Coal-fired power plant nitrogen oxide emission prediction method based on improved random forest algorithm

Abstract

The application discloses a coal-fired power plant nitrogen oxide emission prediction method based on an improved random forest algorithm, belongs to the field of coal-fired power plant flue gas denitration technology, and comprises the following steps: calculating the maximum information coefficient between all independent variables and dependent variables, preliminarily screening the variables, constructing a random forest regression model and reconstructing the random forest regression model multiple times, monitoring the prediction effect of the reconstructed random forest regression model in real time, comparing and evaluating the prediction performance of the random forest regression model by using a model prediction performance evaluation index, and performing online prediction on real-time data of a power plant flue gas system. The application automatically adjusts the threshold value of variable screening by using the out-of-bag error of the random forest, greatly reduces the difficulty of parameter adjustment, and improves the efficiency of feature selection; the combination of sample randomness and random subspace strategy effectively improves the robustness of the model; and the self-adaptive updating mechanism monitors the applicability of the algorithm evaluation model, effectively guiding the updating.

Description

Technical Field

[0001] This invention discloses a method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm, belonging to the field of flue gas denitrification technology for coal-fired power plants. Background Technology

[0002] my country's energy structure is currently showing a diversified trend. Although new energy sources have developed rapidly, they still suffer from problems such as a small proportion and narrow scope. Thermal power generation still dominates, accounting for nearly 60% of China's annual power generation to date. The combustion of pulverized coal in boilers produces large amounts of harmful gases, such as nitrogen oxides (NOx), sulfur dioxide, and dust, polluting the atmosphere and negatively impacting human health. Due to strict national environmental protection policies, NOx emissions from thermal power plants have attracted widespread attention. Finding an effective technology to eliminate NOx at the inlet of the denitrification reactor online and optimize combustion process control is of great significance. In production practice, power plants are typically equipped with desulfurization and denitrification devices to remove sulfur and NOx from flue gas. Currently, selective catalytic reduction (SCR) is widely used in denitrification equipment due to its simple structure and environmentally friendly reaction process. Timely and accurate detection of NOx emissions is crucial for accurately controlling ammonia injection and improving SCR efficiency. Currently, NOx emission detection mainly relies on traditional continuous emission monitoring systems (CEMS). CEMS requires a large amount of hardware, and its installation and commissioning are relatively complex. Furthermore, the CEMS operates in a harsh environment with significant electromagnetic interference, which can lead to frequent abnormal operating conditions and a heavy maintenance workload. Even under normal operating conditions, there is a considerable time delay in measuring NOx emissions due to sampling and detection delays. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm, which solves the problem that existing CEMS systems cannot provide real-time detection during planned maintenance and equipment upkeep, and reduces the time delay in NOx concentration detection.

[0004] A method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm includes:

[0005] S1. Perform data processing, including data acquisition, removal of outlier samples, data standardization, and dataset partitioning;

[0006] S2. Calculate the maximum information coefficient (MIC) between all independent variables X and dependent variable y;

[0007] S3. Based on the given initial threshold v mic Keep MIC greater than v mic The variables are used to perform initial screening and obtain a variable set;

[0008] S4. Using the variable set obtained in S3, construct a random forest regression model and calculate the out-of-bag error (err) of the random forest regression model. OOB1 ;

[0009] S5. Gradually increase v mic Repeat S3 and S4 until the random forest regression model reaches its error rate. OOB1 To reach the minimum;

[0010] S6. Output err OOB1 The variable set s under the random forest regression model after reaching the minimum mic Reconstruct the random forest regression model;

[0011] S7. Using the importance criterion of random forest variables to analyze s mic Sort the variables;

[0012] S8. Based on the threshold v RF For s mic The variables were then subjected to a second screening, retaining those with an importance index greater than v. RF The variable, re-output s mic ;

[0013] S9. Gradually increase v RF Using the output s of S8 mic Reconstruct the random forest regression model, repeating steps S7 and S8 until the out-of-bag error of the random forest regression model reaches err. OOB2 To reach the minimum, obtain the optimal variable set s. RF ;

[0014] S10. Output the optimal variable set s RF And reconstruct the random forest regression model;

[0015] S11. Monitor the prediction performance of the random forest regression model after S10 reconstruction in real time, and update the model when the prediction performance of the random forest regression model is lower than the threshold.

