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

The invention discloses a method based onA method for generating complexity and power double spectrums of uniform phase modal decomposition relates to the technical field of signal processing. The specific implementation mode of the method comprises the following steps: setting multiple target decomposition frequency points
Figure ZY_1
For the original signal
Figure ZY_2
Performing UPEMD decomposition to obtain the original signal
Figure ZY_3
At the target decomposition frequency point
Figure ZY_4
Lower signal component
Figure ZY_5
The method comprises the steps of carrying out a first treatment on the surface of the Calculating the target decomposition frequency point
Figure ZY_6
Is a component of the signal of (a)
Figure ZY_7
The signal complexity and power spectral density values of (2) to generate a complexity spectrum and a power spectrum. According to the method, a group of mask signals with uniform phase distribution can be used for assisting, uniform phase empirical mode decomposition is introduced, non-stationary and nonlinear signals are decomposed, so that complexity and power double spectrums are generated, UPEMD and complexity and power are combined, an intrinsic mode function IMF can be extracted near a target frequency under the condition of avoiding mode mixing and mode splitting, and additional oscillation residual errors are reduced to the maximum extent.

Description

Complexity and power dual-spectrum generation method based on uniform phase modal decomposition
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a complexity and power dual-spectrum generation method based on uniform phase modal decomposition.
Background
The distribution parameters or distribution laws of non-stationary signals dynamically change over time, which are widely present in complex systems, such as radar, seismic, speech, and medical biology signals. Complexity is an important indicator for assessing the degree of dynamic change (e.g., non-stationarity) of a signal.
However, in the existing complexity analysis process, only the Lempel-Ziv complexity (i.e. LZC) of the original signal is concerned, the variation trend of the multi-frequency LZC is not considered, and in order to preserve the dynamics of the input signal component, the input signal component needs to be split by a nonlinear and non-stationary decomposition method, which is commonly used, such as Empirical Mode Decomposition (EMD), noise-assisted EMD (NA-EMD), and mask EMD, and the EMD can decompose the time sequence into eigenmode functions of a plurality of frequency ranges. However, the EMD has a pattern aliasing problem due to the presence of different frequency components; NA-EMD fills the discontinuous blank in frequency modulation through white noise, so that the problem of modal aliasing can be solved, but modal splitting phenomenon can be caused, namely, signal components in the same frequency band are dispersed in a plurality of IMFs; the mask EMD is similar to the NA-EMD step, but 180-degree phase shift is performed on the mask signal, the average of two corresponding IMFs is calculated in the range of the interested frequency band, so that the target IMF is obtained, the interference of white noise can be avoided by random distribution, the signal interference caused by white noise residues is reduced, and the calculation cost generated by iterative calculation is reduced.
Disclosure of Invention
In view of this, the invention provides a method for generating complexity and power bispectrum based on uniform phase modal decomposition, which can decompose non-stationary and nonlinear signals by introducing Uniform Phase Empirical Mode Decomposition (UPEMD) through the assistance of a set of mask signals with uniform phase distribution, thereby generating complexity and power bispectrum, combining UPEMD with complexity and power, extracting IMF near the target frequency under the condition of avoiding modal mixing and modal splitting, and minimizing additional oscillation residual errors.
The technical scheme for realizing the invention is as follows:
a method for generating a complexity and power bispectrum based on uniform phase modal decomposition comprises the following steps:
setting multiple target decomposition frequency points
Figure SMS_1
For the original signal->
Figure SMS_2
Performing UPEMD decomposition to obtain the original signal
Figure SMS_3
At the target decomposition frequency point->
Figure SMS_4
Lower signal component->
Figure SMS_5
；
Calculating the target decomposition frequency point
Figure SMS_6
Signal component +.>
Figure SMS_7
The signal complexity and power spectral density values of (2) to generate a complexity spectrum and a power spectrum.
