A method for predicting NOx emission of MSWI process based on dynamic modular neural network

Abstract

The application discloses a MSWI process NOx emission prediction method based on a dynamic modular neural network, and belongs to the intelligent modeling field. First, input variables are processed by smoothing and normalization. Then, a working condition feature extraction method based on principal component analysis (PCA) is designed, dynamic division of complex working conditions is realized, and thus the prediction task to be processed is divided into subtasks under different working conditions. In addition, submodels based on long short-term memory (LSTM) neural networks are constructed for different subtasks, and accurate prediction of NOx emission under each working condition is realized. Finally, the outputs of the submodels are integrated by using a cooperative strategy, and the accuracy of the prediction model is further improved. The effectiveness of the DMNN-based prediction model is evaluated based on industrial benchmark testing and actual operation data, and the application effectively solves the problem that the NOx emission concentration of the MSWI process is difficult to accurately predict due to sensor limitations.

Description

Technical Field

[0001] This invention relates to a method for predicting nitrogen oxide emissions during urban solid waste incineration; a NOx emission prediction model based on a dynamic modular neural network is established, achieving accurate prediction of future NOx emissions. This method belongs to both the field of urban solid waste incineration and the field of intelligent modeling. Background Technology

[0002] MSW incineration (MSWI) technology has become a key measure to solve the problem of "solid waste siege" due to its significant effects in harmlessness, volume reduction, and resource recovery. However, the potential secondary pollution during the MSWI process is a major reason for the "NIMBY" effect (not in my backyard) in the construction of solid waste incineration plants. One of the key pollutants emitted—nitrogen oxides (NOx)—is a significant source of acid rain and photochemical smog, posing numerous health problems and safety hazards to society. However, current technologies can only detect NOx emissions at the current moment and cannot provide reference values ​​for future NOx emissions, easily leading to delayed control measures and NOx emission exceeding standards. Therefore, accurate prediction of NOx emissions is crucial for improving the efficiency of denitrification systems and ensuring the safe and stable operation of MSWI plants. Summary of the Invention

[0003] The purpose of this invention is to propose a NOx emission prediction method for the MSWI process based on a dynamic modular neural network (MNN). The method uses a DMNN to construct a NOx emission prediction model to achieve accurate prediction of NOx emissions.

[0004] The technical solution and implementation steps of the present invention are as follows:

[0005] The equipment related to NOx emission concentration prediction includes thermocouple temperature sensors, airflow sensors, liquid flow sensors, a continuous emission monitoring system (MEMS), a distributed control system (DCS), and a host computer. The MEMS includes a NOx concentration detector. These detectors, along with the thermocouple temperature sensors, airflow sensors, and liquid flow sensors, are connected to the DCS via a fieldbus. The data collected by the sensors is transmitted to the I / O communication module in the DCS. Through switches, amplifiers, and A / D converters in the communication module, the analog voltage signals are converted into digital signals that the computer can recognize. These signals are then transmitted to the host computer via an industrial Ethernet network. The host computer acquires the MSWI process data in real time and stores the collected data in a structured query language server database.

[0006] (1) PCA-based working condition feature extraction method.

[0007] The algorithm reflects the current data processing status by detecting key features within a sliding window. The algorithm is described below:

[0008] Set the sliding window size to win_1, and assume the observation sample matrix within the first sliding window is... Indicated, denoted as

[0009]

[0010] Where m represents the number of process variables in the sample, n1 represents the number of samples contained within a window of size win_1, and x1 x2 … x m Let x1, x2, ..., xm represent the m process vectors in the sample matrix, which are the m inputs to the prediction model. When using butanizer data to build the prediction model, x1, x2, ..., xm are the inputs to the prediction model. m Let x1, x2, ..., x3 represent the column top temperature, column top pressure, column top reflux flow rate, next stage flow rate, and sensitive plate temperature at time t; the sensitive plate temperature at time t-1, t-2, and t-3; the average values ​​of column bottom temperatures A and B at time t; and the butane concentration at four times: t-1, t-2, t-3, and t-4, for a total of 13 process variables. In the butane removal column dataset, m = 13. When using actual industrial data from the MSWI process to build a predictive model, x1, x2, ..., x3 represent the values ​​of x1, x2, ..., x4. m These represent the process variables related to NOx emissions from the MSWI process, namely: air flow rate of the left 1-1 section of the combustion grate at time t, air flow rate of the right 1-1 section of the combustion grate at time t, air flow rate of the left 1 section of the drying grate at time t, primary combustion chamber temperature at time t, temperature of the left side of the primary combustion chamber at time t, temperature of the right side of the primary combustion chamber at time t, cumulative primary air volume at time t, cumulative secondary air volume at time t, cumulative urea solution volume at time t, cumulative urea solvent supply flow rate at time t, and NOx emission concentration at time t-1, totaling 11 process variables. In the actual industrial dataset of the MSWI process, m=11.

