# Working Mode Identification Method for High Arch Dam Discharge Structure Based on Improved Wavelet Threshold–EMD and RDT Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Basic Theory

#### 2.1. Improved Wavelet Threshold–EMD Hybrid Algorithm for High Arch Dam Noise Reduction

_{n}is the standard deviation and N is the signal length.

_{j}is the signal data length; j is the number of decomposition layers; and σ is the standard variance of noise, whose calculation formula can be written as:

_{n}(t) is the residual signal of x(t).

#### 2.2. Modal Parameter Identification of High Arch Dam Discharge Structures Based on Improved HHT–RDT Algorithm

_{i}is the ith moment.

#### 2.3. Recognition Process Based on Improved Wavelet Threshold–EMD and RDT Algorithm

## 3. Application Case

#### 3.1. Engineering Data

#### 3.2. Improved Wavelet Threshold–EMD Hybrid Algorithm for Signal Noise Reduction

#### 3.3. Modal Identification of Working Parameters of High Arch Dam Discharge Structures

_{1}–Y

_{10}are obtained. The power spectrum of these components is shown in Figure 10.

_{1}are shown in Figure 11a,b. The logarithmic amplitude curves of the free-decay response signal and the least squares fit are shown in Figure 11c,d.

## 4. Conclusions

- An improved wavelet threshold–EMD hybrid algorithm is proposed for noise reduction pretreatment on measured vibration response data of high arch dams. The improved wavelet threshold algorithm was adapted to overcome the defect of soft and hard threshold function selection, which can effectively eliminate the high-frequency white noise and reduce the influence of the modal aliasing. Then, EMD further eliminates the low-frequency flow noise and white noise, improving the accuracy of filtering and noise reduction.
- An improved wavelet threshold–EMD and RDT algorithm is proposed for working mode identification of high arch dam discharge structures under the working environment load excitation. The proposed method avoids the complicated system ordering process and accurately identifies the modal parameters of high arch dam discharge structures. This method has a simple principle and does not require solving large matrices during calculation. The result has strong robustness and high identification accuracy.
- The engineering examples show that the proposed method can accurately extract the work characteristic information of structures, has good noise reduction capabilities, and has high recognition accuracy. Therefore, this method eases the working modal parameter identification of high arch dam discharge structures and can be used for working modal recognition of other large frequency-intensive structures.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Arrangement of arch dam prototype flood discharge vibration measurement points. (

**a**) The arch dam prototype; (

**b**) Sensor arrangement for the arch dam vibration test; (

**c**) DP-type dynamic displacement sensor; (

**d**) DASP signal acquisition system.

**Figure 4.**Time history signals and power spectra of B2 measuring point under condition 2. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 5.**Time history signals and power spectra of B3 measuring point under condition 2. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 6.**Time history signals and power spectra of B4 measuring point under condition 2. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 7.**Time history signals and power spectra of B8 measuring point under condition 2. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 8.**Time history diagram and the normalized power spectrum diagram after noise reduction. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 9.**Comparison of calculation results of three noise reduction methods. (

**a**) Time history signals; (

**b**) Normalized power spectra.

**Figure 11.**Process of modal parameters identification of Y1 component. (

**a**) Time history; (

**b**) Power spectra; (

**c**) Free attenuation response; (

**d**) Logarithmic amplitude curve.

Condition | Spillway Opening | Upstream Water Level (m) | Downstream Water Level (m) |
---|---|---|---|

1 | Fourth surface spillway and first tunnel spillway | 1196.00 | 1014.36 |

2 | Third, fourth surface spillway and first tunnel spillway | 1196.01 | 1014.50 |

**Table 2.**Comparison of modal identification results of different measuring points of the high arch dam structure.

Modal | Natural Frequency/Hz | Damping Ratio/% | |||||||
---|---|---|---|---|---|---|---|---|---|

Order | B2 | B3 | B4 | B8 | B2 | B3 | B4 | B8 | |

1 | 1.44 | 1.44 | 1.44 | 1.43 | 1.45 | 1.79 | 1.51 | 1.69 1.91 | |

2 | 1.52 | 1.53 | 1.52 | 1.53 | 1.54 | 1.08 | 1.26 | 1.35 | |

3 | 2.21 | 2.19 | 2.19 | 2.20 | 1.45 | 1.28 | 2.24 | 1.46 | |

4 | 2.80 | 2.81 | 2.78 | 2.81 | 1.48 | 1.46 | 2.17 | 1.28 | |

5 | 3.58 | 3.60 | 3.59 | 3.61 | 1.31 | 3.47 | 4.08 | 1.79 | |

6 | 4.32 | 4.31 | 4.32 | 4.28 | 4.38 | 4.96 | 6.5 | 5.6 | |

7 | 4.90 | 4.90 | 4.92 | 4.91 | 2.18 | 1.93 | 3.67 | 2.38 | |

8 | 5.15 | 5.12 | 5.20 | 5.21 | 2.86 | 5.5 | 2.87 | 6.72 | |

9 | 7.24 | 7.28 | 7.30 | 7.26 | 7.67 | 7.16 | 8.12 | 7.47 | |

10 | 9.67 | 9.69 | 9.58 | 9.52 | 4.79 | 6.45 | 6.45 | 5.34 |

**Table 3.**Modal frequency identification of the high arch dam discharge structure with different methods.

Modal Order | Method in the Study/Hz | ERA/Hz | ARX/Hz | ITD/Hz |
---|---|---|---|---|

1 | 1.44 | 1.45 | 1.42 | 1.43 |

2 | 1.52 | 1.53 | 1.47 | 1.51 |

3 | 2.21 | 2.22 | 2.14 | 2.08 |

4 | 2.80 | 2.87 | 2.81 | 2.79 |

5 | 3.58 | 3.74 | 3.68 | 3.63 |

6 | 4.32 | 4.38 | 4.40 | 4.32 |

7 | 4.9 | 4.82 | 4.71 | 4.85 |

8 | 5.15 | 5.09 | 5.03 | / |

9 | 7.24 | 7.36 | 6.98 | 7.01 |

10 | 9.67 | 9.52 | 9.16 | / |

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**MDPI and ACS Style**

Guo, Y.; You, Z.; Wei, B.
Working Mode Identification Method for High Arch Dam Discharge Structure Based on Improved Wavelet Threshold–EMD and RDT Algorithm. *Water* **2022**, *14*, 3735.
https://doi.org/10.3390/w14223735

**AMA Style**

Guo Y, You Z, Wei B.
Working Mode Identification Method for High Arch Dam Discharge Structure Based on Improved Wavelet Threshold–EMD and RDT Algorithm. *Water*. 2022; 14(22):3735.
https://doi.org/10.3390/w14223735

**Chicago/Turabian Style**

Guo, Yingjia, Zongzhe You, and Bowen Wei.
2022. "Working Mode Identification Method for High Arch Dam Discharge Structure Based on Improved Wavelet Threshold–EMD and RDT Algorithm" *Water* 14, no. 22: 3735.
https://doi.org/10.3390/w14223735