基于提升小波的数据处理及过程监测研究
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摘要
现代工业具有规模大、结构复杂,以及现场环境恶劣等特点,如何提取感兴趣的工业数据信息以及对生产过程的监测成为具有挑战性的热点课题之一。小波分析是傅立叶分析之后一种新兴的信号处理技术,在时频分析上具有独特优势,提升小波则为小波的构造引入了更多的灵活性。本文结合小波分析工具对工业数据的滤波、压缩,以及过程监测几个问题进行了研究。
1. 鲁棒滤波问题。数据去噪是数据预处理的重要组成,传统的数据滤波方法有维纳滤波和卡尔曼滤波,由于在线的工业数据去噪过程中强调滤波算法的在线完成以及工业数据本身具有的不确定性,以上两种方法在工程实际应用中很难胜任。小波去噪近年来被广泛研究和应用,但存在几个问题要解决:传统小波变换作为一种线性变换不具备抗差性,对恶劣环境下受粗差干扰以及加性噪声干扰的数据滤波效果很差;区间小波在解决边界效应的同时会带来额外的计算复杂性。为了解决上述问题,本文结合截尾中值滤波器和提升格式提出了一种鲁棒提升小波框架。这种新的方法通过在各级的提升环节中加入截尾中值滤波器来消除短时粗差和加性噪声的干扰,同时利用提升格式下的插值小波来解决边界效应的问题。同时由于提升小波有原位计算的特点和更少的计算量,使其在工程实施中更具优势。
2.一种避免滤波器穿越信号突变边缘的自适应提升小波的设计问题。数据压缩也是数据处理中的一个重要部分,提升小波在构造小波上具有独特优势,可以方便的根据信号的空间特性以及数据处理的要求来设计特定的小波。我们首先研究了空间自适应提升小波完全重构的充分条件,然后利用小波系数不重复进入多尺度分解的这一特点,设计出了将自适应信息无冗余的存储于小波系数的均值插值小波变换,对于一维工业数据的阈值压缩以及二维图像数据的有损编码压缩可以保证其逆变换的稳定性。仿真结果表明,这种方法在保留工业数据重要突变信息的同时能提高压缩比,对于图像则能更好的突出边缘信息。
3.如何评价压缩对工业过程监测影响的问题。首先分析了均方误差以及单点误差作为传统的压缩评价标准的不足,指出它们并不适合评价压缩对后续处理过程的影响;然后结合主元分析(PCA)的过程监测方法提出了一种新的压缩评价
The large scale and complex structure of industrial process, as well as the uncertainty of real environment, make the acquisition of interesting data and implementation of process monitoring system as one of challenges in the fields of control. Wavelet analysis is a powerful tool in the field of signal processing after Fourier analysis;lifting scheme brings the flexibility into the construction of wavelet. In this thesis, we discuss the problems of data denoising, data compression and process monitoring with the tool of wavelet.1. The problem of robust data denoising. Data denoising is an important part of data preprocessing. The traditional data denoising approaches include Winner filter and Kalman filter, but the two methods are inadequate to be applied at the on-line denosing, due to the uncertainty of the process data and the need of computation in time. The wavelet method has been widely used to deal with data denosing in recent years for it's characteristic in time-frequency domain. But there exist two problems should to be solved for on-line process data denosing. Firstly, the wavelet transform is a linearity transform, so it can not resist the disturbance of gross error and combined distribution;secondly, wavelet filters are noncausal in nature and require future measured data for calculating the current wavelet coefficients. Although the interval-wavelet can eliminate the boundary errors and overcome the time delay, it also introduce the additional complexity of calculation. To deal with the problems mentioned above, a generalized robust lifting wavelet filter is proposed in this thesis which includes an Alpha-trimmed means filter during each cascade steps and can solves the boundary effects by the boundary average-interpolating lifting wavelet.2. The design problem of an edge-avoided adaptive wavelet of lifting scheme. Data compression is also an important part of data processing. Lifting scheme brings the flexibility into the construction of wavelet, we can design appropriate wavelet filter according to the local space characteristic of the signal or the special objective of data processing. At first, we give the sufficient condition of perfectly reconstruction
of space-adaptive lifting wavelet, and then we design the adaptive average interpolating wavelet, which store the sign of adaptive information in the wavelet coefficients. No matter the shrinkage compression of process data or the lossy coding compression of image, the method can guarantee the stability of inverse transform. The simulation example demonstrates that the method can improve the compression ratio when preserving the important information in process data, and emphatically preserve the edge information of image under lossy coding compression.3. The problem of how to evaluate the impact of compression on process analyses. We first give an analysis of the two classic criterions: root mean-square error (RMSE) and local point error (LPE), and indicate that the two are unsuitable to describe the impact on data-driven analysis using the compression data. A new impact assessment criterion, detection delay, is suggested. Then the criterion is used in the usual statistical monitoring method principle component analysis (PCA). The theory analysis approves that the infection of the statistic characteristic of process data, likely mean value and variance, will affect the performance of PCA;the simulation on the Tennessee Eastman process also improves that compression will bring remarkable infection on the monitoring of some faults.4. The on-line classification problem of process trend analysis. The hidden Markov tree (HMT) model makes the trend representation, trend feature extraction and the model training all together. It is hard to give a clear classification during the transitions of process state if we use only the scale coefficients to model the process signal, although it works at the classification of stable state of operation. Considering the wavelet coefficients are sparse and characterize the transient information of the process signal, we introduce a novel method of HMT construction, which uses the selective large wavelet coefficients and all the scale coefficients. As the introducing of large wavelet coefficients, we can get the more accurate description of the transitions of process. We also offer the training algorithm, which is an amelioration of the classic EM algorithm, and give an analysis of computation complexity of on-line classification.
