## 1 Introduction
In addition, it should be applicable to any equipment that operates under stationary and non-stationary conditions; it should also be extendable for different components [3]. As a step toward the development of a single framework for system health management, this paper proposes a method to construct an \(HI\) from the vibrational signal, on the basis of unsupervised deep learning. This method establishes an online construction of \(HI\) in the sense that the input data can be acquisitioned while the equipment is being exploited. The proposed method mainly includes three steps: First, healthy raw vibrational signals of the equipment are processed with the continuous wavelet transform (CWT) technique. These 2D images are considered as input of the deep learning model. In the second step, a convolutional autoencoder (CAE) model is developed that is solely trained by the healthy data. Lastly, during online monitoring, in each assessment interval, throughout the entire lifetime of the equipment, the CWT image of the vibrational signal is fed to the trained CAE model. Similar to the training data, the trained autoencoder can reconstruct images with small reconstruction errors. The distance between the normal condition data and the failure stage is measured by the \(MD\) formula and, thus, the \(HI\) is created. In this study, to experimentally evaluate the effectiveness of the proposed methods, we chose the ball bearing. Ball bearings are known as the most widely used rotating machine components, playing an important role in successful and reliable operation of rotary machines. Health prognostic of the ball bearing has great practical significance in reducing the failures of rotating machinery and enhancing machine availability. Thus far, fault detection techniques exist for rolling bearing monitor vibration, acoustic emission, motor current consumption, temperature, and oil debris. Among these techniques, vibration monitoring has proved to be a reliable and effective technique for fault detection in bearings [28]. Therefore, the vibrational analysis technique is selected in this work, and the CAE model is used to extract features from the vibration data. Overall, this study proposes a method to construct a \(HI\) on the basis of an unsupervised deep learning method that describes every instant condition of the bearing and can be regarded as an indicator for a digital twin. In brief, the main contributions of the current work are  
1. The CAE model is only trained by using healthy operation data at the beginning of an asset's life cycle. Therefore, unlike most methods to construct a \(HI\), this model can be trained online without requiring historical failure data from similar assets or fleets. In addition, since the CAE model is trained by the CWT image, it is applicable for equipment that operates under stationary and non-stationary conditions. 2. The values of the bottleneck nodes of the CAE model are used as extracted features. Using these values reduces any dependencies on the prior knowledge, and thus the \(H\!I\) is constructed automatically. The further course of the paper is organized as follows: Section 2 briefly introduces the theoretical background of CWT and convolutional networks. Section 3 presents the proposed methodology to construct the \(H\!I\) in detail. In Section 4, the results of the experimental evaluation are presented and discussed. Section 5 provides the conclusions and future work guidelines.