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.

翻译：现有研究表明，复杂系统的退化表现为多个依赖参数的退化过程。捕捉这些依赖关系对于精确的退化建模和有效的退化控制至关重要。本研究旨在通过因果分析揭示这些依赖关系，重点关注两两因果发现。首先，考虑到参数间物理依赖的稳态特性，提出了一种结合非时序因果发现技术、利用退化增量的因果发现策略。随后，选取了五类非时序因果发现技术（包括基于约束、基于评分、基于函数因果模型、基于梯度以及新兴的基于排序的技术）作为基准方法，以识别最合适的方案。首先基于维纳过程开展数值研究，评估该方法在独立和因果依赖退化路径上的有效性。此外，进行了敏感性分析以评估退化过程特征对因果发现精度的影响。接着，通过两个工程应用（包括二阶多反馈带通滤波器和涡扇发动机）展示了该方法的实际适用性。研究结果表明，所提出的利用退化增量的策略优于依赖原始退化数据的方法。在所有评估技术中，稳定Peter-Clark算法和贪心等价搜索算法在数值案例和工程案例中均表现出稳健且准确的性能，被推荐用于退化路径间的因果发现。代码已在GitHub上开源：https://github.com/dirge1/causal_deg_data。