CN115828073B - Complexity and power dual-spectrum generation method based on uniform phase modal decomposition - Google Patents

Complexity and power dual-spectrum generation method based on uniform phase modal decomposition Download PDF

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CN115828073B
CN115828073B CN202310163886.0A CN202310163886A CN115828073B CN 115828073 B CN115828073 B CN 115828073B CN 202310163886 A CN202310163886 A CN 202310163886A CN 115828073 B CN115828073 B CN 115828073B
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CN115828073A (en
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叶建宏
胡祎东
史文彬
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Beijing Institute of Technology BIT
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Abstract

本发明公开了一种基于均匀相位模态分解的复杂度与功率双谱的生成方法，涉及信号处理技术领域。该方法的具体实施方式包括：设置多个目标分解频点

Figure ZY_1
，对原始信号
Figure ZY_2
进行UPEMD分解，获取所述原始信号
Figure ZY_3
在所述目标分解频点
Figure ZY_4
下的信号分量
Figure ZY_5
；计算所述目标分解频点
Figure ZY_6
的信号分量
Figure ZY_7
的信号复杂度和功率谱密度值，生成复杂度频谱和功率频谱。该实施方式能够通过一组具有均匀相位分布的掩模信号辅助，引入均匀相位经验模态分解，对非平稳、非线性信号进行分解，从而生成复杂度和功率双谱，将UPEMD和复杂度、功率相结合，可在避免模态混合和模态分裂条件下，在目标频率附近提取本征模态函数IMF，最大限度减小附加振荡残差。

Figure 202310163886

The invention discloses a method for generating bispectrum of complexity and power based on uniform phase mode decomposition, and relates to the technical field of signal processing. The specific implementation of the method includes: setting a plurality of target decomposition frequency points

Figure ZY_1
, for the original signal
Figure ZY_2
Perform UPEMD decomposition to obtain the original signal
Figure ZY_3
In the target decomposition frequency point
Figure ZY_4
The signal component under
Figure ZY_5
; Calculate the target decomposition frequency point
Figure ZY_6
signal component of
Figure ZY_7
The signal complexity and power spectral density values of , generate a complexity spectrum and a power spectrum. This embodiment can use a set of mask signals with uniform phase distribution to assist, introduce uniform phase empirical mode decomposition, and decompose non-stationary and nonlinear signals, thereby generating complexity and power bispectrum, combining UPEMD and complexity, The combination of power can extract the intrinsic mode function IMF near the target frequency under the condition of avoiding mode mixing and mode splitting, and minimize the additional oscillation residual.

Figure 202310163886

Description

基于均匀相位模态分解的复杂度与功率双谱的生成方法Complexity and power bispectrum generation method based on uniform phase modal decomposition

技术领域Technical Field

本发明属于信号处理技术领域，具体涉及一种基于均匀相位模态分解的复杂度与功率双谱的生成方法。The present invention belongs to the technical field of signal processing, and in particular relates to a method for generating complexity and power bispectrum based on uniform phase modal decomposition.

背景技术Background Art

非平稳信号的分布参数或分布规律随时间动态变化，其在复杂系统中广泛存在，如雷达、地震、语音和医学生物等信号。复杂度是用于评估信号动态变化程度（如，非平稳性）的重要指标。The distribution parameters or distribution laws of non-stationary signals change dynamically over time. They are widely present in complex systems, such as radar, earthquake, speech, and medical biological signals. Complexity is an important indicator for evaluating the degree of dynamic change of signals (e.g., non-stationarity).

然而，现有的复杂度分析过程中，仅关注原始信号的Lempel-Ziv复杂度（Lempel-Ziv complexity，即LZC），并未对多频率LZC的变化趋势进行考虑，为了保留输入信号分量的动态性，需以非线性、非平稳分解方法进行拆分，常用的有经验模态分解（EMD）、噪声辅助EMD(NA-EMD)、掩模EMD，EMD可将时间序列分解为多个频率范围的本征模态函数。但是，由于不同频率成分的存在，使得EMD存在模式混叠问题；NA-EMD通过白噪声填补频率调制中不连续的空白，可以解决模态混叠问题，但是可能导致模态分裂现象，即同一频率段信号分量分散于多个IMF；掩模EMD与NA-EMD步骤类似，但对掩模信号进行180度相移，于感兴趣频率段范围计算两个相应IMF的平均，得到目标IMF，可以不受随机分布白噪声干扰，降低白噪声残余导致的信号干扰，以及迭代计算产生的计算开销，但是，实际输入信号中存在高频噪声的污染，加上模态分裂导致掩模信号存在残差，使得掩模EMD的适用较为局限。However, in the existing complexity analysis process, only the Lempel-Ziv complexity (LZC) of the original signal is focused on, and the changing trend of multi-frequency LZC is not considered. In order to retain the dynamics of the input signal components, nonlinear and non-stationary decomposition methods are required for decomposition. Commonly used methods include empirical mode decomposition (EMD), noise-assisted EMD (NA-EMD), and mask EMD. EMD can decompose the time series into intrinsic mode functions of multiple frequency ranges. However, due to the existence of different frequency components, EMD has the problem of mode aliasing; NA-EMD can solve the problem of mode aliasing by filling the discontinuous gaps in frequency modulation with white noise, but it may cause mode splitting, that is, the signal components in the same frequency band are scattered in multiple IMFs; Mask EMD is similar to NA-EMD in steps, but the mask signal is phase shifted 180 degrees, and the average of the two corresponding IMFs is calculated in the frequency band of interest to obtain the target IMF, which is not affected by randomly distributed white noise, reduces the signal interference caused by white noise residue, and the computational overhead generated by iterative calculation. However, the actual input signal is contaminated by high-frequency noise, and the mask signal has residuals due to mode splitting, which makes the applicability of Mask EMD more limited.

发明内容Summary of the invention

有鉴于此，本发明提供了一种基于均匀相位模态分解的复杂度与功率双谱的生成方法，能够通过一组具有均匀相位分布的掩模信号辅助，引入均匀相位经验模态分解(UPEMD)，对非平稳、非线性信号进行分解，从而生成复杂度和功率双谱，将UPEMD和复杂度、功率相结合，可在避免模态混合和模态分裂条件下，在目标频率附近提取IMF，最大限度减小附加振荡残差。In view of this, the present invention provides a method for generating complexity and power bispectrum based on uniform phase modal decomposition, which can introduce uniform phase empirical mode decomposition (UPEMD) with the assistance of a set of mask signals with uniform phase distribution, decompose non-stationary and nonlinear signals, thereby generating complexity and power bispectrum. By combining UPEMD with complexity and power, IMF can be extracted near the target frequency while avoiding mode mixing and mode splitting, thereby minimizing the additional oscillation residual.

实现本发明的技术方案如下：The technical solution for implementing the present invention is as follows:

一种基于均匀相位模态分解的复杂度与功率双谱的生成方法，包括：A method for generating complexity and power bispectrum based on uniform phase modal decomposition, comprising:

设置多个目标分解频点

Figure SMS_1
，对原始信号
Figure SMS_2
进行UPEMD分解，获取所述原始信号
Figure SMS_3
在所述目标分解频点
Figure SMS_4
下的信号分量
Figure SMS_5
；Set multiple target decomposition frequency points
Figure SMS_1
, for the original signal
Figure SMS_2
Perform UPEMD decomposition to obtain the original signal
Figure SMS_3
At the target decomposition frequency
Figure SMS_4
The signal component
Figure SMS_5
;

计算所述目标分解频点

Figure SMS_6
的信号分量
Figure SMS_7
的信号复杂度和功率谱密度值，生成复杂度频谱和功率频谱。Calculate the target decomposition frequency point
Figure SMS_6
The signal component
Figure SMS_7
The signal complexity and power spectral density values are used to generate complexity spectrum and power spectrum.

可选地，所述对原始信号

Figure SMS_8
进行UPEMD分解，获取所述原始信号
Figure SMS_9
在所述目标分解频点
Figure SMS_10
下的信号分量
Figure SMS_11
，包括：Optionally, the original signal
Figure SMS_8
Perform UPEMD decomposition to obtain the original signal
Figure SMS_9
At the target decomposition frequency
Figure SMS_10
The signal component
Figure SMS_11
,include:

针对每一个所述目标分解频点

Figure SMS_12
，构建一维频率矩阵
Figure SMS_13
；Decompose the frequency points for each target
Figure SMS_12
, construct a one-dimensional frequency matrix
Figure SMS_13
;

对于所述频率矩阵

Figure SMS_15
，将上一矩阵元素
Figure SMS_19
的输入信号
Figure SMS_22
和模态分解信号
Figure SMS_16
的差值作为下一矩阵元素
Figure SMS_18
的输入信号
Figure SMS_21
，顺次对各个矩阵元素
Figure SMS_23
的输入信号
Figure SMS_14
进行模态分解，直至得到所述目标分解频点
Figure SMS_17
的信号分量
Figure SMS_20
。For the frequency matrix
Figure SMS_15
, the previous matrix element
Figure SMS_19
Input signal
Figure SMS_22
and the modal decomposition signal
Figure SMS_16
The difference is taken as the next matrix element
Figure SMS_18
Input signal
Figure SMS_21
, and then for each matrix element
Figure SMS_23
Input signal
Figure SMS_14
Perform modal decomposition until the target decomposition frequency point is obtained
Figure SMS_17
The signal component
Figure SMS_20
.

