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Mtt-k. Mat*. 77m, cwy VoL 27. No. 4. pp. 491-505, 1992 0094-114X/92 ~Lq.00 + 0.00 Printed in Great Britain. All r iots reserved Co~t G 1992 F,a,atom Prem Ltd

MODELING KNOWLEDGE-BASED SYSTEM FOR OPTIMUM MACHINE DESIGNt,~:

JERZY KOWALSKI ReMo Expert Group, WDK Ostrorop 35, 60-349 Poznan, Poland

(Received i November 1987". received for publication 5 November 1991)

Almtract--This paper describes a problem and procedure-oriented system for using modeling knowledge, to enable the increase of machine performances for different design Ionls. The system organization and operation has been outlined. The applications to solve design optimization problems for typical machine construction have been given. The perspective for complex machine modelinig and optimization has been discussed indodins system location.

INTRODUCTION Dixon and Simmons gave a research program of expert systems for mechanical design [I]. Important applications of a knowledge-based system to a mechanical design were given by Dym [2].

Li and Papalambros have formulated an optimization knowledge-based system emphasising application of symbolic language for preprocessing of optimum design models [3]. However, the authors have not searched for the mathematical model of the design object, which would be adequate for the real design problem. The objective of this paper is to present a modeling knowledge-based system for optimum design of machine construction which facilitates the designer to create an adequate and easy solvable mathematical model of the design object. The system takes into account the degree of complexity for the design structure including a variable number. A variety of design problems and conditions, i.e. need for carrying out parametric, substructural and structural optimization which influences the model production, has been also considered in the system.

Parametric optimization

Based on the selection of an optimum set of variable values for the design object (or object series-type) with a given structure for the assumed optimization criterion by satisfying all constraints imposed on the construction.

Substructural optimization

Based on the selection of an optimum variant of design pair structure for the design object with a given structure from the set of variants for the assumed optimization criterion.

Structural optimization

Based on the selection of an optimum structure variant for the object exactly fulfilling the fixed parameters from the given set of compatible variants considering a production and operating for the assumed selection mask, i.e. a set of pairs of criteria and their scales (%) portions. In this way, the system presented is a problem and procedure-oriented system for using modeling knowledge, to aid the designer's effort in improving machine design performances.

The modeling knowledge-based system for optimum design of machine construction is based on a review of 39 expert references (Moses, Siddall, Canada; Feldbrugge, The Netherlands; Eschenauer, Fandei, Koller, Pahl, Fed. Rep. Germany; Shinno, Japan; Brandt, Golinski, Lesniak,

tBased on the author's lecture given in Stutqgart and Aachen Universities, Fed. Rep. Germany within the DAAD Professors Interchange Prolgram (1990).

~Dedictated to my mother Sabina Kowalska, 1904-1981.

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Pogorzelski, Urbaniec, Poland; Diechtiarenko, Pavlov, Savcenko, Soviet Union; Gregory, Jones, Moe, Pierson, U.K.; Alexander, Freudenstein, Johnson, Klir, Lee, Linstone, Nadler, Rao, Seireg, Wilde, Zhou, U.S.A. [4-36, 60-62] and the author's own research.

The system presented is a synthesis of the author's paper published in the period of 1981-1987. It is based on the abstraction process carried out on quantity, idea, methodology, stratt~ and system levels, nnq~-tively. Figure I shows the creation process for the system. It contains 53 rules and 3 principles for the system-using listed in the paper. However, to obtain details, the author's references [37-39] are recommended.

The rules occurring in the system strongly increase the quality of the optimization model for the design object in the direction of its higher adequacy level to a real design problem and easy solution using a computer. Basically, it is obtained, utilizing the author's idea of a hierarchic two level optimization modeling system controlled according to the principles of classification of the object models as well as principles for selecting optimization criterion and constraints [37, 38, 41]. To fulfil their utility, the rules must also integrate design process, systems theory and the designer's intellect features.

It is noteworthy that the author has also made efforts to adapt Pavlov's hierarchic three level mathematical modeling system [20] to optimum design of machine construction. Because of certain defects of the system, it appeared to be, however, impossible [37].

