Abstract
This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently the first-order sensitivities (i.e., functional derivatives) of operator-valued responses (i.e., model results) of general models of coupled nonlinear physical systems characterized by imprecisely known or and/or uncertain parameters, external boundaries, and internal interfaces between the coupled systems. The explicit mathematical formalism developed within the 1st-CASAM for computing the first-order sensitivities of operator-valued response to uncertain internal interfaces and external boundaries in the models’ phase–space enables this methodology to generalize all of the previously published methodologies for computing first-order response sensitivities. The computational resources needed for using forward versus adjoint operators in conjunction with spectral versus collocation methods for computing the response sensitivities are analyzed in detail. By enabling the exact computations of operator-valued response sensitivities to internal interfaces and external boundary parameters and conditions, the 1st-CASAM presented in this work makes it possible, inter alia, to quantify the effects of manufacturing tolerances on operator-valued responses of physical and engineering systems.
Highlights
The aim of sensitivity analysis is to compute the sensitivities of responses of a computational model with respect to the respective model’s parameters
The specific aim of this work is to generalize the forward/adjoint sensitivity analysis methodology conceived by Cacuci [4,5] for operator-valued model responses, to enable the explicit computation of operator-valued response sensitivities to uncertain phase–space locations of boundaries and interfaces in coupled nonlinear subsystems
Knowledge of such sensitivities is crucial in practice for enabling the quantification of the effects of manufacturing tolerances when constructing any physical system, from benchmark experiments to industrial-size installations
Summary
The aim of sensitivity analysis is to compute the sensitivities (i.e., functional derivatives) of responses (i.e., results of interest) of a computational model with respect to the respective model’s parameters. This work is structured as follows: Section 2 presents the general mathematical framework for computing exactly (in parameter space) and efficiently the sensitivities of a generic operator type to the physical system’s imprecisely known parameters, internal and external boundaries This mathematical framework is called the “first-order comprehensive adjoint sensitivity analysis methodology” (1st-CASAM), where the qualifier “comprehensive” indicates that that all possible uncertain model parameters, including those characterizing the phase–space locations of internal and external boundaries are explicitly taken into consideration. ΑZα )† ∈ RZα denotes a column vector having Zα scalar-valued components representing all of the imprecisely known internal and boundary parameters of the physical systems, including imprecisely known parameters that characterize the interface and boundary conditions. To determine the first G-variation of the response R[u(x), v(y); α; x, y], it is convenient to denote the functions appearing in the argument of the response as being the components of a vector e [u(x), v(y); α]†, which represents an arbitrary “point” in the combined phase–space of the state functions and parameters. The solution of the 1st-LASS will be used to compute the indirect-effect term ind by constructing an equivalent expression (for this indirect-effect term) which would not involve the unknown variations δu(x) and δv(y)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
