管道缺陷检测中超声信号稀疏解卷积及稀疏压缩方法的研究
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摘要
海底管道超声无损检测技术是目前国际无损检测领域的研究热点,开展管道检测相关技术、方法和手段的研究具有重大的理论和现实意义。论文依托国家863项目“海底管道内爬行器及其检测技术”及国家自然科学基金项目“超声信号稀疏分量压缩及其硬件实现”,针对海底管道的检测要求,采用稀疏分量分析的信息处理技术,深入研究管道缺陷检测及海量超声数据的压缩理论与实际问题,为研制具有我国自主知识产权的海洋输油管道超声智能检测系统提供技术基础。
论文首先对稀疏分量分析相关理论进行了探讨和研究,重点研究了稀疏信号的精确重构条件与稀疏分解算法的收敛性。构造了鲁棒性更好的稀疏性度量函数,并给出与证明了所构造稀疏性度量函数的相关性质。为超声信号的稀疏分解与稀疏压缩提供了必要的预备知识。
论文通过分析超声回波窄带性、稀疏性等性质与过完备原子库的结构提出了精简过完备原子库的思想。根据过完备原子库的结构,定义了内置相干累积量和外置相干累积量这两个概念,并通过对这两个概念性质的分析,提出并证明了原子库集合划分定理,在此基础上首次设计出针对超声信号稀疏分解的MP集合搜索快速算法,提出并证明了MP集合搜索定理,完善了MP集合搜索快速算法的理论。在此基础上进一步研究了MP集合搜索快速算法迭代终止条件。通过理论推导,设计出残差比阂值迭代终止条件,克服了传统迭代终止条件针对信噪比较低的超声信号稀疏分解无法选择迭代终止阂值的问题。MP集合搜索快速算法解决了现存稀疏分解技术计算速度十分缓慢的问题,极大地提高了超声信号稀疏分解的速度。
针对管道近表面缺陷难以检测及缺陷检测精度不高等问题,论文从超声信号的卷积模型入手,根据超声反射序列的稀疏性,独立的设计出稀疏序列非线性变换函数,并在此基础上设计了非线性最小熵解卷积算法。同时,在研究稀疏分解方法的基础上,首次设计出加权迭代稀疏解卷积算法,并从理论的角度推导与论证了该算法的原理及其在应用上的灵活性。两种解卷积算法不仅能精确的计算出管道的壁厚,并且可以准确的检测出管道内部缺陷,特别是可以检测出传统方法无法检测的管道近表面缺陷。实验结果显示加权迭代稀疏解卷积算法还起到了良好的滤波作用,这种滤波方法与一般的滤波方法不同,它体现了超声信号本质的特征,反映了每个回波的固有特性。
为了提高海量超声信号的压缩比,论文在研究超声信号的固有特征的基础上,构造了针对超声信号压缩的原子库。在此基础上首次设计出计算效率较高、实时性强的稀疏压缩算法。稀疏压缩算法与本文设计的匹配小波压缩算法相比具有压缩比高、均方根误差小、分解系数算术-几何平均比高及失真小的优点。在无明显失真的情况下,最大压缩比约为200：1。稀疏分解得到的系数还可以直接用来检测油气管道中是否存在缺陷,起到了对超声信号压缩与缺陷检测的两种功能,并且重构的信号有着极好的降噪作用。
Currently, offshore pipeline ultrasonic detection technology is a research hotspot in international non-destructive testing field. It has great theoretical and realistic sense to research the technologies, methods, and approaches for pipeline detection. Based on "863" of the high technology research and development program "Offshore pipeline detection device and inspection technology" and National Natural Science Foundation of China "Sparse compression for ultrasonic signal and its hardware implementation", according to the detection requirements of offshore pipeline, the sparse component analysis method have been used to study the theory and techniques of flaw detection and mass ultrasonic data compression deeply, such theory and technologies explored in the dissertation can provide key technologies for the data analysis system of the pipeline intelligent detection device.
Firstly this dissertation studied the theory of sparse component analysis method, and the exact recovery conditions and astringency have been explored emphatically. Based on the properties of sparse component analysis method, a new sparsity measure function was constructed with better robustness, and the related properties of such function has been given and proved. Such function can provide the essential preliminary knowledge for ultrasonic signal sparse decomposition and sparse compression.
Based on the properties of ultrasonic echo and the construction of the over-complete dictionary, a simplified over-complete dictionary has been provided. According to the structure of over-complete dictionary, the concept of inner cumulative coherence and outer cumulative coherence have been defined, after analysis the properties of this two concept, the over-complete dictionary aggregate divisional theorem was put forward and proved., and based on such theorem, a novel fast batch MP method has been developed which can attain the same effect as MP method, but the computational complexity with the proposed method is greatly reduced. At the same time, the residual ratio iteration termination condition for fast batch MP method has been developed, it can erase the disadvantage of the traditional termination condition which can not terminated in terms of an ultrasonic signal with an extremely low SNR. Such fast batch MP method is fast enough to be implemented in a real-time system.
