## 6 Prediction of Remaining Useful Life
### Damage Prognosis Methodologies  
The main goal of damage prognosis is to predict the remaining useful life (RUL) of the system or structure components before it requires for maintenance or the structure fails. Due to the uncertainty and nonlinearity of the predictive models when damage accumulates, an alternative goal is to estimate the RUL that the system can perform in a safe status under the future loading before one no longer has confidence in the prognosis model [196]. Damage prognosis is initiated and widely studied on the rotating machinery, as reviewed by [197; 198]. [PERSON] et al. [199] reviewed the recent modeling developments for estimating the RUL, which is centered on statistical data driven approaches. [PERSON] et al. [200] and [PERSON] and [PERSON] [201] reviewed the advances in RUL estimation from the industry point of view. [PERSON] et al. [202] provided a concise review of mainstream methods in major aspects of the prognostic and health management framework. The distinction between a damage detection model and a damage prognosis model is that the prognosis model needs to have the ability to estimate the damage evolution in the future, while the detection model only infers the current state of damage and do not necessarily have the ability to model progressive damage mechanisms such as crack growth [203]. In general, the two major categories are physics-based (i.e., model-based) and data-based prognosis methodologies, as detailed below [204].  
Data-based techniques are based on statistical and learning techniques typically from the theory of pattern recognition. Data-based approaches [204; 205] consist of multivariate statistical methods (e.g., static and dynamic principle component, linear and quadratic discriminant, partial least squares, and canonical variate analysis), machine learning methods (e.g., support vector machine, relevant vector machines, radial basis functions, and neural networks), and graphical models such as dynamic Bayesian networks and hidden Markov models. Although the data-based techniques can indicate a change in the presence of the new loading conditions or system configurations, they perform poorly in classifying the nature of the change.  
Physics-based (i.e., model-based) approaches make use of the system models to estimate the RUL or other relevant metrics, which rely on relatively accurate physics-based models for prediction, such as physical failure models [206], filtering models [207], and statistical models. The advantage of physics-based approaches is that the physical knowledge of the system is incorporated into the monitoring process, which is especially useful for predicting system responses to new loading conditions and system configurations such as the damage status. Nevertheless, physics-based approaches are typically more computationally intensive than data-based techniques.  
There are also some hybrid methodologies combining multiple approaches as reviewed by [208]. The selection of damage prognosis model depends on the required accuracy and data availability. The data-driven method is preferred for quick estimations that are less accurate, while the physics-based approach is applied when the accuracy of estimation is important. Typically, the balance between these two approaches depends on the amount of available data and the confidence level of the physics-based model in the predictive accuracy.