Peter B. Backlund

A comparative study of the scalability of alternative metamodelling techniques

Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. The accuracy of these metamodels varies with the scale and complexity of the underlying model. In this article, three metamodelling methods are evaluated with respect to their capabilities for modelling high-dimensional, nonlinear, multimodal functions. Methods analyzed include kriging, radial basis functions, and support vector regression. Each metamodelling technique is used to model a set of single output functions with dimensionality ranging from fifteen to fifty independent variables and modality ranging from one to ten local maxima. The number of points used to train the models is increased until a predetermined error threshold is met. Results show that kriging metamodels perform most consistently across a variety of functions, although radial basis functions and support vector regression are very competitive for highly multimodal functions and functions with large local gradients, respectively. Support vector regression metamodels consistently offer the shortest build and prediction times when applied to large scale multimodal problems.

INDUSTRIAL CASE STUDIES IN PRODUCT FLEXIBILITY FOR FUTURE EVOLUTION: AN APPLICATION AND EVALUATION OF DESIGN GUIDELINES

A product’s flexibility for future evolution is its ability to be quickly and economically adapted to meet changing requirements. In previous work, a set of guidelines has been developed for designing flexible products. In this paper, two similar industrial case studies are presented to investigate the effectiveness of these guidelines for designing small-lot products with flexibility for future evolution. The systems are real products that have been designed and built by the authors, providing unrestricted insight into the design process and outcome of each project. The first product, a large testing system for high pressure seals, was designed without the aid of flexibility for future evolution guidelines. The second product, an automated welding test station, was designed with flexibility for future evolution as a specific deliverable of the final product. The flexibility of each system was measured by considering its adaptability to prototypical change modes. Of the two systems, the welding system was found to be more flexible than the seal testing system. The welding system also served as an example of integrating product flexibility guidelines throughout the development process.

All-Electric Ship Energy System Design Using Classifier-Guided Sampling

The addition of power-intensive electrical systems on the U.S. Navys next-generation all-electric ships (AES) creates significant new challenges in the area of total-ship energy management. Power intensive assets are likely to compete for available generation capacity, and thermal loads are expected to greatly exceed current heat removal capacity. To address this challenge, a total-ship zonal distribution model that includes electric power, chilled water (CW), and refrigerated air (RA) systems is developed. Classifier-guided sampling (CGS), a population-based optimization algorithm for solving problems with discrete variables and discontinuous responses, is used to identify high-performance configurations with respect to fuel consumption. This modeling approach supports early-stage design decisions and performance analyses of notional systems in response to changing operating modes and damage scenarios. A set of configurations that enhance survivability is identified. Results of a comparison study demonstrate that CGS improves the rate of convergence toward superior solutions, on average, when compared to genetic algorithms (GAs).

A classifier-guided sampling method for computationally expensive, discrete-variable, discontinuous design problems

Metamodel-based design is a well-established method for providing fast and accurate approximations of expensive computer models to enable faster optimization and rapid design space exploration. Traditionally, a metamodel is developed by fitting a surface to a set of training points that are generated with an expensive computer model or simulation. A requirement of this process is that the function being approximated is continuous. However, many engineering problems have variables that are discrete and a function response that is discontinuous in nature. In this paper, a classifier-guided sampling method is presented that can be used for optimization and design space exploration of expensive computer models that have discrete variables and discontinuous responses. The method is tested on a set of example problems. Results show that the method significantly improves the rate of convergence towards known global optima, on average, when compared to random search.

Classifier-guided sampling for discrete variable, discontinuous design space exploration: Convergence and computational performance

A classifier-guided sampling (CGS) method is introduced for solving engineering design optimization problems with discrete and/or continuous variables and continuous and/or discontinuous responses. The method merges concepts from metamodel-guided sampling and population-based optimization algorithms. The CGS method uses a Bayesian network classifier for predicting the performance of new designs based on a set of known observations or training points. Unlike most metamodelling techniques, however, the classifier assigns a categorical class label to a new design, rather than predicting the resulting response in continuous space, and thereby accommodates non-differentiable and discontinuous functions of discrete or categorical variables. The CGS method uses these classifiers to guide a population-based sampling process towards combinations of discrete and/or continuous variable values with a high probability of yielding preferred performance. Accordingly, the CGS method is appropriate for discrete/discontinuous design problems that are ill suited for conventional metamodelling techniques and too computationally expensive to be solved by population-based algorithms alone. The rates of convergence and computational properties of the CGS method are investigated when applied to a set of discrete variable optimization problems. Results show that the CGS method significantly improves the rate of convergence towards known global optima, on average, compared with genetic algorithms.

Autonomous Microgrid Design Using Classifier-Guided Sampling

Identifying high-performance, system-level microgrid designs is a significant challenge due to the overwhelming array of possible configurations. Uncertainty relating to loads, utility outages, renewable generation, and fossil generator reliability further complicates this design problem. In this paper, the performance of a candidate microgrid design is assessed by running a discrete event simulation that includes extended, unplanned utility outages during which microgrid performance statistics are computed. Uncertainty is addressed by simulating long operating times and computing average performance over many stochastic outage scenarios. Classifier-guided sampling, a Bayesian classifier-based optimization algorithm for computationally expensive design problems, is used to search and identify configurations that result in reduced average load not served while not exceeding a predetermined microgrid construction cost. The city of Hoboken, NJ, which sustained a severe outage following Hurricane Sandy in October, 2012, is used as an example of a location in which a well-designed microgrid could be of great benefit during an extended, unplanned utility outage. The optimization results illuminate design trends and provide insights into the traits of high-performance configurations.Copyright

Classifier-Guided Sampling for Discrete Variable, Discontinuous Design Space Exploration

Estimation of density algorithms (EDAs) have been developed for optimization of discrete, continuous, or mixed discrete and continuous simulation-based design problems. EDAs construct a probability distribution on the set of highest performing designs and sample the distribution for the next generation of solutions. In previous work, the authors have demonstrated how classifier-guided sampling can also be used for discrete variable, discontinuous design space exploration. In this paper we develop the rationale for using classifier-guided sampling as a simple step beyond EDAs that not only improves the characterization of the highest performing designs but also identifies the poorly performing designs and exploits that information for faster convergence to optimal solutions. The resulting method is novel in its use of Bayesian priors to model the inherent uncertainty in a probability distribution that is based on a limited number of samples from the design space. The new classifier-guided method is applied to several example problems and convergence rates are presented that compare favorably to random search and a basic EDA implementation.© 2013 ASME