[0016] S12. The predictive performance of the random forest regression model is compared and evaluated using model prediction performance evaluation indicators;

[0017] S13. Perform online prediction of real-time data from the power plant flue gas system.

[0018] S1 includes:

[0019] A time-series operation dataset of the power plant flue gas system was obtained. Outlier samples in the dataset were removed using the Laida criterion. The dataset was then resampled, and the data in the dataset were standardized using standard scores. The standardized dataset was then divided into training and test sets.

[0020] S1.1. The time-series operation dataset of the power plant flue gas system is D(X,y), where X∈R N×m N represents the sample size, m represents the number of auxiliary variables, y is the nitrogen oxide concentration, which is the dependent variable, and R represents the set to which the independent variable belongs;

[0021] S1.2. The Laida criterion is used to remove outliers from the dataset, including calculating the standard deviation σ according to the Bessel formula:

[0022]

[0023]

[0024] In the formula: Let v be the average value of y. i Let y be the i-th bias, n be the number of samples, and y be the bias. i Let be the nitrogen oxide concentration value of the i-th sample;

[0025] If a certain sample data y i v i Satisfy | v i If |>3σ, then the sample data is considered outlier and should be removed.

[0026] S1.3. The formula for standardizing the data in the dataset using standard scores is:

[0027]

[0028] Where x is a value of X before standardization. It is the mean of x. It is the standard deviation, x normalization Let x be the standardized value of x after removing outliers from X(X,y);

[0029] S1.4. Divide the standardized dataset into a training set and a test set, using 70% of the total data as the training set and the remaining 30% as the test set.

[0030] S2 includes:

[0031] S2.1. Calculate the mutual information I(X,y) between X and y:

[0032]

[0033] Where p(x) represents the marginal probability density of x, p(y) represents the marginal probability density of y, and p(x,y) represents the joint probability density of the two variables.

[0034] S2.2. Calculate the maximum information MI on grid G. * :

[0035] MI * (D, h, v) = maxI(D|G);

[0036] Among them, MI * (D, h, v) represents MI * It is a function of D, h, and v, where D = {(x...} i y i Let D|G be a finite set of ordered pairs, where D|G represents the distribution of points in D across cells in G, and h and v are the grid sizes.

[0037] S2.3. MI * Normalization:

[0038]

[0039] In the formula, M(D) h，v For normalized MI * ;

[0040] S2.4. In M(D) h，v The highest normalized value obtained is taken as the MIC:

[0041] MIC = max{M(D)} h，v}

[0042] The set of variables obtained in S3 includes:

[0043] MIC(X j ,y)≥v mic ;

[0044] Among them, X j Let X be the j-th variable.

[0045] The random forest regression model in S4 is {f(x, Θ}. k )}, k represents the number of trees, Θ k These are random variables. Each tree model outputs a numerical value, and the average of the trees represents the prediction result of the random forest regression model. The random forest regression model parameters are adjusted using 10x cross-validation on the training set data, and the error rate is calculated. OOB1 ,include:

[0046] S4.1. From MIC(X) j Extract n from y) tree Each of the 3 self-bootsampling sets contains a MIC(X) j Two-thirds of the data in y);

[0047] S4.2. Use bootstrap sampling to generate an unpruned regression tree, randomly sampling m... tree There are 10 predictor variables, from which the best split point is selected from the variables stored in X;

[0048] S4.3. By merging n tree The predicted value is calculated based on the prediction of each tree.

[0049] S4.4. Calculate err OOB1 :

[0050]

[0051] in, These are predicted values.

