# A Weigh-in-Motion Characterization Algorithm for Smart Pavements Based on Conductive Cementitious Materials

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## Abstract

**:**

## 1. Introduction

## 2. Smart Pavement-Based Weigh-In-Motion System

#### Measurement Principle

## 3. Algorithm for WIM Characterization

- Identification of weights, time shifts, and number of axles from the signal collected in the initial pavement section by minimizing Equation (10);
- Reconstruction of the signal (Equation (9)) from the initial pavement section;
- Temporal identification of vehicle through the computation of correlation between the reconstructed signal and the measured signal from the subsequent pavement sections; and
- Determination of vehicle speed through the averaging of temporal identification data.

## 4. Numerical Simulations

#### 4.1. Numerical Model

#### 4.2. Results and Discussion

#### 4.2.1. Results of WIM

#### 4.2.2. Noise Study

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Smart pavement-based weigh-in-motion (WIM) system illustrating (

**a**) the integrated smart pavement within the bridge system; and (

**b**) the electrical principle.

**Figure 2.**Illustration of the piezoresistive material with two different electrode configuration showing the orientation of mechanical stresses $\sigma $: (

**a**) electrode setup adapted from [51]; and (

**b**) smart pavement segment between two consecutive electrodes.

**Figure 3.**(

**a**) The unloaded and loaded (at time t) voltage distributions across electrodes (

**a**) for the axle located between the 1st and 4th electrodes; and (

**b**) for the axle located between the 4th and 6th electrodes. (

**c**) Typical basis signal $\psi \left(t\right)$ obtained from the passing of an axle.

**Figure 4.**Comparison of low and high frequency components of a typical signal: (

**a**) time domain; and (

**b**) frequency domain.

**Figure 5.**Basis signal search procedure: (

**a**) normalization and matching of the signals to find the first basis signal ${\mathbf{H}}_{1}{\psi}_{1}^{H}$; (

**b**) matching of remaining signal to find the second basis signal ${\mathbf{H}}_{2}{\psi}_{2}^{H}$; (

**c**) visualization of time shift operators ${H}_{1}$ and ${H}_{2}$, and scale factors ${a}_{1}$ and ${a}_{2}$; and (

**d**) reconstructed signal.

**Figure 6.**(

**a**) Finite element model (FEM) of the bridge showing the change in potential along smart pavement sections, where smart pavement sections are under a charge of 30V, and (

**b**) analytical versus numerical influence lines for the Von Mises Stress at the end of the bridge.

**Figure 7.**Weight estimations for the first simulation case; (

**a**) type 1 truck; (

**b**) type 2 truck; and (

**c**) type 3 truck.

**Figure 9.**Axle span-to-vehicle length estimation errors (with +/- standard deviation intervals) as functions of noise level for: (

**a**) type 1 truck; (

**b**) type 2 truck; and (

**c**) type 3 truck.

**Figure 10.**Mean weight estimation error (with +/- standard deviation intervals) as functions of noise level for: (

**a**) type 1 truck; (

**b**) type 2 truck; and (

**c**) type 3 truck.

**Figure 11.**Mean speed estimation error (with +/- standard deviation intervals) as functions of noise level for: (

**a**) type 1 truck; (

**b**) type 2 truck; and (

**c**) type 3 truck.

**Table 1.**Cross-correlation tables of the estimated signals (${\widehat{\mathsf{\Psi}}}^{H}$) against measured signals (${\mathsf{\Psi}}^{H}$) from each pavement section (P1 to P3) under the first simulation case for each type of truck:

Type 1 | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ | Type 2 | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ | Type 3 | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.91 | 0.48 | ${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.95 | 0.53 | ${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.97 | 0.35 |

${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.74 | 1.00 | 0.63 | ${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.73 | 1.00 | 0.70 | ${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.69 | 1.00 | 0.70 |

${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.43 | 0.54 | 1.00 | ${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.66 | 0.57 | 1.00 | ${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.25 | 0.44 | 1.00 |

**Table 2.**WIM simulation inputs and outputs, listing results for the estimation of axle spacings (axle sp) and axle weights (axle w), along with the percentage estimation error (err)).

