Reliability-based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope.

El‐Khoury, Omar; Shafieezadeh, Abdollah

Current reliability-based control techniques have been successfully applied to linear systems; however, incorporation of stochastic nonlinear behavior of systems in such control designs remains a challenge. This paper presents two reliability-based control algorithms that minimize failure probabilities of nonlinear hysteretic systems subjected to stochastic excitations. The proposed methods include constrained reliability-based control (CRC) and unconstrained reliability-based control (URC) algorithms. Accurate probabilistic estimates of nonlinear system responses to stochastic excitations are derived analytically using enhanced stochastic averaging of energy envelope proposed previously by the authors. Convolving these demand estimates with capacity models yields the reliability of nonlinear systems in the control design process. The CRC design employs the first-level and second-level optimizations sequentially where the first-level optimization solves the Hamilton-Jacobi-Bellman equation and the second-level optimization searches for optimal objective function parameters to minimize the probability of failure. In the URC design, a single optimization minimizes the probability of failure by directly searching for the optimal control gain. Application of the proposed control algorithms to a building on nonlinear foundation has shown noticeable improvements in system performance under various stochastic excitations. The URC design appears to be the most optimal method as it reduced the probability of slight damage to 8.7%, compared with 11.6% and 19.2% for the case of CRC and a stochastic linear quadratic regulator, respectively. Under the Kobe ground motion, the normalized peak drift displacement with respect to stochastic linear quadratic regulator is reduced to 0.78 and 0.81 for the URC and CRC cases, respectively, at comparable control force levels. Copyright © 2017 John Wiley & Sons, Ltd.

ENERGY development; LINEAR systems; STOCHASTIC processes; CONSTRAINTS (Physics); MATHEMATICAL optimization

Earthquake Engineering & Structural Dynamics, 2017, Vol 46, Issue 14, p2381

0098-8847

Academic Journal

10.1002/eqe.2909