A joint diagonalisation approach for linear stochastic systems

  • Authors:

  • C. F. Li;S. Adhikari;Song Cen;Y. T. Feng;D. R. J. Owen

  • Affiliations:

  • School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom;School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom;Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China and AML, School of Aerospace, Tsinghua University, Beijing 100084, China;School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom;School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom

  • Venue:
  • Computers and Structures
  • Year:
  • 2010

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Abstract

In stochastic finite element problems the solution of a system of coupled linear random algebraic equations is needed. This problem in turn requires the calculation of the inverse of a random matrix. Over the past four decades several approximate analytical methods and simulation methods have been proposed for the solution of this problem in the context of probabilistic structural mechanics. In this paper we present a new solution method for stochastic linear equations. The proposed method is based on Neumann expansion and the recently developed joint diagonalisation solution strategy. Unlike the classical Neumann expansion, here only the inversion of a diagonal matrix is needed. Numerical examples are given to illustrate the use of the expressions derived in the paper.