Reasoning

path type III F31

F4

Reasoning F41 F42

path type IV

F5

Combined F51

reasoning path

F511 F512

F513

Legend

Structure layer

S1

S2

S21

S3

S31

S42

S41

S5

S512

S511

S513

functions.

In this functional modeling framework, if a desired function (or physical structure) may only be actualized when other functions are present, the latter should first be synthesized as supportive functions to generate a more complete functional design. On the other hand, a desired function is not decomposed into sub-functions, unless a matching physical structure can not be found to realize the desired function. The proposed approach can prevent the domain problem being decomposed “too fine”, causing combinatorial explosion.

Generally, a desired function (overall functional requirement, sub-function or supportive function) or a physical structure can be accomplished in the following generalized functional reasoning path types:

• Functional reasoning path type I: a desired function is realized by a physical structure through function-structure mapping.

• Functional reasoning path type II: a desired function is supported by supportive functions through functional supportive synthesis, which are then realized by physical structures.

Function

Structure

Decomposed into or Realized by relation

Supported by relation

Figure 2. The features of the proposed functional modeling framework.

• Functional reasoning path type III: a physical structure is supported by supportive functions through functional supportive synthesis, which are then realized by other physical structures.

• Functional reasoning path type IV: a desired function is broken down into simple sub-functions through functional decomposition, which are then realized by physical structures.

For example, in the functional reasoning path type I, a desired function F1 in the function layer is realized by a physical structure S1 in the structure layer through function-structure mapping process. However, if a desired function (or physical structure) may only be actualized due to the presence of some other functions, the latter should first be synthesized

as supportive functions to generate a more complete functional design through functional supportive synthesis process. For example, in functional reasoning path type II, a desired function F2 may only be fully actualized due to the presence of a supportive function F21. Both functions F2 and F21 are then realized by physical structures S2 and S21 respectively. In functional reasoning path type III, a physical structure S3 may only be fully actualized due to the presence of a supportive function F31 that is then realized by the other physical structure S31. If a desired function is too complex and cannot be realized by any available structure directly, it will be broken down into simple sub-functions for further function-structure mapping. For example, in functional reasoning path type IV, a desired function F4 is first decomposed into sub-functions F41 and F42, followed by a further function-structure mapping process.