Membrane Fouling Detection Method for Membrane Modules Based on Multi-Feature Information Fusion

Abstract

The present invention discloses a method for detecting membrane fouling of a membrane module based on multi-feature information fusion, comprising the following steps: collecting membrane fouling data; classifying and encoding the membrane fouling data; using image processing technology to expand the data set to obtain a time-domain picture set, and obtaining a frequency-domain data set by using image Fourier transform; dividing both the time-domain picture set and the frequency-domain data set into a training set, a test set and a validation set according to a certain ratio respectively; constructing a CBAM-MIL-CNN network model, and adjusting and optimizing the CBAM-MIL-CNN network model; inputting the test set data information into the optimized CBAM-MIL-CNN network model to identify the membrane fouling state of the membrane module. The network model of the present invention is applied to the detection of membrane fouling of the membrane module. The comprehensive performance of the network model is excellent, and it can effectively realize the efficient classification and positioning of all membrane fouling, enabling the membrane method water treatment to improve the effluent quality while reducing energy consumption, and providing a theoretical basis for actual production.

Description

Technical Field

[0001] The present invention belongs to the technical field of membrane fouling detection of membrane modules. Background Art

[0002] The membrane bioreactor (MBR) is a new type of sewage and wastewater treatment system that organically combines membrane separation technology and biological treatment technology. Compared with the traditional activated sludge method, MBR has the advantages of high effluent quality, high operating organic load, low sludge production, and easy implementation of automatic control. However, there are also problems such as easy clogging of ultrafiltration and microfiltration membranes and serious membrane fouling. Membrane fouling is the main factor causing membrane module failures. Membrane fouling causes varying degrees of damage to membrane modules, such as reducing the effluent efficiency and affecting water quality, and even requires replacing membrane modules, increasing the operating cost. Therefore, the membrane fouling diagnosis technology of membrane modules is gradually becoming the research focus in the water treatment field. Due to the intricate and strongly correlated coupling relationships existing in membrane modules and their interiors, and also involving uncertain factors and uncertain information, faults with properties such as randomness, secondary, concurrency, and propagation frequently occur. The traditional fault diagnosis methods for single devices, subsystems, and subunits are difficult to discover the correlation relationships between component units, resulting in a high probability of misdiagnosis and missed diagnosis. Different from shallow learning algorithms, deep learning algorithms have better capabilities in approximating complex functions. Such algorithms generally include multi-hidden layer structures to achieve the layer-by-layer transformation of data features and ensure the most effective information extraction and feature expression.

[0003] Due to the dynamic and non-linear characteristics of membrane water treatment systems, traditional diagnostic models are inefficient, ignoring potential and valuable features during the offline modeling phase, resulting in false alarms and inaccurate imputations. Methods based on Probabilistic Principal Component Analysis (PPCA) have been widely applied in the field of process monitoring. However, traditional PPCA methods are still limited to linear dimensionality reduction. Although the non-linear projection model of PPCA can be obtained through Gaussian process mapping, this model still lacks robustness and is vulnerable to process noise. Therefore, Wang et al. proposed a non-linear process monitoring and fault diagnosis method based on the Bayesian-Gaussian Latent Variable Model (Bay-GPLVM). Bay-GPLVM can obtain the posterior distribution instead of a point estimate of the latent variable, so this model is more robust. Baklouti et al. proposed a Maximum Double Adaptive Exponentially Weighted Moving Average (EWMA) based on particle filtering for fault detection in wastewater treatment processes. By monitoring the state variables of the model, the developed strategy is applied to enhance fault detection in the wastewater treatment process. The developed statistical chart is used to detect average faults and / or drifts in the system, where the particle filtering method is used to estimate the non-linear unknown state of the process. However, the particle filter introduces uncertainty into the model when estimating the state and parameters of time-varying non-linear systems. In addition, most real-world systems are multivariate and uncertain, and process models are not available. Therefore, to extend to multivariate systems, data-driven models including latent variable models are also needed to account for the uncertainty in the data. Che Mid proposed a fault detection method based on parameter estimation using multi-parametric programming. In the paper, the non-linear ordinary differential equation model was transformed into an algebraic equation using the Euler method. Then, by formulating the Karush-Kuhn-Tucker (KKT) optimality conditions, a squared system of parameter non-linear algebraic equations was obtained. Then, by symbolically solving the equations representing the KKT conditions, the model parameters were obtained as explicit functions of the measurements. The estimated model parameters were compared with the normal operation for fault detection. If the residuals of the model parameters exceed a certain threshold, a fault is detected. Based on this, Che Mid regarded the substrate concentration, inhibition coefficient, and specific growth rate in the influent as model parameters and obtained them as explicit functions of the measurements using multi-parametric programming, and monitored them for fault detection and diagnosis. Ba-Alawi et al. proposed an inclusive framework for missing data imputation and sensor self-verification based on the integration of Variational Autoencoders (VAE) and Deep Residual Network Structure (ResNet VAE). By learning the latent probability distribution of the input data, complex features are automatically extracted, reducing the risk of gradient vanishing. The reliability of faulty sensors is improved by inputting missing data, detecting anomalies, identifying the source of faults, and reconstructing the faulty data to the normal state. Qiao et al. proposed a Data Knowledge Driven (DKD) diagnostic method for detecting fault points and root cause variables.The DKD model combines the advantages of data-driven and knowledge-based methods, capable of extracting the causal relationships and probabilities between process variables, identifying the root cause variables from potential failure variables, thereby improving the diagnostic performance. To ensure process safety and effluent quality, Han et al. proposed an intelligent fault detection (IFD) method based on self-organizing type-2 fuzzy neural network (SOT2FNN) and intelligent recognition method for detecting and identifying different types of faults. Based on the data-driven model and intelligent recognition algorithm, as well as the information transmission intensity algorithm and adaptive second-order algorithm, the sludge volume index (SVI) is predicted with high precision, and the target-related recognition algorithm (TRIA) is used to extract relevant information to identify the fault type. However, the interrelationships behind these methods focus on the correlations between variables rather than causal relationships, indicating that a set of variables are possible causes of the fault occurrence and failing to find the true root cause variables of the fault occurrence.

