A Soft Sensor Method for Effluent BOD Based on Self-Organizing Feedforward Small-World Neural Network

Abstract

A soft measurement method for effluent BOD based on a self-organizing feedforward small-world neural network relates to the field of control and is directly applied to the field of sewage treatment. The present invention solves the disadvantages of inconvenient measurement of parameters for past sewage quality monitoring, long measurement period, poor model stability, and high cost. Introducing the small-world attribute into the general neural network model improves the calculation accuracy. A soft measurement method for the effluent BOD concentration based on an adaptive pruning type feedforward small-world neural network is proposed, which has the advantages of good real-time performance, convenient measurement, and stable model. Aiming at the disadvantage of the fixed structure of the small-world neural network model, the present invention introduces a self-organizing method to make the structure of the network adaptive during the training process, and automatically adjusts the model structure by splitting important neurons and merging unimportant neurons with their most relevant neurons. By introducing the self-organizing method, the present invention not only obtains a more compact model structure but also improves the prediction performance of the model.

Description

Technical Field:

[0001] The present invention is a method for predicting effluent BOD based on a self-organizing feedforward small-world neural network, aiming to achieve real-time prediction of BOD concentration. It relates to the field of control and is directly applied to the field of sewage treatment. Background Art:

[0002] Biochemical Oxygen Demand (BOD) is the amount of dissolved oxygen consumed during the biochemical reaction process in which microorganisms decompose biodegradable organic matter present in water, indirectly reflecting the amount of biodegradable organic matter in water. BOD is an important indicator reflecting the content of organic pollutants in water and is also one of the most widely used environmental indicators in the sewage treatment process. Therefore, real-time and effective measurement of effluent BOD during the sewage treatment process is of great significance for sewage treatment.

[0003] Currently, methods for BOD measurement include traditional dilution and inoculation method, manometric method, microbial sensor rapid determination method, and temperature increase method, etc. The dilution and inoculation method takes 5 days for determination, with complex operation process and poor timeliness; the manometric method is improved to be an automatic determination with simple operation, but still requires a cultivation time, is difficult to quickly reflect the water quality condition, and is subject to the sensitivity and precision of the instrument, with low accuracy of experimental results; the microbial electrode method has high requirements for measuring instruments such as microbial sensors, high cost, and narrow measurement range; the temperature increase method directly acts on the biochemical process, shortening the cultivation cycle, but with low precision. Therefore, how to quickly and effectively detect the effluent BOD concentration, improve the detection ability of key water quality parameters in sewage treatment plants, and accelerate urban sewage treatment has always been a difficult problem in the sewage treatment process.

[0004] In order to achieve real-time measurement of effluent BOD during the sewage treatment process, many scholars have proposed soft-sensor modeling methods, which use easily measurable variables to predict difficult-to-measure variables through models and are widely used in the sewage treatment field due to their easy operation. The present invention designs a soft-sensor method for effluent BOD based on a self-organizing feedforward small-world neural network to predict effluent BOD with low cost and high efficiency. Summary of the Invention:

[0005] 1. Technical problems that the present invention needs to and can solve:

[0006] The present invention proposes a soft-sensor method for effluent BOD based on a self-organizing feedforward small-world neural network to predict the effluent BOD concentration in sewage treatment, solving the problem of difficult real-time detection of effluent BOD during the sewage treatment process and improving its prediction accuracy.

[0007] 2. Specific technical solutions of the present invention:

[0008] The present invention provides a soft measurement method for biochemical oxygen demand (BOD) of sewage treatment effluent based on a self-organizing feedforward small-world neural network. The algorithm comprises the following steps:

[0009] Step 1: Data preprocessing;

[0010] Select M input variables related to the effluent BOD, normalize them to [-1, 1] according to formula (1), and the output variable is the effluent BOD, which is normalized to [0, 1] according to formula (2):

[0011]

[0012]

[0013] where F m represents the m-th auxiliary variable, x m and y respectively represent the normalized m-th auxiliary variable and the output variable, O represents the output variable; min(F m ) and max(F m ) respectively represent the minimum value and the maximum value in the m-th auxiliary variable; min(O) and max(O) respectively represent the minimum value and the maximum value in the output variable;

[0014] Step 2: Design a feedforward small-world neural network model;

[0015] Step 2.1: Construct an L-layer standard feedforward neural network model; its structure consists of an input layer, an output layer, and L - 2 hidden layers, with full connections between adjacent layers. Randomly initialize the connection weights W and V, where W is the hidden layer connection matrix and V is the output layer connection matrix, and their value ranges are [-1, 1];

[0016] Step 2.2: Design the reconnection method of the feedforward neural network; calculate the maximum number of reconnection edges N max as:

[0017] N max = min(N1, N2) (3)

[0018] where N1 represents the number of adjacent connections allowed for rewiring, and N2 represents the number of cross-layer connections allowed for rewiring, which are calculated respectively as:

[0019]

[0020]

[0021] Introduce a predefined parameter reconnection probability p, and its value range is [0, 1]; define the number of reconnection edges N R = round(p * N max), randomly select N R connections, and rewire according to the Watts-Strogatz rule: disconnect the selected connection from one end and then reconnect it to another neuron. If there is already a connection between these two neurons, cancel and select another neuron for rewiring until a new rewired connection is generated; repeat until the number of rewired edges reaches the predefined N R ;

[0022] Step 2.3: Design the topological structure of the feedforward small-world neural network model; the expressions of each layer after rewiring are as follows:

[0023] ① Input layer: The number of neurons in the input layer is set to M, representing M measured auxiliary variables, and the input vector is denoted as Let it represent the i-th input auxiliary variable of the input layer, then the output of the i-th neuron is calculated as:

[0024]

[0025] ② Hidden layer: The output of the j-th hidden neuron in the l-th layer (1 < l < L) is expressed as:

[0026]

[0027] In the formula, n s represents the number of neurons in the s-th layer (1 ≤ s ≤ l - 1), represents the connection weight from the i-th neuron in the s-th layer directly to the j-th neuron in the l-th layer, represents the output of the i-th neuron in the s-th layer, and the activation function f(·) of the hidden neuron is the sigmoid function;

[0028] ③ Output layer: The output layer contains an output neuron o, and its output is calculated by summing the linear weights of its inputs, defined as

[0029]

[0030] where represents the connection weight between the j-th neuron in the l-th layer (1 ≤ l ≤ L - 1) of the neural network and the output neuron, represents the output of the j-th neuron in the l-th layer (1 ≤ l ≤ L - 1), and n l represents the number of neurons in the l-th layer of the neural network;

[0031] Step 3: Design the self-organization algorithm of the feedforward small-world network;

[0032] Step 3.1: Define the performance index:

[0033]

[0034] Among them, Q is the number of samples, d q and represent the expected output of the q-th sample and the actual output of the neural network respectively;

[0035] Step 3.2: Initialize the training iteration number as t = 0, the splitting coefficient θ split , the merging coefficient θ merge , the maximum iteration number T max and the expected training RMSE value, i.e., E d , T max The value range of T is [5000, 10000], and the value range of E d is (0, 0.3];

[0036] Step 3.3: Increase the training iteration step t by 1; when t < T max execute Steps 3.4 to 3.8 to update the algorithm parameters, otherwise jump to Step 3.9;

[0037] Step 3.4: Use the batch backpropagation (BP) algorithm for training. In each iteration training, adjust according to the following formula;

[0038] ① The connection weight from the j-th neuron in the s-th layer to the output neuron:

[0039]

[0040] Among them

[0041]

[0042]

[0043] Among them, d q and represent the expected output of the q-th sample and the actual output of the neural network respectively, δ o (t) represents the difference between the expected output of the q-th sample and the actual output of the neural network, and represent the connection weight from the j-th neuron in the s-th layer to the output neuron and its change value respectively, represents the output of the j-th neuron in the s-th layer, t represents the t-th iteration of the neural network, η represents the learning rate, and Q represents the total number of samples;

[0044] ② The connection weight between the i-th neuron in the s-th layer and the j-th neuron in the l-th layer is updated according to the following:

[0045]

[0046] Among them

[0047]

[0048]

[0049] and respectively represent the connection weight and its change value from the \(i\)-th neuron in the \(s\)-th layer to the \(j\)-th neuron in the \(l\)-th layer, represents the connection weight from the \(j\)-th neuron in the \(l\)-th layer to the \(k\)-th neuron in the \(d\)-th layer, represents the output of the \(j\)-th neuron in the \(s\)-th layer, represents the output of the \(j\)-th neuron in the \(l\)-th layer, \(t\) represents the \(t\)-th iteration of the neural network, and \(\eta\) represents the learning rate, and respectively represent the errors between the expected output and the actual output of the \(j\)-th neuron in the \(l\)-th layer and the \(k\)-th neuron in the \(d\)-th layer;

