A multi-index identification method for membrane fouling based on a cascaded neural network

Abstract

The present invention proposes a multi-index identification method for membrane fouling based on a cascaded neural network. It is characterized in that this method takes into account the interference of irrelevant input variables on the output index, can avoid the influence of irrelevant variables on the output based on the cascaded structure, and adjusts the parameters of the cascaded neural network through a hierarchical learning algorithm to achieve the prediction of multi-indicators of membrane fouling, solves the problem that the prediction accuracy of multi-indicators of membrane fouling cannot meet the requirements, and has high prediction accuracy and identification effect.

Description

Technical Field

[0001] Based on the operating characteristics of the membrane bioreactor sewage treatment process, a multi-index identification method for membrane fouling is designed by using a cascaded neural network based on a hierarchical learning algorithm, realizing the prediction of multiple indexes related to membrane fouling in the membrane bioreactor sewage treatment process; the multiple indexes related to membrane fouling refer to the membrane permeability, membrane pore radius and membrane life in the membrane bioreactor sewage treatment process, and these indexes are important indicators for measuring whether membrane fouling occurs, the severity of membrane fouling and the characteristics of membrane fouling. The multi-index identification method for membrane fouling based on a cascaded neural network can improve the accuracy in the multi-index identification model, obtain accurate prediction results, and comprehensively characterize membrane fouling. Background Art

[0002] With the improvement of sewage treatment technology, the membrane bioreactor sewage treatment process has become a key sewage regeneration and recycling technology in China due to its advantages such as simple operation and high treatment efficiency. However, in the process of treating sewage by using a membrane bioreactor (MBR), membrane fouling is a problem that cannot be ignored. Membrane fouling will cause a decline in the sewage treatment effect, an increase in production energy consumption and usage costs, and even cause the collapse of the sewage treatment process. At present, the main way to solve the membrane fouling problem is to clean and replace the membrane regularly. In the actual sewage treatment process, there is no strict, objective and quantitative standard for membrane cleaning and replacement, which is mainly based on human experience. However, frequent cleaning will lead to the corrosion and fracture of the membrane filaments, resulting in a reduction in membrane life, an increase in production energy consumption and operating costs, which seriously affect the further large-scale application of MBR. An effective method to reduce the harm of membrane fouling is to comprehensively characterize the membrane fouling phenomenon on the basis of accurately predicting the membrane fouling condition. The membrane fouling phenomenon can be identified through the prediction of multiple indexes. However, the accuracy of the prediction of multiple indexes related to membrane fouling needs to be improved. Therefore, researching new methods to improve the accuracy of multi-variable identification of membrane fouling has important practical application value for ensuring the safe operation of MBR and the improvement of the technical level of the sewage treatment process.

[0003] The present invention designs a multi-index identification method for membrane fouling based on a cascaded neural network. Firstly, a multi-index identification model based on a cascaded neural network is established. Secondly, a hierarchical learning algorithm is used to complete the parameter adjustment of the cascaded neural network. This algorithm can improve the prediction accuracy of the cascaded neural network and obtain an accurate identification effect. Summary of the Invention

[0004] The present invention proposes a multi-index identification model for membrane fouling based on a cascaded neural network. This model takes into account the interference of irrelevant input variables on the output index, and based on the cascaded structure, it can avoid the influence of irrelevant variables on the output. Moreover, it adjusts the parameters of the cascaded neural network through a hierarchical learning algorithm to achieve the prediction of multi-index of membrane fouling, solves the problem that the prediction accuracy of multi-index of membrane fouling cannot meet the requirements, and has high prediction accuracy and identification effect.

