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    Stochastic Harmonic Function Representation of Random Fields for Material Properties of Structures

    Source: Journal of Engineering Mechanics:;2018:;Volume ( 144 ):;issue: 007
    Author:
    Chen Jianbing;He Jingran;Ren Xiaodan;Li Jie
    DOI: 10.1061/(ASCE)EM.1943-7889.0001469
    Publisher: American Society of Civil Engineers
    Abstract: Taking account of the spatial variation of material properties is of paramount importance to the safety and reliability evaluation of engineering structures. This necessitates the highly efficient and accurate representation of random fields of material properties. Although theoretically it is only an extension of stochastic process representation, in practice this is nontrivial because the dimension of space increases. To reduce the number of basic random variables and improve the accuracy, a stochastic harmonic function (SHF) representation method for homogenous random fields is proposed. Compared to the classical spectral representation method, besides the phase angles, the wave numbers of each harmonic component are also random variables, of which the supports could be specified by the Voronoi partition of the bounded wave-number domain. It is rigorously proved that the proposed SHF representation could reproduce the target wave-number spectral density exactly rather than approximately with a finite number of random variables. In practice, for the same number of random variables and samples, it is numerically proved that the SHF is accurate to the target wave-number spectral density, while spectral representation is only accurate on specific points. Further, it is demonstrated that the SHF fields are homogeneous and asymptotically Gaussian, with the convergence rate being higher than the spectral representation method. In contrast to the Karhunen-Loève expansion, on the other hand, the solution of the integral equation is avoided. The response analysis of a shear wall with random-field material parameters is taken as an example to illustrate the application of the proposed method. It is shown that the scale of fluctuation will affect the variation of dissipated energy greatly, and thereby will affect the reliability. Problems to be further studied are also discussed.
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      Stochastic Harmonic Function Representation of Random Fields for Material Properties of Structures

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    contributor authorChen Jianbing;He Jingran;Ren Xiaodan;Li Jie
    date accessioned2019-02-26T07:41:38Z
    date available2019-02-26T07:41:38Z
    date issued2018
    identifier other%28ASCE%29EM.1943-7889.0001469.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4248763
    description abstractTaking account of the spatial variation of material properties is of paramount importance to the safety and reliability evaluation of engineering structures. This necessitates the highly efficient and accurate representation of random fields of material properties. Although theoretically it is only an extension of stochastic process representation, in practice this is nontrivial because the dimension of space increases. To reduce the number of basic random variables and improve the accuracy, a stochastic harmonic function (SHF) representation method for homogenous random fields is proposed. Compared to the classical spectral representation method, besides the phase angles, the wave numbers of each harmonic component are also random variables, of which the supports could be specified by the Voronoi partition of the bounded wave-number domain. It is rigorously proved that the proposed SHF representation could reproduce the target wave-number spectral density exactly rather than approximately with a finite number of random variables. In practice, for the same number of random variables and samples, it is numerically proved that the SHF is accurate to the target wave-number spectral density, while spectral representation is only accurate on specific points. Further, it is demonstrated that the SHF fields are homogeneous and asymptotically Gaussian, with the convergence rate being higher than the spectral representation method. In contrast to the Karhunen-Loève expansion, on the other hand, the solution of the integral equation is avoided. The response analysis of a shear wall with random-field material parameters is taken as an example to illustrate the application of the proposed method. It is shown that the scale of fluctuation will affect the variation of dissipated energy greatly, and thereby will affect the reliability. Problems to be further studied are also discussed.
    publisherAmerican Society of Civil Engineers
    titleStochastic Harmonic Function Representation of Random Fields for Material Properties of Structures
    typeJournal Paper
    journal volume144
    journal issue7
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)EM.1943-7889.0001469
    page4018049
    treeJournal of Engineering Mechanics:;2018:;Volume ( 144 ):;issue: 007
    contenttypeFulltext
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