A method for the evaluation of the response probability density function of some linear dynamic systems subjected to non-Gaussian random load

Settineri, D.; Falsone, G.

doi:10.1016/j.probengmech.2014.03.008

Cited by 17 publications

(13 citation statements)

References 12 publications

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“…The number of the negligible blocks obviously depends also on the system damping. These considerations allow a strong reduction of the computational effort, even with reference to the previous approach reported in Settineri and Falsone (2015).…”

Section: Probability Transformation Methodsmentioning

confidence: 99%

“…The aim of the present paper is to give the definition of an approach that is able to give, instant by instant, a direct relation between the pdfs of input and output of a linear structural system subjected to assigned stochastic process excitations. It represents an extension to the dynamical systems of the probability transformation method (PTM), previously introduced by Falsone and Settineri, first for the static problems (Falsone and Settineri, 2013a;Falsone and Settineri, 2013b) and then, for a first attempt, in the dynamical case (Settineri and Falsone, 2015). In particular, in the present work a different numerical integration approach is used in such a way that some computational drawbacks highlighted in Settineri and Falsone (2015) are overcome, arriving to an effective approach, for both accuracy and computational effort.…”

Section: Introductionmentioning

confidence: 99%

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A probability transformation method (PTM) for the dynamic stochastic response of structures with non-Gaussian excitations

Falsone

Laudani

2018

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Purpose This paper aims to present an approach for the probabilistic characterization of the response of linear structural systems subjected to random time-dependent non-Gaussian actions. Design/methodology/approach Its fundamental property is working directly on the probability density functions of the actions and responses. This avoids passing through the evaluation of the response statistical moments or cumulants, reducing the computational effort in a consistent measure. Findings It is an efficient method, for both its computational effort and its accuracy, above all when the input and output processes are strongly non-Gaussian. Originality/value This approach can be considered as a dynamic generalization of the probability transformation method recently used for static applications.

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Section: Probability Transformation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A probability transformation method (PTM) for the dynamic stochastic response of structures with non-Gaussian excitations

Falsone

Laudani

2018

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“…By substituting Equation (25) into Equation (26) and utilizing the conjugate properties of the eigenvalues and eigenvectors (Equation 19), one obtains…”

Section: Explicit Expression For Seismic Responses Of Structuresmentioning

confidence: 99%

“…By substituting Equations (20), (25), and (26) into Equation (29) and using the Euler formula to expand the obtained expression, one obtains…”

Section: Explicit Expression For Seismic Responses Of Structuresmentioning

confidence: 99%

“…However, the pseudo‐excitation method can be computationally prohibitive in practical analysis because it generally requires a large number of dynamic analyses to obtain a solution. Settineri and Falsone 26 and Su et al 27 used several direct integration schemes to derive an explicit expression for the response vector of MDOF systems in term of the seismic excitation. This expression can be further used to evaluate the time‐dependent statistical moment and probability density of stochastic responses.…”

Section: Introductionmentioning

confidence: 99%

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Semi‐analytical solutions for stochastic response of non‐classically damped linear structures to arbitrary time‐frequency modulated seismic excitations

Wang

et al. 2020

Earthq Engng Struct Dyn

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This paper presents a semi‐analytical method for stochastic response analysis of non‐classically damped linear structures subjected to non‐stationary seismic excitations modeled by arbitrary time‐frequency modulating functions. In this method, the inherent randomness of seismic excitation process is characterized by a set of orthogonal random variables obtained using the spectral representation method. Then, by adopting piecewise polynomials to interpolate the time‐frequency modulating function of seismic excitation, an explicit expression for the structural stochastic response in term of the orthogonal random variables is derived using the complex modal analysis. This expression can be used not only to efficiently predict the seismic response of structures subjected to an arbitrary excitation sample, but also to directly evaluate the structural response statistics in the time domain. Finally, a robust algorithm is proposed to determine the optimal locations of segmentation points for the piecewise polynomials, the computational efficiency can be further improved. In the numerical application, a typical non‐classically damped structural system subjected to two models of non‐stationary seismic excitations are studied. The classical evolutionary spectral method and the Monte Carlo simulation are used to verify the accuracy and efficiency of the proposed method. The effects of several parameters such as the order of polynomials on the performance of the proposed method are investigated.

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Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

Das

Tesfamariam

2023

Earthq Engng Struct Dyn

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This study presents an efficient reliability analysis method using probability density evolution method (PDEM) and stochastic spectral embedding (SSE) based surrogate model. The PDEM is used to estimate the structural response's probability density function (PDF). The PDEM is derived based on the principle of probability conservation where generalized density evolution equations (GDEEs) are decoupled from the physical system. The GDEEs are solved using finite difference method coupled with total variation diminishing, in which a set of representative points of random parameters are generated using the generalized F-discrepancy scheme. To obtain satisfactory accuracy of the numerical solution, representative points are needed, which becomes computationally expensive for complex structures. To reduce the computation burden, the SSE is used, which approximates the original response surface. The SSE is a class of supervised machine learning algorithm where it is trained by few observations and enables output prediction as spectral representation. This is achieved by minimizing the residual using domain decomposition technique. To illustrate the proposed SSE-based PDEM, three numerical examples are investigated, including the reliability analysis of four-branch problem and shear building frame subjected to ground acceleration, and the reliability-based design optimization of a moment-resisting frame coupled with the nonlinear energy sink with negative stiffness and sliding friction. Numerical results show that the proposed SSE-based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs.

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A method for the evaluation of the response probability density function of some linear dynamic systems subjected to non-Gaussian random load

Cited by 17 publications

References 12 publications

A probability transformation method (PTM) for the dynamic stochastic response of structures with non-Gaussian excitations

A probability transformation method (PTM) for the dynamic stochastic response of structures with non-Gaussian excitations

Semi‐analytical solutions for stochastic response of non‐classically damped linear structures to arbitrary time‐frequency modulated seismic excitations

Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

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