A new fault detection method for non-Gaussian process based on robust independent component analysis

Conventional fault detection method based on fast independent component analysis (FastICA) is sensitive to outliers in the modeling data and thus may perform poorly under the adverse effects of outliers. To solve such problem, a new fault detection method for non-Gaussian process based on robust independent component analysis (RobustICA) is proposed in this paper. A RobustICA algorithm which can effectively reduce the effects of outliers is firstly developed to estimate the mixing matrix and extract non-Gaussian feature called independent components (ICs) by robust whitening and robust determination of the maximum non-Gaussian directions. Furthermore, a monitoring statistic for each extracted IC is constructed to detect process faults. Simulations on a simple example of the mixing matrix estimation and a fault detection example in the continuous stirred tank reactor system demonstrate that the RobustICA achieves much higher estimation accuracy for the mixing matrix and the ICs than the commonly used FastICA algorithm, and the RobustICA-based fault detection method outperforms the conventional FastICA-based fault detection method in terms of the fault detection time and fault detection rate.     

Measures of preferred direction for environmental and ecological circular data

Circular or angular variables indicating direction or cyclical time can be of great interest to scientists studying ecology, biology or environmental issues. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called “wrap-around effect” on the circle, which exists because there is no natural minimum or maximum. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for its circular nature. Three choices for summarizing the preferred direction (the sample circular mean, sample circular median and a circular analog of the Hodges–Lehmann estimator) are discussed, with examples from environmental and ecological applications. Similar to the linear data case, the relative emphases of different methods sometimes yield different measures of preferred direction in the presence of outliers or lack of symmetry in the original data. Received: November 2003 / Revised: June 2004     

Distributions of personal VOC exposures: a population-based analysis

Information regarding the distribution of volatile organic compound (VOC) concentrations and exposures is scarce, and there have been few, if any, studies using population-based samples from which representative estimates can be derived. This study characterizes distributions of personal exposures to ten different VOCs in the U.S. measured in the 1999-2000 National Health and Nutrition Examination Survey (NHANES). Personal VOC exposures were collected for 669 individuals over 2-3 days, and measurements were weighted to derive national-level statistics. Four common exposure sources were identified using factor analyses: gasoline vapor and vehicle exhaust, methyl tert-butyl ether (MBTE) as a gasoline additive, tap water disinfection products, and household cleaning products. Benzene, toluene, ethyl benzene, xylenes chloroform, and tetrachloroethene were fit to log-normal distributions with reasonably good agreement to observations. 1,4-Dichlorobenzene and trichloroethene were fit to Pareto distributions, and MTBE to Weibull distribution, but agreement was poor. However, distributions that attempt to match all of the VOC exposure data can lead to incorrect conclusions regarding the level and frequency of the higher exposures. Maximum Gumbel distributions gave generally good fits to extrema, however, they could not fully represent the highest exposures of the NHANES measurements. The analysis suggests that complete models for the distribution of VOC exposures require an approach that combines standard and extreme value distributions, and that carefully identifies outliers. This is the first study to provide national-level and representative statistics regarding the VOC exposures, and its results have important implications for risk assessment and probabilistic analyses.     

A new procedure to optimize the selection of groups in a classification tree: Applications for ecological data

Agglomerative cluster analyses encompass many techniques, which have been widely used in various fields of science. In biology, and specifically ecology, datasets are generally highly variable and may contain outliers, which increase the difficulty to identify the number of clusters. Here we present a new criterion to determine statistically the optimal level of partition in a classification tree. The criterion robustness is tested against perturbated data (outliers) using an observation or variable with values randomly generated. The technique, called Random Simulation Test (RST), is tested on (1) the well-known Iris dataset [Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugenic. 7, 179–188], (2) simulated data with predetermined numbers of clusters following Milligan and Cooper [Milligan, G.W., Cooper, M.C., 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179] and finally (3) is applied on real copepod communities data previously analyzed in Beaugrand et al. [Beaugrand, G., Ibanez, F., Lindley, J.A., Reid, P.C., 2002. Diversity of calanoid copepods in the North Atlantic and adjacent seas: species associations and biogeography. Mar. Ecol. Prog. Ser. 232, 179–195]. The technique is compared to several standard techniques. RST performed generally better than existing algorithms on simulated data and proved to be especially efficient with highly variable datasets.