Amit Kumar Rathi

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: The present study aims to investigate uncertainty quantification followed by reliability analysis of structure with homogeneous non-normal random fields. In stochastic finite element formulation, these continuous fields are discretized by different methods (e.g. Karhunen-Loeve Expansion) which transformed it into a set of random variables. However, this discretization often leads to large number of random variables, especially for multiple random fields. With this in view, two different meta-model based approaches are presented in this study using high dimensional model representation (HDMR) for efficient stochastic computation. First, an adaptive multiple finite difference HDMR (AMFD-HDMR) is proposed that decomposes the original performance function into summands of smaller dimensions. These subfunctions are modeled by polynomial chaos expansion (PCE) using moving least square technique which utilizes the benefits of orthogonality of the basis functions and provides adaptive interpolation between the support points. These support points are generated in a sparse grid framework based on the hierarchial tensor products of the sub-grids and the appropriate statistical properties. An iterative scheme is developed with the aim to create new support points in the desired locations such as most probable failure point and/or maxima/minima. Later, a dimension adaptive multiple finite difference HDMR (dAMFD-HDMR) is proposed utilizing sensitivity analysis to further improve the efficiency and accuracy. In the second proposal, an intermittent HDMR formulation is suggested based on the individual and mutual contributions of the significant dimensions. Once the meta-model is built, Monte Carlo simulation is performed over it, thus bypassing the time exhaustive computation of the original performance function. Numerical studies are carried out using composite plate to prove the merits of the proposed algorithms compared to other methods available in the literature.

Abstract: 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

Abstract: A state-of-the-art review on the response control of structures mainly using the passive tuned mass damper(s) (TMD/s) is presented. The review essentially focuses on the response control of wind- and earthquake-excited structures and covers theoretical backgrounds of the TMD and research developments therein. To put the TMD within a proper frame of reference, the study begins with a qualitative description and comparison of passive control systems for protecting structures subjected to wind-imparted forces and forces induced due to earthquake ground motions. A detailed literature review of the TMD is then provided with reference to both, the theoretical and experimental researches. Specifically, the review focuses on descriptions of the dynamic behavior and distinguishing features of various systems, viz. single TMD (STMD), multiple tuned mass dampers (MTMDs), and spatially distributed MTMDs (d-MTMD) which have been theoretically developed and experimentally tested both at the component level and through small-scale structural models. The review clearly demonstrates that the TMDs have a potential for improving the wind and seismic behaviors of prototype civil structures. In addition, the review shows that the MTMDs and d-MTMDs are relatively more effective and robust, as reported. The paper shows the scope of future research in development of time and frequency domain analyses of structures installed with the d-MTMDs duly considering uncertainties in the structural parameters and forcing functions. In addition, the consideration of nonlinearity in structural material and geometry is recommended for assessment of the performance of the STMD, MTMDs, or d-MTMDs.

Abstract: Particle damping, an effective passive vibration control technology, is developing dramatically at the present stage, especially in the aerospace and machinery fields. The aim of this paper is to provide an overview of particle damping technology, beginning with its basic concept, developmental history, and research status all over the world. Furthermore, various interpretations of the underlying damping mechanism are introduced and discussed in detail. The theoretical analysis and numerical simulation, together with their pros and cons are systematically expounded, in which a discrete element method of simulating a multi-degree-of-freedom structure with a particle damper system is illustrated. Moreover, on the basis of previous studies, a simplified method to analyze the complicated nonlinear particle damping is proposed, in which all particles are modeled as a single mass, thereby simplifying its use by practicing engineers. In order to broaden the applicability of particle dampers, it is necessary to implement the coupled algorithm of finite element method and discrete element method. In addition, the characteristics of experimental studies on particle damping are also summarized. Finally, the application of particle damping technology in the aerospace field, machinery field, lifeline engineering, and civil engineering is reviewed at length. As a new trend in structural vibration control, the application of particle damping in civil engineering is just at the beginning. The advantages and potential applications are demonstrated, whereas the difficulties and deficiencies in the present studies are also discussed. The paper concludes by suggesting future developments involving semi-active approaches that can enhance the effectiveness of particle dampers when used in conjunction with structures subjected to nonstationary excitation, such as earthquakes and similar nonstationary random excitations.

Abstract: Uncertainties, such as material dispersion, loading fluctuation and cognitive inconsistency, widely exist in active vibration control systems, and more importantly, the controller performance is generally sensitive to the parametric deviation Thus, the uncertainty-oriented safety assessment for the controlled structure is of great significance in practical engineering In view of the limitation of uncertain samples, a novel non-probabilistic time-variant reliability assessment (NTRA) approach, which combines the set-theoretical convex model and the first-passage method, is proposed for vibration suppression problems under the linear quadratic regulator (LQR) control scheme Boundary rules and the time-dependency features of the controlled responses are first determined using the space-state transformation and the convex process theory For safety reasons, a new time-variant reliability index is defined under the area-ratio principle, and its solution details are further discussed Two engineering examples and one experimental case are presented to demonstrate the validity and applicability of the developed methodology

Abstract: The use of TMDs is commonly discouraged for structures subjected to short-duration, pulse-like ground motions such as near-field earthquake excitations. Friction tuned mass damper (FTMD) is an innovative device compound of the traditional linear TMD with the idea of a friction damper which is still in the developmental stage for the seismic applications. The present paper investigates the performance of TMD and FTMD for seismic control of tall buildings under near-field earthquakes including soil-structure interaction (SSI) effects. A 40-story structure with a height-to-width ratio of four, a uniform mass distribution and a linear stiffness distribution in its height is considered in this study. Different conditions of the ground state are also considered for numerical studies. A design process based on a multi-objective cuckoo search (MOCS) algorithm is utilized for the optimum design of TMD and FTMD parameters. The simulation results indicate that ignoring the SSI effects may result in an inappropriate and unrealistic estimation of seismic responses and performance of TMD and FTMD in the high-rise structure. In terms of maximum displacement, acceleration, and drift of floors, it is found that the FTMD is capable of mitigating the structural responses better than the TMD. The efficiency of the FTMD is also compared with the TMD from the energy point of view for dissipation of the seismic input energy. The results show the superiority of the FTMD in the reduction of the maximum seismic input, kinetic and strain energies of the main structure, which confirm the capability of the FTMD being more than the TMD for mitigation of the seismic damages in the tall structure during near-field earthquakes. By increasing the soil softness, an increased trend is often achieved in the maximum seismic input and damage energies, thus ignoring the SSI effects may give an unrealistic result of the performance of TMD and FTMD in reducing the damage of seismic-excited tall buildings.