可选地，顺次对各个矩阵元素

Figure SMS_24
的输入信号
Figure SMS_25
进行模态分解，包括：Optionally, for each matrix element
Figure SMS_24
Input signal
Figure SMS_25
Perform modal decomposition, including:

对所述原始信号

Figure SMS_26
的相位进行划分，生成不同相位
Figure SMS_27
下的所述矩阵元素
Figure SMS_28
的掩模信号
Figure SMS_29
；The original signal
Figure SMS_26
The phase is divided to generate different phases
Figure SMS_27
The matrix element below
Figure SMS_28
The mask signal
Figure SMS_29
;

分别将各个相位下的所述掩模信号

Figure SMS_30
加入所述矩阵元素
Figure SMS_31
的输入信号
Figure SMS_32
，得到所述矩阵元素
Figure SMS_33
在各个相位下的分解输入信号
Figure SMS_34
；The mask signal at each phase is
Figure SMS_30
Add the matrix elements
Figure SMS_31
Input signal
Figure SMS_32
, get the matrix element
Figure SMS_33
Decomposed input signal at each phase
Figure SMS_34
;

利用不同相位下所述分解输入信号

Figure SMS_35
的多个极值点，对所述分解输入信号
Figure SMS_36
进行分解，得到所述矩阵元素
Figure SMS_37
的模态分解信号
Figure SMS_38
。Decompose the input signal using different phases
Figure SMS_35
multiple extreme points of the decomposed input signal
Figure SMS_36
Decompose to obtain the matrix elements
Figure SMS_37
The modal decomposition signal
Figure SMS_38
.

可选地，所述利用不同相位下所述分解输入信号

Figure SMS_39
的多个极值点，对所述分解输入信号
Figure SMS_40
进行分解，得到所述矩阵元素
Figure SMS_41
的模态分解信号
Figure SMS_42
，包括：Optionally, the decomposition of the input signal using different phases
Figure SMS_39
multiple extreme points of the decomposed input signal
Figure SMS_40
Decompose to obtain the matrix elements
Figure SMS_41
The modal decomposition signal
Figure SMS_42
,include:

将所述分解输入信号

Figure SMS_43
作为待分解信号
Figure SMS_44
；The decomposed input signal
Figure SMS_43
As the signal to be decomposed
Figure SMS_44
;

识别所述待分解信号

Figure SMS_45
的多个极值点，通过三次样条插值法对多个所述极值点进行拟合，得到所述极值点的上包络线
Figure SMS_46
和下包络线
Figure SMS_47
，对所述上包络线
Figure SMS_48
和所述下包络线
Figure SMS_49
进行平均，确定所述极值点的平均包络线
Figure SMS_50
；Identify the signal to be decomposed
Figure SMS_45
The multiple extreme value points are fitted by cubic spline interpolation method to obtain the upper envelope of the extreme value points
Figure SMS_46
and lower envelope
Figure SMS_47
, for the upper envelope
Figure SMS_48
and the lower envelope
Figure SMS_49
Averaging is performed to determine the average envelope of the extreme points
Figure SMS_50
;

对所述待分解信号

Figure SMS_51
和所述平均包络线
Figure SMS_52
进行差运算，得到中间信号
Figure SMS_53
；The signal to be decomposed
Figure SMS_51
and the average envelope
Figure SMS_52
Perform a difference operation to obtain the intermediate signal
Figure SMS_53
;

判断所述中间信号

Figure SMS_54
是否存在负的局部极大值和正的局部极小值，如果否，确定所述中间信号
Figure SMS_55
满足本征模态函数IMF标准，得到合格IMF信号
Figure SMS_56
；Determine the intermediate signal
Figure SMS_54
Is there a negative local maximum and a positive local minimum? If not, determine the intermediate signal
Figure SMS_55
Satisfy the intrinsic mode function IMF standard and obtain qualified IMF signal
Figure SMS_56
;

从所述分解输入信号

Figure SMS_57
中移除所述合格IMF信号
Figure SMS_58
，判断剩余信号
Figure SMS_59
是否为常数或者呈单调趋势，如果是，提取不同相位的分解结果中的第一合格IMF信号
Figure SMS_60
，平均化处理后得到所述矩阵元素
Figure SMS_61
的模态分解信号
Figure SMS_62
。Decompose the input signal from the
Figure SMS_57
Remove the qualified IMF signal
Figure SMS_58
, determine the remaining signal
Figure SMS_59
Is it a constant or monotonic trend? If so, extract the first qualified IMF signal from the decomposition results of different phases.
Figure SMS_60
, after averaging, the matrix elements are obtained
Figure SMS_61
The modal decomposition signal
Figure SMS_62
.

可选地，所述目标分解频点

Figure SMS_63
的信号分量为所述频率矩阵
Figure SMS_64
的最后一个矩阵元素
Figure SMS_65
的分解结果，即
Figure SMS_66
。Optionally, the target decomposition frequency
Figure SMS_63
The signal components are the frequency matrix
Figure SMS_64
The last matrix element of
Figure SMS_65
The decomposition result is
Figure SMS_66
.

可选地，所述极值点包括局部极大值和局部极小值；所述通过三次样条插值法对多个所述极值点进行拟合，得到所述极值点的上包络线

Figure SMS_67
和下包络线
Figure SMS_68
，包括：Optionally, the extreme value points include local maximum values and local minimum values; the upper envelope of the extreme value points is obtained by fitting the multiple extreme value points by cubic spline interpolation method.
Figure SMS_67
and lower envelope
Figure SMS_68
,include:

根据所述待分解信号

Figure SMS_69
的多个所述局部极大值，利用三次样条插值法拟合得到所述上包络线
Figure SMS_70
；According to the signal to be decomposed
Figure SMS_69
The upper envelope is obtained by fitting the multiple local maximum values of
Figure SMS_70
;

根据所述待分解信号

Figure SMS_71
的多个所述局部极小值，利用三次样条插值法拟合得到所述下包络线
Figure SMS_72
。According to the signal to be decomposed
Figure SMS_71
The lower envelope is obtained by fitting the multiple local minima of
Figure SMS_72
.

可选地，所述计算所述目标分解频点

Figure SMS_73
的信号分量
Figure SMS_74
的信号复杂度和功率谱密度值，包括：Optionally, the calculation of the target decomposition frequency point
Figure SMS_73
The signal component
Figure SMS_74
Signal complexity and power spectral density values, including:

将所述目标分解频点

Figure SMS_75
下的信号分量
Figure SMS_76
作为后处理输入信号
Figure SMS_77
；Decompose the target frequency points
Figure SMS_75
The signal component
Figure SMS_76
As post-processing input signal
Figure SMS_77
;

对所述后处理输入信号

Figure SMS_78
进行LZC处理，得到所述后处理输入信号
Figure SMS_79
的信号复杂度；The post-processing input signal
Figure SMS_78
Perform LZC processing to obtain the post-processing input signal
Figure SMS_79
The signal complexity of

利用快速傅立叶变换函数和所述后处理输入信号

Figure SMS_80
的信号长度，计算所述后处理输入信号
Figure SMS_81
的功率谱密度值。Post-process the input signal using the Fast Fourier Transform function and the
Figure SMS_80
The signal length is calculated by post-processing the input signal
Figure SMS_81
The power spectral density value of .

可选地，所述对所述后处理输入信号

Figure SMS_82
进行LZC处理，得到所述后处理输入信号
Figure SMS_83
的信号复杂度，包括：Optionally, the post-processing input signal
Figure SMS_82
Perform LZC processing to obtain the post-processing input signal
Figure SMS_83
The signal complexity includes:

根据二值化阈值

Figure SMS_84
，对所述后处理输入信号
Figure SMS_85
进行二值化处理，得到二值化序列
Figure SMS_86
；According to the binary threshold
Figure SMS_84
, for the post-processed input signal
Figure SMS_85
Perform binarization to obtain a binary sequence
Figure SMS_86
;

设定所述二值化序列

Figure SMS_87
的历史序列
Figure SMS_88
和当前序列
Figure SMS_89
；Set the binary sequence
Figure SMS_87
Historical sequence
Figure SMS_88
and the current sequence
Figure SMS_89
;

递增所述历史序列

Figure SMS_90
的末位元素的元素序号
Figure SMS_91
，将所述二值化序列
Figure SMS_92
中与所述历史序列
Figure SMS_93
递增后的元素序号
Figure SMS_94
对应的序列元素
Figure SMS_95
添加至当前序列
Figure SMS_96
；Increment the history sequence
Figure SMS_90
The element number of the last element of
Figure SMS_91
, the binary sequence
Figure SMS_92
In the historical sequence
Figure SMS_93
Incremented element number
Figure SMS_94
The corresponding sequence element
Figure SMS_95
Add to current sequence
Figure SMS_96
;

将所述历史序列

Figure SMS_97
与所述当前序列
Figure SMS_98
进行拼接，去除末位元素后得到组合序列
Figure SMS_99
；The historical sequence
Figure SMS_97
With the current sequence
Figure SMS_98
Perform concatenation and remove the last element to obtain the combined sequence
Figure SMS_99
;

判断所述当前序列

Figure SMS_100
是否存在于所述组合序列
Figure SMS_101
中，如果否，递增差异标识符
Figure SMS_102
，将所述当前序列
Figure SMS_103
和所述历史序列
Figure SMS_104
进行拼接，作为新的历史序列
Figure SMS_105
，并将所述当前序列
Figure SMS_106
更新为空集合；Determine the current sequence
Figure SMS_100
Is there a combination sequence?
Figure SMS_101
If not, increment the difference identifier
Figure SMS_102
, the current sequence
Figure SMS_103
and the historical sequence
Figure SMS_104
Splice as a new historical sequence
Figure SMS_105
, and the current sequence
Figure SMS_106
Update to an empty collection;

判断所述新的历史序列

Figure SMS_107
是否等于所述二值化序列
Figure SMS_108
，如果是，对所述差异标识符
Figure SMS_109
进行归一化处理，得到所述二值化序列
Figure SMS_110
的信号复杂度
Figure SMS_111
。Determine the new historical sequence
Figure SMS_107
Is it equal to the binary sequence
Figure SMS_108
, if so, the difference identifier
Figure SMS_109
Perform normalization processing to obtain the binary sequence
Figure SMS_110
The signal complexity
Figure SMS_111
.