[0004] In recent years, as a breakthrough in the field of modern artificial intelligence, deep learning can automatically learn valuable features from the original feature set or even the original data, which means that deep learning can largely get rid of the dependence on advanced signal processing technologies, manual feature extraction, and cumbersome feature selection technologies. Therefore, deep learning has been widely applied in the field of fault diagnosis due to its powerful learning ability and feature extraction ability. Zhao et al. proposed a fault diagnosis method based on deep belief nets (DBN), which adaptively extracts features from the original time series signals, increasing flexibility. The simulation results show the effectiveness of this method in fault diagnosis. The structural parameters of a typical DBN model are determined by the learning rate. Therefore, Zhang, Liu et al. applied the optimized DBN to improve the fault diagnosis accuracy. Deep learning models require a large amount of data to optimize parameters and are prone to overfitting. More and more researchers optimize convolutional neural networks, simplifying the diagnosis process and improving the diagnosis efficiency and performance, verifying the superiority of the application of CNN networks in such problems. Zhang et al. processed the data using the backward difference strategy and introduced a convolutional neural network with global average pooling (CNN-GAP) for feature extraction and fault classification. The experimental results show that this method has advantages in diagnosis accuracy and reliability. Wang et al. proposed a fault detection model under unbalanced data conditions based on wavelet packet decomposition (WPD) and bilayer convolutional neural network (biCNN). WPD obtains richer information of various time and frequency scales from the collected fault samples, which helps to solve the problem of data imbalance. The improved biCNN combines local and full convolutional stages for feature extraction and fault detection. In addition, since CNN cannot autonomously select important channels, models based on the attention mechanism have successfully improved this problem. From Squeeze and Excitation Networks (SENet) to Selective Kernel Networks (SKNet) and then to convolutional block attention module (ECA), CNN has been optimized to varying degrees. Zhang Hongbin et al. utilized the heterogeneous layer features with good complementarity in SENet to achieve heterogeneous layer feature fusion and improve the accuracy rate. Fu et al. added the ECA module to YOLOv4 and verified the effectiveness of the improved algorithm.

[0005] When studying the problem of analog circuit faults, the above-mentioned literature all starts from the time domain or frequency domain perspective, and there are problems such as complex models and difficulties in extracting essential features in deep learning for fault diagnosis. Summary of the Invention

[0006] The object of the present invention is to provide a method for detecting membrane fouling of a membrane module based on multi-feature information fusion.

[0007] Based on the above object, the present invention adopts the following technical solutions:

[0008] A method for detecting membrane fouling of a membrane module based on multi-feature information fusion includes the following steps:

[0009] 1) Collect membrane fouling data;

[0010] 2) Classify and encode the membrane fouling data;

[0011] 3) Use image processing technology to expand the data set to obtain a time-domain picture set, and use image Fourier transform to obtain a frequency-domain data set;

[0012] 4) Divide the time-domain picture set and the frequency-domain data set in step 3) into a training set, a test set, and a validation set respectively according to a certain proportion;

[0013] 5) Construct a CBAM-MIL-CNN network model, input the training set data information into the CBAM-MIL-CNN network model to verify the error of the CBAM-MIL-CNN network model, and then input the validation set data information into the CBAM-MIL-CNN network model to adjust and optimize the CBAM-MIL-CNN network model;

[0014] 6) Input the test set data information into the optimized CBAM-MIL-CNN network model to identify the membrane fouling state of the membrane module.

[0015] The CBAM-MIL-CNN model in step 5) is composed of network model unit 1, network model unit 2, and pattern recognition unit 3. Network model unit 1 and network model unit 2 have the same network structure. The network structure of network model unit 1 and network model unit 2 both includes an input layer, convolutional layers a, b, c, d, and e with activation functions added respectively, and a CBAM module. Batch normalization layers and pooling layers are sequentially added to convolutional layers a, b, and e respectively. The CBAM module is connected to the output ends of convolutional layers a and b, or the output ends of the batch normalization layers or pooling layers on convolutional layers a and b. Pattern recognition unit 3 splices and outputs the feature information of network model unit 1 and network model unit 2 using a fully connected layer, and sends it to a softmax classifier for classification and recognition.

[0016] A batch normalization layer, a CBAM module, and a pooling layer are sequentially added to the output ends of convolutional layer a and convolutional layer b.

[0017] In step 5), the information of the time-domain picture set is input into network model unit 1, and the information of the frequency-domain data set is input into network model unit 2.

[0018] In step 5), the activation function is the Relu activation function, and the optimization strategy of the CBAM-MIL-CNN network model is the AdamW optimizer, which is composed of the Adam optimizer and weight decay.

[0019] In step 5), the convolutional kernel size of convolutional layer a is 3*3, the stride is 4*4, and the number of channels is 64. After convolution, batch normalization, feature extraction by the CBAM module, and pooling, an output of size 30*30*64 is obtained; the convolutional kernel size of convolutional layer b is 5*5, the stride is 1*1, and the number of channels is 128. After convolution, batch normalization, feature extraction by the CBAM module, and pooling, an output of size 12*12*128 is obtained; the convolutional kernel sizes of convolutional layer c and convolutional layer d are 3*3, the stride is 1*1, and the number of channels is 256. After convolution, an output of size 12*12*256 is obtained; the convolutional kernel of convolutional layer e is 3*3, the stride is 1*1, and the number of channels is 64. After convolution, batch normalization, and pooling, an output of size 5*5*64 is obtained; there are 2 fully connected layers in pattern recognition unit 3, and the numbers of the 2 fully connected layers are set to 2048 and 512 respectively.

[0020] In step 5), the CBAM module includes a channel attention module and a spatial attention module.

[0021] The membrane module is a series tubular membrane module or a parallel hollow fiber membrane module.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention constructs a model (CBAM-MIL-CNN) based on the combination of a multi-input convolutional neural network and a self-attention mechanism, which is applied to the detection of membrane fouling in membrane modules. First, the CBAM-MIL-CNN network model has two input layers, which extract time-domain features and frequency-domain features respectively. In addition, a batch normalization layer (batch normalization, BN layer) is added between the convolutional layer and the pooling layer, which can effectively reduce overfitting. Secondly, a convolutional block attention module (CBAM) is added after the batch normalization layer, which can effectively reduce the model complexity and improve the network performance. The network model has excellent comprehensive performance in the membrane fouling diagnosis experiments of a series-connected tubular membrane device and a parallel-connected hollow fiber membrane module, and can effectively achieve the efficient classification and localization of all membrane fouling, enabling the membrane method water treatment to improve the effluent quality while reducing energy consumption, providing a theoretical basis for actual production. Description of the Drawings

