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.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Phase identification of triphenylene-based discotic monomer and its main chain polymers

A monomer, 2,3,6,7,10,11-hexakispentyloxy triphenylene (HPT) possesses a triphenylene core as a discotic mesogen. Polymers containing this discotic mesogen have been studied using wide-angle X-ray and electron diffraction. HPT is known to show a discotic liquid crystal phase, noted as D-ho (h for hexagonal bidimensional lattice, o for ordered molecular spacing in each column). In this paper, however, HPT Liquid crystalline phases, heated up from the crystalline state and cooled down from the isotropic state, were characterized in the diameter dimensions. In addition. the diameters of the columns are close to a parameter of two separate crystals. A core orientation was, therefore, proposed in the mesophase obtained by heating the crystalline. In order to distinguish these differences, the D-ho phase was divided to include the D-hcd and D-hco phases. Molecular modeling was performed to help our understanding of the orientation. The D-hcd and D-hco phases were used to characterize the phases of the discotic polymeric analogs by comparing their column diameters to those of the monomers. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

AN INTEGRATED CALCIUM-FLUORIDE CRYSTAL IR THIN-LAYER CELL AND ITS APPLICATION TO IDENTIFICATION OF ELECTROCHEMICAL REDUCTION PRODUCT OF BILIRUBIN

An integrated CaF2 crystal optically transparent infrared (ir) thin-layer cell was designed and constructed without using any soluble adhesive materials. It is suitable for both aqueous and nonaqueous systems, and can be used not only in ir but also in uv-vis studies. Excellent electrochemical and spectroelectrochemical responses were obtained in evaluating this cell by cyclic voltammetry and steady-state potential step measurements for both ir and uv-vis spectrolectrochemistry with ferri/ferrocyanide in aqueous solution, and with ferrocene/ferrocenium in organic solvent as the testing species, respectively. The newly designed ir cell was applied to investigate the electrochemical reduction process of bilirubin in situ, which provided direct information for identifying the structure of the reduction product and proposing the reaction mechanism.