可选地，在所述当前序列

Figure SMS_112
未存在于所述组合序列
Figure SMS_113
中的情况下，将所述二值化序列
Figure SMS_114
中与所述当前序列
Figure SMS_115
的末位元素对应的下一位序列元素，添加至所述当前序列
Figure SMS_116
。Optionally, in the current sequence
Figure SMS_112
Not present in the combined sequence
Figure SMS_113
In the case of
Figure SMS_114
The current sequence
Figure SMS_115
The next sequence element corresponding to the last element of is added to the current sequence
Figure SMS_116
.

有益效果：Beneficial effects:

（1）创新性地提出了一种基于均匀相位模态分解的复杂度与功率双谱的生成方法和系统，适用于非平稳、非线性信号的复杂度与功率的频谱可视化，为复杂系统信号的分析提供了新特征维度，用于反映复杂系统信号于宽广频率的复杂度与功率变化。(1) An innovative method and system for generating complexity and power bispectra based on uniform phase modal decomposition is proposed. The method is suitable for spectral visualization of complexity and power of non-stationary and nonlinear signals, and provides a new feature dimension for the analysis of complex system signals, which is used to reflect the complexity and power changes of complex system signals over a wide frequency range.

（2）基于EMD非线性、非平稳的分解特性，以及均匀相位模态的分量强化与零和性质，创新性地提出一套基于均匀相位模态分解的复杂度与功率双谱的生成方法和系统。(2) Based on the nonlinear and non-stationary decomposition characteristics of EMD and the component enhancement and zero-sum properties of uniform phase modes, we innovatively propose a method and system for generating complexity and power bispectra based on uniform phase modal decomposition.

（3）本发明基于非平稳、非线性、可控中心频率的均匀相位经验模态分解（UPEMD）技术，将输入动态信号分解为不同中心频率的信号分量。再进行Lepel-Ziv复杂度和功率分析，计算多频率信号分量的复杂度和功率，从而构建面向高动态信号的复杂度和功率频谱体系，适用于构建非平稳、非线性信号于多频率分量的复杂度与功率变化。(3) The present invention is based on the uniform phase empirical mode decomposition (UPEMD) technology of non-stationary, nonlinear, and controllable center frequency, which decomposes the input dynamic signal into signal components with different center frequencies. Then, Lepel-Ziv complexity and power analysis is performed to calculate the complexity and power of multi-frequency signal components, thereby constructing a complexity and power spectrum system for high dynamic signals, which is suitable for constructing the complexity and power changes of non-stationary and nonlinear signals in multi-frequency components.

（4）融合了UPEMD均匀相位掩模信号概念、LZC算法与功率谱密度计算，提出了一套LZC复杂度与功率谱密度值的频谱构建方法，旨在反映时间序列中LZC复杂度与功率谱密度在较宽频率谱上的动态变化。其中，UPEMD引入了掩模算法，即将掩模相位以均匀、频率可变的正弦信号预先加入至欲分解的时间序列中，目的有二：其一，增强目标频率分量的感知，从而控制目标频率IMF的频率分布；其二，通过等相位移动掩模信号去除外加掩模信号残余。由于EMD的非平稳与非线性特性，UPEMD克服了傅里叶变换在非平稳、非线性信号分解存在的谐波分量。(4) The concept of uniform phase mask signal of UPEMD, LZC algorithm and power spectrum density calculation are integrated, and a spectrum construction method of LZC complexity and power spectrum density values is proposed, aiming to reflect the dynamic changes of LZC complexity and power spectrum density in time series on a wider frequency spectrum. Among them, UPEMD introduces a mask algorithm, that is, the mask phase is pre-added to the time series to be decomposed in the form of a uniform, frequency-variable sinusoidal signal, with two purposes: first, to enhance the perception of the target frequency component, thereby controlling the frequency distribution of the target frequency IMF; second, to remove the residual of the external mask signal by moving the mask signal with equal phase. Due to the non-stationary and nonlinear characteristics of EMD, UPEMD overcomes the harmonic components existing in the decomposition of non-stationary and nonlinear signals by Fourier transform.

（5）相较于传统的单频点复杂度分析，本发明可以实现非线性、非连续信号的多频点的LZC频谱的生成。(5) Compared with the traditional single-frequency complexity analysis, the present invention can realize the generation of multi-frequency LZC spectrum of nonlinear and discontinuous signals.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为根据本发明实施例的基于均匀相位模态分解的复杂度与功率双谱的生成方法的主要流程的示意图。FIG1 is a schematic diagram of the main process of a method for generating complexity and power bispectrum based on uniform phase modal decomposition according to an embodiment of the present invention.

图2为根据本发明实施例的UPEMD的分解过程的主要流程的示意图。FIG. 2 is a schematic diagram of the main flow of the decomposition process of UPEMD according to an embodiment of the present invention.

图3为根据本发明实施例的信号复杂度和功率谱密度值的计算方法的主要流程的示意图。FIG. 3 is a schematic diagram of the main flow of a method for calculating signal complexity and power spectrum density values according to an embodiment of the present invention.

图4为UPEMD与EMD分解效果的对比示意图。FIG4 is a schematic diagram showing the comparison of the decomposition effects of UPEMD and EMD.

图5为逻辑斯谛映射输出与

Figure SMS_117
值的关系示意图。Figure 5 shows the logistic mapping output and
Figure SMS_117
Schematic diagram of the relationship between values.

图6（a）为无阈值的逻辑斯谛映射LZC频谱的示意图。FIG6( a ) is a schematic diagram of the LZC spectrum of the logistic map without threshold.

图6（b）为有阈值的逻辑斯谛映射LZC频谱的示意图。FIG6( b ) is a schematic diagram of the LZC spectrum of the logistic map with a threshold.

图7（a）为线性信号的功率谱示意图；Figure 7 (a) is a schematic diagram of the power spectrum of a linear signal;

图7（b）为非线性信号的功率谱示意图；Figure 7(b) is a schematic diagram of the power spectrum of a nonlinear signal;

图7（c）为经过UPEMD分解的线性信号的功率谱示意图；Figure 7 (c) is a schematic diagram of the power spectrum of the linear signal after UPEMD decomposition;

图7（d）为经过UPEMD分解的非线性信号的功率谱示意图；Figure 7 (d) is a schematic diagram of the power spectrum of the nonlinear signal after UPEMD decomposition;

图8为根据本发明实施例的基于均匀相位模态分解的复杂度与功率双谱的生成系统的主要模块的示意图。FIG8 is a schematic diagram of main modules of a system for generating complexity and power bispectrum based on uniform phase modal decomposition according to an embodiment of the present invention.

具体实施方式DETAILED DESCRIPTION

下面结合附图并举实施例，对本发明进行详细描述。The present invention is described in detail below with reference to the accompanying drawings and embodiments.

本发明提供了一种基于均匀相位模态分解的复杂度与功率双谱的生成方法，如图1所示，本发明的基于均匀相位模态分解的复杂度与功率双谱的生成方法包括如下步骤：The present invention provides a method for generating a complexity and power bispectrum based on uniform phase modal decomposition. As shown in FIG1 , the method for generating a complexity and power bispectrum based on uniform phase modal decomposition of the present invention comprises the following steps:

步骤1，设置多个目标分解频点

Figure SMS_118
，对原始信号
Figure SMS_119
进行UPEMD分解，获取所述原始信号
Figure SMS_120
在所述目标分解频点
Figure SMS_121
下的信号分量
Figure SMS_122
。Step 1: Set multiple target decomposition frequency points
Figure SMS_118
, for the original signal
Figure SMS_119
Perform UPEMD decomposition to obtain the original signal
Figure SMS_120
At the target decomposition frequency
Figure SMS_121
The signal component
Figure SMS_122
.

在本发明实施例中，原始信号为非平稳、非线性信号，可以表示为

Figure SMS_123
，为了对原始信号
Figure SMS_124
在多频率上进行展示，根据复杂度和功率双谱的展示需要，选定需要展示的多个目标分解频点
Figure SMS_125
。In the embodiment of the present invention, the original signal is a non-stationary, nonlinear signal, which can be expressed as
Figure SMS_123
, in order to
Figure SMS_124
Display on multiple frequencies, and select multiple target decomposition frequency points to be displayed according to the complexity and power dual spectrum display needs.
Figure SMS_125
.

步骤11，针对每一个所述目标分解频点

Figure SMS_126
，构建一维频率矩阵
Figure SMS_127
。Step 11: Decompose the frequency points of each target
Figure SMS_126
, construct a one-dimensional frequency matrix
Figure SMS_127
.

在本发明实施例中，为了减少高频分量对目标分解频点

Figure SMS_136
的目标信号分量的污染，针对每一个目标分解频点
Figure SMS_130
，建立一维频率矩阵
Figure SMS_140
。频率矩阵
Figure SMS_131
包括
Figure SMS_146
个矩阵元素，前
Figure SMS_138
个矩阵元素
Figure SMS_145
，第
Figure SMS_132
个矩阵元素为
Figure SMS_141
，也即，
Figure SMS_128
。其中，
Figure SMS_139
为采样频率；
Figure SMS_134
为分解系数，目标分解频点
Figure SMS_143
和分解系数
Figure SMS_133
的值决定了每个高频分量的加入频率；
Figure SMS_144
，
Figure SMS_135
表示对
Figure SMS_142
进行取整操作，
Figure SMS_137
表示由
Figure SMS_147
至1的序列
Figure SMS_129
，序列步长为-1。In the embodiment of the present invention, in order to reduce the impact of high frequency components on the target decomposition frequency point
Figure SMS_136
The pollution of the target signal components is analyzed for each target frequency point.
Figure SMS_130
, build a one-dimensional frequency matrix
Figure SMS_140
. Frequency Matrix
Figure SMS_131
include
Figure SMS_146
matrix elements, the first
Figure SMS_138
Matrix elements
Figure SMS_145
,
Figure SMS_132
The matrix elements are
Figure SMS_141
, that is,
Figure SMS_128
.in,
Figure SMS_139
is the sampling frequency;
Figure SMS_134
is the decomposition coefficient, the target decomposition frequency
Figure SMS_143
and decomposition coefficients
Figure SMS_133
The value of determines the frequency at which each high-frequency component is added;
Figure SMS_144
,
Figure SMS_135
Express
Figure SMS_142
Perform rounding operation,
Figure SMS_137
Indicated by
Figure SMS_147
Sequence to 1
Figure SMS_129
, the sequence step is -1.

