data Acquisition and Preliminary Processing; Data collection and preliminary processing of NOx concentration at the SCR inlet from the power plant's Distributed Control System (DCS) and System-Specific Information (SIS).

[0211] Historical operational data related to degree. The data collection period is 90 consecutive days of operation, with a sampling interval of 1 minute.

[0212] The raw data includes:

[0213] The target variable is the measured NOx concentration at the SCR inlet, which is measured by CEMS and has a fixed delay of approximately 2-3 minutes.

[0214] Auxiliary variables (initial candidate set, 35 in total) include process parameters reflecting combustion state and flue gas conditions, such as total air volume, total coal volume, unit load, main steam pressure, opening degree of secondary air dampers at each level, output of each coal mill, oxygen content, and flue gas temperature.

[0215] 2. Data preprocessing;

[0216] 2.1 Time Delay Estimation and Data Reconstruction Based on MIC;

[0217] Due to the physical distance and system response differences between the measurement points of each auxiliary variable and the CEMS measurement points, there is an asynchronous time lag with NOx concentration. To eliminate this timing mismatch, the maximum information coefficient (MIC) is used for delay estimation.

[0218] Step S201: Construct an initial matrix from the collected 90 days of data (excluding invalid operating conditions such as start-up and shutdown). Assume there are n = 120,000 valid sample points and m = 35 auxiliary variables. Construct the auxiliary variable matrix. and target variable vector .

[0219] Step S202, for each auxiliary variable Preset maximum delay time Minutes. Construct its delayed sequence. .

[0220] Step S203, calculate sequentially Each column (i.e., the sequence at different delay times) is related to the target variable. The MIC value between [a certain value]. Taking the "total air volume" variable as an example, the curve of its MIC value changing with the delay time may show a peak. Assuming that during the delay... If the MIC reaches its maximum value of 0.85 at 1 minute, then the optimal delay time for this variable is determined. .

[0221] Step S204: Repeat the above steps for all 35 auxiliary variables to obtain the optimal delay time for each variable. Based on these delay times, the original data matrix is ​​reconstructed to generate a new synchronization data matrix:

[0222] ;

[0223] After reconstruction, the data dimensions remain the same. However, each variable has been aligned with the moment when its impact on NOx concentration is greatest.

[0224] 2.2 Optimal selection of training samples based on Markov-LHS-MOGA;

[0225] Industrial data is large in volume and contains redundancy; directly using all the data for training is inefficient and prone to introducing noise. This invention employs the Markov-LHS-MOGA method for intelligent sample selection.

[0226] Step S211, for the reconstructed dataset A density-based clustering algorithm was used to classify operating conditions. Based on core parameters such as load and air-coal ratio, the operating states were clustered into K=5 typical operating conditions (e.g., high load stable combustion, low load stable combustion, increasing load, decreasing load, and changing coal quality). Each sample was labeled with an operating condition tag. .

[0227] Step S212: Calculate the transition frequency of the working condition label sequence and construct a 5x5 state transition probability matrix. .For example, This indicates that the probability of transitioning from condition 2 to condition 3 is 10%.

[0228] Step S213, starting from the initial working condition (such as working condition 1), based on the matrix Length generated through Monte Carlo simulation Virtual working condition path sequence This path statistically reflects the evolution of actual operating conditions.

[0229] Step S214, along the simulated working condition path, at each path point Corresponding actual sample subset In this process, Latin hypercube sampling (LHS) is performed. A fixed number of samples is drawn for each operating condition. A set of samples. LHS ensures that the sample points are uniformly distributed in the feature space of each working condition. This stage yields the initial sample set. , approximately One sample.

[0230] Step S215, with Based on this, a multi-objective genetic algorithm (MOGA) is launched for fine optimization.

[0231] Encoding: Individual It is a length of The binary string, where 1 indicates that the corresponding sample is selected, and 0 indicates that it is not selected.

[0232] Objective function: As shown in formulas (28) and (29), minimize This embodiment sets... =0.7, . The calculation is performed as follows: a lightweight random forest model is trained using the selected samples, and then the mean squared error of the model's predictions over all 120,000 samples is calculated.

[0233] Optimization process: The MOGA population size was set to 100, and it evolved for 200 generations through selection, crossover, and mutation operations. Ultimately, the optimal solution balancing prediction error and sample size was selected on the Pareto front, resulting in the final preferred sample set. It contains approximately 1,500 samples.

[0234] Sample partitioning: The final optimal sample set will be selected. The dataset is randomly divided into a training set (1200 sets), a validation set (150 sets), and a test set (150 sets) in a ratio of 8:1:1.

