A comprehensive study on causal discovery between degradation paths
Pith reviewed 2026-05-10 15:52 UTC · model grok-4.3
The pith
Causal links between degradation paths are best uncovered by analyzing increments rather than raw measurements.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Considering the steady-state characteristic of physical dependencies between parameters, a causal discovery strategy using degradation increments is proposed combined with non-temporal causal discovery techniques. Numerical studies based on Wiener process show effectiveness on independent and dependent paths, with sensitivity analysis on process characteristics. In engineering applications including a second-order multiple-feedback band pass filter and a turbofan engine, the increment-based approach outperforms raw data methods, with stable Peter-Clark and greedy equivalence search exhibiting robust performance.
What carries the argument
Degradation increments, which are the differences in degradation measurements over time, used as input to non-temporal causal discovery algorithms to recover pairwise causal relations.
If this is right
- Accurate causal graphs from increments can improve multivariate degradation models for reliability prediction.
- Recommended methods like stable Peter-Clark allow consistent identification of causal directions across different degradation scenarios.
- Sensitivity to degradation characteristics such as drift and variance helps tune the approach for specific systems.
- Practical use in engineering systems like engines enables targeted maintenance on causal root degradations.
Where Pith is reading between the lines
- If the steady-state assumption holds more broadly, this could extend causal analysis to other time-series degradation without needing specialized temporal methods.
- Combining these causal structures with physics-based models might yield hybrid predictive tools for system health.
- Future work could test the methods on larger numbers of parameters or with missing data common in real monitoring.
- Applying the recommended algorithms in real-time monitoring systems would allow dynamic updating of degradation causal networks.
Load-bearing premise
Physical dependencies between degradation parameters are steady-state, so that increments capture the causal structure without needing to model time explicitly.
What would settle it
Observing that raw degradation data yields more accurate causal graphs than increments when the true causal structure is known from a Wiener process simulation with injected dependencies.
read the original abstract
Existing studies indicate that complex system degradation is characterized by degradation of multiple dependent parameters. Capturing the dependencies is crucial for accurate degradation modeling and effective degradation control. This work aims to uncover these dependencies through causal analysis, focusing on pairwise causal discovery. Firstly, considering the steady-state characteristic of physical dependencies between parameters, a causal discovery strategy using degradation increments is proposed combined with non-temporal causal discovery techniques. Then, five types of non-temporal causal discovery techniques, including constraint-based, score-based, functional causal model-based, gradient-based and the emerging ordering-based technique, are selected as benchmark methods to identify the most suitable approach. Numerical studies based on Wiener process are first conducted to investigate the method effectiveness on both independent and causally dependent degradation paths. Additionally, sensitivity analysis is performed to evaluate how degradation process characteristics affect the accuracy of causal discovery. Then, two engineering applications are given to show the practical applicability of the approach, including a second-order multiple-feedback band pass filter and a turbofan engine. Our findings indicate that the proposed strategy, which uses degradation increments, outperforms methods that rely on raw degradation data. Among all evaluated techniques, stable Peter-Clark and greedy equivalence search exhibit robust and accurate performance across both numerical and engineering cases, which are recommended for causal discovery between degradation paths. The code is available on GitHub: https://github.com/dirge1/causal_deg_data.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes using degradation increments (rather than raw paths) together with standard non-temporal causal discovery algorithms to recover pairwise causal dependencies among parameters in complex-system degradation. It benchmarks five families of methods (constraint-based, score-based, FCM-based, gradient-based, ordering-based) first on controlled Wiener-process simulations with known ground truth, then on two real engineering datasets (second-order band-pass filter and turbofan engine). The central empirical claim is that the increment-based strategy outperforms raw-data approaches and that stable PC and GES are the most robust and accurate across both regimes; the authors therefore recommend these two algorithms for practical use. Reproducible code is provided.
Significance. If the numerical findings generalize and the engineering-case evaluation can be placed on firmer ground, the work supplies immediately usable guidance for identifying causal structure in multivariate degradation data, which is relevant to reliability engineering, prognostics, and control. The controlled Wiener-process experiments, sensitivity analysis, and public code are clear strengths that raise the paper’s value even if the real-data claims require qualification.
major comments (2)
- [§4] §4 (Engineering Applications, band-pass filter and turbofan cases): the claim that stable PC and GES exhibit “robust and accurate performance” on these datasets cannot be quantitatively verified because no independent ground-truth causal graph is available from physics or prior literature. Unlike the Wiener-process experiments, where SHD/precision metrics can be computed against injected edges, accuracy here appears to rest on qualitative inspection or an unstated assumed structure. This directly weakens the cross-regime recommendation that forms the paper’s main practical takeaway.
