Explicit calibration and simulation of stochastic fields by low-order ARMA processes

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    Abstract

    A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory to the process via an extension to autoregressive moving average (ARMA) processes. The ARMA format incorporates a more detailed correlation structure by including previous values of the simulated process. Alternatively, a more detailed correlation structure can be obtained by including additional 'state-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest memory -the single-step autoregressive model - is analyzed in detail, and an efficient multi-step calibration procedure is developed. The calibration makes direct use of conditional correlations and means, expressed explicitly in terms of the zero and k-step correlation matrices of the stochastic field. The correlation structure of an isotropic turbulent wind field is developed from the generalized von K̀arm̀an spectrum in terms of the Airy function, and the simulation procedure is illustrated for turbulent wind with Airy or exponential function representation of the correlation structure. In spite of the basic simplicity of the simulation algorithm, the details of the transverse correlation, that should satisfy an integral condition for consistency, is represented well.
    Original languageEnglish
    Title of host publicationECCOMAS Thematic Conference - COMPDYN 2011 : 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering: An IACM Special Interest Conference, Programme
    Publication date2011
    Publication statusPublished - 2011
    Event3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - Corfu, Greece
    Duration: 25 May 201128 May 2011
    Conference number: 3
    http://www.compdyn2011.org/

    Conference

    Conference3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering
    Number3
    Country/TerritoryGreece
    CityCorfu
    Period25/05/201128/05/2011
    Internet address

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