Robust prediction method for membrane permeability based on adaptive division according to working conditions

Abstract

The membrane permeability robust prediction method based on working condition adaptive division belongs to the field of sewage treatment and resource utilization. Due to the influence of different working conditions on the MBR sewage treatment process, unbalanced samples exist in the membrane pollution related data, which may reduce the prediction performance. In order to solve this problem, the present application proposes a membrane permeability robust prediction method based on working condition adaptive division to predict the membrane permeability. First, a cross-entropy index based on spatial membership calculation is proposed, which can adaptively divide the membrane pollution related data set by evaluating the data fluctuation characteristics of the input information; second, a nonlinear regression model is used to predict the membrane permeability. The results show that the method can effectively predict the value of the membrane permeability.

Description

Technical Field

[0001] This invention designs a robust membrane permeability prediction method based on adaptive operating condition partitioning, enabling intelligent prediction of membrane fouling during wastewater treatment in membrane bioreactors (MBRs). Since the degree of membrane fouling can be measured by membrane permeability, predicting membrane permeability is crucial for understanding the extent of membrane fouling. Membrane permeability prediction in wastewater treatment, as a vital step in early warning of membrane fouling, is an important branch of advanced manufacturing technology and falls under the field of wastewater treatment and resource utilization. Background Technology

[0002] With the continuous development and progress of industrialization and urbanization, the direct discharge of industrial and domestic wastewater has caused serious water pollution problems, affecting national economic and social benefits. Therefore, for comprehensive and sustainable development, the development of wastewater treatment and resource recovery technologies is particularly urgent in today's society, and the emergence of MBR (Membrane Bioreactor) wastewater treatment technology provides a new wastewater treatment method. MBR combines biological technology and membrane wastewater treatment technology, offering high effluent quality and a small footprint, exhibiting significant advantages over traditional wastewater treatment processes, and has become a highly efficient wastewater treatment technology. However, membrane fouling also brings problems such as high energy consumption and high costs. Therefore, predictive research on membrane fouling is of great significance, providing important support for improving the pretreatment capacity for membrane fouling.

[0003] This invention designs a robust membrane permeability prediction method based on adaptive partitioning of operating conditions. It mainly involves adaptively partitioning the input dataset for predicting membrane permeability and designing a nonlinear regression prediction model to establish the relationship between input and output variables, thereby achieving the prediction of membrane permeability during MBR wastewater treatment. Summary of the Invention

[0004] This invention provides a robust prediction method for membrane permeability based on adaptive partitioning of operating conditions. This method improves the prediction dynamic error caused by different operating conditions by designing a cross-entropy index to continuously and adaptively partition the input data related to the predicted membrane permeability. At the same time, a nonlinear regression model is designed to predict membrane permeability, thereby improving the stability and prediction accuracy of membrane fouling output.

[0005] The present invention adopts the following technical solution and implementation steps:

[0006] 1. A robust prediction method for membrane permeability based on adaptive operating condition partitioning, comprising the following steps:

[0007] (1) Determine the input variables and output variables to be predicted: This invention mainly focuses on the intelligent prediction of membrane permeability in the wastewater treatment process of membrane bioreactor. Five variables are determined as relevant variables for predicting membrane permeability: product water pressure, product water flow rate, aeration rate, ORP in the anoxic zone and nitrate in the aerobic zone. The membrane permeability value is used as the output variable.

[0008] (2) Design a condition classification method for partitioning the input dataset for predicting membrane permeability, which performs continuous partitioning of imbalanced samples in the dataset, specifically as follows:

[0009] ① Obtain the product water pressure data as a vector x1 = [x 11 ,…,x 1N The water production flow data is a vector x2 = [x 21 ,…,x 2N The aeration volume data is a vector x3 = [x 31 ,…,x 3N The ORP data for the hypoxic region is a vector x4 = [x 41 ,…,x 4N ], the nitrate data in the aerobic zone is a vector x5 = [x 51 ,…,x 5N Construct the training sample matrix as X = [x1, ..., x2]. i ,…,x m ] T x i =[x i1 ,…,x in ,…,x iN ], n=1,…,N, i=1,…,m, where m and N are the number of relevant variables and the number of samples, respectively, and T represents the transpose of the matrix;