[0024] Figure 1 , (a) is the structure of the MIL-CNN model; (b) is the structure diagram of CBAM; (c) is the typical structure of the channel attention module CBAM; (d) is the typical structure of the spatial attention module SAM;

[0025] Figure 2 is the CBAM-MIL-CNN model of the present invention;

[0026] Figure 3 , (a) Test results of the model of the present invention on the training set, test set and validation set; (b) Loss function of different deep learning optimization algorithms during training parameters;

[0027] Figure 4 , (a) is the membrane fouling signal feature map of the series-connected tubular membrane module; (b) is the membrane fouling feature distribution of the series-connected tubular membrane module;

[0028] Figure 5 , (a) is the diagram of the independent membrane fouling diagnosis experiment of the series-connected tubular membrane; (b) is the relationship between the membrane fouling feature loss function and the number of iterations of the series-connected tubular membrane device;

[0029] Figure 6 , (e) Decompose and extract the feature map of 9 types of fault data by the wavelet transform method (WTF); (f) is the energy change diagram composed of the features after dimensionality reduction by the LargeVis algorithm;

[0030] Figure 7 Diagnosis experiments are carried out on the inputs of BP, SVM and ELM networks, and the comparison diagram of the diagnosis results with the deep network model;

[0031] Figure 8, (a) is the signal feature map of membrane fouling in a parallel hollow fiber membrane module; (b) is the fouling characteristic distribution of the parallel hollow fiber membrane module;

[0032] Fig. 9 , (c) is the experimental diagram of independent membrane fouling diagnosis of hollow fiber membranes; (d) is the relationship between the membrane fouling characteristic loss function and the number of iterations of the parallel hollow fiber membrane module;

[0033] Fig.10 , (e) is the wavelet transform energy spectrum diagram under each membrane fouling mode of hollow fiber membranes; (f) is the feature dimensionality reduction diagram of the LargeVis algorithm for hollow fiber membranes;

[0034] Fig.11 is the diagram of the diagnosis experimental accuracy rate and average running time of the parallel hollow fiber membrane module;

[0035] Fig.12 is the performance comparison result of the ablation experiment. Specific implementation manners

[0036] The present invention will be further described below in conjunction with specific implementation manners and the accompanying drawings.

[0037] Traditional CNN and BN layer

[0038] CNN is a type of feedforward neural network that contains convolutional calculations and has a deep structure. Its basic structure is cascaded by a convolutional layer, a pooling layer, an activation layer, and a fully connected layer.

[0039] 1) As the core convolution of CNN, convolution is essentially a mathematical operation. The calculation formula of the convolutional layer is:

[0040]

[0041] In the formula, f is the activation function, l is the number of layers of the network, K is the convolutional kernel, is the index vector of the feature map in the layer, is the bias of the j-th unit in the l-th layer.

[0042] The convolutional neural network can effectively extract features. In addition, the local connection and shared weight method adopted by CNN reduces the complexity of the deep network and, on the other hand, reduces the risk of overfitting.

[0043] As the depth of the deep neural network increases, there are problems such as difficult training and slow convergence speed. Adding a batch normalization layer (BN) after the convolutional layer can effectively improve this. By using normalization means, the input values of any neuron in each layer of the neural network are converted into a standard normal distribution with a mean of 0 and a variance of 1, so as to obtain a larger gradient, which can effectively avoid gradient disappearance, accelerate the learning convergence speed, and effectively improve the training speed.

[0044] The forward propagation process of the BN layer is as follows:

[0045] 1) Calculate the sample mean.

[0046]

[0047] Among them, m is the number of samples, and x is the sample.

[0048] 2) Calculate the sample variance.

[0049]

[0050] 3) Standardize the sample data.

[0051]

[0052] Among them, ε is a random value to ensure that the denominator is not zero.

[0053] 4) Perform translation and scaling processing.

[0054]

[0055] Among them, γ and β are learning parameters.

[0056] MIL-CNN model

[0057] In order to make full use of the powerful feature extraction ability of CNN, this paper adopts the multiple-convolutional neural networks (MIL-CNN) model, and its structure is as Figure 1 (a) shown. Compared with the traditional CNN, the multiple input layers of MIL-CNN have the advantage of combining the time-domain information map and frequency-domain information map of the fault data, making the feature extraction more comprehensive, thus effectively improving the accuracy of fault diagnosis. The specific steps of MIL-CNN are as follows:

[0058] 1) Send images to perform operations such as convolution and pooling at model unit 1 (Net1) and model unit 2 (Net2), and forward the information using the forward function;

[0059] 2) Aggregate the information of Net1 and Net2, and process it with the fully connected layer of model unit 3 (Net3);

[0060] 3) Calculate the cross-entropy loss based on the output of the label and soft-max layer;

[0061] 4) Backpropagate the loss and update the weights and biases in Net3;

[0062] 5) Update the parameters in Net1;

[0063] 6) Update the parameters in Net2.

[0064] CBAM module

[0065] Precisely extracting fault features is a prerequisite for improving the accuracy of fault diagnosis. In the convolution and pooling of convolutional neural networks, it is defaulted that each channel of the feature map (FM) is equally important. However, due to the different importance of the information carried, it is unreasonable to consider the channel importance the same. The convolutional attention module CBAM is based on the processing mechanism of the human visual system, ignoring unimportant factors and focusing all attention on important areas to improve the classification accuracy. Specifically, different weights are assigned to each piece of information, and the greater the weight, the more important the information. The CBAM structure is as Figure 1 shown in (b), which contains two independent sub-modules, the channel attention module (CAM) and the spatial attention module (SAM). Compared with SE-Net, in the channel attention module CAM, parallel global max pooling (GMP) and the spatial attention SAM module are added. In this way, the obtained information will be more comprehensive, and the distribution of the importance of information will be more reasonable, which is of great help to improving the subsequent diagnosis accuracy.

[0066] Figure 1 (c) is the typical structure of the channel attention module CBAM. The input feature map F(H W C) respectively undergoes global max pooling and global average pooling based on width and height to obtain two feature maps of 1×1×C. Then, they are sent into a two-layer neural network (MLP). The number of neurons in the first layer is C / r (r is the reduction rate), and the activation function is ReLU. The second layer has one neuron with the number of C, and the two-layer neural network is shared. Then, based on the element-wise sum of the MLP output features, a sigmoid activation operation is performed to generate the final channel attention feature, that is, M_c. Finally, element-wise multiplication is performed on M_c and the input feature map F to generate the input feature required for the spatial attention module.

