Design space computation based on general design theory applied to knowledge formulation in simulation-based production planning
Introduction
Due to the acceleration of digitalization in the manufacturing industry, engineering activities relating to the design and planning of manufacturing systems and processes are increasingly being performed virtually in order to shorten lead time and improve the quality of designs and plans. Model-based systems engineering (MBSE) is a key engineering discipline in support of these activities to model, simulate, and evaluate facility layouts, as well as process plans, production, and maintenance schemes before the respective activities are executed across the manufacturing systems’ lifecycles [1]. However, essential knowledge about manufacturing systems and processes has yet to be sufficiently captured in these activities following MBSE, because the knowledge gained from simulation processes is limited to relations about independent pairs of design parameters as inputs and performances specified by functional requirements as outputs. As far as complex engineered systems such as manufacturing systems are concerned, such input-output relations cannot be merely decoupled [2]. Thus, essential knowledge about manufacturing systems and processes thus exists as a mixture of relations regarding inputs, outputs, and (relations regarding) input-output relations.
In order to complement and capture such essential knowledge about manufacturing systems and processes in the context of MBSE, this paper proposes the use of general design theory (GDT) [3,4], which mathematically formulates knowledge regarding design objects and processes. The motivation behind the use of GDT is that the algebraic structures of design objects and processes formulated in GDT (i.e., topological spaces in a set of entities and mapping among them) may correspond to (i.e., be as expressive as) logical arguments of knowledge employed by engineers and designers. Although scholars in the field of computer science study general relationships between algebraic and logical structures (e.g., [5]), they have not yet investigated its applications within specific domains (such as GDT in the design domain).
This study presents an algorithm to compute a design space comprised as a directed graph based on GDT, given a set of entities explored in the design process. The nodes represent partial sets of attributes and functions of the entities, whereas the arrows are the inclusion relations among the partial sets, which partly comprise a function from partial sets of attributes to those of functions. The paper also presents algorithms to extend a design space based on the formulation of design alternatives and functional refinement process based on GDT (see. Section 2.3).
The areas of focus of the present study and that of related work can be presented on a three-dimensional map shown in Fig. 1. Each axis corresponds to the progress of a design process over time, with the design space characterized by concepts such as functions and attributes, as well as the level of abstraction. Related work based on the study of GDT dealt with metamodels [6] (MM) as an intermediate mapping between two topological spaces (i.e., attribute space TA and function space TF) in GDT. Function-Behavior-State modeling [7] incorporates the continuous views of metamodels, which shifted from functions to attributes (incl. behaviors and states). However, they have not studied metamodels considering the properties of topological spaces that accompany GDT. The novelty and originality of this study are in analysis of GDT and its application based on such mathematical properties.
This paper is structured as follows. In Sec. 2, GDT is briefly reviewed, and the model of a design space based on GDT as a directed graph (called a design space graph in this paper) is presented. Design solutions, design alternatives, and functional refinement process are then formulated in Section 2. In Section 3, an overview of an algorithm to compute and extend a design space graph is shown. In Section 4, a simulation-based production planning case study demonstrates computation of a design space graph and its application to formulation of knowledge in production planning based on a set of simulation experiments. In Section 5, the study is summarized, and conclusions are drawn. The formulation in this paper is based on the author's previous work [8], which reported on the formulation of mathematical design theories such as axiomatic design (AD) [9], design structure matrices (DSM) [10], and GDT, in a unified manner using category theory [11,12].
Section snippets
Design spaces
In GDT, the design space explored in a design process consists of a set of entities (incl. non-existent entities as entity concepts) serving as design objects that are classified into a set of attributes and functions within the space. Mathematically, the design space is defined by two topological spaces called attribute space TA and function space TF, and the continuous function from TA to TF. TA and TF are defined by the ordered pairs (S, OA) and (S, OF), where S is a set of entities serving
Inputs of the computation process
This section presents an overview of an algorithm to compute a design space graph described in Section 2. The inputs of the algorithm are (1) an initial set of attributes A0 and functions F0 considered in the design process; and (2) a set of entities explored in the design process S0. Each element s of S0 is associated with s.a (s.f), a partial set of A0 (F0) characterizing s. Here, s.a and s.f are nodes of the design space graph. Fig. 7 (a) shows an example of such inputs, S0 (four entities s1–
Overview of the case study
In order to illustrate computation of a design space graph and its application to formulation of knowledge useful in the design and planning activities of manufacturing systems and processes, this section presents a case study in the context of production planning for a manufacturing testbed at a research site of AIST. Here, the machining of test pieces with variations on the scales and materials types was assigned as new tasks, and these were integrated into the existing production plan.
Summary and conclusions
This study has proposed a mathematical model of a design space based on GDT as a directed graph, which is computed based on a set of entities classified in accordance with given attributes and functions. The topological properties of the design space have been used to logically describe relations among the functions and the attributes (such as the union, intersection, and implication) and to compute such relations in the design process. The formulation of design alternatives and functional
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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