[0010] ② Radial basis function neural networks are used for data classification. The topology of a radial basis function neural network consists of three layers: an input layer, a radial basis function (RBF) layer, and an output layer. The connection method of the neural network is determined as mR⁻¹, meaning the input layer has m neurons, the RBF layer has R neurons, and the output layer has 1 neuron. The network center value, width, and weights are V(t) = [v₁(t), v₂(t), ..., vₙ(t)]. i (t),…,v m (t)] T B(t) = [b1(t), b2(t), ..., b i (t),…,b m (t)] T andω(t)=[ω1(t),ω2(t),…,ω j (t),…,ω R (t)]T Where j = 1, 2, ..., R, v i (t)=[v i1 (t),v i2 (t),…,v ij (t),…,v iR (t)],b i (t)=[b i1 (t),b i2 (t),…,b ij (t),…,b iR (t)],c ij (t) and b ij (t) represents the center value and width between the i-th output of the input layer and the j-th input of the RBF layer at time t, ω j V(t) represents the weight between the j-th neuron in the RBF layer and the output layer neuron at time t. During initialization, all internal elements of V(t), B(t), and ω(t) are 1. The activation level function defined in the clustering method is used as the radial basis function. The output of each node in the RBF layer is the activation level of the corresponding fuzzy set, i.e.

[0011]

[0012] Among them, Γ k (x) represents the membership function of the k-th neuron in the RBF layer, k = 1, 2, ..., R, x = [x1, x2, ..., xn]. m ], v k It is the center of the k-th membership function, v j It is the center of the j-th membership function, q is the fuzzy coefficient and q≥1, ||.|| represents the 1-norm of the matrix, is the sum of the absolute values ​​of each element in the matrix, and ∑ represents the summation symbol;

[0013] The normalized activation level of each node in the RBF layer is calculated as follows:

[0014] u kn =Γ k (x n (2)

[0015] Among them, u kn This represents the membership degree of the nth data group to the kth cluster;

[0016] ③ρ k The weights between the k-th node of the RBF layer and the output layer nodes are represented as a linear function, specifically calculated as follows:

[0017]

[0018] in, ak This represents the weight parameters calculated between the k-th node of the RBF layer and the output layer node, a. k =[a k0 ,a k1 ,…,a km ] T Weight parameter a k The calculation formula is:

[0019]

[0020] Where y = [y k (x1),y k (x2),…,y k (x N )] T , U k Let represent the membership matrix, which is an N-dimensional square matrix.

[0021]

[0022] ④ The output of the output layer node is calculated as follows

[0023]

[0024] Among them, y k (x n () indicates the output value of the nth data group belonging to the kth class;

[0025] ⑤ Calculate the probability of the kernel function output. The output of the g-th kernel function is calculated as follows:

[0026]

[0027] Among them, s g (x n ) represents the output of the g-th kernel function, g = 1, ..., c, l = 1, ..., c, where c represents the number of classes in the sample, y g (x n ) represents the output value of the nth data group belonging to the gth category, y l (x n ) represents the output value of the nth group of data belonging to the lth category, and exp represents the exponential function with the natural constant e as the base;

[0028] ⑥ The cross-entropy loss function for each data point is:

[0029]

[0030] Wherein, CE(x) n ) represents data x nThe cross-entropy loss, ln represents the logarithmic function with a constant e as the base, and the matrix is ​​defined. Represents the nth set of data x n Does it belong to class g?

[0031]

[0032] The weight of each data point is defined using cross-entropy loss, and the specific calculation is as follows:

[0033]

[0034] Among them, w n The weight of the nth data group is λ, where 0 ≤ λ ≤ 1; the position of the new center point is updated based on the newly obtained weight value, specifically calculated as follows:

[0035]

[0036] Among them, v k This indicates the position of the center point of the k-th membership function after the update;

[0037] ⑦ The update stop condition is

[0038]

[0039] Where EC(t) represents the stopping criterion at time t, and y zn This represents the true class label of the nth data point, and max represents taking the maximum value, max(s) g (x n )) represents the maximum output probability calculated by the kernel function, l(y zn ,max(s g (x n The value ')' indicates that if the true class is equal to the predicted class output by the kernel function, the value is 1; otherwise, it is 0.

[0040]

[0041] If the current EC(t) is less than the previous EC(t-1), then proceed to step ② to continue training and update the cluster center position. If the current EC(t) is greater than the previous EC(t-1), then the update process terminates.

