Hong Yi Li

An explicit formula for the inverse of a pentadiagonal Toeplitz matrix

In this paper, we mainly consider finding an explicit formula for the inverse of a pentadiagonal Toeplitz matrix. For that purpose, we first factorize the modified form of a pentadiagonal Toeplitz matrix by two tridiagonal Toeplitz matrices, and then use the Sherman-Morrison-Woodbury inversion formula. As a result, an explicit inverse of a pentadiagonal Toeplitz matrix is obtained under certain assumptions. And numerical experiments are given to show the effectiveness of our results.

A New Signal Classification Method Based on EEMD and FCM and its Application in Bearing Fault Diagnosis

In order to diagnose nonlinear and non-stationary fault signals in bearings, a new method is presented based on the ensemble empirical decomposition (EEMD) and the fuzzy c-means (FCM) clustering algorithm. At first, the bearing fault signals were decomposed using EEMD and the intrinsic mode functions (IMF) were produced. Second the energy ratios of these IMFs were computed and taken as the characteristic parameters for the FCM clustering algorithm. Then the FCM clustering method was conducted to classify the bearing fault signals into different classes. Finally, on the basis of the preceding classification results, we diagnosed a bearing fault through taking its distances between different cluster centers as the criteria. Experiments showed that the bearing fault signal classification results conformed to actualities well. The new signal classification method can be effectively utilized in bearing fault diagnosis.

Identification of Power Quality Disturbances Based on FFT and Attribute Weighted Artificial Immune Evolutionary Classifier

Nowadays, the issue of Electromagnetic Compatibility is of great importance and urgency. In this paper, we propose a novel hybrid automatic identification system for power quality disturbances, which lays foundations for further analyzing the electromagnetic compatibility. Specifically, we firstly extract features by using the FFT and envelope detection method. Then we utilize the attribute weighted artificial immune evolutionary Classifier (AWAIEC) for classification of power quality disturbance events. Experimental results have shown that the proposed method performs better than existing approaches.

An ICA and AIS Based Method for Electromagnetic Compatibility Analysis

This paper proposes a novel approach for analyzing and predicting electromagnetic compatibility (EMC). The proposed method mainly consists of two parts. First, we separate input mixed signals from an electromagnetic environment by using fastICA, based on which, subsequently, we train a immune evolutionary network classifier (IENC). The classifier then finally could be used to analysis and predict electromagnetic compatibility. Experimental results have demonstrated the validity of the proposed algorithm.

Improved Schur complement preconditioners for block-Toeplitz systems with small size blocks

In this paper, we employ the preconditioned conjugate gradient method with the Improved Schur complement preconditioners for Hermitian positive definite block-Toeplitz systems with small size blocks. Schur complement preconditioners have been proved to be an effective method for such block-Toeplitz systems (Ching etźal. 2007). The modification is based on Taylor expansion approximation. We prove that the matrices preconditioned by improved Schur preconditioners have more clustered spectra compared to that of the Schur complement preconditioners. Hence, preconditioned conjugate gradient type methods will converge faster. Numerical examples are given to demonstrate the efficiency of the proposed method.

Preconditioning Toeplitz-plus-diagonal linear systems using the Sherman-Morrison-Woodbury formula

In order to solve the Toeplitz-plus-diagonal linear systems arising from image restorations efficiently, we propose a sparse approximate inverse preconditioner based on the Sherman-Morrison-Woodbury formula. The preconditioner can be constructed through an incomplete factorization combined with some dropping strategies. When the preconditioner is applied to the conjugate gradient method for solving the Toeplitz-plus-diagonal linear systems, numerical results show that our preconditioning method is more effective than other existing ones.

An Improved ICA Algorithm Based on the Negative Entropy and Simulated Annealing Algorithm

The Independent Component Analysis (ICA) is a classical algorithm for exploring statistically independent non-Gaussian signals from multi-dimensional data, which has a wide range of applications in engineering, for instance, the blind source separation. The classical ICA measures the Gaussian characteristic by kurtosis, which has the following two disadvantages. Firstly, the kurtosis relies on the value of samples, and is not robust to outliers. Secondly, the algorithm often falls into local optima. To address these drawbacks, we replace the kurtosis by negative entropy, utilize the simulated annealing algorithm for optimization, and finally propose an improved ICA algorithm. Experimental results demonstrate that the proposed algorithm outperforms the classical ICA in its robustness to outliers and convergent rate.

A Simulation and Prediction Method of the Height of Wheat Based on BP Neural Networks and the Ant Colony Algorithm

This paper focuses on the simulation and prediction problem of height of the crops, particularly the wheat, which plays a significantly important role in its yield, in different growing stages. Our model bases on the BP neural network and the ant colony algorithm. Both of these two algorithms has their own advantages and disadvantages. However, through observations, we find that their advantages and disadvantages seem to be complementary, by which we propose the combination algorithm. This combination algorithm can conquer the local optimum problem of the BP Neural Network, and could overcome the shortcomings of the weak local optimum searching capability of the ant colony algorithm. The experiments show that the our proposed algorithm can hopefully yield good simulation and prediction results of the height of wheat in different growing stages.

A Preconditioning Framework for the Empirical Mode Decomposition Method

The empirical mode decomposition (EMD) is a useful method for processing nonlinear and nonstationary signals. However, it usually suffers from the mode mixing problem due to the existence of intermittence and interferences of noises in signals. In this paper, a preconditioning framework for the EMD method is proposed in order to alleviate the mode mixing problem. The key points of the preconditioning before implementing the EMD method lie in two aspects: On the one hand, the interferences of noises in the original signal are reduced by filtering; on the other hand, the assisted signals are added to the denoised signal to improve properties of the signal data. Under this framework, the preconditioned forms of the complementary ensemble empirical mode decomposition method and the masking signal-assisted empirical mode decomposition method are presented, respectively. The effectiveness of the proposed methods is illustrated by numerical simulations and applications to real-world signals.

A One-Stop Method for EMI Analysis Based on Wavelet Packet and SOM

The analysis of electromagnetic interferences (EMI) has been a heated problem in the field of Electromagnetic Compatibility (EMC). As the demand of efficiency and effectiveness is getting higher, the traditional methods have become the short board in analysis process. These methods havent provided a solution to analyze the relation among multiple EMI signals, and the data clustering and mining are currently done manually. To address this problem, in this paper we propose a one-stop method based on the wavelet packet decomposition (WPD) and self-organized feature map (SOM), aiming to provide a systematical and solution to extract and analyze multiple EMI signals. Experimental results are also provided to demonstrate the validity and efficiency of the proposed method.