Multivariate Statistical Process Monitoring Using Robust Nonlinear Principal Component Analysis

The principal component analysis （PCA） algorithm is widely applied in a diverse range of fields for performance assessment, fault detection, and diagnosis. However, in the presence of noise and gross errors, the nonlinear PCA （NLPCA） using autoassociative bottle-neck neural networks is so sensitive that the obtained model differs significantly from the underlying system. In this paper, a robust version of NLPCA is introduced by replacing the generally used error criterion mean squared error with a mean log squared error. This is followed by a concise analysis of the corresponding training method. A novel multivariate statistical process monitoring （MSPM） scheme incorporating the proposed robust NLPCA technique is then investigated and its efficiency is assessed through application to an industrial fluidized catalytic cracking plant. The results demonstrate that, compared with NLPCA, the proposed approach can effectively reduce the number of false alarms and is, hence, expected to better monitor real-world processes.

Taiwan’ Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis to Multi-Channel Total Electron Content Records

This research uses eigenvalue characteristics of nonlinear principal component analysis （NLPCA） and principal component analysis （PCA） to investigate total electron content （TEC） anomalies associated with Taiwan＇s Chi-Chi earthquake of 21 September 1999 （LT） （M_w=7.6）. The transforms are used for ionospheric TEC from 01 August to 20 September 1999 （local time） using data from 13 GPS receivers. The data were collected at 22°N-26°N Lat. and 120°E-122°E Long.. Applying the NLPCA to the multi-channel total electron content records of GPS receivers, the earthquake-associated TEC anomalies were represented by large principal eigenvalues of NLPCA （〉0.5 in a normalized set） on 14 August and 17, 18, and 20 September, with allowance given for the Dst index, which was quiet for the study period. Comparisons were then made with other researchers who also found TEC anomalies on September 17, 18, and 19 associated with the Chi-Chi earthquake, which cannot be detected by PCA.Consideration is also given for reported ground level geomagnetic field activity that occurred between mid-August and late October, leading up to and including the Chi-Chi and Chia-Yi earthquakes, which are associated with the same series of faults. It is possible that Aug. 14 is representative of an earthquake-associated TEC anomaly. This is an interesting result given how much earlier than the earthquake it occurred.

Nonlinear Principal Component Analysis Using Strong Tracking Filter

The paper analyzes the problem of blind source separation （BSS） based on the nonlinear principal component analysis （NPCA） criterion. An adaptive strong tracking filter （STF） based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.

Advances in adaptive nonlinear manifolds and dimensionality reduction

Recent decades have witnessed a much increased demand for advanced,effective and efficient methods and tools for analyzing,understanding and dealing with data of increasingly complex,high dimensionality and large volume.Whether it is in biology,neuroscience,modern medicine and social sciences or in engineering and computer vision,data are being sampled,collected and cumulated in an unprecedented speed.It is no longer a trivial task to analyze huge amounts of high dimensional data.A systematic,automated way of interpreting data and representing them has become a great challenge facing almost all fields and research in this emerging area has flourished.Several lines of research have embarked on this timely challenge and tremendous progresses and advances have been made recently.Traditional and linear methods are being extended or enhanced in order to meet the new challenges.This paper elaborates on these recent advances and discusses various state-of-the-art algorithms proposed from statistics,geometry and adaptive neural networks.The developments mainly follow three lines:multidimensional scaling,eigen-decomposition as well as principal manifolds.Neural approaches and adaptive or incremental methods are also reviewed.In the first line,traditional multidimensional scaling(MDS)has been extended not only to be more adaptive such as neural scale,curvilinear component analysis(CCA)and visualization induced self-organizing map(ViSOM)for online learning,but also to be more local scaling such as Isomap for enhanced flexibility for nonlinear data sets.The second line extends linear principal component analysis(PCA)and has attracted a huge amount of interest and enjoyed flourishing advances with methods like kernel PCA(KPCA),locally linear embedding(LLE)and Laplacian eigenmap.The advantage is obvious:a nonlinear problem is transformed into a linear one and a unique solution can then be sought.The third line starts with the nonlinear principal curve and surface and links up with adaptive neural network approaches such as self-organizing map(SOM)and ViSOM.Many of these frameworks have been further improved and enhanced for incremental learning and mapping function generalization.This paper discusses these recent advances and their connections.Their application issues and implementation matters will also be briefly enlightened and commented on.