QUANTIFICATION OF EPISTEMIC UNCERTAINTY DUE TO DATA SPARSITY AND UPDATING BASED ON THE FRAMEWORK VIA SYNTHESIZING PROBABILITY DENSITY EVOLUTION METHOD AND CHANGE OF PROBABILITY MEASURE

Aleatory uncertainty and epistemic uncertainty generally exist simultaneously in engineering design. A variety of studies, including, e.g., the Monte Carlo simulation, orthogonal polynomial expansion and probability density evolution method, have been carried out in terms of the aleatory uncertainty. However, rather limited attention has been paid to the epistemic uncertainty, especially the coupling of aleatory and epistemic uncertainty. In the present paper, in order to represent the epistemic uncertainty due to data sparsity or data updating, the Bootstrap method and Bayesian update method are introduced, respectively. Further, the newly developed compatible framework via synthesizing the probability density evolution method (PDEM) and the change of probability measure (COM) is incorporated to develop a highly efficient approach for the quantification and propagation of uncertainty and reliability evaluation of systems involving not only aleatory but also epistemic uncertainty. Numerical algorithms are elaborated. Therefore, a path from observed data to quantification and propagation of uncertainty and reliability evaluation is shaped. Three engineering cases with real data, including a stability analysis of infinite slope model, a stability analysis of retaining wall model, and a reliability analysis of roof truss structure, are illustrated, demonstrating the accuracy and efficiency of the proposed method.