An intelligent detection method for the nitrogen content in the effluent of urban sewage treatment process based on cascaded modular neural network

Abstract

The present invention relates to an intelligent detection method for the nitrogen content in the effluent of the urban sewage treatment process based on a cascaded modular neural network. First, the input variables of the model are selected through mutual information, and Module 1 is established to predict the effluent NH4-N. Then, considering the high correlation between the effluent NH4-N and the effluent TN, the predicted value of the effluent NH4-N in Module 1 is combined with other easily measurable variables to design Module 2 for predicting the effluent TN. In addition, to ensure the efficiency and generalization performance of the entire soft measurement model based on HMN, the two modules are constructed by a radial basis function (GM-RBF) network based on the growth and merging mechanism. Through the node growth and merging strategy and the second-order learning algorithm, the computational efficiency and generalization ability of the model are improved. Finally, the effectiveness of the soft measurement model based on HMN is evaluated through actual industrial data, and the present invention effectively solves the problem that it is difficult to accurately detect the ammonia nitrogen and total nitrogen in the effluent in real time during the urban sewage treatment process due to environmental or instrument limitations.

Description

Technical Field

[0001] The present invention relates to an intelligent detection method for the nitrogen content in the effluent of the urban sewage treatment process; a prediction model for the nitrogen content in the effluent based on a cascaded modular neural network is established, realizing the synchronous prediction of ammonia nitrogen in the effluent and total nitrogen in the effluent. It belongs to both the field of urban sewage treatment and the field of intelligent modeling. Background Art

[0002] Driven by the rapid growth of population and economy, the global demand for sustainable water supply is increasing continuously, and the effective treatment of sewage helps the recycling of water. Therefore, sewage treatment has become a hot topic in academia and industry in the past few decades, and the key effluent quality plays an important guiding role in the monitoring and control of the sewage treatment process. However, due to technical and economic limitations, it is still difficult to obtain reliable measurement values of some effluent parameters online, and these parameters include the nitrogen content parameters in the effluent, such as ammonia nitrogen (NH4-N) and total nitrogen (TN), which are the key nutrients leading to eutrophication. Therefore, the accurate prediction of NH4-N and TN has important theoretical significance and application value for improving the nitrogen removal efficiency of wastewater treatment plants (WWTP). Summary of the Invention

[0003] The purpose of the present invention is to propose an intelligent detection method for the nitrogen content in the effluent of the urban sewage treatment process based on a hierarchical modular neural network (HMN), and use the HMN to construct a prediction model for the nitrogen content in the effluent to achieve accurate prediction of the nitrogen content in the effluent.

[0004] The present invention adopts the following technical solutions and implementation steps:

[0005] (1) Establish the HMN, and the design process is as follows:

[0006] ① Module 1 is established by an RBF neural network, and different input signals are processed according to different tasks. The input of Module 1 is expressed as

[0007] u = [u1, u2,..., u n T (1)

[0008] where After that, the output of Module 1 established based on the RBF neural network is expressed as:

[0009]

[0010] where c j and σ j ​are the center and width of the j-th hidden layer node of the RBF neural network in Module 1, and w j represents the corresponding output weight, and J1 is the number of hidden layer nodes of the RBF neural network;

[0011] ② Similarly, Module 2 is also established by an RBF neural network. Different from the construction of traditional modular neural networks, the input of Module 2 includes not only the input signals from the external environment but also the output of Module 1. Therefore, the input layer is expressed as:

[0012]

[0013] where Therefore, the output of Module 2 is expressed as

[0014]

[0015] where c j and σ j are the center and width of the j-th hidden layer node of the RBF neural network in Module 2, and w j represents the corresponding output weight, and J2 is the number of hidden layer nodes of the RBF neural network;

[0016] The HMN is constructed according to the signal propagation direction. First, Module 1 is trained based on the training samples. Then, the predicted value of the effluent NH4-N in Module 1 is added to the input of Module 2 to complete the sub-network design. During this period, the convergence and generalization of the sub-network are particularly important for the HMN;

[0017] (2) RBF self-organization structure design method based on growth and merging mechanism

[0018] To ensure the compactness and generalization of the sub-network and the HMN, an RBF self-organization structure design method based on growth and merging mechanism is proposed. Taking the first RBF sub-network as an example, initially, there are no nodes in the RBF hidden layer. To eliminate the error between the network output and the desired output, the error correction algorithm is used to continuously add RBF hidden layer nodes. Therefore, in each iteration, each RBF node is located at the highest error peak or the lowest error trough;

