This dissertation presents a stochastic framework for modeling the degradation processes of components in complex engineering systems using sensor based signals. Chapters 1 and 2 discuses the challenges and the existing literature in monitoring and predicting the performance of complex engineering systems. Chapter 3 presents the degradation model with the absorbing failure threshold for a single unit and the RLD estimation using the first-passage-time approach. Subsequently, we develop the estimate of the RLD using the first-passage-time approach for two cases: information prior distributions and non-informative prior distributions. A case study is presented using real-world data from rolling elements bearing applications. Chapter 4 presents a stochastic methodology for modeling degradation signals from components functioning under dynamically evolving environmental conditions. We utilize in-situ sensor signals related to the degradation process, as well as the environmental conditions, to predict and continuously update, in real-time, the distribution of a component’s residual lifetime. Two distinct models are presented. The first considers future environmental profiles that evolve in a deterministic manner while the second assumes the environment evolves as a continuous-time Markov chain. Chapters 5 and 6 generalize the failure-dependent models and develop a general model that examines the interactions among the degradation processes of interconnected components/subsystems. In particular, we model how the degradation level of one component affects the degradation rates of other components in the system. Hereafter, we refer to this type of component-to-component interaction caused by their stochastic dependence as degradation-rate-interaction (DRI). Chapter 5 focuses on the scenario in which these changes occur in a discrete manner, whereas, Chapter 6 focuses on the scenario, in which DRIs occur in a continuous manner. We demonstrate that incorporating the effects of component interactions significantly improves the prediction accuracy of RLDs. Finally, we outline the conclusion remarks and a future work plan in Chapter 7.

Lathes are frequently used in industrial production. It is an important parameter to calculate the force exerted by the cutter head on the raw material. Knowing the force acting on the cutting tool will aid in predicting the displacement of the cutting edge as well as predict displacement of the workpiece. The main purpose of this paper is to find a way to calculate the force exerted on the cutting tool tip. The magnitude of the tooltip force is estimated without the use of a force sensor. Instead, strain sensors are used to collect strain signals, and acceleration sensors are used to collect acceleration signals. Combine these two signals to calculate the magnitude of force. The force-strain frequency response function is calculated. The force-strain FRF acts as a bridge connecting force and strain signals. Calculate the input force signal on the cutting tool tip using the strain signal. In this way, is available to obtain the force time-image. Changes in force can be predicted by looking for force-time laws. In this thesis using MATLAB software for simulation and actual experimental measurements. Verify the reliability of the calculation method. The method and MATLAB code for calculating force-strain FRF are researched and written. Simulate the cutting tool input-output model in MATLAB. Combined with the actual experimental measurement results, the accuracy and limitations of this calculation method are analyzed. Discuss directions for future work.