[0005] A multi-index identification method for membrane fouling based on a cascaded neural network, characterized by comprising the following steps:

[0006] (1) Determine the input and output variables of the multi-index identification model for membrane fouling

[0007] Taking the sewage treatment process of a membrane bioreactor as the research object, conduct a characteristic analysis of the sewage treatment process variables, and select the process variables related to the membrane water permeability, membrane pore radius, and membrane life as the inputs of the identification model: water production pressure, water production flow rate, nitrate in the aerobic zone, oxidation-reduction potential in the anoxic zone, aeration volume, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, chemical oxygen demand of the effluent, total phosphorus of the effluent, total nitrogen of the effluent; the input variable x(t) is normalized to [0, 1] according to formula (1),

[0008] x(t) = (A(t) - A min ) / (A max - A min ) (1)

[0009] where A(t) is the actual value of the input variable at time t, A min is the minimum value of the input variable, and A max is the maximum value of the input variable;

[0010] The output of the identification model is the membrane water permeability, membrane pore radius, and membrane life; the output variable y(t) is normalized to [0, 1] according to formula (2),

[0011] y(t) = (B(t) - B min ) / (B max - B min ) (2)

[0012] where B(t) is the actual value of the output variable at time t, B min is the minimum value of the output variable, and B max is the maximum value of the output variable;

[0013] (2) Establish a multi-variable intelligent identification model based on a cascaded neural network

[0014] The topological structure of the multi-variable intelligent identification model consists of three sub-networks, each with three layers: an input layer, a hidden layer, and an output layer. The mathematical descriptions of each layer in the intelligent identification model are as follows:

[0015] Sub-network 1: Input layer: This layer has 5 nodes, and the output value of this input layer is expressed as

[0016]

[0017] where is the output value of the i-th neuron in the input layer, is the i-th input value, represents the water production flow rate (m 3 / h), represents the water production pressure (kPa), represents the nitrate in the aerobic zone (mg / l), represents the oxidation-reduction potential in the anoxic zone (mV), represents the aeration rate (m 3 / h);

[0018] Hidden layer: This layer has 4 nodes, and the output is

[0019]

[0020] where θ 1 (t) is the output of the hidden layer, its dimension is 1×4, and the input vector x 1 (t) is expressed as W 1 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and its dimension is 5×4;

[0021] Output layer: This layer has 1 node, and the output value is

[0022]

[0023] where is the output of sub-network 1, and the output value is the membrane water permeability (LHM / bar), v 1 (t) is the weight vector connecting the hidden layer and the output layer, its dimension is 4×1, and it randomly takes values in the interval (0,1];

[0024] Sub-network 2: Input layer: This layer has 6 nodes, and the output value of this input layer is expressed as

[0025]

[0026] where is the output value of the k-th neuron in the input layer, is the i-th input value, represents the transmembrane pressure difference (kPa), represents turbidity (NTU), represents conductivity (μs / cm), represents total organic carbon (mg / l), represents sulfate (mg / l);

[0027] Hidden layer: This layer has 5 nodes. The output is

[0028]

[0029] where θ 2 (t) is the output of the hidden layer, its dimension is 1×5, and the input vector x 2 (t) is expressed as W 2 (t) is the weight matrix connecting the input layer and the hidden layer, its dimension is 6×5, and it is randomly taken in the interval (0,1];

[0030] Output layer: This layer has 1 node, and the output value is

[0031]

[0032] where is the output of sub-network 2, and the output value is the pore radius of the membrane (nm), v 2 (t) is the weight vector connecting the hidden layer and the output layer, its dimension is 5×1, and it is randomly taken in the interval (0,1];

[0033] Sub-network 3: Input layer: This layer has 8 nodes, and the output value of this input layer is expressed as

[0034]

[0035] where is the output value of the j-th neuron in the input layer, is the j-th input value of the input layer, and i.e., the pore radius value of the membrane output in the previous part, represents the cumulative chlorine contact value (ppm·h), represents the chemical oxygen demand of the effluent (mg / l), represents the total phosphorus of the effluent (mg / l), represents the total nitrogen of the effluent (mg / l), represents the water production flow (mg / l), represents the membrane water permeability (LHM / bar), represents the transmembrane pressure difference (kPa);

