A soft measurement method for total phosphorus concentration in effluent based on fuzzy random configuration network

Abstract

A soft measurement method for total phosphorus concentration in effluent based on fuzzy randomized configuration networks (FRAM) relates to the field of industrial artificial intelligence and is directly applied to wastewater treatment. This invention integrates the advantages of both FRAM and TS fuzzy inference rules, designing a novel neural-fuzzy model called the Fuzzy Randomized Configuration Network (FRAM) to further enhance the nonlinear processing capability, self-learning capability, and fuzzy inference capability of FRAM, thereby achieving accurate and efficient measurement of total phosphorus concentration in wastewater effluent from wastewater treatment processes.

Description

Technical fields:

[0001] This invention relates to the field of industrial artificial intelligence and is directly applied to the field of wastewater treatment. Background technology:

[0002] Wastewater treatment is a crucial pathway for water resource management and prevention. It involves effectively treating urban sewage and industrial wastewater to meet national discharge standards. The aim is to achieve water resource reuse while protecting the ecological environment. Monitoring the total phosphorus concentration in the effluent is a key indicator of water quality. Excessively high total phosphorus concentrations can lead to eutrophication, severely damaging surrounding ecosystems such as fish and aquatic life. Monitoring effluent total phosphorus allows for timely detection of problems in the wastewater treatment process, enabling prompt adjustments to ensure compliance with discharge standards and minimizing environmental impact. Therefore, timely and effective monitoring of effluent total phosphorus is of paramount importance.

[0003] Currently, common methods used in my country's wastewater treatment plants to measure total phosphorus in wastewater include chemical analysis and spectrophotometry. While these methods offer high accuracy, they also suffer from drawbacks such as complex operation, long testing cycles, high costs, and high consumption, making it difficult to achieve timely and effective measurement of total phosphorus concentration in effluent. In recent years, with the rapid development of digital information technology, data-driven soft measurement technologies have seen rapid growth due to their simplicity and ease of operation. Among these, stochastic learning models, represented by stochastic configuration networks, have experienced rapid development and are widely used in fields such as industrial data modeling due to their computational simplicity, strong approximation ability, and rapid learning. However, it is worth noting that actual wastewater treatment processes are influenced by a series of biochemical reactions and various complex uncertainties, resulting in highly nonlinear, complex, uncertain, and fuzzy characteristics in the collected water quality data. Furthermore, stochastic configuration networks are limited in their ability to handle the modeling and interpretability of such complex fuzzy systems. To this end, this invention integrates the advantages of random configuration networks and TS fuzzy inference rules, and designs a neural-fuzzy model called fuzzy random configuration network to further improve the nonlinear processing capability, self-learning capability and fuzzy inference capability of random configuration networks, thereby achieving accurate and efficient measurement of total phosphorus concentration in wastewater effluent from wastewater treatment processes. Summary of the Invention

[0004] This invention presents a soft measurement method for total phosphorus concentration in effluent using a fuzzy stochastic configuration network with self-learning capabilities. The model employs the TS fuzzy inference rule for reasoning and processing fuzzy information, while simultaneously using a stochastic configuration algorithm for adaptive learning and optimization of the network structure and parameters. Specifically, this method introduces the TS fuzzy inference system into the stochastic configuration network to replace the original hidden layers, and adds enhancement layers to improve the model's fuzzy inference and nonlinear processing capabilities, thereby achieving accurate and efficient measurement of total phosphorus concentration in effluent.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] Step 1: Wastewater treatment process water quality data collection and preprocessing; Based on the actual water quality data collected during wastewater treatment at a certain wastewater treatment plant, nine variables were selected as input variables for the model: ① temperature, ② anaerobic terminal oxidation-reduction potential (OPR), ③ aerobic front-end dissolved oxygen concentration (DO), ④ aerobic terminal dissolved oxygen concentration (DO2), ⑤ suspended solids concentration (TSS), ⑥ pH value, ⑦ effluent oxidation-reduction potential (OPR2), ⑧ effluent ammonia nitrogen concentration, and ⑨ effluent nitrate nitrogen concentration (NO3-N). The effluent total phosphorus concentration (TP) was used as the output variable for the model output.

