Directional search algorithm for hierarchical model development and selection

A comprehensive directional search algorithm is developed for the model development and selection of hierarchical models systems. A hierarchical model system is a system of nested single-level models that includes different model candidates that can be constructed and calibrated independently. Adjusted single-level model candidates for hierarchical (multi-level) model selection are constructed following the general process of probabilistic single-level model development and selection. An uncertainty propagation matrix is defined to capture the uncertainty levels for all the possible candidate model systems. The uncertainty propagation measurements in the uncertainty propagation matrix are calculated based on the uncertainty propagation theory. A directional search algorithm is proposed to improve the efficiency of finding the best hierarchical model system. The best model system has the desired balance between accuracy and conciseness. The search direction at every search step is determined based on the importance measures of the single-level models. As two examples of the proposed hierarchical model development and selection process, the best hierarchical model systems are determined for the modeling of the concrete carbonation depth and the modeling of the flutter capacity for cable-stayed bridge decks.