[0235] 3. Training and optimization of base learner models: Using the optimized training set, three base learners are trained in parallel.

[0236] Random Forest (RF) model;

[0237] Hyperparameter optimization: Grid search was used, and the results were evaluated on the validation set. The optimal parameters were: number of decision trees n_estimators = 300, maximum depth max_depth = 15, and minimum number of samples per leaf node min_samples_leaf = 5.

[0238] Training and Functionality: The RF model is trained using the optimal parameters. This model can not only make predictions but also output a ranking of the importance of variables (based on formula (9)) to assist in feature selection. In this embodiment, the top 10 most important variables are retained as inputs to subsequent GRU and CNN models to reduce complexity.

[0239] Gated cyclic unit (GRU) model;

[0240] Hyperparameter optimization: Differential evolution algorithm was used for optimization. The fitness function was the validation set RMSE. The optimized network structure was: 2-layer GRU, with 128 neurons in the first layer and 64 neurons in the second layer; time step = 30 (i.e., using data from the past 30 minutes to predict the current state); learning rate = 0.001; batch size = 32.

[0241] Training: A sliding window method was used to construct time-series samples. The input consisted of 30 steps of historical data for 10 key variables selected by random number processing (RF), and the output was the NOx concentration at the current time. The Adam optimizer was used for training for 100 epochs.

[0242] One-dimensional convolutional neural network (1D CNN) model;

[0243] Hyperparameter optimization: Differential evolution algorithm is also used. The optimal structure is: two convolutional layers (32 and 64 kernels respectively, with kernel sizes of 5 and 3), followed by a max pooling layer, and then flattened into two fully connected layers (100 and 50 neurons respectively). The input is the same key variable as GRU: a 30-step history sequence.

[0244] Training: Use the same data and optimizer as GRU for training.

[0245] 4. Initialization of the RLS fusion unit;

[0246] The validation set data was input into the trained RF, GRU, and 1D CNN models respectively to obtain three sets of predicted values. .

[0247] These three predicted values ​​are used as new input features, i.e., for the validation set... Given samples, construct the input vector of the fusion unit. The corresponding output is the actual NOx concentration. .

[0248] Using all of the validation set For the data pairs, the initial weight vector of the RLS fusion unit was calculated offline using the classical least squares method. and the initial covariance matrix This completes the "cold start" of the RLS fusion unit.

[0249] 5. Online integrated forecasting and updating;

[0250] Simulate an online operating environment and validate using independent test set data. Set the CEMS measurement delay. One sampling point (i.e., 3 minutes).

[0251] Steps S6 and S7 (first 3 minutes):

[0252] At t=1, the latest process variable data is input into the three base learners to obtain the prediction vector. .

[0253] Will Input an initialized RLS fusion unit and compute the ensemble predictions. , and output.

[0254] Since the true value has not yet been reached, the RLS parameters are not updated at this time. This process is repeated at t=2 and 3.

[0255] Step S8 (Start online update at the 4th minute and thereafter):

[0256] At t=4, first repeat S6-S7 and output the predicted value. .

[0257] At this point, the actual NOx concentration measurement at time t=1 Arrive at the system.

[0258] Key update: Using the prediction vector stored at time t=1 and the actual value that just arrived This forms a new data pair. Substituting this into the RLS recursive formula:

[0259] ;

[0260] ;

[0261]

[0262] After the update, the weights changed from Become The model has been fine-tuned based on the latest error information.

[0263] In subsequent time steps (t=5,6,...), this "prediction-store-delayed update" cycle is repeated. Each update uses the latest error to adjust the weight distribution of the three base learners in the final prediction, thereby enabling the model to adapt to operating condition drift.

[0264] Example 3: Model validation and universality analysis based on harmful gas emission data from large-scale farms;

[0265] To verify the universality and effectiveness of the method proposed in this invention in different industrial scenarios, this embodiment applies it to the task of predicting the concentration of harmful gases (taking NH3 concentration as an example) in large-scale farms.

[0266] 1. Data sources and preprocessing;

[0267] The dataset originates from real-world operational records of a large-scale livestock farm in China, comprising 12,520 data sets collected at 30-second intervals over a 45-day period. Feature variables include 23 auxiliary variables such as pen temperature, humidity, ventilation negative pressure, animal density, and feed intake; the target variable is NH3 concentration. The original training set contained 9,080 data sets, of which 5,216 were selected using the Markov-LHS-MOGA sample optimization method to form the training set. An additional 860 sets were used as the validation set, and 2,580 sets as the independent test set. Outlier removal based on kernel density estimation was performed only on the training set; the validation and test sets retained their original distributions to evaluate the model's true generalization ability.

