# Wireless-Based Identification and Model Updating of a Skewed Highway Bridge for Structural Health Monitoring

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## Abstract

**:**

## 1. Introduction

## 2. Operational Modal Analysis of a Skewed Highway Bridge

#### 2.1. Bridge Description

#### 2.2. Operational Modal Analysis

## 3. FE Model Updating with Experimental Modal Data

#### 3.1. Manual Tuning

#### 3.2. Sensitivity-Based FE Model Updating

**x**, according to the 1-norm. In Equation (1), ${W}_{\mathsf{\epsilon}}$ is the diagonal weighting matrix, which provides a means to balance the contributions from each individual residual. In detail, the following weighting factors were considered:

_{ij}| > 5%, for each individual θj, led to the six parameters for updating, as shown in Table 4. In total, fourteen model parameters had been investigated. The others that were discarded for updating included the stiffness of the boundary springs in the longitudinal, lateral, and vertical directions, respectively (in total, six on one side of the bridge) and the elastic modulus of the close-ends of the two box girders, respectively.

#### 3.3. The Updating Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Cross section B1-B1 of the bridge, as indicated in Figure 3 (units in meters).

**Figure 3.**The measurement nodes on the bridge deck, labeled from No. 1 to No. 34, in which the reference ones are denoted by R (units in meters).

**Figure 5.**Comparison of the experimental and numerical mode shapes: (

**a**) those of the updated FE model (n3); (

**b**) those of the identified results (WL3).

**Figure 6.**FE models built with 3D solid elements: (

**a**) the initial model; (

**b**) the manually tuned model.

**Figure 7.**Plot of the vertical modal displacements along the transversal cross section. Note: The modal displacements are normalized to the maximum unity for the first thirty-three nodes.

Mode | Wired | WL1 | WL2 | WL3 | ||||
---|---|---|---|---|---|---|---|---|

No. | f_{w} [Hz] | f_{wl1} [Hz] | Δf_{wl1} [%] | f_{wl2} [Hz] | Δf_{wl2} [%] | f_{wl3} [Hz] | Δf_{wl3} [%] | MAC |

1 | 7.41 | 7.49 | 1.1 | 7.42 | 0.1 | 7.54 | 1.8 | 0.98 |

2 | 8.04 | 8.3 | 3.2 | 8.03 | −0.1 | 8.04 | 0.0 | 0.90 |

3 | 12.67 | 12.4 | −2.1 | 13.24 | 4.5 | 13.08 | 3.2 | 0.97 |

4 | 17.14 | 17.37 | 1.3 | 15.37 | −10.3 | 15.28 | −10.9 | 0.87 |

5 | 20.13 | 19.96 | −0.8 | 22.17 | 10.1 | 21.99 | 9.2 | 0.95 |

6 | 29.05 | 29.18 | 0.4 | 29.32 | 0.9 | 29.24 | 0.7 | 0.96 |

7 | 36.06 | 36.92 | 2.4 | 35.66 | −1.1 | 34.96 | −3.1 | 0.68 |

_{wl}−f

_{w})/f

_{w}; MAC values were calculated between Wired and WL2.

Components | E (MPa) | n | G (MPa) | q (kg/m^{3}) |
---|---|---|---|---|

Box Girder | 32,373 | 0.2 | 13,489 | 2500 |

Slab | 32,373 | 0.2 | 13,489 | 2500 |

Side Barriers | 16,187 | 0.2 | 6745 | 2500 |

Exp. Mode | No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

f_{wl3} [Hz] | 7.54 | 8.04 | 13.08 | 15.28 | 21.99 | 29.24 | 34.96 | |

Initial FE Model | f_{n1} [Hz] | 7.46 | 8.36 | 12.29 | n/a | 21.41 | 27.64 | 34.23 |

Δf [%] | −1.1 | 4.0 | −6.0 | n/a | −2.6 | −5.5 | −2.1 | |

MAC | 0.95 | 0.77 | 0.91 | n/a | 0.77 | 0.88 | 0.84 | |

Manually Tuned FE Model | f_{n2} [Hz] | 7.48 | 7.95 | 13.14 | 15.13 | 22.23 | 28.85 | 33.48 |

Δf [%] | −0.8 | −1.1 | 0.5 | −1.0 | 1.1 | −1.3 | −4.2 | |

MAC | 0.97 | 0.86 | 0.94 | 0.69 | 0.79 | 0.88 | 0.77 | |

Updated FE Model | f_{n3} [Hz] | 7.75 | 7.95 | 12.70 | 15.19 | 21.97 | 29.55 | 35.08 |

Δf [%] | 2.8 | −1.1 | −2.9 | −0.6 | −0.1 | 1.1 | 0.3 | |

MAC | 0.97 | 0.93 | 0.90 | 0.64 | 0.80 | 0.87 | 0.80 |

_{n}− f

_{wl3})/f

_{wl3}; MAC values are calculated between the experimental and numerical modes.

Box Girder | Slab | Side Barrier | ||||
---|---|---|---|---|---|---|

E_{b} (MPa) | q (kg/m^{3}) | E_{b} (MPa) | q (kg/m^{3}) | E_{b} (MPa) | q (kg/m^{3}) | |

Initial | 32,373 | 2,500 | 32,373 | 2,500 | 16,187 | 2,500 |

Updated | 33,069 | 2,418 | 35,371 | 2,835 | 18,208 | 3,283 |

Δθ | 2% | −3% | 9% | 13% | 12% | 31% |

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## Share and Cite

**MDPI and ACS Style**

He, L.; Reynders, E.; García-Palacios, J.H.; Carlo Marano, G.; Briseghella, B.; De Roeck, G.
Wireless-Based Identification and Model Updating of a Skewed Highway Bridge for Structural Health Monitoring. *Appl. Sci.* **2020**, *10*, 2347.
https://doi.org/10.3390/app10072347

**AMA Style**

He L, Reynders E, García-Palacios JH, Carlo Marano G, Briseghella B, De Roeck G.
Wireless-Based Identification and Model Updating of a Skewed Highway Bridge for Structural Health Monitoring. *Applied Sciences*. 2020; 10(7):2347.
https://doi.org/10.3390/app10072347

**Chicago/Turabian Style**

He, Leqia, Edwin Reynders, Jaime H. García-Palacios, Giuseppe Carlo Marano, Bruno Briseghella, and Guido De Roeck.
2020. "Wireless-Based Identification and Model Updating of a Skewed Highway Bridge for Structural Health Monitoring" *Applied Sciences* 10, no. 7: 2347.
https://doi.org/10.3390/app10072347