进一步地，经过多次试验可知，

Figure SMS_148
的值为2.2时分解效果最佳。Furthermore, after many experiments, it is known that
Figure SMS_148
The decomposition effect is best when the value of is 2.2.

步骤12，对于所述频率矩阵

Figure SMS_150
，将上一矩阵元素
Figure SMS_153
的输入信号
Figure SMS_155
和模态分解信号
Figure SMS_149
的差值作为下一矩阵元素
Figure SMS_154
的输入信号
Figure SMS_157
，顺次对各个矩阵元素
Figure SMS_158
的输入信号
Figure SMS_151
进行模态分解，直至得到目标分解频点
Figure SMS_152
的信号分量
Figure SMS_156
。Step 12, for the frequency matrix
Figure SMS_150
, the previous matrix element
Figure SMS_153
Input signal
Figure SMS_155
and the modal decomposition signal
Figure SMS_149
The difference is taken as the next matrix element
Figure SMS_154
Input signal
Figure SMS_157
, and then for each matrix element
Figure SMS_158
Input signal
Figure SMS_151
Perform modal decomposition until the target decomposition frequency is obtained
Figure SMS_152
The signal component
Figure SMS_156
.

在本发明实施例中，各个矩阵元素

Figure SMS_159
的输入信号
Figure SMS_160
经过UPEMD分解得到模态分解信号
Figure SMS_161
的确定过程如图2所示，本发明的UPEMD的分解过程包括如下步骤：In the embodiment of the present invention, each matrix element
Figure SMS_159
Input signal
Figure SMS_160
After UPEMD decomposition, the modal decomposition signal is obtained
Figure SMS_161
The determination process is shown in FIG2 . The decomposition process of the UPEMD of the present invention includes the following steps:

步骤21，对所述原始信号

Figure SMS_162
的相位进行划分，生成不同相位
Figure SMS_163
下的所述矩阵元素
Figure SMS_164
的掩模信号
Figure SMS_165
。Step 21, the original signal
Figure SMS_162
The phase is divided to generate different phases
Figure SMS_163
The matrix element below
Figure SMS_164
The mask signal
Figure SMS_165
.

在本发明实施例中，根据矩阵元素

Figure SMS_166
对应的频率，生成不同相位下的矩阵元素
Figure SMS_167
的掩模信号
Figure SMS_168
，如下式（1）所示：In the embodiment of the present invention, according to the matrix element
Figure SMS_166
Corresponding frequencies generate matrix elements at different phases
Figure SMS_167
The mask signal
Figure SMS_168
, as shown in the following formula (1):

Figure SMS_169
（1）
Figure SMS_169
(1)

上式中，

Figure SMS_170
表示掩模信号的幅度；
Figure SMS_171
表示原始信号
Figure SMS_172
相位划分的个数，相位划分方式为均匀划分，划分单位可以根据需要进行选择性设置；
Figure SMS_173
表示相位序号，
Figure SMS_174
，每一个相位序号
Figure SMS_175
对应一个掩模信号
Figure SMS_176
。In the above formula,
Figure SMS_170
represents the amplitude of the mask signal;
Figure SMS_171
Represents the original signal
Figure SMS_172
The number of phase divisions. The phase division method is uniform division. The division unit can be selectively set as needed.
Figure SMS_173
Indicates the phase number,
Figure SMS_174
, each phase number
Figure SMS_175
Corresponding to a mask signal
Figure SMS_176
.

步骤22，分别将各个相位下的所述掩模信号

Figure SMS_177
加入所述矩阵元素
Figure SMS_178
的输入信号
Figure SMS_179
，得到所述矩阵元素
Figure SMS_180
在各个相位下的分解输入信号
Figure SMS_181
。Step 22: respectively convert the mask signal at each phase
Figure SMS_177
Add the matrix elements
Figure SMS_178
Input signal
Figure SMS_179
, get the matrix element
Figure SMS_180
Decomposed input signal at each phase
Figure SMS_181
.

在本发明实施例中，在进行经验模态分解（EMD）之前，分别对输入信号

Figure SMS_182
和各个相位下的掩模信号
Figure SMS_183
进行和运算，确定和运算的结果
Figure SMS_184
为不同相位下的矩阵元素
Figure SMS_185
进行EMD的分解输入信号，如下式（2）所示：In the embodiment of the present invention, before performing empirical mode decomposition (EMD), the input signal
Figure SMS_182
And the mask signal at each phase
Figure SMS_183
Perform an AND operation and determine the result of the AND operation
Figure SMS_184
are matrix elements at different phases
Figure SMS_185
The input signal is decomposed by EMD as shown in the following formula (2):

Figure SMS_186
（2）
Figure SMS_186
(2)

在本发明实施例中，需要说明的是，频率矩阵

Figure SMS_187
的第一个矩阵元素
Figure SMS_188
的输入信号
Figure SMS_189
即为原始信号
Figure SMS_190
，即
Figure SMS_191
。In the embodiment of the present invention, it should be noted that the frequency matrix
Figure SMS_187
The first matrix element of
Figure SMS_188
Input signal
Figure SMS_189
The original signal
Figure SMS_190
,Right now
Figure SMS_191
.

步骤23，利用不同相位下所述分解输入信号

Figure SMS_192
的多个极值点，对所述分解输入信号
Figure SMS_193
进行分解，得到所述矩阵元素
Figure SMS_194
的模态分解信号
Figure SMS_195
。Step 23, using the decomposed input signal under different phases
Figure SMS_192
multiple extreme points of the decomposed input signal
Figure SMS_193
Decompose to obtain the matrix elements
Figure SMS_194
The modal decomposition signal
Figure SMS_195
.

步骤231，将所述分解输入信号

Figure SMS_196
作为待分解信号
Figure SMS_197
。Step 231: Decompose the input signal
Figure SMS_196
As the signal to be decomposed
Figure SMS_197
.

在本发明实施例中，分解的初始时刻，将矩阵元素

Figure SMS_198
的分解输入信号
Figure SMS_199
作为EMD的待分解信号
Figure SMS_200
，利用EMD对待分解信号
Figure SMS_201
进行分解。In the embodiment of the present invention, at the initial moment of decomposition, the matrix elements
Figure SMS_198
Decomposition of the input signal
Figure SMS_199
As the signal to be decomposed by EMD
Figure SMS_200
, use EMD to decompose the signal
Figure SMS_201
Decompose.

步骤232，识别所述待分解信号

Figure SMS_202
的多个极值点，通过三次样条插值法对多个所述极值点进行拟合，得到所述极值点的上包络线
Figure SMS_203
和下包络线
Figure SMS_204
，对所述上包络线
Figure SMS_205
和所述下包络线
Figure SMS_206
进行平均，确定所述极值点的平均包络线
Figure SMS_207
。Step 232: Identify the signal to be decomposed
Figure SMS_202
The multiple extreme value points are fitted by cubic spline interpolation method to obtain the upper envelope of the extreme value points
Figure SMS_203
and lower envelope
Figure SMS_204
, for the upper envelope
Figure SMS_205
and the lower envelope
Figure SMS_206
Averaging is performed to determine the average envelope of the extreme value points
Figure SMS_207
.

在本发明实施例中，极值点为待分解信号

Figure SMS_208
的局部极大值和局部极小值，通过待分解信号
Figure SMS_209
的多个局部极大值和多个局部极小值，拟合待分解信号
Figure SMS_210
的极值点的平均包络线
Figure SMS_211
，具体地：In the embodiment of the present invention, the extreme point is the signal to be decomposed
Figure SMS_208
The local maximum and local minimum of the signal to be decomposed
Figure SMS_209
Multiple local maxima and local minima of the signal to be decomposed
Figure SMS_210
The average envelope of the extreme points
Figure SMS_211
, specifically:

根据待分解信号

Figure SMS_212
的多个局部极大值，利用三次样条插值法拟合得到上包络线
Figure SMS_213
；根据待分解信号
Figure SMS_214
的多个局部极小值，利用三次样条插值法拟合得到下包络线
Figure SMS_215
；对上包络线
Figure SMS_216
和下包络线
Figure SMS_217
进行平均，确定平均包络线
Figure SMS_218
，如下式（3）所示：According to the signal to be decomposed
Figure SMS_212
The upper envelope is obtained by fitting multiple local maxima of
Figure SMS_213
; According to the signal to be decomposed
Figure SMS_214
The lower envelope is obtained by fitting multiple local minima of
Figure SMS_215
; For the upper envelope
Figure SMS_216
and lower envelope
Figure SMS_217
Averaging to determine the average envelope
Figure SMS_218
, as shown in the following formula (3):

Figure SMS_219
(3)
Figure SMS_219
(3)

步骤233，对所述待分解信号

Figure SMS_220
和所述平均包络线
Figure SMS_221
进行差运算，得到中间信号
Figure SMS_222
。Step 233: the signal to be decomposed
Figure SMS_220
and the average envelope
Figure SMS_221
Perform a difference operation to obtain the intermediate signal
Figure SMS_222
.

在本发明实施例中，将待分解信号

Figure SMS_223
减去平均包络线
Figure SMS_224
，得到中间信号
Figure SMS_225
，如下式（4）所示：In the embodiment of the present invention, the signal to be decomposed
Figure SMS_223
Subtract the mean envelope
Figure SMS_224
, and get the intermediate signal
Figure SMS_225
, as shown in the following formula (4):

Figure SMS_226
(4)
Figure SMS_226
(4)

步骤234，判断所述中间信号

Figure SMS_227
是否存在负的局部极大值和正的局部极小值，如果是，将所述中间信号
Figure SMS_228
作为新的待分解信号
Figure SMS_229
，转至步骤232；如果否，转至步骤235。Step 234, determine the intermediate signal
Figure SMS_227
Are there negative local maxima and positive local minima? If so, the intermediate signal
Figure SMS_228
As a new signal to be decomposed
Figure SMS_229
, go to step 232; if not, go to step 235.

