# 基于小波分析的桥梁变形监测数据处理模型Data Processing Model of Bridge Deformation Monitoring Data Based on Wavelet Analysis

DOI: 10.12677/GST.2018.62012, PDF, HTML, XML, 下载: 819  浏览: 1,957

Abstract: Deformation monitoring can analyze and evaluate the safety status of engineering facilities and is an important research content of engineering survey. This article will study the basic principles of wavelet analysis, simulate deformation monitoring data, and establish the data processing models of deformation monitoring. MATLAB software’s wavelet function is used to write the relevant program. The RMSE, SNR and other indicators are used to guide the wavelet decomposition, extract the gross error, and determine the optimal wavelet base and the maximum decomposition scale. At the same time, the wavelet threshold denoising function is studied to determine the best threshold denoising function. Finally, an optimal model is established according to the simulation experiment, and an example of deformation monitoring data is processed, and the processing result is analyzed and the accuracy is evaluated.

1. 引言

2. 研究区概况与研究方法

2.1. 研究区概况

2.2. 研究思路与方法

3. 变形监测数据及分析

Figure 1. The accumulative total settlement changes over time

Figure 2. The speed of sinking varies with time

Table 1. Bridge deformation monitoring data

4. 变形监测条件确定

4.1. 变形监测数据处理模型

$X=\left\{\begin{array}{l}\mathrm{cos}\left(2\text{π}\cdot 10t\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(0 (1)

4.2. 确定最大分解尺度

Db小波具有良好的正则性，n值越大，正则性就越好，即光滑性就越好，因此具有良好的分析特性。实验采用db10小波对噪声信号进行不同尺度的分解，图5图6图7图8分别为非平稳信号的不同

Figure 3. Non-stationary signal image

Figure 4. The signal after adding the noise

Figure 5. 1-level decomposition of non-stationary signals

Figure 6. 2-level decomposition of non-stationary signal

Figure 7. 3-level decomposition of non-stationary signals

Figure 8. 4-level decomposition of non-stationary signals

4.3. 最优小波基的选取

5. 桥梁变形监测处理

5.1. 变形监测数据的粗差探测

Figure 9. Raw data image and denoised data image

Figure 10. The original signal image and the decomposed low frequency signal

Table 2. Root mean square error at different levels of decomposition and relative changes

Table 3. Signal to noise ratio of all kinds of wavelet

Figure 11. High-frequency information after the decomposition

Table 4. Gross error detection results

Figure 12. The original signal and reconstruction signal

Table 5. 4, 5 Interpolation results

Table 6. 6, 7, 8, 10 Interpolation results

Table 7. 12, 13, 15 Interpolation results

5.2. 小波阈值去噪

$|{w}_{ij}|\ge \lambda$ 时， $\stackrel{^}{{w}_{ij}}={w}_{ij}$ ；当 $|{w}_{ij}|<\lambda$$\stackrel{^}{{w}_{ij}}=0$ 。该方法为硬阈值去噪法 [11] 。采用该方法对信号进行去噪后，再重构信号，去噪后的信号如下图13所示。

Figure 13. The signal after the gross error is removed and the hard threshold denoising.

Figure 14. The signal after the gross error is removed and the soft threshold denoising

$\stackrel{^}{{w}_{ij}}=\left\{\begin{array}{l}sign\left({w}_{ij}\right)\left(|{w}_{ij}|-\frac{\lambda }{\mathrm{exp}\left(\frac{|{w}_{ij}|-\lambda }{\lambda }\right)}\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}|{w}_{ij}|\ge \lambda \\ 0,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}|{w}_{ij}|<\lambda \end{array}$ (2)

Figure 15. Remove the signal after the gross error and the signal after the new threshold denoising

Table 8. Signal-to-noise ratio and mean square error of various threshold functions after denoising

5.3. 去噪结果

6. 结果精度验证

Table 9. Deformation monitoring data after denoising (mm)

Figure 16. The sinking speed of the original signal and the sinking speed of the de-noised signal

7. 结果分析

8. 结论

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