# Prognostics of Electromechanical Actuator with Partial Time Scaling Invariant Temporal Alignment
## 2 State-Of-The-Art of the Prognostic Methods with Time Series Alignment  
Aligning time series data involves putting in relation each component of the pattern vector, i.e., each relevant sensitive parameter, between source data (unknown ones) and those recorded in a learning database (structured set of available data). This alignment is based on minimizing a criterion measuring the distance between these series. Extrapolating data based on time series alignment requires the alignment of source data and a database of past recorded behaviors. This type of method is known as TBSP in the literature. Considering a database with the expected behaviors of the data that we wish to extrapolate, such as run-to-failure time series, this procedure needs less information than the deep neural network counterparts to obtain a relevant result. The idea is to compare test time series with the data in the learning database with a similarity measure. The most used similarity criterion in the state-of-the-art is the Euclidean distance and its variants. Then, the most similar candidates to the test data are fused. The latter model is chosen depending on the nature of the wanted output, an actual time instant, or the extrapolation of test data.  
Dynamic Time Warping (DTW) was introduced by [3] as an algorithm to realize time series alignment, with many variants being realized afterwards. Other methods are also used for curve registration, such as the warplet approach of [4]. The first mention of a similarity-based method for RUL prediction was made by [5] to adapt it to the Commercial Modular Aero-Propulsion System Simulation (CMAPSS) [6] data set.  
Later, [7] described a detailed framework applied to weld joint monitoring, namely the Ball Grid Array (BGA), in vibrating environments, or on a stochastic model of simulated data [8] as Similarity-Based Residual Life Prediction (SBRLP). The advantages of such an approach are numerous. It allows the realization of a prognosis with little available data, which is often the case in an industrial environment. Moreover, we can enrich the comparison database as the product's life cycle progresses. Thus, without changing the method, the determination of the RUL will be all the more precise. However, if the database is not rich enough, the predictions will be subject to high uncertainty; this is the major drawback of the method.  
The literature on predicting RUL from similarity measures or time series alignment uses data processing only or hybrid methods. The most widely used data set in the literature is the data set CMAPSS created by [6], composed of multivariate signals representing the degradation of a simulated jet engine.  
Figure 3: Ball screw actuator instrumented on test bench, from [2]. Reprinted/adapted with permission from [2]. 2021, EidFor our part, we have chosen to validate our approach on data closer to an industrial application, from an aging bench of roller screw actuators, in the context of an aeronautical application.  
The advantage of a standard data set is that it can provide comparable results between the work of different research teams. However, the massive use of CMAPSS [6] testifies to the recurrent problem of the lack of usable industrial data in PHM. Indeed, the few industrial data sets used are confidential, so the reproducibility of results between studies is not guaranteed. However, despite its demonstrated quality, the CMAPSS [6] academic data set only covers the analysis of several realizations of a single system in aeronautics. To overcome this, Refs. [8; 9; 10] use simulated stochastic models representing the degradation trend--anonymized vibration signals from an industrial data set.