- [§2 and §3] §2 (Proposed strategy) and §3 (Numerical studies): the justification for switching to increments rests on the “steady-state characteristic of physical dependencies.” No formal derivation or diagnostic test is supplied to delineate when this assumption holds versus when transient or non-stationary effects dominate; the sensitivity analysis varies drift/diffusion parameters but does not explicitly probe violations of the steady-state premise. Because the increment-based advantage is load-bearing for the outperformance claim, this gap needs explicit discussion or additional experiments.
minor comments (2)
- [Abstract] Abstract and §1: the term “non-temporal causal discovery techniques” is used without a one-sentence gloss or key reference; adding a brief parenthetical (e.g., “constraint- and score-based methods that ignore temporal ordering”) would improve accessibility.
- [§3] Figure captions and tables in §3: several panels compare raw versus increment data but do not report the exact number of Monte-Carlo replications or the precise SHD/precision values used to declare “outperformance”; adding these numbers would make the numerical claims easier to reproduce from the text alone.
Simulated Author's Rebuttal
We thank the referee for the constructive and detailed report. The comments correctly identify areas where our claims require qualification and where additional justification would strengthen the paper. We respond point-by-point below and will make targeted revisions.
read point-by-point responses
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Referee: [§4] §4 (Engineering Applications, band-pass filter and turbofan cases): the claim that stable PC and GES exhibit “robust and accurate performance” on these datasets cannot be quantitatively verified because no independent ground-truth causal graph is available from physics or prior literature. Unlike the Wiener-process experiments, where SHD/precision metrics can be computed against injected edges, accuracy here appears to rest on qualitative inspection or an unstated assumed structure. This directly weakens the cross-regime recommendation that forms the paper’s main practical takeaway.
Authors: We agree that quantitative verification is impossible without an independent ground-truth graph for the real datasets. Our §4 evaluation is qualitative: recovered edges for the band-pass filter are checked against the known circuit diagram and component physics, while turbofan results are interpreted against established degradation propagation patterns in engine literature. We will revise §4 and the conclusions to explicitly state that quantitative support (SHD, precision, etc.) is limited to the Wiener-process simulations with known ground truth, and that the engineering cases provide only consistency checks and practical applicability demonstrations. The recommendation for stable PC and GES will be rephrased to emphasize the simulation benchmarks as the primary evidence, with real-data results serving as illustrative rather than confirmatory. revision: partial
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Referee: [§2 and §3] §2 (Proposed strategy) and §3 (Numerical studies): the justification for switching to increments rests on the “steady-state characteristic of physical dependencies.” No formal derivation or diagnostic test is supplied to delineate when this assumption holds versus when transient or non-stationary effects dominate; the sensitivity analysis varies drift/diffusion parameters but does not explicitly probe violations of the steady-state premise. Because the increment-based advantage is load-bearing for the outperformance claim, this gap needs explicit discussion or additional experiments.
Authors: The increment approach is motivated by the standard modeling of degradation as processes with stationary increments once initial transients have decayed, as in Wiener-process formulations common in reliability engineering. We acknowledge that the manuscript provides only a brief physical intuition rather than a formal derivation or explicit diagnostic. In revision we will add a dedicated paragraph in §2 deriving the rationale from the properties of stochastic degradation models (with supporting references) and discussing the conditions under which the steady-state assumption may fail. We will also extend the sensitivity analysis in §3 with a new experiment that injects controlled initial transients and compares increment-based versus raw-data performance, thereby directly probing the assumption. revision: yes
Circularity Check
No circularity: empirical benchmarking on controlled simulations
full rationale
The paper proposes a strategy of using degradation increments (instead of raw paths) for pairwise causal discovery and then empirically benchmarks five families of non-temporal algorithms (PC, GES, etc.) first on Wiener-process simulations whose ground-truth edges are injected by construction, then on two engineering datasets. No derivation, equation, or performance metric is obtained by fitting a parameter to the target quantity and renaming the fit as a prediction. No self-citation is invoked as a uniqueness theorem or load-bearing premise. The central recommendation rests on external, falsifiable accuracy measures (SHD, precision, etc.) computed against known structures in the numerical cases; the engineering cases are presented only as applicability demonstrations, not as quantitative accuracy claims. This is a standard non-circular empirical study.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Physical dependencies between degradation parameters are steady-state
Reference graph
Works this paper leans on
-
[1]
[1]W. Lin, Y . Chai, L. Fan, et al. Remaining useful life prediction using nonlinear multi -phase Wiener process and variational Bayesian approach. Reliability Engineering & System Safety. 2024, 242: 109800. [2]S.-S. Chen, X. -Y . Li, W. -R. Xie. Reliability modeling and statistical analysis of accelerated degradation process with memory effects and unit-...