[0011] Given sample matrix The sample mean vector μ is represented as:

[0012]

[0013]

[0014] in Represents the sample matrix The average value of each eigenvector is obtained by averaging the rows, as shown in equation (3). Let x represent the i-th value in vector μ, where i = 1, 2, ..., m, and m represents the number of process variables.ij This represents the value of the i-th process variable in the j-th sample, where j = 1, 2, ..., n1, and n1 represents the number of samples contained within a window of size win_1.

[0015] matrix After subtracting the mean from all samples (decentralization), the result is:

[0016]

[0017] in, This represents the decentralized matrix. Let represent the value of the i-th feature in the j-th sample after decentering, where i = 1, 2, ..., m, j = 1, 2, ..., n1, and m and n1 represent the number of process variables and the number of samples contained in a window of size win_1, respectively.

[0018] Calculate the sample matrix covariance matrix

[0019]

[0020] in express The transpose of .

[0021] Solve the covariance matrix The eigenvalues ​​and their corresponding unit eigenvectors, The eigenvalues ​​λ satisfy

[0022]

[0023]

[0024] Where I is the identity matrix, obtained according to equation (6) eigenvalues

[0025] λ1≥λ2≥…≥λ Q (8)

[0026] Where Q is the number of eigenvalues, substitute the eigenvalues ​​in equation (8) into the following equation to find the eigenvector α corresponding to each eigenvalue.

[0027]

[0028] in Let λ be the covariance matrix. k Let α represent any value among the eigenvalues, and let Ι be the identity matrix. The representation of Ι is shown in equation (7). k α represents any value taken by any vector in the eigenvectors. k =[α1k ,α 2k ,...,α mk ] T (k = 1, 2, ..., Q0);

[0029] Set a cumulative variance contribution rate threshold θ, if it satisfies

[0030]

[0031] Then, the first Q0 principal components are selected for further analysis. Q0 is the number of principal components determined when equation (10) is satisfied. The number of principal components is equal to the number of eigenvalues, so the number of eigenvalues ​​is also Q0 at this time. k This represents any one of the eigenvalues. Currently, in most studies, the cumulative variance contribution rate threshold is selected to be above 0.8, i.e., θ≥0.8. Therefore, the threshold θ is set to 0.85 in this paper.

[0032] A linear transformation is performed using the unit eigenvectors α corresponding to the Q0 eigenvalues ​​as coefficients to obtain the Q0 principal components:

[0033]

[0034] Where α k =[α 1k ,α 2k ,...,α mk ] T (k = 1, 2, ..., Q0),

[0035] sample matrix Substituting into the principal component equation (11), we obtain the principal component values ​​of n1 samples. The j-th sample x j =[x 1j ,x 2j ,...,x mj ] T The k-th principal component value z of (j = 1, 2, ..., n1) kj for:

[0036]

[0037] Where α 1k ,α 2k ,...,α mk Let x represent the 1st, 2nd, ..., mth values ​​in the kth unit eigenvector, respectively. 1j ,x 2j ,...,x mj Let Q1, Q2, ..., m be the process variables in the j-th sample, respectively, where j = 1, 2, ..., n1, i = 1, 2, ..., m, and k = 1, 2, ..., Q0.

[0038] According to equation (12), the k-th principal component z can be... k Represented as z k =[z k1 ,z k2 ,...,z kn1 Then calculate the k-th principal component z. k With variable x i Factor loading ρ(z) k ,x i ), which represents the k-th principal component z. k With variable x i correlation coefficient

[0039]

[0040] Where, α ik Let α be a unit eigenvector, representing the k-th eigenvector. k The i-th dimension in σ. ii It is variable x i The variance, i.e., the covariance matrix The diagonal elements, k = 1, 2, ..., Q0, i = 1, 2, ..., m.

[0041] The factor loading matrix is ​​represented as follows

[0042]

[0043] Then Q0 principal components are paired with the original variable x. i Contribution rate υ of (i = 1, 2, ..., m) i

[0044]

[0045] Among them, the contribution rate υ i This represents the Q0 principal components and the variable x. i The sum of squares of the correlation coefficients. Then the contribution rate υ of the Q0 principal components to each variable is expressed as...

[0046] υ=[υ1,υ2,...,υ m (16)

[0047] Where m represents the sample matrix The number of process variables included. As the complex operating conditions inside the MSWI furnace change, the importance of the variables will change, that is, the contribution rate of the principal components to each variable υ. i This will also change, so the contribution rates υ are reordered in descending order.

[0048] sort(υ) = [υ max,...,υ min (17)

[0049] The `sort()` function sorts the data in descending order. max υ represents the value with the largest contribution rate. min This represents the value with the minimum contribution rate. A threshold ψ is set; if this condition is met...

