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A Study on the Influence of Speed on Road Roughness Sensing: The SmartRoadSense Case^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. A Study on the Vertical Acceleration Sensed in the Car Cabin

#### 2.1. Road Surface Model

#### 2.2. Quarter-Car Model of Suspensions

#### 2.3. The Power of Vertical Acceleration

## 3. System Architecture

## 4. Experimental Results

## 5. Improving Data Aggregation

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Frequency response of the system that relates the vertical acceleration in the car cabin to the vertical acceleration at ground level according to the quarter-car model.

**Figure 8.**${P}_{\mathrm{PE}}$ vs. speed together with the fitted gamma law for the motorway cluster.

**Figure 10.**${P}_{\mathrm{PE}}$ vs. speed together with the fitted gamma law for the trunk roads cluster.

**Figure 11.**Frequency histogram of the collected samples per speed related to the trunk roads cluster.

**Figure 12.**${P}_{\mathrm{PE}}$ vs. speed together with the fitted gamma law for the primary roads cluster.

**Figure 13.**Frequency histogram of the collected samples per speed related to the primary roads cluster.

**Figure 14.**${P}_{\mathrm{PE}}$ vs. speed together with the fitted gamma law for the secondary roads cluster.

**Figure 15.**Frequency histogram of the collected samples per speed related to the secondary roads cluster.

**Figure 16.**Spread of the whole data (primary roads green, secondary roads red, trunk roads blue, motorways gray).

**Figure 18.**Section of Central-East Italy with highlighted the roads covered by the SmartRoadSense project.

**Figure 19.**Plot of the typical roughness index calculated by SmartRoadSense over the map of Figure 18.

**Figure 20.**Plot of the new roughness index obtained after the application of (16).

**Table 1.**Coefficients of the Quarter-car transfer function using the parameters available in the literature.

${\mathit{K}}_{\mathit{s}}$, ${\mathit{K}}_{\mathit{t}}$, ${\mathit{C}}_{\mathit{s}}$, M, and m | $\mathit{A}\phantom{\rule{3.33333pt}{0ex}}\left({\mathbf{s}}^{4}\right)$ | $\mathit{B}\phantom{\rule{3.33333pt}{0ex}}\left({\mathbf{s}}^{3}\right)$ | $\mathit{C}\phantom{\rule{3.33333pt}{0ex}}\left({\mathbf{s}}^{2}\right)$ | $\mathit{D}\phantom{\rule{3.33333pt}{0ex}}\left(\mathbf{s}\right)$ |
---|---|---|---|---|

Davis and Thompson [41] | 2.653×10${}^{-6}$ | 0.1326×10${}^{-3}$ | 0.01651 | 0.06513 |

Butsuen [42] | 3.375×10${}^{-6}$ | 0.1078×10${}^{-3}$ | 0.01672 | 0.06250 |

Gillespie [35] | 3.375×10${}^{-6}$ | 0.1057×10${}^{-3}$ | 0.01673 | 0.06125 |

Fialho and Balas [43] | 5.356×10${}^{-6}$ | 0.1093×10${}^{-3}$ | 0.01909 | 0.05948 |

Verros et al. [44] | 7.500×10${}^{-6}$ | 0.2066×10${}^{-3}$ | 0.02717 | 0.09500 |

Allison (Comfort) [45] | 1.305×10${}^{-4}$ | 0.5943×10${}^{-4}$ | 0.65069 | 0.04930 |

Allison (Handling) [45] | 0.129×10${}^{-6}$ | 4.5278×10${}^{-3}$ | 0.64435 | 3.75576 |

Salem and Aly [46] | 4.883×10${}^{-6}$ | 0.1758×10${}^{-3}$ | 0.01750 | 0.09375 |

**Table 2.**Fitting parameters of $P\left(v\right)=\widehat{q}{v}^{\gamma}$. Coefficients (with 95% confidence bounds).

$\widehat{\mathit{q}}$ | γ | |
---|---|---|

$|{A}_{y}{|}^{2}$ | $26.60\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(15.78\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}18.01\times {10}^{-3})$ | $1.19\phantom{\rule{3.33333pt}{0ex}}(1.06,\phantom{\rule{3.33333pt}{0ex}}1.32)$ |

${P}_{\mathrm{PE}}$ | $14.93\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(18.54\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}23.62\times {10}^{-3})$ | $1.21\phantom{\rule{3.33333pt}{0ex}}(1.11,1.31)$ |

**Table 3.**Fitting parameters of ${P}_{\mathrm{PE}}\left(v\right)=\widehat{q}{v}^{\gamma}$. Coefficients (with 95% confidence bounds).

Road | $\widehat{\mathit{q}}$ | γ |
---|---|---|

Motorway | $16.89\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(15.78\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}18.01\times {10}^{-3})$ | $0.76\phantom{\rule{3.33333pt}{0ex}}(0.74,\phantom{\rule{3.33333pt}{0ex}}0.78)$ |

Trunk | $20.97\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(18.54\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}23.62\times {10}^{-3})$ | $0.79\phantom{\rule{3.33333pt}{0ex}}(0.75,\phantom{\rule{3.33333pt}{0ex}}0.83)$ |

Primary | $20.20\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(19.32\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}21.10\times {10}^{-3})$ | $0.77\phantom{\rule{3.33333pt}{0ex}}(0.76,\phantom{\rule{3.33333pt}{0ex}}0.79)$ |

Secondary | $24.82\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(23.64\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}26.03\times {10}^{-3})$ | $0.81\phantom{\rule{3.33333pt}{0ex}}(0.79,\phantom{\rule{3.33333pt}{0ex}}0.82)$ |

All | $49.52\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}(48.63\times {10}^{-3},\phantom{\rule{3.33333pt}{0ex}}50.42\times {10}^{-3})$ | $0.48\phantom{\rule{3.33333pt}{0ex}}(0.48,\phantom{\rule{3.33333pt}{0ex}}0.49)$ |

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**MDPI and ACS Style**

Alessandroni, G.; Carini, A.; Lattanzi, E.; Freschi, V.; Bogliolo, A.
A Study on the Influence of Speed on Road Roughness Sensing: The SmartRoadSense Case. *Sensors* **2017**, *17*, 305.
https://doi.org/10.3390/s17020305

**AMA Style**

Alessandroni G, Carini A, Lattanzi E, Freschi V, Bogliolo A.
A Study on the Influence of Speed on Road Roughness Sensing: The SmartRoadSense Case. *Sensors*. 2017; 17(2):305.
https://doi.org/10.3390/s17020305

**Chicago/Turabian Style**

Alessandroni, Giacomo, Alberto Carini, Emanuele Lattanzi, Valerio Freschi, and Alessandro Bogliolo.
2017. "A Study on the Influence of Speed on Road Roughness Sensing: The SmartRoadSense Case" *Sensors* 17, no. 2: 305.
https://doi.org/10.3390/s17020305