【摘要】：隨著電子測(cè)量與信號(hào)處理技術(shù)的發(fā)展,信號(hào)的非平穩(wěn)、非線性特征被廣泛地應(yīng)用在故障診斷、系統(tǒng)辨識(shí)和生物醫(yī)學(xué)儀器等領(lǐng)域。能否有效地提取這些特征通常影響著整個(gè)系統(tǒng)的性能。信號(hào)的時(shí)間-頻率分布作為一種非平穩(wěn)非線性特征得到了越來(lái)越多的重視。希爾伯特-黃變換(HHT)為提取信號(hào)的時(shí)間-頻率特征提供了一種自適應(yīng)并有效的手段。HHT方法的核心是一種自適應(yīng)的信號(hào)分解算法,稱為經(jīng)驗(yàn)?zāi)B(tài)分解(EMD)算法。目前EMD方法缺乏系統(tǒng)的數(shù)學(xué)框架,導(dǎo)致其存在一系列影響分解質(zhì)量的關(guān)鍵問題。本論文通過(guò)對(duì)EMD進(jìn)行深入研究,重點(diǎn)針對(duì)其存在的頻率分辨率問題、模態(tài)混疊問題和采樣率問題建立有效的理論框架并進(jìn)行優(yōu)化和改進(jìn)。取得的主要研究成果為：1.提出一種以輸入信號(hào)高階微分過(guò)零點(diǎn)時(shí)刻作為特征的均值計(jì)算方法。在篩分過(guò)程中,該方法不通過(guò)對(duì)極值點(diǎn)插值生成上下包絡(luò)得到均值,而是通過(guò)直接對(duì)特征點(diǎn)插值得到均值。為說(shuō)明特征選擇的合理性,對(duì)兩個(gè)命題進(jìn)行了理論證明。其一,選用信號(hào)偶數(shù)階微分過(guò)零點(diǎn)作為特征計(jì)算得到的均值信號(hào)與理想均值信號(hào)相關(guān)。其二,提高微分階數(shù)能提高EMD的頻率分辨率。理論分析表明高階微分過(guò)零點(diǎn)作為一種時(shí)間尺度,能夠反映線性信號(hào)的局部振蕩情況。實(shí)驗(yàn)結(jié)果表明該改進(jìn)算法能有效地提高EMD方法對(duì)線性信號(hào)的頻率分離能力,性能符合理論預(yù)期。2.設(shè)計(jì)并實(shí)現(xiàn)一種非等間隔節(jié)點(diǎn)的B樣條非線性濾波器,并基于該濾波器提出一種自適應(yīng)的濾波篩分算法。理論證明了以下四個(gè)命題,并作為算法的依據(jù)。其一,包絡(luò)對(duì)稱或近似對(duì)稱的信號(hào),其理想均值信號(hào)的局部時(shí)間尺度信息可以通過(guò)其包絡(luò)時(shí)間尺度計(jì)算得到。其二,對(duì)包絡(luò)非對(duì)稱的情況,拐點(diǎn)時(shí)間尺度與理想均值信號(hào)的時(shí)間尺度相關(guān)。其三,等間隔B樣條最小二乘擬合(簡(jiǎn)稱B樣條擬合)具有低通濾波器性質(zhì),濾波器的截止頻率由節(jié)點(diǎn)間距決定。其四,非等間隔B樣條擬合具有時(shí)變低通濾波器性質(zhì),其局部截止頻率由局部節(jié)點(diǎn)間隔決定�；谝陨厦},給出一種基于時(shí)變?yōu)V波的篩分算法,對(duì)非平穩(wěn)信號(hào)有較好的分離效果。3.針對(duì)模態(tài)混疊問題,首先提出一種根據(jù)極值點(diǎn)分布進(jìn)行自適應(yīng)擬合迭代的算法。與著名的聚合經(jīng)驗(yàn)?zāi)B(tài)分解(EEMD)進(jìn)行了對(duì)比,EEMD雖然能在一定程度上保證分解結(jié)果時(shí)間尺度的完整性,但是犧牲了EMD方法針對(duì)局部時(shí)間尺度進(jìn)行分解的優(yōu)勢(shì),而且耗時(shí)巨大。對(duì)比分析結(jié)果表明,本論文提出的迭代算法不但能有效消除噪聲對(duì)信號(hào)極值點(diǎn)的干擾,而且能很好地保留EMD局部分解的優(yōu)點(diǎn)。然后,同樣針對(duì)模態(tài)混疊問題,提出一種基于全局時(shí)間尺度的均值計(jì)算方法。該算法基于本論文的B樣條濾波器的截止頻率特性理論成果,提出一種三試探尺度理論框架,可用于均值信號(hào)的篩選和提取。理論分析表明該改進(jìn)方法有較好的收斂性。與EEMD進(jìn)行比較,結(jié)果表明本文方法有更高的頻率解析精度,對(duì)噪聲或間斷的干擾有更好的抑制性能。4.提出一種對(duì)極值點(diǎn)時(shí)刻進(jìn)行重新采樣的均值計(jì)算方法。與EMD方法相比,該方法不依賴于信號(hào)極值點(diǎn)的準(zhǔn)確位置和取值,因此不容易受到低采樣率的影響。仿真結(jié)果表明,該方法能在接近奈奎斯特頻率的低采樣率下獲得較高的性能。與基于插值的解決方案相比,本文方法的精度更高。在低采樣率情況下給出本征模態(tài)函數(shù)(IMF)的補(bǔ)充定義。IMF要求信號(hào)的包絡(luò)必須關(guān)于時(shí)間軸對(duì)稱。我們通過(guò)分析表明該條件只在采樣率較高的場(chǎng)合才成立。結(jié)合HHT時(shí)頻分析方法的本質(zhì),使用瞬時(shí)帶寬對(duì)IMF進(jìn)行補(bǔ)充定義,使IMF在低采樣率下也能保證性能。實(shí)驗(yàn)結(jié)果證實(shí)了該定義的正確性。
[Abstract]:With the development of the electronic measurement and signal processing technology, the non-stationary and non-linear features of the signal are widely used in the fields of fault diagnosis, system identification and biomedical instruments. The ability to efficiently extract these features generally affects the performance of the overall system. The time-frequency distribution of the signal has gained more and more attention as a non-stationary non-linear feature. The Hilbert-Huang transform (HHT) provides an adaptive and effective means to extract the time-frequency characteristics of the signal. The core of the HHT method is an adaptive signal decomposition algorithm called the empirical mode decomposition (EMD) algorithm. At present, the EMD method lacks the mathematical framework of the system, resulting in a series of key problems affecting the decomposition quality. In this paper, the EMD is deeply researched, and the effective theoretical framework is set up for the problem of frequency resolution, the problem of mode aliasing and the sampling rate, and the optimization and improvement are made. The main research results are as follows:1. In this paper, a method for calculating the mean value of an input signal high-order differential zero-crossing time is proposed. In the process of screening, the method does not generate the mean value of the upper and lower envelope by the interpolation of the extreme point, but the average value is obtained by directly interpolating the characteristic points. In order to explain the rationality of feature selection, two propositions have been proved. First, the average signal obtained by using the signal even-order differential