Comparison of Robustness of Three Filter Design Strategies Using Genetic Programming and Bond Graphs

Abstract

A possible goal in robust design of dynamic systems isto find a system topology under which the sensitivityof performance to the values of component parameters isminimised. This can provide robust performance in theface of environmental change (resistance variation withtemperature, for example) and/or manufacturing-inducedvariability in parameter values. In some cases, atopology that is relatively insensitive to parametervariation may allow use of less expensive (loosertolerance) components. Cost of components, in someinstances, also depends on whether 'standard-sized'components may be used or custom values are required.This is true whether the components are electricalcomponents, mechanical fasteners, or hydraulicfittings. However, using only standardsized orpreferred-value components introduces an additionaldesign constraint. This chapter uses geneticprogramming to develop bond graphs specifying componenttopology and parameter values for an example task,designing a passive analog low pass filter withfifth-order Bessel characteristics. It explores threealternative design approaches. The first uses'standard' GP and evolves designs in which componentscan take on arbitrary values (i.e., custom design). Thesecond approach adds random noise to each parameter andevaluates each design ten times; then, at the end ofthe evolution, for the best design found, it 'snaps'its parameter values to a small (component specific)set of standard values. The third approach uses onlythe small set of allowable standard values throughoutthe evolutionary process, evaluating each design tentimes after addition of noise to each standardparameter value. Then the best designs emerging fromeach of these three procedures are compared forrobustness to parameter variation, evaluating each ofthem one hundred times with random perturbations oftheir parameters. Results indicated that, for thispreliminary study, the third method produced the mostrobust designs, and the second method was better thanthe first.