# Auralization of Accelerating Passenger Cars Using Spectral Modeling Synthesis

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## Abstract

**:**

## 1. Introduction

## 2. Model Development

#### 2.1. Overview

**Figure 1.**Sketch of the geometrical situation showing the two source positions S1 and S2, the inclination angle of the road α, the distance D, the instantaneous vehicle speed v, emission angle $\phi $, immmission angle θ and source–receiver distance r.

**Figure 2.**Simulation flowchart of the auralization of accelerating passenger cars. The input variables marked by a * are time dependent.

#### 2.2. Emission Module

#### 2.2.1. Sound of Tires

#### 2.2.2. Driving Dynamics

**Figure 3.**Simulation results: The upper graphs (

**a**,

**b**) show two simulated engine condition courses of an accelerating Ford Focus 1.8i with different accelerations and driving styles. The gray triangles show the interpolation grid spanned by the measuring points marked as circles, as introduced in Section 2.2.3. The lower two graphs (

**c**,

**d**) show the spectrograms of the corresponding synthesized pass-by sounds (normalized to 0 dB). Their calculation is elucidated in Section 2.3.

#### 2.2.3. Sound of Propulsion

#### 2.3. Propagation Filtering

- Propagation delay
- Doppler effect (frequency shift and amplification)
- Convective amplification
- Geometrical spreading
- Ground reflection
- Air absorption

#### 2.3.1. Effects Due to Source Motion and Propagation Delay

**Figure 6.**Non-linear distortions (aliasing) due to different resampling strategies: linear interpolation (

**a**) and Hamming sinc interpolations with different filter lengths, $b=10$ for (

**b**) and $b=100$ for (

**c**), respectively. The simulation was performed for a source emitting a 1 kHz pure tone that travels at constant speed $v=150$ km/h and passes a static receiver at a distance of $D=7.5$ m.

#### 2.3.2. Ground Effect

**Figure 7.**Simulated ground effect spectra for a point source at a height of 0.3 m in the reference situation (

**a**) with a receiver at a height of 1.2 m at a horizontal distance of $D=7.5$ m and propagation over hard ground (flow resistivity 20,000 kPa·s·m${}^{-2}$); and a distant situation (

**b**) with a receiver at a height of 2 m at horizontal distance $D=100$ m and propagation over grassy ground (flow resistivity 200 kPa·s·m${}^{-2}$).

#### 2.3.3. Air Absorption

#### 2.4. Reproduction Rendering

## 3. Model Parameter Estimation

#### 3.1. Tire Noise

**Figure 8.**Photographs showing the measurement set-ups for tire noise (

**a**) and propulsion noise (

**b**). In (

**a**), the coast-by situation is depicted with two measurement microphones placed at different distances and a camera connected to a laptop; (

**b**) shows the lab with a passenger car on the chassis dynamometer, the airstream fan in front of the car and two microphones on the floor at the left-hand room edge (emission angles $\phi ={60}^{\circ}$ and 120${}^{\circ}$).

**Figure 9.**Measured tire noise regression parameters ${A}_{i}$ (

**a**) and ${B}_{i}$ (

**b**) of 13 tires and the values according to the Harmonoise model [21] (dotted lines).

#### 3.2. Propulsion Noise

**Figure 10.**Signal analysis flowchart to obtain the synthesizer parameters of propulsion noise as described in Section 2.2.3 from audio recordings.

#### 3.2.1. Resampling

**Figure 11.**Normalized spectrogram (

**a**) of the measured sound pressure signal with tracked double ignition frequency (drawn as a black line) and power spectral density (

**b**) of the original and asynchronously resampled sound pressure signal, respectively. The recording was conducted at the rear of the BMW with an inline, four-cylinder engine idling at 1100 rpm.

#### 3.2.2. Order Analysis

**Figure 12.**Magnitude frequency response of the engine order analysis filter bank (

**a**) and engine order suppression filter (

**b**) for engine speed $n=1000$ rpm, engine orders $\nu =1,1.5,2,...,15$ and ${N}_{\mathrm{cyl}}=4$.

**Figure 13.**Comparison of engine order levels with idling engine (white) and full load (black) at 1000 (

**a**) and 3000 rpm (

**b**). Recorded at the rear of a VW Touran 1.6 FSI.

**Figure 14.**Comparison of sound pressure signals of a recording (

**a**) and the corresponding synthesis consisting of engine orders with estimated phases (

**b**). For the purpose of illustration only, the four dominant engine orders (colored lines) are used. The recording was conducted at the rear of a Ford Focus 1.8i at 1000 rpm and full load.

#### 3.2.3. Noise Analysis

**Figure 15.**Power spectral densities illustrating the effect of the order suppression filter, which is applied to a recording of an inline, four-cylinder engine idling at 4000 rpm.

**Figure 16.**Level fluctuation signal (

**a**) of the 2.5-kHz 1/3 octave band and its square root of the autocorrelation function (

**b**) from a recording taken at the front of an idling four-cylinder diesel engine at 870 rpm, corresponding to an ignition period of 34 ms. The right plot indicates that for this band, the level standard deviation, σ, amounts to about 5 dB.

**Figure 17.**Level fluctuation standard deviations, σ, in 1/3 octave bands measured at the front of two diesel engine and three gasoline engine cars idling at 900 rpm.

#### 3.2.4. Background Noise Corrections

**Figure 18.**Normalized spectrogram of a microphone position in front of a Ford Focus 1.8i at 4000 rpm and full load on the dynamometer. The dropping tonal component around 100 Hz stems from the briefly switched off airstream fan of the lab.

#### 3.2.5. Backpropagation

## 4. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix Code of the Frequency Tracking Algorithm

${\text{\%initialization}}$ |

M = size (q,1) ; ${\text{\%totaltimesteps}}$ |

N = size (q,2) ; ${\text{\%totalfrequencybins}}$ |

Q(1 ,:) = q(1 ,:) ; ${\text{\%initoftotalscoreatfirsttimestep}}$ |

${\text{\%forwardprocessing}}$ |

for m = 2:M |

for k = 1:N |

kb = max(k−c,1) |

kt = min(k+c,N) |

[max Val, maxIdx] = max(Q(m−1,kb:kt)) |

Q(m,k) = q(m,k) + maxVal; |

B(m,k) = kb + maxVal − 1; |

end |

end |

${\text{\%endpointofoptimalpath}}$ |

[~, P(M)] = max(Q(M,:)); |

${\text{\%backtracking}}$ |

for m = M:−1:2 |

P(m−1) = B(m,P(m)); |

end |

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Pieren, R.; Bütler, T.; Heutschi, K. Auralization of Accelerating Passenger Cars Using Spectral Modeling Synthesis. *Appl. Sci.* **2016**, *6*, 5.
https://doi.org/10.3390/app6010005

**AMA Style**

Pieren R, Bütler T, Heutschi K. Auralization of Accelerating Passenger Cars Using Spectral Modeling Synthesis. *Applied Sciences*. 2016; 6(1):5.
https://doi.org/10.3390/app6010005

**Chicago/Turabian Style**

Pieren, Reto, Thomas Bütler, and Kurt Heutschi. 2016. "Auralization of Accelerating Passenger Cars Using Spectral Modeling Synthesis" *Applied Sciences* 6, no. 1: 5.
https://doi.org/10.3390/app6010005