Robustness of slope-compensated asymmetric bistable energy harvesters under parametric uncertainty

Abstract

Bistable harvesters are attractive for capturing broadband vibration energy, yet their strong nonlinearity makes them sensitive to fabrication errors. This work evaluates the robustness of an asymmetric harvester that is corrected in situ by tilting its support, allowing gravity to cancel the magnetic mismatch. All mechanical, electrical, and geometric parameters are modeled as independent uniform variables, including the tilt angle, with coefficients of variation between 5 and 40%. A polynomial-chaos surrogate, coupled with Sobol global sensitivity metrics, identifies the factors that truly govern the spread of mean electrical power, while probability maps visualize the likelihood of performance gains or losses. Across every uncertainty level, excitation amplitude and frequency dominate the variance budget; electromechanical coupling follows at a distance, and damping terms are marginal. Once the support is set to the optimum tilt, a mounting or machining error of up to 3° changes the mean power by less than 10% and never becomes a leading driver of variability. Conversely, a 30% increase in either drive parameter retains a better than 60% chance of doubling the harvested power. These findings establish a clear, quantitative robustness margin for slope-angle compensation. Designers can, therefore, relax geometric tolerances and focus on adaptive strategies that track the operating vibration environment, leading to lighter, cheaper, and more reliable bistable energy harvesters.