[0019]

[0020]

[0021] where z p and are the desired output and the actual output of the network for the p-th sample respectively, j max represents the training sample with the largest absolute error at the j-th iteration, and P represents the size of the training samples in Module 1;

[0022] Then, initialize the center vector and connection weights corresponding to the j-th RBF node according to the j-th max training sample:

[0023]

[0024]

[0025] The width of the hidden layer nodes is calculated according to the minimum Euclidean distance between the newly added node and other existing RBF nodes

[0026] σ j = min{dist(c j , c i≠j )} (9)

[0027] Each time the network structure changes, a second-order algorithm is used to adjust all parameters. Due to the particularity of the activation function of the RBF neural network, its nodes perform local learning, which is determined by the corresponding centers and widths. Therefore, if two RBF hidden layer nodes are adjusted to the closest distance during the parameter adjustment process, these two nodes may provide approximately the same response to some input information. Therefore, a merging strategy is proposed to reduce the redundancy of the structure;

[0028] For example, if the k-th node and the l-th node satisfy condition (10), then these two nodes will be merged into a new node:

[0029] dist(c k , c l ) < min{σ k , σ l}, k ≠ l. (10)

[0030]

[0031] σ k,l = max{σ k , σ l} (12)

[0032] w k,l = w k + w l (13)

[0033] where c k,l , σ k,l and w k,l are the center, width and weight of the newly added node, respectively;

[0034] During the construction of the sub-network, the growth and merging of the hidden layer nodes are repeated until the desired training accuracy is achieved, thus establishing a structurally compact HNM;

[0035] (3) Adjust the parameters using a second-order algorithm

[0036] To accelerate the convergence rate and improve the training accuracy of the HMN, a second-order learning algorithm is used to adjust the parameters of the sub-network, including the centers, widths, and connection weights of the hidden layer nodes. The update rule for the parameters is given by the following equation

[0037] θ t+1 = θ t - (Q t + μ t I) -1 g t (14)

[0038] where θ t+1 and θ t represent all the parameters at time t + 1, Q t represents the Hessian matrix at time t, μ t is the learning rate at time t, I is the identity matrix, and g t is the gradient vector at time t;

[0039] To reduce the computational complexity, the quasi-Hessian matrix Q is expressed as the sum of p quasi-Hessian sub-matrices q, and the gradient vector g is transformed into the sum of p gradient sub-vectors η:

[0040]

[0041]

[0042] where q p is the quasi-Hessian sub-matrix, η p is the gradient sub-vector, and both q p and η p are obtained from the Jacobian vector j p :

[0043]

[0044]

[0045]

[0046] where H is the number of parameters to be adjusted, including the centers, widths, and connection weights of the hidden layer nodes. Taking the RBF sub-network with j hidden layer nodes in Module 1 as an example, H = (n + 2) * j, where j represents the number of neurons in the hidden layer and n represents the number of input nodes. In addition, the elements of the Jacobian row vector can be expressed as

[0047]

[0048]

[0049]

[0050] Note that the sub-network structure and parameter adjustment method in Module 2 are the same as those in Module 1.

[0051] (4) Prediction model based on HMN

[0052] The specific implementation of the prediction model based on HNM is as follows:

[0053] ① Preprocess the data collected from the real urban sewage treatment plant and represent it as D = {(x1, y1), (x2, y2),..., (x P+S , y P+S )}, and then divide the data set into a training set and a test set, denoted as D1 = {(x1, y1), (x2, y2),..., (x P , y P )}, D2 = {(x P+1 , y P+1 ), (x2, y P+2 ),..., (x P+S , y P+S )};

[0054] ② Based on mutual information analysis, determine the input variables of the effluent NH4-N and effluent TN sub-network modules respectively;

[0055] ③ The input and output vectors used to construct Module 1 are represented as {u1, u2,..., u P} and {z1, z2,..., z P}, and then use RBF based on the growth and merging mechanism to establish the sub-network in Module 1. The output of Module 1 is represented as

[0056] ④ Add the predicted output of Module 1 to the input vector of Module 2. Then the input of Module 2 is represented as The corresponding output of Module 2 is {y1, y2,..., y P};

[0057] During the training process of the above two modules, the learning rate μ is set to 0.01, and the number of iterations is set to 50. When the model completes the last iteration, the HMN model training is completed, and it is applied to the test set to realize the prediction of effluent NH4-N and effluent TN.

