Adaptive Matching Pursuit (mp) Algorithm-based Signal Decomposition And Its Application

As one o f the rapid developing subjects, signal processing plays a most important part in structural health monitoring, modal parameter identification, mechanical fault diagnosis, damage detection and seismic analysis. Matching pursuit (MP) algorithm, which is proposed based on wavelet transform, has the property of higher time-frequency resolution. For the MP algorithm, the signal atom structure can be arbitrarily chosen according to the prior knowledge without beforehand frequency band partition, so MP algorithm is objective. Unfortunately, MP is a greedy algorithm and the computational efficiency is very low. Therefore the application to engineering is restricted. For this reason, the performance and application of MP algorithm is studied and the method of calculation efficiency is improven in this paper. The main work and researches are as follows:1. Systematically review the method of signal analysis and processing, the development situation and the existing problems. The development and application of adaptive signal decomposition algorithm based MP algorithm are highlighted. The MP method which can adaptively decompose signals according to the characteristics of the waveform is also pointed out.2. The generation process of the time-frequency atom and over-complete atom structure, as well as the the basic theory of the MP algorithm are introduced in details. The time-frequency characteristics of common several atoms are compared. Comparative analysis and simulation results show that MP algorithm can adaptively decompose signal efficiently. With the combination of the Wigner-Ville distribution, the cross-interference terms can be effectively eliminated.3. Propose the fast MP algorithm based on atom structures optimization and Matlab matrix operations. MP algorithm is a greedy algorithm and the matching efficiency is very low. It will spend enormous amount of time when calculating the Wigner-Ville distribution of each match component and superposing them linearly. Based on the existing MP algorithm, the Hilbert transform of the reconstructed signals is utilized to replace several times of Wigner-Ville distribution to improve computational efficiency and complete adaptive signal decomposition. Simulation results show that the proposed method is simple and easily operated and the MP algorithm is efficiently improved.4. Propose the optimum matching filtering of MP algorithm. MP algorithm can chose atom structures according to the prior knowledge, so it has good filtering properties. Comparison among the Empirical mode decomposition (EMD), wavelet and MP algorithm in noise reduction for different noise level signals, the results show that MP filtering is the best. Even the signal to noise ratio is very low (50%noise level), the denoising effect is satisfactory.5. The structure modal parameter identification based on MP algorithm is studied. The presented fast MP algorithm is applied to the modal parameter identification from vibration responses of the testing cantilever under free vibration and stiffness mutation. The finite element analysis results are compared with those of identification. The feasibility and effectiveness in practical applications for the fast MP algorithm is investigated.