# A New Life Prediction Scheme for Mechanical System with Considering the Mission Profile Switching
## 1 Introduction  
Prognostics and health management (PHM) is very crucial in modern industries, as the mechanical system is becoming larger, more complicated, and more automated. Traditional maintenance strategies such as breakdown corrective maintenance and scheduled preventive maintenance find it hard to deal with the increasing demand of reliability and efficiency. Prognostic, which is one part of the PHM system, has been widely researched in recent years [1; 2]. It is a key technique to predict the remaining useful life (RUL) of the machine and further to establish reasonable maintenance plans. Therefore, the unplanned downtime, the maintenance cost, and the safety risk can be reduced. The life prediction methods can be roughly divided into two categories: Model-based methods and data-driven methods. Although the model-based methods [3; 4; 5] have clear theoretical basis and high prediction accuracy, it is still very difficult to establish and solve the physical model of complicated equipment. With the advantage that need not construct a complicated physical model, data-driven methods have been extensively studied in the past decades. For example, a recurrent neural network based the health indicator of bearing was proposed by [PERSON] et al. [6]. [PERSON] et al. [7] estimated the RUL of bearing by using the time-frequency features and multi-scale convolutional neural network. [PERSON] et al. [8] proposed a new deep learning method-based prediction framework for bearing RUL prediction by using an auto-encoder and deep neural networks (DNNs). As the long short-term memory (LSTM) neural network can be used as a complex non-linear element to construct a larger depth neural network, the LSTM neural network [9; 10] is also used to predict the RUL. The abovementioned methods can all achieve superior prediction results under a single operating condition. However, the change ofdifferent operating condition is the more general scenario in actual applications. For the situation of variable operation conditions, [PERSON] et al. [11], [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14] only predicted the RUL under variable operating conditions by putting forward innovative characteristic parameters or health indicators, but did not propose the prediction method suitable for variable operating conditions. Although [PERSON] et al. [15] and [PERSON] et al. [16] proposed the prediction methods suitable for the variable operating condition by using the historical data and Monte Carlo simulation, the complexity of the calculation process limited the wide use of the methods. Furthermore, the similarity trajectory method (STM) [17; 18; 19; 20; 21], which is simpler to calculate, was widely used to predict the RUL of the mechanical system under variable operating conditions [22; 23; 24; 25; 26]. The STM is an effective method to deal with the life prediction under variable operating conditions. However, the precondition of all the methods mentioned above is that the operating condition in the prediction process should be consistent with that of the training samples. This means that the life of mechanical systems is an extrapolation of the current state. Nevertheless, in order to accomplish different tasks, the mechanical systems often need to constantly switch mission profile (detailed definition and description is give in Section 2) in practice. For the mission profile switching in the prediction, the Bayesian technique [27], Markov process [28], and Wiener process [29] are widely used to deal with the problem. Besides, [PERSON] et al. [30] proposed a stochastic mathematical model to calculate the residual life distributions of partially degraded systems. [PERSON] et al. [31] proposed an integrated prognostics method for gear under time-varying operating conditions with considering the influence of uncertainty. [PERSON] et al. [32] proposed a prognostic model for the system with considering the performance degrades with usage and recovers in storage.