An improved computational method for sensitivity analysis: Green's function method with ‘AIM’

TL;DR: In this paper, a survey of sensitivity derivatives for discrete structural systems is presented, primarily focusing on publications developed in nonstructural fields such as electronics, control, and physical chemistry which are directly applicable to structural problems.

TL;DR: All the good practices in each discipline of variable importance analysis (VIA) techniques are reviewed and compared, so as to instruct the practitioners to choose the optimal methods to meet different analysis purposes, and to guide current research on VIA.

TL;DR: A review of kinetic uncertainty quantification in combustion chemistry can be found in this paper, where the authors provide a self-contained review about the mathematical principles and methods of uncertainty quantization and their application in highly complex, multi-parameter combustion chemistry problems.

TL;DR: In this article, the salient features of the most popular statistical methods currently used for local and global sensitivity and uncertainty analysis of both large-scale and small-scale situations are discussed.

TL;DR: In this article, the BakerHausdorff formula for non-commuting variables is proved in Section I1 of the present paper together with some applications which concern the addition theorem of the exponential function for noncommuting variable.

TL;DR: A new method, called the QZ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B with particular attention to the degeneracies which result when B is singular.

TL;DR: In this article, the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients is investigated, and it is shown via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to ∂ci/∂kl ǫ, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients.

TL;DR: In this article, the sensitivity analysis presented in this paper is nonlinear and thus permits one to study the effects of large deviations from the nominal parameter values, and since all parameters are varied simultaneously, one can explore regions of parameter space where several parameters deviate simultaneously from their nominal values.