# Operational Modal Analysis of Bridge Structures with Data from GNSS/Accelerometer Measurements

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## Abstract

**:**

## 1. Introduction

## 2. Principle of GNSS Dynamic Deformation Monitoring

## 3. AFEC Mixed Filtering

_{i}can be gained by preprocessing signal x

_{i}collected by the GNSS and neglecting the minor constituent. In the dynamic deformation monitoring of the structure of GNSS, the measurement error is caused by many factors. In GNSS short-baseline double-difference solution processing, errors caused by tropospheric and ionospheric delays, satellite ephemeris errors, satellite clock errors, receiver clock errors and receiver position errors can be weakened. Some errors can’t be weakened, such as multi-path error and random noise. Ignoring minor components, such as the errors caused by earth tides and load tide, the preprocessed signal X

_{i}can be expressed as

_{i}is the GNSS test data at the test point i after preprocessing; n is the data length; ${R}_{i}(n)$ is the real vibration information of the bridge structure; ${D}_{i}(n)$ is the multipath errors of signals; and ${N}_{i}(n)$ is the random noise of signals.

- (1)
- Multipath errors ${D}_{i}(n)$ are eliminated by Chebyshev high-pass filtering, and the fundamental vibrational frequency of the test bridge structure was calculated as 0.83 Hz by using finite element analysis. The pass-band frequency of an 8-order I-type Chebyshev high-pass filter was designed at 0.4 Hz. This 8-order I-type Chebyshev high-pass filter was used to process the GNSS monitoring data X
_{i}, obtaining the signal after the multipath error was eliminated: ${Y}_{i}={N}_{i}(n)+{R}_{i}(n)$. - (2)
- The random noise ${N}_{i}(n)$ was weakened by the EMD filter based on the autocorrelation function. First, the EMD of the signal Y
_{i}was implemented, obtaining m intrinsic modal functions (IMF1, IMF2,…, IMFm) and one residual component (R_{1}). The autocorrelation function of m IMFs was calculated, and whether these IMFs were noise components was determined. The IMFs that were not noise components and the residual component were reconstructed, obtaining the AFEC-filtered signal ${y}_{i}={R}_{i}(n)$.

## 4. Expanded ARMA_RDT

#### 4.1. Expanded RDT

_{i}(i = 1, 2, …, n) and having a length of s. Subsequently, the signals of these n sections are superposed and averaged, thus obtaining the free vibration signal of the system. According to theoretical deduction, this vibration signal is the free attenuation signal of the structural system under initial displacement [21]. When the random excitation meets zero-mean Gaussian distribution, theoretical deduction reveals that this vibration signal is the free attenuation signal of the structural system under initial displacement.

_{i}+ s yields:

#### 4.2. ARMA Model

_{t}.

## 5. Engineering Applications and Discussions

#### 5.1. Stability Test of Equipment

#### 5.2. Engineering Background and Measuring Point Arrangement

#### 5.3. Identification of Dynamic Displacement from AFEC Mixed Filtering

_{i}). The original vertical displacement sequence (x

_{1}) and signal after preprocessing (X

_{1}) at the #1 measuring point are shown in Figure 8.

#### 5.4. Modal Analysis

## 6. Conclusions

- (1)
- The GNSS technique possesses a certain engineering application value in vibration displacement monitoring and modal parameter identification of large engineering structures.
- (2)
- The proposed AFEC mixed filtering algorithm can not only eliminate multipath errors and random noise in the GNSS-RTK data effectively but can also increase the vertical vibration displacement accuracy of the bridge structure to less than 1 mm.
- (3)
- The expanded ARMA_RTD modal identification method can be used to process the GNSS monitoring data of real bridge structures and can identify the modal parameters of the structure quickly and effectively. It can provide key data for online monitoring or active control and the earthquake resistance evaluation of structures.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**GNSS-RTK (Global Navigation Satellite System Real-time Kinematic Technology) working mode.

**Figure 2.**GNSS-RTK system composition where (

**a**) is the GNSS-RTK system; (

**b**) is the reference station; and (

**c**) is the mobile station.

**Figure 3.**AFEC mixed filtering (an algorithm combing autocorrelation function-based empirical mode decomposition and Chebyshev filter) flow chart.

**Figure 5.**Stability test data: (

**a**) #1 monitoring point elevation data; and (

**b**) #2 monitoring point elevation data.

**Figure 7.**Instruments layout where (

**a**) is the reference station; (

**b**) is the #1 mobile station; (

**c**) is the #2 mobile station and (

**d**) is the arrangement of accelerometers.

**Figure 8.**GNSS-RTK elevation signal: (

**a**) original signal-${x}_{1}$; and (

**b**) signal after pretreatment-X

_{1}.

**Figure 10.**Normalized autocorrelation of the random noise and common signal. (

**a**) Random noise; (

**b**) Common signal; (

**d**) Normalized autocorrelation and (

**d**) Normalized autocorrelation.

**Figure 15.**GNSS-RTK signal after AFEC (an combination algorithm of autocorrelation function-based empirical mode decomposition (EMD) and Chebyshev mixed filtering) and power spectrum analysis: (

**a**) GNSS-RTK signal after AFEC; (

**b**) Power spectrum analysis of GNSS-RTK signal after AFEC.

**Figure 16.**Acceleration signal after AFEC and power spectrum analysis: (

**a**) acceleration signal after AFEC; (

**b**) Power spectrum analysis of acceleration signal after AFEC.

**Figure 17.**Finite element modal analysis: (

**a**) First order mode; (

**b**) second-order mode; (

**c**) third-order mode; (

**d**) fourth-order mode; (

**e**) five-order mode.

Frequency (Hz) | First-Order | Second-Order | Third-Order | Fourth-Order | Five-Order |
---|---|---|---|---|---|

Theoretical value | 0.84 | 1.82 | 2.59 | 2.91 | 4.18 |

Result from Accelerometer | 0.82 | 1.71 | 2.57 | 2.82 | 3.98 |

Relative difference (%) | 2.38 | 6.04 | 0.77 | 3.09 | 4.78 |

Result from GNSS-RTK | 0.81 | 1.77 | 2.45 | 2.78 | 4.03 |

Relative difference (%) | 3.57 | 2.75 | 5.4 | 4.47 | 3.59 |

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**MDPI and ACS Style**

Xiong, C.; Lu, H.; Zhu, J.
Operational Modal Analysis of Bridge Structures with Data from GNSS/Accelerometer Measurements. *Sensors* **2017**, *17*, 436.
https://doi.org/10.3390/s17030436

**AMA Style**

Xiong C, Lu H, Zhu J.
Operational Modal Analysis of Bridge Structures with Data from GNSS/Accelerometer Measurements. *Sensors*. 2017; 17(3):436.
https://doi.org/10.3390/s17030436

**Chicago/Turabian Style**

Xiong, Chunbao, Huali Lu, and Jinsong Zhu.
2017. "Operational Modal Analysis of Bridge Structures with Data from GNSS/Accelerometer Measurements" *Sensors* 17, no. 3: 436.
https://doi.org/10.3390/s17030436