Uncertainty and Worst-Case Analysis in Electrical Measurements Using Polynomial Chaos Theory

In this paper, the authors propose an analytical method for estimating the possible worst-case measurement due to the propagation of uncertainty. This analytical method uses polynomial chaos theory (PCT) to formally include the effects of uncertainty as it propagates through an indirect measurement. The main assumption is that an analytical model of the measurement process is available. To demonstrate the use of PCT to assess a worst-case measurement, the authors present two examples. The first one involves the use of PCT to estimate the possible worst case of a measurement due to the propagation of parametric uncertainty of a low-pass filter. This case study concerns the analysis of nonlinear effects on the propagation of uncertainty of a signal-conditioning stage used in power measurement. In this paper, the PCT method is applied to determine the probability density function (pdf) of magnitude and phase of the frequency response of the filter and their impact on the power measurement. Of particular interest is the use of PCT to determine the worst-case, expected-case, and best-case effects of the filter, avoiding the reconstruction of the complete pdf of the filter output. The results illustrate the potential of this method to determine the significant boundary of measurement uncertainty, even when the uncertainty propagates through a nonlinear nonpolynomial function. In the second example, the authors use PCT to perform a worst-case analysis for an indirect measurement of a loop impedance. For both examples, the PCT method is compared with the numerical Monte Carlo analysis and the analytical method described in the guide on uncertainty on measurements (GUM).