[0036] Hidden layer: This layer has 7 nodes. The output is

[0037]

[0038] where θ 3 (t) is the output of the hidden layer, which has a dimension of 1×7, and the input vector X 3 (t) is expressed as W 3 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and its dimension is 8×7;

[0039] Output layer: This layer has 1 node, and the output value is

[0040]

[0041] where is the output of sub-network 3 in the cascaded neural network, and the output value is the membrane life (mouths), v 3 (t) is the weight vector connecting the hidden layer and the output layer, which has a dimension of 7×1 and randomly takes values in the interval (0,1];

[0042] (3) Adjust the parameters of the multivariable identification model using the hierarchical learning algorithm

[0043] ① Parameter initialization of the cascaded neural network:

[0044] N represents the number of iterations, taking the value of 500, and the initial value of time t is 1;

[0045] ② Determine the loss function J(t) of the cascaded neural network. The loss function of the cascaded neural network is as follows:

[0046]

[0047] where h = 1, 2, 3, J h (t) represents the loss function of the h-th part of the cascaded neural network, y h (t) and are the expected output and predicted output of the i-th sub-network of the cascaded neural network respectively;

[0048] ③ Update the parameters of the multivariable identification model using the hierarchical learning algorithm. The update rules of the parameters W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t) are as follows:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] where r is the learning rate, with a value of 0.1;

[0056] ④ Analyze the influence of the output error e(t) of the cascaded neural network on the parameters W 1 (t), v 1 (t), W 2 (t), v 2 (t), and W 3 (t) and v 3 (t), and the specific influence rules are as follows:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] where p = 1, 2; q = 1, 2, 3; J p+1 (t) and J q (t) are the loss functions of the (p + 1)-th and q-th sub-networks of the cascaded neural network respectively, and are the predicted output values of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively, θ p+1 (t), θ p (t), and θ q (t) are the hidden layer output vectors of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively; W p (t) and W q (t) are the weight matrices connecting the input layer and the hidden layer of the p-th and q-th sub-networks respectively, v p (t) and vq (t) are the weight vectors of the connected hidden layer and the output layer of the p-th and q-th sub-networks respectively;

[0064] ⑤ When t < N, increment t by 1 and go to step ②; otherwise, end the training. Take the W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t) as the weights of the cascaded neural network to establish a prediction model;

[0065] (4) Multivariate identification of membrane fouling

[0066] Use the trained multivariate identification model to predict the membrane water permeability, membrane pore radius, and membrane life; use the water production pressure, water production flow rate, nitrate in the aerobic zone, redox potential in the anoxic zone, aeration volume, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, chemical oxygen demand of the effluent, total phosphorus of the effluent, and total nitrogen of the effluent. After normalizing them to [0, 1] according to formula (1), use them as the input variables of the model. According to formulas (3)-(11), obtain the membrane water permeability value, membrane pore radius value, and membrane life value output by the model. The output variables of the prediction data are normalized to [0, 1] according to formula (2), and the output value of the model is denormalized according to formula (25).

[0067]

[0068] where is the g-th predicted value, g = 1, 2, 3.

[0069] The innovation of the present invention lies in:

[0070] (1) Aiming at the problem of identifying multiple variables related to membrane fouling, a multivariate identification method for membrane fouling based on a cascaded neural network is proposed. This method establishes an identification model based on a cascaded neural network. By using the characteristics of the cascaded structure, it can avoid the influence of irrelevant input variables on the output variables of the model;

[0071] (2) Aiming at the problem of low accuracy in multivariate identification of membrane fouling, a multi-layer learning algorithm is proposed. This method considers that the parameters of the network are affected by the output errors of different sub-networks, and uses the output errors of the cascaded neural network to update the parameters of the network, so that the cascaded neural network has optimal parameters and improves the prediction accuracy of the network. Description of the Drawings