[0050]

[0051] The value of ψ is consistent with the cumulative variance contribution rate θ, i.e., ψ = 0.85. F is determined based on the value of ψ, where F represents the number of contribution rate values ​​obtained when equation (17) is satisfied. Equation (18) shows that the first F variables in the current window have the greatest correlation with the principal components. The first F key features are selected as the reference vector for identifying the operating conditions in this window, as shown in equation (19), and the corresponding operating conditions are constructed accordingly.

[0052]

[0053] in, Representing the sample matrix respectively The F variables with the strongest correlation are selected, and the window is moved according to a set step size. Key features within the window are detected sequentially, and these key features are stored as reference vectors for working condition identification in the historical working condition database. The historical working condition database is then represented as follows:

[0054] condition_library=[con_1,con_2,...,con_W] (20)

[0055] Where con_1, con_2, ..., con_W represent the reference vectors for identifying different working conditions, and W represents the number of working conditions.

[0056] In this invention, different sliding window sizes and movement step sizes are selected based on specific datasets. The experimental verification phase includes two datasets: a butanizer dataset and an actual industrial dataset of the MSWI process. In the butanizer dataset, based on existing research, the sliding window size is 600. Considering the slow changes in this dataset, the movement step size is set to 300. In the actual industrial dataset of the MSWI process, the sliding window size is 600. Considering the complex and fluctuating operating conditions within the furnace, the movement step size is set to 100.

[0057] (2) Subnetwork construction based on LSTM

[0058] The design of sub-networks is crucial for constructing MNNs. Since recurrent neural networks excel in time series processing and effectively address time-varying characteristics, this paper selects LSTM neural networks as the NOx emission prediction method. LSTM neural networks consist of input gates, forget gates, output gates, and memory gates. Through input, output, and forget operations, the vanishing gradient problem inherent in general neural networks can be effectively overcome.

[0059] The internal structure of LSTM cells is as follows Figure 2 As shown, different doors are marked with different colors. The calculation process for each door is as follows.

[0060] Forgotten Gate:

[0061] f t =σ(W f ·[h t-1 ,x t ]+b f ) (twenty one)

[0062] Input Gate:

[0063] i t =σ(W i ·[h t-1 ,x t ]+b t ) (twenty two)

[0064] Unit status gate:

[0065]

[0066]

[0067] Output gate:

[0068] o t =σ(W o [h t-1 ,x t ]+b o (25)

[0069] Combining equations (21)-(25), the final output of the LSTM neural network is

[0070]

[0071] Where, x t h represents the input variables of the LSTM neural network at time t, i.e., a series of process variables such as air volume, temperature, and urea solution volume at time t. t-1 This represents the output of the LSTM neural network at time t-1. W f W i Wc and W o These are the weight matrices for the forget gate, input gate, cell state gate, and output gate, respectively; b f b i b c and b o These are the biases for the forget gate, input gate, cell state gate, and output gate, respectively; f t i t C t and o t These are the outputs of the forget gate, input gate, cell state gate, and output gate, respectively. This represents the output of the LSTM; σ(·) and tanh(·) represent the activation functions, and their calculation formulas are as follows:

[0072]

[0073]

[0074] Where U represents the input to the activation function in each gate, i.e.

[0075] Forgotten Gate:

[0076] U f =W f ·[h t-1 ,x t ]+b f (29)

[0077] Input Gate:

[0078] U i =W i ·[h t-1 ,x t ]+b i (30)

[0079] Unit states:

[0080] U c =W c ·[h t-1 ,x t ]+b c (31)

[0081] Output gate:

[0082] U o =W o ·[h t-1 ,x t ]+b o (32)

[0083] (3) Collaborative cooperation strategy

[0084] During the testing phase, Euclidean distance was used to measure the test samples. Similarity to historical data:

[0085]

[0086]

[0087]

[0088] in This represents the g-th sample in the test set. and Let these represent the first process variable and the m-th process variable of the g-th sample in the test, respectively. and Let them represent the first process variable and the m-th process variable of the j-th sample in the training set, respectively. Let g represent the distance between the g-th sample in the test set and each sample in the training set, where g = 1, 2, ..., G, j = 1, 2, ..., N, and G and N represent the number of samples in the test set and training set, respectively. Based on equation (35), select the test sample... nearest training sample The operating condition corresponding to this sample is the test sample. Operating condition categories.

[0089] After determining the operating condition category of the test samples, the corresponding sub-networks are activated, and a collaborative strategy is used to integrate the output layer of the MNN:

[0090]

[0091] in, This indicates the NOx emission forecast results. This represents the predicted output of a subnetwork, r = 1, 2, ..., R, where R represents the number of activated subnetworks.