[0042] (3) Design a prediction model based on nonlinear regression. Obtain the partitioned sample matrix X according to steps (1) and (2) as the input sample matrix X(t) at time t, X(t) = [x1(t), ..., x p (t),…,x h (t)],x p (t)=[x 1p (t),…,xip (t),…,x mp (t)] T x ip (t) represents the input at time t, i = 1, ..., m, p = 1, 2, ..., h, where h is the prediction time domain length, and the corresponding training output is the membrane permeability y(t), y(t) = [y1(t), ..., y2(t)]. p (t),…,y h [t], using the regression equation to obtain the predicted value at time t+1. The formula for calculating the nonlinear regression prediction model is as follows:

[0043] y(t)=α(t)X(t) T X(t)+β(t)X(t)+γ(t) (13)

[0044] Where y(t) represents the training output value at time t, x(t) represents the input value at time t, α(t), β(t), and γ(t) are the parameters of the regression equation, and α(t) = [α1(t), ..., α p (t),…,α h (t)] T α p (t)=[α p1 (t),…,α pi (t),…,α pm [(t)],β(t)=[β1(t),…,β p (t),…,β h (t)] T ,β p (t)=[β p1 (t),…,β pi (t),…,β pm [(t)],γ(t)=[γ1(t),…,γ p (t),…,γ h (t)] T During initialization, all internal elements are random numbers in the range (0,1). The regression equation matrix W(t) = [α(t), β(t), γ(t)] is updated to...

[0045] W(t)=(Φ T (t)Φ(t)) -1 Φ T (t)Y(t) (14)

[0046] in,(.) -1 Represents the inverse of a matrix.

[0047]

[0048] (4) Based on the membrane permeability prediction model, select the prediction input sample matrix, Z(t+1)=[z1(t+1),…,z p (t+1),…,z h (t+1)],z p (t+1)=[z 1p (t+1),…,z ip (t+1),…,z mp (t+1)] T The model's predicted output at time t+1 is

[0049]

[0050] in, This represents the model's predicted output value at time t+1.

[0051] The inventiveness of this invention is mainly reflected in:

[0052] This invention addresses the issue of reduced prediction accuracy caused by imbalanced input data in the prediction of membrane permeability. It proposes an adaptive classification method that analyzes the fluctuation characteristics of the input data to classify operating conditions, thereby improving the dynamic error problem caused by data imbalance and enhancing prediction accuracy. Attached Figure Description

[0053] Figure 1 This is a graph showing the results of the membrane permeability prediction based on the present invention;

[0054] Figure 2 This is an error graph of the membrane permeability prediction in this invention; Detailed Implementation

[0055] This invention designs a robust prediction method for membrane permeability based on adaptive division of operating conditions; five variables are selected as input variables for predicting membrane permeability: product water pressure, product water flow rate, aeration rate, ORP in the anoxic zone and nitrate in the aerobic zone, and membrane permeability value is used as the output variable, while the membrane fouling status is evaluated and warned.

[0056] The experimental data came from the daily water quality analysis report of a wastewater treatment plant; the sampling time for the input variables was 5 minutes. After data preprocessing, the experimental samples had 400 sets of data remaining. All 400 sets of data were divided into two parts: 200 sets of data were used as training samples and the remaining 200 sets of data were used as test samples.

[0057] The present invention adopts the following technical solution and implementation steps:

[0058] 1. A robust prediction method for membrane permeability based on adaptive operating condition partitioning, comprising the following steps:

[0059] (1) Determine the input variables and output variables to be predicted: This invention mainly focuses on the intelligent prediction of membrane permeability in the wastewater treatment process of membrane bioreactor. Five variables are determined as relevant variables for predicting membrane permeability: product water pressure, product water flow rate, aeration rate, ORP in the anoxic zone and nitrate in the aerobic zone. The membrane permeability value is used as the output variable.

[0060] (2) Design a condition classification method for partitioning the input dataset for predicting membrane permeability, which performs continuous partitioning of imbalanced samples in the dataset, specifically as follows:

[0061] ① Obtain the product water pressure data as a vector x1 = [x 11 ,…,x 1N The water production flow data is a vector x2 = [x 21 ,…,x 2N The aeration volume data is a vector x3 = [x 31 ,…,x 3N The ORP data for the hypoxic region is a vector x4 = [x 41 ,…,x 4N ], the nitrate data in the aerobic zone is a vector x5 = [x 51 ,…,x 5N Construct the training sample matrix as X = [x1, ..., x2]. i ,…,x m ] T x i =[x i1 ,…,x in ,…,x iN ], n=1,…,N, i=1,…,m, where m and N are the number of relevant variables and the number of samples, respectively, m=5, N=200, and T represents the transpose of the matrix;