[0072] Figure 1 is the prediction result diagram of the membrane water permeability of the present invention

[0073] Figure 2It is the prediction result diagram of the pore radius of the membrane of the present invention

[0074] Figure 3 It is the prediction result diagram of the membrane life of the present invention

[0075] Figure 4 It is the prediction error diagram of the water permeability of the membrane of the present invention

[0076] Figure 5 It is the prediction error diagram of the pore radius of the membrane of the present invention

[0077] Figure 6 It is the prediction error diagram of the membrane life of the present invention Specific embodiments

[0078] The present invention proposes a multi-index identification model for membrane fouling based on a cascaded neural network. This model considers the interference of irrelevant input variables on the output index, and based on the cascaded structure, it can avoid the influence of irrelevant variables on the output. And by adjusting the parameters of the cascaded neural network through a hierarchical learning algorithm, the prediction of multiple indexes of membrane fouling is realized, solving the problem that the prediction accuracy of multiple indexes of membrane fouling cannot meet the requirements, and having high prediction accuracy and identification effect.

[0079] A multi-index identification method for membrane fouling based on a cascaded neural network, characterized by comprising the following steps:

[0080] (1) Determine the input and output variables of the multi-index identification model for membrane fouling

[0081] Taking the sewage treatment process of a membrane bioreactor as the research object, analyzing the characteristics of the sewage treatment process variables, and selecting the process variables related to the water permeability of the membrane, the pore radius of the membrane and the membrane life as the inputs of the identification model: water production pressure, water production flow rate, nitrate in the aerobic zone, oxidation-reduction potential in the anoxic zone, aeration volume, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, chemical oxygen demand of the effluent, total phosphorus of the effluent, total nitrogen of the effluent; the input variable x(t) is normalized to [0,1] according to formula (1),

[0082] x(t) = (A(t) - A min ) / (A max - A min ) (1)

[0083] where A(t) is the actual value of the input variable at time t, A min is the minimum value of the input variable, and A max is the maximum value of the input variable;

[0084] The output of the identification model is the water permeability of the membrane, the pore radius of the membrane and the membrane life; the output variable y(t) is normalized to [0,1] according to formula (2),

[0085] y(t) = (B(t) - B min ) / (B max - B min ) (2)

[0086] where B(t) is the actual value of the output variable at time t, B min is the minimum value of the output variable, and B max is the maximum value of the output variable;

[0087] (2) Establish a multi-variable intelligent identification model based on a cascaded neural network

[0088] The topological structure of the multi-variable intelligent identification model consists of three sub-networks, each with three layers: an input layer, a hidden layer, and an output layer; the mathematical descriptions of each layer in the intelligent identification model are as follows:

[0089] Sub-network 1: Input layer: This layer has 5 nodes, and the output value of this input layer is expressed as

[0090]

[0091] where is the output value of the i-th neuron in the input layer, is the i-th input value, represents the water production flow rate (m 3 / h), represents the water production pressure (kPa), represents the nitrate in the aerobic zone (mg / l), represents the oxidation-reduction potential in the anoxic zone (mV), represents the aeration rate (m 3 / h);

[0092] Hidden layer: This layer has 4 nodes, and the output is

[0093]

[0094] where θ 1 (t) is the output of the hidden layer, its dimension is 1×4, and the input vector x 1 (t) is expressed as W 1 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and its dimension is 5×4;

[0095] Output layer: This layer has 1 node, and the output value is

[0096]

[0097] where is the output of Sub-network 1, and the output value is the membrane water permeability (LHM / bar), v 1 w(t) is the weight vector connecting the hidden layer and the output layer, and its dimension is 4×1, randomly taking values in the interval (0,1];

[0098] Sub-network 2: Input layer: This layer has 6 nodes, and the output value of this input layer is denoted as

[0099]

