Lifting Wavelet-based Data Processing And Process Monitoring

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 reconstructionof 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.