A method for bounding imprecise probabilistic criteria when using a sequential decision process for the design of structural systems

Uncertainty is an integral part of decision making in engineering design. Ideally, when designing structural systems for wind, seismic and other types of hazards, multiple design candidates are compared with respect to uncertain decision criteria in order to identify the optimal, or non-dominated, designs. However, when the decision criteria are obtained from a computationally intensive numerical analysis, e.g., using the performance based earthquake engineering framework for the seismic design of buildings, it might not be feasible to derive precise distributions of the decision criteria for a large number of design alternatives. This work is motivated by the desire to efficiently explore large sets of design alternatives when the decision criteria are probabilistic and computationally intensive to generate. It is hypothesized that the availability of precise distributions of decision criteria for all designs under consideration is not necessary at all points in time during the design process, and appropriate decisions can be made on the basis of imprecise distributions of decision criteria by using confidence intervals to bound their imprecision. To that end, a sequential decision process employing mean-risk analysis and stochastic dominance rules is presented where models of increasing fidelity are used in a sequence to discriminate the dominated designs from the design space on the basis of imprecise distributions of decision criteria. The modeling fidelity is sequentially increased while decreasing imprecision in the decision criteria thus revealing more dominated design solutions. The utility of the methodology is demonstrated through two design examples: (1) a multi-objective discrete choice problem of designing a two bar truss with uncertainty in the material properties and geometric configuration, and (2) the design of a structural frame where the performance is evaluated on the basis of estimated uncertain seismic losses.