Optionally, the pair of original signals
Figure SMS_8
Performing UPEMD decomposition to obtain the original signal +.>
Figure SMS_9
At the target decomposition frequency point->
Figure SMS_10
Lower signal component->
Figure SMS_11
Comprising:
decomposing frequency points for each target
Figure SMS_12
Constructing a one-dimensional frequency matrix->
Figure SMS_13
；/>
For the frequency matrix
Figure SMS_15
The last matrix element +.>
Figure SMS_19
Input signal +.>
Figure SMS_22
And modal decomposition signal
Figure SMS_16
Is the next matrix element +.>
Figure SMS_18
Input signal +.>
Figure SMS_21
For each matrix element in turn->
Figure SMS_23
Input signal +.>
Figure SMS_14
Performing modal decomposition until the target decomposition frequency point +.>
Figure SMS_17
Signal component +.>
Figure SMS_20
。
Optionally, for each matrix element in sequence
Figure SMS_24
Input signal +.>
Figure SMS_25
Performing modal decomposition, comprising:
for the original signal
Figure SMS_26
Dividing the phases of (a) to generate different phases +.>
Figure SMS_27
The matrix elements below->
Figure SMS_28
Mask signal +.>
Figure SMS_29
；
Respectively applying the mask signals in each phase
Figure SMS_30
Adding the matrix element->
Figure SMS_31
Input signal +.>
Figure SMS_32
Obtaining said matrix element->
Figure SMS_33
Decomposing the input signal in the respective phase +.>
Figure SMS_34
；
Using the decomposition of the input signal at different phases
Figure SMS_35
For the decomposed input signal
Figure SMS_36
Decomposing to obtain the matrix element +.>
Figure SMS_37
Modal decomposition signal->
Figure SMS_38
。
Optionally, the decomposing the input signal with different phases
Figure SMS_39
Is added to the decomposed input signal +.>
Figure SMS_40
Decomposing to obtain the matrix element +.>
Figure SMS_41
Modal decomposition signal->
Figure SMS_42
Comprising:
decomposing the input signal
Figure SMS_43
As signal to be decomposed->
Figure SMS_44
；
Identifying the signal to be decomposed
Figure SMS_45
Fitting a plurality of extreme points by a cubic spline interpolation method to obtain an upper envelope line of the extreme 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 to determine the average envelope of the extreme points +.>
Figure SMS_50
；
For the signal to be decomposed
Figure SMS_51
And the mean envelope +.>
Figure SMS_52
Performing difference operation to obtain intermediate signal +.>
Figure SMS_53
；
Judging the intermediate signal
Figure SMS_54
Whether there are a negative local maximum and a positive local minimum, and if not, determining the intermediate signal +.>
Figure SMS_55
Meets the IMF standard of the intrinsic mode function to obtain qualified IMF signals +.>
Figure SMS_56
；
From said decomposed input signal
Figure SMS_57
Removing said qualified IMF signal +.>
Figure SMS_58
Judging the residual signal->
Figure SMS_59
Whether it is constant or monotonous, if so, extracting the first qualified IMF signal in the decomposition results of different phases>
Figure SMS_60
Averaging to obtain the matrix element +.>
Figure SMS_61
Modal decomposition signal->
Figure SMS_62
。
Optionally, the target decomposition frequency point
Figure SMS_63
Is the frequency matrix +.>
Figure SMS_64
Is>
Figure SMS_65
Decomposition result of->
Figure SMS_66
。
Optionally, the extreme points include local maxima and local minima; fitting a plurality of extreme points by a cubic spline interpolation method to obtain an upper envelope curve of the extreme points
Figure SMS_67
And lower envelope->
Figure SMS_68
Comprising:
according to the signal to be decomposed
Figure SMS_69
Fitting the local maxima to the upper envelope by means of cubic spline interpolation>
Figure SMS_70
；
According to the signal to be decomposed
Figure SMS_71
Fitting the local minimum to obtain the lower envelope by means of cubic spline interpolation>
Figure SMS_72
。
Optionally, the target decomposition frequency point is calculated
Figure SMS_73
Signal component +.>
Figure SMS_74
Signal complexity and power spectral density values of (1), comprising:
decomposing the target frequency point
Figure SMS_75
Lower signal component->
Figure SMS_76
As post-processing input signal +.>
Figure SMS_77
；
For the post-processing input signal
Figure SMS_78
Performing LZC processing to obtain the post-processed input signal +.>
Figure SMS_79
Is a signal complexity of (2);
using a fast fourier transform function and said post-processing input signal
Figure SMS_80
Calculating the signal length of said post-processed input signal +.>
Figure SMS_81
Is a power spectral density value of (2).
