Active noise control at low frequencies for outdoor live music events using the conjugate gradient least square method

Sound field control can be applied to the problem of reducing noise emissions from outdoor live music events. One method employed in this type of applications is pressure matching. Different approaches can be used to find a solution to this problem. Many of these methods can provide reduction of more than 10 dB in the frequency range of a subwoofer, between 30 and 120 Hz, thus reducing the loudness to half the original.

Such a performance is adequate, but it comes with drawbacks and/or practical limitations such as side lobes that can create new problems in new areas, computational cost, difficult parameter selection, etc. The method proposed here uses the conjugate gradient least square to compute a solution while providing an easier way to find a suitable regularization and at the same time controlling the radiation pattern of the solution to reduce the possibility of side lobes.

In addition, the use of an active set-type methods allows to include explicit constraints on the amplitude of the solution to avoid amplification and non-linear behavior of the transducers. After introducing the theory, the performances are compared to other more established methods through simulations and outdoor measurements performed at a 2:1 scale to show properties and practical aspects of the method proposed.

These experiments show that 10 dB insertion loss are achieved over a broad frequency range with peaks larger than 20 dB. We investigate the difference in performance between the different methods and use simulated versus measured transfer functions to derive the filters. We also analyze the numerical properties of the solutions provided by the different methods and relate them to the spatial properties of the corresponding sound fields.

Furthermore, we present a convergence study to evaluate the effect that grids of different resolutions used in the simulations have on the insertion loss for different degrees of regularization. Finally, we present also a sensitivity analysis of the proposed method to uncertainties in the speed of sound and show how the regularization directly affects the robustness of the method against such inaccuracies.