Mark Schwabacher

Using modeling knowledge to guide design space search

Automated search of a space of candidate designs is an attractive way to improve the traditional engineering design process. To make this approach work, however, an automated design system must include both knowledge of the modeling limitations of the method used to evaluate candidate designs and an effective way to use this knowledge to influence the search process. We argue that a productive approach is to include this knowledge by implementing a set of model constraint functions which measure how much each modeling assumption is violated. The search is then guided by using the values of these model constraint functions as constraint inputs to a standard constrained nonlinear optimization numerical method. A key result of our work is a successful demonstration of the application of AI techniques to an important engineering problem. In an empirical study of parametric conceptual aircraft design, we observed a cost improvement of two orders of magnitude. The principal contribution of our work is a new design optimization methodology which makes explicit the interaction between models of artifacts, and validity models of artifact models.

High-Performance Supersonic Missile Inlet Design Using Automated Optimization

A multilevel design strategy for supersonic missile inlet design is developed. The multilevel design strategy combines an efe cient simple physical model analysis tool and a sophisticated computational e uid dynamics (CFD) Navier ‐ Stokes analysis tool. The efe cient simple analysis tool is incorporated into the optimization loop, and the sophisticated CFD analysis tool is used to verify, select, and e lter the e nal design. The genetic algorithms and multistart gradient line search optimizers are used to search the nonsmooth design space. A geometry model for the supersonic missile inlet is developed. A supersonic missile inlet that starts at Mach 2.6 and cruises at Mach 4 was designed. Signie cant improvement of the inlet total pressure recovery has been obtained. Detailed e owe eld analysis is also presented.

Automated Design Optimization for the P2 and P8 Hypersonic Inlets

An automated design methodology incorporating industry-standard Navier ‐ Stokes codes and a gradient-based optimizer has been developed. This system is used to redesign the well-known NASA P2 and P8 hypersonic inlets. First, the Navier ‐ Stokes simulations of the original P2 and P8 inlet designs are validated using numerical convergence studies and comparison with wind-tunnel experimental data for the original inlets published by NASA in the early 1970s. Second, the P2 and P8 inlets are redesigned with the objective of canceling the cowl shock (and, in the case of the P8 inlet, the additional cowlgenerated compression ) at the centerbody by appropriate contouring of the centerbody boundary. The original inlets were intended to achieve these same objectives, but detailed experimental measurements indicated that a substantial ree ected shock system was present. The choice of the objective function, which is used to drive the optimization, has a signie cant impact on the e nal design. Several different formulations for the objective function have been employed, and improvements of 60 ‐ 90% in the objective function have been achieved. This automated design system represents one of the e rst successful combinations of numerical optimization methods with Reynolds-averaged Navier ‐ Stokes e uid dynamics simulation for high-speed inlets, and demonstrates a new area in which high-performance computing may have considerable impact on problems of military and industrial signie cance.

Multilevel Simulation and Numerical Optimization of Complex Engineering Designs

Multilevel representations have been studied extensively by artie cial intelligence researchers. We present a general method that utilizes the multilevel paradigm to attack the problem of performing multidiscipline engineering design optimization in the presence of many local optima. The method uses a multidisciplinary simulator at multiple levels of abstraction, paired with a multilevel search space. We tested the method in the domain of conceptual design of supersonic transport aircraft, focusing on the airframe and the exhaust nozzle, and using sequential quadratic programming as the optimizer at each level. We found that using multilevel simulation and optimization can decrease the cost of design space search by an order of magnitude.

Learning to set up numerical optimizations of engineering designs

Gradient-based numerical optimization of complex engineering designs offers the promise of rapidly producing better designs. However, such methods generally assume that the objective function and constraint functions are continuous, smooth, and defined everywhere. Unfortunately, realistic simulators tend to violate these assumptions, making optimization unreliable. Several decisions that need to be made in setting up an optimization, such as the choice of a starting prototype and the choice of a formulation of the search space, can make a difference in the reliability of the optimization. Machine learning can improve gradient-based methods by making these choices based on the results of previous optimizations. This paper demonstrates this idea by using machine learning for four parts of the optimization setup problem: selecting a starting prototype from a database of prototypes, synthesizing a new starting prototype, predicting which design goals are achievable, and selecting a formulation of the search space. We use standard tree-induction algorithms (C4.5 and CART). We present results in two realistic engineering domains: racing yachts and supersonic aircraft. Our experimental results show that using inductive learning to make setup decisions improves both the speed and the reliability of design optimization.