Optionally, said pair of post-processing input signals
Figure SMS_82
Performing LZC processing to obtain the post-processed input signal +.>
Figure SMS_83
Comprises:
according to a binarization threshold
Figure SMS_84
For the post-processing input signal +.>
Figure SMS_85
Performing binarization to obtain binarization sequence +.>
Figure SMS_86
；
Setting the binarization sequence
Figure SMS_87
History sequence of->
Figure SMS_88
And the current sequence->
Figure SMS_89
；
Incrementing the history sequence
Figure SMS_90
Element number of last element of (2)>
Figure SMS_91
The binarization sequence +.>
Figure SMS_92
Is equal to the history sequence->
Figure SMS_93
Incremental element number ∈ ->
Figure SMS_94
Corresponding sequence element->
Figure SMS_95
Added to the current sequence->
Figure SMS_96
；
The history sequence is processed
Figure SMS_97
Is +.>
Figure SMS_98
Splicing and removingRemoving last element to obtain combined sequence
Figure SMS_99
；
Judging the current sequence
Figure SMS_100
Whether or not present in said combined sequence->
Figure SMS_101
If not, increment the difference identifier
Figure SMS_102
The current sequence +.>
Figure SMS_103
And the history sequence->
Figure SMS_104
Splicing is performed as a new history sequence +.>
Figure SMS_105
And the current sequence +.>
Figure SMS_106
Updating to be an empty set;
judging the new history sequence
Figure SMS_107
Whether or not equal to said binarization sequence +.>
Figure SMS_108
If so, the difference identifier +.>
Figure SMS_109
Carrying out normalization treatment to obtain the binarization sequence +.>
Figure SMS_110
Signal complexity +.>
Figure SMS_111
。
Optionally, in the current sequence
Figure SMS_112
Is not present in the combined sequence->
Figure SMS_113
In the case of (2), the binarization sequence +.>
Figure SMS_114
Is->
Figure SMS_115
The next bit sequence element corresponding to the last bit element of said current sequence +.>
Figure SMS_116
。
The beneficial effects are that:
(1) The method and the system for generating the complexity and power double spectrum based on uniform phase modal decomposition are innovatively provided, are suitable for frequency spectrum visualization of complexity and power of non-stationary and nonlinear signals, provide a new feature dimension for analysis of complex system signals, and are used for reflecting complexity and power changes of the complex system signals in wide frequency.
(2) Based on the nonlinear and non-stationary decomposition characteristics of EMD and the component reinforcement and zero sum properties of uniform phase modes, a set of generation method and system based on the complexity and power dual-spectrum of uniform phase mode decomposition are innovatively provided.
(3) The invention decomposes an input dynamic signal into signal components of different center frequencies based on a non-stationary, non-linear, uniform Phase Empirical Mode Decomposition (UPEMD) technique of controllable center frequencies. And then, lepel-Ziv complexity and power analysis is carried out, and the complexity and power of the multi-frequency signal components are calculated, so that a high-dynamic signal-oriented complexity and power spectrum system is constructed, and the method is suitable for constructing the complexity and power change of non-stationary and nonlinear signals on the multi-frequency components.
(4) The UPEMD uniform phase mask signal concept, the LZC algorithm and the power spectral density calculation are fused, and a set of spectrum construction method for the LZC complexity and the power spectral density value is provided, so that the dynamic change of the LZC complexity and the power spectral density on a wider frequency spectrum in a time sequence is reflected. The UPEMD introduces a masking algorithm, i.e. the mask phase is pre-added to the time sequence to be decomposed with a sinusoidal signal of uniform and variable frequency, the purpose is two: firstly, the perception of the target frequency component is enhanced, so that the frequency distribution of the target frequency IMF is controlled; and secondly, removing the residual of the externally applied mask signal by the mask signal with equal phase shift. UPEMD overcomes harmonic components present in fourier transform at non-stationary, nonlinear signal decomposition due to the non-stationary and nonlinear nature of EMD.
(5) Compared with the traditional single-frequency point complexity analysis, the method can realize the generation of the LZC frequency spectrum of the multi-frequency points of the nonlinear and discontinuous signals.
Drawings
Fig. 1 is a schematic diagram of a main flow of a method for generating a complexity and power bispectrum based on uniform phase modal decomposition according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a main flow of a decomposition process of UPEMD according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a main flow of a method for calculating signal complexity and power spectral density values according to an embodiment of the present invention.
FIG. 4 is a graph showing the comparison of UPEMD and EMD decomposition effects.
