# A Data-Driven Fault Tree for a Time Causality Analysis in an Aging System
## 2 Time Causality Analysis Methods
The main advantage of LSTM over an ANN is its ability to learn long-term dependencies between input features and over the equipment lifetime to give accurate RUL prediction. [PERSON], [PERSON] [21] developed an adaptive neuro-fuzzy inference system (ANFIS) algorithm that combines the ANN and a fuzzy rule-based model to predict the RUL of aircraft engines. The ANFIS algorithm has been applied to maintenance scheduling problems. Although the data-driven models offer an accurate prediction of the RUL, they suffer from a lack of interpretability [22]. This is because they are too shallow to understand the fault causality structure and its changes over time. Therefore, an expert may not be able to deeply understand the cause-effect relations within a complex system. With regard to this challenge, several methods have been proposed to simplify and unlock the model interpretability. [PERSON], [PERSON] [23] employed the Deep Belief Network (DBN) to model the geometric error structure of the backlash error. The DBN was built using restricted Boltzmann machines and energy-based models to predict the fault geometric. [PERSON], [PERSON] [24] have proposed a dynamic extraction knowledge method that illustrates the relationship between the environmental stresses and the system failure modes using a fuzzy causality diagram and a Bayesian rough set of multiple decision classes to weigh the extracted knowledge. [PERSON], [PERSON] [25] addressed the challenge of maintenance action recommendation for industrial systems based on remote monitoring and diagnosis. They proposed an interpretable event-based decision tree that graphically identifies some problems associated with particular events and conducts evidence-based decisions. [PERSON], [PERSON] [26] used Dynamic Bayesian Networks (DBNs) to quantify the failure prognostic in complex systems. The fault time series data are divided into several periods and a Bayesian network is constructed for each period. The obtained networks are connected through the chronology of periods to depict the changes in the fault causality structure over time and quantify the fault behaviour. On the other hand, the achieved data-driven methods attempt to unlock the time-dependent relations between the system variables in an interpretable manner in addition to capturing the change in the fault causality through the periods. However, building an interpretable data-driven model that can directly grasp the influence of the system aging on the fault causality structure and summarize the fault behaviour in one model, is a challenge that still needs to be overcome. The main motivation of this study is to build an interpretable time causality analysis model that characterizes, first, the hierarchical causality structure between the fault event, intermediate causes, and root-causes; and second, the influence of the system aging on that structure over time. Thus, the proposed ITCA methodology will achieve the fault prognosis task in an efficient way through anticipating the fault event based on the causal relations discovered over time. It will be developed in the following section.