###### Abstract  
Rolling bearings are some of the most crucial components in rotating machinery systems. Rolling bearing failure may cause substantial economic losses and even endanger operator lives. Therefore, the accurate remaining useful life (RUL) prediction of rolling bearings is of tremendous research importance. Health indicator (HI) construction is the critical step in the data-driven RUL prediction approach. However, existing HI construction methods often require extraction of time-frequency domain features using prior knowledge while artificially determining the failure threshold and do not make full use of sensor information. To address the above issues, this paper proposes an end-to-end HI construction method called a multi-scale convolutional autoencoder (MSCAE) and uses LSTM neural networks for RUL prediction. MSCAE consists of three convolutional autoencoders with different convolutional kernel sizes in parallel, which can fully exploit the global and local information of the vibration signals. First, the raw vibration data and labels are input into MSCAE, and then, MSCAE is trained by minimizing the composite loss function. After that, the vibration data of the test bearings are fed into the trained MSCAE to extract HI. Finally, RUL prediction is performed using the LSTM neural network. The superiority of the HI extracted by MSCAE was verified using the PHM2012 challenge dataset. Compared to state-of-the-art HI construction methods, RUL prediction using MSCAE-extracted HI has the highest prediction accuracy. MSCAE; RUL; rolling bearing; health indicator +
Footnote †: journal: Applied  
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Rolling bearings are the joints of rotating machinery and play an essential role in industrial production, intelligent manufacturing, and transportation [1; 2]. Bearing mounting methods, lubricant quality, bearing operating environment, load and speed can all affect bearing vibration and life [3; 4; 5]. Once the rolling bearing fails, it will cause the machinery and equipment to stop working, causing substantial economic loss or even threatening the operator's life [6]. Therefore, timely analysis of their working conditions and prediction of their remaining useful life (RUL) is of great research importance [7]. The Prognostic and Health Management (PHM) refers to the use of sensor monitoring data to predict, monitor, and manage the health status of a system through models and algorithms [8; 9; 10; 11; 12]. RUL prediction is a crucial technique in PHM and is defined as the time interval between the current moment and when a system or internal component fails [10; 11]. Currently, RUL prediction methods are mainly divided into model-based and data-driven methods [13]. The model-based method uses a mathematical approach to construct a physical model of the degradation trend of mechanical components [14]. However, modern mechanical systems have dramatically increased in complexity, have highly coupled internal components, and often operate in severe environments with heavy loads, variable operating conditions, and multiple noise levels [15]. Therefore, building accurate degradation models is a challenging task, limiting the development of model-based methods. The data-driven method is based on machine learning algorithms to construct a mapping relationship between the monitoring data from the sensors and the RUL [16]. Deep learning is currently one of the up-to-date research directions in machine learning. With its powerful data processing and feature extraction capabilities, deep learning is widely used in computer vision, natural language processing, and fault diagnosis [17]. With the advantages of deep learning, more and more researchers are applying it in the RUL prediction model. [PERSON] et al. [18] proposed a multi-scale convolutional attention network. The multi-sensor data are first fused, and then, feature extraction is performed using a multi-scale convolution module with a self-attentive mechanism. Finally, regression analysis is performed on the high-level representation using a dynamic dense layer.