A response surface method for stochastic dynamic analysis

Alibrandi, Umberto

doi:10.1016/j.ress.2014.01.003

Cited by 33 publications

(16 citation statements)

References 29 publications

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“…The most common approach is to take r experimental points by varying the random variable values across several standard deviations x i = T i − 1 (±h), where T i represents the transformation of the x i variables from the real space to the Gaussian non-correlated space (Alibrandi 2014). Consider the regression model, linear or not, following observations…”

Section: Response Surface Methodsmentioning

confidence: 99%

Adaptive response surface method supporting finite element calculations: an application to power electronic module reliability assessment

Martín¹,

Micol²,

Pérès³

2016

Struct Multidisc Optim

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To cite this version:Carmen Martin, Alexandre Micol, François Pérès. Adaptive response surface method supporting finite element calculations: an application to power electronic module reliability assessment. Structural and Multidisciplinary Optimization, Springer Verlag (Germany), 2016, 54 ( 6) Abstract In this paper a method is proposed, introducing an adaptive response surface allowing, on the one hand, to minimize the number of calls to finite element codes for the assessment of the parameters of the response surface and, on the other hand, to refine the solution around the design point by iterating through the procedure. This method is implemented in a parallel environment to optimize the calculation time with respect of the architecture of a computational cluster.

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Section: Response Surface Methodsmentioning

confidence: 99%

Adaptive response surface method supporting finite element calculations: an application to power electronic module reliability assessment

Martín¹,

Micol²,

Pérès³

2016

Struct Multidisc Optim

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“…There are a limited number of combinations of nonlinear structure and excitation models for which the exact solution of the response PDFs can be derived. For general applications, the PDF can be approximated by use of FORM‐based approach, expansion method, and response surface method . Approximation methods to solve Fokker‐Planck approximations can also be used .…”

Section: Review Of Gm‐elmmentioning

confidence: 99%

Gaussian mixture–based equivalent linearization method (GM‐ELM) for fragility analysis of structures under nonstationary excitations

Wang

Song

2019

Earthq Engng Struct Dyn

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Summary Gaussian mixture–based equivalent linearization method (GM‐ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. To overcome these technical challenges and promote applications of GM‐ELM to earthquake engineering practice, an efficient GM‐ELM‐based fragility analysis method is proposed for nonstationary excitations. To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity‐augmented version of GM‐ELM. Moreover, the GM‐ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses. The proposed extensions generalize expressions and philosophies of the existing response combination formulations of GM‐ELM to facilitate efficient fragility analysis for nonstationary excitations. The proposed methods are demonstrated by numerical examples using realistic ground motions, including design code–conforming nonstationary ground motions.

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“…Figure 1 shows the design point of this problem. Generate N (N = 10,000) samples in the 1201-D standard normal space, and the polar features of each sample are calculated by means of equations (5) and (6). The samples are then mapped to a 2D plot as shown in Figure 2 with their class labels calculated by calling the limit state function (12).…”

Section: Duffing Oscillator Subjected To White Noisementioning

confidence: 99%

“…Because that the dynamic response of a mechanical system with uncertain parameters possesses probabilistic features which depend on the probabilistic distribution of the system parameters, the study of the stochastic responses of structures with uncertain parameters is of significant interest in many engineering applications. In recent years, a series of papers [1][2][3][4][5][6] have shown that the failure problem of vibration systems can be solved by applying the computational tools of structural reliability methods. In these approaches, the failure event of a vibration system is expressed as implicit functions of the input uncertainties, that is, the limit state functions of the system.…”

Section: Introductionmentioning

confidence: 99%

Study on the application of dimensionality reduction method on reliability and reliability sensitivity analysis of random vibration systems

Sun

Yan

et al. 2015

Advances in Mechanical Engineering

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The application of dimensionality reduction method on the reliability and reliability sensitivity analysis of vibration systems was examined. The dimensionality of a vibration reliability problem was reduced to only two independent dimensions by the means of polar transformation. As the safe and failure classes of samples are clearly distinguishable and occupy a standard position in a two-dimensional plot in the case that the important direction exists, the relevant samples are selected visually. The reliability and reliability sensitivity problems were solved using the position of the relevant samples. Before the reliability and reliability sensitivity estimation, an essential visualization analysis is conducted to examine the capacity of the method in terms of the existence of the important direction which is used to reduce the dimensionality of the reliability problem. In order to calculate the design point correctly, the improved Hasofer-Lind-RackwitzFiessler method was extended with a procedure for determining the perturbation in the calculation of the gradient vector by finite differences according to the numerical precision of the limit state function. The dimensionality reduction method saves the numbers of calling limit state function a lot and has the same accuracy as Monte Carlo method. Examples involving single and multiple degree-of-freedom nonlinear vibration systems were used to demonstrate the approach.

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A response surface method for stochastic dynamic analysis

Cited by 33 publications

References 29 publications

Adaptive response surface method supporting finite element calculations: an application to power electronic module reliability assessment

Adaptive response surface method supporting finite element calculations: an application to power electronic module reliability assessment

Gaussian mixture–based equivalent linearization method (GM‐ELM) for fragility analysis of structures under nonstationary excitations

Study on the application of dimensionality reduction method on reliability and reliability sensitivity analysis of random vibration systems

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