[0052] S7 includes:

[0053] S7.1. For each decision tree t k Input data from outside the bag The mean squared error (OOB_MSE) between the predicted and actual values ​​is obtained. k :

[0054]

[0055] in, This represents the number of samples outside the bag of the k-th decision tree. This represents the predicted value of the k-th decision tree;

[0056] S7.2. Remove variable X in j Calculate the mean squared error (OOB_MSE) between the j-th predicted value and the true value using the residual variables. k，j :

[0057] S7.3.X j For decision tree t k Predicted mean square error results for:

[0058]

[0059] S7.4. Traverse each decision tree of the random forest regression model to obtain X. j For the mean squared error of all decision trees, X j Important results IMP j for:

[0060]

[0061] Where K is the number of decision trees to build a random forest.

[0062] The secondary screening in S8 includes:

[0063] IMP j ≥v RF .

[0064] S11 includes:

[0065] S11.1. Define a monitoring window for model performance, and initialize the window size to Mw;

[0066] S11.2. Calculate the prediction error for each sample using a random forest regression model. The formula for calculating the prediction error is as follows:

[0067]

[0068] In the above formula, err represents the prediction error, and yu represents the actual value of nitrogen oxides in the power plant;

[0069] S11.3. Calculate the median prediction error within the window. If the median error is greater than the threshold δ, provide an updated alarm signal.

[0070] S11.4. Update the training dataset with the newest data from the most recent window, and delete the previous data from the initial training set. The sample;

[0071] S11.5. Reconstruct the random forest regression model using the new training dataset.

[0072] S12 includes:

[0073] Model performance is evaluated using performance metrics, including root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R²). 2 :

[0074]

[0075]

[0076]

[0077] S13 includes: acquiring real-time data X q Standardize the data and use S RF The corresponding random forest regression model completes the prediction of the dependent variable y and outputs the prediction results.

[0078] Compared with existing technologies, this invention has the following advantages: It automatically adjusts the variable selection threshold using the out-of-bag error of random forests, greatly reducing the difficulty of parameter adjustment and improving the efficiency of feature selection; it effectively improves the robustness of the model by combining sample randomization and random subspace strategies; the adaptive update mechanism effectively guides updates by evaluating the model's applicability through monitoring algorithms; this invention can quickly select beneficial variables from massive historical data; the prediction model parameter setting method is simple, efficient, and convenient for on-site personnel; and the model update strategy makes the prediction model suitable for long-term application. Attached Figure Description

[0079] Figure 1 This is a technical flowchart of the present invention;

[0080] Figure 2 It is the prediction curve of the static random forest test set;

[0081] Figure 3 This is the error curve of the static random forest test set. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0083] A method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm includes:

[0084] S1. Perform data processing, including data acquisition, removal of outlier samples, data standardization, and dataset partitioning;

[0085] S2. Calculate the maximum information coefficient (MIC) between all independent variables X and dependent variable y;

[0086] S3. Based on the given initial threshold v mic Keep MIC greater than v mic The variables are used to perform initial screening and obtain a variable set;

[0087] S4. Using the variable set obtained in S3, construct a random forest regression model and calculate the out-of-bag error (err) of the random forest regression model. OOB1 ;

[0088] S5. Gradually increase v mic Repeat S3 and S4 until the random forest regression model reaches its error rate. OOB1 To reach the minimum;

[0089] S6. Output err OOB1 The variable set s under the random forest regression model after reaching the minimum mic Reconstruct the random forest regression model;

[0090] S7. Using the importance criterion of random forest variables to analyze s mic Sort the variables;

[0091] S8. Based on the threshold v RF For s mic The variables were then subjected to a second screening, retaining those with an importance index greater than v. RF The variable, re-output s mic ;

[0092] S9. Gradually increase v RF Using the output s of S8 mic Reconstruct the random forest regression model, repeating steps S7 and S8 until the out-of-bag error of the random forest regression model reaches err. OOB2 To reach the minimum, obtain the optimal variable set s. RF ;

[0093] S10. Output the optimal variable set s RF And reconstruct the random forest regression model;

[0094] S11. Monitor the prediction performance of the random forest regression model after S10 reconstruction in real time, and update the model when the prediction performance of the random forest regression model is lower than the threshold.

