Improved Process Monitoring Using Nonlinear Principal Component Models

This paper presents two new approaches for use in complete process monitoring. The firstconcerns the identification of nonlinear principal component models. This involves the application of linear
principal component analysis (PCA), prior to the identification of a modified autoassociative neural network (AAN) as the required nonlinear PCA (NLPCA) model. The benefits are that (i) the number of the reduced set of linear principal components (PCs) is smaller than the number of recorded process variables, and (ii) the set of PCs is better conditioned as redundant information is removed. The result is a new set of input data for a modified neural representation, referred to as a T2T network. The T2T NLPCA model is then used for complete process monitoring, involving fault detection, identification and isolation. The second approach introduces a new variable reconstruction algorithm, developed from the T2T NLPCA model. Variable reconstruction can enhance the findings of the contribution charts still widely used in industry by reconstructing the outputs from faulty sensors to produce more accurate fault isolation. These ideas are illustrated using recorded industrial data relating to developing cracks in an industrial glass melter process. A comparison of linear and nonlinear models, together with the combined use of contribution charts and variable reconstruction, is presented.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

Deflation based nonlinear canonical correlation analysis

This paper introduces two new techniques for determining nonlinear canonical correlation coefficients between two variable sets. A genetic strategy is incorporated to determine these coefficients. Compared to existing methods for nonlinear canonical correlation analysis (NLCCA), the benefits here are that the nonlinear mapping requires fewer parameters to be determined, consequently a more parsimonious NLCCA model can be established which is therefore simpler to interpret. A further contribution of the paper is the investigation of a variety of nonlinear deflation procedures for determining the subsequent nonlinear canonical coefficients. The benefits of the new approaches presented are demonstrated by application to an example from the literature and to recorded data from an industrial melter process. These studies show the advantages of the new NLCCA techniques presented and suggest that a nonlinear deflation procedure should be considered. (c) 2006 Elsevier B.V. All rights reserved.

Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

Antioxidant activity of coffee model systems

Coffee model systems prepared from combinations of chlorogenic acid (CGA), N-alpha-acetyl-1-arginine (A), sucrose (S), and cellulose (C) were roasted at 240 degreesC for 4 min prior to analysis by UV-visible spectrophotometry, capillary zone electrophoresis (CZE), and the ABTS radical cation decolorization assay. The A/CGA/S/C and A/S/C systems were also fractionated by gel filtration chromatography. Antioxidant activity of the systems showed a positive, nonlinear relationship with the amount of CGA remaining after roasting. Sucrose degradation was a major source of color in the heated systems. There was no relationship between antioxidant activity and color generation.

Information sharing and reporting systems in the UK and Ireland: Professional barriers to reporting child maltreatment concerns

Across the UK recent policy developments have focused on improved information sharing and inter-agency cooperation. Professional non-reporting of child maltreatment concerns has been consistently highlighted as a problem in a range of countries and the research literature indicates that this can happen for a variety of reasons. Characteristics such as the type of abuse and the threshold of evidence available are key factors, as are concerns that reporting will damage the professional-client relationship. Professional discipline can also impact on willingness to report, as can personal beliefs about abuse, attitudes towards child protection services and experiences of court processes. Research examining the role of organisational factors in information sharing and reporting emphasises the importance of training and there are some positive indications that training can increase professional awareness of reporting processes and requirements and help to increase knowledge of child abuse and its symptoms. Nonetheless, this is a complex issue and the need for training to go beyond simple awareness raising is recognised. In order to tackle non-reporting in a meaningful way, childcare professionals need access to on-going multidisciplinary training which is specifically tailored to address the range of different factors which impact on reporting attitudes and behaviours.

Improved Linear Transmit Processing for Single-User and Multi-User MIMO Communications Systems

In this paper, we propose a novel linear transmit precoding strategy for multiple-input, multiple-output (MIMO) systems employing improper signal constellations. In particular, improved zero-forcing (ZF) and minimum mean square error (MMSE) precoders are derived based on modified cost functions, and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders. The superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results. The novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi-user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi-user channels. In both cases, the improved precoding schemes yield significant performance gain compared to the conventional counterparts.

Appearance of the frequency-doubling stimulus at threshold.

PURPOSE. It has been argued that the threshold for detecting frequency-doubling (FD) technology perimeter stimuli differs from the threshold for perceiving spatial structure (pattern) in the same targets. Thresholds for perceiving spatial structure have typically been assessed using orientation-identification experiments. The authors investigated the influence of orientation, edge profile, and psychophysical method on the origin of the reported differences in detection and orientation-identification thresholds for FD gratings.

METHODS. Detection and orientation-identification thresholds were determined in 12 observers with the use of FD stimuli (0.25 cyc/deg, 25 Hz) presented centrally and at 15° eccentricity. Edge profile (square- and Gaussian-windowed) and orientation (horizontal, vertical, and oblique) were independently modified. Detection thresholds were also measured for spatially uniform flickering targets (25 Hz). Orientation-identification thresholds using a two-alternative forced choice (2-AFC) and a two-interval forced choice (2-IFC) method were also compared in five experienced observers.

RESULTS. Orientation-identification and detection thresholds did not significantly differ under any condition tested. Orientation-identification thresholds obtained with 2-AFC were not significantly different from those obtained with 2-IFC. Thresholds for spatially uniform flicker were significantly lower than for FD stimuli.

CONCLUSIONS. The authors found that orientation-identification and detection thresholds for FD gratings did not differ and argue that recent findings to the contrary arise from the inappropriate use of spatially uniform flicker targets as alternatives in 2-IFC experiments.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.