Stochastic optimization of nonlinear energy sinks

Ethan Boroson, Samy Missoum

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.

Original languageEnglish (US)
Pages (from-to)633-646
Number of pages14
JournalStructural and Multidisciplinary Optimization
Volume55
Issue number2
DOIs
StatePublished - Feb 1 2017

Fingerprint

Stochastic Optimization
Energy
Sampling
Random variables
Support vector machines
Kriging
Switches
Stiffness
Random Design
Selection of Variables
Damper
Min-max
Parameter Design
Small Perturbations
Acute
Dimensionality
Discontinuity
Support Vector Machine
Switch
Refinement

Keywords

  • Discontinuities
  • Generalized max-min
  • Kriging
  • Nonlinear energy sinks
  • Stochastic optimization
  • Support vector machine

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

Cite this

Stochastic optimization of nonlinear energy sinks. / Boroson, Ethan; Missoum, Samy.

In: Structural and Multidisciplinary Optimization, Vol. 55, No. 2, 01.02.2017, p. 633-646.

Research output: Contribution to journalArticle

@article{7b9f5a657d014ef08e2fa82cd26fd09e,
title = "Stochastic optimization of nonlinear energy sinks",
abstract = "Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.",
keywords = "Discontinuities, Generalized max-min, Kriging, Nonlinear energy sinks, Stochastic optimization, Support vector machine",
author = "Ethan Boroson and Samy Missoum",
year = "2017",
month = "2",
day = "1",
doi = "10.1007/s00158-016-1526-y",
language = "English (US)",
volume = "55",
pages = "633--646",
journal = "Structural and Multidisciplinary Optimization",
issn = "1615-147X",
publisher = "Springer Verlag",
number = "2",

}

TY - JOUR

T1 - Stochastic optimization of nonlinear energy sinks

AU - Boroson, Ethan

AU - Missoum, Samy

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.

AB - Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.

KW - Discontinuities

KW - Generalized max-min

KW - Kriging

KW - Nonlinear energy sinks

KW - Stochastic optimization

KW - Support vector machine

UR - http://www.scopus.com/inward/record.url?scp=84976891102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976891102&partnerID=8YFLogxK

U2 - 10.1007/s00158-016-1526-y

DO - 10.1007/s00158-016-1526-y

M3 - Article

AN - SCOPUS:84976891102

VL - 55

SP - 633

EP - 646

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 2

ER -