A hybrid chaos control approach of the performance measure functions for reliability-based design optimization

A reliability‐based fatigue design for mechanical components under material variability

“…Though they can succeed to convergence for concave problems, the nonconvergence still occurs when performance functions are highly nonlinear. 27 Keshtegar and Hao proposed a hybrid self-adaptive mean value method by combining self-adjusted mean value method and AMV method based on sufficient descent condition. For example, Yang and Yi utilized stability transformation method of chaos control for the convergence control of AMV procedure.…”

Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint

“…Although the advanced mean value (AMV) method is efficient for convex performance measure function, it exhibits periodic values, bifurcations and chaos phenomenon for both concave and highly nonlinear function [19]. To overcome this problem, a modified chaos control (MCC) method was proposed by the authors [20], which can be formulated as…”

“…λ is the chaos control factor. When λ is equal to 1, the MCC method is identical to the AMV method and it is suitable for convex problem; When 0 oλ o1, the MCC can solve the concave performance function robustly [20]. Based on MCC, the ACC method is further developed by the authors, where the control factor is selected adaptively during the iterative process.…”

“…The advanced mean value (AMV) method is efficient for convex performance function, but it exhibits periodic values, bifurcations and chaos phenomenon in iterative process for concave functions [19]. Consequently, the modified chaos control (MCC) and adaptive chaos control method (ACC) [20,21] were proposed by the authors.…”

Metamodel Assisted Robust Optimization under Interval Uncertainly Based on Reverse Model

“…The former performs the robust optimization by using the probability distribution of variable variations, usually mean and variance of uncertain variables, such as approximation-based methods (Parkinson et al 1993;Hughes 2001), sampling-based methods (Tsutsui et al 1997) and reliability-based design optimization (Royset et al 2001;Du et al 2008;Chen et al 2014;Meng et al 2015). The main shortcoming of these methods is that the probability distribution of the uncertainty variables must be known in advance.…”