[0067] CAM: Figure 1(d) is the typical structure of the Spatial Attention Module SAM. The output feature map F’ of the Channel Attention Module is used as the input feature map of this module. First, global maximum pooling and global average pooling based on channels are performed to obtain two hw1 feature maps, and then a concatenation operation (channel splicing) is performed based on channels. Then, through a 7*7 convolution operation (7*7 is better than 3*3), the dimension is reduced to 1 channel, that is, H W 1. Sigmoid generates a spatial attention feature, which is M_s. Finally, the obtained result is multiplied by the feature map input to the module to finally obtain the required feature.

[0068] SAM: Image Fourier Transform

[0069] For an image f(x, y) with a size of M×N pixels, its discrete Fourier transform F(u, v) is given by Equation (6):

[0070]

[0071] where u = 0, 1, 2, 3…M - 1; v = 0, 1, 2, 3…N - 1.

[0072] According to F(u, v), f(x, y) can be obtained through the inverse Fourier transform, as shown in Equation (7):

[0073]

[0074] where x = 0, 1, 2, 3…M - 1; y = 0, 1, 2, 3…N - 1.

[0075] Equations (6) and (7) constitute the two-dimensional discrete Fourier transform pair of the image. In the equations: The variables u and v are the transform components or frequency components, and x and y are the spatial components or image variables. According to the Fourier transform formula (6), F(u, v) is the frequency-domain image spectrum, and extracting its amplitude can obtain the intensity of the image signal f(x, y) at each frequency point (u, v). The amplitude spectrum, phase spectrum, and energy spectrum of the Fourier transform are respectively:

[0076]

[0077]

[0078] E(u, v) = R 2 (u, v) + I 2 (u, v) (10)

[0079] where R(u, v) and I(u, v) are the real part and imaginary part of F(u, v) respectively.

[0080] Embodiment

[0081] A membrane fouling detection method based on multi-feature information fusion includes the following steps:

[0082] 1) Collect membrane fouling data;

[0083] 2) Classify and encode the membrane fouling data;

[0084] 3) Use image processing technology to expand the data set to obtain a time-domain picture set, and use image Fourier transform to obtain a frequency-domain data set;

[0085] 4) Divide both the time-domain picture set and the frequency-domain data set in step 3) into a training set, a test set, and a validation set according to a certain ratio;

[0086] 5) Construct a CBAM-MIL-CNN network model, input the training set data information into the CBAM-MIL-CNN network model, verify the error of the CBAM-MIL-CNN network model, and then input the validation set data information into the CBAM-MIL-CNN network model to adjust and optimize the CBAM-MIL-CNN network model;

[0087] 6) Input the test set data information into the optimized CBAM-MIL-CNN network model to identify the membrane fouling state of the membrane module.

[0088] In step 5), the CBAM-MIL-CNN model is composed of network model unit 1, network model unit 2, and pattern recognition unit 3, as Figure 2As shown, the network model unit 1 (Net1) and the network model unit 2 (Net2) have the same network structure. The network structures of the network model unit 1 (Net1) and the network model unit 2 (Net2) both include an input layer, a convolutional layer a (in the figure, it is the convolutional layer a + ReLU activation function 1), a convolutional layer b (in the figure, it is the convolutional layer b + ReLU activation function 7), a convolutional layer c (in the figure, it is the convolutional layer c + ReLU activation function 8), a convolutional layer d (i.e., the convolutional layer d + ReLU activation function 9), and a convolutional layer e (i.e., the convolutional layer e + ReLU activation function 10). In the network model unit 1, the input is the time-domain picture set information with a size of 256*256, and in the network model unit 2, the input is the frequency-domain data set information with a size of 256*256. The convolutional layer a + ReLU activation function 1 and the convolutional layer b + ReLU activation function 7 are respectively sequentially added with a BN layer 3, a CBAM module 6, and a pooling layer 2. The CBAM module 6 includes a channel attention module and a spatial attention module. The convolutional layer e + ReLU activation function 10 is added with a BN layer 3 and a pooling layer 2. The pattern recognition unit 3 uses a fully connected layer 4 to splice and output the feature information of the network model unit 1 and the network model unit 2, and sends it to a softmax classifier (soft-max layer 5) for classification and recognition, and uses a cross-entropy loss function.

[0089] In step 5), the optimization strategy of the CBAM-MIL-CNN network model is the AdamW optimizer, and the AdamW optimizer is composed of the Adam optimizer and weight decay.

[0090] In step 5), the fault picture set of size 256*256 generated by overlapping sampling is input into the convolutional layer for feature extraction. The parameter settings are as follows: the convolutional kernel size of convolutional layer a is 3*3, the stride is 4*4, and the number of channels is 64. After convolution, an output of size 62*62*64 is obtained. After convolutional layer a, a ReLU activation function is connected to retain the effect of convolutional layer a and improve the non-linear expression ability to obtain an output of size 62*62*64. A BN layer is added to accelerate the network convergence to obtain an output of size 62*62*64; after inputting the CBAM module for feature extraction and splicing, a pooling layer with a size of 3*3 and a stride of 2*2 is connected to reduce the number of parameters and accelerate network learning, and an output of size 30*30*64 is obtained; the convolutional kernel size of convolutional layer b is 5*5, the stride is 1*1, and the number of channels is 128. After convolution, an output of size 26*26*128 is obtained, and a ReLU activation function and a BN layer are added to obtain outputs of size 26*26*128; after inputting the CBAM module for feature extraction and splicing, a pooling layer with a size of 3*3 and a stride of 2*2 is connected to obtain an output of 12*12*128; the convolutional kernel sizes of convolutional layer c and convolutional layer d are 3*3, the stride is 1*1, and the number of channels is 256. After convolution, an output of size 12*12*256 is obtained; the convolutional kernel of convolutional layer e is 3*3, the stride is 1*1, and the number of channels is 64. After convolution, an output of size 12*12*64 is obtained. Then, a ReLU activation function and a BN layer (batch normalization layer) are connected without changing the output size, and a pooling layer with a size of 3*3 and a stride of 2*2 is added to obtain an output of 5*5*64; there are 2 fully connected layers in the pattern recognition unit 3. The numbers of the 2 fully connected layers are set to 2048 and 512 respectively. Finally, the softmax layer is used to judge the probabilities of 9 kinds of faults for output.

