Numerical Techniques to Evaluate Moments of Dynamic System Response Page: 1 of 6
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
S\O;1H o c
Numerical techniques to evaluate moments of dynamic system response
Richard V. Field, Jr., Thomas L. Paez, John R. Red-Horse
Sandia National Laboratories', Albuquerque, NM 87185
rvfield@sandia.gov, tlpaez@sandia.gov, jrredho@sandia.gov
Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engi-
neering applications. The effects that this uncertainty has upon a given system response
are a matter of some concern. Techniques which provide insight to these effects will be
required as modeling and prediction becomes a more vital tool in the engineering design
process. The purpose of this paper is to outline a procedure to evaluate uncertainty in
dynamic system response exploiting various numerical methods. Specifically, the goal is
to attain the statistics of the response with minimal computational effort. Numerical inter-
polation and integration techniques are utilized in conjunction with the iterative form of
the Advanced Mean Value (AMV+) method to efficiently and accurately estimate statis-
tical moments of the response random process. A numerical example illustrating the use of
this analytical tool in a practical framework is presented.
Introduction
Certain response characteristics of structural dynamic systems exhibit behavior that can
only be quantified to within some level of uncertainty. These uncertainties are often incor-
porated into system models as parametric quantities, such as material and geometrical
properties. A previous paper [4] developed a technique for the analysis of this class of
uncertainty using a probabilistic approach where the system parameters are assumed to be
random variables with known probability distributions. The technique, suitable for
approximating the response cumulative distribution function (CDF) at given response
levels, is based on the AMV method, an approach that was developed specifically for
application to system reliability analysis by Wu and Wirsching [5]. AMV is strongly moti-
vated by the fact that the relationship mapping the random parameters to the response
quantity of interest is approximated using point analyses, or function evaluations. Thus,
the analytical functional relationship is not required.
In this article, the issue of evaluating statistical moments is addressed through the use of a
numerical quadrature scheme. The goal is to achieve pertinent statistical information at a
cost which is far lower than what is necessary to evaluate the full CDF. This method
discussed herein involves three steps: (1) using the iterative form of AMV, AMV+, to esti-
mate the CDF at a discrete number of abscissa values, (2) implementing interpolation tools
to approximate the CDF and corresponding PDF at arbitrary abscissa locations, and (3)
using numerical integration tools to compute the moments of the response. The work
presented here is aimed at refining the method reported in [1], which proved promising but
became inaccurate when considering highly non-Gaussian response variables.
t Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a
Lockheed Martin Company, for the United States Department of Energy under Contract DE-
ACO4-94AL85000.
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Field, Richard V., Jr.; Paez, Thomas L. & Red-Horse, John R. Numerical Techniques to Evaluate Moments of Dynamic System Response, article, March 24, 1999; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc692892/m1/1/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.