Calculating frequency response functions for uncertain systems using complex affine analysis

This paper is concerned with the effect of parametric uncertainty upon the response of mechanical systems. Two uncertainty propagation techniques are employed and compared against a benchmark based upon randomly scanning input parameter ranges. The first technique, complex interval analysis, is computationally very efficient but suffers from the issue of dependency which may result in large overestimation of the system response. The second technique, namely complex affine analysis, is presented here for the first time and it keeps track of variable dependencies throughout the calculation thus limiting overestimation, albeit at some computational expense. The methods are demonstrated on the problem of calculation of the frequency response functions of a simple lumped mass system with uncertain parameters for purposes of transparency of the presented ideas, although these ideas are equally applicable to more complex systems. It transpired that the complex affine analysis performed significantly better than its interval counterpart. (c) 2005 Elsevier Ltd. All rights reserved.