## 1 Introduction  
Performance degradation, which is almost inevitable for mechanical equipment, results in machinery damage, severe financial losses due to replacement or repair work and machine downtimes, or even personnel injury. Thus, prognostics and health management (PHM) has emerged as an engineering discipline to improve availability, reliability, and safety of equipment. As a crucial task in the lifecycle monitoring of complex equipment, PHM is used to monitor the equipment condition and to design robust and accurate models in order to assess the health state of equipment, as well as to define appropriate maintenance strategies [1]. In recent years, improving PHM methods by the Industry 4.0 paradigm, such as digital twin and predictive maintenance, attracts the attention of researchers [2; 3; 4; 5]. In a digital twin, a virtual counterpart of the physical system during its whole life is created, with abilities such as analyzing, evaluating, optimizing, and predicting [6]. [PERSON] et al. [5] presented a digital twin model for rotating machinery to diagnose the unbalance faults, on the basis of the dynamic behavior of the rotor system and vibrational status monitoring. [PERSON] et al. [4] proposed a new approach for PHM, driven by digital twin for complex equipment. In this approach, a five-dimensional digital twin model is constructed to identify the health conditions of wind turbine gearboxes. [PERSON] et al. [7] proposed a prognostic approach to detect the incipient faults of rotating machines by means of their vibrational status monitoring. [PERSON] et al. [8] presented a two-phase digital twin to diagnose the fault using a deep transfer learning method. In this approach, the trained knowledge of the deep neural network is transferred from the virtual space to the physical space for real-time monitoring and predictive maintenance. Traditionally, a digital twin uses physical-based simulation tools to describe the current behavior of a system [3]. However, due to manufacturing tolerances and material variances, describing a complex system in a simulation environment usually contains a strong deviation from reality [9]. One solution is to obtain a digital representation of the expected behavior of the physical system directly from measured data [3]. For this purpose, the first step is to construct a (multi) digital health indicator (_HI_) that describes different aspects of the physical component state during the whole life of the component. This _HI_ should represent the deviation between the initial conditions of the component and its actual conditions during lifetime [1]. This _HI_ can be further used for remaining useful life (RUL) estimation by implementing statistical estimation techniques, such as exponential degradation model [10], particle filter [11], or Kalman filter [12]. Therefore, defining an appropriate and sensitive _HI_ that reflects the deviation degree from normal health conditions is now a hot research topic in the RUL estimation field. In general, constructing a _HI_ can be performed in three steps: (1) signal acquisition, (2) signal processing, and (3) feature extraction [13]. Vibration measurement provides a very efficient way of monitoring the dynamic conditions of a machine, such as unbalancedness, misalignment, mechanical looseness, structural resonance, wear, and shaft bow. [14]. Developing each failure mode leads to varying system dynamic behavior, resulting in significant deviation in vibration patterns [15]. Vibration signals generated by the faulty component can be analyzed in the time domain [16], frequency domain [17], or time-frequency domain [18]. Using the time-domain techniques for feature extraction requires the recording of the time-series vibrations over a long period of time to obtain suitable parameters to reveal fault evolution. However, obtaining the necessary data for a complex equipment may be expensive or even impossible. Using frequency-domain techniques such as fast Fourier transform (FFT) are powerful diagnostic tools in stationary conditions [18].