[0095] S12. The predictive performance of the random forest regression model is compared and evaluated using model prediction performance evaluation indicators;

[0096] S13. Perform online prediction of real-time data from the power plant flue gas system.

[0097] S1 includes:

[0098] A time-series operation dataset of the power plant flue gas system was obtained. Outlier samples in the dataset were removed using the Laida criterion. The dataset was then resampled, and the data in the dataset were standardized using standard scores. The standardized dataset was then divided into training and test sets.

[0099] S1.1. The time-series operation dataset of the power plant flue gas system is D(X,y), where X∈R N×m N represents the sample size, m represents the number of auxiliary variables, y is the nitrogen oxide concentration, which is the dependent variable, and R represents the set to which the independent variable belongs;

[0100] S1.2. The Laida criterion is used to remove outliers from the dataset, including calculating the standard deviation σ according to the Bessel formula:

[0101]

[0102]

[0103] In the formula: Let v be the average value of y. i Let y be the i-th bias, n be the number of samples, and y be the bias. i Let be the nitrogen oxide concentration value of the i-th sample;

[0104] If a certain sample data y i v i Satisfy | v i If |>3σ, then the sample data is considered outlier and should be removed.

[0105] S1.3. The formula for standardizing the data in the dataset using standard scores is:

[0106]

[0107] Where x is a value of X before standardization. It is the mean of x. It is the standard deviation, x normalization Let x be the standardized value of x after removing outliers from D(X,y);

[0108] S1.4. Divide the standardized dataset into a training set and a test set, using 70% of the total data as the training set and the remaining 30% as the test set.

[0109] S2 includes:

[0110] S2.1. Calculate the mutual information I(X,y) between X and y:

[0111]

[0112] Where p(x) represents the marginal probability density of x, p(y) represents the marginal probability density of y, and p(x,y) represents the joint probability density of the two variables.

[0113] S2.2. Calculate the maximum information MI on grid G. * :

[0114] MI * (D,h,v)=max I(D|G);

[0115] Among them, MI * (D,h,v) represents MI * It is a function of D, h, v, where D = {(x i ,yi Let D|G be a finite set of ordered pairs, where D|G represents the distribution of points in D across cells in G, and h and v are the grid sizes.

[0116] S2.3. MI * Normalization:

[0117]

[0118] In the formula, M(D) h,v For normalized MI * ;

[0119] S2.4. In M(D) h,v The highest normalized value obtained is taken as the MIC:

[0120] MIC = max{M(D)} h,v}

[0121] The set of variables obtained in S3 includes:

[0122] MIC(X j ,y)≥v mic ;

[0123] Among them, X j Let X be the j-th variable.

[0124] The random forest regression model in S4 is {f(x,Θ} k )}, k represents the number of trees, Θ k These are random variables. Each tree model outputs a numerical value, and the average of the trees represents the prediction result of the random forest regression model. The random forest regression model parameters are adjusted using 10x cross-validation on the training set data, and the error rate is calculated. OOB1 ,include:

[0125] S4.1. From MIC(X) j Extract n from y) tree Each of the 3 self-bootsampling sets contains a MIC(X) j Two-thirds of the data in (y, y);

[0126] S4.2. Use bootstrap sampling to generate an unpruned regression tree, randomly sampling m... tree There are 10 predictor variables, from which the best split point is selected from the variables stored in X;

[0127] S4.3. By merging m tree The predicted value is calculated based on the prediction of each tree.

[0128] S4.4. Calculate err OOB1 :

[0129]

[0130] in, These are predicted values.

