Robust Design of TMD for Vibration Control of Uncertain Systems Using Adaptive Response Surface Method
01 Jan 2015-pp 1505-1517
TL;DR: In this paper, the effect of randomness in system parameters on robust design of tuned mass damper (TMD) is examined in a study where mean and standard deviation based robust design optimization (RDO) scheme is suggested.
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.
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TL;DR: In this paper, the tuned mass damper parameters were designed for structural systems based on combining linear matrix inequality with genetic algorithm, in which the possible coupling of those uncertainties is avoided.
Abstract: The tuned mass damper parameters designing for structural systems based on combining linear matrix inequality with genetic algorithm is of concern in this paper. Firstly, based on matrix transform, the novel model description with a singular style for structural systems is obtained, in which the possible coupling of those uncertainties is avoided. Secondly, an approach, which combines linear matrix inequality with genetic algorithm, is taken in this work to solving the optimization problems, and the optimized tuned mass damper parameters can be obtained by solving the optimization problems such that the tuned-mass-damper-controlled systems have a prescribed level of vibration attenuation performance. Furthermore, the obtained results are also extended to the uncertain cases. Finally, the effectiveness of the obtained theorems is demonstrated by numerical simulation results.
4 citations
Cites methods from "Robust Design of TMD for Vibration ..."
...The most common TMD designing methods are LQR, LQG, sliding mode control, pole assignment, control, energy-to-peak control, fuzzy control, and so on [19-23]....
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TL;DR: In this article , a robust control strategy based on a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control, is presented.
Abstract:
This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H¥ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models, and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.
2 citations
TL;DR: In this article , the optimal saturation nonlinear control (OSNC) and active learning Kriging (ALK) method were combined to solve the vibration control problems of uncertain systems with both random and multidimensional parallelepiped (MP) convex variables.
Abstract: This paper addresses the vibration control problems of uncertain systems with both random and multidimensional parallelepiped (MP) convex variables by uniting the optimal saturation nonlinear control (OSNC) and an active learning Kriging (ALK) method. This method can be named ALK-MP-OSNC. The dynamic equations of the controlled systems can be written in ODE forms, and the functions containing saturation nonlinearities on the right side of each of ODE equation can be approximately replaced via using the Kriging model. The efficiency of the Kriging model can be improved through combining the differential evolution (DE) global optimal algorithm with the distance constraint condition. A three-pendulum system, a satellite motion and a moving-mass beam system are employed to demonstrate the performance of the improved ALK-MP-OSNC. Results indicates that the proposed method can efficiently drive the uncertain pendulum system to a chaotic behavior and the other two uncertain systems to a periodic motion. The efficiency and the accuracy of the proposed method can be researched through comparing with the original ALK and the Monte Carlo simulation. In conclusion, the proposed method can be applied to complex engineering fields such as aerospace engineering, civil engineering, ocean engineering, and space deployable engineering.
1 citations
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TL;DR: In this paper, a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads was conducted in which the floor decks and isolation system together can be viewed as a giant tuned mass damper to reduce the seismic force of the truss.
Abstract: In seismic retrofit of a long-span truss bridge in Japan, a new retrofit scheme was applied in which the existing bearings of the bridge were replaced by a new floor deck isolation system. The floor decks and isolation system together can be viewed as a giant tuned mass damper (TMD) to reduce the seismic force of the truss. This motivates a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads in this paper. Kanai–Tajimi spectrum is selected to model the earthquake excitation. It is shown that, when ratio of the characteristic ground frequency in the Kanai–Tajimi spectrum to the structural frequency is above three, the ground motion can be assumed to be a white noise to design TMD. For a smaller ground frequency ratio, simple formulas of the optimal TMD parameters are obtained. The dependence of optimal TMD parameters on mass ratio especially for large TMD is highlighted. It is found that the optimal TMD has lower tuning frequency and higher damping ratio as the mass ratio increases. For a large mass ratio, TMD becomes very effective in minimizing the primary structure response and robust against uncertainties in the parameters of the system.
293 citations
01 Jan 1960
265 citations
TL;DR: In this paper, the stability boundary of TMD-structure systems subject to linear self-excited forces is derived in a closed form using the perturbation solutions, procedures for optimizing the TMD parameters for various types of loading are explained and the optimal values are derived.
Abstract: Modal properties of tuned mass damper (TMD)-structure two-degree-of-freedom (2DOF) linear systems are studied employing a perturbation technique. Using the perturbation solutions, formulas relevant to designing the TMD for various types of loading are obtained; they are expressed as a function of mass ratio, tuning ratio, damping ratio of the TMD and damping ratio of the structure. Equivalent additional dampings of the structure due to the TMD are derived for random and harmonic forces. Matched expressions of equivalent damping, which are valid for detuned, i.e. non-optimal, conditions are also presented. The stability boundary of TMD-structure systems subject to linear self-excited forces is derived in a closed form. Using the perturbation solutions, procedures for optimizing the TMD parameters for various types of loading are explained and the optimal values are derived. The formulas obtained in this study can be used with good accuracy for mass ratios less than 0.02.
235 citations
TL;DR: In this article, a reliability based optimization of TMD parameters in seismic vibration control under bounded uncertain system parameters is presented, where the first-passage probability of failure of the system is taken as the performance objective.
Abstract: A reliability based optimization of Tuned Mass Damper (TMD) parameters in seismic vibration control under bounded uncertain system parameters is presented. The study on TMD with random parameters in a probabilistic framework is noteworthy. But, it cannot be applied when the necessary information about parameters uncertainties is limited. In such cases, the interval method is a viable alternative. Applying matrix perturbation theory through a first order Taylor series expansion about the mean values of the uncertain parameters’ conservative dynamic response bounds are obtained assuming a small degree of parameter uncertainty. The first-passage probability of failure of the system is taken as the performance objective. Using the interval extension of the performance objective, the vibration control problem under bounded uncertainties is transformed to the appropriate deterministic optimization problems yielding the lower and upper bound solutions. A numerical study is performed to elucidate the effect of parameters’ uncertainties on the TMD parameters’ optimization and the safety of the structure.
122 citations
TL;DR: In this article, a single-degree-of-freedom system with uncertain parameters, subject to random vibrations and equipped with a tuned mass damper device (TMD), is considered and the optimization problem concerns the selection of TMD mechanical characteristics able to enlarge the efficiency of the strategy of vibration reduction.
Abstract: This paper is focused on the comparison between different approaches in structural optimization. More precisely, the conventional deterministic optimum design, based on the assumption that the only source of uncertainty concerns the forcing input, is compared to robust single-objective and multi-objective optimum design methods. The analysis is developed by considering as case of study a single-degree-of-freedom system with uncertain parameters, subject to random vibrations and equipped with a tuned mass damper device (TMD). The optimization problem concerns the selection of TMD mechanical characteristics able to enlarge the efficiency of the strategy of vibration reduction. Results demonstrate the importance of performing a robust optimum design and show that the multi-objective robust design methodology provides a significant improvement in performance stability, giving a better control of the design solution choice.
95 citations