Nonlinear uncertainty quantification, sensitivity analysis, and uncertainty propagation of a dynamic electrical circuit

The development of a statistically-based process for verification and validation of computational experiments is presented in this study. The process can be used to identify sources of uncertainty, quantify magnitudes of uncertainty, and propagate uncertainty through a model. Model form error was identified through prototype experiments with the system and subsystem, and methods for reducing model form error are presented. Existing validation metrics are applied to the system in this analysis, and a new statistical validation metric is introduced. The methodology for performing Uncertainty Analysis (UA), nonlinear Sensitivity Analysis (SA), and nonlinear Uncertainty Propagation (UP) is presented in this investigation as part of the validation process. The results of this portion of the methodology guided the development of the experimental design and evaluation. Experimental validation experiments were developed for a simple electrical system in order to demonstrate the computational-to-experimental validation process. The process is applicable to any system, but a simple example was chosen so that any interested person can follow the implementation. Despite the simplicity of the system selected, the analysis proved to be complicated and tedious, while also identifying many avenues for future work. A numerical example is presented along with the relevant data in sufficient detail to demonstrate how the analysis was performed. By applying this new process, the electrical system is studied from a statistical perspective, with an emphasis on uncertainty quantification and propagation. The sensitivity analysis discovered that the behavior of each component varied significantly, and several critical parameters were identified. By identifying and quantifying the uncertainty in each parameter, the quality of the computational model can be improved, and decisions can be made with quantifiable confidence