Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Influence of heated catalyzer on thermal distribution of substrate in HWCVD system

Based on Stefan-Boltzman and Lambert theorems, the radiation energy distribution on substrate (REDS) from catalyzer with parallel filament geometry has been simulated by variation of filament and system layout in hot-wire chemical vapor deposition. The REDS uniformity is sensitive to the distance between filament and substrate d(f-s) when d(f-s) less than or equal to 4 cm. As d(f-s) > 4 cm, the REDS uniformity is independent of d(f-s) and is mainly determined by filament number and filament separation. Two-dimensional calculation shows that the REDS uniformity is limited by temperature decay at filament edges. The simulation data are in good agreement with experiments. (C) 2003 Elsevier Science B.V. All rights reserved.

Influence of heated catalyzer on thermal distribution of substrate in HWCVD system

Based on Stefan-Boltzman and Lambert theorems, the radiation energy distribution on substrate (REDS) from catalyzer with parallel filament geometry has been simulated by variation of filament and system layout in hot-wire chemical vapor deposition. The REDS uniformity is sensitive to the distance between filament and substrate d(f-s) when d(f-s) less than or equal to 4 cm. As d(f-s) > 4 cm, the REDS uniformity is independent of d(f-s) and is mainly determined by filament number and filament separation. Two-dimensional calculation shows that the REDS uniformity is limited by temperature decay at filament edges. The simulation data are in good agreement with experiments. (C) 2003 Elsevier Science B.V. All rights reserved.

Abel Inversion of Axially-Symmetric Shock Wave Flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.

Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.