[0268] 2. Validation of the sample selection method;

[0269] To verify the effectiveness of the Markov-LHS-MOGA sample selection method, a comparative experiment was conducted on a farm dataset. As shown in Table 2, the prediction performance (measured by MSE and MAE) and training time of training GRU, RF, and 1D CNN base learners were compared using the original training set, the sample set initially selected by Markov-LHS only, and the sample set optimized by Markov-LHS-MOGA.

[0270] Table 2. Comparison of Sampling Algorithms (Dataset from Large-Scale Farms);

[0271] .

[0272] Experimental results show that models trained with Markov-LHS-MOGA optimized samples achieve better MSE and MAE metrics on GRU and RF, while the metrics on CNN fluctuate slightly but remain close. The training time of all models is significantly reduced (by approximately 13%-40%), verifying the effectiveness of this method in improving modeling efficiency and alleviating overfitting.

[0273] 3. Base learner hyperparameter optimization and training;

[0274] Using the optimized training set, the hyperparameters of GRU and 1D CNN were optimized using the differential evolution algorithm, and the hyperparameters of RF were optimized using grid search. The optimization results of GRU and CNN are shown in Table 3.

[0275] Table 3. Hyperparameter settings for GRU and 1D CNN (large-scale farms);

[0276] .

[0277] Then, three base learners are trained in parallel.

[0278] 4. RLS-GRC model construction, prediction, and online updating;

[0279] A blending strategy is employed, using the prediction results of the base learners on the validation set to initialize the RLS fusion unit offline (forgetting factor λ=0.9). During the testing phase, such as... Figure 6 As shown, the static base model exhibits an increase in prediction error due to changes in operating conditions within the sample point range [500, 1000]. However, after adopting the RLS online update strategy proposed in this invention, the prediction error of the RLS-GRC model is more stable across the entire test set, and the error in this range decreases significantly (e.g., ...). Figure 7 As shown in the figure, it exhibits excellent adaptability to various working conditions.

[0280] 5. Overall performance comparison;

[0281] The RLS-GRC model was compared with single static models (GRU, RF, 1D-CNN) and single dynamic models (RLS-GRU, RLS-RF, RLS-CNN), and the results are shown in Table 4. Evaluation metrics included RMSE, MAE, MAPE, ME, and the coefficient of determination R².

[0282] Table 4. Comparison of performance indicators of different models (large-scale farms);

[0283] .

[0284] The results show that:

[0285] 1. The effectiveness of the RLS update strategy: After introducing RLS update, the performance of each single dynamic model (RLS-GRU, RLS-RF, RLS-CNN) is significantly improved compared with its static version (RMSE is reduced by 14.2%~17.5%), which proves the necessity of online adaptive update.

[0286] 2. Advantages of the ensemble model: The RLS-GRC ensemble model proposed in this invention achieves optimal performance across all evaluation metrics. Its RMSE is reduced by 22.1% compared to the best static model (RF), with an R² of 0.893. This fully demonstrates that integrating the complementary advantages of RF, GRU, and 1D CNN as base learners outperforms all single models.

[0287] 3. Predicting stability, such as Figure 7 As shown, the predicted values ​​of the RLS-GRC model are more closely distributed with the measured values ​​near the ideal diagonal, further demonstrating its higher prediction accuracy and stability.

[0288] The three embodiments described above demonstrate that the RLS-based online ensemble model update method proposed in this invention not only performs significantly in predicting NOx concentrations in coal-fired power plants but also exhibits excellent performance in predicting harmful gas concentrations in large-scale livestock farms. This method effectively overcomes the performance degradation problem of static models under dynamic conditions through systematic data preprocessing (MIC delayed alignment), efficient sample selection (Markov-LHS-MOGA), complementary base learner ensembles (RF, GRU, 1D CNN), and an RLS-driven online fusion update mechanism. It significantly improves the accuracy, robustness, and long-term applicability of the prediction model, and possesses broad industrial application prospects.

