Multiobjective shape optimization of speed humps

Abstract

This paper presents a new approach to the shape optimization of road speed humps. The proposed approach is based on multiobjective genetic optimization of the hump profile while taking into account the separation phenomenon, which occurs when the front tires of the vehicle momentarily lose contact with the road surface. The optimization is carried out for speeds up to twice the authorized speed (throughout this article, the term authorized speed refers to speed limits enforced in speed reduction [bump] areas of the roads) rather than for illegally high speeds as adopted by many of the previous works. A 6-degree of freedom non-linear dynamic model is used to identify the speeds at which separation occurs, and hump profiles associated with these speeds are discarded as infeasible solutions. Three independent objective functions are selected for optimization. They include the maximum vertical acceleration experienced by the driver when crossing the hump below the authorized speed limit (to be minimized), the same vertical acceleration at speeds above the authorized speed (to be maximized), and the ascending ratio of the “speed—vertical acceleration” curve (to be maximized). These objective functions are evaluated for more than 10,000 humps of two popular profile types (sinusoidal and flat top with straight ramps) and optimum profiles for three speed limits of 20, 25, and 30km/h are determined using the multiobjective nondominated sorting genetic algorithm II. As a result, a Pareto front of at least ten optimal points is achieved for each of the two hump profile types. Furthermore, to incorporate the economical aspects of the real-world problem, Pareto optimal points for the two profile types were compared based on their lateral section areas (an indication of the manufacturing cost). The comparison shows that sinusoidal humps more often than not outdo their flat top rivals economically.