Optimization methods for choosing sensor and actuator locations in an actively controlled double-panel partition

The present study addresses the optimization of the locations of the error sensors and the control actuators in an active noise control system. This system is implemented on a double- panel partition in order to improve its sound insulation characteristics in the low frequency range. A model of the active control system, allowing both structural and acoustical control, is developed and combined with a finite element model of the double-panel partition. This yields a discrete description of the actively controlled structure, resulting in a combinatorial optimization problem. As the optimal solution for this problem can only be found by enumeration, a genetic algorithm is generally used to generate a near-optimum solution, requiring however a lot of useless function evaluations. In order to overcome this severe drawback of the genetic algorithm a number of non-linear optimization methods are also tested. As these methods can only handle continuous problems, interpolating functions are used to approximate the dynamic behavior of the structure in between the finite element nodes. Finally the performances of the methods are compared in terms of quality of the obtained solution, computation time and algorithm complexity. This comparison shows that the best gradient method converges faster and yields a better final solution than the best genetic algorithm.