[0100] where is the output value of the k-th neuron in the input layer, is the i-th input value, represents the transmembrane pressure difference (kPa), represents the turbidity (NTU), represents the conductivity (μs / cm), represents the total organic carbon (mg / l), represents the sulfate (mg / l);

[0101] Hidden layer: This layer has 5 nodes. The output is

[0102]

[0103] where θ 2 (t) is the output of the hidden layer, its dimension is 1×5, and the input vector x 2 (t) is expressed as W 2 (t) is the weight matrix connecting the input layer and the hidden layer, and its dimension is 6×5, randomly taking values in the interval (0,1];

[0104] Output layer: This layer has 1 node, and the output value is

[0105]

[0106] where is the output of Sub-network 2, and the output value is the membrane pore radius (nm), v 2 (t) is the weight vector connecting the hidden layer and the output layer, and its dimension is 5×1, randomly taking values in the interval (0,1];

[0107] Sub-network 3: Input layer: This layer has 8 nodes, and the output value of this input layer is denoted as

[0108]

[0109] where is the output value of the j-th neuron in the input layer, is the j-th input value of the input layer, and i.e., the pore radius value of the output of the previous part, represents the cumulative chlorine contact value (ppm·h), represents the chemical oxygen demand of the effluent (mg / l), represents the total phosphorus of the effluent (mg / l), represents the total nitrogen of the effluent (mg / l), represents the water production flow rate (mg / l), represents the membrane water permeability (LHM / bar), represents the transmembrane pressure difference (kPa);

[0110] Hidden layer: This layer has 7 nodes. The output is

[0111]

[0112] where θ 3 (t) is the output of the hidden layer, its dimension is 1×7, and the input vector X 3 (t) is expressed as W 3 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and its dimension is 8×7;

[0113] Output layer: This layer has 1 node, and the output value is

[0114]

[0115] where is the output of sub-network 3 in the cascaded neural network, and the output value is the membrane life (mouths), v 3 (t) is the weight vector connecting the hidden layer and the output layer, its dimension is 7×1, and it randomly takes values in the interval (0,1];

[0116] (3) Use the hierarchical learning algorithm to adjust the parameters of the multivariable identification model

[0117] ① Parameter initialization of the cascaded neural network:

[0118] N represents the number of iterations, taking the value of 500, and the initial value of time t is 1;

[0119] ② Determine the loss function J(t) of the cascaded neural network. The loss function of the cascaded neural network is as follows:

[0120]

[0121] where h = 1, 2, 3, J h (t) represents the loss function of the h-th part of the cascaded neural network, yh (t) and are the expected output and the predicted output of the i-th sub-network of the cascaded neural network respectively;

[0122] ③ Update the parameters of the multivariable identification model using the hierarchical learning algorithm. The parameters W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t) are updated according to the following rules:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] where r is the learning rate, and its value is 0.1;

[0130] ④ Analyze the influence of the output error e(t) of the cascaded neural network on the parameters W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t). The specific influence rules are as follows:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] where p = 1, 2; q = 1, 2, 3; J p+1 (t) and J q(t) are the loss functions of the (p + 1)-th and q-th sub-networks of the cascaded neural network respectively, and are the predicted output values of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively, and θ p+1 (t), θ p (t), and θ q (t) are the hidden layer output vectors of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively; W p (t) and W q (t) are the weight matrices connecting the input layer and the hidden layer of the p-th and q-th sub-networks respectively, and v p (t) and v q (t) are the weight vectors connecting the hidden layer and the output layer of the p-th and q-th sub-networks respectively;

[0138] ⑤ When t < N, increment t by 1 and go to step ②; otherwise, end the training, and use the obtained W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t), and v 3 (t) as the weights of the cascaded neural network to establish a prediction model;

[0139] (4) Multivariate identification of membrane fouling

[0140] Use the trained multivariate identification model to predict the membrane water permeability, membrane pore radius, and membrane life; use the water production pressure, water production flow rate, nitrate in the aerobic zone, redox potential in the anoxic zone, aeration rate, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, effluent chemical oxygen demand, effluent total phosphorus, and effluent total nitrogen. After normalizing them to [0, 1] according to formula (1), use them as the input variables of the model. According to formulas (3)-(11), obtain the membrane water permeability value, membrane pore radius value, and membrane life value output by the model. The output variables of the prediction data are normalized to [0, 1] according to formula (2), and the output value of the model is inverse-normalized according to formula (25),

[0141]

[0142] where is the g-th predicted value, and g = 1, 2, 3.

