A conditional filter for reduction of the search space in genetic algorithm optimisation of sensor and actuator location in active vibration control

This paper concerns active vibration reduction of flexible structures with low natural damping using piezoelectric patches bonded to the surface. Optimisation of the location of these transducers can be approached using the genetic algorithm, but the search space is very large for complex structures with the multiple transducers needed to suppress several vibration modes. A placement strategy including conditional filter is proposed to reduce search time, achieve global optimal solution with genetic algorithm program stability, and hence increase the efficiency of the optimisation process. This filter works by eliminating repeated genes in the chromosome and by exploring symmetries in the vibrating structure. An isotropic plate is investigated according to Hamilton's principle and finite element method based on the first order shear deformation theory to account for the effects of piezoelectric mass, stiffness and electromechanical coupling. The genetic algorithm including the conditional filter was applied to locate four and ten sensor/actuator pairs based on minimization of linear quadratic index as an objective function, suppressing the first six vibration modes of a cantilever plate. The results are compared with previous published results for the same problem. It is shown that the placement strategy using the conditional filter greatly reduces the run time to find the global optimal solution, and that the vibration reduction achieved is an improvement on previous published results.