在本发明实施例中，在中间信号

Figure SMS_230
存在负的局部极大值和正的局部极小值的情况下，表示信号的分解不满足IMF标准，故而需要对中间信号进行再次分解，将中间信号
Figure SMS_231
作为新的待分解信号
Figure SMS_232
，即
Figure SMS_233
，转至步骤232再次分解，以保证信号分解满足IMF标准。In the embodiment of the present invention, the intermediate signal
Figure SMS_230
When there are negative local maxima and positive local minima, it means that the decomposition of the signal does not meet the IMF standard, so the intermediate signal needs to be decomposed again.
Figure SMS_231
As a new signal to be decomposed
Figure SMS_232
,Right now
Figure SMS_233
, go to step 232 to decompose again to ensure that the signal decomposition meets the IMF standard.

步骤235，确定所述中间信号

Figure SMS_234
满足本征模态函数IMF标准，得到合格IMF信号
Figure SMS_235
。Step 235, determine the intermediate signal
Figure SMS_234
Satisfy the intrinsic mode function IMF standard and obtain qualified IMF signal
Figure SMS_235
.

在本发明实施例中，在中间信号

Figure SMS_238
不存在负的局部极大值和正的局部极小值的情况下，表示信号的分解满足IMF标准，将中间信号
Figure SMS_239
作为合格IMF信号
Figure SMS_241
，即
Figure SMS_237
，其中，
Figure SMS_240
表示矩阵元素
Figure SMS_242
的分解输入信号
Figure SMS_243
分解后得到的各个合格IMF信号
Figure SMS_236
的序号。In the embodiment of the present invention, the intermediate signal
Figure SMS_238
In the absence of negative local maxima and positive local minima, it means that the decomposition of the signal meets the IMF standard.
Figure SMS_239
As a qualified IMF signal
Figure SMS_241
,Right now
Figure SMS_237
,in,
Figure SMS_240
Represents a matrix element
Figure SMS_242
Decomposition of the input signal
Figure SMS_243
The qualified IMF signals obtained after decomposition
Figure SMS_236
Serial number.

步骤236，从所述分解输入信号

Figure SMS_244
中移除所述合格IMF信号
Figure SMS_245
，判断剩余信号
Figure SMS_246
是否为常数或者呈单调趋势，如果是，转至步骤237；如果否，将所述剩余信号
Figure SMS_247
作为新的待分解信号
Figure SMS_248
，转至步骤232。Step 236, decomposing the input signal
Figure SMS_244
Remove the qualified IMF signal
Figure SMS_245
, determine the remaining signal
Figure SMS_246
Is it a constant or a monotonic trend? If yes, go to step 237; if not,
Figure SMS_247
As a new signal to be decomposed
Figure SMS_248
, go to step 232.

在本发明实施例中，对所述分解输入信号

Figure SMS_249
和各个合格IMF信号
Figure SMS_250
进行差运算，得到剩余信号
Figure SMS_251
，如下式（5）所示：In an embodiment of the present invention, the decomposed input signal
Figure SMS_249
and various qualified IMF signals
Figure SMS_250
Perform difference operation to obtain the residual signal
Figure SMS_251
, as shown in the following formula (5):

Figure SMS_252
(5)
Figure SMS_252
(5)

判断剩余信号

Figure SMS_254
的变化趋势，在剩余信号
Figure SMS_257
为常数或者呈单调趋势的情况下，表示EMD分解结束，可以将矩阵元素
Figure SMS_260
的分解输入信号
Figure SMS_255
通过多个IMF进行表示；在剩余信号
Figure SMS_256
非常数或者呈非单调趋势的情况下，表示EMD分解结果不满足要求，继续将剩余信号
Figure SMS_259
作为新的待分解信号
Figure SMS_261
，即
Figure SMS_253
，对剩余信号继续进行分解，直至剩余信号
Figure SMS_258
满足要求。Determine the remaining signal
Figure SMS_254
The trend of the remaining signal
Figure SMS_257
When it is a constant or shows a monotonic trend, it means that the EMD decomposition is over, and the matrix elements
Figure SMS_260
Decomposition of the input signal
Figure SMS_255
It is represented by multiple IMFs; in the residual signal
Figure SMS_256
If the EMD decomposition result does not meet the requirements, the remaining signal
Figure SMS_259
As a new signal to be decomposed
Figure SMS_261
,Right now
Figure SMS_253
, continue to decompose the remaining signal until the remaining signal
Figure SMS_258
Meet the requirements.

步骤237，提取不同相位的分解结果中的第一合格IMF信号

Figure SMS_262
，平均化处理后得到所述矩阵元素
Figure SMS_263
的模态分解信号
Figure SMS_264
。Step 237, extracting the first qualified IMF signal from the decomposition results of different phases
Figure SMS_262
, after averaging, the matrix elements are obtained
Figure SMS_263
The modal decomposition signal
Figure SMS_264
.

在本发明实施例中，对于矩阵元素

Figure SMS_265
，分别提取不同相位下的单相分解结果中的第一合格IMF信号
Figure SMS_266
，作为矩阵元素
Figure SMS_267
的IMF信号
Figure SMS_268
。In the embodiment of the present invention, for the matrix element
Figure SMS_265
, respectively extract the first qualified IMF signal in the single-phase decomposition results under different phases
Figure SMS_266
, as the matrix element
Figure SMS_267
IMF signal
Figure SMS_268
.

在本发明实施例中，对频率矩阵

Figure SMS_269
的最后一个矩阵元素
Figure SMS_270
进行分解，即可得到目标分解频点
Figure SMS_271
的信号分量
Figure SMS_272
。In the embodiment of the present invention, the frequency matrix
Figure SMS_269
The last matrix element of
Figure SMS_270
Decompose to get the target decomposition frequency point
Figure SMS_271
The signal component
Figure SMS_272
.

步骤2，计算所述目标分解频点

Figure SMS_273
的信号分量
Figure SMS_274
的信号复杂度和功率谱密度值，生成复杂度频谱和功率频谱。Step 2: Calculate the target decomposition frequency points
Figure SMS_273
The signal component
Figure SMS_274
The signal complexity and power spectral density values are used to generate complexity spectrum and power spectrum.

传统的LZC算法在计算各个分解频点的复杂度时，根据输入信号序列中新模式出现的比例量化信号复杂度。具体地，传统的LZC算法通过输入信号序列的平均值（即序列平均值）对输入信号序列进行二值化，假设本发明的UPEMD分解结果的信号幅值很小，相较输入信号可忽略不记，由于二值化处理仅考虑信号均值，使得传统的LZC算法计算得到的LZC复杂度受噪声干扰严重。When calculating the complexity of each decomposed frequency point, the traditional LZC algorithm quantifies the signal complexity according to the proportion of new patterns appearing in the input signal sequence. Specifically, the traditional LZC algorithm binarizes the input signal sequence by the average value of the input signal sequence (i.e., the sequence average value). Assuming that the signal amplitude of the UPEMD decomposition result of the present invention is very small and can be ignored compared to the input signal, since the binarization process only considers the signal mean, the LZC complexity calculated by the traditional LZC algorithm is seriously interfered by noise.

在本发明实施例中，如图3所示，本发明的信号复杂度和功率谱密度值的计算方法，包括如下步骤：In an embodiment of the present invention, as shown in FIG3 , the method for calculating the signal complexity and power spectrum density value of the present invention comprises the following steps:

步骤31，将所述目标分解频点

Figure SMS_275
下的信号分量
Figure SMS_276
作为后处理输入信号
Figure SMS_277
。Step 31: Decompose the target frequency points
Figure SMS_275
The signal component
Figure SMS_276
As post-processing input signal
Figure SMS_277
.

步骤32，对所述后处理输入信号

Figure SMS_278
进行LZC处理，得到所述后处理输入信号
Figure SMS_279
的信号复杂度。Step 32, post-processing the input signal
Figure SMS_278
Perform LZC processing to obtain the post-processing input signal
Figure SMS_279
signal complexity.

步骤321，根据二值化阈值

Figure SMS_280
，对所述后处理输入信号
Figure SMS_281
进行二值化处理，得到二值化序列
Figure SMS_282
。Step 321, based on the binarization threshold
Figure SMS_280
, for the post-processed input signal
Figure SMS_281
Perform binarization to obtain a binary sequence
Figure SMS_282
.

在本发明实施例中，二值化阈值

Figure SMS_283
可以是后处理输入信号
Figure SMS_284
的全部信号分量的信号值的中值或者均值，其中，信号值小于等于二值化阈值
Figure SMS_285
的信号分量的二值化结果为0、信号值大于二值化阈值
Figure SMS_286
的信号分量的二值化结果为1，从而得到后处理输入信号
Figure SMS_287
的二值化序列
Figure SMS_288
，如下式（6）所示：In the embodiment of the present invention, the binarization threshold
Figure SMS_283
Can be a post-processed input signal
Figure SMS_284
The median or mean of the signal values of all signal components, where the signal value is less than or equal to the binarization threshold
Figure SMS_285
The binarization result of the signal component is 0, and the signal value is greater than the binarization threshold
Figure SMS_286
The binarization result of the signal component is 1, thus obtaining the post-processing input signal
Figure SMS_287
The binary sequence
Figure SMS_288
, as shown in the following formula (6):

Figure SMS_289
（6）
Figure SMS_289
(6)

步骤322，设定所述二值化序列

Figure SMS_290
的历史序列
Figure SMS_291
和当前序列
Figure SMS_292
。Step 322, setting the binary sequence
Figure SMS_290
Historical sequence
Figure SMS_291
and the current sequence
Figure SMS_292
.

