David Shahan

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.

An industrial trial of a set-based approach to collaborative design

A set-based multiscale and multidisciplinary design method has been proposed in which distributed designers manage interdependencies by exchanging targets and Pareto sets of solutions. Prior research has shown that the set-based method (SBM) has the potential to reduce the number of costly iterations between design teams, relative to centralized optimization approaches, while expanding the variety of highquality, system-wide solutions. These results have been obtained with representative examples in a laboratory setting. The goal of this research is to investigate whether similar results are obtained from an industrial trial, implemented in an industry design environment. The SBM is applied to the design of a downhole module for our industrial partners at Schlumberger, a developer of oilfield tools and services. The design was conducted on location at Schlumberger by an intern who converted the existing Schlumberger design process into a set-based design process. Results indicate that the SBM delivers the benefits predicted in the laboratory, along with a host of advantageous side effects, such as a library of back-up design options for future design projects.

Dynamically variable negative stiffness structures

A novel active structure supports loads while dynamically and continuously changing stiffness by more than 100× in less than 10 ms. Variable stiffness structures that enable a wide range of efficient load-bearing and dexterous activity are ubiquitous in mammalian musculoskeletal systems but are rare in engineered systems because of their complexity, power, and cost. We present a new negative stiffness–based load-bearing structure with dynamically tunable stiffness. Negative stiffness, traditionally used to achieve novel response from passive structures, is a powerful tool to achieve dynamic stiffness changes when configured with an active component. Using relatively simple hardware and low-power, low-frequency actuation, we show an assembly capable of fast (<10 ms) and useful (>100×) dynamic stiffness control. This approach mitigates limitations of conventional tunable stiffness structures that exhibit either small (<30%) stiffness change, high friction, poor load/torque transmission at low stiffness, or high power active control at the frequencies of interest. We experimentally demonstrate actively tunable vibration isolation and stiffness tuning independent of supported loads, enhancing applications such as humanoid robotic limbs and lightweight adaptive vibration isolators.

Bayesian networks for set-based collaborative design

A set-based approach to collaborative design is presented, in which Bayesian networks are used to represent promising regions of the design space. In collaborative design exploration, complex multilevel design problems are often decomposed into distributed subproblems that are linked by shared or coupled parameters. Collaborating designers often prefer conflicting values for these coupled parameters, resulting in incompatibilities that require substantial iteration to resolve, extending the design process lead time without guarantee of achieving a good design. In the proposed approach to collaborative design, each designer builds a locally developed Bayesian network that represents regions of interest in his design space. Then, these local networks are shared and combined with those of collaborating designers to promote more efficient local design space search that takes into account the interests of one’s collaborators. The proposed method has the potential to capture a designer’s preferences for arbitrarily shaped and potentially disconnected regions of the design space in order to identify compatible or conflicting preferences between collaborators and to facilitate a compromise if necessary. It also sets the stage for a flexible and concurrent design process with varying degrees of designer involvement that can support different designer strategies such as hill-climbing or region identification. The potential benefits are the capture of expert knowledge for future use as well as conflict identification and resolution. This paper presents an overview of the proposed method as well as an example implementation for the design of an unmanned aerial vehicle.

Implications of Alternative Multilevel Design Methods for Design Process Management

Multilevel design problems are typically decomposed into a hierarchy of distributed and strongly coupled sub-problems, each solved by design teams with specialized knowledge and tools. There are two contrasting approaches to formulating and solving such collaborative design problems: (1) highly iterative exchanges of single design solutions, as in point-based optimization approaches, and (2) minimally iterative exchanges of multiple solutions, as in set-based approaches. In this article, the effects of these alternative approaches on the overall lead time of a design process are explored. A discrete event simulation is developed to evaluate the lead times of highly iterative and minimally iterative multilevel design strategies and the sensitivity of those lead times to the level of noise in the design environment for a range of designer work loads. Designer work loads include not only the multilevel design task of interest, but also secondary design jobs that consume designer time. Noise is represented as variability in task processing times, arrival rates, and iteration levels. An example design process for an unmanned aerial vehicle is used to compare set-based and point-based design strategies. The results of the simulations indicate that the lead times of minimally iterative, set-based design processes are more robust to busy design environments than highly iterative, point-based alternatives. Accordingly, it may be advantageous to favor richer, but less frequent, exchanges of information in a multilevel design process, even if more effort is required to generate those sets of information.

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.

Bayesian Network Classifiers and Design Flexibility Metrics for Set-Based, Multiscale Design With Materials Design Applications

A set-based approach is presented for solving multi-scale or multi-level design problems. The approach incorporates Bayesian network classifiers (BNC) for mapping design spaces at each level and flexibility metrics for intelligently narrowing the design space as the design process progresses. The approach is applied to a hierarchical composite materials design problem, specifically, the design of composite materials with macroscopic mechanical stiffness and loss properties surpassing those of conventional composites. This macroscopic performance is achieved by embedding small volume fractions of negative stiffness (NS) inclusions in a host material. To design these materials, the set-based, multilevel design approach is coupled with a hierarchical modeling strategy that spans several scales, from the behavior of microscale NS inclusions to the effective properties of a composite material containing those inclusions and finally to the macroscopic performance of components. The approach is shown to increase the efficiency of multi-level design space exploration, and it is particularly appropriate for top-down, performance-driven design, as opposed to bottom-up, trial-and-error modeling. The design space mappings also build intuitive knowledge of the problem and promising regions of the design space, such that it is almost trivial to identify designs that yield preferred system-level performance.© 2014 ASME

Hierarchical Design of Composite Materials With Negative Stiffness Inclusions Using a Bayesian Network Classifier

Recent research in the field of composite materials has shown that it is theoretically possible to produce composite materials with macroscopic mechanical stiffness and loss properties that surpass those of conventional composites. This research explores the possibility of designing and fabricating these composite materials by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design, however, is a nontrivial task. This paper presents a hierarchical multiscale material model for these materials, coupled with a set-based, multilevel design approach based on Bayesian network classifiers. Bayesian network classifiers are used to map promising regions of the design space at each hierarchical modeling level, and then the maps are intersected to identify sets of multilevel or multiscale solutions that are likely to provide desirable system performance. Length scales range from the behavior of the structured microscale negative stiffness inclusions to the effective properties of mesoscale composite materials to the performance of an illustrative macroscale component — a vibrating beam coated with the high stiffness, high loss composite material.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