On-line multiscale filtering of random and gross errors without process models
On-line multiscale filtering of random and gross errors without process models
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DOI：
10.1002/aic.690450513
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发表时间：
1999-05-01
期刊：
影响因子：
3.7
通讯作者：
Bakshi, BR
中科院分区：
文献类型：
--
作者：
Nounou, MN;Bakshi, BR
对于缺乏精确模型的过程，单变量滤波修正是一种流行的方法。线性滤波器是最常用的在线滤波；然而，它们是单尺度的，最适合于校正在时间和频率上具有相同分辨率的包含特征和噪声的数据。因此，对于多尺度数据，线性滤波器被迫权衡噪声去除的程度与保留的特征的准确性。相比之下，FMH和小波阈值等非线性滤波方法是多尺度的，但不能用于在线整流，提出了基于小波阈值的在线非线性滤波技术。OLMS整流采用小波阈值法对二进长度的移动窗口中的数据进行处理，去除随机误差。采用小波阈值与多尺度中值滤波相结合的方法去除粗误差。理论分析表明，使用Haar小波的OLMS整流包含了二进长度的均值滤波器，而使用更光滑的边界校正小波的整流类似于自适应指数平滑。如果不需要在线进行整流测量，则可以通过对每个窗口中的整流信号进行平均来进一步提高整流质量，从而克服TI整流中遇到的边界效应。综合和工业数据表明了在线多尺度和边界校正平移不变校正方法的优越性。
Darn Rectification by univariate filtering is popular for processes lacking an accurate model. Linear filters are most popular for online filtering; however they are single-scale best suited for rectifying data containing features and noise that are at the same resolution in time and frequency. Consequently, for multiscale data, linear filters are forced to tr ade off the extent of noise removal with the accuracy of the features retained. In contrast nonlinear filtering methods, such as FMH and wavelet thresholding, are multiscale, but they cannot be used for online rectification A technique is presented for online nonlinear filtering based on wavelet thresholding. OLMS rectification applies wavelet thresholding to data in a moving window of dyadic length to remove random errors. Gross errors are removed by combining wavelet thresholding with multiscale median filtering. Theoretical analysis shows that OLMS rectification using Haar wavelets subsumes mean filters of dyadic length, while rectification with smoother boundary corrected wavelets is analogous to adaptive exponential smoothing. If the rectified measurements are not needed online, the quality of rectification can be further improved by averaging the rectified signals in each window, overcoming the boundary effects encountered in TI rectification. Synthetic and industrial data show the benefits of the online multiscale and boundary corrected translation invariant rectification methods.