Claims

1. A multi-index identification method for membrane fouling based on a cascaded neural network, characterized in that, Including the following steps: (1) Determine the input and output variables of the membrane fouling multi-index identification model Taking the sewage treatment process of the membrane bioreactor as the research object, conduct a characteristic analysis of the sewage treatment process variables, and select the process variables related to the membrane water permeability, membrane pore radius, and membrane life as the inputs of the identification model: water production pressure, water production flow rate, nitrate in the aerobic zone, oxidation-reduction potential in the anoxic zone, aeration volume, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, chemical oxygen demand of the effluent, total phosphorus of the effluent, total nitrogen of the effluent; the input variable x(t) is normalized to [0,1] according to formula (1), x(t) = (A(t) - A min ) / (A max - A min ) (1) where A(t) is the actual value of the input variable at time t, A min is the minimum value of the input variable, A max is the maximum value of the input variable; The outputs of the identification model are membrane water permeability, membrane pore radius, and membrane life; the output variable y(t) is normalized to [0,1] according to formula (2), y(t) = (B(t) - B min ) / (B max - B min ) (2) where B(t) is the actual value of the output variable at time t, B min is the minimum value of the output variable, B max is the maximum value of the output variable; (2) Establish a multi-variable intelligent identification model based on a cascaded neural network The topological structure of the multi-variable intelligent identification model includes three sub-networks, and each sub-network has three layers: an input layer, a hidden layer, and an output layer; the mathematical descriptions of each layer in the intelligent identification model are as follows: Sub-network 1: Input layer: This layer has 5 nodes, and the output value of this input layer is expressed as wherein is the output value of the i-th neuron in the input layer, is the i-th input value, represents the water production flow rate (m 3 / h), represents the water production pressure (kPa), represents the nitrate in the aerobic zone (mg / l), represents the oxidation-reduction potential in the anoxic zone (mV), represents the aeration rate (m 3 / h); Hidden layer: This layer has 4 nodes, and the output is where θ 1 (t) is the output of the hidden layer, which has a dimension of 1×4, and the input vector x 1 (t) is expressed as W 1 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and it has a dimension of 5×4; Output layer: This layer has 1 node, and the output value is Among them is the output of sub-network 1, and the output value is the membrane water permeability (LHM / bar), v 1 (t) is the weight vector connecting the hidden layer and the output layer, and its dimension is 4×1, randomly taking values in the interval (0,1]; Sub-network 2: Input layer: This layer has 6 nodes, and the output value of this input layer is expressed as wherein is the output value of the k-th neuron in the input layer, is the i-th input value, represents the transmembrane pressure difference (kPa), represents the turbidity (NTU), represents the conductivity (μs / cm), represents the total organic carbon (mg / l), represents the sulfate (mg / l); Hidden layer: This layer has 5 nodes; the output is where θ 2 (t) is the output of the hidden layer, whose dimension is 1×5, and the input vector x 2 (t) is expressed as W 2 (t) is the weight matrix connecting the input layer and the hidden layer, whose dimension is 6×5 and randomly takes values in the interval (0,1]; Output layer: This layer has 1 node, and the output value is Among them is the output of sub-network 2, and the output value is the pore radius (nm), v 2 (t) is the weight vector connecting the hidden layer and the output layer, and its dimension is 5×1, randomly taking values in the interval (0,1]; Sub-network 3: Input layer: This layer has 8 nodes, and the output value of this input layer is expressed as wherein is the output value of the j-th neuron in the input layer, is the j-th input value in the input layer, and i.e., the pore radius value of the previous part