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Many industrial and environmental processes are characterized as complex spatio-temporal systems. Such systems known as distributed parameter systems (DPSs), which are often modeled with nonlinear coupled partial differential equations, are usually highly complex and it is difficult to establish the relation between model inputs, model output and parameters. Most importantly, the solutions of physics-based models commonly differ from the real measurements. Hence, the aim of the thesis is to elucidate a systematic framework that allows to gain an understanding of the behavior of nonlinear distributed parameter system. Ultimately, the framework reduces the disagreement between the computational model predictions and the measurements of the real processes. For most of real world applications, the model users have some background knowledge about the considered system. This available background knowledge is exploited in this thesis, by formulating the state of knowledge in form of uncertainties in Bayesian sense. The uncertainties are described by random variables or random field and are quantified by Uncertainty Quantification (UQ) approaches to gain the knowledge about the system. The appropriate UQ approaches are selected and combined systematically in order to analyze and identify systems. The framework proposed in this thesis includes the uncertainty propagation, the sensitivity analysis and the Bayesian parameter calibration. The main challenge of applying the UQ to the nonlinear distributed parameter systems is the computational efforts. By the conventional method such as sampling-based method, it requires numerous simulation evaluations. This computational effort is diminished

Framework for Analysis and Identification of Nonlinear Distributed Parameter Systems using Bayesian Uncertainty Quantification based on Generalized Polynomial Chaos