[0007] Step 2: Design a soft measurement model for total phosphorus concentration in effluent based on a fuzzy random configuration network;

[0008] The construction process of this soft measurement model includes an input layer, a fuzzy inference module, an enhancement layer, and an output layer; the fuzzy inference module consists of a fuzzy membership layer and a fuzzy rule layer. Therefore, the proposed fuzzy ad-hoc configuration network comprises five layers: an input layer, a fuzzy membership layer, a rule layer, an enhancement layer, and an output layer. The main construction process and key functional implementations of the model are detailed below:

[0009] Step 2.1: The input layer is used to pass data; the data is passed to the fuzzy membership layer through the input layer. The number of nodes in the input layer is 9, which is the same as the number of input variables.

[0010] Step 2.2: The fuzzy membership layer is used to fuzzify the input data. In this layer, the cluster centers C and the number of clusters K of the samples are set based on the k-means method, and these are used to set the fuzzy membership function to fuzzify the input data. Here, the Gaussian membership function is selected as the fuzzy membership function.

[0011] The fuzzy membership function is represented as follows:

[0012]

[0013] in, and Let x represent the k-th fuzzy rule and the sample x, respectively. n The center and width of the membership function corresponding to the i-th feature, and d represents the cluster centers obtained by the k-means method, and d is the number of features of the sample.

[0014] Step 2.3: The rule layer is used to extract fuzzy rules; in this layer, fuzzy rules are extracted from the input data based on the TS fuzzy rules, and the output of the fuzzy inference module for the nth sample is obtained as follows:

[0015]

[0016] here Let be the fuzzy consequent parameter factor corresponding to the k-th fuzzy rule. Here, it is set to a random number that follows a normal distribution [0,1], i = 1, 2, ..., d, where d is 9 to represent the dimension of the input feature. Let represent the i-th input variable of the n-th sample, k = 1, 2, ..., K represent the k-th fuzzy rule, and K be the total number of fuzzy rules. The activation intensity of each fuzzy rule after normalization is expressed as:

[0017]

[0018] This represents the activation intensity of the k-th fuzzy rule corresponding to the n-th sample, where n = 1, 2, ..., N represents the n-th sample, and N is the total number of samples. It can be calculated using the following formula:

[0019]

[0020] in, This indicates that the nth sample corresponds to the i-th input variable. The corresponding fuzzy membership values, i = 1, 2, ..., d are the input feature dimensions, and k = 1, 2, ..., K are the number of fuzzy rules.

[0021] Therefore, the output of the fuzzy module can be described in matrix form as follows:

[0022]

[0023] in, This represents the activation intensity matrix of each fuzzy rule after normalization.

[0024] Represents a diagonal matrix composed of fuzzy afterimage parameters;

[0025] Step 2.4: The enhancement layer is used to extract nonlinear information from fuzzy rules; the number of nodes L in this layer can be constructed based on the feature distribution of the input data using a random configuration algorithm. Here, the maximum number of nodes L is set. max =30. The purpose is to supplement some nonlinear information in the fuzzy system. The output H of this layer node is:

[0026]

[0027] Where N is the number of samples, and L is the number of nodes in the enhancement layer; the activation function of the nodes in the enhancement layer... Using the sigmoid function, the activation function for the j-th boosting node is expressed as follows:

[0028]

[0029] Where, <·> represents the inner product of Euclidean space; H0(x n ) represents the output of the nth sample after passing through the fuzzy module, w j ,b j are the input weights and thresholds of the j-th node in the enhancement layer, respectively, which are randomly generated in [-λ, λ] and constrained by the inequality condition (14) of the random allocation algorithm, where x is a positive real number; n This represents the nth sample, where n = 1, 2, ..., N; at this time, the output H of the jth hidden node is... j (X) is represented as:

[0030]

[0031] Step 2.5: By fusing the outputs of the enhancement layer and the fuzzy inference model, the input Z of the network output layer is obtained. Z is a matrix composed of the output H0 of the fuzzy rule layer and the output H of the enhancement layer, i.e.:

[0032]

[0033]

[0034] Set β j If is the output weight vector of the j-th hidden node, then the output of the current network is:

[0035]

[0036] The current network output residual is:

[0037] e L =ff L =[e L,1 ,e L,2 .e L,M(12)

[0038] The current network output residual ||e L ||For:

[0039]

[0040] Where m = 1, 2, ..., M, represents the number of nodes in the output layer. If the output residual of the current network is ||e L ||Failed to meet the network's preset error tolerance requirements, i.e., ||e L ||≤e P ,e P To preset the tolerance error threshold, e is set here. P If the value is 0.001, the network will select new hidden nodes for the construction of the network enhancement layer nodes according to the random allocation algorithm. At this point, the number of network enhancement layer nodes is L = L + 1. Set the termination condition ||e L ||≤e P or L≥L max ,L max =30 is a preset maximum number of nodes in the enhancement layer. Network construction stops when the model meets the above termination condition. The random allocation algorithm used in this design can be briefly described as follows:

[0041] Suppose that Γ:={H1,H2,H3,…} represents a set of real-valued functions, and span(Γ) represents a dense function space of Γ in L2 space. There exists 0 ≤ ||H|| ≤ b H ,in Given positive real numbers; 0 < r < 1, and a sequence of non-negative real values ​​{μ} L}, And μ L ≤(1-r),. For L=1,2,..., define the error reduction factor δ for the Lth hidden node. L as follows:

[0042]

[0043] δ L,m δ L For the m-th output component, M is the output dimension, ||e L-1,m || 2 The squared value of the L2 norm of the network output error after constructing the (L-1)th hidden node; wherein the generated hidden node satisfies the condition

[0044]

[0045] The output weight β between the hidden layer and the output layer is calculated as follows:

[0046]

[0047] Then for the objective function f, we can obtain in

[0048] To minimize the structural and empirical risks of the model, a loss function with a regularization term is used here. To ensure that the minimum approximation error is obtained while simultaneously obtaining the minimum output weight β, that is:

[0049]

[0050] Here, Y is the expected output of the network, Z is obtained through formula (8), η is the penalty parameter, set to η = 0.001, and I represents the identity matrix; therefore, the output weights of the network can be calculated by the following formula:

[0051] β=(Z T Z+ηI) -1 Z T Y (18)

[0052] Step 3: Based on Step 2, the constructed fuzzy randomized network is obtained, and the total phosphorus concentration in the effluent of the urban sewage treatment process is measured based on the constructed model to obtain the measured value of the total phosphorus concentration in the effluent.

[0053] This invention addresses the impact of a series of biochemical reactions and highly complex uncertainties in wastewater treatment processes, which lead to highly nonlinear, complex, and uncertain fuzzy characteristics in the collected data. To achieve accurate and effective monitoring of effluent total phosphorus concentration, a novel soft measurement model for effluent total phosphorus concentration based on a fuzzy stochastic configuration network is proposed. This method utilizes a TS fuzzy inference system to enable fuzzy inference capabilities in the constructed model. Furthermore, a stochastic configuration algorithm autonomously constructs the model's parameters and structure based on collected water quality data, thereby improving the measurement performance of effluent total phosphorus. Therefore, the proposed method has the following advantages:

[0054] 1) It can autonomously generate the corresponding network structure and parameters based on the characteristics of the data stream acquired by the wastewater treatment plant;

[0055] 2) By introducing the TS fuzzy system into the stochastic configuration network, the model has a certain fuzzy reasoning ability and naturally inherits the general approximation ability of SCNs.