[0091] Among them: for the input feature map F(C×H×W) of the CBAM module, global max pooling and global average pooling are respectively performed on each channel to obtain C values! Then, these C values are used as the input of the input layer of the fully connected neural network. The number of neurons in the middle hidden layer is compressed to C / r (r is the compression ratio), and the number of neurons in the output layer is C. The results are obtained respectively (the ReLU activation function is used in the hidden layer and the Sigmoid activation function is used in the output layer)! The weight of 1×1×C is obtained by global max pooling, and the weight of 1×1×C is obtained by global average pooling. Then, the corresponding positions of these two 1×1×C weight maps are added, and finally, the result of Channel Attention with a dimension of 1×1×C is output using the Sigmoid activation function.

[0092] CBAM-MIL-CNN Model Structure Parameters

[0093] When building a model, using multiple small convolutional kernels stacked together is much more effective than using a single large convolutional kernel alone. Without changing the connectivity, it greatly reduces the number of parameters and the computational complexity. Of course, the convolutional kernel is not the smaller the better. In the present invention, multiple relatively small convolutional kernels are selected for convolution. Deep learning models are usually trained by the stochastic gradient descent algorithm. There are many variants of the stochastic gradient descent algorithm, such as Adam, RMSProp, Adadelta, etc. These algorithms all require setting the learning rate in advance. The learning rate determines the distance that the weights move in the gradient direction in a mini-batch. A low learning rate can ensure the retention of local minima, but the training process takes a longer time and is prone to overfitting. While a high learning rate reduces the training time, it is prone to gradient explosion. Although the BN layer can effectively alleviate this problem, an appropriate learning rate still has an impact on the superiority of the model that cannot be ignored. Therefore, the training should start with a relatively large learning rate because at the beginning, the initial random weights are far from the optimal value. During the training process, the learning rate should decrease to allow for fine-grained weight updates.

[0094] Different from the traditional fixed learning rate, in the present invention, a learning rate decay factor α is set, and the learning period is set as t. Every other period, the learning rate τ is multiplied by an α, and its expression is:

[0095] τ t+1 = τ t ·α (11)

[0096] where α = 0.1.

[0097] Randomly select the training set, test set, and validation set of the training set to test the model. As Figure 3 (a) shows, when the model is trained using the decaying learning rate, the loss value is around 10 -6 or so and gradually tends to be stable. The loss value of the fixed learning rate is very different from the former, and it cannot tend to be stable under the same number of iterations. The dynamic learning rate adopted in the present invention is of great importance to the stability of the model.

[0098] During the experiment, the AdamW optimizer was used to continuously update the network training parameters, and the network was trained using the dynamic learning rate. The loss functions of different deep learning optimization algorithms during training parameters were compared. As Figure 3As shown in (b). Among them, although the Adadelta optimization algorithm does not depend on the global learning rate and has a good acceleration effect in the initial and middle stages of training, it only accumulates terms with fixed weight values and does not directly store these terms. It only approximately calculates the corresponding average value, resulting in jittering around the local minimum repeatedly in the later stage of training. The RMSprop optimization algorithm still depends on the global learning rate. The Adam optimization algorithm uses the first-order moment estimation and second-order moment estimation of the gradient to dynamically adjust the learning rate of each parameter, so that the learning rate has a fixed range of step sizes in each update, keeping the parameter updates stable. The Adam algorithm combines the advantages of the Adadelta algorithm in handling sparse gradients and the RMSprop algorithm in handling non-stationary targets, and calculates different adaptive learning rates for different parameters. In the present invention, the AdamW optimizer, that is, the Adam optimizer + weight decay, is adopted, and the effect is the same as that of Adam + L2 regularization, but the computational efficiency is higher. Because L2 regularization requires adding a regularization term to the loss function and then calculating the gradient, and finally backpropagating, while AdamW directly adds the gradient of the regularization term to the backpropagation formula, avoiding manually adding the regularization term to the loss function.

[0099] The CBAM-MIL-CNN model of the present invention is constructed on the model of the convolutional neural network, and the parameters involved are shown in Table 1 below.

[0100] Table 1 Structural parameters of the CBAM-MIL-CNN model

[0101]

[0102] Experimental objects and acquisition and processing of membrane fouling data

[0103] Using computational fluid dynamics (CFD) software, aiming at the problem that the membrane flux is vulnerable to factors such as influent flow rate and temperature, resulting in membrane fouling, the experiments in this paper take the series tubular membrane device and the parallel hollow fiber membrane module as the research objects, and accurately classify the factors causing membrane fouling in the two.

[0104] The present invention uses overlapping sampling for data augmentation to obtain more training samples to enhance the generalization ability of the machine learning model. When using overlapping sampling for data augmentation, that is, when obtaining training fault features, there is partial overlap between each segment of fault features and the subsequent segment of features. Computational fluid dynamics (CFD) software is used to simulate and calculate the water production in the MBR system to collect fault data. During the simulation time, 168,000 points are sampled for each type of fault. Assuming that the length of each fault sample is 65,536 and the offset is 1,024, then after overlapping sampling, 100 samples can be made. The fault samples are converted into a grayscale image set with a size of 256×256 after normalization.

[0105] For each experimental subject in the present invention, 9 types of membrane fouling are selected, and 100 samplings are taken for each type of membrane fouling. Each sampling has 256 * 256 * 100 points, which are divided into images of size 256 * 256, with 100 images for each type. There are a total of 900 images for 9 types of faults, and labels (codes) are added to each type of fault. The training set, validation set, and test set are selected according to the ratio of 7:2:1.

[0106] Table 2 shows the membrane fouling patterns of the membrane device. Among them, when the transmembrane pressure difference is constant, membrane fouling is mainly affected by the concentration difference of COD (C) between inlet and outlet water, the concentration difference of BOD (B) between inlet and outlet water, the concentration of mixed suspended solids (X), and the hydraulic retention time (H).

