## 5 Application of the OW-Fxlms Algorithm to ANC of Interior Noise
### Application of Adaptive Algorithms to ANC for Interior Noise  
In order to drive the vehicle with the ANC system on the road, five speakers, a control computer, monitor, and the dSPACE control board were placed in the test vehicle, and the microphones were attached to the roof of the test vehicle. In this case, a multichannel ANC system was used. The algorithm is the expansion of a channel ANC. The Simulink based block diagram used for this test is plotted as shown in Figure 15. There are 5 subsystems which include adaptive order filter and OW-FXLMS algorithm to control the interior noise measured by 4 microphone and 5 secondary speakers. S1, S2, S3, S4 and S5 means the secondary speaker and M1, M2, M3 and M4 means the microphone attached in the car. The primary source which was recorded inside of test car and supplied to the multi-channel ANC system. In each subsystem, the OW-FXLMS algorithms update the adaptive filter using the error signals (E1, E2, E3, E4) measured from 4 microphones and primary source signal. For example, the output of subsystem 1 is the sound signal for speaker S1 sound and error signals (e1\(j\)) which is related to each \(j\)-th reference order signal. The sum of error signals (e1\(j\)) is the error signal of M1. In the real time process, primary source is not necessary and the signals from error microphones become noise source signal.  
Figure 14: Transfer function \(S(z)\) of the secondary path and impulse response \(s(n)\) of the secondary path. (**a**) Transfer function; (**b**) Impulse response.  
When the engine speed increased under a no-load condition, the ANC system was operated and the sound pressure of the interior noise was measured by error microphones. The engine speed was increased from 1000 rpm to 4500 rpm. The engine was under the no-load condition for this test, and the engine speed was increased rapidly from 800 rpm at idle to 4500 rpm during the course of 2 s. Figure 16a illustrates a comparison of the time history of the interior noise at the driver seat, which was controlled by two active control systems. Figure 16b illustrates the spectrum analysis of the interior noise signal. The PSD of the interior noise signal was reduced to 30 dB above 80 Hz. Figure 16c,d illustrate the results of order analysis of the interior noise. At 1200 rpm, there is a booming noise, and the other wide booming noise occurred from 3000 to 4500 rpm. These booming noises were attenuated by the controllers. The controller with the OW- FxLMS algorithm with a short filter length (\(L=30\)) demonstrated the best performance among the three algorithms. Since the optimal length of weight vector is 18,000/RPM, a short filter length (\(L=30\)) is sufficient for the control of these booming noises. This algorithm achieved a significant reduction in the interior noise around 4500 rpm, which is the second-order boom noise as shown in Figure 16c,d. The sound pressure level (SPL) of the interior noise was reduced to 25 dB.  
This booming noise corresponds to the resonance of the second path, as shown in Figure 14. The OW-FxLMS algorithm with a long length (\(L=300\)) and the FxLMS-algorithm-based adaptive notch filter reduced the booming noise, but not sufficiently, since the frequency bandwidth of the adaptive filters used for these algorithms is too narrow to reduce wideband noise, and the speed is changed too quickly (within 2 s). The disadvantage of the OW- FxLMS algorithm with a long length (\(L=30\)) is the generation of a beating sound at idle speed owing to its wide bandwidth. However, the sound pressure of the beat noise was too low to be heard.  
Figure 15: Multichannel ANC algorithm with 5 subsystems used for this test based on Simulink.