Summary Recent development of system identification using Bayesian models or stochastic filtering provides probabilistic descriptions (i.e., probability density function or statistical parameters like mean and variance) of the identified model parameters (e.g., mass, stiffness, and damping). Optimal design of passive controllers for these systems whose parameters are uncertain has remained an open problem. With this in view, the present study aims to develop numerical solution scheme for the optimal design of tuned mass damper (TMD) operating in uncertain environment. Deterministic design of TMD in these cases suffers detuning as the system parameters are random. Thus, a reliability‐based design optimization (RBDO) scheme is presented in this paper for better performance of the TMD when exposed to uncertainties. To solve the RBDO problem, response surface methodology is used along with the moving least squares technique. Dual response surfaces are used for separate handling of optimization and reliability analysis. First response surface performs optimization of the design variables of TMD, while the second response surfaces are used for the estimation of the statistical properties like mean and variance to satisfy the constrained conditions. Numerical analysis is presented to show the effectiveness of the proposed algorithm for RBDO of single degree of freedom‐TMD system as a proof of concept. The proposed meta‐model‐based algorithm can be applied for the optimal design of controller for large structures where conventional technique may face difficulty to handle both optimization and uncertainty quantification simultaneously. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents the state-of-the-art on different moving least square (MLS)-based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity applications. The aim is to improve the performance of MLS-based dimension decomposition in terms of accuracy, number of function evaluations and computational time for large-dimensional problems. With this in view, multiple finite difference high dimension model representation (HDMR) scheme is developed. This anchored decomposition is implemented starting from an initial reference point and progressively evolving in successive iterations. Most probable point (MPP) of failure is identified in every iteration and is used as the reference point for the next decomposition until it converges. Hermite polynomials in MLS framework are used between the support points for efficient interpolation. The support points are generated sequentially using multiple sparse grids based on the Clenshaw–Curtis scheme. Once the global response surface is constructed using the support points generated in each iteration, importance sampling is employed for reliability analysis. Six different benchmark problems are solved to show its performance vis-à-vis other methods. Finally, reliability-based design of a composite plate is demonstrated, clearly showing the advantage and superiority of the proposed improvements in MLS-based multiple dimension decomposition (MDD).

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The effect of randomness in system parameters on robust design of tuned mass damper (TMD) is examined in this work. For this purpose, mean and standard deviation based robust design optimization (RDO) scheme is suggested. The performance of TMD is evaluated using the percentage reduction of the root mean square (RMS) of the output displacement. Adaptive response surface method (ARSM) is used for the optimization and for the estimation of first two moments. In this context, moving least square (MLS) based regression technique is used for better fitting of the response surface. A comparative numerical study is conducted to show the effectiveness of the proposed method to improve the reliability of the controller.

The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.