work page 2024
-
[2]
Mathematical Problems in Engineering
Markov Chain‐Based Aeroengine Performance Degradation Forecast Approach Using Exhaust Gas Temperature. Mathematical Problems in Engineering. 2014, 2014(1): 832851. [21]B. Kurt. Prediction of performance degradation in turbofan engines with fuel flow parameter. Neural Computing and Applications. 2024, 36(6): 2973-2982. [22]S. Zheng, J. Liu, Y . Chen. BiGra...
work page 2014
-
[3]
[23]S. Zheng, C. Wang, E. Zio, et al. Fault detection in complex mechatronic systems by a hierarchical graph convolution attention network based on causal paths. Reliability Engineering & System Safety. 2024, 243: 109872. [24]J. Liu, S. Zheng, C. Wang. Causal graph attention network with disentangled representations for complex systems fault detection. Re...
work page 2024
-
[4]
[29]Y . Liu, B. Jafarpour. Graph attention network with Granger causality map for fault detection and root cause diagnosis. Computers & Chemical Engineering. 2024, 180: 108453. [30]Y . Yang, W. Kang, X. Liu. Fault diagnosis based on online dynamic integration model and transfer entropy. Measurement. 2022, 193: 110946. [31]S. Duan, K. Zhu, P. Song, et al. ...
work page 2024
-
[5]
[35]R. Guo, L. Cheng, J. Li, et al. A survey of learning causality with data: Problems and methods. ACM Computing Surveys. 2020, 53(4): 1-37. [36]D. Colombo, M.H. Maathuis. Order-independent constraint-based causal structure learning. Journal of Machine Learning Research. 2014, 15(1): 3741-3782. [37]D.M. Chickering. Optimal structure identification with g...
work page 2020
-
[6]
[41]X. Zheng, C. Dan, B. Aragam, et al. Learning sparse nonparametric dags. International Conference on Artificial Intelligence and Statistics, 2020:3414-3425. [42]Z. Xu, Y . Li, C. Liu, et al. Ordering -Based Causal Discovery for Linear and Nonlinear Relations. The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024: [43]Y . Uc...
work page 2020
-
[7]
[44]W. Liu, F. Liu, W. Fang, et al. Causal discovery and reasoning for geotechnical risk analysis. Reliability Engineering & System Safety. 2024, 241: 109659. [45]N. Clavijo, A. Melo, R.M. Soares, et al. Variable selection f or fault detection based on causal discovery methods: Analysis of an actual industrial case. Processes. 2021, 9(3):
work page 2024
-
[8]
[47]L. Shen, Y . Wang, Q. Zhai, et al. Degradation modeling using stochastic processes with random initial degradation. IEEE Transactions on Reliability. 2018, 68(4): 1320-1329. [48]J. Li, Z. Wang, Y . Zhang, et al. Degradation data analysis based on a generalized Wiener process subject to measurement error. Mechanical Systems and Signal Processing. 2017,...
work page 2018
-
[9]
424-438. [54]T. Schreiber. Measuring information transfer. Physical review letters. 2000, 85(2):
work page 2000
-
[10]
[55]G. Sugihara, R. May, H. Ye, et al. Detecting causality in complex ecosystems. Science. 2012, 338(6106): 496-500. [56]Z. Zhang, L. Zeng, T. Xu, et al. A Single-Channel Multifrequency Simultaneous Excitation System Using Bandpass Filter Circuit Modules for Lamb Wave -Based Damage Imaging. IEEE Transactions on Instrumentation and Measurement. 2025, 74: 1-11
work page 2012
discussion (0)
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