在本发明实施例中，二值化序列

Figure SMS_295
，历史序列
Figure SMS_298
包括二值化序列
Figure SMS_301
中的一个或多个元素，也即，
Figure SMS_294
，其中，
Figure SMS_297
。比如，二值化序列
Figure SMS_300
，历史序列
Figure SMS_302
的初始值为二值化序列
Figure SMS_293
的第一个元素
Figure SMS_296
，即
Figure SMS_299
。In the embodiment of the present invention, the binary sequence
Figure SMS_295
, historical sequence
Figure SMS_298
Including binary sequences
Figure SMS_301
One or more elements in , that is,
Figure SMS_294
,in,
Figure SMS_297
For example, the binary sequence
Figure SMS_300
, historical sequence
Figure SMS_302
The initial value of is a binary sequence
Figure SMS_293
The first element of
Figure SMS_296
,Right now
Figure SMS_299
.

在本发明实施例中，当前序列

Figure SMS_303
的初始值为空集合。In this embodiment of the present invention, the current sequence
Figure SMS_303
The initial value of is the empty collection.

步骤323，递增所述历史序列

Figure SMS_304
的末位元素的元素序号
Figure SMS_305
，将所述二值化序列
Figure SMS_306
中与所述历史序列
Figure SMS_307
递增后的元素序号
Figure SMS_308
对应的序列元素
Figure SMS_309
添加至当前序列
Figure SMS_310
。Step 323, increment the historical sequence
Figure SMS_304
The element number of the last element of
Figure SMS_305
, the binary sequence
Figure SMS_306
In the historical sequence
Figure SMS_307
Incremented element number
Figure SMS_308
The corresponding sequence element
Figure SMS_309
Add to current sequence
Figure SMS_310
.

在本发明实施例中，比如，历史序列

Figure SMS_312
的末位元素的元素序号
Figure SMS_315
，将二值化序列
Figure SMS_317
中与历史序列
Figure SMS_313
递增后的元素序号
Figure SMS_316
对应的序列元素
Figure SMS_318
添加至当前序列
Figure SMS_319
，更新前的当前序列
Figure SMS_311
为空、更新后的当前序列
Figure SMS_314
。In the embodiment of the present invention, for example, the historical sequence
Figure SMS_312
The element number of the last element of
Figure SMS_315
, the binary sequence
Figure SMS_317
In the historical sequence
Figure SMS_313
Incremented element number
Figure SMS_316
The corresponding sequence element
Figure SMS_318
Add to current sequence
Figure SMS_319
, the current sequence before update
Figure SMS_311
Empty, updated current sequence
Figure SMS_314
.

步骤324，将所述历史序列

Figure SMS_320
与所述当前序列
Figure SMS_321
进行拼接，去除末位元素后得到组合序列
Figure SMS_322
。Step 324: convert the historical sequence
Figure SMS_320
With the current sequence
Figure SMS_321
Perform concatenation and remove the last element to obtain the combined sequence
Figure SMS_322
.

在本发明实施例中，比如，将历史序列

Figure SMS_323
与当前序列
Figure SMS_324
进行拼接，去除末位元素
Figure SMS_325
后得到组合序列
Figure SMS_326
。In the embodiment of the present invention, for example, the historical sequence
Figure SMS_323
With the current sequence
Figure SMS_324
Perform splicing and remove the last element
Figure SMS_325
Then we get the combined sequence
Figure SMS_326
.

步骤325，判断所述当前序列

Figure SMS_327
是否存在于所述组合序列
Figure SMS_328
中，如果是，转至步骤326；如果否，转至步骤327。Step 325, determine the current sequence
Figure SMS_327
Is there a combination sequence?
Figure SMS_328
If yes, go to step 326; if no, go to step 327.

在本发明实施例中，比如，当前序列

Figure SMS_329
未存在于组合序列
Figure SMS_330
中。In the embodiment of the present invention, for example, the current sequence
Figure SMS_329
Not present in combined sequence
Figure SMS_330
middle.

步骤326，将所述二值化序列

Figure SMS_331
中与所述当前序列
Figure SMS_332
的末位元素对应的下一位序列元素，添加至所述当前序列
Figure SMS_333
，转至步骤323。Step 326: Binarize the sequence
Figure SMS_331
The current sequence
Figure SMS_332
The next sequence element corresponding to the last element of is added to the current sequence
Figure SMS_333
, go to step 323.

在本发明实施例中，比如，当前序列

Figure SMS_336
的末位元素为
Figure SMS_337
，将二值化序列
Figure SMS_339
中与
Figure SMS_335
对应的下一位序列元素
Figure SMS_338
，添加至当前序列
Figure SMS_340
，更新前的当前序列
Figure SMS_341
、更新后的当前序列
Figure SMS_334
，转至步骤323，重新进行判断。In the embodiment of the present invention, for example, the current sequence
Figure SMS_336
The last element of
Figure SMS_337
, the binary sequence
Figure SMS_339
Zhongyu
Figure SMS_335
The corresponding next sequence element
Figure SMS_338
, add to the current sequence
Figure SMS_340
, the current sequence before update
Figure SMS_341
, updated current sequence
Figure SMS_334
, go to step 323 and make a new judgment.

步骤327，递增差异标识符

Figure SMS_342
，将所述当前序列
Figure SMS_343
和所述历史序列
Figure SMS_344
进行拼接，作为新的历史序列
Figure SMS_345
，并将所述当前序列
Figure SMS_346
更新为空集合。Step 327, increment the difference identifier
Figure SMS_342
, the current sequence
Figure SMS_343
and the historical sequence
Figure SMS_344
Splice as a new historical sequence
Figure SMS_345
, and the current sequence
Figure SMS_346
Update to an empty collection.

在本发明实施例中，差异标识符

Figure SMS_347
用于表示两个序列之间的不重复性，比如，在当前序列
Figure SMS_348
未存在于组合序列
Figure SMS_349
中的情况下，将历史序列
Figure SMS_350
更新为当前序列
Figure SMS_351
和历史序列
Figure SMS_352
的拼接值
Figure SMS_353
。In the embodiment of the present invention, the difference identifier
Figure SMS_347
Used to indicate the non-repetitiveness between two sequences, for example, in the current sequence
Figure SMS_348
Not present in combined sequence
Figure SMS_349
In the case of
Figure SMS_350
Update to current sequence
Figure SMS_351
and historical sequence
Figure SMS_352
The splicing value
Figure SMS_353
.

步骤328，判断所述新的历史序列

Figure SMS_354
是否等于所述二值化序列
Figure SMS_355
，如果是，转至步骤329；如果否，转至步骤323。Step 328, determine the new historical sequence
Figure SMS_354
Is it equal to the binary sequence
Figure SMS_355
, if yes, go to step 329; if no, go to step 323.

在本发明实施例中，在新的历史序列

Figure SMS_356
与二值化序列
Figure SMS_357
相同的情况下，表示二值化序列
Figure SMS_358
已判断完毕，后续根据差异标识符
Figure SMS_359
计算信号复杂度；在新的历史序列
Figure SMS_360
与二值化序列
Figure SMS_361
不同的情况下，继续对二值化序列
Figure SMS_362
进行判断。In this embodiment of the present invention, in the new historical sequence
Figure SMS_356
With the binary sequence
Figure SMS_357
In the same case, it represents a binary sequence
Figure SMS_358
The judgment has been completed, and the subsequent
Figure SMS_359
Calculate signal complexity; in the new history sequence
Figure SMS_360
With the binary sequence
Figure SMS_361
In different cases, continue to binarize the sequence
Figure SMS_362
Make a judgment.

步骤329，对所述差异标识符

Figure SMS_363
进行归一化处理，得到所述二值化序列
Figure SMS_364
的信号复杂度。Step 329, the difference identifier
Figure SMS_363
Perform normalization processing to obtain the binary sequence
Figure SMS_364
signal complexity.

在本发明实施例中，根据差异标识符

Figure SMS_365
与差异标识符
Figure SMS_366
的对数的比值，计算二值化序列
Figure SMS_367
的信号复杂度，如下式（7）所示：In the embodiment of the present invention, according to the difference identifier
Figure SMS_365
With difference identifier
Figure SMS_366
The ratio of the logarithm of
Figure SMS_367
The signal complexity is as shown in the following formula (7):

Figure SMS_368
（7）
Figure SMS_368
(7)

步骤33，利用快速傅立叶变换函数和所述后处理输入信号

Figure SMS_369
的信号长度，计算所述后处理输入信号
Figure SMS_370
的功率谱密度值。Step 33, using the fast Fourier transform function and the post-processing input signal
Figure SMS_369
The signal length is calculated by post-processing the input signal
Figure SMS_370
The power spectral density value of .

在本发明实施例中，如下式（8）所示：In the embodiment of the present invention, as shown in the following formula (8):

Figure SMS_371
（8）
Figure SMS_371
(8)

上式中，

Figure SMS_374
为快速傅里叶变换；
Figure SMS_375
为取模函数，用于对后处理输入信号
Figure SMS_378
的各个频率点取模，生成一维信号矩阵
Figure SMS_373
；
Figure SMS_376
为
Figure SMS_377
的转置矩阵；
Figure SMS_379
为后处理输入信号
Figure SMS_372
的信号长度。In the above formula,
Figure SMS_374
is the fast Fourier transform;
Figure SMS_375
is the modulo function used to post-process the input signal
Figure SMS_378
Take the modulus at each frequency point to generate a one-dimensional signal matrix
Figure SMS_373
;
Figure SMS_376
for
Figure SMS_377
The transposed matrix of
Figure SMS_379
Input signal for post-processing
Figure SMS_372
signal length.

