# Stacked Ensemble of Recurrent Neural Networks for Predicting Turbocharger Remaining Useful Life
## 1 Introduction  
Unplanned downtime, which means any period of time a machine is not available for use, has been shown to be one of the largest sources of cost and lost production time. Predictive Maintenance (PM), also known as conditioned-based maintenance, aims to mitigate these issues. As the name suggests, the promise of predictive maintenance is to predict upcoming failures, based on the actual condition (or state) of the system, in order to perform required maintenance at the best possible time. Doing so will increase system functionality and availability while reducing the collateral failure costs associated with corrective maintenance and redundant replacements caused by preventive maintenance. There is a rich history of research on vehicle predictive maintenance focusing on single vehicle readouts [1, 2]. However, relying on single readouts to predict possible future failures means conditioning the future on current observed state of the vehicle only. This corresponds to assuming that the future is independent of the past, given the current observable state, i.e., Markovian. In the context of automotive industry this assumption, however, is quite unrealistic due to limited number of sensors and high amount of noise in the data. More intuitively, the signs of future failures are not necessarily fully encoded in the current sensor readings. There have been several methods developed over the years for predictive maintenance based on data sequences. They generally represent three categories--Autoregressive Moving Average (ARMA)-based, Hidden Markov Model (HMM)-based, and Recurrent Neural Networks (RNN)-based approaches. The first category, ARMA-based, aims to predict the future values of a time series by regression over the past values of the dependent variable (Autoregressive Model), and also modeling the stochastic part of time series (Moving Average Model). As an example of the first category, [PERSON] et al. [3] adopted an 8 th-order ARMA model for forecasting failures of semiconductor Assembly and Test (ATM) factory. They transformed the raw data to a Machine Factor indicator which is defined as a function of downtime and productive time, then the ARMA model is used on this indicator to predict future failures. More recently, [PERSON] et al. [4] proposed a pipeline consisting of combination of data-driven techniques and ARMA model to predict failures of engine valves. Another alternative for sequence analysis is HMMs. They were considered suitable for predictive maintenance, since they can represent state of health of a component as hidden variables and the measurements as observed variables, while modeling the sequence through transition probabilities. [PERSON] et al. [5] proposed an integrated framework using HMM for Bearing Fault Diagnostics. First, they applied Principle Component Analysis (PCA) for feature extraction, then HMM is used to produce a health degradation signal which is fed as input to an adaptive prognostic method. [PERSON] and [PERSON] [6] used a combination of HMM and fuzzy model for maintenance of bus transportation systems. They generated several fuzzy rules that determine whether maintenance is required or not, where probabilities obtained from HMM are used as input to the fuzzy model. This paper focuses on the third group of models, namely Recurrent Neural Networks (RNN). RNNs, due to their ability to model long term non-linear dependencies over time, were shown to be a promising approach in many domains, including predictive maintenance. [PERSON] et al. [7] employed RNN for the case study of fault diagnosis of large-scale power plant. They proposed a meta-heuristic optimization algorithm for simultaneous structural design and parameter optimization of the RNN. [PERSON] et al. [8] used RNN for fault prediction of motor bearing data. To feed the RNN with stationary signal, they tackle the non-stationary nature of the data by decomposing it using empirical model decomposition. The change in trend is obtained through entropy calculation and used as an input by RNN. [PERSON] et al.