Second-Moment Design of Dynamic Systems with Uncertain Excitations and Uncertain Parameters via Differentiable Meta-Models  
Author Gordon J. Savage


Co-Author(s) Young Kap Son


Abstract The second-moment design concept is readily understood by engineers. The response uncertainties are expressed in terms of expected values (first moments) and covariances (second moments) of the input parameters. Various indexes can be formulated to measure the performance of the system. This paper addresses second-moment design of nonlinear dynamic systems with uncertainty in both the component parameters and excitations. In order to reduce the computational effort needed for design purposes, meta-models are introduced as computationally efficient surrogates. The component parameters and excitations must have some known bounds. Herein a novel, differentiable, meta-model that finds the response of dynamic systems with simultaneous component parameter uncertainty and excitation uncertainty is presented. Operationally, training sets of parameters are interleafed with the training excitations and then linked to the response matrix (obtained via the mechanistic model) through a least-squares paradigm. Singular value decomposition (SVD) is used to advantage to separate parameter and excitation information. The explicit form of the meta-model allows for easy determination of derivatives that are required in a Taylor series approximation of means and covariances. The efficacy of the metamodel is shown through the design of a nonlinear, quarter automobile, system. The accuracy, increased computation speed and robustness of the methodology provide the impact of the work herein. The sources of errors are identified and ways to mitigate them are discussed.


Keywords Second-moment design, Dynamic systems, Uncertain inputs, Differentiable meta-models, Singular Value Decomposition, Performance indexes
    Article #:  2426
Proceedings ISSAT International Conference on Reliability and Quality in Design 2018
August 2-4, 2018 - Toronto, Ontario, Canada