[0062] ② Radial basis function neural networks are used for data classification. The topology of a radial basis function neural network consists of three layers: an input layer, a radial basis function (RBF) layer, and an output layer. The connection method of the mR-1 neural network is determined, i.e., the input layer has 5 neurons, the RBF layer has 10 neurons, and the output layer has 1 neuron. The network center value, width, and weights are V(t) = [v1(t), v2(t), ..., v...]. i (t),…,v m (t)] T B(t) = [b1(t), b2(t), ..., b i (t),…,b m (t)] T andω(t)=[ω1(t),ω2(t),…,ω j (t),…,ω R(t)] T Where i = 1, 2, ..., 5, j = 1, 2, ..., 10, v i (t)=[v i1 (t),v i2 (t),…,v ij (t),…,v iR (t)],b i (t)=[b i1 (t),b i2 (t),…,b ij (t),…,b iR (t)],c ij (t) and b ij (t) represents the center value and width between the i-th output of the input layer and the j-th input of the RBF layer at time t, ω j V(t) represents the weight between the j-th neuron in the RBF layer and the output layer neuron at time t. During initialization, all internal elements of V(t), B(t), and ω(t) are 1. The activation level function defined in the clustering method is used as the radial basis function. The output of each node in the RBF layer is the activation level of the corresponding fuzzy set, i.e.

[0063]

[0064] Among them, Γ k (x) represents the membership function of the k-th neuron in the RBF layer, k = 1, 2, ..., 10, x = [x1, x2, ..., xk]. m ], v k It is the center of the k-th membership function, v j It is the center of the j-th membership function, q is the fuzzy coefficient and q = 2, ||.|| represents the 1-norm of the matrix, is the sum of the absolute values ​​of each element in the matrix, and ∑ represents the summation symbol;

[0065] The normalized activation level of each node in the RBF layer is calculated as follows:

[0066] u kn =Γ k (x n (17)

[0067] Among them, u kn This represents the membership degree of the nth data group to the kth cluster;

[0068] ③ρ k The weights between the k-th node of the RBF layer and the output layer nodes are represented as a linear function, specifically calculated as follows:

[0069]

[0070] in, a k This represents the weight parameters calculated between the k-th node of the RBF layer and the output layer node, a. k =[a k0 ,a k1 ,…,a km ] T Weight parameter a k The calculation formula is:

[0071]

[0072] Where y = [y k (x1),y k (x2),…,y k (x N )] T , U k Let represent the membership matrix, which is an N-dimensional square matrix.

[0073]

[0074] ④ The output of the output layer node is calculated as follows

[0075]

[0076] Among them, y k (x n () indicates the output value of the nth data group belonging to the kth class;

[0077] ⑤ Calculate the probability of the kernel function output. The output of the g-th kernel function is calculated as follows:

[0078]

[0079] Among them, s g (x n ) represents the output of the g-th kernel function, g = 1, ..., c, l = 1, ..., c, c represents the number of classes in the sample, c = 2, y g (x n ) represents the output value of the nth data group belonging to the gth category, y l (x n ) represents the output value of the nth group of data belonging to the lth category, and exp represents the exponential function with the natural constant e as the base;

[0080] ⑥ The cross-entropy loss function for each data point is:

[0081]

[0082] Wherein, CE(x) n ) represents data x nThe cross-entropy loss, ln represents the logarithmic function with a constant e as the base, and the matrix is ​​defined. Represents the nth set of data x n Does it belong to class g?

[0083]

[0084] The weight of each data point is defined using cross-entropy loss, and the specific calculation is as follows:

[0085]

[0086] Among them, w n Let λ represent the weight of the nth data group, λ = 0.5; the position of the new center point is updated based on the newly obtained weight value, specifically calculated as follows:

[0087]

[0088] Among them, v k This indicates the position of the center point of the k-th membership function after the update;

[0089] ⑦ The update stop condition is

[0090]

[0091] Where EC(t) represents the stopping criterion at time t, and y zn This represents the true class label of the nth data point, and max represents taking the maximum value, max(s) g (x n )) represents the maximum output probability calculated by the kernel function, l(y zn ,max(s g (x n The value ')' indicates that if the true class is equal to the predicted class output by the kernel function, the value is 1; otherwise, it is 0.

[0092]

[0093] If the current EC(t) is less than the previous EC(t-1), then proceed to step ② to continue training and update the cluster center position. If the current EC(t) is greater than the previous EC(t-1), then the update process terminates.

