A TOOL FOR DESIGN EXPLORATION AND OPTIMIZATION WITH DYNAMIC POWERTRAIN SIMULATION MODELS

Powertrain system design and integration for ground vehicles is often accomplished using a dynamic simulation to evaluate vehicle performance. This paper applies modern multidisciplinary design, analysis, and optimization methods to facilitate powertrain system design through dynamic simulation analysis. A collection of surrogate modeling-based MDAO tools are applied to a representative powertrain example to explore the available design space, analyze the feasibility of system performance goals, and make decisions about systems design. Surrogate modeling is shown to facilitate visualization, information synthesis, and decision making in a highly dimensional design problem. Surrogate-based optimization is also demonstrated on the example powertrain design problem to uncover a Pareto frontier of design options for further analysis. INTRODUCTION In the design of a powertrain system for a ground vehicle, it is common to use a dynamic simulation model to assess the powertrain-based vehicle performance. It is necessary to perform several iterations with different combinations of design and control variables in order seek an optimal design of such a system. This becomes all the more difficult when the detailed simulation models are composed of different component models, e.g., engine, transmission, cooling, and take considerable time to run through each iteration. System designers would benefit greatly if a design exploration and optimization approach was available that could seamlessly assimilate the powertrain simulation model, run iterations in an automated way, and provide results for evaluation. This paper presents an approach developed under contract with the US Army Tank Automotive Research, Development and Engineering Center (TARDEC) for the Advanced Powertrain Demonstrator Program. The main focus of this paper is to demonstrate the capability available from an approach that can help a powertrain system designer identify better and balanced designs while reducing design process time and resources. This paper uses a simplified powertrain integration design problem to illustrate the application of a suite of modern multi-disciplinary design, analysis, and optimization (MDAO) methods. While not an in-depth analysis of any one method, the approach gives a general review of how MDAO might be applied in the context of the given problem. The background of and reasons behind each Proceedings of the 2016 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) A Tool For Design Exploration and Optimization With Dynamic Powertrain Simulation Models, Cooper, et al. UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited. GDLS: Approved for public release, LogNo. -2016-23, Distribution Unlimited, June 1, 2016. Page 2 of 10 method used are discussed, as well as some potential expansions that might be needed for increased complexity. The methods themselves provide a starting point for understanding the application of MDAO to complex problems, and can be tuned to a given problem as necessary. This is accomplished in a two-part approach for utilizing MDAO on the powertrain integration that will allow for an interactive design space exploration as well as optimization of the powertrain model. POWERTRAIN SYSTEM DESIGN The powertrain system design problem under consideration involves exploring the design space to identify a powertrain solution that best meets vehicle performance and other design criteria. This involves studying how component performance characteristics such as power densities (e.g., for the engine) affect the powertrain size and weight which then influence similar vehicle parameters that affect the vehicle powertrain-based mobility performance. The design exploration capability allows one to explore upfront and understand, for example, the net effect of improvement in an individual component performance versus their overall system integration burden. MULTI-DISCIPLINARY DESIGN ANALYSIS AND OPTIMIZATION Multi-disciplinary design, analysis, and optimization (MDAO) is a growing field revolving around the design and optimization of complex systems, in which the strong interaction of multiple disciplines and subsystems necessitates the collaborative manipulation of design parameters throughout the system [1]. Interdisciplinary couplings and often a diversity of conflicting constraints and objectives can create a high dimensional problem that is difficult to navigate manually or with traditional techniques. The practice of MDAO involves the integration of analysis, optimization and decision making techniques to solve complex engineering problems spanning multiple disciplines and subsystems. The process can bridge traditional engineering disciplines (e.g., structures, thermal, control) as well as other lifecycle and economic system properties (e.g., cost, reliability). Utilizing advance modeling and simulation (M&S), MDAO has become an essential part of the design and analysis of complex systems, allowing decentralized teams to collaborate on approaches satisfying multiple, often conflicting, design objectives. General Dynamics, Land Systems (GDLS) has developed a representative dynamic ground vehicle powertrain representative modeling and simulation architecture in MathWorks® Simulink® which serves as the foundation for illustrating this proposed effort. The need for engineers to analyze and predict complex systems and technologies has led to the development of increasingly complex and accurate modeling and simulation tools. Surrogate models, or metamodels, are mathematical approximations of more computationally expensive analysis or experiments, build from a small, targeted number of evaluations over the design space. While they provide many benefits, surrogates are primarily designed to help relieve the intensive computational cost or run time of high fidelity analysis [2]. Design-of-Experiment (DOE) methods are commonly used to generate the smallest necessary sample of observations that can be used to build a surrogate. Once data is available, surrogates can be built using a multitude of techniques spanning various fidelities. Polynomial response surfaces are often the most common surrogating techniques, and can also be used to screen inputs for more efficient modeling. Other common surrogate techniques involve artificial neural networks, support vector machines, Gaussian process prediction (Kriging), and radial based functions. More advanced approaches may include multifidelity methods combining surrogates of different fidelities to model complex design spaces [3]. Surrogate models have been used for a variety of analyses and in an assortment of industries, including the automotive industry [4-6]. Surrogate models can be used as an enabler to help designers and decision-makers explore and understand the design space. Because prediction runs of the surrogate models are so computationally inexpensive (particularly when compared to the time consuming modeling and simulation environment they represent), they can be used to facilitate interactive design space visualization to help designers identify relationships and areas of interest [6, 7]. In essence, they can be used as a real-time means to answer questions about the design space. Surrogates also can be used to characterize and explore design spaces probabilistically, using approaches like Monte Carlo Simulation (MCS) or Bayesian methods [4]. These methods can allow for design under uncertainty, accounting for noise variables (e.g., requirements, environment) that are beyond the designer’s control, as well as to illustrate the difficulties of achieving design goals in terms of their probability [5]. Design trade-offs can be conducted manually, by manipulating the surrogates directly to achieve the desired design effect, or automatically, by using them in concert with some optimization or other computational logic. The application of MDAO also encompasses optimization, and often multi-objective optimization. Designers should seek to thoroughly understand the nature of a design space and the tradeoffs that lie therein, but optimization provides mathematical and/or logical means to help identify promising solutions in complex and multi-dimensional problems. Multi-objective optimization is one of the central pillars of MDAO, and encompasses mathematical optimization problems that involve satisfying more than one objective function simultaneously (and potentially multiple Proceedings of the 2016 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) A Tool For Design Exploration and Optimization With Dynamic Powertrain Simulation Models, Cooper, et al. UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited. GDLS: Approved for public release, LogNo. -2016-23, Distribution Unlimited, June 1, 2016. Page 3 of 10 constraints). In most non-trivial design problems, a set of Pareto-optimal solutions exist, each of which represents a feasible option where improvement in any one objective will result in degradation of another. A simple example is a decision maker’s desire to maximize a vehicle’s payload, survivability, and range. However, the more payload and/or survivability (e.g., armor), the lower the maximum range will be, assuming all other variables remain constant. The set of all these potential solutions is referred to as the Pareto Frontier and is one of the simplest means to represent the tradeoffs a decision maker has to make. Various multiobjective optimization methods and approaches are often concerned with thorough and efficient means to identify Pareto optimal solutions based on the decision makers’ preferences between objectives. By utilizing multi-objective optimization methods like the NSGA-II [8] used in the example here, a subset of Pareto optimal solutions can be found for the designer to explore and select from. Moreover, by integrating a surrogate based o