TITLE:
Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters
AUTHORS:
Dan Gabriel Cacuci
KEYWORDS:
Fifth-Order Sensitivity Analysis of Bernoulli Model, Uncertain Model Parameters, Uncertain Model Domain Boundaries, Uncertain Model Boundary Conditions
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.12 No.1,
March
22,
2022
ABSTRACT: This work
presents the application of the recently developed “Fifth-Order Comprehensive
Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)”
to a simplified Bernoulli model. The 5th-CASAM-N builds upon and
incorporates all of the lower-order (i.e.,
the first-, second-, third-, and fourth-order) adjoint sensitivities analysis
methodologies. The Bernoulli model comprises a nonlinear model response,
uncertain model parameters, uncertain model domain boundaries and uncertain
model boundary conditions, admitting closed-form explicit expressions for the
response sensitivities of all orders. Illustrating the specific mechanisms and
advantages of applying the 5th-CASAM-N for the computation of the
response sensitivities with respect to the uncertain parameters and boundaries
reveals that the 5th-CASAM-N provides a fundamental step towards
overcoming the curse of dimensionality in sensitivity and uncertainty analysis.