[0094] (4) Design a prediction model based on nonlinear regression. Obtain the partitioned sample matrix X according to steps (1) and (2) as the input sample matrix X(t) at time t, X(t) = [x1(t), ..., x2(t)]. p (t),…,x h (t)],x p (t)=[x 1p (t),…,xip (t),…,x mp (t)] T x ip (t) represents the input at time t, p = 1, 2, ..., h, where h is the prediction time domain length, and the corresponding training output is the membrane permeability y(t), y(t) = [y1(t), ..., y2(t)]. p (t),…,y h [t], using the regression equation to obtain the predicted value at time t+1. The formula for calculating the nonlinear regression prediction model is as follows:

[0095] y(t)=α(t)X(t) T X(t)+β(t)X(t)+γ(t) (28)

[0096] Where y(t) represents the training output value at time t, x(t) represents the input value at time t, α(t), β(t), and γ(t) are the parameters of the regression equation, and α(t) = [α1(t), ..., α p (t),…,α h (t)] T α p (t)=[α p1 (t),…,α pi (t),…,α pm [(t)],β(t)=[β1(t),…,β p (t),…,β h (t)] T ,β p (t)=[β p1 (t),…,β pi (t),…,β pm [(t)],γ(t)=[γ1(t),…,γ p (t),…,γ h (t)] T During initialization, all internal elements are random numbers in the range (0,1). The regression equation matrix W(t) = [α(t), β(t), γ(t)] is updated to...

[0097] W(t)=(Φ T (t)Φ(t)) -1 Φ T (t)Y(t) (29)

[0098] in,(.) -1 Represents the inverse of a matrix.

[0099]

[0100] (4) Based on the membrane permeability prediction model, select the prediction input sample matrix, Z(t+1)=[z1(t+1),…,z p (t+1),…,z h (t+1)],z p (t+1)=[z 1p (t+1),…,z ip (t+1),…,z mp (t+1)] T The model's predicted output at time t+1 is

[0101]

[0102] in, This represents the model's predicted output value at time t+1.