[0050] Step 3.5: Calculate the training RSME according to formula (15):

[0051]

[0052] where \(Q\) is the total number of training samples, \(d\) q and are respectively the expected output and the actual output of the \(q\)-th sample. When RMSE is greater than the expected RSME value \(E\) d or the number of iterations \(t\) reaches the set maximum value \(T\) max stop training, otherwise go to Step 3.5; \(T\) max ranges from \([5000, 10000]\);

[0053] Step 3.6: Calculate the hub centrality values of all nodes in the network;

[0054] ① The hub and authority values of the network nodes are respectively initialized as \(h(0)=[1, 1, \ldots, 1]\) T and \(a(0)=[1, 1, \ldots, 1]\) T ;

[0055] ② The hub and authority values of each node are iteratively updated according to the formula:

[0056] h (k) =Aa (k-1) (16)

[0057] a (k) =Ah (k-1) (17)

[0058] where k represents the number of iteration steps, and A is the adjacency matrix of connection weights

[0059] A = (w ij ) (18)

[0060] where when there is a direct connection between node i and node j, w ij is 1, otherwise w ij is 0;

[0061] ③ Normalize the hub and authority values of the nodes according to the following formula:

[0062]

[0063]

[0064] where ||·|| is the first norm, calculated as the sum of the absolute values of each element, and represent the hub and authority values of node i at the k-th iteration respectively;

[0065] ④ The iteration continues until the hub and authority values converge;

[0066] Step 3.7: Evaluation of neuron importance based on hub centrality; For each hidden layer neuron, calculate the hub centrality value of each neuron and the average hub centrality of all neurons in the network through Step 3.4 For each hidden layer neuron, if then it is considered that this neuron is an important neuron that needs to be split, and go to Step 3.8; θ split is a predefined splitting threshold, and its value range is [1.1, 1.4]; if then it is considered that this neuron is an unimportant neuron that needs to be merged, and go to Step 3.9; θ merge is a predefined splitting threshold, and its value range is [0.8, 1);

[0067] Step 3.8: Split of important nodes; The important node is denoted as the a-th node in the s-th layer. The input weights of the two new neurons a1 and a2 obtained by splitting are the same as those of neuron a, that is

[0068]

[0069] where is the connection weight from the i-th node in the l1 (1 ≤ l1 ≤ s - 1) layer to the a1-th node in the s-th layer, is the connection weight from the i-th node in the l1 layer to the a2-th node in the s-th layer, is the connection weight from the i-th node in the l1 layer to the a-th node in the s-th layer;

[0070] The connection weights from the two new nodes to the neurons in the hidden layer and the connection weights to the output neuron o are defined as follows:

[0071]

[0072]

[0073] where represents the connection weight from the a1-th node in layer s to the j-th node in layer l2 (s < l2 < L), represents the connection weight from the a1-th node in layer s to the output neuron o; represents the connection weight from the a2-th node in layer s to the j-th node in layer l2, represents the connection weight from the a2-th node in layer s to the output neuron o; represents the connection weight from the a-th node in layer s to the j-th node in layer l2, represents the connection weight from the a-th node in layer s to the output neuron o; α is the mutation parameter, and its value range is (0, 1), and generally takes a value close to the middle value;

[0074] Step 3.7: Merge the unimportant node with its most relevant neuron; the unimportant node is denoted as the b-th node in layer s, and its relationship with other neurons in the same layer is calculated based on the Pearson correlation coefficient and defined as:

[0075]

[0076] where is the output vector of the i-th node in layer s, and σ i are the mean and standard deviation of in all training samples respectively, is the output vector of the b-th node in layer s, and σ b are the mean and standard deviation of in all training samples respectively, q represents the q-th sample, and Q is the total number of samples;

[0077] Select the neuron c with the highest correlation as the neuron to merge with the unimportant neuron b, and the merged new neuron b'. The connections from the neurons in layer l (1 ≤ l < s) to the neuron b' in layer s are constructed according to the rewiring rule of Watt-Strogatz with the same rewiring probability p as in Step 2.2, and the initial connection weights are randomly set within the range of [-1, 1];

[0078] The output weights of the new neuron b' to the neurons in the hidden layer and to the output neuron are defined as:

[0079]

[0080]

[0081] Among them, is the connection weight from the neuron b' in the s-th layer to the j-th neuron in the l2 layer, representing the connection weight from the neuron b in the s-th layer to the j-th neuron in the l2 layer, representing the connection weight from the neuron c in the s-th layer to the j-th neuron in the l2 layer; representing the connection weight from the neuron b' to the output neuron, representing the connection weight from the neuron b to the output neuron, representing the connection weight from the neuron c to the output neuron; is the output of the neuron b in the s-th layer, is the output of the neuron c in the s-th layer, is the output of the neuron b' in the s-th layer, The calculation is as follows:

[0082]

[0083] Where represents the number of neurons in the l1-th layer (1 ≤ l1 ≤ s - 1), is the connection weight from the i-th neuron in the l1-th layer to the neuron b' in the s-th layer, is the output of the i-th neuron in the l1-th layer;

[0084] Step 3.9: Calculate the training RSME according to formula (15); when the RMSE is greater than the expected RSME value E d or the number of iterations t reaches the set maximum value T max stop training, otherwise repeat steps 3.3 to 3.9;

[0085] Step 4: Effluent BOD prediction;

[0086] Use the test sample data as the input of the trained self-organizing feedforward small-world neural network, obtain the output of the neural network, and perform anti-normalization on it to obtain the predicted value of the effluent BOD concentration.

[0087] 3. Compared with the prior art, the present invention has the following obvious advantages and beneficial effects:

[0088] (1) The soft measurement method for measuring the effluent BOD using auxiliary variables solves the drawbacks of inconvenient measurement of parameters, long measurement period, poor model stability, and high cost in the past sewage water quality monitoring. Introducing the small-world property into the general neural network model improves the calculation accuracy. A soft measurement method for the effluent BOD concentration based on an adaptive pruning type feedforward small-world neural network is proposed, which has the advantages of good real-time performance, convenient measurement, and stable model.

[0089] (2) Aiming at the drawback of the fixed structure of the small-world neural network model, the present invention introduces a self-organization method to make the structure of the network adaptive during the training process. The model structure is automatically adjusted by splitting important neurons and merging unimportant neurons with their most relevant neurons.

[0090] (3) Aiming at the drawbacks of redundant structure and high calculation cost of the pruning type small-world neural network model, the present invention introduces a self-organization method, which can perform structure adjustment from any given structure to make the structure compact, thereby shortening the training time. Both a more compact model structure is obtained and the prediction performance of the model is improved. Description of the Drawings:

[0091] Figure 1 is the training RMSE graph of the effluent BOD concentration of the present invention;

[0092] Figure 2 is the fitting graph of the prediction effect of the effluent BOD concentration of the present invention;

[0093] Figure 3 is the prediction error graph of the effluent BOD concentration of the present invention; Detailed Implementation Manner:

[0094] The present invention obtains a soft measurement method for the effluent BOD based on a self-organizing feedforward small-world neural network, realizes the real-time measurement of the BOD concentration according to the data collected during the sewage treatment process, solves the problem that it is difficult to measure the effluent BOD concentration in real time during the sewage treatment process, and improves the real-time monitoring level of the water quality of urban sewage treatment plants;

[0095] The experimental data comes from 365 samples of a sewage treatment plant in Beijing in 2011. Each sample includes the following 10 auxiliary variables: (1) Effluent total nitrogen concentration; (2) Effluent ammonia nitrogen concentration; (3) Influent total nitrogen concentration; (4) Influent BOD concentration; (5) Influent ammonia nitrogen concentration; (6) Effluent phosphate concentration; (7) Concentration of suspended solids in the biochemical mixed liquid (MLSS); (8) Dissolved oxygen concentration in the biochemical pool (DO); (9) Influent phosphate concentration; (10) Influent COD concentration; The 365 groups of all samples are divided into two parts: 265 groups of data are used as training samples, and the remaining 100 groups of data are used as measurement samples;

[0096] Step 1: Data preprocessing;