[0107] Table 2 Membrane Fouling Patterns of Membrane Device

[0108] Membrane fouling failure mode type <![CDATA[Tolerance 1 > <![CDATA[Tolerance 2 > f1 No trouble - - f2 C is too big 5％ 5％ f3 C is too small 5％ 5％ f4 B is too big 5％ 5％ f5 B is too small 5％ 5％ fi5 X is too big 7％ 5％ f7 X is too small 7％ 5％ f8 H is too big 7％ 5％ f9 H is too small 7％ 5％

[0109] In order to better accelerate the training speed of the network model, make the data easy to calculate and obtain more generalized results, the input data is normalized, and the mathematical expression is:

[0110]

[0111] Experimental Procedure

[0112] The experimental procedure of the present invention includes collecting fault data, fault classification coding, data preprocessing, data analysis and partitioning, building a CBAM-MIL-CNN model, prediction coding, and result analysis, etc. The specific steps are as follows:

[0113] 1) Collect membrane fouling data;

[0114] 2) Classify and code the membrane fouling data;

[0115] 3) Use resampling image processing technology to expand the data set to obtain a time-domain picture set, and use image Fourier transform to obtain a frequency-domain data set;

[0116] 4) Divide the time-domain picture set and frequency-domain data set obtained in step 3) into a training set, a test set, and a validation set according to the ratio of 7:2:1 respectively;

[0117] 5) Build a CBAM-MIL-CNN network model, input the training set data information into the CBAM-MIL-CNN network model to verify the error of the CBAM-MIL-CNN network model, and then input the validation set data information into the CBAM-MIL-CNN network model to adjust and optimize the CBAM-MIL-CNN network model;

[0118] 6) Compare the actual coding of the test set with the predicted coding generated by the model. If the predicted coding is consistent with the actual coding result, the classification is correct. If the predicted coding is inconsistent with the actual coding result, the classification is wrong.

[0119] 7) Further analysis of the CBAM-MIL-CNN model from the perspective of average accuracy, average precision, average recall, running time, and determination coefficient R 2 From this perspective, we can judge the performance of the model.

[0120] 1. Diagnosis results and analysis of membrane fouling of series tubular membrane modules

[0121] The membrane fouling modes of the serial tubular membrane module are set to three conditions: too large, too small, and normal. Among them, the tolerance of the inlet and outlet COD concentration difference and the inlet and outlet BOD concentration difference is set to 5%, and the tolerance of the mixed suspension solid concentration and hydraulic retention time is set to 7%, as shown in the tolerance in Table 2 above. 1 As shown. When the size of the membrane fouling influencing factor in the series tubular membrane device exceeds the set tolerance, it indicates that it is too large; when it is lower than the set tolerance, it is too small; when the membrane fouling influencing factor is within the set tolerance, it indicates that it is normal without deviation. According to the importance analysis of membrane fouling factors, since the difference in inlet and outlet COD concentration, the difference in inlet and outlet BOD concentration, the solid concentration of mixed suspension, and the hydraulic retention time have a more obvious impact on membrane fouling, the above four influencing factors are selected as research objects for analysis.

[0122] Figure 4-7 The results of the membrane fouling diagnosis experiment of the series tubular membrane module are shown in Figure 2. Figure 4 (a) is the characteristic diagram of membrane fouling signal of series tubular membrane module, and the membrane fouling characteristics can be accurately extracted. Figure 4 (b) is the distribution of membrane fouling characteristics of the serial tubular membrane module. It can be seen that only the f3 and f5 membrane fouling categories have a small overlap, and the remaining membrane fouling category data are highly separated. The same membrane fouling category data are closely aggregated, which is beneficial to improving the correct diagnosis rate of the fault diagnosis model of the present invention. In 10 independent membrane fouling diagnosis experiments, 9 faults can be accurately identified without error, such as Figure 5 (a) shown. Figure 5 (b) is the relationship between the membrane fouling characteristic loss function of the series tubular membrane module and the number of iterations. The loss function value is finally 10 -8Nearby and relatively stable, indicating that the model has very excellent robustness. At the same time, a comparative experiment was conducted between the diagnostic method adopted in the present invention and some traditional fault diagnosis methods. Since a large amount of data was extracted from the data set in a short period of time, the difference between data is very subtle and the data contrast is not strong enough. Therefore, the three models of BP (back propagation) neural network, support vector machine (SVM), and extreme learning machine (ELM) cannot accurately extract features, and thus cannot effectively classify the membrane fouling data. Therefore, when using traditional methods, it is necessary to preprocess the data first. The method is as follows: The wavelet transform method (WTF) is used to decompose 9 types of fault data to extract features, such as Figure 6 (e) shown. The LargeVis algorithm is used to reduce the dimension of the features of 9 types of fault data. As shown in Figure 6 (f), it is the energy change diagram composed of the features after dimensionality reduction by the LargeVis algorithm. At this time, the feature data becomes more obvious than before. These features are used as the input of the BP, SVM, and ELM networks for diagnostic experiments, and the diagnostic results are compared with the deep network model. The results are as shown in Figure 7 .

[0123] From Figure 7It is known that membrane fouling diagnosis can also be achieved by using shallow learning after data processing, but the accuracy is relatively low. In 10 experimental tests of the series-connected tubular membrane device, the accuracy of the membrane fouling diagnosis model is not high, and the diagnostic accuracy is all below 75%. The average accuracy of the WTF-LargeVis-ELM diagnosis model is only 57.39%, which is the worst among all diagnostic models. After using a deep network, the diagnostic accuracy is significantly improved. The membrane fouling diagnosis accuracy of the fault diagnosis model based on the deep learning method remains at a high level, proving the superiority of the deep network in the membrane fouling diagnosis of the series-connected tubular membrane module. The MIL-CNN network is superior to the traditional CNN network, and after adding the SENet module and the SKNet attention module to the MIL-CNN network, its membrane fouling diagnosis rate has been improved to varying degrees. The average accuracies of the four methods of MIL-CNN, CNN, SENet-CNN, and SKNet-CNN are 96.16%, 95.48%, 96.25%, and 95.76% respectively. Among them, the CBAM-MIL-CNN network has the best membrane fouling diagnosis effect, with 3 times of error-free accurate classification, and the average correct rate is 98.47%. The diagnostic accuracy of 10 independent experiments is higher than that of other models, indicating that adding the attention mechanism module will make the model extract features more reasonably. The present invention can reduce the number of model parameters and the risk of overfitting in membrane fouling diagnosis, improve the generalization ability of the model, accurately and quickly extract the important features of membrane fouling, and maintain a high membrane fouling diagnosis accuracy. Therefore, the diagnostic method of the present invention has great superiority over other methods in the membrane fouling diagnosis of the series-connected tubular membrane module.

