Abstract
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
Highlights
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject
The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances
The history regarding the deterministic computation of second-order sensitivities of model responses to model parameters reveals that many particular applications which used -computed 2nd-order response sensitivities have been published over the years, the generic mathematical framework of the 2nd-order adjoint sensitivity analysis methodology was presented in [3] for linear systems and in [4] nonlinear systems
Summary
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” abbreviated as “5th-CASAM-N.” The 5th-CASAM-N generalizes the previous mathematical works on this topic, which stems from the framework of the first-order adjoint sensitivity analysis methodology for generic nonlinear systems established in [1]. The results obtained in [13] [14] [15] have motivated the development in [16] of the 4th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems (4th-CASAM-L), which was applied in [17] [18] [19] [20] to the PERP benchmark for computing exactly and efficiently the most important. “The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (nth-CASAM-L), which enables the exact and efficient computation of sensitivities, of any order, of model responses to model parameters, including imprecisely known domain boundaries, enabling the quantification of uncertainties stemming, among other factors, from manufacturing tolerances. The “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to be presented in this work generalizes and extends the mathematical framework presented in [24].
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