[0097] Ten auxiliary variables related to the effluent BOD are used as input variables, including: (1) Effluent total nitrogen concentration; (2) Effluent ammonia nitrogen concentration; (3) Influent total nitrogen concentration; (4) Influent BOD concentration; (5) Influent ammonia nitrogen concentration; (6) Effluent phosphate concentration; (7) Concentration of suspended solids in the biochemical mixed liquid (MLSS); (8) Dissolved oxygen concentration in the biochemical pool (DO); (9) Influent phosphate concentration; (10) Influent COD concentration; They are normalized to [-1, 1] according to formula (1), and the output variable is the effluent BOD, which is normalized to [0, 1] according to formula (2):

[0098]

[0099]

[0100] Among them, F m represents the m-th auxiliary variable, O represents the output variable, x m and y respectively represent the normalized m-th auxiliary variable and output variable; min(F m ) and max(F m ) respectively represent the minimum and maximum values of the m-th auxiliary variable; min(O) and max(O) respectively represent the minimum and maximum values of the output variable;

[0101] Step 2: Design a feedforward small-world neural network model;

[0102] Step 2.1: Construct an L-layer standard feedforward neural network model; its structure consists of an input layer, an output layer, and L - 2 hidden layers, with full connections between adjacent layers. The connection weights W and V are randomly initialized, where W is the hidden layer connection matrix and V is the output layer connection matrix, and their value ranges are [-1, 1]; In this embodiment, L takes 4;

[0103] Step 2.2: Design the reconnection method of the feedforward neural network; Calculate the maximum number of edges that can be reconnected N max as:

[0104] N max = min(N1, N2) (3)

[0105] where N1 represents the number of adjacent connections allowed for rewiring, and N2 represents the number of cross-layer connections allowed for rewiring, which are calculated respectively as:

[0106]

[0107]

[0108] Introduce the predefined parameter of rewiring probability p, whose value range is [0, 1]; define the number of rewired edges N R = round(p * N max ), randomly select N R connections, and perform rewiring according to the Watts-Strogatz rule: disconnect the selected connection from one end and then reconnect it to another neuron. If there is already a connection between these two neurons, cancel it and then select another neuron for rewiring until a new rewired connection is generated; repeat until the number of rewired edges reaches the predefined N R edges; the value range of the rewiring probability p is [0, 1]. Research shows that the small-world property is better when taking a value near the middle. Therefore, in this embodiment, p is taken as 0.5;

[0109] Step 2.3: Design the topological structure of the feedforward small-world neural network model; the expressions of each layer after rewiring are as follows:

[0110] ① Input layer: The number of neurons in the input layer is set to M, representing M measured auxiliary variables. The input vector is denoted as representing the i-th input auxiliary variable of the input layer. Then the output of the i-th neuron is calculated as:

[0111]

[0112] ② Hidden layer: The output of the j-th hidden neuron in the l-th layer (1 < l < L) is expressed as:

[0113]

[0114] In the formula, n s represents the number of neurons in the s-th layer (1 ≤ s ≤ l - 1), represents the connection weight from the i-th neuron in the s-th layer directly connecting to the j-th neuron in the l-th layer, represents the output of the i-th neuron in the s-th layer. The activation function f(·) of the hidden neuron is the sigmoid function;

[0115] ③ Output layer: The output layer contains an output neuron o, and its output is calculated by summing the linear weights of its inputs, defined as

[0116]

[0117] where represents the connection weight between the j-th neuron in the l-th layer (1 ≤ l ≤ L - 1) of the neural network and the output neuron, represents the output of the j-th neuron in the l-th layer (1 ≤ l ≤ L - 1), and n l represents the number of neurons in the l-th layer of the neural network;

[0118] Step 3: Design a feedforward small-world network self-organization algorithm;

[0119] Step 3.1: Define performance metrics:

[0120]

[0121] where Q is the number of samples, d q and represent the expected output of the q-th sample and the actual output of the neural network, respectively;

[0122] Step 3.2: Initialize the training iteration count as t = 0, the splitting coefficient θ split , the merging coefficient θ merge , the maximum iteration count T max and the expected training RMSE value, i.e., E d , T max has a value range of [5000, 10000], and E d has a value range of (0, 0.3]; to have sufficient iteration counts to train the neural network, in this embodiment, T max is taken as 10000; to enable the model to achieve better performance metrics, E d is generally taken as a value slightly closer to 0, and in this embodiment, E d is taken as 0.1;

[0123] Step 3.3: Increase the training iteration step count t by 1; when t < T max , execute Steps 3.4 to 3.8 to update the algorithm parameters, otherwise jump to Step 3.9;

[0124] Step 3.4: Use the batch backpropagation (BP) algorithm for training, and in each iterative training, adjust according to the following formula;

[0125] ① The connection weight from the j-th neuron in the s-th layer to the output neuron:

[0126]

[0127] where

[0128]

[0129]

[0130] where d q and represent the expected output of the q-th sample and the actual output of the neural network, respectively, and δ o (t) represents the difference between the expected output and the actual output of the neural network for the q-th sample, and respectively represent the connection weight from the j-th neuron in the s-th layer to the output neuron and its change value, represents the output of the j-th neuron in the s-th layer, t represents the t-th iteration of the neural network, η represents the learning rate, and Q represents the total number of samples;

[0131] ② The connection weight between the i-th neuron in the s-th layer and the j-th neuron in the l-th layer is updated as follows:

[0132]

[0133] where

[0134]

[0135]

[0136] and respectively represent the connection weight from the i-th neuron in the s-th layer to the j-th neuron in the l-th layer and its change value, represents the connection weight from the j-th neuron in the l-th layer to the k-th neuron in the d-th layer, represents the output of the j-th neuron in the s-th layer, represents the output of the j-th neuron in the l-th layer, t represents the t-th iteration of the neural network, and η represents the learning rate, and respectively represent the errors between the expected output and the actual output of the j-th neuron in the l-th layer and the k-th neuron in the d-th layer;

[0137] Step 3.5: Calculate the training RSME according to formula (15):

[0138]

[0139] where Q is the total number of training samples, d q and are respectively the expected output and the actual output of the q-th sample. When RMSE is greater than the expected RSME value E d or the number of iterations t reaches the set maximum value T max stop training, otherwise go to Step 3.5; T max ranges from [5000, 10000]. To have sufficient iteration times to train the neural network, in this embodiment, T max is taken as 10000;

[0140] Step 3.6: Calculate the hub centrality values of all nodes in the network;

[0141] ① The hub and authority values of the network nodes are respectively initialized as h(0) = [1, 1, …, 1] T and a(0) = [1, 1, …, 1] T ;

[0142] ② The hub and authority values of each node are iteratively updated according to the formula:

[0143] h (k) = Aa (k-1) (16)

[0144] a (k) = Ah (k-1) (17)

[0145] where k represents the number of iteration steps, and A is the adjacency matrix of connection weights

[0146] A = (w ij ) (18)

[0147] where when there is a direct connection between node i and node j, w ij is 1, otherwise w ij is 0;

[0148] ③ Normalize the hub and authority values of the nodes according to the following formula:

[0149]

[0150]

[0151] where ||·|| is the first norm, calculated as the sum of the absolute values of each element, and respectively represent the hub and authority values of node i at the k-th iteration;

[0152] ④ The iteration continues until the hub and authority values converge;

[0153] Step 3.7: Evaluation of neuron importance based on hub centrality; For each hidden layer neuron, the hub centrality value of each neuron and the average hub centrality of all neurons in the network are calculated through Step 3.4 For each hidden layer neuron, if then it is considered that the neuron is an important neuron that needs to be split, and go to Step 3.8; θ split is a predefined splitting threshold, and its value range is [1.1, 1.4]; If then it is considered that the neuron is an unimportant neuron that needs to be merged, and go to Step 3.9; θ mergeis the predefined splitting threshold, and its value range is [0.8, 1); in this embodiment, θ split takes 1.3, and θ merge takes 0.9;

[0154] Step 3.8: Split important nodes; the important node is denoted as the ath node in the sth layer. The input weights of the two new neurons a1 and a2 obtained by splitting are the same as those of neuron a, that is

[0155]

[0156] where is the connection weight from the ith node in the l1th (1 ≤ l1 ≤ s - 1) layer to the a1th node in the sth layer, is the connection weight from the ith node in the l1th layer to the a2th node in the sth layer, is the connection weight from the ith node in the l1th layer to the ath node in the sth layer;

[0157] The connection weights from the two new nodes to the hidden layer neurons and the connection weights to the output neuron o are defined as follows:

[0158]

[0159]

