A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks
Abstract
:1. Introduction
- A
- RCA problem in industrial processes
- B
- Source analysis in brain networks
2. Materials
2.1. Industrial Process Case: Root Cause Analysis of Plant-Wide Oscillations
2.2. Brain Network Case: Localization of Seizure Onset Zones in the Human Brain
3. Methods and Results
3.1. Taxonomy of Causality Detection Methods
3.1.1. Predictive Model-Based Branch
- A.
- Linear prediction
- (1)
- GC and MVGC
- (2)
- DTF and PDC
- B.
- Nonlinear prediction
- (1)
- CCM
3.1.2. Information-Theoretic Branch
- (1)
- TE
3.1.3. Time Delay Estimation-Based Branch
- (1)
- CCF
- (2)
- PSI
3.2. RCA of Plant-Wide Oscillations
3.2.1. Time-Domain Methods
3.2.2. Frequency-Domain Methods
3.2.3. Improved Frequency-Domain Methods
3.3. Localization of SOZs in the Human Brain
3.4. CCM in Both Cases
4. Discussion
4.1. RCA of Plant-Wide Oscillations
4.2. Localization of SOZs in the Human Brain
- i.
- The GC and TE methods, which are widely used for identifying the root cause of fault in industrial processes, work poorly on brain networks. On one hand, bivariate causality detection methods (TE, GC, and PSI) cannot rule out indirect, redundant causal relations. As a consequence, the causal information outflow that results from any of them shows similar trends across SOZ and non-SOZ channels, making it difficult to identify the SOZ. On the other hand, to address the requirement for stationarity of the time series used in the causal inference in this case, we used sliding windows whose width was limited. However, both TE and GC have a high requirement for the number of samples.
- ii.
- Multivariate methods (ffDTF, swPDC, and MVGC) are more effective. Of those methods, the ffDTF and swPDC, which detect causal effects in the frequency domain, produced the most promising results.
- iii.
- As for PSI, it may be inapplicable in this case. Bidirectional interactions are the dominant interaction scenario in the majority of cortico–cortical connections. In such situations, the interpretation of the phase difference spectrum (and consequently PSI) as well as the CCF becomes complicated and may fail at correctly describing the directionality. See Witham et al. (2011) and Vinck et al. (2015) for further discussion [68,69].
- iv.
- In brain networks, CCM does not converge and consequently fails to discover causations. A possible reason for the nonconvergence is that CCM assumes that the dynamic system is described by a nonlinear model and has a specific trajectory. However, the dynamics of the brain connectivity pattern changes with time.
4.3. Summary
4.4. Discussions of Interpretative Pitfall
4.5. Future Directions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Supplementary Introduction to Time Series Causality Detection Methods
Parameter/Variable | Meaning |
“Cause” variable in bivariate causal relations | |
“Effect” variable in bivariate causal relations | |
“Cause” variable in multivariate causal relations | |
“Effect” variable in multivariate causal relations | |
Order of AR or MVAR model | |
Dimension of the shadow manifold or embedding vector | |
Time delay of the shadow manifold or embedding vector | |
Number of neighbors used in prediction of CCM or k-NN |
Appendix A.1. Significance Test of GC
Appendix A.2. Improvements of DTF and PDC
Appendix A.3. Calculation of TE
Appendix A.4. DTE
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Propagation Networks of Faults in Industrial Processes | Effective Connectivity Networks of Human Brains | |
---|---|---|
Stationarity of time series | Nearly stationary or nonstationary [49] | Nonstationary [50] |
Stability of connection pattern | Relatively stable in a given state | Transient and unstable |
System dynamics | Linear or nonlinear | Nonlinear and with chaos behaviors [40,51] |
Network characteristic | Regular or complex [52] | Complex [53] |
A priori knowledge | Piping and instrumentation diagrams (P&IDs), etc. [25] | Lacking |
Method | Parameter Settings |
---|---|
GC MVGC |
|
TE DTE |
|
CCM |
|
Parameter Settings in DTF and PDC | |
---|---|
MVAR model |
|
Significance determination |
|
Method | Parameter Settings | |
---|---|---|
TE |
| |
MVGC |
| |
ffDTF swDTF swPDC |
| |
PSI |
|
LC1 | FC1 | TC1 | PC2 | FC5 | LC2 | FC8 | TC2 | |
---|---|---|---|---|---|---|---|---|
LC1 | −0.90 | −0.75 | \ | 0.87 | 0.75 | 0.37 | −0.84 | |
FC1 | −0.48 | 0.28 | \ | −0.55 | −0.19 | −0.77 | 0.84 | |
TC1 | −0.91 | 0.81 | 0.66 | −0.91 | −0.93 | 0.01 | 0.78 | |
PC2 | −0.30 | 0.38 | 0.10 | \ | \ | \ | \ | |
FC5 | 0.83 | −0.91 | −0.79 | \ | 0.80 | 0.49 | −0.89 | |
LC2 | 0.93 | −0.85 | −0.90 | \ | 0.96 | 0.24 | −0.86 | |
FC8 | −0.31 | −0.45 | 0.58 | 0.51 | −0.19 | −0.49 | −0.46 | |
TC2 | \ | 0.64 | \ | \ | \ | −0.01 | −0.59 |
TE | GC | -NN | CRRA | CCM | CCF | DTF | PDC | PSI | |
---|---|---|---|---|---|---|---|---|---|
Time domain | √ | √ | √ | √ | √ | √ | |||
Frequency domain | √ | √ | √ | ||||||
Linear relation | √ | √ | √ | √ | √ | √ | √ | √ | |
Nonlinear relation | √ | √ | |||||||
Parameterized | √ | √ | √ | √ | |||||
Nonparametric | √ | √ | √ | √ | √ | ||||
Bivariate | √ | √ | √ | √ | √ | √ | √ | √ | √ |
Multivariate | √ | √ | √ | √ | √ | ||||
Number of samples required | high | high | low | high | medium | low | high | high | low |
Computational load | high | low | medium | low | medium | low | medium | medium | low |
Insensitive to noise | √ | √ | √ | √ | |||||
Direct causality | √ a | √ b | √ | √ | |||||
Number of a priori parameters c | ) | ) | ) | ) | ) | 0 | ) | ) | 0 |
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Zhou, S.; Cai, H.; Chen, H.; Ye, L. A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks. Sensors 2024, 24, 4908. https://doi.org/10.3390/s24154908
Zhou S, Cai H, Chen H, Ye L. A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks. Sensors. 2024; 24(15):4908. https://doi.org/10.3390/s24154908
Chicago/Turabian StyleZhou, Sun, He Cai, Huazhen Chen, and Lishan Ye. 2024. "A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks" Sensors 24, no. 15: 4908. https://doi.org/10.3390/s24154908
APA StyleZhou, S., Cai, H., Chen, H., & Ye, L. (2024). A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks. Sensors, 24(15), 4908. https://doi.org/10.3390/s24154908