# Multidisciplinary Design Optimization (MDO)

## MDO Overview

Every engineer wants to create the best design possible. This is challenging, as the definition of "best" varies from one design situation to another, and typically there are tradeoffs and interdependencies to manage. For instance, if we wanted to design a very fast car, then we would need a large and powerful engine. However, larger engines require more space and weight, which increases the aerodynamic drag and thus reduces the fuel economy. While expert designers can draw from their experience to identify such relationships, this is more difficult when highly innovative designs or novice designers are involved. It is especially challenging when the outcomes or tradeoffs span multiple design teams or subsystems, as the engineers who specialize in engine thermodynamics are not the same people as those who specialize in car body shape aerodynamics. This has motivated research in model-based systems engineering (MBSE) to coordinate different disciplinary models and their interconnections, as well as MDO to efficiently optimize these complex products.

MDO is a set of methods that can be used to manage and solve optimization problems that include more than one subsystem. In the car example above, these subsystems include components such as the engine, the car body shape, and the chassis for structural support. In another example, pictured below, aircraft design involves simulations of the aerodynamics and the structural strength, which requires models of the geometry, fluid dynamics, structural mechanics, and flight range. However, coordinating the interdependencies among these different simulation models leads to time consuming and computationally intractable design problems to optimize, even when using supercomputers. Most optimization algorithms require hundreds or even thousands of simulations, and these numbers increase with the number of design variables. Finding ways to make this process more efficient is an active area of research for the Design SPACE Laboratory. Some of our projects in this space are summarized below.

## MDO Architectures

An MDO architecture specifies the way that a problem is mathematically formulated to coordinate the interdepencies across disciplinary models. Different architectures have their own benefits and drawbacks, and understanding which architectures perform better in which situations can aid engineering teams in implementing MDO methods. Some architectures include the ability to “parallelize,” or run more than one simulation at the same time, and to run separate simulations different amounts of times. This is useful when one simulation takes much longer than another. Others allow many levels of the system and its subsystems to be modeled. Finding the right architecture for a given system is a challenge in this relatively new field of MDO, as designers must consider the time it takes to find a solution, the quality of that solution, and the ease of creating the architecture.

Our work is comparing two MDO architectures in the context of a simulation-based aircraft design problem, where the disciplinary models include a computational fluid dynamics (CFD) model of the aerodynamics and a finite element analysis (FEA) model of the structural stresses. The architectures are multidisciplinary feasible (MDF), where the simulations are executed sequentially in every optimization iteration, and individual discipline feasible (IDF), where the simulations are executed separately and coupling variables and constraints are introduced to ensure feasibility. Our progress to date has been published in the following paper:

Chell, B. W., Hoffenson, S., & Blackburn, M. R. (2019), "A Comparison of Multidisciplinary Design Optimization Architectures with an Aircraft Case Study," AIAA Science and Technology Forum and Exposition, San Diego, January 7-11.

## Multi-fidelity Optimization (MFO)

MFO is an approach that leverages different model types to more efficiently optimize complex systems. Low-fidelity models can be run quickly but are not so accurate. High-fidelity models are more accurate but take substantial time (often on the order of hours or days) or computational resources (sometimes requiring supercomputers or multiple parallel computers) to run. MFO leverages the fast run times of lower-fidelity models to reduce the number of runs required of the higher-fidelity models. This can result in significant savings of time and computing resources, while leading to comparable or even better solutions. Our research to date has applied a filtering model management strategy, which takes the optimal solution from the low-fidelity model and uses it as the starting point of the high-fidelity model. These results are documented in the following work:

Chell, B., Hoffenson, S., and Blackburn, M.R. (2019), "Comparing multifidelity model management strategies for multidisciplinary design optimization," ASME 2019 International Design Engineering Technical Conferences, Anaheim, California, August 18-21.

## Mission-Level Optimization

Through collaborative work with our industry partners, we have identified the need for a new approach that we are calling mission-level optimization (MLO). MLO aims to optimize products and systems more specifically for the context in which they will be used. Missions, whether they are military operations or transporting an object from point A to point B, can be most directly characterized with a binary output: success or failure. Traditional design optimization approaches typically assume a continuous objective that can improve incrementally: For example, a car’s maximum speed can be increased from 140 mph to 150 mph. However, the mission-level objective may simply be that, across the expected range of transport scenarios, the car can successfully move the necessary quantity of people and goods safely and time-effectively between the scenario's starting point and destination. This discrete success/failure objective, as well as the inherently high uncertainty found in mission-level problems, requires new methods. In the Design SPACE Lab, we have begun to define and formulate MLO problems, drawing from existing optimization, design, gaming, and statistical methods. Our research to date is published in the following papers:

Chell, B., Hoffenson, S., Ray, D., Jones, R. D., and Blackburn, M. R. (2019), "Optimizing for mission success using a stochastic gaming simulation," *Journal of Cyber Security and Information Systems*, 7(3), pp. 7–12.

Chell, B., Hoffenson, S., Kruse, B., and Blackburn, M.R. (2020), "Mission-Level Optimization: A New Approach to Complex Systems Design for Highly Stochastic Life Cycle Use Case Scenarios," ASME 2020 International Design Engineering Technical Conferences, St. Louis, MO, August 16-19.