FIG. 5 shows the logic-based output of the map
Figure SMS_117
The relationship of the values is schematically shown.
FIG. 6 (a) is a schematic diagram of thresholdless logistic mapped LZC spectrum.
FIG. 6 (b) is a diagram of a thresholded logistic mapped LZC spectrum.
FIG. 7 (a) is a schematic diagram of the power spectrum of a linear signal;
FIG. 7 (b) is a schematic diagram of the power spectrum of a nonlinear signal;
FIG. 7 (c) is a power spectrum diagram of a linear signal subjected to UPEMD decomposition;
FIG. 7 (d) is a power spectrum diagram of a nonlinear signal subjected to UPEMD decomposition;
fig. 8 is a schematic diagram of main modules of a complexity and power bispectrum generation system based on uniform phase modal decomposition according to an embodiment of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The invention provides a method for generating a complexity and power double spectrum based on uniform phase modal decomposition, which is shown in figure 1, and comprises the following steps:
step 1, setting a plurality of target decomposition frequency points
Figure SMS_118
For the original signal->
Figure SMS_119
Performing UPEMD decomposition to obtain the original signal +.>
Figure SMS_120
At the target decomposition frequency point->
Figure SMS_121
Lower signal component->
Figure SMS_122
。
In the embodiment of the invention, the original signal is a non-stationary and non-linear signal and can be expressed as
Figure SMS_123
For the purpose of->
Figure SMS_124
The display is carried out on multiple frequencies, and the display requirement of the double spectrum of the complexity and the power is selected according to the display requirementMultiple target decomposition frequency points to be displayed +.>
Figure SMS_125
。
Step 11, for each target decomposition frequency point
Figure SMS_126
Constructing a one-dimensional frequency matrix->
Figure SMS_127
。
In the embodiment of the invention, in order to reduce the decomposition frequency point of the high-frequency component to the target
Figure SMS_136
Is carried out for each target decomposition frequency point +.>
Figure SMS_130
Establishing a one-dimensional frequency matrix->
Figure SMS_140
. Frequency matrix->
Figure SMS_131
Comprises->
Figure SMS_146
The matrix elements, before->
Figure SMS_138
Individual matrix elements->
Figure SMS_145
First->
Figure SMS_132
The matrix elements are->
Figure SMS_141
That is, in other words,
Figure SMS_128
. Wherein (1)>
Figure SMS_139
Is the sampling frequency;
Figure SMS_134
For the decomposition coefficient, target decomposition frequency point +.>
Figure SMS_143
And decomposition coefficient->
Figure SMS_133
The value of (2) determines the addition frequency of each high frequency component;
Figure SMS_144
，
Figure SMS_135
Representation pair->
Figure SMS_142
Performing rounding operation, and->
Figure SMS_137
The expression is represented by->
Figure SMS_147
Sequence to 1->
Figure SMS_129
The sequence step size is-1.
Further, as can be seen from a plurality of experiments,
Figure SMS_148
the best time-division effect is obtained when the value of (2) is 2.2.
Step 12, for the frequency matrix
Figure SMS_150
The last matrix element +.>
Figure SMS_153
Input signal +.>
Figure SMS_155
And Modal resolution Signal->
Figure SMS_149
Is the next matrix element +.>
Figure SMS_154
Input signal +.>
Figure SMS_157
For each matrix element in turn->
Figure SMS_158
Input signal +.>
Figure SMS_151
Performing modal decomposition until the target decomposition frequency point is obtained>
Figure SMS_152
Signal component +.>
Figure SMS_156
。
In an embodiment of the invention, each matrix element
Figure SMS_159
Input signal +.>
Figure SMS_160
Obtaining a modal decomposition signal by UPEMD decomposition>
Figure SMS_161
As shown in fig. 2, the decomposition process of the UPEMD of the present invention includes the steps of:
step 21, for the original signal
Figure SMS_162
Dividing the phases of (a) to generate different phases +.>
Figure SMS_163
The matrix elements below->
Figure SMS_164
Mask signal +.>
Figure SMS_165
。
In the embodiment of the invention, the matrix elements are used for
Figure SMS_166
Corresponding frequencies, generating matrix elements +.>
Figure SMS_167
Mask signal +.>
Figure SMS_168
The following formula (1) shows:
Figure SMS_169
（1）
in the above-mentioned method, the step of,
Figure SMS_170
representing the amplitude of the mask signal;
Figure SMS_171
Representing the original signal +.>