[0056] 3) Since the generation of fuzzy rules is related to the distribution characteristics of the model's input and output data, it helps to improve the interpretability and reliability of the model to a certain extent.

[0057] 4) By enhancing the nonlinearity of the fuzzy rules through the enhancement layer, the nonlinearity processing capability of the model is further improved;

[0058] 5) Through autonomous learning of network parameters and structure, the model has good fuzzy reasoning and nonlinear processing capabilities, enabling it to better measure the total phosphorus concentration in the effluent accurately and efficiently. Attached Figure Description

[0059] Figure 1 This is a basic flowchart of the algorithm of the present invention;

[0060] Figure 2 A basic structure diagram of a fuzzy random configuration network;

[0061] Figure 3 This is a graph showing the total phosphorus test results in the effluent for this example.

[0062] Figure 4 This is a graph showing the error in the total phosphorus test of the effluent in this example. Detailed Implementation

[0063] The experimental data consisted of 492 sets of water quality data obtained from a real wastewater treatment plant during the wastewater treatment process. By analyzing the total phosphorus concentration in the effluent during the wastewater treatment process, nine variables were selected as input variables for the model: ① temperature, ② anaerobic terminal oxidation-reduction potential (OPR), ③ aerobic front-end dissolved oxygen (DO), ④ aerobic terminal dissolved oxygen (DO2), ⑤ suspended solids (TSS), ⑥ pH value, ⑦ effluent OPR2, ⑧ effluent ammonia nitrogen concentration, and ⑨ effluent nitrate nitrogen concentration (NO3-N). The total phosphorus concentration (TP) was used as the output variable for the model. Here, 75% of the samples were selected as the training set, and the remaining 25% as the test set. The main steps are as follows:

[0064] Step 1: Data Preprocessing

[0065] Choose an input variable, denoted as X = {x in |i=1,2,…,d,n=1,2,…,N}, where i is the dimension of the input features, here i=9; N is the number of samples. in This is represented as the i-th feature value corresponding to the n-th data point. The total phosphorus concentration in the effluent is selected as the output variable, denoted as Y = {y...} n |n=1,2,…,N},y nThis represents the expected output value corresponding to the nth sample. Here, because the collected water quality data have different dimensions and the data values ​​corresponding to different variables vary significantly, a normalization operation is performed on the collected water quality data to avoid the influence of different feature values ​​and dimensions on the performance of the constructed model. Specifically, the input variable X and the corresponding output variable Y of the model are normalized according to the following formula:

[0066]

[0067]

[0068] Here, X and Y represent the data after normalization, and their values ​​range from [0,1].

[0069] Step 2: Design a soft measurement model for total phosphorus concentration in effluent based on a fuzzy random configuration network;

[0070] The construction process of this soft measurement model includes an input layer, a fuzzy inference module, an enhancement layer, and an output layer; the fuzzy inference module consists of a fuzzy membership layer and a fuzzy rule layer. Therefore, the proposed fuzzy ad-hoc configuration network comprises five layers: an input layer, a fuzzy membership layer, a rule layer, an enhancement layer, and an output layer. The main construction process and key functional implementations of the model are detailed below:

[0071] Step 2.1: Based on the data collected by the system, the data is passed to the fuzzy membership layer through the input layer. The number of nodes in the input layer is 9, the same as the number of input variables. Each node in this layer represents the feature value of each sample. This layer contains d = 9 nodes, and the connection weight between this layer and the next layer is 1, used to pass the feature components of the input samples. Assuming the nth sample is used for network training, the input of this layer is...

