From Complex Problems to Simple Solutions: a Systematic Approach

Abstract

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. 

  The approach is illustrated by three case studies.