[0131] S7 includes:

[0132] S7.1. For each decision tree t k Input data from outside the bag The mean squared error (OOB_MSE) between the predicted and actual values ​​is obtained. k :

[0133]

[0134] in, This represents the number of samples outside the bag of the k-th decision tree. This represents the predicted value of the k-th decision tree;

[0135] S7.2. Remove variable X in j Calculate the mean squared error (OOB_MSE) between the j-th predicted value and the true value using the residual variables. k,j :

[0136] S7.3.X j For decision tree t k Predicted mean square error results for:

[0137]

[0138] S7.4. Traverse each decision tree of the random forest regression model to obtain X. j For the mean squared error of all decision trees, X j Important results IMP j for:

[0139]

[0140] Where K is the number of decision trees to build a random forest.

[0141] The secondary screening in S8 includes:

[0142] IMP j ≥v RF .

[0143] S11 includes:

[0144] S11.1. Define a monitoring window for model performance, and initialize the window size to Mw;

[0145] S11.2. Calculate the prediction error for each sample using a random forest regression model. The formula for calculating the prediction error is as follows:

[0146]

[0147] In the above formula, err represents the prediction error, and yu represents the actual value of nitrogen oxides in the power plant;

[0148] S11.3. Calculate the median prediction error within the window. If the median error is greater than the threshold δ, provide an updated alarm signal.

[0149] S11.4. Update the training dataset with the newest data from the most recent window, and delete the previous data from the initial training set. The sample;

[0150] S11.5. Reconstruct the random forest regression model using the new training dataset.

[0151] S12 includes:

[0152] Model performance is evaluated using performance metrics, including root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R²). 2 :

[0153]

[0154]

[0155]

[0156] S13 includes: acquiring real-time data X q Standardize the data and use S RF The corresponding random forest regression model completes the prediction of the dependent variable y and outputs the prediction results.

[0157] The technical process of this invention is as follows: Figure 1As shown, the experimental subject used in this embodiment is a 1030MW super-subcritical thermal power plant in China. The basic process is as follows: raw coal is first ground into powder using a coal mill. After drying, the powder is blown into the once-through boiler via primary air through a coal pipe, while secondary air provides sufficient oxygen and tangential power for boiler combustion. Combustion of the pulverized coal converts fuel into heat energy, which in turn directly converts water into supercritical steam, driving a turbine to generate electricity. 390 auxiliary variables were collected from the thermal power plant, totaling 5184 samples. The sampling period was 72 hours, and the sampling frequency was 50 seconds. After removing outliers, 5012 samples remained. The unit load was changed from 600MW to 1000MW. Performance verification was conducted under stable operating conditions, increased load, and decreased load conditions. Based on the time series, the first 3456 collected samples (approximately 70% of historical data) were selected as the training set, and the remaining 30% (1556 samples) were used as the test set. All auxiliary variables of the historical data were normalized using Z-Score. MIC was used for preliminary selection of important variables. First, initialize a small threshold based on experience, then increase the threshold by 0.01 steps. A random forest regression model is built, and 10x cross-validation is performed on the training dataset to adjust the model's parameters. The iteration count is 20, with 50 trees and 5 leaf nodes. Considering the randomness of OOB error calculation, each iteration is run independently 10 times to obtain optimal results. Table 1 shows the OOB error and RMSE results on the training set obtained during the main iteration.

[0158] Table 1 Results for different Vmic values

[0159] 0.1 13.3224 1.8031 376 0.15 12.9798 1.7614 359 0.2 12.7679 1.7954 345 0.25 13.495 1.8544 326 0.3 12.8646 1.7862 312 0.31 12.6948 1.8033 310 0.32 12.5396 1.7969 305 0.33 12.7246 1.7996 299 0.34 15.1845 1.9675 290