of the output, represents the cumulative chlorine contact value (ppm·h), represents the effluent chemical oxygen demand (mg / l), represents the effluent total phosphorus (mg / l), represents the effluent total nitrogen (mg / l), represents the water production flow rate (mg / l), represents the membrane water permeability (LHM / bar), represents the transmembrane pressure difference (kPa); Hidden layer: This layer has 7 nodes; the output is where θ 3 (t) is the output of the hidden layer, whose dimension is 1×7, and the input vector X 3 (t) is expressed as W 3 (t) is the weight matrix connecting the input layer and the hidden layer, randomly taking values in the interval (0,1], and its dimension is 8×7; Output layer: This layer has 1 node, and the output value is Among them is the output of sub-network 3 in the cascaded neural network, and the output value is the membrane life (mouths), v 3 (t) is the weight vector connecting the hidden layer and the output layer, and its dimension is 7×1, randomly taking values in the interval (0,1]; (3) Use the hierarchical learning algorithm to adjust the parameters of the multi-variable identification model ① Parameter initialization of the cascaded neural network: N represents the number of iterations, with a value of 500, and the initial value of time t is 1; ② Determine the loss function J(t) of the cascaded neural network. The loss function of the cascaded neural network is as follows: where h = 1, 2, 3, J h (t) represents the loss function of the h-th part of the cascaded neural network, y h (t) and are the expected output and the predicted output of the i-th subnet of the cascaded neural network, respectively; ③ Update the parameters of the multivariable identification model using the hierarchical learning algorithm. The parameters of the multivariable identification model, \(W\) 1 (t), \(v\) 1 (t), \(W\) 2 (t), \(v\) 2 (t), \(W\) 3 (t) and \(v\) 3 (t) are updated according to the following rules: where r is the learning rate, with a value of 0.1; ④ Analyze the influence of the output error e(t) of the cascaded neural network on the parameters W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t), and the specific influence rules are as follows: where p = 1, 2; q = 1, 2, 3; J p+1 (t) and J q (t) are the loss functions of the (p + 1)-th and q-th sub-networks of the cascaded neural network respectively, and are the predicted output values of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively, θ p+1 (t), θ p (t) and θ q (t) are the hidden layer output vectors of the (p + 1)-th, p-th, and q-th sub-networks of the cascaded neural network respectively; W p (t) and W q (t) are the weight matrices connecting the input layer and the hidden layer of the p-th and q-th sub-networks respectively, v p (t) and v q (t) are the weight vectors connecting the hidden layer and the output layer of the p-th and q-th sub-networks respectively; ⑤ When t < N, increment t by 1 and go to step ②; otherwise, end the training, and use the W 1 (t), v 1 (t), W 2 (t), v 2 (t), W 3 (t) and v 3 (t) obtained after the training ends as the weights of the cascaded neural network to establish a prediction model; (4) Multi-variable identification of membrane fouling Use the trained multi-variable identification model to predict the membrane water permeability, membrane pore radius, and membrane life; use the water production pressure, water production flow rate, nitrate in the aerobic zone, oxidation-reduction potential in the anoxic zone, aeration volume, transmembrane pressure difference, turbidity, conductivity, total organic carbon, sulfate, water production flow rate, cumulative chlorine contact value, chemical oxygen demand of the effluent, total phosphorus of the effluent, total nitrogen of the effluent, which are normalized to [0,1] according to formula (1), as the input variables of the model. According to formulas (3)-(11), obtain the membrane water permeability value, membrane pore radius value, and membrane life value output by the model. The output variables of the predicted data are normalized to [0,1] according to formula (2), and the output value of the model is inverse-normalized according to formula (25), Among them is the g-th predicted value at time t, where g = 1, 2, 3

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