[0160] where represents the connection weight from the a1th node in the sth layer to the jth node in the l2th (s < l2 < L) layer, represents the connection weight from the a1th node in the sth layer to the output neuron o; represents the connection weight from the a2th node in the sth layer to the jth node in the l2th layer, represents the connection weight from the a2th node in the sth layer to the output neuron o; represents the connection weight from the ath node in the sth layer to the jth node in the l2th layer, represents the connection weight from the ath node in the sth layer to the output neuron o; α is the mutation parameter, and its value range is (0, 1). Generally, it takes a value close to the middle value; in this embodiment, α takes 0.5;

[0161] Step 3.7: Merge unimportant nodes with their most relevant neurons; the unimportant node is denoted as the bth node in the sth layer. Calculate its relationship with other neurons in the same layer based on the Pearson correlation coefficient, which is defined as:

[0162]

[0163] where is the output vector of the ith node in the sth layer, and σ iare the mean and standard deviation among all training samples, respectively, is the output vector of the b-th node in the s-th layer, and σ b are the mean and standard deviation among all training samples, respectively. q represents the q-th sample, and Q is the total number of samples;

[0164] Select the neuron c with the highest correlation as the neuron to merge with the unimportant neuron b. The new neuron b' obtained by merging is constructed according to the rewiring rule of Watt - Strogatz with the same rewiring probability p as in step 2.2 for the connections from neurons in the l-th layer (1 ≤ l < s) to the neuron b' in the s-th layer. The initial connection weights are randomly set within the range of [-1, 1];

[0165] The output weights from the new neuron b' to the hidden layer neurons and to the output neurons are respectively defined as:

[0166]

[0167]

[0168] where, is the connection weight from the neuron b' in the s-th layer to the j-th neuron in the l2 layer, representing the connection weight from the neuron b in the s-th layer to the j-th neuron in the l2 layer, represents the connection weight from the neuron c in the s-th layer to the j-th neuron in the l2 layer; represents the connection weight from the neuron b' to the output neuron, represents the connection weight from the neuron b to the output neuron, represents the connection weight from the neuron c to the output neuron; is the output of the neuron b in the s-th layer, is the output of the neuron c in the s-th layer, is the output of the neuron b' in the s-th layer, The calculation is as follows:

[0169]

[0170] where represents the number of neurons in the l1-th layer (1 ≤ l1 ≤ s - 1), is the connection weight from the i-th neuron in the l1-th layer to the neuron b' in the s-th layer, is the output of the i-th neuron in the l1-th layer;

[0171] Step 3.9: Calculate the training RSME according to formula (15); when RMSE is greater than the expected RSME value Ed or when the number of iterations t reaches the set maximum value T max stop training, otherwise repeat steps 3.3 to 3.9;

[0172] Step 4: Effluent BOD prediction;

[0173] Use the test sample data as the input of the trained self-organizing feedforward small-world neural network to obtain the output of the neural network, and perform anti-normalization on it to obtain the predicted value of the effluent BOD concentration.

[0174] In this embodiment, the prediction results are as Figure 2 shown. X-axis: number of samples, unit is piece / sample, Y-axis: predicted effluent BOD concentration, unit is mg / L. The solid line is the actual output value of the effluent BOD concentration, and the dashed line is the predicted output value of the effluent BOD concentration; the error between the actual output value of the effluent BOD concentration and the predicted output value of the effluent BOD concentration is as Figure 3 shown. X-axis: number of samples, unit is piece / sample, Y-axis: prediction error of the effluent BOD concentration, unit is mg / L; the results demonstrate the effectiveness of the soft measurement method for the effluent BOD concentration based on the self-organizing feedforward small-world neural network.

[0175] Tables 1 - 23 are the experimental data of the present invention. Among them, Tables 1 - 11 are training samples: effluent total nitrogen concentration, effluent ammonia nitrogen concentration, influent total nitrogen concentration, influent BOD concentration, influent ammonia nitrogen concentration, effluent phosphate concentration, biochemical MLSS concentration, DO concentration in the biochemical pool, influent phosphate concentration, influent COD concentration, and measured effluent BOD concentration. Tables 12 - 22 are training samples: effluent total nitrogen concentration, effluent ammonia nitrogen concentration, influent total nitrogen concentration, influent BOD concentration, influent ammonia nitrogen concentration, effluent phosphate concentration, biochemical MLSS concentration, DO concentration in the biochemical pool, influent phosphate concentration, influent COD concentration, and measured effluent BOD concentration. Table 23 is the predicted value of the effluent BOD of the present invention.

[0176] Training samples:

[0177] Table 1. Auxiliary variable effluent total nitrogen (mg / L)

[0178] 6.9024 9.2161 9.5541 4.6629 12.9340 7.7823 12.4587 12.8927 10.5681 11.9979 6.6957 12.1535 7.4653 13.5979 6.1292 6.0854 12.7176 12.8052 12.5036 4.8307 12.9511 13.3468 11.1954 13.1383 6.1049 12.7274 12.8343 5.6830 13.0739 13.1772 6.9511 7.4556 11.5529 8.9097 12.7298 13.4889 9.8921 7.8021 12.4064 12.4757 7.3985 8.5900 10.3869 13.1553 12.4951 13.0690 13.6574 6.7383 12.7055 6.2970 5.7426 13.5359 12.8574 12.6204 5.2234 5.3049 11.5298 6.9328 13.3657 12.4769 12.0100 7.0957 5.9748 4.7444 4.9766 5.1614 6.4027 10.5049 6.5365 6.2167 6.8404 13.5116 8.7213 4.9888 12.7116 13.0897 12.2119 6.0453 6.3128 6.2082 6.2739 11.4581 13.6311 13.0626 11.2647 12.4295 12.4526 12.4647 6.3492 13.0167 5.6574 7.1274 12.7736 7.6526 13.2927 10.2301 13.1809 12.9559 11.2660 8.9705 12.7784 11.6331 13.3231 7.1967 6.7091 12.6106 13.1030 7.4629 10.1596 7.6003 12.2581 8.4587 11.3401 6.4805 12.9960 7.4994 13.1748 6.4951 8.0647 6.0574 11.6502 6.0161 13.4921 12.5316 7.9492 12.7347 11.4945 12.3091 11.5894 10.8769 13.5274 7.4581 7.5930 13.2805 7.3511 6.9888 6.3395 5.8094 7.0544 9.3900 11.3511 8.3274 5.8921 7.7012 6.6021 5.0860 12.8064 6.6410 7.4678 7.3584 8.1960 4.6653 10.7225 6.3347 13.2745 6.9523 5.9894 5.7681 12.7638 5.9334 12.6945 12.5085 12.7225 11.7134 11.3122 6.8234 12.7505 14.0574 7.3024 12.8380 13.4106 12.4404 11.3924 13.7732 7.8277 7.1140 12.7736 13.9153 9.0204 12.4891 12.2848 6.3699 5.1954 11.4702 8.8210 7.4532 8.4783 9.9480 12.5498 6.4015 13.3523 6.1426 6.1936 7.1468 12.0757 12.3578 12.8343 5.4921 13.1857 11.0313 4.8258 12.1389 8.8262 6.5158 6.4198 13.3681 6.8891 7.3413 12.2264 12.4185 5.3328 11.5407 12.5426 12.2435 6.4052 13.2198 4.9960 11.7936 12.8538 7.2976 13.0678 10.8258 5.6891 9.1742 4.9073 6.2994 12.3663 12.9413 11.2319 13.1723 12.5693 11.8860 7.4343 12.5681 12.1426 12.2313 8.9207 12.9109 12.9705 12.5134 6.2289 12.8064 5.3766 6.1851 12.9802 5.9796 13.4143 13.6149 7.9334 12.2848 7.4702 11.2915 6.4404 12.5219 12.1207 12.6386 6.4404 12.0660 6.7772 6.7675 6.7869 12.7783 12.7821 12.9000 5.3267

[0179] Table 2. Auxiliary variable effluent ammonia nitrogen (mg / L)

[0180]

[0181]

[0182] Table 3. Auxiliary variable influent total nitrogen (mg / L)

[0183]

[0184]

[0185] Table 4. Auxiliary variable influent BOD (mg / L)

