The Harmonic Decomposition Reconstruction for the Exponential Radon Transform

The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.

Plate/shell topological optimization subjected to linear buckling constraints by adopting composite exponential filtering function

In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function（CEF） is selected as filtering functions for element weight, the element stiffness matrix and the element geometric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete” to “continuous” and back to “discrete”. The buckling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algorithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.

CHEBYSHEV APPROXIMATION OF THE SECOND KIND OF MODIFIED BESSEL FUNCTION OF ORDER ZERO

The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.

Open-Circuit Faults Diagnosis in Direct-Drive PMSG Wind Turbine Converter

The condition monitoring and fault diagnosis have been identified as the key to achieving higher availabilities of wind turbines.Numerous studies show that the open-circuit fault is a significant contributor to the failures of wind turbine converter.However,the multiple faults combinations and the influence of wind speed changes abruptly,grid voltage sags and noise interference have brought great challenges to fault diagnosis.Accordingly,concerning the open-circuit fault of converters in direct-driven PMSG wind turbine,a diagnostic method for multiple open-circuit faults is proposed in this paper,which is divided into two tasks:The first one is the fault detection and the second one is the fault localization.The detection method is based on the relative current residuals after exponential transformation and on an adaptive threshold,and the localization method is based on the average values of fault phase currents.The scheduled diagnosis method is available to both the generator-side converter and the grid-side converter,allowing to detect and locate single and double open-circuit faults.For validating this,robustness test and multiple open-circuit faults diagnosis are presented in a 2-MW direct-driven PMSG wind turbine system,the results validate the reliability and effectiveness of the proposed method.

Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.

Reconstruction Results about the Exponential Radon Transform

In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.