Uncertainty quantification in the assessment of human exposure to pulsed or multi-frequency fields

Objective: pulsed fields or waveforms with multi-frequency content have to be assessed with suitable methods. This paper deals with the uncertainty quantification associated to these methods. Approach: among all possible approaches, the weighted peak method (WPM) is widely employed in standards and guidelines, therefore, in this paper, we consider its implementation both in time domain and frequency domain. For the uncertainty quantification the polynomial chaos expansion theory is used. By means of a sensitivity analysis, for several standard waveforms, the parameters with more influence on the exposure index are identified and their sensitivity indices are quantified. The output of the sensitivity analysis is used to set up a parametric analysis with the aim of evaluating the uncertainty propagation of the analyzed methods and, finally, also several measured waveforms generated by a welding gun are tested. Main results: it is shown that the time domain implementation of the weighted peak method provides results in agreement with the basilar mechanisms of electromagnetic induction and electrostimulation. On the opposite, the WPM in frequency domain is found to be too sensitive to parameters that should not influence the exposure index because its weight function includes sharp variations of the phase centered on real zeros and poles. To overcome this issue, a new definition for the phase of the weight function in frequency domain is proposed. Significance: it is shown that the time domain implementation of the WPM is the more accurate and precise. The standard WPM in frequency domain has some issues that can be avoided with the proposed modification of the phase definition of the weight function. Finally, all the codes used in this paper are hosted on a GitHub and can be freely accessed at https://github.com/giaccone/wpm_uncertainty.