1 2 3 1 2 3 4 5 6 7 8 9 10 11 12 16 24 25 26 27 Int J Adv Manuf Technol (2001) 0:●●●–●●● 28  2001 Springer-Verlag London Limited 31 33 34 35 A Heuristic State–Space Approach to the Functional Design of 36 Mechanical Systems 37 W. Y. Zhang, S. B. Tor and G. A. Britton 38 Design Research Center, School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 39 Singapore 639798 40 41 42 This paper presents a knowledge-based approach for auto- 43 mating the functional design of mechanical systems. By using 44 our proposed automated functional reasoning strategy, which 45 is based on a heuristic search method, a set of physical 46 behaviours can be reasoned out automatically from the desired 47 functions. The interconnection of these behaviours is possible 48 when the functional outputs of one are compatible to the 49 corresponding functional requirements of the next one. Though 50 the design space for behavioural configuration is very large, by 51 defining its heuristic evaluation function as a fuzzy multicriteria 52 decision-making (FMCDM) problem, the proposed heuristic 53 search method can lead to a near optimum design solution in 54 a reasonable time. A case study for the automated functional 55 design of an automatic assembly system is given to illustrate 56 the operation of the proposed heuristic search method, and to 57 show its effectiveness in functional reasoning and optimising 58 the final design. 59 Keywords: Automated design; Functional design; Functional 60 reasoning; Fuzzy multicriteria decision-making; Heuristic 61 search; Knowledge-based 62 63 1. Introduction 64 For many years, computer-aided design (CAD) has provided 65 industry with advanced geometric modelling and conceptualis- 66 ation techniques, relieving designers and engineers of the mun- 67 dane tasks of drafting, while improving accuracy, consistency, 68 and productivity. CAD has proved to be an invaluable tool for 69 designers and is very suitable for the downstream stage of 70 design. However, what is more critical is the upstream stage 71 of design, that is, the initial and most abstract stage of the 72 design process, starting with a desired specification and 73 resulting in concept variants. This is the area where CAD 1 20 Correspondence and offprint requests to: Dr S. B. Tor, School of 21 Mechanical and Production Engineering, Nanyang Technological Uni- 22 versity, Nanyang Avenue, Singapore 639798. E-mail: msbtor 23 ntu.edu.sg 1 AMT: Advanced Manufacturing Technology - Springer 2 17-01-02 15:10:27 Rev 16.03x AMT$$$077P 74 technology is still not well developed. Conceptual design, being 75 the early stage of design, is characterised by information that 76 is often imprecise and inadequate. Essentially, this stage is 77 function-driven and function-oriented, because the main design 78 focus at this stage is to find a design solution which is able 79 to achieve the desired functions. Functional design is a new 80 perspective in the research of this design process. 81 The major drawback of traditional CAD technology is that 82 it cannot perform functional design automation based on the 83 information provided in a set of specifications. It does not 84 have the in-built intelligence to perform reasoning; it lacks the 85 knowledge to make decisions and it does not possess the 86 ability to draw conclusions from available inadequate and 87 approximate information. All these tasks have to be carried 88 out by the designer manually. With the recent advances in 89 the field of artificial intelligence (AI), particularly symbolic 90 representation and related problem-solving methods, automation 91 in some functional design domains becomes possible. Arpaia 92 et al. [1] have made use of rule-based reasoning approaches 93 for the automatic design of measurement systems, in mapping 94 from the logical attributes to the physical components of the 95 instrument. Li et al. [2] have adopted a synthesis strategy 96 based on rule-based reasoning and the best-first heuristic search 97 method to automate the computational synthesis of the concep- 98 tual design of mechanisms. Gorti et al. [3] developed an object- 99 oriented representation for product and design processes, using 100 design operators, to update and transform design contexts. The 101 software provides partial design automation, with some aspects 102 being carried out manually and others automatically. Tor et al. 103 [4] have adopted a functional reasoning approach to automate 104 the design of the collapsible core for uPVC pipe fittings. In this 105 approach, four different types of knowledge, namely relational 106 knowledge, qualitative knowledge, computational knowledge, 107 and context knowledge are used to bind together function, 108 behaviour, and structure in a functional design hierarchy. 109 The study presented in this paper differs from others in that 110 it has a distinct automated functional reasoning strategy, which 111 is based on a best-first heuristic search method. With our 112 proposed functional reasoning strategy, a set of physical behav- 113 iours can be reasoned out automatically from the desired 114 functions. The interconnection of these behaviours is possible