The received signal in ultrasonic pulse-echo inspection can be modelled as a convolution between an impulse response and the reflection sequence that is the impulse characteristic of the inspected object. In order to improve the time resolution so that the overlap between echoes from closely spaced reflectors becomes small, this dissertation presents a non-linear minimum entropy deconvolution algorithm that is robust to deconvolution ultrasonic signals. The robustness is obtained by including a non-linear function which can increase the sparsity of the iteration output and decrease the influence of the added noise. Meanwhile, based on the study of sparse decompose method, the dissertation presents an innovation weighted iteration sparse deconvolution algorithm and the theoretical investigation of the proposed algorithm principle, the algorithm is very flexible for its application. The two deconvolution algorithm can not only calculates the thickness of the pipeline wall accuracy, but also detect the flaw in pipeline with high precise, especially the near surface flaw which the traditional method can not. The experiment results show the weighted iteration sparse deconvolution algorithm can take a role of filtering that is not the same comparing to the normal filter method, it can show the intrinsic character of the ultrasonic signal, and reflect the intrinsic property of each echo wave.
Based on the properties of ultrasonic echo, a simplified over-complete dictionary in which some atoms is ultrasonic wavelet has been provided, and the sparse compression algorithm was presented for ultrasonic signal compression. Because the ultrasonic wavelet is the approximation of the ultrasonic echo, the ultrasonic signal has a sparsest representation, and the sparsity of weight vectors attained by decomposing the ultrasonic signal using the sparse compression algorithm is very big. The energy of the sparse weight vectors is highly centralized, only a limited number of non-zero weight vectors can reconstruct the ultrasonic signal with a minimal loss in signal quality. Comparing with the matching wavelet compression algorithm, the sparse compression algorithm is capable of compressing the ultrasonic signal at higher compression rates、smaller root-mean-square error、minimal loss in signal quality and higher ratio of arithmetic mean to geometric mean. For compressing the ultrasonic signal, the sparse compression algorithm can achieve the biggest compression rates about 200:1 with virtually no loss in signal quality. Because the amount of the atoms in the over-complete dictionary is very small, it is fast enough to be implemented in a real-time data compression system. Because the ultrasonic wavelet is the approximation of the ultrasonic echo, the sparse compression algorithm can not only give better sparse representations and better compression results, but also give excellent performance for feature extraction and ultrasonic signal denoising.
论文首先对稀疏分量分析相关理论进行了探讨和研究,重点研究了稀疏信号的精确重构条件与稀疏分解算法的收敛性。构造了鲁棒性更好的稀疏性度量函数,并给出与证明了所构造稀疏性度量函数的相关性质。为超声信号的稀疏分解与稀疏压缩提供了必要的预备知识。
论文通过分析超声回波窄带性、稀疏性等性质与过完备原子库的结构提出了精简过完备原子库的思想。根据过完备原子库的结构,定义了内置相干累积量和外置相干累积量这两个概念,并通过对这两个概念性质的分析,提出并证明了原子库集合划分定理,在此基础上首次设计出针对超声信号稀疏分解的MP集合搜索快速算法,提出并证明了MP集合搜索定理,完善了MP集合搜索快速算法的理论。在此基础上进一步研究了MP集合搜索快速算法迭代终止条件。通过理论推导,设计出残差比阂值迭代终止条件,克服了传统迭代终止条件针对信噪比较低的超声信号稀疏分解无法选择迭代终止阂值的问题。MP集合搜索快速算法解决了现存稀疏分解技术计算速度十分缓慢的问题,极大地提高了超声信号稀疏分解的速度。
针对管道近表面缺陷难以检测及缺陷检测精度不高等问题,论文从超声信号的卷积模型入手,根据超声反射序列的稀疏性,独立的设计出稀疏序列非线性变换函数,并在此基础上设计了非线性最小熵解卷积算法。同时,在研究稀疏分解方法的基础上,首次设计出加权迭代稀疏解卷积算法,并从理论的角度推导与论证了该算法的原理及其在应用上的灵活性。两种解卷积算法不仅能精确的计算出管道的壁厚,并且可以准确的检测出管道内部缺陷,特别是可以检测出传统方法无法检测的管道近表面缺陷。实验结果显示加权迭代稀疏解卷积算法还起到了良好的滤波作用,这种滤波方法与一般的滤波方法不同,它体现了超声信号本质的特征,反映了每个回波的固有特性。
为了提高海量超声信号的压缩比,论文在研究超声信号的固有特征的基础上,构造了针对超声信号压缩的原子库。在此基础上首次设计出计算效率较高、实时性强的稀疏压缩算法。稀疏压缩算法与本文设计的匹配小波压缩算法相比具有压缩比高、均方根误差小、分解系数算术-几何平均比高及失真小的优点。在无明显失真的情况下,最大压缩比约为200：1。稀疏分解得到的系数还可以直接用来检测油气管道中是否存在缺陷,起到了对超声信号压缩与缺陷检测的两种功能,并且重构的信号有着极好的降噪作用。
Currently, offshore pipeline ultrasonic detection technology is a research hotspot in international non-destructive testing field. It has great theoretical and realistic sense to research the technologies, methods, and approaches for pipeline detection. Based on "863" of the high technology research and development program "Offshore pipeline detection device and inspection technology" and National Natural Science Foundation of China "Sparse compression for ultrasonic signal and its hardware implementation", according to the detection requirements of offshore pipeline, the sparse component analysis method have been used to study the theory and techniques of flaw detection and mass ultrasonic data compression deeply, such theory and technologies explored in the dissertation can provide key technologies for the data analysis system of the pipeline intelligent detection device.
