## 1 Introduction
[6] combined both coefficient-based and residual-based approaches with the ARMAX model and used the normalized Kolmogorov-Smirnov statistical distance between two sets of ARMAX model residuals obtained from the input-output process for the undamaged and damaged states. They validated their approach on a small-scale five-story frame using aluminum floor slabs and bronze columns. _In addition to_ pure TS methods, [PERSON] et al. [15] combined singular spectrum analysis (SSA) with the ARMAX model to detect minor damage, e.g., small cracks in concrete structures. There are some drawbacks limiting the use of AR series modeling in practice. The most notable is the requirement of stationary input, which is difficult to achieve in real SHM applications, where TS data (i.e., vibration signals) collected from sensors after earthquakes are usually non-stationary. Thus, elaborate data pre-processing (e.g., segmenting, detrending, and de-nosing) and stationarity checks are inevitable before modeling; however, these methods lack a systematic pipeline and may not guarantee stationarity. In this paper, we proposed a systematic two-stage pipeline to adopt differencing as a pre-processing approach before TS fitting to satisfy the stationarity condition. This approach is known as auto-regressive integrated moving-average (ARIMA) modeling [16]. There are very few cases in the literature that used ARIMA in SHM. [PERSON] & [PERSON] [17] formulated a vector seasonal ARIMA model whose coefficients varied with time and were identified using an adaptive Kalman filter. Through the analysis of signals recorded during and after the construction of an instrumented bridge, they observed changes in the model coefficients related to damage under normal operational and environmental conditions. Recently, [PERSON] & [PERSON] [18] compared the resultsbetween SSA and ARIMA in the problem of forecasting short-term and long-term structural strain variations. The implementation of machine learning (ML) in SHM pattern recognition is a mature subject with well-developed and efficient algorithms [19]. ML has three major categories: unsupervised learning, supervised learning, and reinforcement learning based on data characteristics. In this paper, we only consider supervised learning, which uses well-labeled data based on domain knowledge to analyze the input data and produce an inferred mapping function [20]. The new unseen data sample can be assigned labels according to this mapping relationship. In SHM, a supervised learning algorithm learns hidden relationships between some features extracted from the data and the corresponding damaged state of the structure. Thus, the feature extraction is an important part in applying ML in SHM where previous studies [2; 3; 9] designed functions for efficient damage features, e.g., combinations of coefficients of the AR models. However, the definition of such functions is based on intuitive feature engineering and is data-dependent. For more general scenarios, these functions may not be effective and the extracted features in this way may not be sufficient for the ML classification. Thus, this inspired us to consider engaging all coefficients of the AR series model as the damage features in the ML classification, which is thought to automatically maintain the information. Most past validation experiments were based on computer simulation data, e.g., generated by the finite element method (FEM) or on reduced-scale experimental data but with pre-assigned damage patterns and locations, e.g., with component replacement or section reduction. However, during natural hazards, e.g., earthquakes, structural damage may differ from the idealization in these artificial cases. For example, refs. [3; 9] used the ASCE benchmark steel frame tests where the damage patterns were artificially designed by decreasing the cross-sectional areas to simulate stiffness degradation after damage. [PERSON] & [PERSON] [21] used numerically simulated three-story shear building using FEM. [PERSON] et al.