Figure SMS_172
The number of the phase divisions is equal division, and the division units can be selectively set according to the needs;
Figure SMS_173
Indicates the phase number +.>
Figure SMS_174
Each phase sequence number->
Figure SMS_175
Corresponds to a mask signal->
Figure SMS_176
。/>
Step 22, respectively converting the mask signals in each phase
Figure SMS_177
Adding the matrix element->
Figure SMS_178
Input signal +.>
Figure SMS_179
Obtaining said matrix element->
Figure SMS_180
Decomposing the input signal in the respective phase +.>
Figure SMS_181
。
In an embodiment of the present invention, prior to Empirical Mode Decomposition (EMD), the input signals are separately processed
Figure SMS_182
And mask signals at the respective phases +.>
Figure SMS_183
Performing a sum operation, determining the result of the sum operation +.>
Figure SMS_184
For matrix elements in different phases->
Figure SMS_185
The decomposed input signal of the EMD is represented by the following formula (2):
Figure SMS_186
（2）
in the embodiment of the present invention, it should be noted that the frequency matrix
Figure SMS_187
Is +.>
Figure SMS_188
Is input to the input signal of (a)
Figure SMS_189
I.e. original signal +.>
Figure SMS_190
I.e. +.>
Figure SMS_191
。
Step 23, decomposing the input signal using the signals at different phases
Figure SMS_192
Is added to the decomposed input signal +.>
Figure SMS_193
Decomposing to obtain the matrix element +.>
Figure SMS_194
Modal decomposition signal->
Figure SMS_195
。
Step 231, decomposing the input signal
Figure SMS_196
As signal to be decomposed->
Figure SMS_197
。
In the embodiment of the invention, matrix elements are added at the initial moment of decomposition
Figure SMS_198
Is a component of the input signal->
Figure SMS_199
Signal to be resolved as EMD +.>
Figure SMS_200
Treatment of the decomposed signal with EMD>
Figure SMS_201
And decomposing.
Step 232, identifying the signal to be decomposed
Figure SMS_202
Fitting a plurality of extreme points by a cubic spline interpolation method to obtain an upper envelope line of the extreme points>
Figure SMS_203
And lower envelope->
Figure SMS_204
For the upper envelope curve
Figure SMS_205
And the lower envelope->
Figure SMS_206
Averaging to determine average envelope of the extreme points
Figure SMS_207
。
In the embodiment of the invention, the extreme point is the signal to be decomposed
Figure SMS_208
Local maxima and local minima of (2) by means of the signal to be decomposed +.>
Figure SMS_209
Fitting the signal to be decomposed +.>
Figure SMS_210
Mean envelope of extreme points +.>
Figure SMS_211
Specifically:
according to the signal to be decomposed
Figure SMS_212
Fitting by cubic spline interpolation to obtain upper envelope curve
Figure SMS_213
The method comprises the steps of carrying out a first treatment on the surface of the According to the signal to be decomposed->
Figure SMS_214
Fitting by cubic spline interpolation to obtain lower envelope curve
Figure SMS_215
The method comprises the steps of carrying out a first treatment on the surface of the For the upper envelope->
Figure SMS_216
And lower envelope->
Figure SMS_217
Averaging to determine an average envelope +.>
Figure SMS_218
The following formula (3) shows:
Figure SMS_219
(3)
step 233, for the signal to be decomposed
Figure SMS_220
And the mean envelope +.>
Figure SMS_221
Performing difference operation to obtain intermediate signal +.>
Figure SMS_222
。
In the embodiment of the invention, the signal to be decomposed
Figure SMS_223
Subtracting the average envelope +.>
Figure SMS_224
Obtaining an intermediate signal
Figure SMS_225
The following formula (4) shows:
Figure SMS_226
(4)/>
step 234, determining the intermediate signal
Figure SMS_227
Whether there are a negative local maximum and a positive local minimum, and if so, the intermediate signal is +.>
Figure SMS_228
As a new signal to be decomposed->
Figure SMS_229
Go to step 232; if not, go to step 235.
In the embodiment of the invention, in the intermediate signal
Figure SMS_230
If there are a negative local maximum and a positive local minimum, the intermediate signal needs to be decomposed again to decompose the intermediate signal because the decomposition of the signal does not satisfy the IMF standard
Figure SMS_231
As a new signal to be decomposed->
Figure SMS_232
I.e. +.>
Figure SMS_233
Turning to step 232, the decomposition is again performed to ensure that the signal decomposition meets IMF criteria.