在本发明实施例中，根据目标分解频点

Figure SMS_380
下的信号分量
Figure SMS_381
的信号复杂度和功率谱密度值，生成原始信号
Figure SMS_382
的复杂度频谱和功率频谱，复杂度频谱以目标分解频点
Figure SMS_383
为横坐标、LZC值为纵坐标，展示了LZC值随各个分解频点的变化趋势，反映了原始信号
Figure SMS_384
在宽广频段/频谱中的复杂度变化；功率频谱以目标分解频点
Figure SMS_385
为横坐标、功率谱密度值为纵坐标，展示了功率谱密度值随各个分解频点的变化趋势，反映了原始信号
Figure SMS_386
在宽广频段/频谱中的功率变化。In the embodiment of the present invention, according to the target decomposition frequency point
Figure SMS_380
The signal component
Figure SMS_381
The signal complexity and power spectral density values of the original signal are generated
Figure SMS_382
The complexity spectrum and power spectrum of the target frequency decomposition
Figure SMS_383
The horizontal axis is LZC value, and the vertical axis is LZC value, which shows the changing trend of LZC value with each decomposition frequency point, reflecting the original signal
Figure SMS_384
Complexity variation over a wide frequency band/spectrum; power spectrum decomposed into target frequency points
Figure SMS_385
The horizontal axis is the power spectrum density value, and the vertical axis is the power spectrum density value, which shows the change trend of the power spectrum density value with each decomposition frequency point, reflecting the original signal
Figure SMS_386
Power variations across a wide frequency band/spectrum.

在本发明实施例中，如图4所示，本发明的仿真信号A为白噪声，由图4可以看出，相较于EMD而言，UPEMD在获取目标分解频点

Figure SMS_387
的信号分量
Figure SMS_388
时具备相对窄带的优势，也即，UPEMD分解得到的信号频段具有频率可控性且频宽更窄，精确度相比于EMD更高，更适合获取不同目标分解频点的信号分量In the embodiment of the present invention, as shown in FIG. 4 , the simulation signal A of the present invention is white noise. As can be seen from FIG. 4 , compared with EMD, UPEMD is more efficient in obtaining the target decomposition frequency point.
Figure SMS_387
The signal component
Figure SMS_388
It has the advantage of relatively narrowband, that is, the signal frequency band decomposed by UPEMD is frequency controllable and has a narrower bandwidth. It has higher accuracy than EMD and is more suitable for obtaining signal components at different target decomposition frequency points.

在本发明实施例中，本发明的仿真信号B为逻辑斯谛映射（logistic map）生成的混沌信号，混沌信号的生成如下式（9）所示：In the embodiment of the present invention, the simulation signal B of the present invention is a chaotic signal generated by a logistic map. The generation of the chaotic signal is shown in the following formula (9):

Figure SMS_389
（9）
Figure SMS_389
(9)

上式中，

Figure SMS_390
为预先给定的数值，决定了混沌信号的生成样式，通过多项式映射确定输出序列的规律性，
Figure SMS_391
为迭代次数，
Figure SMS_392
。如图5所示，
Figure SMS_393
初始值为0.3，随着
Figure SMS_394
值变大，逻辑斯谛映射的输出逐渐从具有周期模式的序列向混沌序列移动，反映了序列复杂性的增加。In the above formula,
Figure SMS_390
The predetermined value determines the generation pattern of the chaotic signal, and the regularity of the output sequence is determined by polynomial mapping.
Figure SMS_391
is the number of iterations,
Figure SMS_392
As shown in Figure 5,
Figure SMS_393
The initial value is 0.3.
Figure SMS_394
As the value of becomes larger, the output of the logistic map gradually moves from a sequence with a periodic pattern to a chaotic sequence, reflecting the increase in sequence complexity.

在生成的复杂度频谱和功率频谱时，为了更好的展示效果，根据预设的信号阈值，对所述目标分解频点

Figure SMS_395
的信号分量进行筛选，判断目标分解频点
Figure SMS_396
的各个信号分量是否需要被忽略，将筛选出的信号分量组成后处理输入信号，计算筛选出的后处理输入信号的信号复杂度和功率谱密度值，生成复杂度频谱和功率频谱。其中，信号阈值可以根据不同应用场景的信号特征调试。比如，图6（b）中信号阈值为0.08，由图6（a）和图6（b）的逻辑斯谛映射的LZC频谱可以看出，对逻辑斯谛映射经过UPEMD分解得到的信号分量进行阈值筛选后，得到的LZC频谱相较于无阈值筛选的LZC频谱更加稳定，LZC值越大表示其复杂度越高，图6（a）中未筛选的LZC频谱在周期性输出对应R值下出现抖动，表明其缺乏对UPEMD分解所得信号的选择能力。其中，在生成LZC频谱的过程中，可以将目标分解频点
Figure SMS_397
下的信号分量中不满足信号阈值的信号分量的LZC值设置为0.01，表示其存在但可忽略不记。When generating the complexity spectrum and power spectrum, in order to better display the effect, the target frequency points are decomposed according to the preset signal threshold.
Figure SMS_395
The signal components are screened to determine the target decomposition frequency point
Figure SMS_396
Whether each signal component needs to be ignored, the screened signal components are combined into a post-processing input signal, the signal complexity and power spectral density value of the screened post-processing input signal are calculated, and the complexity spectrum and power spectrum are generated. Among them, the signal threshold can be adjusted according to the signal characteristics of different application scenarios. For example, the signal threshold in Figure 6 (b) is 0.08. It can be seen from the LZC spectrum of the logistic map in Figure 6 (a) and Figure 6 (b) that after the signal components obtained by the logistic map after UPEMD decomposition are threshold-screened, the obtained LZC spectrum is more stable than the LZC spectrum without threshold screening. The larger the LZC value, the higher its complexity. The unscreened LZC spectrum in Figure 6 (a) jitters at the corresponding R value of the periodic output, indicating that it lacks the ability to select the signal obtained by UPEMD decomposition. Among them, in the process of generating the LZC spectrum, the target decomposition frequency point can be
Figure SMS_397
The LZC value of the signal component that does not meet the signal threshold in the signal components below is set to 0.01, indicating that it exists but can be ignored.

如图7（a）和图7（c）所示，本发明的仿真信号C是由10Hz与90Hz正弦信号叠加的线性信号；如图7（b）和图7（d）所示，本发明的仿真信号D是由10Hz与90Hz正弦信号拼接而成的非线性信号。由仿真信号C仿真信号D的对照可以看出，基于均匀相位模态分解的复杂度与功率双谱在非线性信号分析上的优势，图中非线性信号的功率谱出现谐波分量，但是UPEMD功率谱不会，充分体现了UPEMD功率谱在非线性信号的可视化优势。As shown in Figure 7 (a) and Figure 7 (c), the simulation signal C of the present invention is a linear signal superimposed by 10Hz and 90Hz sinusoidal signals; as shown in Figure 7 (b) and Figure 7 (d), the simulation signal D of the present invention is a nonlinear signal spliced by 10Hz and 90Hz sinusoidal signals. From the comparison of simulation signal C and simulation signal D, it can be seen that based on the complexity of uniform phase modal decomposition and the advantages of power bispectrum in nonlinear signal analysis, the power spectrum of the nonlinear signal in the figure has harmonic components, but the UPEMD power spectrum does not, which fully reflects the visualization advantage of UPEMD power spectrum in nonlinear signals.

图8是根据本发明实施例的基于均匀相位模态分解的复杂度与功率双谱的生成系统的主要模块的示意图，如图8所示，本发明的基于均匀相位模态分解的复杂度与功率双谱的生成系统包括：FIG8 is a schematic diagram of main modules of a system for generating complexity and power bispectrum based on uniform phase modal decomposition according to an embodiment of the present invention. As shown in FIG8 , the system for generating complexity and power bispectrum based on uniform phase modal decomposition of the present invention includes:

UPEMD分解模块，用于设置多个目标分解频点

Figure SMS_398
，对原始信号
Figure SMS_399
进行UPEMD分解，获取所述原始信号
Figure SMS_400
在所述目标分解频点
Figure SMS_401
下的信号分量
Figure SMS_402
。UPEMD decomposition module, used to set multiple target decomposition frequencies
Figure SMS_398
, for the original signal
Figure SMS_399
Perform UPEMD decomposition to obtain the original signal
Figure SMS_400
At the target decomposition frequency
Figure SMS_401
The signal component
Figure SMS_402
.

复杂度模块，用于计算所述目标分解频点

Figure SMS_403
的信号分量
Figure SMS_404
的信号复杂度，生成复杂度频谱。Complexity module, used to calculate the target decomposition frequency points
Figure SMS_403
The signal component
Figure SMS_404
The complexity of the signal is determined by generating a complexity spectrum.

功率模块，用于计算所述目标分解频点

Figure SMS_405
的信号分量
Figure SMS_406
的功率谱密度值，生成功率频谱。Power module, used to calculate the target decomposition frequency point
Figure SMS_405
The signal component
Figure SMS_406
The power spectral density value of is used to generate the power spectrum.

