Comparison of robustness of three filter design strategies using genetic programming and bond graphs

A possible goal in robust design of dynamic systems is to find a system topology under which the sensitivity of performance to the values of component parameters is minimized. This can provide robust performance in the face of environmental change (e.g., resistance variation with temperature) and/or manufacturing-induced variability in parameter values. In some cases, a topology that is relatively insensitive to parameter variation may allow use of less expensive (looser tolerance) components. Cost of components, in some instances, also depends on whether "standard-sized" components maybe used or custom values are required. This is true whether the components are electrical components, mechanical fasteners, or hydraulic fittings, However, using only standard-sized or preferred value components introduces an additional design constraint. This chapter uses genetic programming to develop bond graphs specifying component topology and parameter values for an example task, designing a passive analog low-pass filter with fifth-order Bessel characteristics. It explores three alternative design approaches. The first uses "standard" GP and evolves designs in which components can take on arbitrary values (i.e., custom design). The second approach adds random noise to each parameter; then, at the end of evolution, for the best design found, it "snaps" its parameter values to a small (component-specific) set of "standard" values. The third approach uses only the small set of allowable standard values throughout the evolutionary process, evaluating each design after addition of noise to each standard parameter value. Then the best designs emerging from each of these three procedures are compared for robustness to parameter variation, evaluating each of them with random perturbations of their parameters. Results indicated that, the third method produced the most robust designs, and the second method was better than the first.