Utilizing Gauss-Hermite quadrature to evaluate uncertainty in dynamic system

Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engineering applications. The effects that this uncertainty has upon a given system response is a matter of some concern. Techniques which provide insight to these effects will be required as modeling and prediction become a more vital tool in the engineering design process. As might be expected, this is a difficult proposition and the focus of many research efforts. The purpose of this paper is to outline a procedure to evaluate uncertainty in dynamic system response exploiting Gauss-Hermite numerical quadrature. Specifically, numerical integration techniques are utilized in conjunction with the Advanced Mean Value (AMV) method to efficiently and accurately estimate moments of the response process. A numerical example illustrating the use of this analytical tool in a practical framework is presented.