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 probabilistic optimal design methodology is presented in which time-invariant uncertain structural parameters are modelled by random variables with prescribed probability distribution, and a reliability-based performance index is considered in the proposed design which properly accounts for uncertainties in load and structural models.
Abstract: This study investigates the effects of structural uncertainties on the design and performance evaluation of passive tuned mass dampers (TMD) used for vibration control. A probabilistic optimal design methodology is presented in which time-invariant uncertain structural parameters are modelled by random variables with prescribed probability distribution. Unlike conventional TMD designs based on minimizing the mean-square response, a reliability-based performance index is considered in the proposed design which properly accounts for uncertainties in load and structural models. An approximate asymptotic expansion is used to compute the multidimensional reliability integrals arising in the proposed optimal design methodology. Accuracy and effectiveness issues are addressed by comparing results obtained using this approximation with corresponding results obtained by numerical integration. The importance of structural uncertainties is demonstrated by applying the methodology to a single degree of freedom structure subjected to broadband excitations that are modelled by stationary white noise. It is found that the consideration of structural uncertainties improves substantially the robustness of the TMD design. Also, the reliability-based TMD-design methodology results into significantly larger structural reliability compared to that obtained by the conventional design approach based on minimizing the mean-square response.
67 citations
TL;DR: In this paper, an adaptive compensation mechanism for suspended pendulum TMDs is proposed, where a three-dimensional pendulum is augmented with a tuning frame to adjust its natural frequency, and two adjustable air dampers adjust damping.
Abstract: Detuning, resulting from deterioration, inadvertent changes to structure properties, and design forecasting, can lead to a significant loss of performance in tuned mass dampers (TMDs). To overcome this issue, an adaptive compensation mechanism for suspended pendulum TMDs is proposed. The adaptive pendulum mass damper is a three-dimensional pendulum, augmented with a tuning frame to adjust its natural frequency, and two adjustable air dampers adjust damping. The adjustments for the natural frequency and damping compensation are achieved using a system of stepper motors and a microcontroller. There are two major components in the proposed methodology: identification and control, one followed by the other, in that order. The identification is carried out using spectral information obtained from the structural acceleration responses. The performance of the adaptive pendulum system is studied via both experiments and simulations. The main contribution of this paper is to develop an effective means of compensation for detuning in TMDs, while retaining the simplicity of passive pendulum TMDs. The proposed methodology allows pendulum TMDs to be tuned in place using relatively simple hardware and algorithms, based on ambient vibration measurements only.
60 citations
TL;DR: In this article, four optimum design methods for a dynamic absorber are compared when they are applied to a single-degree-of-freedom system with primary damping, and they can be used on other complex systems, including continuous systems.
Abstract: The optimal design of a dynamic absorber can be classified into time domain optimization and frequency domain optimization. In this paper, four optimum design methods for a dynamic absorber are compared when they are applied to a single-degree-of-freedom system with primary damping. Furthermore, they can be used on other complex systems, including continuous systems. These four optimum methods are (1) the equal peak method, (2) the minimal variance method, (3) the energy method, and (4) the area ratio method. The design objective of these methods is to seek the optimal tuning and damping ratios of the dynamic absorber, whether in the time domain or in the frequency domain.
29 citations
05 Apr 2010
TL;DR: In this paper, the performance of TMDs in reducing the nonlinear response of irregular buildings under bi-directional horizontal ground motions, considering the SoilStructure Interaction (SSI), was investigated.
Abstract: This paper investigates the performance of Tuned Mass Dampers (TMD) in reducing the nonlinear response of irregular buildings under bi-directional horizontal ground motions, considering the SoilStructure Interaction (SSI). A number of 3-D steel moment resisting frames with different levels of eccentricities in orthogonal directions are considered. One pair of TMDs with optimal parameters is placed at the roof level along two orthogonal directions. The optimal location of the TMDs in plan has been determined in a previous study. The infinite underlying soil medium is modeled by a discrete model using the concept of Cone Models. The shear wave velocity of the soil is varied to represent different soil types. Material damping of soil is also considered with some correction. These models are subjected to a number of bi-directional horizontal ground motions according to the soil type. Extensive parametric studies carried out to investigate the performance of TMDs in controlling the nonlinear seismic-induced response of the structural models, considering the SSI effect. Story shear forces and drifts are considered for comparison purposes. The OpenSees program is used for the required numerical analyses.
5 citations