[0160] As shown in Table 1, when the model achieves the minimum OOB error, the RMSE on the training set is relatively small. During iteration, both the OOB error and RMSE do not change linearly with increasing thresholds. For example, using v... mic The OOB error ratio at 0.25 is compared to using v. mic=0.2 is much larger. This phenomenon indicates that it is difficult to obtain the optimal variable set for regression modeling by relying solely on the MIC threshold. The main reason is that MIC only examines the correlation between auxiliary variables and the target variable, without comprehensively considering the influence of auxiliary variables in the regression model. This finding is consistent with previous analyses. Based on the above results, this step retains 305 variables. In order to eliminate redundant variables for regression modeling, in the second step, variables are reselected according to the variable importance index of the random forest. In this work, the initial threshold starts from 0.1, and the step size increases by 0.02. The parameters of the random forest regression model are the same as in the first step. The OOB error and RMSE calculated for each iteration are shown in Table 2. As the number of important variables increases, the number of retained important variables decreases, but the OOB error does not decrease linearly because the performance of the regression model is related not only to the dependence of auxiliary variables on the target variable, but also to the combined effect of all variables in the regression model.

[0161] Table 2 Different v RF The result of the value

[0162]

[0163] Based on the results in Table 2, a total of 61 important variables were selected to construct the NOx prediction model. Based on the variable selection results, a static random forest regression model can be constructed to predict NOx emissions. Figure 2 and Figure 3 The performance of the static random forest regression model on the test dataset is demonstrated. Figure 2 The prediction curve is given. Figure 3Error curves are presented. Within the range of 1-1400, the model exhibits good predictive performance with small and relatively stable prediction errors. After 1400 points, the prediction error shows an upward trend. The slope of the median curve, plotted by taking the median error every 50 points, increases significantly between 1400 and 1450 points. Specifically, the median error at 1450 points is 3.403, and the median error at 1500 points is 4.410. This phenomenon is caused by the inherent limitations of static models. When operating conditions change, the fixation of training samples and model parameters leads to performance degradation. Therefore, when static models are used on an industrial scale, manual maintenance is required, increasing the workload for long-term model application. In this example, Mw is set to 50, and based on experience, the threshold δ is set to 3.0. When the median error is greater than or equal to δ, the training set is updated, and the random forest regression model is reconstructed. According to the median error curve of the static model, the first update occurs at 1400, and the second update occurs at 1500. Specifically, the updated median errors are 2.9054 for 1450, 2.9345 for 1500, and 2.1542 for 1550. The results show that the updated model has a good linear relationship with the test set, and the RMSE and MAE are significantly reduced. The R-squared value of the updated model is... 2 The value increased slightly, indicating that the strategy improved the model's ability to interpret the test data.

[0164] To compare the performance of the proposed variable selection and NOx emission prediction methods, this section establishes a comparative model based on the MIC variable selection results. Due to the randomness of random forests, each experiment was run independently 10 times to obtain the optimal results. Five traditional methods—SVR, BP network, PLS, GPR, and DT regression—were used to compare the 61 selected important variables. Table 3 describes the performance of static random forests based on different variable sets selected according to MIC. mic Within the range of 0.1–0.45, the performance of static random forests fluctuates slightly. Where v mic The best results are obtained by RF when v = 0.1. mic Increasing the value of MIC to 0.5 effectively reduces the size of the variable set, but the performance of the random forest does not change significantly. The results indicate that, due to the strong redundancy between variables, relying solely on MIC cannot yield the optimal modeling variable set.

[0165] Table 3 Static Random Forests using MIC for Different Variable Sets

[0166] 0.1 0.9285 3.8745 2.8235 376 0.15 0.927 3.914 2.8872 359 0.2 0.9237 4.0039 2.8839 345 0.25 0.927 3.9154 2.8571 326 0.3 0.9245 3.981 2.934 312 0.31 0.9271 3.9126 2.8803 310 0.32 0.9275 3.9016 2.8327 305 0.33 0.9271 3.9117 2.8525 299 0.34 0.9216 4.0581 2.9755 290 0.4 0.9227 4.0292 2.9362 215 0.45 0.9238 3.9991 2.9271 159 0.5 0.9228 4.0236 2.9571 65 0.55 0.9232 4.0157 2.9617 30