[0058] (5) Prediction of Effluent NH4-N and Effluent TN Concentrations

[0059] The present invention has the following obvious advantages and beneficial effects:

[0060] 1 The HMN prediction model has high computational efficiency. When predicting effluent NH4-N (Table III), the model speed of this method is superior to the other four methods, demonstrating the computational efficiency of the GM-RBF network. Regarding effluent TN (Table V), although the total modeling time (4.4381 s) is slightly longer than that of ELM (2.4167 s) and ErrCor (3.6878 s), this is acceptable because the constructed HMN-based prediction model is for two target parameters.

[0061] 2 The HMN prediction model has a compact structure. The compactness of the model is measured by the number of hidden layer nodes in the RBF sub-network. Table III shows that the number of hidden layer nodes in HMN is 18, achieving the prediction of effluent NH4-N and effluent TN. Compared with other methods, GM-RBF with 7 hidden layer nodes has higher prediction performance.

[0062] 3 HMN has high generalization ability. The generalization ability of the HMN model is evaluated by its RMSE, MAPE, and R 2 on the test set. Tables III and V show that the HMN-based prediction model has higher test accuracy compared with other methods, indicating that the model has good generalization performance. Description of the Drawings

[0063] Figure 1 is the structure diagram of HMN;

[0064] Figure 2 is the framework of the nitrogen content prediction model for effluent based on HMN;

[0065] Figure 3 is the correlation between effluent NH4-N and input variables;

[0066] Figure 4 is the correlation between effluent TN and input variables;

[0067] Figure 5 is the prediction result of effluent NH4-N by HMN on the test set;

[0068] Figure 6 is the prediction error of effluent NH4-N by HMN on the test set;

[0069] Figure 7 is the prediction result of effluent TN by HMN on the test set;

[0070] Figure 8is the prediction error of the effluent TN of HMN on the test set; Detailed implementation mode

[0071] The present invention uses a training data set to establish an HMN neural network model for predicting the concentration of nitrogen content in the effluent; uses a test data set to verify the accuracy of the HMN neural network prediction model for predicting the nitrogen content in the effluent.

[0072] As an embodiment, industrial data from a sewage treatment plant in Beijing is used to evaluate the effectiveness of the method proposed by the present invention. The industrial data set contains 365 samples and a total of 23 variables. The detailed description is shown in Table I. After preprocessing, 270 samples are used for training, and the remaining 90 samples are used for testing. The simulation is carried out in the environment of Microsoft Windows 10.0 and MATLAB 2016b.

[0073] (1) Construction of the HMN model

[0074] The construction of the HMN for urban sewage treatment process applications includes two parts: determining the input of the HMN through feature selection and the sub-network design based on the GM-RBF network.

[0075] In order to reduce the computational complexity and improve the accuracy, the variables highly correlated with the output are used as the input of the HMN. The mutual information metric is used to measure the correlation between the nitrogen content parameter in the effluent and other variables. The mutual information between variable x and variable y is calculated by the following formula

[0076]

[0077] where P(x,y) represents the joint probability distribution of variable x and variable y, and P(x) and P(y) represent the marginal probability densities.

[0078] Select the variables highly correlated with the nitrogen content in the effluent as the input of the model, such as Figure 4 and Figure 5 As shown, therefore, the influent temperature (T_in), effluent temperature (T_ef), influent total phosphorus (TP_in), mixed liquor suspended solids (MLSS), influent TN (TN_in) and influent NH4-N (NH4-N_in) are selected as the input variables of module 1. In addition, the influent temperature (T_in), effluent temperature (T_ef), effluent NH4-N (NH4-N_ef), influent TN (TN_in), influent TP (TP_in) and MLSS are used as the input of module 2. After determining the input, the training samples are used to construct the HMN. The detailed composition of the HMN is shown in Table II.

[0079] (2) Prediction performance of the HMN model

[0080] To evaluate the effectiveness of the method, the root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R 2 ) mean percentage error were used to quantitatively evaluate the prediction accuracy, and the calculations are as follows:

[0081]

[0082]

[0083]

[0084] where y i and represent the true value and predicted value of the i-th test sample, respectively, represents the average value of all test samples, and S represents the size of the test samples

[0085] Figure 5 is the predicted result of the effluent NH4-N. The RMSE is 0.6241, the MAPE is 10.6320%, and the R 2 value is 0.9640. The predicted results of the effluent TN are as Figure 7 shown (RMSE 0.3758, MAPE 2.6535%, R2 0.9885). The predicted values of HMN are almost the same as the actual values, indicating that the proposed method has a high prediction accuracy for the nitrogen content in the effluent.

