Model-based design optimization of a hybrid electric vehicle

Last week’s post surveyed the trend of integration between design exploration and optimization software and systems modeling and 0D/1D simulation tools. This week’s case study shows how the two technologies were used together in development of a new hybrid electric vehicle (HEV) to achieve the competing goals of improving fuel efficiency and meeting emissions targets.

Executive summary—A leading automotive OEM used Noesis SolutionsOptimus design optimization and process integration software in conjunction with Maplesoft’s MapleSim multi-domain systems modeling and simulation tool in developing the HEV’s combined electric and combustion propulsion system. Optimus was used to automate the traditional guess-and-correct simulation-based design process, its optimization algorithms efficiently directing the system simulation campaign to identify the best HEV configurations. Using Optimus’ capabilities for design of experiments (DOE), response surface modeling (RSM) and multi-objective optimization (MOO), engineers improved fuel efficiency by 21% and traveling performance (legal emissions compliance) by 15%. With MapleSim providing HEV modeling and Optimus controlling simulation workflow execution, the design optimization was accomplished in just two weeks.

Payback/ROI—process optimization and design optimization

Process optimization:

  • Automating the traditional guess-and-correct simulation-based design process—Optimus directed an automated HEV system simulation campaign to deliver the optimum balance between fuel efficiency and robust legal compliance with emissions regulations.
  • Driving MapleSim multi-domain HEV system simulations without user intervention—Optimus’ direct interface to MapleSim let engineers establish the parametric connection between the two applications without programming.

Design optimization:

  • Exploring the entire design space up front—The Latin-hypercube DOE method automatically determined a virtual experiment plan that collected the most relevant design information with minimum simulation cost.
  • Steering design optimization by gaining insight into the underlying interrelations—The radial basis function generated an RSM (response surface model) that showed how design parameters influence design objectives, providing the insight needed to identify regions that best balance conflicting objectives.
  • Drastically reducing multi-objective design optimization time—The non-dominated sorting evolutionary algorithm (NSEA+) performed design optimization directly on the RSM metamodel, delivering optimum design alternatives ultra-fast.

Background—HEV technology drives greener mobility solutions

Automobile Hybrid Engine
Hybrid electric vehicle engine
Source: Noesis Solutions

Hybrid electric vehicles (HEVs) are developed primarily in response to environmental concerns, offering greater fuel efficiency and lower emissions than combustion-only powertrains. In a series hybrid vehicle, only the electric motor is directly connected to the drivetrain; the internal combustion engine (ICE) works as a generator that powers the electric motor and recharges the batteries. The use of a considerably smaller ICE than a comparably sized conventional vehicle results in lower exhaust emissions. Also, the ICE can be geared to run at maximum efficiency, further improving fuel economy.

HEV development deals with the complex interplay between structural, mechanical, thermal and electromagnetic phenomena. In this case study, engineers modeled the HEV system in MapleSim, known for elegantly handling the complex mathematics of multi-domain system models. With its efficient symbolic computation technology, the software executes a single system simulation in about 60 seconds, processing the 10,000+ calculation steps resulting from a one-hour time history recorded during a representative driving-cycle test.

The challenge for HEV development engineers is to obtain extreme fuel efficiency while complying with mandated emissions targets. Authorities grant compliance for a specific HEV system type when the system’s exhaust emissions are within the tolerated test cycle emissions window. The traveling performance—the difference between the actual and the legally defined emissions levels—needs to be minimized to a certain extent to ensure robust legal compliance with emissions regulations. Optimus was used to automate and direct the HEV development process to help engineers push fuel efficiency while still maintaining the desired success rate with regard to emissions compliance.

First, the engineers automated the MapleSim simulation process by sketching the process flow in Optimus’ graphic drag-and-drop editor. Using a direct interface based on Optimus’ Open Access technology, they quickly established the parametric connection with MapleSim without needing any programming skills. Then Optimus’ optimization algorithms enabled them to direct the simulation campaign to identify the best possible design configuration.

Process flow
Source: Noesis Solutions

The result was that Optimus identified the best possible tradeoff between the partially conflicting fuel-efficiency and traveling-performance objectives by balancing the input variables—engine speed (2000rpm to 5000rpm), number of battery cells (20 to 60), and the charge level (10% to 90%) that initiates battery recharging by the ICE.

Targeting simulation toward optimized HEV designs

Design optimization typically starts with design of experiments (DOE). Such a virtual experiment plan is set up to collect the most relevant design information at minimum simulation cost. In this case, the Latin-hypercube method was used to ensure uniform sampling across the design space. This method executed the 200 experiments in under four hours. DOE identified correlations that allowed engineers to understand the underlying model physics. Scatter diagrams revealed that high engine speed results in low fuel efficiency, and more battery cells yield better compliance with emissions regulations (low traveling performance).

Fuel-efficiency RSM and RSM slice charts showing the input variable values that satisfy the fuel-efficiency objective (high target value)
Source: Noesis Solutions

Traveling-performance RSM and RSM slice charts showing the input variable values that satisfy the traveling-performance objective (low target value)
Source: Noesis Solutions

This set of virtual experiments drove subsequent response surface modeling (RSM) to manually assess where specific design outputs were highest or lowest. The radial basis function (with cubic spline) performed accurate interpolation in a matter of minutes. RSM slice charts indicated that high fuel efficiency requires around 40 battery cells and a low-to-medium battery recharge level. The charts also showed that low values for all design parameters lead to the targeted low traveling performance.

As the response surface quality was very good, the RSM was also used as the basis for the multi-objective HEV system optimization. Multi-objective design optimization typically results in a Pareto front rather than a single optimum solution. The engineers set population size and Pareto front size both to 20. The non-dominated sorting evolutionary algorithm (NSEA+) can handle combined discrete and continuous input variables and reliably converges toward a global Pareto front. By performing optimization on the RSM metamodel, the NSEA+ processing time for the 140 calculations was reduced from hours to a matter of seconds.

Multi-objective design optimization typically results in a Pareto front rather than a single optimum solution
Source: Noesis Solutions

Optimization identified two specific design optima: the fuel efficiency optimum (11.8 kilometer per liter—up by 39%) and the traveling performance optimum (2477—22% better). Since both optima were Pareto line end points, a compromise Pareto optimum needed to be found in between. With both objectives equally weighted, the single tradeoff HEV system configuration yielded 11.3 kilometers per liter and a 2970 traveling performance value.

Maple 4B
Optimus identified the Pareto front of optimal HEV system configurations, optimizing multiple (partly) conflicting design objectives

Source: Noesis Solutions

Thus, the optimized HEV design was 21% more fuel-efficient and had a 15% better traveling performance than the initial design. Optimus automated the MapleSim simulation workflow and provided critical insights up front, then directed simulation toward the optimum HEV configurations.

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Latin hypercubes, radial basis functions, and other quantitative and algorithmic methods that drive design exploration and optimization will be the topic of a future post.