zero-crossing as the characteristic is correlated with the ideal mean signal. Second, the improvement of the differential order can improve the frequency resolution of EMD. The theoretical analysis shows that the high order differential zero crossing is a time scale and can reflect the local oscillation of the linear signal. The experimental results show that the improved algorithm can effectively improve the frequency separation capability of the EMD method to the linear signal, and the performance is in accordance with the theoretical expectation. A non-uniform B-spline nonlinear filter is designed and implemented, and an adaptive filtering and screening algorithm is proposed based on the filter. The following four propositions are proved and used as the basis of the algorithm. First, the envelope is symmetrical or approximately symmetrical, and the local time scale information of the ideal mean signal can be calculated by its envelope time scale. Secondly, when the envelope is asymmetric, the time scale of the inflection point is related to the time scale of the ideal mean signal. Third, the equal-interval B-spline least square fitting (B-spline fitting) has a low-pass filter property, and the cut-off frequency of the filter is determined by the node spacing. And the local cut-off frequency of the four-and non-equal-interval B-spline fitting has a time-varying low-pass filter property, and the local cut-off frequency is determined by the local node interval. Based on the above proposition, a screening algorithm based on time-varying filtering is presented, which has good separation effect on non-stationary signals. In order to solve the problem of mode aliasing, an algorithm for adaptive fitting iteration based on the distribution of the extreme points is proposed. In contrast to the well-known empirical mode decomposition (EEMD), EEMD can ensure the completeness of the time scale of the decomposition results to a certain extent, but the advantage of EMD method for the decomposition of the local time scale is sacrificed, and the time consuming is huge. The results of the comparative analysis show that the iterative algorithm proposed in this paper can not only effectively eliminate the interference of the noise to the extreme point of the signal, but also can well retain the local decomposition of the EMD. Then, a method for calculating the mean time scale based on the global time scale is proposed. Based on the theoretical results of the cut-off frequency characteristic of the B-spline filter in this paper, a three-probe-scale theoretical framework is proposed, which can be used to filter and extract the mean signal. The theoretical analysis shows that the improved method has better convergence. Compared with EEMD, the results show that the method has higher frequency resolution precision, and can better restrain the noise or intermittent interference. This paper presents a method for calculating the mean value of re-sampling at the time of the extreme point. Compared with the EMD method, the method does not depend on the accurate position and the value of the signal extreme point, so that the method is not easy to be affected by the low sampling rate. The simulation results show that the method can obtain higher performance at a low sampling rate close to the Nyquist frequency. The accuracy of this method is higher as compared to an interpolation-based solution. An additional definition of the eigenmode function (IMF) is given at a low sampling rate. The IMF requires the envelope of the signal to be axisymmetric with respect to time. The analysis shows that the condition is only established when the sampling rate is high. In combination with the nature of the HHT time-frequency analysis method, the IMF is defined by the instantaneous bandwidth, so that the IMF can guarantee the performance at a low sampling rate. The experimental results confirm the correctness of the definition.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN713;TN911.6

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