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.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Some advances in study of crack identification problems

In the present paper, the crack identification problems are investigated. This kind of problems belong to the scope of inverse problems and are usually ill-posed on their solutions. The paper includes two parts: (1) Based on the dynamic BIEM and the optimization method and using the measured dynamic information on outer boundary, the identification of crack in a finite domain is investigated and a method for choosing the high sensitive frequency region is proposed successfully to improve the precision. (2) Based on 3-D static BIEM and hypersingular integral equation theory, the penny crack identification in a finite body is reduced to an optimization problem. The investigation gives us some initial understanding on the 3-D inverse problems.

Fiber Dispersion and Nonlinearity Influences on Transmissions of AM and FM Data Modulation Signals in Radio-Over-Fiber System

Transmission properties of data amplitude modulation (AM) and frequency modulation (FM) in radio-over-fiber (RoF) system are studied numerically. The influences of fiber dispersion and nonlinearity on different microwave modulation schemes, including double side band (DSB), single side band (SSB) and optical carrier suppression (OCS), are investigated and compared. The power penalties at the base station (BS) and the eye opening penalties of the recovered data at the end users are both calculated and analyzed. Numerical simulation results reveal that the power penalty of FM can be drastically decreased due to the larger modulation depth it can achieve than that of AM. The local spectrum broadening around subcarrier microwave frequency of AM due to fiber nonlinearity can also be eliminated with FM. It is demonstrated for the first time that the eye openings of the FM recovered data can be controlled by its modulation depths and the coding formats. Negative voltage encoding format was used to further decrease the RF frequency thus increase the fluctuation period considering their inverse relationship.

High-power electroabsorption modulator for radio over fibre system

An electroabsorption modulator using an intra-step quantum well (IQW) active region is fabricated for a radio over fibre system. The strain-compensated InGaAsP/InGaAsP IQW shows good material quality and improved modulation properties, high extinction ratio efficiency (10 dB V-1) and low capacitance (< 0.42 pF), with which high frequency (> 15 GHz) can be obtained. High-speed measurement under high-power excitation shows no power saturation up to an excitation power of 21 dBm. To our knowledge, the input optical power is the highest reported for a multi-quantum well EAM without a heat sink.

The radio counter-jet of the QSO 3C 48

We present multi- frequency radio observational results of the quasar 3C 48. The observations were carried out with the Very Large Array ( VLA) at five frequencies, 0.33, 1.5, 4.8, 8.4, and 22.5 GHz, and with the Multi- Element Radio Linked Interferometer Network ( MERLIN) at the two frequencies of 1.6 and 5 GHz. The source shows a one- sided jet to the north within 1", which then extends to the northeast and becomes diffuse. Two bright components ( N2 and N3), containing most of the flux density, are present in the northern jet. The spectral index of the two components is alpha(N2) similar to -0.99 +/- 0.12 and alpha(N3) similar to - 0.84 +/- 0.23 ( S proportional to nu(alpha)). Our images show the presence of an extended structure surrounding component N2, suggestive of strong interaction between the jet and the interstellar medium ( ISM) of the host galaxy. A steep- spectrum component, labelled S, located 0.25 " southwest to the flat- spectrum component which could be the core of 3C 48, is detected at a significance of > 15 sigma. Both the location and the steepness of the spectrum of component S suggest the presence of a counter- jet in 3C 48.