1. 鲁棒滤波问题。数据去噪是数据预处理的重要组成,传统的数据滤波方法有维纳滤波和卡尔曼滤波,由于在线的工业数据去噪过程中强调滤波算法的在线完成以及工业数据本身具有的不确定性,以上两种方法在工程实际应用中很难胜任。小波去噪近年来被广泛研究和应用,但存在几个问题要解决:传统小波变换作为一种线性变换不具备抗差性,对恶劣环境下受粗差干扰以及加性噪声干扰的数据滤波效果很差;区间小波在解决边界效应的同时会带来额外的计算复杂性。为了解决上述问题,本文结合截尾中值滤波器和提升格式提出了一种鲁棒提升小波框架。这种新的方法通过在各级的提升环节中加入截尾中值滤波器来消除短时粗差和加性噪声的干扰,同时利用提升格式下的插值小波来解决边界效应的问题。同时由于提升小波有原位计算的特点和更少的计算量,使其在工程实施中更具优势。
2.一种避免滤波器穿越信号突变边缘的自适应提升小波的设计问题。数据压缩也是数据处理中的一个重要部分,提升小波在构造小波上具有独特优势,可以方便的根据信号的空间特性以及数据处理的要求来设计特定的小波。我们首先研究了空间自适应提升小波完全重构的充分条件,然后利用小波系数不重复进入多尺度分解的这一特点,设计出了将自适应信息无冗余的存储于小波系数的均值插值小波变换,对于一维工业数据的阈值压缩以及二维图像数据的有损编码压缩可以保证其逆变换的稳定性。仿真结果表明,这种方法在保留工业数据重要突变信息的同时能提高压缩比,对于图像则能更好的突出边缘信息。
3.如何评价压缩对工业过程监测影响的问题。首先分析了均方误差以及单点误差作为传统的压缩评价标准的不足,指出它们并不适合评价压缩对后续处理过程的影响;然后结合主元分析(PCA)的过程监测方法提出了一种新的压缩评价
The large scale and complex structure of industrial process, as well as the uncertainty of real environment, make the acquisition of interesting data and implementation of process monitoring system as one of challenges in the fields of control. Wavelet analysis is a powerful tool in the field of signal processing after Fourier analysis;lifting scheme brings the flexibility into the construction of wavelet. In this thesis, we discuss the problems of data denoising, data compression and process monitoring with the tool of wavelet.1. The problem of robust data denoising. Data denoising is an important part of data preprocessing. The traditional data denoising approaches include Winner filter and Kalman filter, but the two methods are inadequate to be applied at the on-line denosing, due to the uncertainty of the process data and the need of computation in time. The wavelet method has been widely used to deal with data denosing in recent years for it's characteristic in time-frequency domain. But there exist two problems should to be solved for on-line process data denosing. Firstly, the wavelet transform is a linearity transform, so it can not resist the disturbance of gross error and combined distribution;secondly, wavelet filters are noncausal in nature and require future measured data for calculating the current wavelet coefficients. Although the interval-wavelet can eliminate the boundary errors and overcome the time delay, it also introduce the additional complexity of calculation. To deal with the problems mentioned above, a generalized robust lifting wavelet filter is proposed in this thesis which includes an Alpha-trimmed means filter during each cascade steps and can solves the boundary effects by the boundary average-interpolating lifting wavelet.2. The design problem of an edge-avoided adaptive wavelet of lifting scheme. Data compression is also an important part of data processing. Lifting scheme brings the flexibility into the construction of wavelet, we can design appropriate wavelet filter according to the local space characteristic of the signal or the special objective of data processing. At first, we give the sufficient condition of perfectly reconstruction
of space-adaptive lifting wavelet, and then we design the adaptive average interpolating wavelet, which store the sign of adaptive information in the wavelet coefficients. No matter the shrinkage compression of process data or the lossy coding compression of image, the method can guarantee the stability of inverse transform. The simulation example demonstrates that the method can improve the compression ratio when preserving the important information in process data, and emphatically preserve the edge information of image under lossy coding compression.3. The problem of how to evaluate the impact of compression on process analyses. We first give an analysis of the two classic criterions: root mean-square error (RMSE) and local point error (LPE), and indicate that the two are unsuitable to describe the impact on data-driven analysis using the compression data. A new impact assessment criterion, detection delay, is suggested. Then the criterion is used in the usual statistical monitoring method principle component analysis (PCA). The theory analysis approves that the infection of the statistic characteristic of process data, likely mean value and variance, will affect the performance of PCA;the simulation on the Tennessee Eastman process also improves that compression will bring remarkable infection on the monitoring of some faults.4. The on-line classification problem of process trend analysis. The hidden Markov tree (HMT) model makes the trend representation, trend feature extraction and the model training all together. It is hard to give a clear classification during the transitions of process state if we use only the scale coefficients to model the process signal, although it works at the classification of stable state of operation. Considering the wavelet coefficients are sparse and characterize the transient information of the process signal, we introduce a novel method of HMT construction, which uses the selective large wavelet coefficients and all the scale coefficients. As the introducing of large wavelet coefficients, we can get the more accurate description of the transitions of process. We also offer the training algorithm, which is an amelioration of the classic EM algorithm, and give an analysis of computation complexity of on-line classification.
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