【摘要】：經(jīng)驗(yàn)?zāi)B(tài)分解（empirical mode decomposition，EMD）算法是一種嶄新的能夠自適應(yīng)地處理非平穩(wěn)信號(hào)的時(shí)頻分析方法，目前逐漸展露出了在非平穩(wěn)信號(hào)處理中的獨(dú)特優(yōu)勢(shì)，具有重要的理論研究?jī)r(jià)值和廣闊的應(yīng)用前景。本文從系統(tǒng)的角度深入分析了EMD算法，并著重研究了該算法包絡(luò)生成中三次樣條插值與極值點(diǎn)個(gè)數(shù)的關(guān)系。在此基礎(chǔ)上提出了一個(gè)抑制端點(diǎn)效應(yīng)的新方法，并針對(duì)直升機(jī)聲信號(hào)和爆破地震動(dòng)信號(hào)進(jìn)行了應(yīng)用研究。 從系統(tǒng)角度，，把EMD算法看做一個(gè)多級(jí)串聯(lián)的灰箱系統(tǒng)，指出三次樣條插值是EMD算法中至關(guān)重要的一步。通過(guò)對(duì)三次樣條插值算法的分析，給出了第二類邊界條件和非扭結(jié)點(diǎn)邊界條件下不同極值點(diǎn)個(gè)數(shù)的插值結(jié)果的均方差表達(dá)式，并在此基礎(chǔ)上討論了極值點(diǎn)個(gè)數(shù)與插值結(jié)果的關(guān)系。通過(guò)信號(hào)仿真并與實(shí)測(cè)信號(hào)對(duì)比驗(yàn)證了增加的極值點(diǎn)數(shù)大于一定數(shù)目后，插值結(jié)果不受增加極值點(diǎn)個(gè)數(shù)影響的結(jié)論。 通過(guò)對(duì)鏡像對(duì)稱法、資料擴(kuò)充法和資料重建法進(jìn)行對(duì)比研究，總結(jié)了三種端點(diǎn)效應(yīng)抑制方法的特點(diǎn)和效率性，并在此基礎(chǔ)上提出了一種抑制端點(diǎn)的效應(yīng)的EMD改進(jìn)算法。本方法能夠在保留資料擴(kuò)充法適應(yīng)性的同時(shí)，提高了運(yùn)算效率。通過(guò)對(duì)仿真信號(hào)和實(shí)測(cè)信號(hào)的EMD分解結(jié)果分析，證明該方法高速有效。 將EMD算法應(yīng)用于了直升機(jī)聲信號(hào)的分析中。通過(guò)對(duì)直升機(jī)聲信號(hào)的分析，不僅發(fā)現(xiàn)其主要特性是頻譜為基頻和諧波成分，而且證明對(duì)短時(shí)信號(hào)EMD算法比Fourier變換的分析結(jié)果更優(yōu)。由于直接應(yīng)用Fourier變換不易提取直升機(jī)聲信號(hào)的諧波集，而本文經(jīng)過(guò)EMD分解可以將不同的諧波成分分解到不同的IMF子帶。據(jù)此并結(jié)合直升機(jī)聲信號(hào)的頻譜特點(diǎn)，提出了一種新的峰值判別準(zhǔn)則——距離衰減準(zhǔn)則。對(duì)EMD的分解結(jié)果做Fourier變換，再通過(guò)峰值判別準(zhǔn)則提取諧波集，更易于目標(biāo)識(shí)別與分類。 爆破地震動(dòng)信號(hào)也是一類典型的非線性信號(hào)，本文在對(duì)爆破地震動(dòng)信號(hào)進(jìn)行特性分析基礎(chǔ)上，應(yīng)用EMD算法對(duì)實(shí)測(cè)的爆破地震動(dòng)信號(hào)進(jìn)行了分析，研究了其速度特征和微差時(shí)間，為地震動(dòng)信號(hào)研究提供了新途徑。 本文的研究為EMD算法的改進(jìn)研究提供了有益的理論依據(jù)，并拓展了EMD算法的應(yīng)用領(lǐng)域。
[Abstract]:Empirical Mode decomposition (empirical mode decomposition,EMD) algorithm is a new time-frequency analysis method which can deal with non-stationary signals adaptively. At present, it gradually shows its unique advantages in non-stationary signal processing, and has important theoretical research value and broad application prospects. In this paper, the EMD algorithm is analyzed systematically from a systematic point of view, and the relationship between cubic Spline interpolation and the number of extremum points in envelope generation of the algorithm is studied. On this basis, a new method to suppress the end-point effect is proposed, and the application of helicopter acoustic signal and blasting ground motion signal is studied. From the system point of view, the EMD algorithm is regarded as a multi-stage series gray box system, and it is pointed out that cubic Spline interpolation is an important step in EMD algorithm. Based on the analysis of cubic spline interpolation algorithm, the mean square error expressions of interpolation results with different number of extreme points under the boundary conditions of the second kind of boundary conditions and non-kink points are given, and the relationship between the number of extreme points and the interpolation results is discussed. Through signal simulation and comparison with the measured signal, it is verified that the interpolation results are not affected by the increase of the number of extreme points when the number of extreme points is more than a certain number. By comparing the mirror symmetry method, the data expansion method and the data reconstruction method, the characteristics and efficiency of the three end effect suppression methods are summarized, and an improved EMD algorithm for suppressing the end point effect is proposed. This method can not only preserve the adaptability of the data expansion method, but also improve the operation efficiency. Through the analysis of the EMD decomposition results of the simulation signal and the measured signal, it is proved that the method is high speed and effective. The EMD algorithm is applied to the analysis of helicopter acoustic signal. Through the analysis of helicopter acoustic signal, it is found that the main characteristic of helicopter acoustic signal is that the spectrum is fundamental frequency and harmonic component, and it is proved that the EMD algorithm of short-time signal is better than the analysis result of Fourier transform. Because it is not easy to extract the harmonic set of helicopter acoustic signal by direct application of Fourier transform, different harmonic components can be decomposed into different IMF subbands by EMD decomposition in this paper. Based on the spectrum characteristics of helicopter acoustic signal, a new peak criterion, distance attenuation criterion, is proposed. The decomposition results of EMD are transformed by Fourier, and the harmonic sets are extracted by peak discriminant criterion, which is easier to recognize and classify targets. Blasting ground motion signal is also a kind of typical nonlinear signal. Based on the analysis of the characteristics of blasting ground motion signal, the measured blasting ground motion signal is analyzed by using EMD algorithm, and its velocity characteristics and millisecond time are studied, which provides a new way for the study of ground motion signal. The research in this paper provides a useful theoretical basis for the improvement of EMD algorithm, and expands the application field of EMD algorithm.
【學(xué)位授予單位】：北京理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

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本文編號(hào)：2505079