From Complex Problems to Simple Solutions: a Systematic Approach

Len Malinin

《International Journal of Systematic Innovation》 1卷1期 (2010/01) Pp. 61-71

https://doi.org/10.6977/IJoSI.201001_1(1).0005

摘要

A common problem familiar to many researchers dealing with complex technical systems (which can be formally described as non-stationary and/or non-linear multi-degree of freedom systems) is the need to find a meaningful solution which would have physical sense, would explicitly show dependence on the parameters and allow interpretation. Several decades ago the culture of building first approximation, asymptotical or slow time solutions was highly developed and practiced. Nowadays, with the advent of modern computers and numerical packages it often seems straightforward to generate a solution for the given set of parameters and boundary conditions. Therefore, the acuteness of this problem may be less obvious for the researcher. However, this ＂frontal attack＂ solution in some cases may be impractical (for instance, if this is an optimal control problem, the solution may require rapid changes of the control, which are hard to realize). In other cases, when the question arises as to what happens with the solution when the parameters change, the only answer may be to run the analysis again, which can be time consuming and still not show an interpretable dependency on the parameters. Using a model solution can also help in optimization of a complex system, requiring multiple design iterations. The transition to a model solution in this case can be based on identifying a single characteristic or parameters of the system which has to meet contradictory requirements. While identification of such parameter may not be obvious, it can lead to resolving the contradiction for the model system using known problem solving tools (from the game theory to TRIZ). This solution needs then be mapped back to the initial system. The contradiction-solving model solution often offers a way to reach the goal of the project in a different way, obviating the need for the intensive numerical solution. The approach is illustrated by three case studies.

關鍵字

closed-form solutions ； contradictions ； design optimization ； model system