[0072] Step 2.2: Based on the k-means method, set the cluster centers C and the number of clusters K for the samples, and use them to set the fuzzy membership function to fuzzify the input data. Here, the Gaussian function is chosen as the fuzzy membership function. In the fuzzy membership layer, each node represents a corresponding linguistic variable value. The output of the node in this layer is the membership function of the input component belonging to the fuzzy set. Therefore, the i-th input variable of the n-th input sample... The corresponding fuzzy membership degree is It can be obtained by calculating the Gaussian membership function, where the center of the Gaussian membership function is the cluster center C obtained by k-means, k = 1, 2, ... K, representing the fuzzy rule, which is the same as the number of clusters K.

[0073] Step 2.3: Extract fuzzy rules from the input data based on TS fuzzy rules. In the fuzzy rule layer, each node represents a fuzzy rule used to match the corresponding fuzzy rule antecedent. The output of the fuzzy inference module is as follows:

[0074]

[0075] here Here, is a fuzzy consequent parameter factor, which is set to a random number following a normal distribution [0,1], i = 1, 2, ..., d, where d is 9 to represent the dimension of the input feature; Let i represent the i-th input variable of the n-th sample, and k = 1, 2, ..., K represent the k-th fuzzy rule; The activation strength of each fuzzy rule after normalization:

[0076]

[0077] This represents the activation intensity of the k-th fuzzy rule corresponding to the n-th sample, where n = 1, 2, ..., N represents the n-th sample and N is the total number of samples.

[0078] Therefore, the output of the fuzzy module can be described in matrix form as follows:

[0079]

[0080] in, This represents the activation intensity matrix of each fuzzy rule after normalization.

[0081] Represents a diagonal matrix composed of fuzzy afterimage parameters;

[0082] Step 2.4: Based on the nonlinear information processing capability of the enhancement layer model, the number of nodes L in this layer can be constructed according to the feature distribution of the input data using a random allocation algorithm. Here, the maximum number of nodes L is set to 30. The purpose is to supplement some nonlinear information in the fuzzy system. The output of the nodes in this layer is:

[0083]

[0084] Where N is the number of samples, and L is the number of nodes in the enhancement layer; the activation function of the nodes in the enhancement layer... Using the sigmoid function, the activation function for the j-th boosting node is expressed as follows:

[0085]

[0086] Where, <·> represents the inner product of Euclidean space; H0(x n) represents the output of the nth sample after passing through the fuzzy module, w j ,b j Let be the input weights and thresholds of the j-th node in the enhancement layer, respectively, which are randomly generated in [-λ, λ]. x is a positive real number and is subject to the inequality condition (25) of the random allocation algorithm; n This represents the nth sample, where n = 1, 2, ..., N;

[0087] The inequality constraint for selecting hidden layer node parameters in the network is as follows:

[0088]

[0089] In the formula: e j-1,m (X) represents the m-th output error component for input sample X after the (j-1)-th augmentation node is constructed. This represents the output of the j-th hidden node, j = 1, ..., L, where 0 < r < 1 is the error reduction factor, μ. j ≤(1-r) is a non-negative real number sequence and

[0090] The output of the j-th hidden node at this point:

[0091]

[0092] Step 2.5: The input to the network output layer is obtained by fusing the outputs of the enhancement layer and the fuzzy inference model; Z is the matrix composed of the output H0 of the fuzzy rule layer and the output H of the enhancement layer, i.e.:

[0093]

[0094]

[0095] Set β j If is the output weight vector of the j-th hidden node, then the output of the current network is:

[0096]

[0097] Given the objective function f, the output residual of the current network is:

[0098] e L =ff L =[e L,1 ,e L,2 .e L,M (31)

[0099] The current network output residual ||e L ||For:

[0100]

