REMOTE MICROPHONE SOUND-FIELD VIRTUAL SENSING METHOD USING NEURAL NETWORK FOR ACTIVE NOISE CONTROL SYSTEM

Active noise control has been implemented in various applications as a highly flexible, customizable and adaptive lightweight noise control technique which also serves as effective complementary counterpart to passive noise control techniques (such as sound absorbing packages). As on-chip computing power advances, low-cost implementation of active noise control algorithms targeting at controlling noise in large spatial regions is made more possible than ever before, which also excited another wave of active research on this topic in recent years after the emerging and flourishing active noise control research era in the 1990's. To control larger space, the use of a multi-input and output (MIMO) system is necessary, since the controller needs to be designed based on the measured sound information in the targeted control region (these sensors are referred to error microphones). However, it is not practical to add a limitless number of error microphones to populate the whole control region, and it is sometimes not even possible to locate the error microphone directly at targeted locations when the system is in operation due to practical constraints (e.g., in a car cabin, it is not possible to place microphones in people's ears). Therefore, the virtual sensing technique have been to predict the sound at targeted locations from remote measurements. One of the challenges in virtual sensing is its performance robustness under a time-varying acoustic environment. The purpose of this work is mainly to use the time-varying acoustic environment introduced by a person's head motion as an example case study to explore the possibility of virtual sensing the sound at the person's two ears for different head positions based on acoustic data measured at a small-sized microphone array located behind the head without any auxiliary motion tracking devices. More specifically, it is to develop a machine learning based data-driven model that uses the cross-spectral matrix of sound signals measured at the remote microphones to predict the frequency response functions between remote microphone measurements and sound at ears (i.e., the virtual sensing frequency response functions) under different head positions.

To get the data to train a neural network model, a measurement setup was suggested in the paper. A HATS dummy system that mimics the human hearing system with two microphones at the ear location was placed between the noise source and the reference microphone array composed of five microphones. Treating two ear microphone locations as the desired location of virtual sensors and microphone arrays as reference microphones, different measurements were taken by slightly changing the location and angle of the HATS dummy. A cross-spectrum density matrix was calculated with the measured data, and a frequency response matrix was calculated between the microphone array and the ear microphones, which would be used to make input data and target data for the neural network, respectively. With the cross-spectrum data, Dimension reduction was processed. A covariance matrix with the vectorized cross-spectrum density matrix was calculated, and power variation was evaluated to understand which frequency bands are sensitive to the change in the acoustic environment. In the hyperparameter choice, log-cosh was used for the loss function, LeakyRelu was used for the activation function, and Adam optimizer was selected. After comparing different learning rate strategies, a cosine decay with an initial learning rate of 0.003 was used for the learning rate setup. Frequency response with the target range from 51 Hz to 2000 Hz was estimated successfully with the listed neural networks setting with mean square error as 0.1205 and mean absolute error as 0.2025. Its error was compared with the standard deviation of the frequency response across the measurements. The error from the estimation was significantly lower than the standard deviation, which shows that the frequency response estimation using a neural network could increase the performance of active noise control with a virtual sensor even with the change in the acoustic environment.