[0186] 8.8200 11.1400 11.5800 8.7400 5.6200 14.4867 7.3400 5.1400 12.9000 8.4200 8.9800 7.6200 11.1800 8.1400 8.1800 6.1000 5.3800 5.2600 7.9400 9.3800 6.1000 7.1600 7.1800 4.7800 10.7400 5.1000 5.0200 10.2600 5.1000 6.2200 9.5400 7.1800 9.3400 10.5400 6.2600 6.9080 12.0200 10.1000 5.3400 5.5800 9.4600 6.9800 5.4200 4.7800 6.8600 8.9400 5.9000 15.7000 7.2600 6.4200 7.8600 5.9800 9.2600 5.1800 7.6200 7.2200 9.3000 9.6200 5.5000 7.1000 5.9800 8.9800 7.6200 8.3400 6.7400 9.2200 6.5800 6.7000 6.1800 11.1800 14.3400 5.7000 6.4600 7.1400 5.2600 6.3400 7.1400 9.5000 8.1400 11.7800 10.6600 5.5000 6.6560 7.6640 5.6600 5.4200 5.5000 6.0200 8.8200 5.0200 8.9800 7.3400 5.5000 9.6200 6.1400 12.4600 6.2200 5.1400 5.6200 5.4600 6.2200 9.5000 7.1000 9.1400 8.6600 4.7800 6.7800 10.1800 6.4600 9.7800 6.1000 7.5000 10.5000 6.7000 4.9400 9.6200 8.7800 9.0200 9.0600 8.4200 5.3800 8.0200 8.3000 6.3800 9.0200 9.1400 10.0200 6.8200 9.4200 11.9400 5.7400 8.1800 10.0200 8.6200 7.5400 7.5000 9.5400 6.0200 7.7400 11.3000 8.9400 8.0200 6.8200 9.9400 5.0600 6.9000 5.7400 9.2200 12.1800 9.6600 8.5400 9.4600 12.4200 9.5400 6.3400 6.5800 12.0200 5.6200 8.1400 7.2200 5.5000 6.4200 5.7400 9.6600 8.8600 9.2600 5.9800 5.9000 8.1000 7.1000 7.0200 8.7000 9.0200 6.4040 10.3800 12.2600 5.0200 6.1520 5.2600 8.9000 5.7400 10.3800 7.0600 9.1800 6.0600 6.1800 13.6778 5.3000 6.1400 10.4200 5.9800 12.9000 6.1800 10.2600 8.0200 7.5400 5.3800 9.0600 6.5800 11.4600 7.9400 6.9400 13.2733 8.5000 8.2200 6.4600 8.9400 8.2600 5.0200 4.9000 7.6600 7.4200 5.6200 8.6600 8.4200 5.3000 9.3000 9.8200 5.1000 9.3000 4.9000 5.5400 8.5800 12.8689 7.5400 8.7000 8.7800 4.9400 8.7000 5.9400 5.4200 7.6600 14.8911 5.9000 5.9000 7.9000 5.6600 5.5400 6.9400 6.6200 7.0200 6.4600 8.5000 7.8600 5.0200 5.9400 6.0600 5.6200 9.5800 7.3400 13.1800 8.8200 12.0600 5.7400 8.5400 5.0200 8.4200 6.7400 5.8200 7.2200 9.4200 8.1680 4.7000 5.8600 9.1400

[0187] Table 5. Auxiliary variable influent ammonia nitrogen (mg / L)

[0188]

[0189]

[0190] Table 6. Auxiliary variable effluent phosphate (mg / L)

[0191]

[0192]

[0193] Table 7. Auxiliary variable biochemical MLSS (mg / L)

[0194] 11.8633 11.3526 11.3039 11.3465 13.8151 12.5990 10.0270 14.7758 10.9269 14.3623 9.5284 14.7150 12.8240 14.2529 12.6112 12.3740 14.0887 14.6177 15.0312 12.3740 14.9156 11.2127 15.2561 12.5808 11.8572 13.5840 14.0644 11.5350 14.8366 14.5569 9.4372 5.5884 12.2038 12.9152 14.6663 11.3830 10.7932 12.3497 12.3862 11.4559 12.8422 10.8783 10.0574 14.5569 10.2398 14.6420 15.0676 12.5382 10.3007 11.7903 12.5990 15.0008 14.5447 13.2861 11.2127 12.3132 12.0214 9.2548 14.7758 10.1122 14.2590 11.3951 11.7356 10.8357 12.6294 11.9180 11.6566 14.4961 11.3526 12.0579 5.8802 15.1528 10.6837 11.3221 12.2281 15.0190 14.8001 12.6659 9.5893 11.4498 11.2431 14.6663 11.3343 10.6959 10.5682 12.1916 11.9545 14.1009 9.2913 12.2342 11.3039 11.8511 11.6566 9.7960 14.1556 10.6107 11.3708 12.3923 14.2438 9.2548 14.6177 12.0944 14.3076 12.1004 12.1065 13.9489 10.4101 4.5000 14.3076 13.0064 14.4292 11.2249 11.1823 10.9999 12.6598 12.9030 14.7515 9.1332 11.7660 11.8633 14.3927 11.6566 14.4718 10.4283 12.6720 14.3684 11.5958 14.6055 11.5897 10.6412 14.2529 5.3512 9.6805 14.5447 5.7951 12.6659 11.4255 11.8998 11.5046 12.6659 12.2160 11.5046 11.8998 12.7510 11.6201 12.7632 11.6322 9.5710 12.2646 9.8750 11.7295 12.0761 10.6837 11.8998 11.1762 11.4316 11.4559 12.0031 12.5078 11.6383 14.2529 14.4900 14.1495 12.5382 12.7754 9.8689 14.4718 11.8694 9.7960 10.5317 12.5382 12.7693 12.8544 11.4559 9.9358 12.7024 14.0887 11.9788 9.5224 14.3684 11.5471 12.2160 12.5139 11.8998 10.4101 5.6066 12.9152 9.9298 10.5135 12.3740 14.2529 11.2188 10.5803 5.8438 14.4657 14.9278 11.7660 11.2066 14.2225 10.9938 10.5803 14.7028 13.1767 12.4774 9.7291 10.9391 9.6075 11.4255 13.9428 14.1374 12.3619 15.7000 14.2529 14.2529 11.3708 15.2136 12.2768 12.7024 12.5808 12.4835 14.4049 10.4527 12.6051 13.1280 10.9391 11.7903 14.0097 14.3441 12.5382 14.6785 11.8694 15.5723 12.7328 10.6351 11.3161 15.1224 9.7291 14.3562 10.1669 10.3493 10.8418 14.2590 10.9877 9.5710 14.6116 12.1795 14.7454 14.0948 12.0944 14.9643 12.5017 12.4531 12.7814 11.0911 14.4779 14.2225 9.5041 14.7271 11.3586 11.2613 9.3764 11.5958 14.3502 11.8390 11.4498

[0195] Table 8. Auxiliary variable biochemical pool DO (mg / L)

[0196]

[0197]

[0198] Table 9. Auxiliary variable influent phosphate (mg / L)

[0199]

[0200]

[0201] Table 10. Auxiliary variable influent COD (mg / L)

[0202] 8.0872 10.3192 9.1633 10.1598 7.4495 9.2829 8.0872 7.3698 10.6779 7.3299 8.7648 8.7648 4.5000 11.2758 10.3591 8.5256 10.3591 9.3228 11.3555 10.2794 8.1669 10.0402 10.0801 9.8808 9.5619 9.2032 8.3662 11.0765 11.0765 10.5584 8.4459 10.9171 9.1633 9.2431 10.0402 8.7648 9.8808 8.7648 8.0473 9.9206 7.2502 8.4858 6.0544 7.7683 8.2865 10.5584 13.6673 10.1598 9.1633 8.7648 8.4060 10.5185 8.8445 8.4459 9.3228 8.5256 10.1598 7.3299 8.1669 8.7648 8.8445 6.7719 10.0801 9.6018 10.5185 7.2502 9.2829 9.2829 9.2431 8.4459 11.8737 9.4822 9.0438 10.0402 8.1669 11.0367 11.7142 11.3157 10.4388 10.5584 11.3954 9.1633 9.2431 14.1854 8.5655 7.6488 8.0872 7.5690 10.6381 7.6886 9.3626 7.6886 8.4858 10.2395 9.8808 7.4893 8.0872 9.3626 7.0907 9.1633 11.1961 10.4786 6.1740 8.9641 8.8046 11.6345 8.5655 6.8117 9.0438 7.8879 10.7178 10.4786 9.6416 9.8011 8.4858 10.0801 8.5256 10.0801 8.6851 8.8445 8.3662 10.7975 8.0473 7.9676 6.5726 9.6815 10.5584 9.0039 9.2829 10.5584 6.7719 10.5982 11.2758 10.2794 8.8843 11.9534 8.1669 10.0402 9.6815 6.9712 10.7975 9.8808 8.4858 10.0801 10.1598 7.2103 8.8445 8.6452 9.8409 8.8046 9.6815 9.8011 11.1164 8.7648 8.2466 11.5947 9.9206 8.8843 10.1598 10.5584 8.5655 5.6957 9.8808 12.0331 11.2758 9.7214 10.4786 9.2431 9.1633 9.4423 9.7612 9.0039 10.5584 8.8046 9.5221 11.4352 8.0473 7.9676 8.7648 8.1669 9.5619 7.8879 9.1633 8.7249 9.6815 10.3591 9.6815 7.9676 9.0438 14.6637 9.0836 9.6416 9.6815 11.6744 8.1270 6.7719 7.0907 10.3192 7.4893 10.0801 10.1199 10.9171 8.6851 10.0402 10.0402 7.8879 9.1633 10.2794 7.5690 8.6851 9.4822 7.5292 9.7612 7.6886 10.2395 9.3626 11.0765 11.7142 7.4495 9.8011 6.0943 7.5690 12.1128 9.1235 10.5982 9.6815 6.6922 7.2502 11.6345 9.8409 8.7648 8.8046 10.5584 10.0402 8.4459 9.4423 7.6488 8.7249 7.9676 7.1705 11.1961 9.3626 9.9206 11.3555 7.9676 5.6957 9.6815 7.6886 7.6488 5.6160 13.3085 10.1598 12.7904 8.2865 8.8445 9.2032 7.8480 7.0110 10.6779 10.6779 5.6559 9.8808 9.8409 8.9242 8.8046