[0167] SVR was implemented using the Libsvm toolbox, while other algorithms, such as GPR, BP, DT, and PLS, were implemented using MATLAB toolboxes. PLS extracted 40 features based on a variance contribution greater than 80%. GPR and SVR parameters remained at their default values. The number of leaf nodes in the DT algorithm was set to 9 using the toolbox's default optimization algorithm. BP employed a three-layer structure with sigmoid activation function in the hidden layer and purelin activation function in the output layer. The number of neurons in the hidden layer was 90, adjusted through five rounds of cross-validation. When evaluating prediction performance, RMSE described the accuracy of the predictions; the model's accuracy increased as the root mean square error decreased. MAE measured the mean absolute error between the predicted and labeled values ​​on the experimental dataset; the model's accuracy increased as the MAE decreased. The correlation coefficient described the explanatory power; the closer the value was to 1, the stronger the model's explanatory power.

[0168] Table 4 Results of different models

[0169] Update RF 0.9596 2.9042 2.0185 Static RF 0.9282 3.874 2.9295 GPR 0.8987 4.6006 3.4278 DT 0.8783 5.0419 3.6766 BP 0.8384 5.8107 4.3982 PLS 0.7948 6.5472 4.7151 SVR 0.784 6.7167 4.6343

[0170] Table 4 shows the performance of all compared models. Among the static methods, Random Forest performs best, followed by GPR, DT, and BP. PLS and SVR are less efficient. The results indicate that ensemble learning methods outperform traditional single-model-based approaches when handling multi-condition data. The update-strategy-based model exhibits the best performance, with the lowest MAE (2.0185) and RMSE (2.9042), suggesting that timely model updates are necessary for long-term industrial applications. Experimental analysis shows that this method has higher prediction accuracy and a wider prediction range compared to traditional methods. Practical application of this method is beneficial for improving the efficiency of NOx emission prediction.

[0171] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that 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. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm, characterized in that, include: S1. Perform data processing, including data acquisition, removal of outlier samples, data standardization, and dataset partitioning; S2. Calculate all independent variables. and dependent variable The maximum information coefficient (MIC) between them; S3. Based on the given initial threshold ,reserve Greater than The variables are used to perform initial screening and obtain a variable set; S4. Using the variable set obtained in S3, construct a random forest regression model and calculate the out-of-bag error of the random forest regression model. ; S5. Gradually increase Repeat steps S3 and S4 until the random forest regression model reaches its maximum value. To reach the minimum; S6. Output The set of variables in the random forest regression model after reaching the minimum Reconstruct the random forest regression model; S7. Using the importance criterion of random forest variables to... Sort the variables; S8. Based on the threshold right The variables were then subjected to a second screening, retaining those with an importance index greater than [value missing]. The variable, re-output ; S9. Gradually increase Using S8 output Reconstruct the random forest regression model, repeating steps S7 and S8 until the out-of-bag error of the random forest regression model is reached. To reach the minimum, obtain the optimal variable set. ; S10. Output the optimal variable set And reconstruct the random forest regression model; S11. Monitor the prediction performance of the random forest regression model after S10 reconstruction in real time, and update the model when the prediction performance of the random forest regression model is lower than the threshold. S12. The predictive performance of the random forest regression model is compared and evaluated using model prediction performance evaluation indicators; S13. Perform online prediction of real-time data from the power plant flue gas system; The set of variables obtained in S3 includes: ； in, For X's One variable; The random forest regression model in S4 is k represents the number of trees. These are random variables; each tree model outputs a numerical value. The average of the trees represents the prediction result of the random forest regression model. The random forest regression model parameters are adjusted by performing 10-fold cross-validation on the training set data. ,include: S4.

1. From Extract Each self-sampling set contains [number] self-sampling sets. Two-thirds of the corresponding data volume; S4.