Step 235, determining the intermediate signal
Figure SMS_234
Meets the IMF standard of the intrinsic mode function to obtain a qualified IMF signal
Figure SMS_235
。
In the embodiment of the invention, in the intermediate signal
Figure SMS_238
In the absence of negative local maxima and positive local minima, the decomposition of the signal is shown to meet IMF criteria, the intermediate signal +.>
Figure SMS_239
As qualified IMF signal->
Figure SMS_241
I.e.
Figure SMS_237
Wherein->
Figure SMS_240
Representing matrix elements->
Figure SMS_242
Is a component of the input signal->
Figure SMS_243
The respective qualified IMF signals obtained after decomposition +.>
Figure SMS_236
Is a sequence number of (c).
Step 236 of decomposing the input signal from said
Figure SMS_244
Removing said qualified IMF signal +.>
Figure SMS_245
Judging the residual signal->
Figure SMS_246
Whether constant or monotonic, if so, go to step 237; if not, the residual signal is sent
Figure SMS_247
As a new signal to be decomposed->
Figure SMS_248
Go to step 232.
In an embodiment of the present invention, the input signal is decomposed
Figure SMS_249
And the respective qualifying IMF signals->
Figure SMS_250
Performing difference operation to obtain residual signal +.>
Figure SMS_251
The following formula (5) shows:
Figure SMS_252
(5)
judging the residual signal
Figure SMS_254
In the residual signal +.>
Figure SMS_257
In the case of a constant or monotonic trend, which indicates the end of the EMD decomposition, the matrix element may be +.>
Figure SMS_260
Is a component of the input signal->
Figure SMS_255
Represented by a plurality of IMFs; in the residual signal->
Figure SMS_256
If the EMD decomposition result does not meet the requirement, the residual signal is continued to be +.>
Figure SMS_259
As a new signal to be decomposed->
Figure SMS_261
I.e. +.>
Figure SMS_253
The decomposition of the residual signal is continued until the residual signal +.>
Figure SMS_258
Meets the requirements.
Step 237, extracting the first qualified IMF signals in the decomposition results of different phases
Figure SMS_262
Averaging to obtain the matrix element +.>
Figure SMS_263
Modal decomposition signal->
Figure SMS_264
。
In an embodiment of the invention, for matrix elements
Figure SMS_265
Extracting first qualified IMF signals ++in single-phase decomposition results under different phases respectively>
Figure SMS_266
As matrix element->
Figure SMS_267
IMF signal->
Figure SMS_268
。
In the embodiment of the invention, the frequency is subjected to matrix
Figure SMS_269
Is>
Figure SMS_270
Decomposing to obtain target decomposition frequency point +.>
Figure SMS_271
Signal component +.>
Figure SMS_272
。
Step 2, calculating the target decomposition frequency point
Figure SMS_273
Signal component +.>
Figure SMS_274
The signal complexity and power spectral density values of (2) to generate a complexity spectrum and a power spectrum.
The conventional LZC algorithm quantizes the signal complexity according to the proportion of new patterns occurring in the input signal sequence when calculating the complexity of each decomposition frequency point. Specifically, the conventional LZC algorithm performs binarization on the input signal sequence through an average value (i.e., a sequence average value) of the input signal sequence, and supposing that the signal amplitude of the UPEMD decomposition result of the present invention is small, compared with the input signal, the signal amplitude of the UPEMD decomposition result is negligible, and because the binarization process only considers the signal average value, the LZC complexity calculated by the conventional LZC algorithm is severely interfered by noise.
In the embodiment of the present invention, as shown in fig. 3, the method for calculating the signal complexity and the power spectral density value of the present invention includes the following steps:
step 31, decomposing the target frequency point
Figure SMS_275
Lower signal component->
Figure SMS_276
As a post-processing input signal
Figure SMS_277
。
Step 32, for said post-processing input signal
Figure SMS_278
LZC processing is carried out to obtain the post-processing input signal
Figure SMS_279
Is used for the signal complexity of (a).