[0101] Where m = 1, 2, ..., M, represents the number of nodes in the output layer. If the output residual of the current network is ||e L ||Failed to meet the network's preset error tolerance requirements, i.e., ||e L ||≤e P ,e P To preset the tolerance error threshold, e is set here. P If the value is 0.001, the network will select new hidden nodes for the construction of the network enhancement layer nodes according to the random allocation algorithm. At this point, the number of network enhancement layer nodes is L = L + 1. Set the termination condition ||e L ||≤e P or L≥L max ,L max =100 is a preset maximum number of nodes in the enhancement layer. Network construction stops when the model meets the above termination condition. In this design, the following randomized allocation algorithm is used to learn the network parameters and results, which can be briefly described as follows:

[0102] Suppose that Γ:={H1,H2,H3,…} represents a set of real-valued functions, and span(Γ) represents a dense function space of Γ in L2 space. There exists 0 ≤ ||H|| ≤ b H ,in Given positive real numbers; 0 < r < 1 and a non-negative real value sequence {μ} L}, And μ L ≤(1-r),. For L=1,2,..., define the error reduction factor δ for the Lth hidden node. L as follows:

[0103]

[0104] δ L,m δ L For the m-th output component, M is the output dimension, ||e L-1,m || 2 The squared value of the L2 norm of the network output error after constructing the (L-1)th hidden node; wherein the generated hidden node satisfies the condition

[0105]

[0106] The output weight β between the hidden layer and the output layer is calculated as follows:

[0107]

[0108] Then for the objective function f, we can obtain in β j =[β j,1 ,β j,2 ,...,β j,M ] T .

[0109] To minimize the structural and empirical risks of the model, a loss function with a regularization term is used here. To ensure that the minimum approximation error is obtained while simultaneously obtaining the minimum output weight β, that is:

[0110]

[0111] Here, Y represents the desired output of the network, and the input matrix Z of the output layer is obtained through formula (7). Here, η is the penalty parameter, set to η = 0.001, and I represents the identity matrix. Therefore, the output weights of the network can be calculated using the following formula:

[0112] β=(Z T Z+ηI) -1 Z T Y (37)

[0113] Step 3: Based on Step 2, the constructed fuzzy randomized network is obtained, and the total phosphorus concentration in the effluent of the urban sewage treatment process is measured based on the constructed model to obtain the measured value of the total phosphorus concentration in the effluent.