In this way, the system presented may not be treated as any sophisticated front-ended optimization algorithm, but an effective aid to arrive at the optimized machine design.

The main application fields of the system are: static optimization based on nonlinear program- ming and determined models. However, it contains general principles for creating a possibly adequate model for optimization problems under risk and uncertainty.

Referring to dynamic optimization, the formulation of the model located at the upper level of abstraction for this problem appeared to be difficult [39]. Therefore, the dynamic optimization has been excluded from the system.

The system presented is coherent. However, the generalization degree for these considerations must be properly balanced. It would be aimless to search for much far-reaching correctness occurring in the models of design objects differing by their application.

The system presented is not a black box, but a tool which facilitates the creation of conscious product models by the designer. Therefore, it can not be treated as a panacea for all problems occurring in the design optimization of mechanical systems.

SYSTEM ORGANIZATION AND OPERATION Let us describe the system organization and operation. The system is defined as the ordered

doublet: MgBS ffi (SSU, ASU) , (l)

where $$U is a STRATEGY subsystem, and ASU denotes an APPLICATION subsystem. One may treat the STRATEGY subsystem as the ordered doublet:

SSU ffi ~,K. M) . (2)

Here K is a set of knowledge base, including inference engine, creating the heart of the system, and M is a set of methodologies for different design problem classes.

The set of knowledge base, including inference engine, is given as the ordered I 1 component set:

K ffi (P,); i ffi I, 2 . . . . . !!. (3)

Here PI is an information library subset including strategy skeletal idea, but the subsets P2-PII are operating subsets.

The subset P, contains the following input information: 1. Expert reference lists in the field of design optimization of mechanical sys-

tems [4-36]. 2. Strategy objective [37, 38, 41].

494 Jmz~ Kow~

3. Main application fields: static optimization based on nonlinear programming parametric, substructural and structural optimization; determined models [37, 38, 41].

4. Basic ideas outlined [37, 38, 41]. The operation subsets are arranged as follows:

p, m Subset of the rules of thumb for creating hierarchic two-level optimiTa_tion modeling system (rules 1-4).

P3 = Subset of the rules of thumb for classifying optimization models (rules 5-6). P, m Subset of the rules of thumb for selecting optimization criterion (rules 7-15). ,as =' Subset of the rules of thumb for selecting constraints (rules 16--21). /'6 = Subset of the rules of thumb for an integrating modeling idea within design

process (rules 22-25). /'7 = Subset of the rules of thumb for a connecting modeling idea within bases of

the systems theory (rules 26-28). Ps--Subset of the rules of thumb for complex product optimization (rules

29-3O). /'9 = Subset of the rules of thumb for approximate optimization of construction

shape (rule 3 I). Pm= Subset of the rules of thumb for minute detail of the modeling idea in

optimization problems under risk and uncertainty (rules 32-33). P,, = Subset of the rules of thumb for connecting the modeling idea within designer's

intellect features (rules 34-35). The rules are as follows:~"

i. Definition of the optimization model including index assessment for object reflexion in the model [37, 38, 41].

2. Brief basic pre-design for the optimization modeling system: creation ofan object kinematic diagram, structure graph and geometric models of design elements; variable identification; initial selection of optimization criterion [37, 38, 41].

3. General element specification of an analytic-structural model (upper level of abstrac- tion) [37, 38, 41] including object-system modeling [43].

4. Specification of quantity model elements (lower level of abstraction) including principles for model transformation [37, 38, 41].

5. Criteria for product model classification: means of interrelation: optimization criterion *-. object elements; effects of object structure and body complexity [37, 38, 41].

6. Basic classes and subclasses of product models [37, 38, 41]. 7. Set of machine construction features for creating optimization criteria [37, 38, 41] including

decomposition problem [43]. 8. Recommendations for selecting the optimization criterion type based on objective function,

comparative factor, scaling and preference functions including utilization assessment for fuzzy set theory [38, 41].

9. Recommendations for polyoptimization problem formulation [37, 41]. 10. Recommendations for decomposition-making based on variable number and its limitation

[37, 38, 43]. 11. Definition of additive dimensionless scaling function and preference function (scaling

function interrelated with distance function) for uniform not too large objects including geometric representation [38, 40-42].

