Conjugate unscented transformation–based uncertainty analysis of energy harvesters

Abstract

This article presents a probabilistic approach to investigate the effect of parametric uncertainties on the mean power, tip deflection, and tip velocity of linear and nonlinear energy harvesting systems. Recently developed conjugate unscented transformation algorithm is used to compute the statistical moments of the output variables with multidimensional Gaussian uncertainty in parameters. The principle of maximum entropy is used to construct the probability density function of output variables from the knowledge of obtained statistical moments. The probability density functions for mean power were significantly complicated in shape with two and three distinct peaks for the nonlinear monostable and nonlinear bistable harvesters, respectively. Monte-Carlo simulations with N = 8 × 104 samples for monostable harvester and N = 6.5 × 104 samples for bistable harvester were used for validating the probability density functions. It is concluded that conjugate unscented transformation methodology affords a significant computational advantage without compromising accuracy. In addition, using conjugate unscented transformation method, we show that the dependence of mean power on parameters (excitation frequency, excitation amplitude, etc.), when multidimensional uncertainties are present, is decidedly different relative to a purely deterministic trend. The discrepancy in predicted power between the deterministic and uncertain trends for the monostable harvester, for instance, reach a maximum of 100%, 234%, and 110% for base frequency, base acceleration, and magnet gap, respectively. The deterministic trend consistently overestimates the harvested power relative to the uncertain trends. This work, therefore, may have applications in evaluating “worst case scenario” for harvested power. The major advantage of the presented methodology relative to extant techniques in energy harvesting literature is the accurate and computationally effective applicability to multidimensional uncertainty in parameters.