Topology deals with geometric properties which are dependent only upon the relative positions of the components of figures and not upon such concepts as length, size, and magnitude. Topology supports design and representation of mechanical devices, communication and transportation networks, topographic maps, and planning and controlling of complex activities. In addition, aspects of topology are closely related to symbolic logic, which forms the foundation of artificial intelligence. By approaching engineering design from this abstract point of view, it is possible to use topological methods to study collections of geometric objects or collections of entities that are of concern in design analysis or synthesis. The importance of topological representation and reasoning in analysis, design, and manufacturing is heightened by the contemporary view that stresses the need for conceptual design.

For typical optimization problems, the design space of interest is well defined: It is a subset of Rn, where n is the number of (continuous) variables. Constraints are often introduced to eliminate infeasible regions of this space from consideration. Many engineering design problems can be formulated as search in such a design space. For configuration design problems, however, the design space is much more difficult to define precisely, particularly when constraints are present. Configuration design spaces are discrete and combinatorial in nature, but not necessarily purely combinatorial, as certain combinations represent infeasible designs. One of our primary design objectives is to drastically reduce the effort to explore large combinatorial design spaces. We believe it is imperative to develop methods for mathematically defining design spaces for configuration design. The purpose of this paper is to outline our approach to defining configuration design spaces for engineering design, with an emphasis on the mathematics of the spaces and their combinations into larger spaces that more completely capture design requirements. Specifically, we introduce design spaces that model physical connectivity, functionality, and assemblability considerations for a representative product family, a class of coffeemakers. Then, we show how these spaces can be combined into a “common” product variety design space. We demonstrate how constraints can be defined and applied to these spaces so that feasible design regions can be directly modeled. Additionally, we explore the topological and combinatorial properties of these spaces. The application of this design space modeling methodology is illustrated using the coffeemaker product family.

The current paper describes the Multidisciplinary Combinatorial Approach (MCA), the idea of which is to develop discrete mathematical representations, called “Combinatorial Representations” (CR) and to represent with them various engineering systems. During the research, the properties and methods embedded in each representation and the connections between them were investigated thoroughly, after which they were associated with various engineering systems to solve related engineering problems. The CR developed up until now are based on graph theory, matroid theory, and discrete linear programming, whereas the current paper employs only the first two. The approach opens up new ways of working with representations, reasoning and design, some of which are reported in the paper, as follows: 1) Integrated multidisciplinary representation—systems which contain interrelating elements from different disciplines are represented by the same CR. Consequently, a uniform analysis process is performed on the representation, and thus on the whole system, irrespective of the specific disciplines, to which the elements belong. 2) Deriving known methods and theorems—new proofs to known methods and theorems are derived in a new way, this time on the basis of the combinatorial theorems embedded in the CR. This enables development of a meta-representation for engineering as a whole, through which the engineering reasoning becomes convenient. In the current paper, this issue is illustrated on structural analysis. 3) Deriving novel connections between remote fields—new connections are derived on the basis of the relations between the different combinatorial representations. An innovative connection between mechanisms and trusses, shown in the paper, has been derived on the basis of the mutual dualism between their corresponding CR. This new connection alone has opened several new avenues of research, since knowledge and algorithms from machine theory are now available for use in structural analysis and vice versa. Furthermore, it has opened opportunities for developing new design methods, in which, for instance, structures with special properties are developed on the basis of known mechanisms with special properties, as demonstrated in this paper. Conversely, one can use these techniques to develop special mechanisms from known trusses.

This paper presents a novel knowledge-based Petri net approach to mechanical systems and assemblies modeling within a design with objects environment. A new unified class of object-oriented knowledge Petri nets, which can incorporate a knowledge-based system with ordinary Petri nets, is defined and used for the unified representations of assembly design and modeling. The object knowledge Petri nets, as a graphical language and a new knowledge-based description scheme, can be used to express the qualitative and quantitative aspects of the assembly design and modeling process in an interactive and integrated way. The four-level hierarchy model is proposed and constructed in terms of function-behaviors, structures, geometries, and features. The function-behavior-structure description is built on more abstract concepts so that it can match well top-down design. The static and dynamic characteristics in the design of assembly can also be captured. With the help of fuzzy logic, the incomplete, imprecise knowledge and uncertainty in the design process can also be dealt with. Therefore, the hybrid design object model can incorporate product data model, top-down design process, and assembly process model using an object-oriented, knowledge-based, feature-based, parametric, and constraint-based modeling approach, and can provide a more accurate and more flexible representation. To verify and demonstrate the effective use of the proposed hybrid design object model, a prototype system has been developed. This research provides a knowledge-intensive framework for intelligent assembly design and modeling.

This paper presents a framework and a prototype for designing Integrated Construction Management (ICM) software applications using reusable components. The framework supports the collaborative development of ICM software applications by a group of ICM application developers from a library of software components. The framework focuses on the use of an explicit software development process to capture and disseminate specialized knowledge that augments the description of the ICM software application components in a library. The importance of preserving and using this knowledge has become apparent with the recent trend of combining the software development process with the software application code. There are three main components in the framework: design patterns, design rationale model, and intelligent search algorithms. Design patterns have been chosen to represent, record, and reuse the recurring design structures and associated design experience in object-oriented software development. The Design Recommendation and Intent Model (DRIM) was extended in the current research effort to capture the specific implementation of reusable software components. DRIM provides a method by which design rationale from multiple ICM application designers can be partially generated, stored, and later retrieved by a computer system. To address the issues of retrieval, the paper presents a unique representation of a software component, and a search mechanism based on Reggia's setcover algorithm to retrieve a set of components that can be combined to get the required functionality is presented. This paper also details an initial, proof-of-concept prototype based on the framework. By supporting nonobtrusive capture as well as effective access of vital design rationale information regarding the ICM application development process, the framework described in this paper is expected to provide a strong information base for designing ICM software.

We present a new representation that allows a rigid-body dynamic simulation to be described as a set of “causal-processes.” A causal-process is an interval of time during which both the behavior and the causes of the behavior remain qualitatively uniform. The representation consists of acyclic, directed graphs that are isomorphic to the flow of causality through the kinematic chain. Forces are the carriers of causality in this domain; thus they are central to the representation. We use this representation to compute the purposes of the geometric features on the parts of a device. To compute the purpose of a particular feature, we simulate the behavior of the device with and without the feature present. We then re-represent the two simulations as causal-processes and identify any causal-processes that exist in one simulation but not the other. Such processes are indicative of the feature's purpose. Because they are already causal descriptions of behavior, they can be directly translated into natural language descriptions of the feature's purpose. We have implemented our approach in a computer program called ExplainIT II.