[0086] In addition, to verify the influence of the predicted value of the effluent NH4-N on the prediction performance of the effluent TN, the predicted value of the effluent NH4-N was removed from the input of the module 2GM-RBF neural network, and the remaining variables were used to predict the effluent TN. The results show that introducing the predicted value of the effluent NH4-N in the input variables can improve the prediction accuracy of the effluent TN. Table III provides the detailed comparison results.

[0087] (3) Comparison results of the HMN model with other algorithms

[0088] To further evaluate the effectiveness of the proposed HMN framework and GM-RBF network, currently common algorithms such as generalized growing and pruning RBF (GGAP-RBF), extreme learning machine (ELM), error correction (ErrCor), and adaptive particle swarm optimization RBF (APSO-RBF) were selected for comparison. These algorithms were compared in terms of modeling speed, modeling accuracy, and model compactness.

[0089] ① Prediction of the effluent NH4-N

[0090] All prediction models are established based on the same training data. The training and test results of the models are shown in Table IV. It can be seen that the network structures of GGAP and ELM are relatively complex. Although the modeling speed of ELM is faster than most other methods, due to its randomness, the ELM algorithm requires multiple trials to achieve better accuracy. In contrast, ErrCor, APSO-RBF, and HMN have relatively smaller architectures. Among these three models, the APSO-RBF model has the lowest prediction accuracy, while HMN has a higher prediction accuracy and is better than ErrCor, indicating the effectiveness of the GM-RBF network growth and merging mechanism.

[0091] ② Prediction of effluent TN

[0092] To illustrate the effectiveness of HMN, the predicted value of effluent NH4-N in the input of the module 2 GM-RBF neural network is removed. The inputs of the five prediction models include influent temperature (T_in), effluent temperature (T_ef), influent TN (TN_in), influent TP (TP_in), and MLSS. The comparison results of each model on the training set and test set are shown in Table V. Similar to the prediction of effluent NH4-N, the prediction accuracies of GGAP, ELM, and APSO-RBF are poor, and the model complexity is high. The structures of the ErrCor and HMN models are relatively compact and have high prediction accuracies. The training time of HMN consists of two parts, 2.3034 seconds for module 1 and 2.1367 seconds for module 2. Although the total modeling time is slightly longer than that of ELM and ErrCor, the constructed model is for two effluent parameters. Similarly, although the model based on HMN requires two more RBF hidden layer nodes than ErrCor, these RBF nodes include the nodes used to construct module 1 to obtain the predicted effluent NH4-N. Therefore, in the online prediction problems of effluent NH4-N and effluent TN, the model based on HMN shows better prediction accuracy than ErrCor with 18 RBF nodes.

[0093] Table I Description of input variables

[0094]

[0095] Table II Structure of HMN

[0096]

[0097] Table III Comparison results of prediction performance of effluent TN under different input variables

[0098]

[0099] Table IV Comparison results of effluent NH4-N prediction of different models

[0100]

[0101] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. It should be noted that the above are only specific embodiments of the present invention and do not limit the present invention. All modulations and optimizations made within the spirit and principle of the present invention shall fall within the scope covered by the claims of the present invention.