[0092] (4) NOx prediction model based on DMNN

[0093] The DMNN-based NOx emission prediction model for the MSWI process mainly consists of four parts: data preprocessing, PCA-based extraction and dynamic partitioning of operating condition features, sub-network construction, and collaborative cooperation strategies. Figure 3 In the middle, X ori ∈R L×m Let L represent the original dataset, m represent the size of the dataset, and m represent the number of process variables. Representing NOx concentration; First, the original dataset undergoes data preprocessing, resulting in a dataset after smoothing, denoising, and normalization preprocessing, represented as follows: N represents the number of samples. Next, a sliding window operation is performed on the training set, and a PCA-based working condition feature extraction method is used to dynamically select features from the data within the window, thereby constructing a working condition identification reference vector and realizing the dynamic classification of complex working conditions. Then, for sub-tasks under different operating conditions, sub-models based on LSTM neural networks are established. Then, in the testing phase, the similarity between the test samples and historical working conditions is calculated using Euclidean distance, and the corresponding sub-model is activated according to the working condition category. Finally, in the output integration phase, a collaborative strategy is used to integrate the activated sub-networks to obtain the final prediction result.

[0094] ① Data preprocessing

[0095] Noise Reduction and Smoothing: During MSWI, the data acquisition equipment operates in a high-temperature, high-dust environment, and the raw data transmitted to the distributed control system is often accompanied by noise. In order to reduce the interference of noise on data analysis, the Rajda criterion is used to smooth the raw data. As shown in Equation (36):

[0096] |x ori -μ ori |≥3σ ori (37)

[0097] Where, x ori Represents the original data, μ ori and σ ori Let x represent the mean and standard deviation of the variable, respectively. The original data x satisfying equation (37) are... ori Values ​​considered outliers and removed from the original data are represented as X after smoothing and denoising. smo Then X smo ∈R N×m N represents the size of the dataset sample, and m represents the number of process variables in the sample.

[0098] Normalization: In order to eliminate the differences between different units of variables, accelerate the convergence speed of subnetworks and improve training accuracy, the Z-score normalization method is adopted in this paper, as shown in Equation (38).

[0099]

[0100] Where, x i This represents the standardized vector of the i-th dimension variable. and Let X represent the mean and standard deviation of variable i, respectively (i = 1, 2, ..., m); the normalized dataset is represented as X. N×m T N represents the size of the dataset, and m represents the number of process variables in the sample;

[0101] ② Modeling method implementation steps

[0102] Based on the above methods, the proposed DMNN-based NOx emission prediction method for the MSWI process is summarized as follows:

[0103] Training phase

[0104] 1) According to equations (37) and (38), for the original dataset ori_data=[X ori Y ori The dataset is preprocessed and represented as dataset = [XY].

[0105] 2) The training set is divided into working condition segments using a PCA-based working condition feature extraction method. A sliding window of size win is set, and the subset within the window is represented as X. win_1 Construct subset X according to equations (1)-(20) win_1 Key features, according to

[0106] A fixed step size is used to move the sliding window, and the working conditions of the subset are detected in turn. The key features are stored in the historical working condition database as reference vectors for working condition identification.

[0107] 3) An LSTM neural network is used to establish a sub-network model based on operating conditions, and the network parameters are optimized using a trial-and-error method;

[0108] 4) Move the sliding window according to the set step size, and repeat steps 2) to 3).

[0109] Testing phase

[0110] 5) Calculate the similarity between the test sample and the training sample according to equations (33)-(35), determine the working condition category of the test sample based on the minimum distance principle, and activate the corresponding sub-networks in sequence;

[0111] 6) According to equation (36), the outputs of the sub-networks are integrated using a collaborative strategy to obtain the final prediction results of the test samples.

[0112] To verify the effectiveness of the proposed method, this paper selects a butanizer benchmark dataset and an actual industrial dataset from a MSWI plant in Beijing for experimental validation. The experiments were conducted using MATLAB_R2019b.lnk on a computer equipped with an Intel(R) Core(TM) i7-7700 CPU@3.60GHz and 8.00GB of RAM. Furthermore, three evaluation metrics were used to assess the model's prediction accuracy: root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). 2 ).

[0113]

[0114]

[0115]

[0116] in and Let represent the expected output and predicted output of NOx for the j-th sample, respectively. This represents the average value of the model's predicted output. Attached Figure Description

[0117] Figure 1 MSWI process flow diagram

[0118] Figure 2 LSTM cell structure diagram

[0119] Figure 3 DMNN-based NOx emission prediction model for the MSWI process

[0120] Figure 4 Variable contribution rate distribution

[0121] Figure 5 DMNN training results

[0122] Figure 6 DMNN test results

[0123] Figure 7 Regression analysis

[0124] Figure 8 Comparison of prediction errors of different methods

[0125] Figure 9 Error distribution of different methods

[0126] Figure 10 Variable contribution rate distribution

[0127] Figure 11 DMNN training results

[0128] Figure 12 DMNN test results

[0129] Figure 13 Regression analysis

[0130] Figure 14 Comparison of prediction errors

[0131] Figure 15 Error distribution of different methods Detailed Implementation

[0132] This invention first uses a butanizer benchmark industrial experiment to verify the effectiveness of the DMNN method; then it uses DMNN to predict the NOx emission concentration of an actual MSWI plant.

