Abstract

This work presents a strategy for dealing in an efficient manner two important problems in computational stochastic mechanics. Namely, Bayesian finite element model updating and reliability-based design of finite element models under stochastic excitation. It is well known that always exist modeling errors and uncertainties associated with the process of constructing a mathematical model of a structure and its future excitation. Thus, the ability to quantify the uncertainties accurately and appropriately is essential for a robust prediction of future response and reliability of structures. In this context, a fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for model updating due to its ability to characterize modeling uncertainties associated with the underlying structural system. Of particular importance are stochastic simulation algorithms due to their generality and versatility. On the other hand, under uncertain conditions the field of reliability-based optimization provides a realistic and rational framework for structural optimization which explicitly accounts for the uncertainties. In this framework the design problem can be formulated as a non-linear constrained optimization problem with multiple design requirements including reliability constraints. Due to the complexity of the problem, the design formulation requires advanced and efficient tools for structural modeling, reliability analysis and mathematical programming. The numerical implementation of the aforementioned updating and design processes are computationally very demanding due to the large number of finite element model analyses required. To cope with this difficulty, a model reduction technique is implemented in this work to carry out the corresponding analyses efficiently. In particular, substructure coupling based on fixed-interface normal component modes and interface constraint modes is considered in the present implementation. The method produces highly accurate models with relatively few component modes. For certain parametrization schemes, from the updating and optimization point of view, the fixed-interface normal modes of each component and the interface constraint modes are computed once during the entire updating and design processes. Validation calculations show that the computational efforts for updating and designing the reduced-order model are decreased drastically by two or three orders of magnitude with respect to the unreduced model, that is, the full finite element model. The proposed methodology is demonstrated with a series of problems involving model updating and stochastic structural optimization applications of finite element models. 1