Optimized neural networks for modeling of loudspeaker directivity diagrams

For the electro-acoustical simulation of sound reinforcement systems, calculation and simulation of the sound field distribution requires measurement and storage of the frequency dependent directivity characteristics (level and phase) of the used loudspeaker models. In modern simulation programs, the spatial resolution can be less than five degrees in third-or even twelfth-octave frequency bands. Therefore, modeling of the directivity diagram of loudspeakers can reduce storage place and simulation time and may even increase the accuracy of the simulation. Modeling-in the sense of mapping the resulting enormous amount of measured data-can be realized very efficiently and with small approximation error using second order neural networks. To reduce the model development time, we in addition created a new adaptation rule for feedforward neural networks with improved convergence behavior. This is achieved only by using the training data and the output error to analytically determine values for the learning parameters' momentum and learning rate in each learning step. We show the advantages of using neural networks with optimized learning parameters by the example of modeling the measured directional response patterns of two real loudspeakers. For measurement we used maximum length sequences (MLSSA).