[0124] 2. Membrane Fouling Diagnosis Results and Analysis of the Parallel Hollow Fiber Membrane Module

[0125] Taking the parallel hollow fiber membrane module as the object for simulation verification. Selecting the CFD software ANSYS, establishing the parallel hollow fiber membrane module to obtain membrane fouling data, setting the tolerances of the COD concentration difference between the inlet and outlet water, the BOD concentration difference between the inlet and outlet water, the mixed suspension solid concentration, and the hydraulic retention time to be all 5%. Similarly, using the tolerance as the basis for membrane fouling diagnosis, when the numerical value of the membrane fouling factor fluctuates within 5% above and below the standard value, it is normal, and when it is higher or lower than 5%, it is too large or too small, and the fault mode is 9 types (as shown in Table 2 above for the tolerance 2 shown), and the membrane fouling diagnosis experiment of the parallel hollow fiber membrane module is carried out under the same experimental conditions. Figure 8-11 This is the experimental result of the membrane fouling diagnosis of the parallel hollow fiber membrane module. Among them Figure 8 (a) is the membrane fouling signal feature map of the parallel hollow fiber membrane module, Figure 8 (b) is the membrane fouling feature distribution of the parallel hollow fiber membrane module. Similarly, 10 independent membrane fouling diagnosis experiments are carried out on the parallel hollow fiber membrane module, and 9 types of faults can be accurately identified, such as Fig. 9 as shown in (c). Fig. 9 (d) shows the relationship between the loss function of membrane fouling characteristics and the number of iterations of the parallel hollow fiber membrane module. Using the data preprocessing method in the membrane fouling diagnosis of the series tubular membrane module, the wavelet transform energy spectrum and the LargeVis algorithm feature dimensionality reduction diagram under each membrane fouling mode are as Fig.10 shown. In the 10 - time diagnostic accuracy experiment of the parallel hollow fiber membrane module, the accuracy of each diagnostic experiment, as well as the average accuracy and average running time of the 10 - time diagnostic experiments are as Fig.11 shown.

[0126] It can be seen from Figure 8-11 that although the line - layer neural network and support vector machine diagnostic models after data processing can diagnose membrane fouling, the misclassification and false judgment are serious, and they cannot complete the accurate diagnosis of membrane fouling. Especially, the misclassification rate of the WTF + LargeVis + ELM model is close to 50%, so it cannot be applied in actual production activities. Although the diagnostic accuracies of the WTF + LargeVis + BP model and the WTF + LargeVis + SVM model have been improved to a certain extent compared with the WTF + LargeVis + ELM model, due to the defects in the model structure and performance, the extraction of membrane fouling characteristics is not sufficient, and they cannot accurately diagnose membrane fouling. The diagnostic performance of the MIL - CNN network optimized by SENet and SKNet for membrane fouling is better than that of the MIL - CNN network, but it is still lower than that of the MIL - CNN network optimized by the CBAM module. This is because CBAM can avoid reducing the dimension, adaptively select the kernel size, simplify the complexity of the model, and improve the diagnostic performance of the model. In the membrane fouling diagnosis experiment of the parallel hollow fiber membrane module, the diagnostic accuracy of the CBAM - MIL - CNN membrane fouling diagnosis model of the present invention is the highest at 99.08% and the lowest at 97.21% in the 10 - time diagnostic experiments. The diagnostic accuracies are all higher than those of other diagnostic models, and the average accuracy is 98.19%. It can already diagnose membrane fouling accurately and quickly.

[0127] Both the membrane fouling test of the series hollow fiber membrane device and the membrane fouling experiment of the parallel hollow fiber membrane module verify the rationality and superiority of the network model of the present invention. CBAM - MIL - CNN does not require complex data preprocessing, greatly reducing the time required by the model; splicing the time - domain and frequency - domain information, the obtained features are more comprehensive, effectively extracting and classifying the membrane fouling characteristics of membrane devices with different structures. Compared with other methods, the diagnostic method of the present invention has obvious advantages in membrane fouling diagnosis.

[0128] 3. Diagnostic Results and Analysis of Different Models for Membrane Fouling under Different Noises

[0129] During the actual operation of the membrane bioreactor, there is environmental noise when the membrane module treats sewage, and there is also noise due to the characteristics of the membrane module itself. These noises generate unnecessary randomness during the acquisition of membrane fouling data. Therefore, it is crucial to add a variable-noise experiment in the membrane fouling diagnosis experiment. In this invention, the membrane fouling data of the parallel hollow fiber membrane module is used as the training sample, and Gaussian white noise with signal-to-noise ratios of -2 - 6 dB is added to the test sample. The CBAM-MIL-CNN model is used for membrane fouling diagnosis. To verify the superiority of the network model of this invention in fault diagnosis, it is compared with MIL-CNN, Squeeze-and-Excitation Networks-MIL-CNN (SENet-CNN), and Selective Kernel Networks-MIL-CNN (SKNet-CNN). At the same time, comparative experiments are conducted with the improved fault diagnosis models proposed by G. Li [G. Li, J. Wu, C. Deng, Z. Chen, X. Shao, Convolutional neural network-based bayesian Gaussian mixture for intelligent fault diagnosis of rotating machinery, IEEE Trans. Instrum. Meas. 70 (2021) 1–10.] and H. Wu [H. Wu, J. Zhao, Deep convolutional neural network model based chemical process fault diagnosis, Comput. Chem. Eng. 115 (2018) 185–197.]. Among them, Wu et al. proposed a chemical process fault diagnosis method based on the DCNN model (abbreviated as DCNN), and this model is composed of a convolutional layer, a pooling layer, a leaky layer, and a fully connected layer. Li et al. proposed a three-step intelligent fault diagnosis method based on CNN and Bayesian-Gaussian mixture (BGM) (abbreviated as CNN-BGM). The membrane fouling diagnosis results obtained by the method in this paper are compared and analyzed with other networks, and the experimental results are shown in Table 3.

