经验模态分解中关键问题的优化理论与方法研究

发布时间：2019-03-21 18:04

【摘要】：随着电子测量与信号处理技术的发展,信号的非平稳、非线性特征被广泛地应用在故障诊断、系统辨识和生物医学仪器等领域。能否有效地提取这些特征通常影响着整个系统的性能。信号的时间-频率分布作为一种非平稳非线性特征得到了越来越多的重视。希尔伯特-黄变换(HHT)为提取信号的时间-频率特征提供了一种自适应并有效的手段。HHT方法的核心是一种自适应的信号分解算法,称为经验模态分解(EMD)算法。目前EMD方法缺乏系统的数学框架,导致其存在一系列影响分解质量的关键问题。本论文通过对EMD进行深入研究,重点针对其存在的频率分辨率问题、模态混叠问题和采样率问题建立有效的理论框架并进行优化和改进。取得的主要研究成果为：1.提出一种以输入信号高阶微分过零点时刻作为特征的均值计算方法。在筛分过程中,该方法不通过对极值点插值生成上下包络得到均值,而是通过直接对特征点插值得到均值。为说明特征选择的合理性,对两个命题进行了理论证明。其一,选用信号偶数阶微分过零点作为特征计算得到的均值信号与理想均值信号相关。其二,提高微分阶数能提高EMD的频率分辨率。理论分析表明高阶微分过零点作为一种时间尺度,能够反映线性信号的局部振荡情况。实验结果表明该改进算法能有效地提高EMD方法对线性信号的频率分离能力,性能符合理论预期。2.设计并实现一种非等间隔节点的B样条非线性滤波器,并基于该滤波器提出一种自适应的滤波筛分算法。理论证明了以下四个命题,并作为算法的依据。其一,包络对称或近似对称的信号,其理想均值信号的局部时间尺度信息可以通过其包络时间尺度计算得到。其二,对包络非对称的情况,拐点时间尺度与理想均值信号的时间尺度相关。其三,等间隔B样条最小二乘拟合(简称B样条拟合)具有低通滤波器性质,滤波器的截止频率由节点间距决定。其四,非等间隔B样条拟合具有时变低通滤波器性质,其局部截止频率由局部节点间隔决定。基于以上命题,给出一种基于时变滤波的筛分算法,对非平稳信号有较好的分离效果。3.针对模态混叠问题,首先提出一种根据极值点分布进行自适应拟合迭代的算法。与著名的聚合经验模态分解(EEMD)进行了对比,EEMD虽然能在一定程度上保证分解结果时间尺度的完整性,但是牺牲了EMD方法针对局部时间尺度进行分解的优势,而且耗时巨大。对比分析结果表明,本论文提出的迭代算法不但能有效消除噪声对信号极值点的干扰,而且能很好地保留EMD局部分解的优点。然后,同样针对模态混叠问题,提出一种基于全局时间尺度的均值计算方法。该算法基于本论文的B样条滤波器的截止频率特性理论成果,提出一种三试探尺度理论框架,可用于均值信号的筛选和提取。理论分析表明该改进方法有较好的收敛性。与EEMD进行比较,结果表明本文方法有更高的频率解析精度,对噪声或间断的干扰有更好的抑制性能。4.提出一种对极值点时刻进行重新采样的均值计算方法。与EMD方法相比,该方法不依赖于信号极值点的准确位置和取值,因此不容易受到低采样率的影响。仿真结果表明,该方法能在接近奈奎斯特频率的低采样率下获得较高的性能。与基于插值的解决方案相比,本文方法的精度更高。在低采样率情况下给出本征模态函数(IMF)的补充定义。IMF要求信号的包络必须关于时间轴对称。我们通过分析表明该条件只在采样率较高的场合才成立。结合HHT时频分析方法的本质,使用瞬时带宽对IMF进行补充定义,使IMF在低采样率下也能保证性能。实验结果证实了该定义的正确性。
[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.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN713;TN911.6

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