Huaiqing Zhang

Measurement Data Fitting Based on Moving Least Squares Method

In the electromagnetic field measurement data postprocessing, this paper introduced the moving least squares (MLS) approximation method. The MLS combines the concept of moving window and compact support weighting functions. It can be regarded as a combination of weighted least squares and segmented least square. The MLS not only can acquire higher precision even with low order basis functions, but also has good stability due to its local approximation scheme. An attractive property of MLS is its flexible adjustment ability. Therefore, the data fitting can be easily adjusted by tuning weighting function’s parameters. Numerical examples and measurement data processing reveal its superior performance in curves fitting and surface construction. So the MLS is a promising method for measurement data processing.

Shape parameter selection for multi-quadrics function method in solving electromagnetic boundary value problems

Purpose n n n n– The multi-quadrics (MQ) function is a kind of radial basis function. And the MQ method has been successfully adopted as a type of meshless method in solving electromagnetic boundary value problems. However, the accuracy of MQ interpolation or solving equations is severely influenced by shape parameter. Thus the purpose of this paper is to propose a case-independent shape parameter selection strategy from the aspect of coefficient matrix condition number analysis. n n n n nDesign/methodology/approach n n n n– The condition number of coefficient matrix is investigated. It is shown that the condition number is only a function of shape parameter and MQ node number, and is irrelevant to the interpolated function which means case-independent. The effective condition number which takes into account the interpolated function is introduced. Then, the relation between the relative root mean square error and condition number is analyzed. Three numerical experiments as transmission line, cable channel and grounding metal box model were carried out. n n n n nFindings n n n n– In the numerical experiments, there is an approximate linear relationship between the logarithm of the condition number and shape parameter, an approximate quadratic relationship with node number. And the optimal shape parameter is corresponding to the early stage of condition number oscillation. n n n n nOriginality/value n n n n– This paper proposed a case-independent shape parameter selection strategy. For a finite precision computation, the upper limit of the condition number is predetermined. Therefore, the shape parameter can be chosen where condition number oscillates in early stage.

A Stable Hankel Transforms Algorithm Based on Haar Wavelet Decomposition for Noisy Data

We proposed the combination of signal denoising technology and Hankel transforms algorithm which were both based on Haar wavelet decomposition. Therefore, one can achieve above two purposes simultaneously while the wavelet decomposition is carried out just for once. The principle and its derivation of the Haar wavelet method for Hankel transforms were put forward. Numerical examples and engineering application showed that the precision of Haar wavelet method is about magnitude of and ; it can maintain good accuracy when using fewer wavelet coefficients. Moreover, it has better anti-noise performance and better computational stability than the filter method, so it can be applied to the Hankel transforms with noisy data.

Improved Parameter Identification Method for Envelope Current Signals Based on Windowed Interpolation FFT and DE Algorithm

Envelope current signals are increasingly emerging in power systems, and their parameter identification is particularly necessary for accurate measurement of electrical energy. In order to analyze the envelope current signal, the harmonic parameters, as well as the envelope parameters, need to be calculated. The interpolation fast Fourier transform (FFT) is a widely used approach which can estimate the signal frequency with high precision, but it cannot calculate the envelope parameters of the signal. Therefore, this paper proposes an improved method based on windowed interpolation FFT (WIFFT) and differential evolution (DE). The amplitude and phase parameters obtained through WIFFT and the envelope parameters estimated by the envelope analysis are optimized using the DE algorithm, which makes full use of the performance advantage of DE. The simulation results show that the proposed method can improve the accuracy of the harmonic parameters and the envelope parameter significantly. In addition, it has good anti-noise ability and high precision.

Sample Data Synchronization and Harmonic Analysis Algorithm Based on Radial Basis Function Interpolation

The spectral leakage has a harmful effect on the accuracy of harmonic analysis for asynchronous sampling. This paper proposed a time quasi-synchronous sampling algorithm which is based on radial basis function (RBF) interpolation. Firstly, a fundamental period is evaluated by a zero-crossing technique with fourth-order Newton’s interpolation, and then, the sampling sequence is reproduced by the RBF interpolation. Finally, the harmonic parameters can be calculated by FFT on the synchronization of sampling data. Simulation results showed that the proposed algorithm has high accuracy in measuring distorted and noisy signals. Compared to the local approximation schemes as linear, quadric, and fourth-order Newton interpolations, the RBF is a global approximation method which can acquire more accurate results while the time-consuming is about the same as Newton’s.

Application of Radial Basis Function Method for Solving Nonlinear Integral Equations

The radial basis function (RBF) method, especially the multiquadric (MQ) function, was proposed for one- and two-dimensional nonlinear integral equations. The unknown function was firstly interpolated by MQ functions and then by forming the nonlinear algebraic equations by the collocation method. Finally, the coefficients of RBFs were determined by Newton’s iteration method and an approximate solution was obtained. In implementation, the Gauss quadrature formula was employed in one-dimensional and two-dimensional regular domain problems, while the quadrature background mesh technique originated in mesh-free methods was introduced for irregular situation. Due to the superior interpolation performance of MQ function, the method can acquire higher accuracy with fewer nodes, so it takes obvious advantage over the Gaussian RBF method which can be revealed from the numerical results.

Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions

The Pravin method for Hankel transforms is based on the decomposition of kernel function with exponential function. The defect of such method is the difficulty in its parameters determination and lack of adaptability to kernel function especially using monotonically decreasing functions to approximate the convex ones. This thesis proposed an improved scheme by adding new base function in interpolation procedure. The improved method maintains the merit of Pravin method which can convert the Hankel integral to algebraic calculation. The simulation results reveal that the improved method has high precision, high efficiency, and good adaptability to kernel function. It can be applied to zero-order and first-order Hankel transforms.