[0133] (1) Prediction of butane concentration at the bottom of the butane removal tower based on DMNN

[0134] The original dataset for the butane debutanizer contains 7 variables and 2394 samples. Table 1 provides a detailed description of these variables. Considering the dynamic characteristics present in the reaction process, a set of optimal enhancement variables is selected for butane concentration prediction, as shown in Equation (42).

[0135]

[0136] Table 1 Description of variables in the butanizer tower

[0137]

[0138] The dataset was divided into training and test sets in a 7:3 ratio. The sliding window size was set to 600, and the window movement step was 300.

[0139] ① PCA-based feature extraction and dynamic segmentation of operating conditions

[0140] Five work condition subsets were obtained from the training set using a PCA-based work condition feature extraction method. The contribution rates of the principal components to each variable under each work condition are shown below. Figure 4 As shown.

[0141] Figure 4 This indicates that the contribution rate of principal components to each variable is different in different windows, meaning that the importance of variables varies in different windows. To further visualize the importance of each variable, the variables are sorted in descending order according to their cumulative contribution rate, as shown in Table 2.

[0142] Table 2. Ranking of variable contribution rates within different windows.

[0143]

[0144] Table 2 shows that the sample distribution is different in different windows, and different working conditions can be distinguished based on the importance of variables. Therefore, the cumulative contribution rate threshold ζ = 0.85 was determined in this paper, and variables with a cumulative contribution rate higher than ζ were established as key features. The key features were used as reference vectors for working condition identification and stored in the historical working condition database.

[0145] ②Prediction of butane concentration at the bottom of the butane removal tower based on DMNN

[0146] After determining the various operating conditions, an LSTM-based sub-network model driven by the operating conditions is established. The results of the bottom butane prediction method based on DMNN on the training and test sets are as follows. Figure 5 and Figure 6 As shown in the figure, the predicted values ​​of the proposed method can closely approximate the actual sampled values.

[0147] To further verify the effectiveness of the proposed method, the DMNN algorithm was compared with four other algorithms—RBF, LSSVM, DBN, and LSTM. Table 3 lists the comparison results of the prediction performance of each method.

[0148] Table 3 Comparison of predicted butane concentration at the bottom of the butane removal tower

[0149]

[0150] Compared with RBF, LSSVM, and DBN, LSTM neural networks show a significant advantage in model accuracy, indicating that the memory properties of LSTM can effectively handle time series data. Building upon this, a PCA-based operating condition feature extraction method further improves the accuracy of butane concentration prediction. Compared to other algorithms, the proposed method achieves an average performance improvement of 65.35% (RMSE), 68.48% (MAPE), and 39.91% (R²). 2 ). Figure 7 This indicates that the butane concentration prediction based on DMNN can better fit the changing trend of the actual value and has high modeling accuracy.

[0151] Similarly, the prediction errors of different methods are as follows: Figure 8 As shown. Figure 8 The superior prediction accuracy of the proposed method is clearly demonstrated. To further evaluate the prediction performance, the error distribution histograms of the five methods are shown below. Figure 9 As shown, compared with other methods, the prediction error of the DMNN method is closer to zero, demonstrating the effectiveness of the method.

[0152] (2) NOx emission prediction for the MSWI process

[0153] This paper presents an experiment based on actual industrial data from a MSWI plant in Beijing. After preprocessing the raw data, samples were taken at 10-second intervals, resulting in 2215 data sets. The first 1550 sets were used for training, and the remaining data were used for testing. Based on the MSWI process and operating characteristics, 10 process variables at time t and the NOx emission concentration at time t-1 were selected as inputs to the prediction model, as shown in Table 4.

[0154] Table 4 Description of NOx Prediction Model Variables

[0155]

[0156] The sliding window size is 600. Considering the frequent changes in the operating conditions of the MSWI process, the window movement step size is set to 100 in this paper.

[0157] ① PCA-based feature extraction and dynamic segmentation of operating conditions

[0158] Using a PCA-based feature extraction method, 11 subsets of work conditions were obtained from the training set. The contribution rates of the principal components to each variable under each work condition are as follows: Figure 10 As shown.

[0159] Figure 10 The results show that the importance distribution of variables varies significantly under different operating conditions, which is closely related to the actual MSWI process. The MSWI operation is complex and variable due to factors such as feed rate, feed composition, and operating methods. As time progresses, the contribution rate of principal components to each variable differs, meaning that the importance of variables varies across different windows. To further visualize the importance of each variable, they are sorted in descending order based on their cumulative contribution rate, as shown in Table 5.

[0160] Table 5. Ranking of variable contribution rates within different windows.

