This thesis presents a novel methodology for fatigue life prognosis of vertical oil well drill strings through the development of a digital twin frame work. A technique is proposed to classify vibration types with their severities and estimate the remaining useful life time of the drill string based on various indirect measurements made at the surface level. The classification was done using a machine learning algorithm developed based on a Hidden Markov Model HMM). Training data for the algorithm were generated using a bond graph simulation of a vertical drill string. A three-dimensional lumped segment bond graph element and an interface element available in the literature were used to develop the simulation. The bond graph elements are developed based on a Newton-Eular formulation and body-fixed coordinates. The simulation was upgraded by introducing a fluid drag model and refining it with accurate element compliance values. Non linear fluid drag force statistical models were developed through the design of experiments(DoE) approach considering the non-linear geometry of the drill pipes,the drilling fluid rheology, and fluid velocity. A series of fluid-structure interaction(FSI) simulations were employed to develop the statistical models for the lateral vibration damping and the axial drag force dueto the drilling fluid flow through the pipe and the annular space. An apparatus was designed and fabricated to verify the FSI simulation. Further, a method was introduced to accurately determine the axial, shear, bending, and torsional compliances of geometrically-complex drill string segments represented by the bond graph elements. The trained HMM-based classifier using bond graph-generated training data selects the appropriate parameter set for the same bond graph to generate stress history for fatigue life prognosis. A generalized fatigue life estimation method was developed using SalomeMeca™, an open-source finite element analysis code. A detailed workflow for multi-axial, non-proportional, and variable amplitude (MNV) fatigue analysisis also provided. Three case studies are presented to demonstrate the significance of the nonlinear fluid drag models, the fatigue prognosis framework, and the digital twin development framework. In the first case study, the bond graph with the developed drag models showed higher stress fluctuations at the drill pipe threaded connection than the one with a static model. The second case study demonstrated the function of the proposed fatigue life prognosis framework as an optimization tool. In the case study, the optimum placement of the stabilizers reduced the drill collar damage by 66% compared to the worst-case scenario. The third case study used a laboratory-scale vertical drill string vibration simulator apparatus designed and fabricated to implement the framework as a proof of concept. It demonstrated the potential to use surface measurements to classify the vibration type and its severity for fatigue life prognosis.