Firstly this dissertation studied the theory of sparse component analysis method, and the exact recovery conditions and astringency have been explored emphatically. Based on the properties of sparse component analysis method, a new sparsity measure function was constructed with better robustness, and the related properties of such function has been given and proved. Such function can provide the essential preliminary knowledge for ultrasonic signal sparse decomposition and sparse compression.
Based on the properties of ultrasonic echo and the construction of the over-complete dictionary, a simplified over-complete dictionary has been provided. According to the structure of over-complete dictionary, the concept of inner cumulative coherence and outer cumulative coherence have been defined, after analysis the properties of this two concept, the over-complete dictionary aggregate divisional theorem was put forward and proved., and based on such theorem, a novel fast batch MP method has been developed which can attain the same effect as MP method, but the computational complexity with the proposed method is greatly reduced. At the same time, the residual ratio iteration termination condition for fast batch MP method has been developed, it can erase the disadvantage of the traditional termination condition which can not terminated in terms of an ultrasonic signal with an extremely low SNR. Such fast batch MP method is fast enough to be implemented in a real-time system.
The received signal in ultrasonic pulse-echo inspection can be modelled as a convolution between an impulse response and the reflection sequence that is the impulse characteristic of the inspected object. In order to improve the time resolution so that the overlap between echoes from closely spaced reflectors becomes small, this dissertation presents a non-linear minimum entropy deconvolution algorithm that is robust to deconvolution ultrasonic signals. The robustness is obtained by including a non-linear function which can increase the sparsity of the iteration output and decrease the influence of the added noise. Meanwhile, based on the study of sparse decompose method, the dissertation presents an innovation weighted iteration sparse deconvolution algorithm and the theoretical investigation of the proposed algorithm principle, the algorithm is very flexible for its application. The two deconvolution algorithm can not only calculates the thickness of the pipeline wall accuracy, but also detect the flaw in pipeline with high precise, especially the near surface flaw which the traditional method can not. The experiment results show the weighted iteration sparse deconvolution algorithm can take a role of filtering that is not the same comparing to the normal filter method, it can show the intrinsic character of the ultrasonic signal, and reflect the intrinsic property of each echo wave.
Based on the properties of ultrasonic echo, a simplified over-complete dictionary in which some atoms is ultrasonic wavelet has been provided, and the sparse compression algorithm was presented for ultrasonic signal compression. Because the ultrasonic wavelet is the approximation of the ultrasonic echo, the ultrasonic signal has a sparsest representation, and the sparsity of weight vectors attained by decomposing the ultrasonic signal using the sparse compression algorithm is very big. The energy of the sparse weight vectors is highly centralized, only a limited number of non-zero weight vectors can reconstruct the ultrasonic signal with a minimal loss in signal quality. Comparing with the matching wavelet compression algorithm, the sparse compression algorithm is capable of compressing the ultrasonic signal at higher compression rates、smaller root-mean-square error、minimal loss in signal quality and higher ratio of arithmetic mean to geometric mean. For compressing the ultrasonic signal, the sparse compression algorithm can achieve the biggest compression rates about 200:1 with virtually no loss in signal quality. Because the amount of the atoms in the over-complete dictionary is very small, it is fast enough to be implemented in a real-time data compression system. Because the ultrasonic wavelet is the approximation of the ultrasonic echo, the sparse compression algorithm can not only give better sparse representations and better compression results, but also give excellent performance for feature extraction and ultrasonic signal denoising.
引文
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