[0161]

[0162] As shown in Table 5, in operating conditions 1, 2, and 6-11, the grate airflow and primary combustion chamber temperature play a crucial role, indicating that oxygen and temperature are currently the main operating factors and have a significant impact on NOx emissions. In operating conditions 3-5, in addition to airflow and temperature, the amount of urea diluent added also becomes a significant factor that cannot be ignored. Whether analyzed from the perspective of NOx generation and emission mechanisms or variable distribution structure, these variables have complex nonlinear relationships with NOx emission prediction. The PCA-based dynamic operating condition feature extraction method decomposes complex operating conditions into simpler, more manageable conditions by analyzing changes in variable importance, thus reducing the difficulty of data analysis.

[0163] ② NOx emission prediction based on DMNN

[0164] The PCA-based operating condition feature extraction method divides complex operating conditions into a series of sub-operating conditions, and then uses LSTM to build a sub-network model driven by operating conditions. The NOx emission prediction results based on DMNN on the training and test sets are as follows: Figure 11 As shown in Table 12, the proposed method achieves good fitting results on both the training and test sets. However, the prediction results for test samples distributed in the 550-650 range exhibit significant deviations. This is related to the drastic and frequent fluctuations in the actual MSWI process conditions, leading to biased predictions for some samples. To further verify the effectiveness of the proposed method, the DMNN algorithm is compared with four other algorithms—RBF, LSVVM, DBN, and LSTM neural networks. Table 6 presents the comparison results of the prediction performance of each method.

[0165] Table 6 Comparison of NOx emission prediction results for the MSWI process

[0166]

[0167]

[0168] Table 6 shows that LSTM neural networks still exhibit significant advantages compared to RBF, LSSVM, and DBN, because LSTM can better handle time series prediction tasks. Furthermore, the PCA-based working condition feature extraction method dynamically partitions complex working conditions, decomposing the prediction task into sub-tasks under different working conditions, further improving NOx prediction accuracy. Compared to other algorithms, the proposed method achieves average performance improvements of 23.25% (RMSE), 26.4% (MAPE), and 8.65% (R²). 2 ). Figure 13 This indicates that the NOx emission prediction results based on DMNN can better fit the changing trend of the actual values ​​and have high prediction accuracy.

[0169] Similarly, the prediction errors of different methods are as follows: Figure 14 As shown in the figure. Compared with other algorithms, the proposed method has smaller error fluctuations and higher prediction accuracy. To further evaluate the prediction performance, the error distribution histograms of the five methods are shown in the figure. Figure 15 As shown, compared with other methods, the prediction error of the DMNN method is closer to zero, demonstrating the effectiveness of the method.

[0170] The comparative results show that the DMNN model proposed in this paper can be effectively applied to industrial benchmark tests of butanizer towers and actual industrial data from MSWI plants. Based on the above experimental results, this invention has the following significant advantages and beneficial effects:

[0171] 1) PCA-based feature extraction and dynamic partitioning of working conditions: Unlike traditional clustering methods, this method can effectively mine key features under complex working conditions and partition complex working conditions by analyzing the importance of features, thereby simplifying the complexity of the task to be processed.

[0172] 2) NOx Prediction Model Based on DMNN: By decomposing complex operating conditions, a sub-network model driven by sub-operating conditions is constructed. The output layer adopts a collaborative strategy for integration. Tables 3 and 6 show that the proposed method achieves the best RMSE, MAPE, and R... 2 The value has high prediction accuracy.