综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (7)

1.一种基于均匀相位模态分解的复杂度与功率双谱的生成方法，其特征在于，包括：1. A method for generating complexity and power bispectrum based on uniform phase modal decomposition, characterized by comprising: 设置多个目标分解频点fd，对原始信号x(t)进行UPEMD分解，获取所述原始信号x(t)在所述目标分解频点fd下的信号分量Cmfd(t)；Setting a plurality of target decomposition frequency points f d , performing UPEMD decomposition on the original signal x(t), and obtaining a signal component C mfd (t) of the original signal x(t) at the target decomposition frequency point f d ; 计算所述目标分解频点fd的信号分量Cmfd(t)的信号复杂度和功率谱密度值，生成复杂度频谱和功率频谱，包括：Calculating the signal complexity and power spectrum density value of the signal component C mfd (t) of the target decomposition frequency point f d to generate a complexity spectrum and a power spectrum, including: 将所述目标分解频点fd下的信号分量Cmfd(t)作为后处理输入信号xu(t)；The signal component C mfd (t) at the target decomposition frequency point f d is used as the post-processing input signal x u (t); 对所述后处理输入信号xu(t)进行LZC处理，得到所述后处理输入信号xu(t)的信号复杂度，包括：Performing LZC processing on the post-processed input signal xu (t) to obtain the signal complexity of the post-processed input signal xu (t) includes: 根据二值化阈值Th，对所述后处理输入信号xu(t)进行二值化处理，得到二值化序列b(E)；设定所述二值化序列b(E)的历史序列P和当前序列Q；递增所述历史序列P的末位元素的元素序号j，将所述二值化序列b(E)中与所述历史序列P递增后的元素序号(j+1)对应的序列元素bj+1添加至当前序列Q；将所述历史序列P与所述当前序列Q进行拼接，去除末位元素后得到组合序列PQγ；判断所述当前序列Q是否存在于所述组合序列PQγ中，如果否，递增差异标识符nd，将所述当前序列Q和所述历史序列P进行拼接，作为新的历史序列P＝P-Q，并将所述当前序列Q更新为空集合；判断所述新的历史序列P是否等于所述二值化序列b(E)，如果是，对所述差异标识符nd进行归一化处理，得到所述二值化序列b(E)的信号复杂度
Figure FDA0004151622540000011
According to the binarization threshold Th , the post-processing input signal xu (t) is binarized to obtain a binarized sequence b(E); a historical sequence P and a current sequence Q of the binarized sequence b(E) are set; the element number j of the last element of the historical sequence P is incremented, and the sequence element bj+ 1 corresponding to the incremented element number (j+1) of the historical sequence P in the binarized sequence b(E) is added to the current sequence Q; the historical sequence P is concatenated with the current sequence Q, and a combined sequence PQγ is obtained after removing the last element; it is determined whether the current sequence Q exists in the combined sequence PQγ, if not, a difference identifier nd is incremented, the current sequence Q is concatenated with the historical sequence P as a new historical sequence P=PQ, and the current sequence Q is updated to an empty set; it is determined whether the new historical sequence P is equal to the binarized sequence b(E), if yes, the difference identifier nd is normalized to obtain the signal complexity of the binarized sequence b(E)
Figure FDA0004151622540000011
 利用快速傅立叶变换函数和所述后处理输入信号xu(t)的信号长度，计算所述后处理输入信号xu(t)的功率谱密度值。The power spectrum density value of the post-processed input signal xu (t) is calculated by using a fast Fourier transform function and the signal length of the post-processed input signal xu (t). 2.如权利要求1所述的方法，其特征在于，所述对原始信号x(t)进行UPEMD分解，获取所述原始信号x(t)在所述目标分解频点fd下的信号分量Cmfd(t)，包括：2. The method according to claim 1, characterized in that the step of performing UPEMD decomposition on the original signal x(t) to obtain a signal component C mfd (t) of the original signal x(t) at the target decomposition frequency point f d comprises: 针对每一个所述目标分解频点fd，构建一维频率矩阵D；For each of the target decomposition frequency points f d , construct a one-dimensional frequency matrix D; 对于所述频率矩阵D，将上一矩阵元素Dn-1的输入信号
Figure FDA0004151622540000021
和模态分解信号
Figure FDA00041516225400000213
的差值作为下一矩阵元素Dn的输入信号
Figure FDA0004151622540000022
顺次对各个矩阵元素Di的输入信号
Figure FDA0004151622540000023
进行模态分解，直至得到所述目标分解频点fd的信号分量Cmfd(t)。For the frequency matrix D, the input signal of the previous matrix element D n-1 is
Figure FDA0004151622540000021
and the modal decomposition signal
Figure FDA00041516225400000213
The difference is used as the input signal of the next matrix element D n
Figure FDA0004151622540000022
The input signal of each matrix element Di is
Figure FDA0004151622540000023
Perform modal decomposition until the signal component C mfd (t) of the target decomposition frequency point f d is obtained. 3.如权利要求2所述的方法，其特征在于，所述顺次对各个矩阵元素Di的输入信号
Figure FDA0004151622540000024
进行模态分解，包括：3. The method according to claim 2, characterized in that the input signal of each matrix element Di is sequentially
Figure FDA0004151622540000024
Perform modal decomposition, including: 对所述原始信号x(t)的相位进行划分，生成不同相位v下的所述矩阵元素Di的掩模信号yM,v(t)；Dividing the phase of the original signal x(t) to generate mask signals y M,v (t) of the matrix elements D i at different phases v; 分别将各个相位下的所述掩模信号yM,v(t)加入所述矩阵元素Di的输入信号
Figure FDA00041516225400000214
得到所述矩阵元素Di在各个相位下的分解输入信号
Figure FDA0004151622540000025
The mask signal y M,v (t) at each phase is added to the input signal of the matrix element Di respectively.
Figure FDA00041516225400000214
Get the decomposed input signal of the matrix element Di at each phase
Figure FDA0004151622540000025
 利用不同相位下所述分解输入信号
Figure FDA0004151622540000026
的多个极值点，对所述分解输入信号
Figure FDA0004151622540000027
进行分解，得到所述矩阵元素Di的模态分解信号
Figure FDA0004151622540000028
Decompose the input signal using different phases
Figure FDA0004151622540000026
multiple extreme points of the decomposed input signal
Figure FDA0004151622540000027
Decompose to obtain the modal decomposition signal of the matrix element Di
Figure FDA0004151622540000028
 4.如权利要求3所述的方法，其特征在于，所述利用不同相位下所述分解输入信号
Figure FDA0004151622540000029
的多个极值点，对所述分解输入信号
Figure FDA00041516225400000210
进行分解，得到所述矩阵元素Di的模态分解信号
Figure FDA00041516225400000211
包括：4. The method according to claim 3, characterized in that the decomposition of the input signal at different phases is performed
Figure FDA0004151622540000029
multiple extreme points of the decomposed input signal
Figure FDA00041516225400000210
Decompose to obtain the modal decomposition signal of the matrix element Di
Figure FDA00041516225400000211
include: 将所述分解输入信号
Figure FDA00041516225400000212
作为待分解信号yv(t)；The decomposed input signal
Figure FDA00041516225400000212
As the signal to be decomposed y v (t); 识别所述待分解信号yv(t)的多个极值点，通过三次样条插值法对多个所述极值点进行拟合，得到所述极值点的上包络线U(t)和下包络线L(t)，对所述上包络线U(t)和所述下包络线L(t)进行平均，确定所述极值点的平均包络线m(t)＝(U(t)+L(t))/2；Identify multiple extreme points of the signal to be decomposed y v (t), fit the multiple extreme points by cubic spline interpolation to obtain upper envelope U(t) and lower envelope L(t) of the extreme points, average the upper envelope U(t) and the lower envelope L(t), and determine the average envelope m(t)=(U(t)+L(t))/2 of the extreme points; 对所述待分解信号yv(t)和所述平均包络线m(t)进行差运算，得到中间信号h(t)；Performing a difference operation on the signal to be decomposed y v (t) and the average envelope m(t) to obtain an intermediate signal h(t); 判断所述中间信号h(t)是否存在负的局部极大值和正的局部极小值，如果否，确定所述中间信号h(t)满足本征模态函数IMF标准，得到合格IMF信号
Figure FDA0004151622540000031
Determine whether the intermediate signal h(t) has a negative local maximum and a positive local minimum. If not, determine whether the intermediate signal h(t) meets the intrinsic mode function IMF standard to obtain a qualified IMF signal.
Figure FDA0004151622540000031
 从所述分解输入信号
Figure FDA0004151622540000032
中移除所述合格IMF信号
Figure FDA0004151622540000033
判断剩余信号
Figure FDA0004151622540000034
是否为常数或者呈单调趋势，如果是，提取不同相位的分解结果中的第一合格IMF信号
Figure FDA0004151622540000035
平均化处理后得到所述矩阵元素Di的模态分解信号
Figure FDA0004151622540000036
Decompose the input signal from the
Figure FDA0004151622540000032
Remove the qualified IMF signal
Figure FDA0004151622540000033
Determine the remaining signal
Figure FDA0004151622540000034
Is it a constant or monotonic trend? If so, extract the first qualified IMF signal from the decomposition results of different phases.
Figure FDA0004151622540000035
After averaging, the modal decomposition signal of the matrix element Di is obtained:
Figure FDA0004151622540000036
 5.如权利要求4所述的方法，其特征在于，所述目标分解频点fd的信号分量为所述频率矩阵D的最后一个矩阵元素Dn+1＝fd的分解结果，即
Figure FDA0004151622540000037
5. The method according to claim 4, characterized in that the signal component of the target decomposition frequency point f d is the decomposition result of the last matrix element D n+1 =f d of the frequency matrix D, that is,
Figure FDA0004151622540000037
 6.如权利要求4所述的方法，其特征在于，所述极值点包括局部极大值和局部极小值；所述通过三次样条插值法对多个所述极值点进行拟合，得到所述极值点的上包络线U(t)和下包络线L(t)，包括：6. The method according to claim 4, wherein the extreme value points include local maximum values and local minimum values; and the step of fitting the plurality of extreme value points by cubic spline interpolation to obtain the upper envelope U(t) and the lower envelope L(t) of the extreme value points comprises: 根据所述待分解信号yv(t)的多个所述局部极大值，利用三次样条插值法拟合得到所述上包络线U(t)；According to the multiple local maximum values of the signal to be decomposed y v (t), the upper envelope U(t) is fitted by using a cubic spline interpolation method; 根据所述待分解信号yv(t)的多个所述局部极小值，利用三次样条插值法拟合得到所述下包络线L(t)。The lower envelope L(t) is obtained by fitting according to the multiple local minimum values of the signal to be decomposed y v (t) using a cubic spline interpolation method. 7.如权利要求1所述的方法，其特征在于，在所述当前序列Q未存在于所述组合序列PQγ中的情况下，将所述二值化序列b(E)中与所述当前序列Q的末位元素对应的下一位序列元素，添加至所述当前序列Q。7. The method as claimed in claim 1 is characterized in that, when the current sequence Q does not exist in the combined sequence PQγ, the next sequence element in the binary sequence b(E) corresponding to the last element of the current sequence Q is added to the current sequence Q.
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