Claims

1. A soft measurement method for total phosphorus concentration in effluent based on fuzzy random configuration networks, characterized in that, Includes the following steps: Step 1: Wastewater treatment process water quality data collection and pretreatment; Based on actual water quality data collected during wastewater treatment at a wastewater treatment plant, the following parameters were selected: ① temperature, ② oxidation-reduction potential (OPR) at the anaerobic end, ③ dissolved oxygen concentration (DO) at the aerobic end, ④ dissolved oxygen concentration (DO2) at the aerobic end, ⑤ suspended solids concentration (TSS), and ⑥ pH value. OPR2 of effluent oxidation-reduction potential Ammonia nitrogen concentration in effluent (NH3-N) Nine variables, including effluent nitrate nitrogen concentration (NO3-N), are used as input variables for the model, while effluent total phosphorus concentration (TP) is used as the output variable for the model. Step 2: Design a soft measurement model for total phosphorus concentration in effluent based on a fuzzy random configuration network; The soft measurement model comprises an input layer, a fuzzy inference module, an enhancement layer, and an output layer. The fuzzy inference module includes a fuzzy membership layer and a fuzzy rule layer. Therefore, the developed fuzzy ad-hoc configuration network consists of five layers: an input layer, a fuzzy membership layer, a rule layer, an enhancement layer, and an output layer. The functions and implementations of each layer are described in detail below. Step 2.1: The input layer is used to pass data; the data is passed to the fuzzy membership layer through the input layer. The number of nodes in the input layer is 9, which is the same as the number of input variables. Step 2.2: The fuzzy membership layer is used to fuzzify the input data. Specifically, the cluster centers C and the number of clusters K are set based on the k-means method. Here, the Gaussian membership function is chosen as the fuzzy membership function, and the cluster centers obtained by the k-means method are used as the centers of the corresponding fuzzy membership functions to achieve fuzzification of the input data. The fuzzy membership function is expressed as follows: in, and Let x represent the k-th fuzzy rule and the sample x, respectively. n The center and width of the membership function corresponding to the i-th feature, and , The cluster centers are obtained by the k-means method, and d is the number of features of the sample. Step 2.3: The rule layer is used to extract fuzzy rules; in this layer, fuzzy rules are extracted from the fuzzified data based on TS fuzzy rules, and the output of the fuzzy inference rules is as follows: here Let be the fuzzy consequent parameter factor corresponding to the k-th fuzzy rule. Here, it is set to a random number that follows a normal distribution in [0,1], i=1,2,…d, where d is 9 to represent the dimension of the input feature. Let represent the i-th input variable of the n-th sample, k=1,2,…K represent the k-th fuzzy rule, and K be the total number of fuzzy rules. The activation intensity of each fuzzy rule after normalization is expressed as: This represents the activation intensity of the k-th fuzzy rule corresponding to the n-th sample, where n=1,2,…N represents the n-th sample and N is the total number of samples; Therefore, the output of the fuzzy rule layer can be described in matrix form as follows: in, This represents the activation intensity matrix of each fuzzy rule after normalization. Represents a diagonal matrix composed of fuzzy afterimage parameters; Step 2.4: The enhancement layer is used to extract nonlinear information from fuzzy rules; the number of nodes L in this layer is set to the maximum number of nodes to be constructed. max =30; When the network's output error precision does not meet the preset error, a new L-th hidden node is added, and the output H is: Where N is the number of samples, and L is the number of nodes in the enhancement layer; the activation function of the nodes in the enhancement layer... Using the sigmoid function, the activation function for the j-th boosting node is expressed as follows: Where, <ꞏ> represents the inner volume of a European-style space; The output of the nth sample after applying the fuzzy rule. Let be the input weights and thresholds of the j-th node in the enhancement layer, respectively. The values ​​are randomly generated and subject to the inequality condition (14) of the random allocation algorithm, where x is a positive real number; n This represents the nth sample, where n = 1, 2, ..., N; The inequality constraint for selecting hidden layer node parameters in the network is as follows: （7） In the formula: This represents the m-th output error component for input sample X after the (j-1)-th augmentation node is constructed; This represents the output of the j-th hidden node, j=1,…L. As the error reduction factor, It is a sequence of non-negative real numbers and At this point, the output of the j-th hidden node... Represented as: Step 2.5: The final input Z of the output layer is obtained by fusing the outputs of the enhancement layer and the fuzzy rule layer; Z is a matrix composed of the output H0 of the fuzzy rule layer and the output H of the enhancement layer, that is: To minimize the structural and empirical risks of the model, a loss function with a regularization term is used here. This ensures that the network's output weights are minimized while obtaining the minimum approximation error. ,Right now: Here, Y is the expected output of the network, and Z is obtained through formula (8). Set the penalty parameter. =0.001, where I represents the identity matrix; therefore, the network's output weight vector The following formula is used to calculate: Where K is the total number of fuzzy rules, and L is the number of enhancement layer nodes; at this time, the network output is: Given an objective function f, which is the same as the desired output Y, the output residual of the current network is: Therefore, the current network's corresponding output error value for: Step 3: Determine whether the fuzzy randomized network constructed in Step 2 meets the termination condition, i.e., the output error reaches the expected error accuracy. , To preset the tolerance error threshold and set =0.001, or the maximum number of enhanced nodes is reached. , The maximum number of hidden nodes is preset; if the termination condition is not met, return to step 2.4, add a new Lth hidden node in the enhancement layer, and stop network construction until the termination condition is met; then, based on the constructed model, measure the total phosphorus concentration in the effluent of the urban sewage treatment process, and finally obtain the measured value of the total phosphorus concentration in the effluent.

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