The equivalent consumption minimization strategy (ECMS) has been considered as a practical energy management strategy for the hybrid electric vehicles (HEVs) because it can be implemented in real time while providing satisfactory performance. However, it is still challenging to adjust an equivalent factor (EF) to its own optimal value in real time because the EF is fundamentally affected by the current driving condition. Although many adaptive ECMSs (A-ECMSs) have been developed to adjust the EF based on a charge-sustaining condition, they do not adequately respond to a change in the driving conditions. In this study, a novel ECMS for the HEVs is proposed to provide the near-optimal performance by considering actual driving conditions. First, the near-optimal condition for the EF is defined to consider a driving condition. Based on it, an iterative scheme is presented to numerically obtain the near-optimal EF. Then, the convergence analysis of the iterative scheme is conducted with practical considerations to implementing the proposed method into real-world applications. Simulation results show that the proposed strategy has better adaptability to changes in the driving conditions with a smaller loss of optimality than conventional A-ECMS which relies only on the charge-sustaining condition. The proposed strategy is also experimentally validated under real-world driving conditions.

In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis,” J. Biomech. Eng., 20, pp. 1135–1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields—the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)—in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.