A Mathematical Functional Decomposition Approach Through Granularity Partition Process in Quotient Space

2018 ◽  
Author(s):  
Y. T. Li ◽  
Y. X. Wang
Keyword(s):  
Conceptual Design ◽  
Quotient Space ◽  
Lower Layer ◽  
Solution Space ◽  
Decomposition Process ◽  
Decomposition Approach ◽  
Functional Decomposition ◽  
Topological Structures ◽  
Functional Reasoning ◽  
Partition Process

Over the past decades, several methodologies have coalesced around the functional decomposition and partial solution manipulation techniques. These methodologies take designers through steps that help decompose a design problem and build conceptual solutions based on the intended, product functionality. However, this kind of subjective decomposition restricts solutions of conceptual design within designers’ intended the local, rather the whole, solution space. In such cases, the ability for AI-based functional reasoning systems to obtain creative conceptual design solutions is weakened. In this paper, a functional decomposition model based on the domain decomposition theory in quotient space is proposed for carrying out functional decomposition without needing functional reasoning knowledge to support. In this model, the functional decomposition is treated as a granularity partition process in quotient space composed of three variables: the domain granularities, the attribute properties, and the topological structures. The closeness degrees and the attribute properties in fuzzy mathematics are utilized to describe the fuzzy equivalence relations between the granularities in the up-layer and in the lower-layer of the functional hierarchies. According to the order characteristics in the partially sequential quotient space, based on the homomorphism principle, the attribute properties and the topological structures corresponding to the lower-layer of the functional hierarchies are constructed then. Here, the attribute properties are expressed with membership functions pointed to the lower-layer from the up-layer of the functional hierarchies, and the topological structures are expressed with matrixes and the directed function network represent the topological connections among the subfunctions in the lower-layer of the functional hierarchies. Through refining the functional decomposition process step by step, and traversing all tree branches and leaf nodes in the functional decomposition tree, the functional hierarchies are obtained. Since the functional decomposition process not need the user to indicate or manage desired functionality, the model presented in this paper can reduce designers’ prejudices or preconceptions on the functional hierarchies, as well as extend the solution space of conceptual design.

scholarly journals Supporting resilient conceptual design using functional decomposition and conflict resolution

2021 ◽  
Vol 48 ◽  
pp. 101262
Author(s):  
Xin Guo ◽  
Ying Liu ◽  
Wu Zhao ◽  
Jie Wang ◽  
Ling Chen
Keyword(s):  
Conflict Resolution ◽  
Conceptual Design ◽  
Functional Decomposition

Behavior-Form Double Directions Creative Conceptual Design Model and Its Quotient Space Implementation

2008 ◽  
Author(s):  
Yu-Xin Wang ◽  
Yu-Tong Li ◽  
Jian-Wei Wang
Keyword(s):  
Conceptual Design ◽  
Design Process ◽  
Quotient Space ◽  
Basic Structure ◽  
Basic Operation ◽  
Decomposition Tree ◽  
Function Decomposition ◽  
Design Variables ◽  
Set Up

This paper presents a novel indirect matching approach between the function layer and the form layer to enhance the capability for the FBS method to obtain the creative conceptual design results. Firstly, the basic operation actions set, which is composed of the basic operation actions obtained by decomposing each function in the lowest level of the function decomposition tree in the FBS model into the sub-functions, in the function layer is regrouped dynamically. This behavior regroup process has introduced the new design variables into the conceptual design process and leads the behavior creativity to produce. On the other hand, considering the multi-functions for each basic structure to have and representing these functions with the basic operation actions, then the basic operation actions set in the form layer is set up. Dynamic regrouping this set in the form layer, the new design variables has been introduced into the conceptual design process, and leads the form creativity to produce. Through the above behavior-form double directions creative process, the solution scope of the conceptual design is enlarged obviously. Therefore, the method present in this paper has enough capability to obtain the creative conceptual results. Furthermore, the model presented in this paper is represented with the quotient space mathematically. The case study has shown that in the function layer, through adjusting the attribute function, which determines the partition grain of the basic operation actions set in the function layer or in the form layer, the new behaviors can be generated.

scholarly journals Revisiting Problem-Solution Co-Evolution in the Context of Team Conceptual Design Activity

2020 ◽  
Vol 10 (18) ◽  
pp. 6303 ◽  
Author(s):  
Tomislav Martinec ◽  
Stanko Škec ◽  
Marija Majda Perišić ◽  
Mario Štorga
Keyword(s):  
Conceptual Design ◽  
Design Education ◽  
Design Research ◽  
Solution Space ◽  
Design Activity ◽  
Problem Solution ◽  
Conceptual Design Phase ◽  
Design Activities ◽  
Conventional Models ◽  
Concept Review

The conventional prescriptive and descriptive models of design typically decompose the overall design process into elementary processes, such as analysis, synthesis, and evaluation. This study revisits some of the assumptions established by these models and investigates whether they can also be applied for modelling of problem-solution co-evolution patterns that appear during team conceptual design activities. The first set of assumptions concerns the relationship between performing analysis, synthesis, and evaluation and exploring the problem and solution space. The second set concerns the dominant sequences of analysis, synthesis, and evaluation, whereas the third set concerns the nature of transitions between the problem and solution space. The assumptions were empirically tested as part of a protocol analysis study of team ideation and concept review activities. Besides revealing inconsistencies in how analysis, synthesis, and evaluation are defined and interpreted across the literature, the study demonstrates co-evolution patterns, which cannot be described by the conventional models. It highlights the important role of analysis-synthesis cycles during both divergent and convergent activities, which is co-evolution and refinement, respectively. The findings are summarised in the form of a model of the increase in the number of new problem and solution entities as the conceptual design phase progresses, with implications for both design research and design education.

A hybrid approach for the automation of functional decomposition in conceptual design

2016 ◽  
Vol 27 (4-6) ◽  
pp. 333-360 ◽  
Author(s):  
Lin Yuan ◽  
Yusheng Liu ◽  
Zhongfei Sun ◽  
Yanlong Cao ◽  
Ahsan Qamar
Keyword(s):  
Conceptual Design ◽  
Hybrid Approach ◽  
Functional Decomposition

Conceptual Design Method Based on Behavior Re-Creation

2007 ◽  
Vol 10-12 ◽  
pp. 198-202
Author(s):  
H.B. Miao
Keyword(s):  
Conceptual Design ◽  
Process Model ◽  
Design Method ◽  
Solution Space ◽  
The Novel ◽  
Creation Process ◽  
Design Scheme ◽  
Mechanical Products ◽  
Basic Behavior ◽  
The Given

Conceptual design for the mechanical products is the most important and complex phase. Most of the human’s creativity is exhibited in this phase. So many researchers in the world have made researches on its theory and methodology. So far there exists an evident limitation for the modern conceptual design methodology. That is to say, the design scheme obtained form conceptual design is only one solution to the given design problem, which cannot guarantee the creativity and novelty of the design scheme. In order to improve the creativity of conceptual design, the re-creation process model for the intelligent conceptual design is presented in this paper based on function-behavior-structure model. This model expanded the problem’s solution space by degrading the space of behavior and granularity, and describing the behavior space using the more basic behavior. The key of re-creation process model is the transformation of behavior and granularity space. Taking the theory of quotient space as the math description tool, the transformation for the space of behavior and granularity is studied in detail in this paper. At last, an example is given to prove that it is easy to obtain the novel and creative design scheme applying the method presented in this paper.

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