Model-Based Posterior Correction for Isolating Structurally Indistinguishable Faults
- 1Convergence of AI, Chonnam National University, Gwangju 61186, Republic of Korea
Abstract
Model-based fault diagnosis narrows down fault candidates by checking the consistency between a mathematical model of the plant and the measurements. Depending on the sensor configuration and the system structure, however, different faults may share an identical residual signature. In such cases, the diagnosis keeps the true fault inside the candidate set but cannot single it out, and this structural indistinguishability is not resolved by tuning thresholds or post-processing the residuals. This paper proposes a method that reuses the diagnostic model on the candidates left by the existing diagnosis in order to rank them. Assuming each candidate to be the true fault and propagating the model forward yields predictions whose comparison with the actual measurements exposes temporal differences that the residual signature does not carry. A limited computational budget is distributed over several candidates so that the comparison is well defined, and the weight given to the two sources of information is adjusted according to how confident the existing diagnosis is. On a three-tank fault diagnosis benchmark, the probability assigned to the true fault at instants where the existing diagnosis selected a different candidate increased from 0.2547 to 0.6735; the isolation accuracy over the three faults sharing an identical residual signature improved from 31.5% to 52.7%; and the accuracy over all seven faults improved from 59.4% to 76.7%. On that benchmark, learning-based methods taking the same residuals as input did not exceed 0.30 on the indistinguishable set even with 512 samples per fault, whereas the proposed method uses no fault data at all. On a second benchmark, an electric motor, the same procedure raised that probability from 0.3523 to 0.7110. Across twelve combinations of fault magnitude and process noise, the method was never below the existing diagnosis, although the gain exceeded 0.34 only in the six where the fault magnitude was at least 12.5 times the process noise standard deviation.
Related
- Posterior Frequencies and the Cost of Not Fitting: A Correction to a Memorization Lower Bound
- A Comparative Optimal Control Study of Protecting Susceptibles and Isolating Infecteds in SIR Models
- Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits
- Porous media modeling and micro‐structurally motivated material moduli determination via the micro‐dilatation theory
- Boundary null controllability of weakly coupled structurally damped beams
BibTeX
@article{min2026modelbased,
title = {{Model-Based Posterior Correction for Isolating Structurally Indistinguishable Faults}},
author = {Young Eui Min and Man-Je Kim},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213857},
url = {https://www.mdpi.com/2227-7390/14/21/3857},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Model-Based Posterior Correction for Isolating Structurally Indistinguishable Faults
AU - Young Eui Min
AU - Man-Je Kim
PY - 2026
DA - 2026/10/22
JO - Mathematics
DO - 10.3390/math14213857
UR - https://www.mdpi.com/2227-7390/14/21/3857
AB - Model-based fault diagnosis narrows down fault candidates by checking the consistency between a mathematical model of the plant and the measurements. Depending on the sensor configuration and the system structure, however, different faults may share an identical residual signature. In such cases, the diagnosis keeps the true fault inside the candidate set but cannot single it out, and this structural indistinguishability is not resolved by tuning thresholds or post-processing the residuals. This paper proposes a method that reuses the diagnostic model on the candidates left by the existing diagnosis in order to rank them. Assuming each candidate to be the true fault and propagating the model forward yields predictions whose comparison with the actual measurements exposes temporal differences that the residual signature does not carry. A limited computational budget is distributed over several candidates so that the comparison is well defined, and the weight given to the two sources of information is adjusted according to how confident the existing diagnosis is. On a three-tank fault diagnosis benchmark, the probability assigned to the true fault at instants where the existing diagnosis selected a different candidate increased from 0.2547 to 0.6735; the isolation accuracy over the three faults sharing an identical residual signature improved from 31.5% to 52.7%; and the accuracy over all seven faults improved from 59.4% to 76.7%. On that benchmark, learning-based methods taking the same residuals as input did not exceed 0.30 on the indistinguishable set even with 512 samples per fault, whereas the proposed method uses no fault data at all. On a second benchmark, an electric motor, the same procedure raised that probability from 0.3523 to 0.7110. Across twelve combinations of fault magnitude and process noise, the method was never below the existing diagnosis, although the gain exceeded 0.34 only in the six where the fault magnitude was at least 12.5 times the process noise standard deviation.
SN - 2227-7390
ER -