Simulation Input | Simulation Output | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Eurocode | simulation case 1 | simulation case 2 | ||||||||

axle sp | axle w | axle sp | err | axle w | err | axle sp | err | axle w | err | |

(m) | (kN) | (m) | (%) | (kN) | (%) | (m) | (%) | (kN) | (%) | |

type 1 | 4.5 | 90 | 4.5 | 0 | 90 | 0 | 4.5 | 0 | 81 | 10 |

190 | 196 | 3 | 177 | 7 | ||||||

type 2 | 4.2 | 80 | 4 | 4 | 77 | 4 | 4.5 | 7 | 93 | 16 |

1.3 | 140 | 1.5 | 15 | 125 | 10 | 1 | 23 | 162 | 15 | |

140 | 155 | 10 | 115 | 17 | ||||||

type 3 | 3.2 | 90 | 3 | 6 | 91 | 1 | ||||

5.2 | 180 | 5.5 | 6 | 171 | 5 | |||||

1.3 | 120 | 2 | 53 | 148 | 23 | |||||

1.3 | 120 | 1.5 | 15 | 158 | 32 | |||||

120 | 46 | 62 |

**Table 3.**Cross-correlation tables of the estimated signals (${\widehat{\mathsf{\Psi}}}^{H}$) against measured signals (${\mathsf{\Psi}}^{H}$) from each pavement section (P1 to P3) for the three types of trucks under $\alpha =$ 2.5%, 10%, and 20% levels of noise.

$\mathit{\alpha}=2.5\%$ | $\mathit{\alpha}=10\%$ | $\mathit{\alpha}=20\%$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{1}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{2}}^{\mathit{H}}$ | ${\mathbf{\Psi}}_{\mathit{P}\mathbf{3}}^{\mathit{H}}$ | ||

${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.91 | 0.48 | 1.00 | 0.96 | 0.46 | 0.73 | 1.00 | 0.91 | |

Type 1 | ${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.72 | 1.00 | 0.66 | 0.73 | 1.00 | 0.48 | 1.00 | 0.75 | 0.65 |

${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.42 | 0.50 | 1.00 | 0.31 | 0.47 | 1.00 | 0.40 | 0.47 | 1.00 | |

${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.95 | 0.53 | 1.00 | 0.99 | 0.53 | 1.00 | 0.90 | 0.44 | |

Type 2 | ${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.73 | 1.00 | 0.70 | 0.75 | 1.00 | 0.68 | 0.80 | 1.00 | 0.94 |

${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.66 | 0.57 | 1.00 | 0.57 | 0.60 | 1.00 | 0.49 | 0.61 | 1.00 | |

${\widehat{\mathsf{\Psi}}}_{P1}^{H}$ | 1.00 | 0.97 | 0.35 | 1.00 | 0.98 | 0.43 | 1.00 | 0.78 | 0.12 | |

Type 3 | ${\widehat{\mathsf{\Psi}}}_{P2}^{H}$ | 0.69 | 1.00 | 0.70 | 0.78 | 1.00 | 0.64 | 0.86 | 1.00 | 0.26 |

${\widehat{\mathsf{\Psi}}}_{P3}^{H}$ | 0.25 | 0.44 | 1.00 | 0.19 | 0.42 | 1.00 | 0.31 | 0.28 | 1.00 |

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**MDPI and ACS Style**

Birgin, H.B.; Laflamme, S.; D’Alessandro, A.; Garcia-Macias, E.; Ubertini, F.
A Weigh-in-Motion Characterization Algorithm for Smart Pavements Based on Conductive Cementitious Materials. *Sensors* **2020**, *20*, 659.
https://doi.org/10.3390/s20030659

**AMA Style**

Birgin HB, Laflamme S, D’Alessandro A, Garcia-Macias E, Ubertini F.
A Weigh-in-Motion Characterization Algorithm for Smart Pavements Based on Conductive Cementitious Materials. *Sensors*. 2020; 20(3):659.
https://doi.org/10.3390/s20030659

**Chicago/Turabian Style**

Birgin, Hasan Borke, Simon Laflamme, Antonella D’Alessandro, Enrique Garcia-Macias, and Filippo Ubertini.
2020. "A Weigh-in-Motion Characterization Algorithm for Smart Pavements Based on Conductive Cementitious Materials" *Sensors* 20, no. 3: 659.
https://doi.org/10.3390/s20030659