Claims

1. A method for intelligent prediction of NOx emissions from a MSWI process based on a dynamic modular neural network. The NOx emission concentration prediction equipment includes thermocouple temperature sensors, airflow sensors, liquid flow sensors, a continuous emission monitoring system, a distributed control system, and a host computer. The continuous emission monitoring system includes a nitrogen oxide concentration detector. These detectors (nitrogen oxide concentration detector, thermocouple temperature sensor, airflow sensor, and liquid flow sensor) are connected to the distributed control system via a fieldbus and transmit the data collected by the sensors to the I / O communication module in the distributed control system. Through the switching selection, amplifier, and A / D converter in the communication module, the analog voltage signal is converted into a digital signal that the computer can recognize and communicates with the host computer via an industrial Ethernet. The host computer acquires the MSWI process data in real time and stores the collected data in a structured query language server database. Its features are, Includes the following steps: Step 1: PCA-based working condition feature extraction method; A fixed-size sliding window is used to detect changes in operating condition features and to dynamically divide operating conditions. The PCA-based operating condition feature extraction method reflects the current operating condition of the data by detecting key features within the sliding window. The algorithm is described as follows: Set the sliding window size to Assume the observation sample matrix within the first sliding window is... Indicated, denoted as (1)； Where m represents the number of process variables in the sample. Indicates size is The number of samples contained within the window. These represent the m process vectors in the sample matrix, which are the m inputs to the prediction model. When using butanizer tower data to build a predictive model These represent the top temperature, top pressure, top reflux flow rate, next stage flow rate, and sensitive plate temperature at time t; the sensitive plate temperatures at times t-1, t-2, and t-3; the average values ​​of bottom temperatures A and B at times t; and the butane concentrations at times t-1, t-2, t-3, and t-4, totaling 13 process variables in the butane removal column data. ; When using actual industrial datasets of MSWI processes to build predictive models These represent the process variables related to NOx emissions from the MSWI process, namely: air flow rate in the left 1-1 section of the combustion section grate at time t; air flow rate in the right 1-1 section of the combustion section grate at time t; air flow rate in the left 1 section of the drying section grate at time t; primary combustion chamber temperature at time t; temperature on the left side of the primary combustion chamber at time t; temperature on the right side of the primary combustion chamber at time t; cumulative primary air volume at time t; cumulative secondary air volume at time t; cumulative urea solution volume at time t; cumulative urea solvent supply flow rate at time t; and NOx emission concentration at time t-1, totaling 11 process variables, which are represented in the actual industrial dataset of the MSWI process. ; Given sample matrix Sample mean vector Represented as: (2)； (3)； in Represents the sample matrix The average value of each eigenvector is obtained by averaging the rows, as shown in equation (3). Representing vectors The i-th value in m represents the number of process variables. This represents the value of the i-th process variable in the j-th sample. , Indicates size is The number of samples contained within the window; matrix After subtracting the mean from all samples, the result is: (4)； in, This represents the decentralized matrix. This represents the value of the i-th feature in the j-th sample after centering. , ,m and These represent the number of process variables and their dimensions, respectively. The number of samples contained within the window; Calculate the sample matrix covariance matrix : (5)； in express The transpose of the matrix; Solve the covariance matrix The eigenvalues ​​and corresponding unit eigenvectors, eigenvalues satisfy (6)； (7)； in As an identity matrix, according to equation (6) we obtain eigenvalues (8)； Where Q is the number of eigenvalues, substitute the eigenvalues ​​in equation (8) into the following equation to find the eigenvector corresponding to each eigenvalue. ; (9)； in Let covariance matrix be the variance matrix. Represents any one of the eigenvalues. As a unit array, The representation is shown in equation (7). This represents any value that a vector in the eigenvectors can take. , ; Set a threshold for cumulative variance contribution rate If satisfied (10)； Then choose the previous one Further analysis of the principal components was conducted. To satisfy the number of principal components determined by equation (10), the number of principal components is equal to the number of eigenvalues, so the number of eigenvalues ​​is also equal at this time. , The threshold represents any value among the feature values. The value was determined to be 0.85; by Unit eigenvectors corresponding to each eigenvalue Perform a linear transformation on the coefficients to obtain Principal components: (11)； in ; sample matrix Substituting into principal component equation (11), we get Principal component values ​​of sample j, the j-th sample The kth principal component value for: (12)； in Let represent the 1st, 2nd, ..., mth values ​​in the kth unit eigenvector, respectively. Let each represent the 1st, 2nd, ..., mth process variables in the j-th sample. , , ; According to equation (12), the k-th principal component is... Represented as Then calculate the k-th principal component. With variables Factor loading It represents the k-th principal component. With variables correlation coefficient (13)； in, Let be the unit eigenvector, representing the k-th eigenvector. The i-th dimension in It is a variable The variance, i.e., the covariance matrix diagonal elements, , ; The factor loading matrix is ​​represented as follows (14)； but Each principal component is paired with the original variables. Contribution rate (15)； Contribution rate express Principal components and variables The sum of the squares of the correlation coefficients, then Contribution rate of each principal component to each variable Represented as (16)； in Represents the sample matrix The number of process variables included; as the complex operating conditions inside the MSWI furnace change, the importance of the variables will change, that is, the contribution rate of the principal components to each variable. This will also change, therefore the contribution rate is ranked in descending order. Reorder (17)； in The function's purpose is to sort data in descending order. This represents the value with the largest contribution rate. This represents the value with the smallest contribution rate; a threshold is set. If the conditions are met (18)； The value of and the cumulative variance contribution rate Maintain consistency. ,in accordance with The value F is determined, where F represents the number of contribution rate values ​​obtained when satisfying equation (17). Equations (16) and (17) indicate that the first F variables have the greatest correlation with the principal components within the current window. The first F key features are selected as the reference vector for identifying the operating conditions within the window, as shown in equation (19), and the corresponding operating conditions are constructed accordingly. (19)； in, Representing