[0203] Table 11. Measured effluent BOD concentration (mg / L)

[0204]

[0205]

[0206] Test samples:

[0207] Table 12. Auxiliary variable effluent total nitrogen (mg / L)

[0208] 12.5450 5.8739 8.4295 6.3286 7.2489 5.8362 13.0872 13.1711 6.5681 13.0872 13.2356 5.8812 9.5222 4.5000 4.5815 13.0021 6.4052 12.5061 11.5140 12.5134 11.7036 13.3936 13.0483 12.6666 12.4271 5.5237 7.4605 7.0447 8.8781 12.4307 6.9426 7.0863 12.0343 12.9280 12.2313 6.5085 11.8422 5.6331 9.5091 7.4690 7.9152 12.3869 5.5298 11.7620 6.6544 9.8702 6.2641 6.4708 11.4106 12.4988 5.0702 11.6489 13.7340 12.9204 12.5766 6.3225 7.0787 12.6362 15.7000 12.1170 6.1912 5.9930 7.6283 13.2047 13.0483 6.2033 8.1303 12.6119 12.9936 8.2021 7.1237 12.9280 5.9359 13.0495 12.7541 12.9632 5.7693 8.8708 5.4143 9.0702 12.6362 11.1857 10.8502 13.0775 7.4775 12.6301 12.7128 8.5401 13.4398 11.4726 13.2647 12.8951 12.2872 12.4404 12.5729 13.3863 8.7711 13.4605 5.8508 6.7578

[0209] Table 13. Effluent ammonia nitrogen of auxiliary variable (mg / L)

[0210]

[0211]

[0212] Table 14. Influent total nitrogen of auxiliary variable (mg / L)

[0213] 8.9296 8.5586 12.9232 9.6257 13.4039 11.5392 9.0312 7.7386 12.1960 8.7752 8.8822 10.1647 15.2323 9.9981 10.1525 8.0074 9.4171 7.4251 6.2605 8.4787 8.2437 6.6369 8.7021 7.1725 8.3649 7.0466 14.3925 12.6388 10.7510 6.3383 12.2562 11.9588 6.7954 7.3614 7.9776 9.2208 6.5889 7.2355 8.3825 11.0720 10.8187 8.1916 11.3550 6.5516 11.5900 15.7000 9.1219 10.8634 10.4504 8.7644 11.0788 10.5289 8.5477 7.6728 7.0737 7.2802 12.1120 7.5145 10.7233 9.7564 8.8897 10.0299 10.5113 7.8311 6.9836 11.2670 13.3617 8.1713 8.7184 11.1262 10.9210 6.9572 7.3763 7.3479 7.7163 8.2539 10.2994 7.5653 6.8577 8.4103 6.5855 10.2222 6.3932 8.7102 10.0895 8.4543 8.5477 10.9386 7.2829 10.2229 7.5727 8.6290 4.8562 8.5003 8.5640 7.7609 7.1427 7.3818 9.2133 12.2366

[0214] Table 15. Influent BOD of auxiliary variable (mg / L)

[0215] 5.8200 5.7800 9.7800 11.6200 8.9000 11.1400 7.5800 6.2200 8.7000 6.1000 6.6200 9.8600 12.4644 9.5400 9.1400 6.4600 11.2200 6.2200 5.7400 5.2600 5.7800 5.7800 4.8600 5.2600 5.5800 7.5400 9.1800 11.6200 10.7000 7.7400 12.9800 15.2956 5.1400 4.9000 7.2200 6.7400 5.2600 7.7000 5.1800 8.2600 9.3000 6.4200 9.3800 5.8600 8.5800 12.0600 7.8600 7.3000 9.0600 5.6600 6.7400 9.5400 6.4600 7.9160 8.1400 8.3400 9.8200 8.4200 4.7800 9.2600 6.2600 10.3000 8.7800 7.4120 6.0600 8.6200 14.0822 9.0200 5.9800 9.8200 9.3000 6.3800 8.0200 6.3000 6.3400 9.1000 9.4200 5.8600 7.3800 5.0600 4.5000 10.9800 6.9400 4.9000 8.8600 5.5000 5.6200 10.2600 5.8600 9.1800 6.1000 5.2600 6.5800 7.5800 7.4200 8.4600 6.2600 7.6200 6.4200 11.3400

[0216] Table 16. Influent ammonia nitrogen of auxiliary variable (mg / L)

[0217] 8.1356 10.8022 8.7933 10.3933 11.1222 10.7889 10.6333 8.4378 10.8644 8.1356 8.0378 11.8689 15.7000 10.3800 9.5844 8.7578 9.8244 8.5356 7.1133 7.8244 8.1533 7.2200 7.7444 7.6778 8.3933 7.7089 15.0556 12.0378 12.0867 10.2111 11.7533 12.6333 8.7133 8.1089 7.6022 9.8733 7.1933 7.9044 7.8600 11.5756 12.7311 7.6022 10.6644 8.3311 12.6067 14.0556 12.6244 12.4778 11.0689 7.6244 12.1356 10.8867 10.2467 9.5844 8.6467 7.8022 12.5222 8.1533 7.3444 9.9933 8.7133 11.0289 10.4733 9.8156 7.6289 10.3222 12.7000 7.6467 7.5978 12.6778 10.6867 7.7667 7.2778 7.3711 8.5533 8.1356 11.8111 7.7622 7.3400 7.5933 7.6022 10.3044 7.9578 8.0911 10.1711 6.8289 7.8867 13.8778 7.4244 10.4956 10.4200 8.0378 10.6556 7.8511 7.7756 8.7756 8.4333 8.1667 8.7933 12.6067

[0218] Table 17. Effluent phosphate of auxiliary variable (mg / L)

[0219] 14.6250 10.1500 10.9500 11.1250 14.5500 11.3500 10.7250 13.9750 11.3750 13.6250 13.4000 11.7250 13.0556 11.3250 11.4000 14.3000 10.8750 14.0000 13.4000 13.5250 12.5500 13.7250 14.0250 14.1000 13.2750 12.4500 15.1000 14.4500 10.3750 13.9250 14.4000 14.1444 13.8500 14.1000 12.9250 8.3500 13.7000 12.3250 11.6750 9.6500 12.3750 12.8250 11.5500 13.5500 9.9750 12.9000 10.4750 9.5250 9.1750 14.2250 11.8500 9.5750 13.2250 13.7750 14.1250 11.6750 10.9750 13.6000 15.5250 6.9750 9.2500 11.5750 12.0250 13.9500 14.2500 11.8750 13.6778 13.3250 13.7500 12.7250 8.2750 13.7250 12.0250 13.8500 14.1500 13.6000 11.8750 11.7000 12.5750 11.5000 13.9500 7.4000 13.7500 14.5750 6.6250 12.9250 14.1250 11.5500 13.9250 7.5250 14.0750 14.3500 13.4750 14.3000 14.1500 14.3000 11.8000 14.5500 10.9000 14.9500

