Uncertainty quantification and reduction using Jacobian and Hessian information

Abstract Robust design methods have expanded from experimental techniques to include sampling methods, sensitivity analysis and probabilistic optimisation. Such typically require many evaluations. We study noise variable cross-term second derivatives of a response quickly identify variables that reduce variability. first compute the uncertainty variance decomposition determine contributing an initial design. Then we Hessian second-derivative matrix cross-terms between variance-contributing proposed change variables. Design with large terms are those can relate coefficients reduction in Sobol indices change. Next, derivative Jacobian indicate which shift mean maintain desired nominal target value. Thereby, changes be variability while maintaining targeted This workflow finds improve robustness minimal four runs per also explore further computation reductions achieved through compounding An example is shown on Stirling engine where top tolerances identified 16 generated 20% less variance.