# On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Empirical Mode Decomposition (EMD) Method

- (a)
- Obtain the original signal;
- (b)
- Identify the positive peaks and negative peaks of the original signal; the upper envelope and the lower envelope can be obtained as connecting maxima and minima of the original signal with the cubic spline separately. Then, the mean value of upper envelop and the lower envelop can be calculated;
- (c)
- Subtract the mean from the original signal to obtain the first intrinsic mode function (IMF1);
- (d)
- The first residual component is calculated by subtracting IMF1 from the original signal. This residual component is treated as a new data and subjected to the same process described above to calculate the next IMF.

#### 2.2. Ensemble Empirical Mode Decomposition (EEMD) Method

## 3. Numerical Modelling of Vehicle Bridge Interaction

## 4. Estimation of the Bridge Frequency Using the EMD Method

#### 4.1. Effect of Road Surface Roughness

#### 4.2. Effect of Noise

#### 4.3. Effect of Vehicle Velocity

## 5. Estimation of Vehicle Frequency Using the EEMD Method

#### 5.1. Effect of Measurement Noise

#### 5.2. Effect of Vehicle Velocity

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The contribution of this study to the state of the art (EMD: empirical mode decomposition, EEMD: ensemble empirical mode decomposition).

**Figure 4.**(

**a**) The acceleration response measured on the vehicle and (

**b**) the fast Fourier transformation (FFT) of the acceleration response.

**Figure 5.**(

**a**) Intrinsic mode functions (IMFs) of the vehicle acceleration response and (

**b**) FFT spectra of the IMFs of the vehicle acceleration response.

**Figure 7.**(

**a**) IMFs of the vehicle acceleration response and (

**b**) FFT of the IMFs of the vehicle acceleration response in the presence of 5% noise.

**Figure 8.**FFT of the IMFs of the vehicle acceleration response when the vehicle speed is (

**a**) 10 m/s and (

**b**) 5 m/s.

**Figure 9.**(

**a**) IMFs obtained from the EEMD of the vehicle acceleration response and (

**b**) FFT spectra of the IMFs.

**Figure 10.**(

**a**) IMFs of the vehicle acceleration response and (

**b**) FFT spectra of the vehicle acceleration response in presence.

**Figure 11.**(

**a**) IMFs of the vehicle acceleration response and (

**b**) FFT of IMFs when the vehicle speed is 5 m/s.

**Figure 12.**(

**a**) IMFs of the vehicle acceleration response and (

**b**) FFT of IMFs when the vehicle speed is 10 m/s.

**Table 1.**Comparison of the first frequency estimated by EMD and EEMD in the presence of measurement noise (FE: finite element).

Extracted Frequency in Presence of 5% Noise (Hz) | Error Compared to the FE Frequency (%) | ||
---|---|---|---|

EMD method | 3.418 Hz | 10.73% | |

EEMD method | 3.906 Hz | 2.01% |

Speed = 5 m/s | Speed = 10 m/s | ||||
---|---|---|---|---|---|

Frequency (Hz) | Error to FE (%) | Frequency (Hz) | Error to FE (%) | ||

EMD method | 3.54 Hz | 7.55% | 3.41 Hz | 10.73% | |

EEMD method | 3.90 Hz | 2.01% | 3.90 Hz | 2.01% |

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**MDPI and ACS Style**

Zhu, L.; Malekjafarian, A. On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle. *Infrastructures* **2019**, *4*, 32.
https://doi.org/10.3390/infrastructures4020032

**AMA Style**

Zhu L, Malekjafarian A. On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle. *Infrastructures*. 2019; 4(2):32.
https://doi.org/10.3390/infrastructures4020032

**Chicago/Turabian Style**

Zhu, Licheng, and Abdollah Malekjafarian. 2019. "On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle" *Infrastructures* 4, no. 2: 32.
https://doi.org/10.3390/infrastructures4020032