Nonlinear PCA with Local Approach for Diesel Engine Fault Detection and Diagnosis

This brief examines the application of nonlinear statistical process control to the detection and diagnosis of faults in automotive engines. In this statistical framework, the computed score variables may have a complicated nonparametric distri- bution function, which hampers statistical inference, notably for fault detection and diagnosis. This brief shows that introducing the statistical local approach into nonlinear statistical process control produces statistics that follow a normal distribution, thereby enabling a simple statistical inference for fault detection. Further, for fault diagnosis, this brief introduces a compensation scheme that approximates the fault condition signature. Experimental results from a Volkswagen 1.9-L turbo-charged diesel engine are included.

Process monitoring approach using fast moving window PCA

This paper introduces a fast algorithm for moving window principal component analysis (MWPCA) which will adapt a principal component model. This incorporates the concept of recursive adaptation within a moving window to (i) adapt the mean and variance of the process variables, (ii) adapt the correlation matrix, and (iii) adjust the PCA model by recomputing the decomposition. This paper shows that the new algorithm is computationally faster than conventional moving window techniques, if the window size exceeds 3 times the number of variables, and is not affected by the window size. A further contribution is the introduction of an N-step-ahead horizon into the process monitoring. This implies that the PCA model, identified N-steps earlier, is used to analyze the current observation. For monitoring complex chemical systems, this work shows that the use of the horizon improves the ability to detect slowly developing drifts.

Forensic analysis of architectural finishes using Fourier transform infrared and Raman spectroscopy, Part I: The resin bases

The ability of Raman spectroscopy and Fourier transform infrared (FT-IR) microscopy to discriminate between resins used for the manufacture of architectural finishes was examined in a study of 39 samples taken from a commercial resin library. Both Raman and FT-IR were able to discriminate between different types of resin and both split the samples into several groups (six for FT-IR, six for Raman), each of which gave similar, but not identical, spectra. In addition, three resins gave unique Raman spectra (four in FTIR). However, approximately half the library comprised samples that were sufficiently similar that they fell into a single large group, whether classified using FT-IR or Raman, although the remaining samples fell into much smaller groups. Further sub-division of the FT-IR groups was not possible because the experimental uncertainty was of similar magnitude to the within-group variation. In contrast, Raman spectroscopy was able to further discriminate between resins that fell within the same groups because the differences in the relative band intensities of the resins, although small, were larger than the experimental uncertainty.

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.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Application of Nonlinear PCA for Fault Detection in Polymer Extrusion Processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.