Stochastic Approach to Control and Identification of Smart Structures

Abstract

To fully exploit new technologies for response mitigation and structural health monitoring, improved design methodologies are desirable. In this paper, a stochastic framework is presented for robust control and identification of structural systems under dynamical loads, such as those induced by wind or earthquakes. A reliability-based stochastic robust control approach is used to design the controller for an active or semi-active control system. Feedback of the incomplete response at earlier time steps is used, without the need for any state estimation. The optimal controller is chosen by minimizing the robust failure probability over a set of possible models for the system. Here, failure means excessive levels of one or more response quantities representative of the performance of the structure and the control devices. When calculating the robust failure probability, the plausibility of each model as a representation of the system's dynamic behavior is quantified by a probability distribution over the set of possible models; this distribution is initially based on engineering judgment but it can be updated using Bayes' Theorem if dynamic data become available from the structure. For this purpose, a probabilistic system identification technique is presented for model updating using incomplete noisy measurements only. This method allows for updating of the uncertainties associated with the values of the parameters controlling the dynamic behavior of the structure by using only one set of stationary or nonstationary response data. This updated probabilistic description of the system can be used to modify the controller for improved performance of the system. It can also be used for structural health monitoring. An example is presented to illustrate the proposed stochastic framework for identification and control of smart structures.

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