Claims

1. A robust prediction method for membrane permeability based on adaptive segmentation of operating conditions, characterized in that... Includes the following steps: (1) Determine the input variables and output variables to be predicted: Intelligent prediction of membrane permeability in the wastewater treatment process of membrane bioreactor is carried out. Five variables are determined as relevant variables for predicting membrane permeability: product water pressure, product water flow rate, aeration rate, ORP in the anoxic zone and nitrate in the aerobic zone. The membrane permeability value is used as the output variable. (2) Design a condition classification method for partitioning the input dataset for predicting membrane permeability, which performs continuous partitioning of imbalanced samples in the dataset, specifically as follows: ① Obtain the product water pressure data as a vector x1 = [x 11 ,…,x 1N The water production flow data is a vector x2 = [x 21 ,…,x 2N The aeration volume data is a vector x3 = [x 31 ,…,x 3N The ORP data for the hypoxic region is a vector x4 = [x 41 ,…,x 4N ], the nitrate data in the aerobic zone is a vector x5 = [x 51 ,…,x 5N Construct the training sample matrix as X = [x1, ..., x2]. i ,…,x m ] T x i =[x i1 ,…,x in ,…,x iN ], n=1,…,N, i=1,…,m, where m and N are the number of relevant variables and the number of samples, respectively, and T represents the transpose of the matrix; ② Radial basis function neural networks are used for data classification. The topology of a radial basis function neural network consists of three layers: an input layer, a radial basis function (RBF) layer, and an output layer. The connection method of the neural network is determined as mR⁻¹, meaning the input layer has m neurons, the RBF layer has R neurons, and the output layer has 1 neuron. The network center value, width, and weights are V(t) = [v₁(t), v₂(t), ..., vₙ(t)]. i (t),…,v m (t)] T B(t) = [b1(t), b2(t), ..., b i (t),…,b m (t)] T andω(t)=[ω1(t),ω2(t),…,ω j (t),…,ω R (t)] T Where j = 1, 2, ..., R, v i (t)=[v i1 (t),v i2 (t),…,v ij (t),…,v iR (t)],b i (t)=[b i1 (t),b i2 (t),…,b ij (t),…,b iR (t)],c ij (t) and b ij (t) represents the center value and width between the i-th output of the input layer and the j-th input of the RBF layer at time t, ω j V(t) represents the weight between the j-th neuron in the RBF layer and the output layer neuron at time t. During initialization, all internal elements of V(t), B(t), and ω(t) are 1. The activation level function defined in the clustering method is used as the radial basis function. The output of each node in the RBF layer is the activation level of the corresponding fuzzy set, i.e. Among them, Γ k (x) represents the membership function of the k-th neuron in the RBF layer, k = 1, 2, ..., R, x = [x1, x2, ..., xn]. m ], v k It is the center of the k-th membership function, v j It is the center of the j-th membership function, q is the fuzzy coefficient and q≥1, ||.|| represents the 1-norm of the matrix, is the sum of the absolute values ​​of each element in the matrix, and ∑ represents the summation symbol; The normalized activation level of each node in the RBF layer is calculated as follows: you kn =C k (x n ) (2) Among them, u kn This represents the membership degree of the nth data group to the kth cluster; ③ρ k The weights between the k-th node of the RBF layer and the output layer nodes are represented as a linear function, specifically calculated as follows: in, a k This represents the weight parameters calculated between the k-th node of the RBF layer and the output layer node, a. k =[a k0 ,a k1 ,…,a km ] T Weight parameter a k The calculation formula is: Where y = [y k (x1),y k (x2),…,y k (x N )] T , U k Let represent the membership matrix, which is an N-dimensional square matrix. ④ The output of the output layer node is calculated as follows Among them, y k (x n () indicates the output value of the nth data group belonging to the kth class; ⑤ Calculate the probability of the kernel function output. The output of the g-th kernel function is calculated as follows: Among them, s g (x n ) represents the output of the g-th kernel function, g = 1, ..., c, l = 1, ..., c, where c represents the number of classes in the sample, y g (x n ) represents the output value of the nth data group belonging to the gth category, y l (x n ) represents the output value of the nth group of data belonging to the lth category, and exp represents the exponential function with the natural constant e as the base; ⑥ The cross-entropy loss function for each data point is: Wherein, CE(x) n ) represents data x n The cross-entropy loss, ln represents the logarithmic function with a constant e as the base, and the matrix is ​​defined. Represents the nth set of data x n Does it belong to class g? The weight of each data point is defined using cross-entropy loss, and the specific calculation is as follows: Among them, w n The weight of the nth data group is λ, where 0 ≤ λ ≤ 1; the position of the new center point is updated based on the newly obtained weight value, specifically calculated as follows: Among them, v k This indicates the position of the center point of the k-th membership function after the update; ⑦ The update stop condition is Where EC(t) represents the stopping criterion at time t, and y zn This represents the true class label of the nth data point, and max represents taking the maximum value, max(s) g (x n )) represents the maximum output probability calculated by the kernel function, l(y zn ,max(s g (x n The value ')' indicates that if the true class is equal to the predicted class output by the kernel function, the value is 1; otherwise, it is 0. If the current EC(t) is less than the previous EC(t-1), then proceed to step ② to continue training and update the cluster center position. If the current EC(t) is greater than the previous EC(t-1), then the update process terminates. (3) Design a prediction model based on nonlinear regression. Obtain the partitioned sample matrix X according to steps (1) and (2) as the input sample matrix X(t) at time t, X(t) = [x1(t), ..., x p (t),…,x h (t)],x p (t)=[x 1p (t),…,x ip (t),…,x mp (t)] T x ip (t) represents the input at time t, i = 1, ..., m, p = 1, 2, ..., h, where h is the prediction time domain length, and the corresponding training output is the membrane permeability y(t), y(t) = [y1(t), ..., y2(t)]. p (t),…,y h [t], using the regression equation to obtain the predicted value at time t+1. The formula for calculating the nonlinear regression prediction model is as follows: Where y(t) represents the training output value at time t, x(t) represents the input value at time t, α(t), β(t), and γ(t) are the parameters of the regression equation, and α(t) = [α1(t), ..., α p (t),…,α h (t)] T α p (t)=[α p1 (t),…,α pi (t),…,α pm [(t)],β(t)=[β1(t),…,β p (t),…,β h (t)] T ,β p (t)=[β p1 (t),…,β pi (t),…,β pm [(t)],γ(t)=[γ1(t),…,γ p (t),…,γ h (t)] T During initialization, all internal elements are random numbers in the range (0,1). The regression equation matrix W(t) = [α(t), β(t), γ(t)] is updated to... in,(.) -1 Represents the inverse of a matrix. (4) Based on the membrane permeability prediction model, select the prediction input sample matrix, Z(t+1)=[z1(t+1),…,z p (t+1),…,z h (t+1)],z p (t+1)=[z 1p (t+1),…,z ip (t+1),…,z mp (t+1)] T The model's predicted output at time t+1 is in, This represents the model's predicted output value at time t+1.

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