小波变换在变形监测数据去噪和信息提取中的应用研究

发布时间：2018-06-17 15:32

本文选题：监测数据去噪 + 小波基选择　；参考：《西南交通大学》2017年硕士论文

【摘要】：小波变换因其具有多分辨分析和时频局部化的优点,特别适合用于对含有多种频率成分且为非平稳序列的变形监测数据进行去噪处理并提取其中的变形信息。在使用小波变换对变形监测数据进行去噪处理时,不同的变形监测数据具有不同的特点(如采样率、受噪声污染程度等),应当选取不同的去噪参数,包括小波基的选取,最佳分解层数的确定以及阈值的选择。这个问题一直是研究的重点.目前许多专家学者就最佳分解层数和阈值的选择问题已经进行了大量的研究探索,而最优小波基的选取还没有一个系统规范的标准。另一方面,工程体的变形信息往往表现为监测数据频率成分的变化。基于这一事实,变形监测数据中的变形信息提取就是要获取数据信号频率出现奇异性的地方。而在使用单子带重构算法对数据信号进行分析的过程中,由于Mallat算法固有的频率混淆,常常会导致提取出错误的特征信息,得到的重构数据也会因为与滤波器卷积而长度发生改变,进而导致边界效应问题。针对以上两个问题,本文在查阅国内外大量文献的基础上,尝试从能量和熵的角度出发,提出了一种能够在一定程度上指导不同变形监测数据选择其适合的最优小波基的融合指标。同时通过研究Mallat算法中频率混淆的产生原因,在单子带重构改进算法的基础上提出抗混叠单子带重构改进算法,以期能够解决频率混淆和信号长度变化的问题。采用本文提出的方法对仿真数据进行小波阈值去噪处理以及特征信息提取。通过分析,证明了小波基选择的融合指标的可靠性和实用性,同时验证了抗混叠单子带重构改进算法能够克服频率混淆的问题,保证了信号长度不受与滤波器卷积的影响,消除了边界效应问题。最后将提出的两种方法应用于变形监测的实测数据处理中,得到了较为满意的结果。
[Abstract]:Because wavelet transform has the advantages of multi-resolution analysis and time-frequency localization, it is especially suitable for de-noising and extracting deformation information from deformation monitoring data with multiple frequency components and non-stationary sequences. When using wavelet transform to Denoise deformation monitoring data, different deformation monitoring data have different characteristics (such as sampling rate, degree of noise pollution, etc.) different denoising parameters should be selected, including the selection of wavelet basis. The determination of the optimal decomposition layer number and the selection of the threshold value. This question has always been the focus of study. At present, many experts and scholars have done a lot of research on the selection of optimal decomposition layer number and threshold, but there is not a systematic standard for the selection of optimal wavelet basis. On the other hand, the deformation information of engineering body is often shown as monitoring the change of frequency component of the data. Based on this fact, the extraction of deformation information from deformation monitoring data is to obtain the singularity of data signal frequency. In the process of data signal analysis using single subband reconstruction algorithm, because of the inherent frequency confusion of Mallat algorithm, it often leads to the extraction of wrong feature information. The length of the reconstructed data will change because of convolution with the filter, which will lead to the boundary effect problem. In view of the above two problems, this paper tries to start from the angle of energy and entropy on the basis of consulting a lot of literature at home and abroad. An optimal wavelet basis fusion index which can guide different deformation monitoring data to a certain extent is proposed. At the same time, by studying the causes of frequency confusion in Mallat algorithm, an improved anti-aliasing single subband reconstruction algorithm is proposed based on the improved single-subband reconstruction algorithm, in order to solve the problems of frequency confusion and signal length change. The method proposed in this paper is used for wavelet threshold denoising and feature information extraction. Through analysis, the reliability and practicability of the fusion index selected by wavelet basis are proved. At the same time, it is proved that the improved anti-aliasing single subband reconstruction algorithm can overcome the problem of frequency confusion and ensure that the signal length is not affected by convolution with filter. The boundary effect is eliminated. Finally, the proposed two methods are applied to the data processing of deformation monitoring, and satisfactory results are obtained.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU196.1

【参考文献】