發(fā)布時間：2019-03-30 16:16

【摘要】：小波脊線的提取是非平穩(wěn)信號時頻分析領(lǐng)域的一項重要內(nèi)容。利用小波脊線包含的信息可以實現(xiàn)對信號瞬態(tài)特征的估計、對信號的分解重構(gòu)和濾波，以及對系統(tǒng)的模態(tài)參數(shù)識別。目前，基于小波系數(shù)模極大值和相位信息的脊線提取算法有其各自的缺陷性。因此，為了減少小波變換的冗余性、提高脊線提取的效率、實現(xiàn)對多脊線信號的精確提取，本文研究了基于小波變換偏微分方程的脊線提取算法，探討了算法中每個過程的實現(xiàn)以及各參數(shù)對結(jié)果的影響，并成功地將該算法應用于信號的分解重構(gòu)以及系統(tǒng)的模態(tài)參數(shù)識別中，仿真實驗的結(jié)果驗證了算法的有效性和準確性。 本文的主要研究工作如下： （1）研究了連續(xù)小波變換的原理和實現(xiàn)過程，從信號小波脊線和小波骨架的概念、方法和應用等方面進行了理論研究，，對小波變換的基函數(shù)進行了變參數(shù)的改進。 （2）實現(xiàn)了一種基于小波變換偏微分方程的脊線提取算法。從小波脊線的模極大值定義和連續(xù)小波變換的偏微分方程開始，詳細推導了算法的原理，設(shè)計了算法的數(shù)值計算實現(xiàn)步驟，結(jié)合該算法和改進的Morlet小波形式，對算法過程中多個參數(shù)的選取進行了詳細地研究，并給出了各參數(shù)選取的基本原則。成功實現(xiàn)了該算法對信號小波脊線的提取和信號各分量的重構(gòu)。 （3）將脊線提取算法應用于系統(tǒng)的模態(tài)參數(shù)識別中。研究了小波脊線和系統(tǒng)模態(tài)參數(shù)的關(guān)系，推導出了小波脊線識別模態(tài)參數(shù)的計算公式。分別用三自由度仿真系統(tǒng)和弧形結(jié)構(gòu)模態(tài)實驗對算法的有效性進行驗證。仿真信號的識別結(jié)果具有很高的精度，弧形結(jié)構(gòu)的模態(tài)頻率識別具有較高的精度，分析了阻尼比產(chǎn)生偏差的原因。 （4）編制開發(fā)了基于MATLAB圖形用戶界面的小波時頻-脊線分析軟件。對軟件進行了總體設(shè)計和需求分析，設(shè)計了軟件的主界面，合理安排軟件各功能模塊的布局，對各功能模塊進行了詳細設(shè)計。選擇簡單實用的控件，采用結(jié)構(gòu)化的編程方式，實現(xiàn)了算法的各個功能。對軟件的主要功能模塊進行了仿真測試與應用，驗證了軟件的算法有效性和技術(shù)實用性。
[Abstract]:Wavelet ridge extraction is an important content in time-frequency analysis of non-stationary signals. The information contained in the wavelet ridge line can be used to estimate the transient characteristics of the signal, to decompose and filter the signal, and to identify the modal parameters of the system. At present, ridge extraction algorithms based on wavelet coefficient modulus Maxima and phase information have their own defects. Therefore, in order to reduce the redundancy of wavelet transform, improve the efficiency of ridge line extraction, and realize the accurate extraction of multi-ridge line signal, the algorithm of ridge line extraction based on partial differential equation of wavelet transform is studied in this paper. The realization of each process in the algorithm and the influence of each parameter on the results are discussed. The algorithm is successfully applied to signal decomposition and reconstruction and modal parameter identification of the system. The simulation results show that the algorithm is effective and accurate. The main work of this paper is as follows: (1) the principle and realization process of continuous wavelet transform are studied, and the concept, method and application of signal wavelet ridge and wavelet skeleton are studied theoretically. The basis function of wavelet transform is improved by changing parameters. (2) A ridge line extraction algorithm based on partial differential equation of wavelet transform is implemented. Starting from the definition of modulus Maxima of wavelet ridge line and partial differential equation of continuous wavelet transform, the principle of the algorithm is deduced in detail, and the steps of numerical calculation are designed. The algorithm is combined with the improved Morlet wavelet form. The selection of several parameters in the process of the algorithm is studied in detail, and the basic principles of the selection of each parameter are given. The algorithm is successfully implemented to extract the wavelet ridge and reconstruct the components of the signal. (3) the ridge line extraction algorithm is applied to the modal parameter identification of the system. The relationship between the wavelet ridge line and the modal parameters of the system is studied, and the formula for calculating the modal parameters of the wavelet ridge line identification is derived. The validity of the algorithm is verified by the three-degree-of-freedom simulation system and the modal experiment of arc structure. The identification results of simulated signals have high accuracy, and the modal frequency identification of arc structures has high accuracy. The reasons for the deviation of damping ratio are analyzed. (4) the wavelet time-frequency-ridge analysis software based on MATLAB graphical user interface is developed. The main interface of the software is designed, the layout of each function module of the software is reasonably arranged, and the function modules are designed in detail. Select the simple and practical control, adopt the structured programming mode, realize each function of the algorithm. The main function modules of the software are simulated and tested and applied to verify the algorithm effectiveness and technical practicability of the software.
【學位授予單位】：南京航空航天大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.6

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本文編號：2450253