Construction of polynomial chaos expansion for uncertain materail parameters from limited experimental data

The knowledge of uncertain parameter distributions is often required to investigate any typical stochastic problem. It may be possible to directly measure some uncertain parameters but quite often is easier to identifying these parameters from system outputs via an inverse problem. In this paper, a robust and efficient method based of non-sampling technique, i.e. generalized polynomial chaos expansion, is presented to identifying the uncertain parameters from experimental modal data. We review the general polynomial chaos theory and relating issues for uncertain parameter identification. An application is presented for which samples of orthotropic plates are tested to measure the modal data. The distribution functions of uncertain parameters are derived from experimental eigen-frequencies via an inverse stochastic problem. The Pearson model is used to identify the type of density functions. This realization then is employed to construct random orthogonal basis for each uncertain parameter.