[0130] Table 3 Diagnosis accuracy rates of different methods under different noises

[0131]

[0132] From the comparison data in Table 3, it can be seen that in the experimental results with different signal-to-noise ratios, the membrane fouling diagnosis accuracy of the CBAM-MIL-CNN-based membrane module is higher than that of other methods. Although the diagnosis method based on MIL-CNN can share convolutional kernels and automatically extract features, using the gradient descent algorithm easily makes the training result converge to a local minimum rather than the global minimum. At the same time, the pooling layer will lose a large amount of valuable information and ignore the correlation between the local and the whole. The methods based on SENet-MIL-CNN and SKNet-MIL-CNN start from the relationship between feature channels, model and represent the relationship between feature channels, enhance useful features and suppress useless features according to the importance degree, and improve the accuracy of membrane fouling diagnosis on the basis of the CNN network. At the same time, the diagnosis accuracy is maintained within a relatively stable range, but dimensionality reduction cannot be avoided, resulting in the diagnosis accuracy of the model being inferior to that of the network model of the present invention. The convolutional layer and pooling layer of the fault diagnosis method proposed by Wu et al. are locally connected through filters, which helps to better extract local patterns or features. At the same time, overfitting can be avoided by using dropout layers and pooling layers. However, since the model still relies on historical fault data samples, it is not applicable to fault diagnosis without historical data or with less historical data. Li et al. combined CNN with the BGM model and proposed an end-to-end intelligent fault diagnosis method. This method can directly use the original signal for end-to-end fault diagnosis without preprocessing the signal, so it cannot accurately describe the causal relationship between conditional features and corresponding fault types. The present invention uses the time-domain information and frequency-domain information of fault data as the input of CNN, extracts features through the convolutional layer, and then uses the fully connected layer to splice the time-domain features and frequency-domain features and input them into the classifier for classification. The batch normalization layer in the model can effectively prevent gradient disappearance, the ReLU layer can improve the expression ability of the nonlinear model, the CBAM module can simplify the model complexity and improve the feature expression ability of the network, and the pooling layer can improve the fault tolerance of the model. Compared with other membrane fouling diagnosis methods, its diagnosis accuracy is higher, the generalization ability is better, and the anti-noise performance is stronger.

[0133] 4. Model Performance Comparison Experiment

[0134] An ablation experiment was carried out using the membrane fouling simulation dataset of the series-connected tubular membrane module, and the average accuracy, average precision, average recall rate, average time, and average determination coefficient R 2 A total of 5 kinds of performances were used as the model judgment basis, and the performances of five models, namely CNN, MIL-CNN, CNN+BN, CNN+BN+CBAM, and MIL-CNN+BN+CBAM, were verified. The results are as Fig.12 shown.

[0135] From Fig.12Analysis shows that after adding the BN layer and the CBAM module to the CNN respectively, the model performance has been improved to varying degrees. While the running time is reduced, the accuracy has been improved by different margins. Moreover, the five performance effects of the MIL-CNN+BN+CBAM model are better than those of the other four network models, thus verifying the effectiveness and superiority of the CBAM-MIL-CNN model of the present invention.

Claims

1. A method for detecting membrane fouling of a membrane module based on multi-feature information fusion, characterized in that, it includes the following steps: 1) Collect membrane fouling data; 2) Classify and encode the membrane fouling data; 3) Use image processing technology to expand the data set to obtain a time-domain picture set, and use image Fourier transform to obtain a frequency-domain data set; 4) Divide the time-domain picture set and the frequency-domain data set in step 3) into a training set, a test set, and a validation set respectively according to a certain proportion; 5) Construct a CBAM-MIL-CNN network model, input the training set data information into the CBAM-MIL-CNN network model, verify the error of the CBAM-MIL-CNN network model, and then input the validation set data information into the CBAM-MIL-CNN network model to adjust and optimize the CBAM-MIL-CNN network model; 6) Input the test set data information into the optimized CBAM-MIL-CNN network model to identify the membrane fouling state of the membrane module; In step 5), the CBAM-MIL-CNN model is composed of network model unit 1, network model unit 2, and pattern recognition unit 3. Network model unit 1 and network model unit 2 have the same network structure. The network structures of network model unit 1 and network model unit 2 both include an input layer, convolutional layer a, convolutional layer b, convolutional layer c, convolutional layer d, and convolutional layer e with activation functions added respectively, and a CBAM module. Batch normalization layers and pooling layers are sequentially added to convolutional layer a, convolutional layer b, and convolutional layer e respectively. The CBAM module is connected to the output ends of convolutional layer a and convolutional layer b, or the batch normalization layers on convolutional layer a and convolutional layer b, or the output ends of the pooling layers. Pattern recognition unit 3 splices and outputs the feature information of network model unit 1 and network model unit 2 using a fully connected layer and sends it to a softmax classifier for classification and recognition; Batch normalization layers, a CBAM module, and a pooling layer are sequentially added to the output ends of convolutional layer a and convolutional layer b.

2. The method for detecting membrane fouling of a membrane module based on multi-feature information fusion according to claim 1, characterized in that, in step 5), the time-domain picture set information is input into network model unit 1, and the frequency-domain data set information is input into network model unit 2.

3. The method for detecting membrane fouling of a membrane module based on multi-feature information fusion according to claim 2, characterized in that, in step 5), the activation function is a Relu activation function, and the optimization strategy of the CBAM-MIL-CNN network model is an AdamW optimizer, and the AdamW optimizer is composed of an Adam optimizer and weight decay.

4. The method for detecting membrane fouling of a membrane module based on multi-feature information fusion according to claim 3, characterized in that, In step 5), the convolution kernel size of convolutional layer a is 3*3, the stride is 4*4, and the number of channels is 64. After convolution, batch normalization, feature extraction by the CBAM module, and pooling, an output of size 30*30*64 is obtained; the convolution kernel size of convolutional layer b is 5*5, the stride is 1*1, and the number of channels is 128. After convolution, batch normalization, feature extraction by the CBAM module, and pooling, an output of size 12*12*128 is obtained; the convolution kernel sizes of convolutional layers c and d are 3*3, the stride is 1*1, and the number of channels is 256. After convolution, an output of size 12*12*256 is obtained; the convolution kernel of convolutional layer e is 3*3, the stride is 1*1, and the number of channels is 64. After convolution, batch normalization, and pooling, an output of size 5*5*64 is obtained; there are 2 fully connected layers in the pattern recognition unit 3, and the number of neurons in the 2 fully connected layers is set to 2048 and 512 respectively.

5. The method for detecting membrane fouling of a membrane module based on multi-feature information fusion according to claim 4, characterized in that in step 5), the CBAM module includes a channel attention module and a spatial attention module.

6. The method for detecting membrane fouling of a membrane module based on multi-feature information fusion according to claim 5, characterized in that the membrane module is a series tubular membrane module or a parallel hollow fiber membrane module.

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