Standard uncertainty evaluation of multivariate polynomial

The uncertainty propagation law helps to infer the uncertainty of unobservable variables from known or assumed relationship with observable variable. Currently only analytical linear approximation or Monte Carlo simulation methods is widely adopted. The former method is limited to weakly nonlinear systems while the latter does not provide any analytical expression that links the uncertainties of input to uncertainties of output quantities. This paper proposes procedures to evaluate the standard uncertainty of multivariate polynomial using basic algebraic manipulation and tabulated Mellin transform. Case studies are presented whereby the effectiveness and practicality of the proposed method is demonstrated. The proposed method can be readily automated using computer algebra systems, thus negating the need for practitioners to perform the actual complex computation. The work theoretically enriches and extends the validity of the analytic approach in the existing uncertainty evaluation framework, thus enabling the analytic evaluation of uncertainty for many nonlinear cases which was previously an impossible task.