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Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations

Published

Author(s)

David E. Gilsinn

Abstract

We begin this expository essay by reviewing with examples what a typical engineer already knows about statistics. We then consider a central question in engineering decision making, i.e., given a computer simulation of high-consequence systems, how do we verify and validate (V & V) and what are the margins of errors of all the important predicted results? To answer this question, we assert that we need three basic tools that already exist in statistical and metrological sciences: (A) Error Analysis. (B) Experimental Design. (C) Uncertainty Analysis. Those three tools, to be known as A B C of statistics, were developed through a powerful linkage between the statistical and metrological sciences. By extending the key concepts of this linkage from physical experiments to numerical simulations, we propose a new approach to answering the V & V question. The key concepts are: (1) Uncertainty as defined in ISO Guide to the Expression of Uncertainty in Measurement (1993). (2) Design of experiments prior to data collection in a randomized or orthogonal scheme to evaluate interactions among model variables. (3) Standard reference benchmarks for calibration, and inter-laboratory studies for weighted consensus mean. To illustrate the need for and to discuss the plausibility of this metrology-based approach, two example problems are presented: (a) Twelve simulations of the deformation of a linearly elastic simple cantilever beam with end point load, and (b) the calculation of a mean time to failure for a uniformly-loaded, 100-column, and single-floor steel grillage on fire.
Proceedings Title
Proceedings of IDETC/CIE 2005: ASME 2005 International Design Engineering Technical Conference & Computers & Information in Engineering Conference
Volume
On CD
Conference Dates
September 24-28, 2005
Conference Location
Long Beach, CA

Citation

Gilsinn, D. (2006), Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations, Proceedings of IDETC/CIE 2005: ASME 2005 International Design Engineering Technical Conference & Computers & Information in Engineering Conference, Long Beach, CA, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150014 (Accessed July 15, 2024)

Issues

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Created January 2, 2006, Updated February 19, 2017