Compressible Diagnosis of Membrane Fouling Based on Transfer Entropy
Abstract
:1. Introduction
- (1)
- Based on the mechanism analysis associated with membrane fouling, the relationship between causal variables and membrane fouling is clarified with the feature extraction algorithm. Then, the related variables of membrane fouling are obtained under different operating conditions. Different from the data-driven diagnosis models in [15,16,17,18,19] with given causal variables, the feature extraction algorithm will enable the proposed CDM to transform raw data into informative representations that can be utilized for diagnosis.
- (2)
- Instead of using a mapping relationship with simple input–output representation such as decision trees [21,22] and the Bayesian network [24,25], a topology based on transfer entropy is constructed. This approach not only provides a qualitative evaluation of the causal relationships between variables by observing the dynamic transfer path, but it also offers a quantitative description of those variables. It helps uncover the path of fault occurrence and further obtain the fault cause priority that may change over time as the operating conditions change.
- (3)
- The information compressible strategy (ICS) is designed to delete redundant or repetitious affiliation relationships between the causal variables. With this strategy, the simplified FTT is obtained with low complexity during the update of fault transfer topology, which can maintain the diagnosis of membrane fouling speedily and accurately.
2. Background of Membrane Fouling
2.1. Membrane Fouling
2.2. Membrane Fouling Diagnosis System
3. Methodology
3.1. Feature Variable Selection
- ➀
- The data of the independent variable is given as P = [p1, p2, …, pj], pj= (p1j, p2j, …, pij)T, i = 1, 2, …, m, j = 1, 2, …, n, and the dependent variable Q = [q1, q2,…, qi]T. The standard treatment is as follows:
- ➁
- The principal component of the variable is found via the following formula:
- ➂
- The cross-validity is used to determine the number of final extracted components with
3.2. Membrane Fouling Detection Model
3.3. Construction of Fault Transfer Topology
3.4. Simplification of Fault Propagation Topology
4. Results and Discussion
4.1. The Feature Variables
4.2. Results of Membrane Fouling Detection Model
4.3. Results of Membrane Fouling Diagnosis Model
4.4. Discussion of Results
- (1)
- Good detection. It is essential for the CDM to identify incidents of membrane fouling with specific causal variables. The proposed autoencoder can summarize thresholds by RMSE for any membrane fouling, assuming it covers the entire normal conditions of the MBR. These thresholds can serve as a reference for operators to monitor the occurrence of membrane fouling without the need for a physical or mathematical model. The results in Figure 6 and Figure 7 also illustrate the efficacy of this method.
- (2)
- Intuitive diagnosis. By constructing a fault transfer topology with the CDM in Figure 8, the dynamic observation of causal relationships between variables facilitates the determination of causal factors leading to membrane fouling. Additionally, to eliminate repetitive affiliation relationships, the fault transfer topology is simplified using an information compressible strategy, as shown in Figure 9 and Figure 10. Table 2 also demonstrates that the proposed CDM significantly enhances the speed and accuracy of diagnosis.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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%Characteristic variable selection | |
1 Standardize the data to obtain E0 and F0 | % Equations (1) and (2) |
2 Obtain the principal component of the variable | % Equation (3) |
3 Determine the number of final extracted components | % Equations (4) and (5) |
Obtain K variables that have a great influence on membrane fouling | |
%Membrane fouling detection model | |
1 Acquire normal data and train an autoencoder | |
2 Obtain the threshold of reconstruction error J0 of normal samples | |
3 Use the autoencoder to detect the data collected in real time, and the reconstruction error J is obtained | |
4 If J > J0, the membrane fouling exists | |
% Calculate the transfer entropy between variables | |
Obtain the influence relationship between variables TY→X | % Equations (9) and (10) |
% Generate adjacency matrix Akk | |
for j = 1: k do | |
for i = j + 1: k do | |
if Tj→i >0 | |
Aji= Tj→i | |
else | |
Aij= Tj→i | |
end for | |
end for | |
FTT is obtained because the relationship between variables is connected by lines according to the adjacency matrix Akk. | |
% Simplify fault transfer topology | |
Set threshold | |
1 Select two data segments with a long time distance from historical data of the two variables | |
2 Calculate of entropy transfer tei between the above two data segments | % Equation (10) |
3 Repeat steps 1 and 2, calculate multiple sets of such transfer entropy NET = [te1, te2,…, tes] | |
4 Calculate the average value and standard deviation of NET to obtain the threshold | % Equation (13) |
Information compressible strategy | |
1 Filter all direct and indirect transfer relationships between variables | |
2 Calculate the score of the structure for each transfer relationship | % Equations (14) and (15) |
3 Choose the transfer relationship corresponding to the highest score | |
The root causal variables are determined according to the simplified fault transfer topology |
Methods | Time (s) | Number of Connections | Accuracy (%) |
---|---|---|---|
FTT with ICS and threshold | 8.3 | 18 | 93.4% |
FTT with threshold | 9.5 | 23 | 91.0% |
Initial FTT | 14.9 | 66 | 86.7% |
BN | 12.1 | - | 85.1% |
ANN | 13.3 | - | 82.3% |
FL | 19.8 | - | 82.1% |
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Wu, X.; Hou, D.; Yang, H.; Han, H. Compressible Diagnosis of Membrane Fouling Based on Transfer Entropy. Appl. Sci. 2024, 14, 8176. https://doi.org/10.3390/app14188176
Wu X, Hou D, Yang H, Han H. Compressible Diagnosis of Membrane Fouling Based on Transfer Entropy. Applied Sciences. 2024; 14(18):8176. https://doi.org/10.3390/app14188176
Chicago/Turabian StyleWu, Xiaolong, Dongyang Hou, Hongyan Yang, and Honggui Han. 2024. "Compressible Diagnosis of Membrane Fouling Based on Transfer Entropy" Applied Sciences 14, no. 18: 8176. https://doi.org/10.3390/app14188176