基于小波提升格式理论的隧道衬砌缺陷定量识别分析

为提高探地雷达信号分析中小波基函数选取或构造的针对性和适应性，降低构造计算复杂性，并使所构造的小波基能更准确提取隧道衬砌结构背后空洞检测信号特征点信息，提出一种根据提升格式小波理论和目标信号波形特征来构造匹配小波的方法，并将所构造的小波基应用于空洞检测信号特征点的识别中。该方法以完全重构滤波器条件和提升格式小波为理论基础，首先选择一个简单而一般的初始双正交滤波器组，通过对初始双正交滤波器进行提升和对偶提升，获得不同的提升算子和对偶提升算子，从而得到更新后含自由变量的高阶滤波器组函数表达；其次，依据探地雷达信号的固有特点，对新滤波器组中重构端小波函数中的自由参数进行优化，并对新小波基与实际探地雷达信号的相似度进行计算和检验，最终构造出既满足线性相位、紧支撑性，又具有与探地雷达信号匹配度高等优势的新双正交小波基。将新小波基应用于室内空腔检测试验及实际工程中空洞缺陷的定量分析中，结果表明，同其他类型小波相比，用提升方法构造的小波能更准确地识别空洞缺陷信号突变点发生的时刻和位置，能更准确地实现隧道工程中空洞缺陷的位置和垂直尺寸的定量分析，从而大大提高探地雷达对缺陷探测的可靠度和准确度。

Quantitative Identification and Analysis of Tunnel Lining Defect Based on the Wavelet Lifting Scheme Theory

To improve the pertinence and adaptability of selecting or constructing wavelet basis functions for ground penetrating radar (GPR) signal analysis, to reduce the calculation complexity of wavelet construction, and to make the constructed wavelet basis more accurately extract the characteristic information of cavity detection signal from a tunnel lining, a method for constructing matching wavelets based on the lifting scheme theory and the waveform characteristics of a target signal is proposed. The constructed wavelet basis is applied to the identification of feature points of the cavity detection signal. First, with the perfect reconstruction filter banks and the lifting scheme wavelet as theoretical foundations, a general and initial biorthogonal filter bank was selected. By lifting and dual lifting the initial biorthogonal filters, different lifting operators and dual lifting operators were obtained and the function expressions of higher order filter banks with free variables were calculated. Second, considering the inherent characteristics of GPR signals, free parameters in the reconstructed wavelet function were optimized and the similarity between the new wavelet basis and the actual GPR signals was computed and tested. Finally, a new biorthogonal wavelet basis was constructed that satisfies not only the requirements of linear phase and tight support, but also has the advantage of high-level matching with GPR signals. The wavelet basis was applied to the indoor cavity detection test and the quantitative analysis of cavity defect in practical engineering. The results show that, as against other types of wavelets, the wavelet constructed through the lifting scheme more accurately identifies the time and position of the burst point in the cavity defect signal and more exactly quantifies the location and vertical height of the cavity, thus greatly improving the reliability and accuracy of GPR for defect detection.