Computer-aided solution to optimization problems in aerospace design engineering

Аuthors

Brodsky A. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: brodski1954@gmail.com

Abstract

Optimization problems are the most often solvable in aerospace design engineering. That’s why tools for solving such problems are really requested and used both in autonomous engineering procedures, mainly aided at search for Pareto solutions, and in their results agreement. Various optimization methods are developed and widely used in practice including in interactive operation. But a designer should know and understand specific conditions, which the constituent elements of formal optimization problem should follow. He also should be able to manually convert his initial applied problem to the form of the relevant optimization algorithm class. If one takes into consideration that the majority of practical problems enable only computational solution, a designer should have knowledge in programming to get the integrated program. The objective of this paper is to develop an approach to programming components construction for solving optimization problems in CAD system so that to assure automation of the whole solution process starting from a verbal description to receiving final results.
The approach is based on the fact that current automation facilities are one of CAD system components. Another obligatory CAD components are mathematical models of design products, e.g. models implemented as application package . It is proposed to use structural properties of mathematical models variables and relations to define the elements of optimization problem formal definition: criteria, controlled variables, target function, functional constraints and to check its validation.
For the used mathematical model for one verbal description there might a lot of correct formal definitions. Thus it is necessary to evaluate their computational complexity. Such evaluation can also be made by analyzing structural properties of the model based on the possibility of formal problem decomposition into the tasks of smaller dimensionality and on exclusion of required calculations out of an optimization cycles. There are no doubts that the final choice of the variant to be used should be made only by a designer himself.
In this paper the requirements are formulated to the computer-aided tools of optimization problems solving in CAD system. The main operators are identified, they implement the following:

• conversion from aninitial verbal description oftask, which was performed byadesigner, tothe formal definition predefined inoptimization methods;
• analysis of initial task validation and its correlation with the used model and the formal conditions of optimization;
• identification of incorrectness reasons;
• generation of many correction variants with evaluation of the necessary computable labor content;
• algorithmization ofthe general procedure ofthe solving.

The general operator scheme of automation instruments operation is formed.
The integration of optimization methods and algorithms of calculation planning by using mathematical models of aerospace engineering makes it possible to sufficiently extend the possibility of solving different engineering tasks in CAD systems.
Taking into consideration the proposed approach in realizing CAD program components one can form computer-aided procedures for searching optimal project decisions and provide their high efficiency as well as convenience for designers.

Keywords:

design process, aerospace engineering, CAD system, optimization problem, method of optimization, mathematical model, structural properties, operator scheme

References

1. Smirnov O.L., Padalko S.N., Piyavskii S.A. SAPR: formirovanie i funktsionirovanie proektnykh module (CAD systems: development and operation of project modules), Moscow, Mashinostroenie,1987, 272 p.
2. Tamm B.G., Tyugu E.Kh. Prikladnaya informatika, Moscow,1985, no.1, pp.5-25.
3. Reklaitis G., Ravindran A., Ragsdell K. Optimizatsiya v tekhnike (Engineering Optimization), Moscow, Mir,1986, 320p.

Download