Bayesian Network Classifiers for Set-Based Collaborative Design

Abstract

Complex engineering design problems are often decomposed into a set of interdependent, distributed subproblems that are solved by domain-specific experts. These experts must resolve couplings between the subproblems and negotiate satisfactory, system-wide solutions. Set-based approaches help resolve these couplings by systematically mapping satisfactory regions of the design space for each subproblem and then intersecting those maps to identify mutually satisfactory system-wide solutions. In this paper, Bayesian network classifiers are introduced for mapping sets of promising designs, thereby classifying the design space into satisfactory and unsatisfactory regions. The approach is applied to two example problems—a spring design problem and a simplified, multilevel design problem for an unmanned aerial vehicle (UAV). The method is demonstrated to offer several advantages over competing techniques, including the ability to represent arbitrarily shaped and potentially disconnected regions of the design space and the ability to be updated straightforwardly as new information about the satisfactory design space is discovered. Although not demonstrated in this paper, it is also possible to interface the classifier with automated search and optimization techniques and to combine expert knowledge with the results of quantitative simulations when constructing the classifiers.

Inductive Design Exploration Method with Active Learning for Complex Design Problems

“…As the number of design points to be evaluated has a direct influence on the accuracy of feasible solution spaces, designers may face difficulty in choosing an appropriate sample size to ensure reasonable accuracy. The results reported by Shahan et al [2] also indicate the dependency of the number of initial training sample points on the shape of a feasible region boundary obtained from Bayesian network classifiers. Furthermore, it is often observed that the identified feasible regions represent a small portion of the initial design space and a large number of sample points are expended in evaluating unsatisfactory design points.…”

“…The detailed In response to these issues, set-based design approaches have become more promising as they tend to attain design requirements by exploring a set of satisfactory design solutions. Shahan et al [2] proposed a set-based collaborative design method that classifies the design space into satisfactory and unsatisfactory regions by employing Bayesian network classifiers. This method is further applied in the hierarchical design of negative stiffness meta-materials at micro-, meso-, and macro-scales [3][4][5].…”

A Comparative Evaluation of Supervised Machine Learning Classification Techniques for Engineering Design Applications

“…3.3 Gaussian Naive Bayes. Bayesian classifiers, which are based on Bayes' theorem, have been found to perform well on a variety of classification problems [3,31,32]. The NB classifier is a well-known representative of the Bayesian classifiers.…”

“…One example is the set-based design, which focuses on solving distributed design problems by delaying commitment to a single point solution and preserving a diversity of options for identifying mutually satisfactory cross-disciplinary solutions [2]. In this context, classifiers have been used to solve distributed, multidisciplinary design problems, which are decomposed into interdependent subproblems that share coupled design variables [3]. A similar set-based approach may be applied to a multiscale or multilevel design problem in which it is important to map the input design space for an upper-level subproblem because it may define the performance constraints of a lower-level subproblem.…”

“…Mapping the boundaries of the feasible design space accurately can be especially important for improving the efficiency of design exploration because it prevents potentially expensive simulation-or experiment-based exploration of infeasible designs [11]. For highly nonlinear, nonconvex design problems, these spaces can be disjoint and assume arbitrary shapes, making it difficult to capture them with simple techniques such as intervals [3,8]. These types of classifiers can also be used as computationally efficient filters for identifying robust designs that meet feasibility constraints or performance thresholds even when the designs themselves are subject to uncontrolled variation, such as manufacturing tolerances [5].…”