A search space toolkit: SST

Abstract The Search Space Toolkit (SST) is a suite of tools for investigating the properties of the continuous search spaces which arise in designing complex engineering artifacts whose evaluation requires significant computation by a numerical simulator. SST has been developed as part of NDA, a computational environment for (semi-)automated design of jet engine exhaust nozzles for supersonic aircraft which resulted from a collaboration between computer scientists at Rutgers University and design engineers at General Electric and Lockheed. Though the design spaces for this sort of engineering artifact are mainly continuous, they typically include features such as unevaluable points, multiple local optima, and large derivatives which cause difficulties for standard numerical optimization methods. The search spaces which SST explores also differ significantly from the discrete search spaces that typically arise in artificial intelligence research, and properly searching such spaces requires a synergistic combination of numerical methods and AI techniques and is a fundamental Al research area. By promoting the design space to be a first class entity, rather than a “black box” buried in the interface between an (unconstrained) optimizer and a simulator, SST allows a more principled approach to automated design.

Intelligent gradient-based search of incompletely defined design spaces

Gradient-based numerical optimization of complex engineering designs offers the promise of rapidly producing better designs. However, such methods generally assume that the objective function and constraint functions are continuous, smooth, and defined everywhere. Unfortunately, realistic simulators tend to violate these assumptions. We present a rule-based technique for intelligently computing gradients in the presence of such pathologies in the simulators, and show how this gradient computation method can be used as part of a gradient-based numerical optimization system. We tested the resulting system in the domain of conceptual design of supersonic transport aircraft, and found that using rule-based gradients can decrease the cost of design space search by one or more orders of magnitude.

NPARC simulation and redesign of the NASA P2 hypersonic inlet

The NPARC Reynolds-averaged Navier-Stokes code was used in a systematic redesign of the NASA P2 hypersonic inlet. The rst phase of the work involved computational experiments to determine appropriate grid densities, etc. for using NPARC to achieve grid-converged simulations of the P2 inlet which adequately matched published experimental data. The second phase of the work involved formulating the redesign of the P2 inlet as a numerical optimization problem which was attacked using state-of-the-art numerical optimization software. The resulting P2 inlet design is signi cantly superior to the original design. In particular, the static pressure distortion at the throat was reduced by more than a factor of ve. 31st Joint Propulsion Conference, San Diego, CA, July 1995 AIAA-95-2760

Learning to Choose a Reformulation for Numerical Optimization of Engineering Designs

It is well known that search-space reformulation can improve the speed and reliability of numerical optimization in engineering design. We argue that the best choice of reformulation depends on the design goal, and present a technique for automatically constructing rules that map the design goal into a reformulation chosen from a space of possible reformulations. We tested our technique in the domain of racing-yacht-hull design, where each reformulation corresponds to incorporating constraints into the search space. We used a standard inductive-learning algorithm, C4.5, to learn rules from a set of training data describing which constraints are active in the optimal design for each goal encountered in a previous design session. We then used these rules to choose an appropriate reformulation for each of a set of test cases. Our experimental results show that using these reformulations improves both the speed and the reliability of design optimization, outperforming competing methods and approaching the best performance possible.

Multilevel modelling for engineering design optimization

Physical systems can be modelled at many levels of approximation. The right model depends on the problem to be solved. In many cases, a combination of models will be more effective than a single model. Our research investigates this idea in the context of engineering design optimization. We present a family of strategies that use multiple models for unconstrained optimization of engineering designs. The strategies are useful when multiple approximations of an objective function can be implemented by compositional modelling techniques. We show how a compositional modelling library can be used to construct a variety of locally calibratable approximation schemes that can be incorporated into the optimization strategies. We analyze the optimization strategies and approximation schemes to formulate and prove sufficient conditions for correctness and convergence. We also report experimental tests of our methods in the domain of sailing yacht design. Our results demonstrate dramatic reductions in the CPU time required for optimization, on the problems we tested, with no significant loss in design quality.