[0289] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. An online update method for an ensemble model for NOx concentration prediction based on RLS, characterized in that, This includes the training phase and the online ensemble prediction and model update phase; among which, The training phase includes the following steps; S1. Data Acquisition; Real-time operating data of coal-fired power plants are collected, including multiple auxiliary variables and the target variable NOx concentration; S2. Data preprocessing; The collected raw data is preprocessed, including time delay estimation and sequence reconstruction of the auxiliary variables based on the maximum information coefficient, and the Markov-LHS-MOGA method is used to optimize the samples of the preprocessed data to obtain training and validation sets. S3. Base learner model training; Three base learner models were trained in parallel using the training set: a random forest model, a gated recurrent unit model, and a one-dimensional convolutional neural network model. S4. Model Validation; The trained base learner model is validated using the validation set. S5. RLS merger initialization; The blending strategy is adopted to obtain the prediction output results of the three base learner models on the validation set. These results are used as input data, and the corresponding real NOx concentration values ​​are used as output data to train the RLS fusion model and complete the offline initialization of parameters. The online integrated prediction and model update phase includes the following steps; S6. Real-time prediction; The auxiliary variable data collected in real time is input into the three base learner models that have been trained, and the predicted values ​​of each model are obtained and combined into a prediction vector. S7. Integrated output; The prediction vector is input into the initialized RLS fusion unit to calculate and output the integrated prediction value of NOx concentration at the current time. S8. Online updates; Once the actual NOx concentration measurement with a time delay arrives, the prediction residual at the current moment is calculated. Based on this residual and the prediction vector, the weight parameters of the fusion unit are updated online using the RLS algorithm to achieve adaptive updating of the model.

2. The method according to claim 1, characterized in that, The time delay estimation based on the maximum information coefficient in step 2 specifically includes: S201, given a containing A matrix of auxiliary variables and a target variable matrix , and It is represented as follows; （21）； （22）； in, , This is the sampling start time. This is the end time of sampling. The number of selected samples; S202, for each auxiliary variable Construct its delayed sequence ,in, ; The maximum delay time for all auxiliary variables; S203, calculate the relationship between each column of the delayed sequence and the target variable matrix. The maximum information coefficient between the two values ​​is used to determine the optimal delay time for this auxiliary variable, which is the delay time that maximizes the maximum information coefficient. ; S204, based on the optimal delay time of all auxiliary variables. For the original auxiliary variable matrix Reconstruct the matrix to obtain a new input matrix. (twenty three); in, The reconstructed auxiliary variable matrix; Indicates the first One auxiliary variable; Indicates the current moment; For the first The optimal delay time for each auxiliary variable; Indicates the first The actual time at which each auxiliary variable should take its value; Indicates the first The values ​​of each auxiliary variable at the optimal delay time; This represents the total number of auxiliary variables.

3. The method according to claim 1, characterized in that, Step 2 uses the Markov-LHS-MOGA method for sample optimization, specifically including: S211, perform density clustering on the dataset after time delay reconstruction to obtain the working condition label sequence for each sample; S212, Construct a Markov state transition probability matrix based on the working condition label sequence; S213, Based on the state transition probability matrix, simulate and generate a working condition path sequence; S214, in each state of the working condition path sequence, extract the sample subset corresponding to the working condition, and perform Latin hypercube sampling on the subset to obtain the initial sample subset; S215, based on the initially selected sample subset, a multi-objective genetic algorithm is used for further optimization. The optimization objective function is: （28）； （29）； in, This represents the total loss function value. The primary objective is to balance model accuracy and sample decimality. Encode the individuals whose states are selected for the sample; This represents the prediction error of the RF model trained on the selected samples across all samples. This is a penalty item; and These are weighting coefficients; Indicates the current individual The number of samples selected; For the initial sample set The total number of samples; Select a proportion for the sample; determine the final optimal sample set by finding the subset of samples that minimizes the objective function.

4. The method according to claim 1, characterized in that, In step S3, before training the base learner model, a hyperparameter optimization step is also included: The hyperparameters of the gated recurrent unit (GRU) model and the one-dimensional convolutional neural network (1D CNN) model are optimized using the differential evolution algorithm. The hyperparameters of the Random Forest (RF) model were optimized using a grid search method.

5. The method according to claim 1, characterized in that, In step S3, the random forest model is used to evaluate variable importance and perform feature selection; the gated recurrent unit model is used to capture long-term dependencies in time series; and the one-dimensional convolutional neural network model is used to extract local temporal features.

6. The method according to claim 1, characterized in that, The online adaptive update process in step S8 is as follows: Let the prediction vector of the base learner at time t be... The fusion weight vector is The covariance matrix is The forgetting factor is When new data pairs with delays , Upon arrival, update in the following order; Calculate the gain vector. (4); Update the weight vector, (5); Update the covariance matrix. (6).

7. The method according to claim 6, characterized in that, The forgetting factor The value range is from 0.8 to 0.

99.

8. The method according to claim 1, characterized in that, In S8, considering the measurement delay of the true NOx concentration, in the early stage of the test... At the first time step, only prediction is performed without updating the fusion parameters; from the second time step... Starting at a certain time step, after the true value is reached, the prediction in S7 and the parameter update in S8 are executed synchronously.

9. The method according to claim 1, characterized in that, The auxiliary variables include at least one of the following: total air volume, total coal volume, main steam pressure, and unit load.

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