Optimal control of structures: A reliability-based approach

Abstract

A probability-based optimal control methodology for use in the design of active tuned-mass dampers is presented. The probabilistic approach provides a rational basis for accounting for both loading and structural modeling uncertainties. A reliability-based performance index is considered which accounts for structural safety considerations in the design of the active tuned-mass damper. This index is directly related to the structural failure probability which is formulated in terms of multi-dimensional integrals over the space of uncertain parameters. A new asymptotic expansion is used to compute approximately these reliability-type integrals. Accuracy issues are addressed by comparing asymptotic results with the ones obtained using numerical integration. A numerical study is carried out to investigate the effects of structural uncertainties on the optimal design and performance of the active mass dampers. It is found that consideration of structural modelling uncertainties improves substantially the performance and robustness of the ATMD design