[0220] Table 18. Biochemical MLSS of auxiliary variable (mg / L)

[0221] 10.8844 12.2220 13.1706 12.4653 5.6370 11.2978 12.7693 14.4961 9.6683 11.4073 10.5743 11.7356 12.8422 11.6991 11.5046 14.4353 12.3801 14.2346 13.9549 12.8666 10.9999 14.3502 14.4718 14.0887 11.9302 12.6598 5.1324 5.6370 11.7052 14.8001 5.9289 12.6112 13.8941 14.5508 14.4535 12.2281 13.9306 12.9456 10.0270 12.3436 12.0640 14.3562 11.3343 14.1313 9.3764 13.0064 11.3343 11.5167 12.1612 11.2857 11.5289 11.3708 12.1612 11.3586 14.9643 12.8422 9.5893 11.3708 14.1009 13.0855 12.0153 11.5958 11.7052 10.9452 14.1009 9.2001 13.1767 14.5569 11.6322 12.5017 9.9845 14.4961 12.8605 14.8062 14.6724 14.3806 11.5532 9.9237 12.4166 9.7899 14.2225 11.0668 14.8183 12.3923 9.6805 14.4718 11.3951 12.1004 14.0887 12.5686 14.4414 12.1856 14.6967 9.8629 10.1304 14.3562 10.6229 14.0644 12.0092 12.4166

[0222] Table 19. Biochemical pool DO of auxiliary variable (mg / L)

[0223] 11.4597 9.0630 7.4959 7.9568 13.4877 8.8786 6.4358 10.0309 8.7403 9.4778 13.5337 9.1551 9.2012 8.9708 7.6342 8.2794 8.1872 9.9387 9.4317 10.9527 13.4416 12.2432 12.3354 10.4918 13.2572 13.1189 11.0449 10.6761 7.5420 13.5337 13.2111 10.1691 10.9527 12.0128 8.6481 8.5560 10.4918 12.5658 12.7502 9.0630 7.9568 12.5658 6.4358 13.0267 8.4177 9.3856 8.6481 8.0490 8.0951 13.2572 8.0490 8.8786 8.0029 8.9708 12.0588 13.1189 6.7584 8.9708 13.6259 8.0490 9.1551 9.1091 11.5058 8.8786 12.4737 7.4498 9.1551 11.4136 11.3214 7.9568 8.7403 11.5979 12.1049 10.1230 12.9807 11.2292 9.4778 12.1049 10.7222 14.0407 12.6119 7.8646 12.0588 13.8564 8.6481 13.2111 11.8284 8.4177 11.0449 9.0169 10.3074 13.7181 11.5519 13.3033 13.2111 11.1831 14.0868 12.3815 8.2333 13.3033

[0224] Table 20. Influent phosphate of auxiliary variable (mg / L)

[0225]

[0226]

[0227] Table 21. Influent COD of auxiliary variable (mg / L)

[0228] 9.2032 7.3698 5.6559 10.2794 13.1093 9.2431 10.8374 10.4388 9.7214 9.3626 9.6018 12.8701 9.8808 10.0801 9.1633 13.1890 11.1164 8.8843 6.0544 7.5292 9.2032 9.8808 8.0075 6.7719 9.3228 8.1270 10.4388 8.8445 11.8737 11.1164 10.3192 10.5982 12.1128 10.2794 10.5584 10.1199 7.9278 8.8843 9.2032 7.1306 8.7648 8.1669 11.9534 9.1633 10.8772 15.7000 13.2687 11.9135 9.8409 7.7683 11.0765 10.6779 10.5185 11.6744 9.8011 8.8843 10.8772 7.7683 4.8587 10.6779 9.6815 11.5548 8.9242 10.5584 8.6053 10.0801 10.3591 8.8046 7.2103 13.6274 9.9206 9.6018 9.1633 8.9242 12.1527 12.0331 14.4644 6.6125 7.0907 7.7683 7.5690 8.8046 9.8409 8.4459 8.5256 8.8445 7.7683 14.7833 8.5256 9.8409 12.3918 10.0004 9.3228 9.1633 8.2865 10.9968 8.5655 9.3626 8.0473 10.7178

[0229] Table 22. Measured effluent BOD concentration (mg / L)

[0230] 11.1429 11.6714 13.1286 12.8571 13.8429 14.5429 12.3143 10.9000 13.3857 10.9143 10.8000 12.6857 14.1000 13.8000 13.8143 10.3000 12.7429 10.2429 10.1286 10.2857 11.4286 11.0429 10.7143 10.7714 11.5143 11.4857 12.6714 14.5857 13.0857 12.2286 14.9571 15.5000 10.3857 10.2857 11.0286 12.1000 10.3143 11.4429 11.5714 12.6143 13.0000 11.1143 14.2857 10.1571 14.0000 13.9000 12.1143 14.0857 12.7286 10.8286 13.9000 12.5000 12.1714 12.6600 12.6000 10.8857 13.1000 12.8000 11.9000 12.5286 11.8857 12.7286 12.8000 12.5200 10.8000 12.9286 14.9000 10.6143 10.9857 13.2000 14.4000 11.1000 11.2286 11.0000 10.2714 10.6571 12.6429 11.7714 11.5286 11.6000 10.2000 12.6286 12.2429 11.7143 14.6571 11.1429 11.2000 13.1429 10.8000 12.7714 10.6000 11.4571 11.2571 11.4000 11.3000 11.2857 11.8571 11.4000 11.9714 11.9857

[0231] Table 23. Effluent BOD concentration predicted by the soft sensing method of the present invention (mg / L)

[0232] 12.0669 12.0669 12.0669 12.0669 12.0669 12.0669 12.0669 12.0669 12.0669 12.0669 13.3483 13.3483 13.3483 13.3483 13.3483 13.3483 13.3483 13.3483 13.3483 13.3483 13.356 13.356 13.356 13.356 13.356 13.356 13.356 13.356 13.356 13.356 13.4958 13.4958 13.4958 13.4958 13.4958 13.4958 13.4958 13.4958 13.4958 13.4958 14.0581 14.0581 14.0581 14.0581 14.0581 14.0581 14.0581 14.0581 14.0581 14.0581 12.3632 12.3632 12.3632 12.3632 12.3632 12.3632 12.3632 12.3632 12.3632 12.3632 10.8788 10.8788 10.8788 10.8788 10.8788 10.8788 10.8788 10.8788 10.8788 10.8788 13.4628 13.4628 13.4628 13.4628 13.4628 13.4628 13.4628 13.4628 13.4628 13.4628 10.8104 10.8104 10.8104 10.8104 10.8104 10.8104 10.8104 10.8104 10.8104 10.8104 11.0117 11.0117 11.0117 11.0117 11.0117 11.0117 11.0117 11.0117 11.0117 11.0117