Claims

1. An intelligent detection method for the nitrogen content in the effluent of the urban sewage treatment process based on a cascaded modular neural network, characterized in that, It includes the following steps: Step 1: Establish a cascaded modular neural network; Module 1: Module 1 is established by an RBF neural network, which processes different input signals according to different tasks. The input of Module 1 is expressed as u = [u1, u2,..., u n T (1)​ Among them x1, x2,..., x N represent all the auxiliary variables that affect the nitrogen content in the effluent. These variables include: influent pH (PH_in), effluent pH (PH_ef), influent suspended solid concentration (SS_in), effluent suspended solid concentration (SS_ef), influent biochemical oxygen demand (BOD_in), effluent biochemical oxygen demand (BOD_ef), influent chemical oxygen demand (COD_in), effluent chemical oxygen demand (COD_ef), sludge settling ratio in the biological tank (SV), mixed liquor suspended solids in the biological tank (MLSS), dissolved oxygen in the biochemical tank (DO), influent oil (Oil_in), effluent oil (Oil_ef), influent ammonia nitrogen (NH4-N_in), effluent ammonia nitrogen (NH4-N_ef), influent chromaticity (Colour_in), effluent chromaticity (Colour_ef), influent total nitrogen (TN_in), effluent total nitrogen (TN_ef), influent total phosphorus (TP_in), effluent total phosphorus (TP_ef), influent water temperature (T_in), effluent water temperature (T_ef), N represents the total number of auxiliary variables, u1, u2,..., u n represent the auxiliary variables that affect the ammonia nitrogen in the effluent, including: influent water temperature (T_in), effluent water temperature (T_ef), influent total phosphorus (TP_in), mixed liquor suspended solids in the biological tank (MLSS), influent total nitrogen (TN_in), and influent NH4-N (NH4-N_in), n represents the number of input variables in Module 1; then, the output of Module 1 established based on the RBF neural network is expressed as: where \(u\) represents the input vector, \(\varphi(\cdot)\) represents the radial basis kernel function, \(\exp(\cdot)\) represents the exponential function with base \(e\), \(c\) j and \(\sigma\) j are the center and width of the \(j\)-th hidden layer node of the RBF neural network in Module 1, \(w\) j represents the corresponding output weight, and \(J_1\) is the number of hidden layer nodes of the RBF neural network; Module 2: Similarly, Module 2 is also established by an RBF neural network. Different from the structure of conventional modular neural networks, the input of Module 2 includes not only the input signals from the external environment but also the output of Module 1. Therefore, the input layer is expressed as: Among them, represents the auxiliary variables affecting the total nitrogen in the effluent, including: influent water temperature (T_in), effluent water temperature (T_ef), effluent NH4-N (NH4-N_ef), influent total nitrogen (TN_in), influent total phosphorus (TP_in), and mixed liquor suspended solids in the biological tank (MLSS), and m represents the number of input variables in Module 2; therefore, the output of Module 2 is expressed as where exp(·) represents the exponential function with base e, r represents the input vector, c j and σ j are the center and width of the j-th hidden layer node of the RBF neural network in Module 2, w j represents the corresponding output weight, and J2 is the number of hidden layer nodes of the RBF neural network; The cascaded modular neural network is constructed according to the direction of signal propagation. First, Module 1 is trained based on training samples. Then, the output of Module 1 is added to the input of Module 2 to complete the design of the sub-network; Step 2: An RBF self-organization structure design method based on the growth and merger mechanism; To ensure the compactness and generalization of the sub-network and the cascaded modular neural network, an RBF self-organization structure design method based on the growth and merger mechanism is proposed. Initially, there are no nodes in the RBF hidden layer. To eliminate the error between the network output and the desired output, the error correction algorithm is used to continuously add RBF hidden layer nodes. Therefore, in each iteration, each RBF node is located at the highest error peak or the lowest error trough; where z p and are the expected output of the p-th sample and the actual output of the network respectively, and e p represents the error between the expected output and the actual output of the p-th sample; j max represents the training sample with the largest absolute error at the j-th iteration, and P represents the size of the training samples in Module 1; Then, according to the j-th max training sample, initialize the center vector and connection weights corresponding to the j-th RBF node: where and represent the input vector and the expected output corresponding to the j-th max sample, respectively, and c j and w j represent the center vector and the connection weight of the j-th RBF node, respectively; The width of the hidden layer nodes is calculated according to the minimum Euclidean distance between the newly added nodes and other existing RBF nodes σ j = min{dist(c j , c i≠j )} (9) Whenever the network structure changes, a second-order algorithm is used to adjust all parameters. Due to the special nature of the activation function of the RBF neural network, its nodes perform local learning, which is determined by the corresponding center vectors and radii. Therefore, if two RBF hidden layer nodes are adjusted to the closest distance during the parameter adjustment process, these two nodes may provide approximately the same response to some input information. Therefore, a merger strategy is developed to reduce redundancy and improve the compactness of the network; If the k-th node and the l-th node satisfy condition (10), then these two nodes will be merged into a new node: dist(c k ,c l ) < min{σ k , σ l}, k ≠ l. (10) σ k,l = max{σ k , σ l} (12) w k,l = w k + w l (13) where dist(c k , c l ) represents the Euclidean distance between the center vectors c k and c l , c k and c l represent the center vectors of the k-th node and the l-th node respectively, c k,l represents the mean of the center vectors corresponding to the k-th node and the l-th node, σ k and σ l represent the widths of the k-th node and the l-th node respectively, w k and w l represent the connection weights of the k-th node and the l-th node respectively, the c k,l , σ k,l and w k,l are the center c, width σ and weight w of the newly added node respectively; Step 3: Adjust the parameters using a second-order algorithm To accelerate the convergence speed and improve the training accuracy of the HMN, a second-order learning algorithm is used to adjust the parameters of the sub-network, including the centers, widths, and connection weights of the hidden layer nodes. The update rules of the parameters are given by the following formula θ t+1 = θ t -(Q t + μ t I) -1 g t (14) where θ t+1 and θ t represent all the parameters at times t + 1 and t, including the center vector c, width, and connection weights, Q t represents the Hessian matrix at time t, μ t is the learning rate at time t, I is the identity matrix, g t is the gradient vector at time t; To reduce the computational complexity, the Hessian-like matrix Q is expressed as the sum of p Hessian-like sub-matrices q, and the gradient vector g is transformed into the sum of p gradient sub-vectors η: where P is the number of samples, q p is the Hessian-like submatrix, η p is the gradient subvector, g is the gradient vector, q p and η p are both obtained from the Jacobian vector j p as follows: Where H is the number of parameters to be adjusted, including the centers, widths, and connection weights of the hidden layer nodes. The calculation formula for H is H = (n + 2) * j, where j represents the number of neurons in the hidden layer and n represents the number of input nodes. j p represents the number of neurons in the hidden layer of the sub-network when the input is the p-th sample, e p represents the error between the actual output and the expected output of the corresponding network when the input is the p-th sample. In addition, the elements of the Jacobian row vector are expressed as where, u p is the p-th input sample, c j , σ j , w j represent the center vector, width, and connection weight corresponding to the j-th neuron in the RBF hidden layer respectively, e p represents the error between the actual output and the desired output of the network corresponding to the p-th input sample, represents the actual output of the network corresponding to the p-th input sample, φ j (u p ) represents the output of the j-th neuron node in the RBF hidden layer corresponding to the p-th input sample; Step 4: A prediction model based on the HMN The specific implementation of the prediction model based on the HNM is as follows: ① After preprocessing the data collected from a real - city sewage treatment plant, it is represented as D = {(x1, y1), (x2, y2),..., (x P+S , y P+S )}, where x1, x2,..., x P+S represent input samples, y1, y2,..., y P+S represent output samples, P represents the size of the training - set samples, S represents the size of the test - set samples. Then, the data set is divided into a training set and a test set in a ratio of 4:

3. The training set and the test set are represented by D1 and D2 respectively. Then D1 = {(x1, y1), (x2, y2),..., (x P , y P )}, D2 = {(x P+1 , y P+1 ), (x2, y P+2 ),..., (x P+S , y P+S )}; ②Based on mutual information analysis, calculate the correlations between the auxiliary variables and the effluent ammonia nitrogen and total nitrogen respectively. In the experiment, the number of auxiliary variables for each module is determined to be 6. Sort the correlations of the variables in descending order, and select the top six auxiliary variables as the inputs of the module. Determine the input variables of the effluent NH4-N and effluent TN sub-network modules respectively. Among them, the influent water temperature (T_in), effluent water temperature (T_ef), influent total phosphorus (TP_in), mixed liquor suspended solids in the biological pool (MLSS), influent total nitrogen (TN_in), and influent NH4-N (NH4-N_in) are selected as the auxiliary variables of module 1, and the influent water temperature (T_in), effluent water temperature (T_ef), effluent NH4-N (NH4-N_ef), influent total nitrogen (TN_in), influent total phosphorus (TP_in), and mixed liquor suspended solids in the biological pool (MLSS) are selected as the auxiliary variables of module 2; ③ The input and output vectors used to construct Module 1 are represented as {u1, u2,..., u P} and {z1, z2,..., z P}, where P represents the number of input samples. Then, an RBF sub-network in Module 1 is established using a growth and merging mechanism, and the output of Module 1 is represented as ④ Add the predicted output of Module 1 to the input vector of Module 2, then the input of Module 2 is expressed as where P represents the number of samples, respectively represent the actual outputs of the networks corresponding to the P input samples in Module 1, r1, r2,..., r P respectively represent the auxiliary variables affecting the nitrogen content in the effluent in Module 2. These auxiliary variables and the actual outputs of the sub-networks in Module 1 together constitute the input vector pair of Module 2 The corresponding output of Module 2 is {y1, y2,..., y P}; During the training process of the above two modules, the learning rate μ is set to 0.01, and the number of iterations is set to 50. When the model completes the last iteration, the HMN model training is completed, and it is applied to the test set to achieve the prediction of effluent NH4-N and effluent TN.

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