Multi-objective grasshopper optimization algorithm for automotive piezoelectric suspension systems

Abstract

This study addresses the inherent design trade-offs among ride comfort, handling stability, and driving safety in automotive suspension systems by employing a Multi-Objective Grasshopper Optimization Algorithm (MOGOA) for the co-design of a suspension integrated with piezoelectric energy harvesters. An equivalent four-degree-of-freedom vibration model incorporating piezoelectric devices is established, and a frequency-domain analysis method is proposed to determine the system’s equivalent stiffness, damping, and dynamic response. The vertical body acceleration, pitch angular acceleration, suspension dynamic deflections, and wheel relative dynamic loads are defined as the conflicting optimization objectives. The MOGOA is then utilized to simultaneously optimize the structural parameters of the piezoelectric device and the suspension’s stiffness and damping coefficients. Simulations under Grade-B road conditions at 60 km/h show that MOGOA outperforms both NSGA-II and MOPSO in terms of convergence and distribution uniformity on the Pareto front. The optimization results explicitly reflect the performance trade-offs: while the vertical body acceleration and pitch angular acceleration are reduced by 29.91% and 14.77%, respectively, the improvement in suspension dynamic deflection is marginal, and the wheel relative dynamic load is slightly compromised. This outcome underscores that these performance metrics cannot be simultaneously optimized to their theoretical minima, necessitating a balanced solution based on specific application priorities. Furthermore, the optimized parameters demonstrate good robustness across different vehicle speeds and road grades. The proposed piezoelectric suspension system, through effective multi-objective optimization, can significantly enhance ride comfort while maintaining its energy recovery potential, offering a viable solution for improving the overall energy efficiency and dynamic performance of electric vehicles.