Claims

1. A soft measurement method for effluent BOD based on self-organizing feedforward small-world neural network, characterized in that It includes the following steps: Step 1: Data preprocessing; Select M input variables related to the effluent BOD, normalize them to [-1, 1] according to formula (1), and the output variable is the effluent BOD, which is normalized to [0, 1] according to formula (2): Among them, F m represents the m-th auxiliary variable, x m and y respectively represent the normalized m-th auxiliary variable and the output variable, O represents the output variable; min(F m ) and max(F m ) respectively represent the minimum value and the maximum value in the m-th auxiliary variable; min(O) and max(O) respectively represent the minimum value and the maximum value in the output variable; The m auxiliary variables are specifically 10 auxiliary variables: (1) Effluent total nitrogen concentration; (2) Effluent ammonia nitrogen concentration; (3) Influent total nitrogen concentration; (4) Influent BOD concentration; (5) Influent ammonia nitrogen concentration; (6) Effluent phosphate concentration; (7) Mixed liquor suspended solids concentration MLSS in the biochemical pool; (8) Dissolved oxygen concentration (DO) in the biochemical pool; (9) Influent phosphate concentration; (10) Influent COD concentration; Step 2: Design a feedforward small-world neural network model; Step 2.1: Construct an L-layer standard feedforward neural network model; its structure consists of an input layer, an output layer, and L - 2 hidden layers. There are fully connected connections between adjacent layers. Randomly initialize the connection weights W and V, where W is the hidden layer connection matrix and V is the output layer connection matrix, and their value ranges are [-1, 1]; Step 2.2: Design the reconnection method of the feedforward neural network; calculate the maximum number of reconnection edges N max It is: N max = min (N1, N2) (3) Where N1 represents the number of adjacent connections allowed to be rewired, and N2 represents the number of cross-layer connections allowed to be rewired, which are calculated respectively as: Introduce a predefined parameter, the rewiring probability p, with a value range of [0, 1]; define the number of rewired edges N R = round(p * N max ), randomly select N R connections, and perform rewiring according to the Watts-Strogatz rule: disconnect the selected connection from one end and then reconnect it to another neuron. If there is already a connection between these two neurons, cancel it and then select another neuron for rewiring until a new rewired connection is generated; repeat until the number of rewired edges reaches the predefined N R edges; Step 2.3: Design the topological structure of the feedforward small-world neural network model; the expressions of each layer after rewiring are as follows: ① Input layer: The number of neurons in the input layer is set to M, representing M measured auxiliary variables. The input vector is denoted as represents the i-th input auxiliary variable of the input layer. Then, the output of the i-th neuron is calculated as: ② Hidden layer: The output of the jth hidden neuron in the lth layer where 1 ≤ l ≤ L is expressed as: where n s represents the number of neurons in the s-th layer, represents the connection weight from the i-th neuron in the s-th layer directly connecting to the j-th neuron in the l-th layer, represents the output of the i-th neuron in the s-th layer, and the activation function f(·) of the hidden neurons is the sigmoid function; where 1 ≤ s ≤ l - 1; ③ Output layer: The output layer contains an output neuron o, and its output is calculated by summing the linear weights of its inputs, defined as Among them represents the connection weight between the j-th neuron in the l-th layer of the neural network and the output neuron, represents the output of the j-th neuron in the l-th layer, n l represents the number of neurons in the l-th layer of the neural network; where 1 ≤ l ≤ L - 1; Step 3: Design a feedforward small-world network self-organization algorithm; Step 3.1: Define performance metrics: where Q is the number of samples, and d q and represent the expected output and the actual output of the neural network for the q-th sample, respectively; Step 3.2: Initialize the training iteration number as t = 0, the splitting coefficient θ split , the merging coefficient θ merge , the maximum iteration number T max and the expected training RMSE value, i.e., E d , T max has a value range of [5000, 10000], and E d has a value range of (0, 0.3]; Step 3.3: Increase the training iteration step \(t\) by 1; when \(t < T\) max execute Steps 3.4 to 3.9 to update the algorithm parameters, otherwise jump to Step 3.10; Step 3.4: Use the batch processing backpropagation BP algorithm for training. In each iterative training, adjust according to the following formula; ① The connection weight from the jth neuron in the sth layer to the output neuron: Where where d q and represent the expected output and the actual output of the neural network for the q-th sample respectively, and δ o (t) represents the difference between the expected output and the actual output of the neural network for the q-th sample, and represent the connection weight and its change value from the j-th neuron in the s-th layer to the output neuron respectively, represents the output of the j-th neuron in the s-th layer, t represents the t-th iteration of the neural network, η represents the learning rate, and Q represents the total number of samples; ② The connection weight between the ith neuron in the sth layer and the jth neuron in the lth layer is updated according to the following: Where and respectively represent the connection weight from the $i$-th neuron in the $s$-th layer to the $j$-th neuron in the $l$-th layer and its change value, represents the connection weight from the $j$-th neuron in the $l$-th layer to the $k$-th neuron in the $d$-th layer, represents the output of the $j$-th neuron in the $s$-th layer, represents the output of the $j$-th neuron in the $l$-th layer, $t$ represents the $t$-th iteration of the neural network, and $\eta$ represents the learning rate, and respectively represent the errors between the expected output and the actual output of the $j$-th neuron in the $l$-th layer and the $k$-th neuron in the $d$-th layer; Step 3.5: Calculate the training RSME according to formula (15): where Q is the total number of training samples, d q and are the expected output and the actual output of the q-th sample respectively. When the RMSE is greater than the expected RSME value E d or the number of iterations t reaches the set maximum value T max stop training, otherwise go to step 3.5; T max ranges from [5000, 10000]; Step 3.6: Calculate the hub centrality values of all nodes in the network; ① The hub and authority values of the network nodes are respectively initialized as h(0) = [1, 1, …, 1] T and a(0) = [1, 1, …, 1] T ; ② The hub and authority values of each node are iteratively updated according to the formula: h (k) = Aa (k-1) (16) a (k) = Ah (k-1) (17) Where k represents the number of iterative steps, and A is the adjacency matrix of the connection weights A = (w ij ) (18) where when there is a direct connection between node i and node j, w ij is 1, otherwise w ij is 0; ③ Normalize the hub and authority values of the nodes according to the following formula: where ||·|| is the 1-norm, calculated as the sum of the absolute values of the individual elements, and represent the hub and authority values of node i at the k-th iteration, respectively; ④ The iteration continues until the hub and authority values converge; Step 3.7: Evaluation of neuron importance based on hub centrality; for each hidden layer neuron, calculate the hub centrality value of each neuron and the average hub centrality of all neurons in the network through Step 3.4 For each hidden layer neuron, if then it is considered that the neuron is an important neuron to be split, and go to Step 3.8; θ split is a predefined splitting threshold, and the value range is [1.1, 1.4]; if then it is considered that the neuron is an unimportant neuron to be merged, and go to Step 3.9; θ merge is a predefined splitting threshold, and the value range is [0.8, 1); Step 3.8: Split important nodes; The important node is denoted as the ath node in the sth layer. The input weights of the two new neurons a1 and a2 obtained by splitting are the same as those of neuron a, that is wherein is the connection weight from the i-th node in the l1 layer to the a1-th node in the s layer, is the connection weight from the i-th node in the l1 layer to the a2-th node in the s layer, is the connection weight from the i-th node in the l1 layer to the a-th node in the s layer; wherein 1 ≤ l1 ≤ s - 1; The connection weights from the two new nodes to the hidden layer neurons and to the output neuron o are defined respectively as follows: Among them represents the connection weight from the a1-th node in the s-th layer to the j-th node in the l2-th layer (s < l2 < L), represents the connection weight from the a1-th node in the s-th layer to the output neuron o; represents the connection weight from the a2-th node in the s-th layer to the j-th node in the l2-th layer, represents the connection weight from the a2-th node in the s-th layer to the output neuron o; represents the connection weight from the a-th node in the s-th layer to the j-th node in the l2-th layer, represents the connection weight from the a-th node in the s-th layer to the output neuron o; α is a mutation parameter, and its value range is (0, 1); Step 3.9: Merge unimportant nodes with their most relevant neurons; The unimportant node is denoted as the bth node in the sth layer. Calculate its relationship with other neurons in the same layer based on the Pearson correlation coefficient, defined as: where is the output vector of the i-th node in the s-th layer, and σ i are the mean and standard deviation, respectively, of all training samples ; is the output vector of the b-th node in the s-th layer, and σ b are the mean and standard deviation, respectively, of all training samples ; q represents the q-th sample and Q is the total number of samples. Select the neuron c with the highest relevance as the neuron to merge with the unimportant neuron b, and obtain the new neuron b'. The connections between the neurons in the l-th (1 ≤ l < s) layer and the neuron b' in the s-th layer are constructed according to the rewiring rule of Watt-Strogatz with the same rewiring probability p as in Step 2.2, and the initial connection weights are randomly set within the range of [-1, 1]; The output weights of the new neuron b' to the hidden layer neurons and to the output neurons are respectively defined as: Among them, is the connection weight from the neuron b' in the s-th layer to the j-th neuron in the l2 layer, representing the connection weight from the neuron b in the s-th layer to the j-th neuron in the l2 layer, representing the connection weight from the neuron c in the s-th layer to the j-th neuron in the l2 layer; represents the connection weight from the neuron b' to the output neuron, represents the connection weight from the neuron b to the output neuron, represents the connection weight from the neuron c to the output neuron; is the output of the neuron b in the s-th layer, is the output of the neuron c in the s-th layer, is the output of the neuron b' in the s-th layer, The calculation is as follows: wherein represents the number of neurons in the l1-th (1 ≤ l1 ≤ s - 1) layer, is the connection weight from the i-th neuron in the l1-th layer to the neuron b' in the s-th layer, is the output of the i-th neuron in the l1-th layer; Step 3.10: Calculate the training RSME according to formula (15); when the RMSE is greater than the expected RSME value E d or the number of iterations t reaches the set maximum value T max stop training, otherwise repeat steps 3.3 to 3.9; Step 4: Effluent BOD prediction; Use the test sample data as the input of the trained self-organizing feedforward small-world neural network to obtain the output of the neural network, and perform anti-normalization on it to obtain the predicted value of the effluent BOD concentration.

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