Sequential nonlinear manifold learning

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorithms in real-time systems necessitates the development of sequential algorithms that perform feature extraction online. This paper presents an efficient online NLDR scheme, Sequential-Isomap, based on incremental singular value decomposition (SVD) and the Isomap method. Example simulations demonstrate the validity and significant potential of this technique in real-time applications such as autonomous systems.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Identification of copper species present in Cu-ZSM-5 catalysts for NOx reduction

The structure of Cu-ZSM-5 catalysts that show activity for direct NO decomposition and selective catalytic reduction of NOx by hydrocarbons has been investigated by a multitude of modern surface analysis and spectroscopy techniques including X-ray photoelectron spectroscopy, thermogravimetric analysis, and in situ Fourier transform infrared spectroscopy. A series of four catalysts were prepared by exchange of Na-ZSM-5 with dilute copper acetate, and the copper loading was controlled by variation of the solution pH. Underexchanged catalysts contained isolated Cu2+OH-(H2O) species and as the copper loading was increased Cu2+ ions incorporated into the zeolite lattice appeared. The sites at which the latter two copper species were located were fundamentally different. The Cu2+OH-(H2O) moieties were bound to two lattice oxygen ions and associated with one aluminum framework species. In contrast, the Cu2+ ions were probably bound to four lattice oxygen ions and associated with two framework aluminum ions. Once the Cu-ZSM-5 samples attained high levels of exchange, the development of [Cu(μ-OH)2Cu]n2+OH-(H2O) species along with a small concentration of Cu(OH)2 was observed. On activation in helium to 500°C the Cu2+OH-(H2O) species transformed into Cu2+O- and Cu+ moieties, whereas the Cu2+ ions were apparently unaffected by this treatment (apart from the loss of ligated water molecules). Calcination of the precursors resulted in the formation of Cu2+O2- and a one-dimensional CuO species. Temperature-programmed desorption studies revealed that oxygen was removed from the latter two species at 407 and 575°C, respectively. © 1999 Academic Press.

Numerical simulation of idealised three-dimensional downburst wind fields

Convective downburst wind storms generate the peak annual gust wind speed for many parts of the non-cyclonic world at return periods of importance for ultimate limit state design. Despite this there is little clear understanding of how to appropriately design for these wind events given their significant dissimilarities to boundary layer winds upon which most design is based. To enhance the understanding of wind fields associated with these storms a three-dimensional numerical model was developed to simulate a multitude of idealised downburst scenarios and to investigate their near-ground wind characteristics. Stationary and translating downdraft wind events in still and sheared environments were simulated with baseline results showing good agreement with previous numerical work and full-scale observational data. Significant differences are shown in the normalised peak wind speed velocity profiles depending on the environmental wind conditions in the vicinity of the simulated event. When integrated over the height of mid- to high rise structures, all simulated profiles are shown to produce wind loads smaller than an equivalent 10 m height matched open terrain boundary layer profile. This suggests that for these structures the current design approach is conservative from an ultimate loading standpoint. Investigating the influence of topography on the structure of the simulated near-ground downburst wind fields, it is shown that these features amplify wind speeds in a manner similar to that expected for boundary layer winds, but the extent of amplification is reduced. The level of reduction is shown to be dependent on the depth of the simulated downburst outflow.