12. Definition of the scaling function for objects-systems [37, 38, 41,43]. 13. Recommendations for scaling factor selection [38, 41]. 14. Method for series-type optimum design [37, 41,44]. 15. Assessment of direct interrelation: product .-. optimization criterion [37, 41]. 16. General classification of constraints [37, 38, 41]. 17. Recommendations for explicit constraint formulation [37, 38, 41].

tDue to limitations, structural components of particular rules have not been given.

18. Reoommendations for elastic preference of inequality constraints: their input for not too large uniform objects [37, 38, 41]; equality constraint formulation for object-systems aided by using artificial variables [37, 38, 41, 43].

19. Application of transcendental, differential and integral equations to constraint formu- lation [38, 411.

20. Constraint significance analysis [38, 41]. 21. Recommendations for optimum decision making aided by different calculation methods

for design pairs[37, 38, 41]. 22. Basic location of the modeling idea in the design process [37, 38, 41]. 23. Step sequence for object pre-design incorporating modeling idea [37, 38, 41]. 24. Recommendations for using effective numerical methods for solving models [37, 38]. 25. Modeling system revision [37, 38, 41]. 26. Subordination degree of modeling idea elements into fundamental aspects of systems

theory (model design and justification) [41]. 27. Subordination degree of modeling idea elements into fundamental operating aspects

(control and communication aspects)[41]. 28. Possibilities and limitations of modeling idea [38, 41]. 29. Three step method for complex product optimization [37, 38, 41]. 30. General recommendations for using uniform means of particular optimization problem

formulation by nonlinear programming for the manufacturing processes of optimized construc- tion [37, 38, 41].

31. General recommendations for variable selection for optimum outer contour problem of the constrnction [41].

32. General recommendations for creating product models at upper levels of abstraction for optimization problems under risk and uncertainty [37, 38].

33. General procedure for creating product models at lower levels of abstraction for optimization problems under risk [37].

34. General classification of the factors combined with a structure of designer's intellect model including elements inspiring development of his features [38, 41].

35. Subordination degree of modeling idea elements into designer's intellect features [41]. The set of methodologies for different design problem classes is given as the ordered doublet:

Here

M -. ; ,MC, MS) . (4)

MC ,~ Subset of methodologies for creating optimization models for classes of recurrent objects in machine design (rules 36-43). It contains the following elementary subsets: MC I for the class "gears and gearboxes" and MC2 for the class "screw construction".

MS -, Subset of methodology for selecting optimum structure for the object exactly fulfilling the fixed parameters (rules 44-47).

The rules are as follows: 36. Characteristic qualities of models for a class of recurrent objects at upper level of

abstraction for MC! [37, 38, 47] and for MC2 [48]. 37. Characteristic qualities of models for a class of recurrent objects at lower level of

abstraction [37, 38, 46--48]. 38. Application of methodically formulated models for a class of recurrent objects to practical

construction [37, 38, 47, 48]. 39. Procedure for creating variants of design pair structure for a class of recurrent objects

[37, 38, 47, 48]. 40. Procedure for arranging variables and parameters for a class of recurrent objects

[37, 38, 47, 48]. 41. Recommendations for selecting optimization criterion for a class of recurrent objects

[37, 38, 46-48]. 42. Recommendations for constraint formulation for a class of recurrent objects including

making rational simplification [37, 38, 47, 48].

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43. Application of methodical recommendations for model creation for a class of recurrent objects to practical design [37, 38, 47, 48].

44. Four step method of structure selection for the object [38, 45]. 45. Recommendations for selection mask-assuming [38, 45]. 46. Recommendations for point allocation for particular strucural variants and criteria [38, 45]. 47. Application ofthe method ofstructure selection to design self-loading trailer geurbox [38, 45].

The APPLICATION subsystem creates a model bank for typical machine construction. It may be treated as the ordered triplet:

ASU = , (5)

where OB is a set of typical design objects, CL denotes a set of optimization model classes and subclasses, and RE i...