Every analysis works with uncertain inputs: material conductivity, surface roughness, leakage flow, the actual operating condition, contact resistance. You would like to know all of them better, but every measurement costs money and time.
Sensitivity analysis is exactly that prioritisation tool.
Local and global
Local sensitivity. Perturbing each input individually by a small amount and observing how much the output changes. Cheap, and usually sufficient. Its limit: it cannot see interactions between inputs and is valid only near that operating point.
Global sensitivity. Sampling the inputs together across their uncertainty ranges. It captures interactions. Because it requires many runs, in practice it is done on a surrogate model.
Uncertainty propagation
Sensitivity tells you how strong an input's effect is. Uncertainty propagation combines that with the input's actual uncertainty range.
The distinction matters: a highly sensitive but very well known input (gravitational acceleration) contributes no uncertainty to the result. An input with low sensitivity but which is entirely unknown may contribute a great deal.
The total uncertainty of the output follows from combining those contributions, and the ASME V&V 20 framework defines that combination together with the validation uncertainty [1].
The practical outcome
The output of a sensitivity study is a ranked list: which input accounts for how much of the uncertainty in the result. That list settles two decisions:
- Which measurement to make. The input with the largest contribution.
- Which tolerance to tighten. If a manufacturing tolerance governs the result, that becomes a design decision.
This is the step that turns an analysis from "producing a number" into decision support. See the significant digits note.
References
- ASME (2009, R2021). V&V 20 — Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer. American Society of Mechanical Engineers, New York.
- Jones, D. R., Schonlau, M. & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13(4), 455–492. DOI: 10.1023/A:1008306431147