Reliability-based control optimization for active base isolation systems

Abstract

A probability-based active control synthesis is proposed for seismic base isolation of a structure that is modeled as a linear dynamical system subjected to uncertain future ground motions that are modeled as a stochastic process. The performance objective is the minimization of the probability of failure, where failure is defined as the first-passage of the system trajectory across a generalized set of hyperplanes in the system response space. Versions of the approach are described for the case with no model uncertainty, as well as for the case with uncertain model parameters with probabilistically distributed values. Numerical issues pertaining to the optimization of the controller are discussed. The method is illustrated in a civil engineering context through application to the eight-storey base isolation benchmark structure model, using an array of ideal active control devices working in tandem with the passive base isolation bearings. Controllers are presented for cases with specified and uncertain earthquake spectral parameters, and for two different actuator configurations. Transient simulations are presented for seven earthquake records, and the performances of the controllers are analyzed under a number of metrics. Comparisons with the performance of a related linear-quadratic controller are presented and discussed, both for stationary as well as transient response.

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