2. Use bootstrap sampling to generate an unpruned regression tree, and randomly sample... One predictor variable, from stored in Select the optimal split point from the variables in the data; S4.

3. By merging The predicted value is calculated based on the prediction of each tree. S4.

4. Calculation : ； in, This is a predicted value; S7 includes: S7.

1. For each decision tree Input data from outside the bag The mean squared error between the predicted and actual values ​​is obtained. : ； in, Indicates the first Number of samples outside the decision tree bag Indicates the first The predicted values ​​of each decision tree; S7.

2. Remove variables in Calculate the first using the remaining variables The mean squared error between each predicted value and the actual value : S7.

3. decision trees Predicted mean square error results for: ； S7.

4. Traverse each decision tree of the random forest regression model to obtain... The mean squared error for all decision trees, Important results for: ； Where K is the number of decision trees to build a random forest.

2. The method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm according to claim 1, characterized in that, S1 includes: A time-series operation dataset of the power plant flue gas system was obtained. Outlier samples in the dataset were removed using the Laida criterion. The dataset was then resampled, and the data in the dataset were standardized using standard scores. The standardized dataset was then divided into training and test sets. S1.

1. The time-series operation dataset of the power plant flue gas system is as follows: ,in N represents the sample size, m represents the number of auxiliary variables, y is the nitrogen oxide concentration, which is the dependent variable, and R represents the set to which the independent variable belongs; S1.

2. Using the Laida criterion to remove outliers from the dataset includes: calculating the standard deviation according to the Bessel formula. : ； ； In the formula: for The average value, For the first There are several biases, where n is the number of samples. For the first The nitrogen oxide concentration values ​​of each sample; If a certain sample data of satisfy If the sample data is deemed abnormal, it will be removed. S1.

3. The formula for standardizing the data in the dataset using standard scores is: ； in, Before standardization One of the values, yes The mean, It is the standard deviation. for After removing outlier samples The value after standardization; S1.

4. Divide the standardized dataset into a training set and a test set, using 70% of the total data as the training set and the remaining 30% as the test set.

3. The method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm according to claim 2, characterized in that, S2 include: S2.

1. Calculate the mutual information between X and y. : ： Where p(x) represents the marginal probability density of x, p(y) represents the marginal probability density of y, and p(x,y) represents the joint probability density of the two variables. S2.

2. Calculate the maximum information on grid G : ； in, express It is about The function, For a finite set of ordered pairs, This represents the distribution of points in D across cells in G, where h and v are the grid sizes; S2.

3. Normalization: ； In the formula, For normalized ; S2.

4. will be The highest normalized value obtained is taken as the MIC: 。 4. The method for predicting nitrogen oxide emissions from coal-fired power plants based on the improved random forest algorithm according to claim 3, characterized in that, The secondary screening in S8 includes: 。 5. The method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm according to claim 4, characterized in that, S11 includes: S11.

1. Define a monitoring window for model performance, and initialize the window size to Mw; S11.

2. Calculate the prediction error for each sample using a random forest regression model. The formula for calculating the prediction error is as follows: ； In the above formula Indicates the prediction error. This represents the actual value of nitrogen oxides in the power plant; S11.

3. Calculate the median prediction error within the window. If the median error is greater than the threshold... If so, it will provide an updated alarm signal; S11.

4. Update the training dataset with the newest data from the most recent window, and delete the previous data from the initial training set. The sample; S11.

5. Reconstruct the random forest regression model using the new training dataset.

6. The method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm according to claim 5, characterized in that, S12 includes: Model performance is evaluated using performance metrics, including root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient. : ； ； 。 7. The method for predicting nitrogen oxide emissions from coal-fired power plants based on an improved random forest algorithm according to claim 6, characterized in that, S13 includes: acquiring real-time data Standardize the data and utilize The corresponding random forest regression model completes the prediction of the dependent variable y and outputs the prediction results. .

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