###### Abstract
In other words, data-driven methods do not require knowledge of the underlying degradation mechanisms. They identify features and characteristics that define the damage initiation and degradation process and use that information to predict the future state of the system. In short, data-driven methods aim to model the non-linear relationship between the system behavior, the aging process, condition monitoring data, and RUL. To mention a few, [PERSON] et al. [10] proposed a data-driven probabilistic framework for RUL prediction of composite materials. The real-time degradation data of composite materials under different loading conditions was obtained based on acoustic emission data. A Non-Homogeneous Hidden Semi Markov Model (NHHSMM) and a Bayesian version of Feedforward Neural Networks (BFFNN) were used for the purpose of RUL prediction. In both the methods, sufficient amount of historical training data was required to train the model. The authors concluded that the NHHSMM method performed better in terms of accuracy. They also suggested that the accuracy of BFFNN can be further improved with a larger amount of training data used for training the neural network model with all possible failure mechanisms incorporated into it. However, obtaining such an extensive dataset would be challenging, especially for mechanical failure modes that involve crack nucleation and growth. Another study by [PERSON] et al. [11] addressed the issue of correlating the extracted features from the degradation data to that of the crack size, inclusive of the uncertainties due to damage geometries, sensor placement, and boundary conditions. In order to achieve this, the authors used a Gaussian process measurement model within a particle filter-based framework. When a new sensor signal is available from the target structure, the measurement model is updated online, and the updated model parameters are used to predict the next state. The proposed methodology was tested on fatigue data from an attachment lug made of LY12 aluminum. Even though the proposedmethod proves to be effective for online prognostic applications, the results indicate a large prediction error in the early cycles. The prediction error decreases to 3% after more than 20,000 cycles, and hence adequate modifications are required to reduce the prediction error in the initial stages of degradation. Based on most of the studies in literature in the field of Structural Health Management (SHM), the Paris-Erdogan model is the most popular damage evolution model used to quantify the evolution of crack growth. The Paris model is extensively used for prognosis of crack growth in other systems as well such as defect propagation in rolling element bearings [12; 13; 14], wind turbine blades [15; 16; 17], and flight control actuators [18; 19]. However, the crack growth behavior in all the aforementioned works has been approximated ignoring the uncertainties due to material properties, environmental conditions, and cyclic mechanical loads. [PERSON] et al. [20; 21] considered the above-mentioned uncertainties and categorized the fatigue crack growth trend into two regimes, namely, crack initiation and crack growth. In the first regime, a micro-crack is triggered due to material surface qualities such as surface irregularities, surface damage, and inhomogeneities. Subsequently in the second regime, the crack grows depending on the applied load and mechanical properties etc. Thus, it is important to model both the regimes and determine the regime-switching transition zone or period to be able to deduce the remaining fatigue life more accurately. The authors in Refs. [20; 21] used a piecewise-deterministic Markov process to combine the Paris model describing the initial stable region of crack propagation and the Forman law model describing the subsequent rapid crack propagation regime. Taking the work of [PERSON] et al. [21] as a motivation, [PERSON] et al.