Uncertainty Analysis of Bistable Vibration Energy Harvesters Based on the Improved Interval Extension

Yi Li,Shengxi Zhou,Grzegorz Litak

doi:10.1007/s42417-019-00134-z

Abstract

PurposeHigh-energy interwell oscillations of the bistable energy harvester (BEH) lead to large-amplitude output voltage. For processing and manufacturing of the BEH, small errors and deviations in the final structure cannot be totally eliminated in practice, which will make the output voltage to be apart away from the design value. Therefore, the geometrical variables, material properties and other parameters should be treated as uncertainties in analysis and are bound to their design.MethodThis paper presents uncertainty analysis of the BEH to reveal the influence of the uncertain system parameters on the energy harvesting performance. The improved interval extension based on the first-order Taylor series is used to predict the lower and upper bounds of the stable high-energy interwell output voltage of the BEH. In detail, uncertain mass, nonlinear stiffness term, damping, capacitance and electromechanical coupling coefficient are considered. Meanwhile, the Monte Carlo simulation is employed to verify the suitability and the accuracy of this method. Especially, this method allows researchers to define the number of the parameter αj according to the categories of uncertain variables.ResultsThe research works show that interval of the output voltage of the BEH can be limited by reducing the number of uncertain variables, and the uncertainty of the output voltage is more sensitive to the electrical uncertain variables than the structural uncertainties.ConclusionDesigners of the BEH should pay enough attention to the errors and tolerances of the electrical output design variables. Specifically, in the design of the BEH, it is more effective to improve the accuracy of the output voltage by limiting the uncertainties of electric parameters than structural parameters. Reducing the number of uncertain parameters through increasing processing precision in production of the BEH can also improve the accuracy of the output voltage.

Highlights

As the rapid development of new materials and electronics in the last 10 years, more and more low-powered embedded electromechanical devices and wireless sensors are used for structural health monitoring [1,2,3,4]
Upper and lower bounds of the output voltage can be predicted by the improved interval extension (IIE) based on the first-order Taylor series
This paper uses the improved interval extension based on the first-order Taylor series to predict the lower and upper bounds of the stable high-energy interwell output voltage of the bistable energy harvester (BEH) with uncertain mass, nonlinear stiffness term, damping, capacitance and electromechanical coupling coefficient

Summary

Introduction

As the rapid development of new materials and electronics in the last 10 years, more and more low-powered embedded electromechanical devices and wireless sensors are used for structural health monitoring [1,2,3,4]. Stanton et al [28] derived a distributed parameter model of magnetic coupled cantilever-based BEH to predict the output voltage and nonlinear response characteristics. For the piezoelectric energy harvester, the mass, the stiffness, the damping, the capacitance, the electromechanical coupling coefficient, etc., are all uncertain variables in design, and these uncertainties can make the output voltage fluctuate around its expected value.

Results

Conclusion