the sample matrix respectively The F variables with the strongest correlation are selected according to a set step size. Moving the window, sequentially detecting key features within the window, and storing these key features as reference vectors for operating condition identification in the historical operating condition database, the historical operating condition database is then represented as follows: (20)； in These represent the working condition identification reference vectors corresponding to different working conditions, and W represents the number of working conditions. Different sliding window sizes and step sizes are selected based on specific datasets. The experimental verification phase includes two datasets: the butanizer dataset and the MSWI process actual industrial dataset. In the butanizer dataset, the sliding window size is 600 and the step size is set to 300. In the MSWI process actual industrial dataset, the sliding window size is 600 and the step size is set to 100. Step 2: Construction of sub-networks based on LSTM; LSTM neural networks were chosen as the NOx emission prediction method. An LSTM neural network consists of input gates, forget gates, output gates, and memory gates. The calculation process for each gate is shown below: Forgotten Gate: (21)； Input Gate: (22)； Unit status gate: (23)； (24)； Output gate: (25)； Combining equations (21)-(25), the final output of the LSTM neural network is (26)； in This represents the input variables of the LSTM neural network at time t, namely the cumulative series of airflow, temperature, and urea solvent supply flow rate at time t. This represents the output of the LSTM neural network at time t-1; , , and These are the weight matrices for the forget gate, input gate, cell state gate, and output gate, respectively. , , and These are the biases for the forget gate, input gate, cell state gate, and output gate, respectively. , , and These are the outputs of the forget gate, input gate, cell state gate, and output gate, respectively. This represents the output of the LSTM. and The activation function is represented by the following formula: (27)； (28)； in, This represents the input to the activation function in each gate, i.e. Forgotten Gate: (29)； Input Gate: (30)； Unit states: (31)； Output gate: (32)； Step 3: Collaborative cooperation strategy; During the testing phase, Euclidean distance was used to measure the test samples. Similarity to historical data: (33)； (34)； (35)； in This represents the g-th sample in the test set. and Let them represent the first process variable and the m-th process variable of the g-th sample in the test set, respectively. and Let them represent the first process variable and the m-th process variable of the j-th sample in the training set, respectively. This represents the distance between the g-th sample in the test set and each sample in the training set. , , and These represent the number of samples in the test set and the training set, respectively; according to equation (35), select samples that are the same size as the test samples. nearest training sample Then the working condition corresponding to that sample is the test sample. The operating condition category; After determining the operating condition category of the test samples, the corresponding sub-networks are activated, and a collaborative strategy is used to integrate the output layer of the MNN: (36)； in This indicates the NOx emission forecast results. This represents the predicted output of the subnetwork. R represents the number of activated subnetworks; Step 4: DMNN-based NOx emission prediction model for the MSWI process; The DMNN-based NOx emission prediction model for the MSWI process consists of four parts: data preprocessing, PCA-based extraction and dynamic partitioning of operating conditions, sub-network construction, and collaborative cooperation strategy. Let L represent the original dataset, m represent the size of the dataset, and m represent the number of process variables. Representing NOx concentration; First, the original dataset undergoes data preprocessing, resulting in a dataset after smoothing, denoising, and normalization preprocessing. N represents the number of samples. Next, a sliding window operation is performed on the training set, and a PCA-based working condition feature extraction method is used to dynamically select features from the data within the window, thereby constructing a working condition identification reference vector and realizing the dynamic classification of complex working conditions. Then, for sub-tasks under different operating conditions, sub-models based on LSTM neural networks are established. Then, in the testing phase, the similarity between the test samples and historical working conditions is calculated using Euclidean distance, and the corresponding sub-model is activated according to the working condition category. Finally, in the output integration phase, a collaborative strategy is used to integrate the activated sub-networks to obtain the final prediction result. During MSWI, the data acquisition equipment operates in a high-temperature and high-dust environment, and the raw data transmitted to the distributed control system is often accompanied by noise. In order to reduce the interference of noise on data analysis, the Rajda criterion is used to smooth the raw data, as shown in Equation (37): (37)； in, Represents the original data. and Let represent the mean and standard deviation of the variables, respectively; the original data satisfying equation (37) Values ​​considered outliers and removed from the original data are represented as follows: ,but N represents the size of the dataset, and m represents the number of process variables in the sample; The Z-score standardization method is adopted, as shown in equation (38): (38)； in, This represents the standardized vector of the i-th dimension variable. and Let represent the mean and standard deviation of variable i, respectively. The normalized dataset is represented as N represents the size of the dataset, and m represents the number of process variables in the sample; The specific implementation steps of the DMNN-based method for predicting NOx emissions from the MSWI process are as follows: Training phase 1) Based on equations (37) and (38), the original dataset is processed. Preprocessing is performed, and the preprocessed dataset is represented as follows: ; 2) The training set is divided into working condition segments using a PCA-based working condition feature extraction method, with a set size of [size missing]. A sliding window, where a subset within the window is represented as Construct subsets according to equations (1)-(20) The key features are used to move the sliding window at a fixed step size to detect the working conditions of the subset in turn, and the key features are stored in the historical working condition database as reference vectors for working condition identification. 3) An LSTM neural network is used to establish a sub-network model based on operating conditions, and the network parameters are optimized using a trial-and-error method; 4) Move the sliding window according to the set step size, and repeat steps 2) to 3); Testing phase 5) Calculate the similarity between the test sample and the training sample according to equations (33)-(35), determine the working condition category of the test sample based on the minimum distance principle, and activate the corresponding sub-networks in sequence; 6) According to equation (36), the outputs of the sub-networks are integrated using a collaborative strategy to obtain the final prediction results of the test samples.

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