Robustness analysis of responses of vibration control structures with uncertain parameters using interval algorithm

The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations

“…Subsequence, Qiu et al [16] also investigate the dynamic response of structures with uncertain-but-bounded parameters subjected to impulsive loadings by the interval modal superposition method and the numerical integration. In [17] , Chen et al extend the first-order perturbation interval analysis method to the problem of structural vibration control. And based on the first-order Taylor expansion and interval mathematics, Chen and Wu [18] change the dynamic response interval optimization problem into an approximate deterministic optimization problem in which the objective is to minimize the upper bound of the dynamic response.…”

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

“…Because uncertainty exists inherently and unavoidably in almost all engineering systems and frequently brings about instability and performance deterioration of dynamic systems, the robustness of a control system with respect to uncertainties as well as its performance toward attenuation of external disturbances are all important. There have been considerable research efforts on dealing with these uncertainties and on robustness analysis and design of various uncertain systems [1][2][3][4][5]. In the past decades, H ∞ robust control theory for uncertain dynamic systems has been well developed and extensively used to deal with the problems of robust stabilization and disturbance attenuation [3,[6][7][8][9][10][11].…”

A new interval uncertain optimization method for structures using Chebyshev surrogate models

“…Chakraborty et al [20] applied the matrix perturbation theory via a first order Taylor series expansion to obtain a conservative dynamic response of interval functions. Chen et al [21] used the first-order Taylor series expansion to analyse robust response of interval vibration control systems. In fact, the linearization model optimization is actually a type of degenerative nested optimization, in which the inner optimization is replaced by the first-order Taylor series expansion.…”