Step 321, according to the binarization threshold value
Figure SMS_280
For the post-processing input signal +.>
Figure SMS_281
Performing binarization to obtain binarization sequence +.>
Figure SMS_282
。
In an embodiment of the present invention, the threshold is binarized
Figure SMS_283
Can be post-processing the input signal +.>
Figure SMS_284
Median or mean value of signal values of all signal components of (a) wherein the signal value is equal to or less than a binarization threshold +.>
Figure SMS_285
The result of the binarization of the signal component of (2) is 0, the signal value is greater than the binarization threshold +.>
Figure SMS_286
The result of the binarization of the signal component of (2) is 1, thereby obtaining a post-processed input signal
Figure SMS_287
Is>
Figure SMS_288
The following formula (6) shows:
Figure SMS_289
（6）
step 322, setting the binarization sequence
Figure SMS_290
History sequence of->
Figure SMS_291
And the current sequence->
Figure SMS_292
。
In an embodiment of the invention, the binarization sequence
Figure SMS_295
History sequence->
Figure SMS_298
Comprising a binarization sequence->
Figure SMS_301
One or more elements of (a), i.e.; a->
Figure SMS_294
Wherein->
Figure SMS_297
. For example, the binarization sequence +.>
Figure SMS_300
History sequence->
Figure SMS_302
The initial value of (2) is the binarization sequence +.>
Figure SMS_293
Is->
Figure SMS_296
I.e. +.>
Figure SMS_299
。
In the embodiment of the invention, the current sequence
Figure SMS_303
The initial value of (1) is an empty set.
Step 323Incrementing the history sequence
Figure SMS_304
Element number of last element of (2)>
Figure SMS_305
The binarization sequence +.>
Figure SMS_306
Is equal to the history sequence->
Figure SMS_307
Incremental element number ∈ ->
Figure SMS_308
Corresponding sequence element->
Figure SMS_309
Added to the current sequence->
Figure SMS_310
。
In embodiments of the invention, for example, a history sequence
Figure SMS_312
Element number of last element of (2)>
Figure SMS_315
The binarized sequence
Figure SMS_317
Chinese and history sequence->
Figure SMS_313
Incremental element number ∈ ->
Figure SMS_316
Corresponding sequence element->
Figure SMS_318
Added to the current sequence->
Figure SMS_319
The current sequence before update->
Figure SMS_311
Empty, updated current sequence +.>
Figure SMS_314
。
Step 324, the history sequence
Figure SMS_320
Is +.>
Figure SMS_321
Splicing, removing last element to obtain combined sequence +.>
Figure SMS_322
。
In an embodiment of the invention, for example, a history sequence is generated
Figure SMS_323
Is +.>
Figure SMS_324
Splicing to remove the last element->
Figure SMS_325
The combined sequence +.>
Figure SMS_326
。
Step 325, determining the current sequence
Figure SMS_327
Whether or not present in said combined sequence->
Figure SMS_328
If yes, go to step 326; if not, go to step 327.
In embodiments of the invention, for example, the current sequence
Figure SMS_329
Are not present in the combined sequences
Figure SMS_330
Is a kind of medium.
Step 326, converting the binarized sequence
Figure SMS_331
Is->
Figure SMS_332
The next bit sequence element corresponding to the last bit element of said current sequence +.>
Figure SMS_333
Go to step 323.
In embodiments of the invention, for example, the current sequence
Figure SMS_336
The last element of (2) is->
Figure SMS_337
Binarization sequence +.>
Figure SMS_339
Middle AND
Figure SMS_335
Corresponding next bit sequence element +.>
Figure SMS_338
Added to the current sequence->
Figure SMS_340
The current sequence before update->
Figure SMS_341
Updated current sequence->
Figure SMS_334
Turning to step 323, the determination is again made.
Step 327, increment differenceIdentifier(s)
Figure SMS_342
The current sequence +.>
Figure SMS_343
And the history sequence->
Figure SMS_344
Splicing is performed as a new history sequence +.>
Figure SMS_345
And the current sequence +.>
Figure SMS_346
Updated to an empty set.
In an embodiment of the invention, the difference identifier
Figure SMS_347
For representing non-repetitiveness between two sequences, e.g. in the current sequence +.>
Figure SMS_348
Are not present in the combined sequence->
Figure SMS_349
In the case of (a) the history sequence +.>
Figure SMS_350
Update to the current sequence->
Figure SMS_351
And history sequence->
Figure SMS_352
Is->
Figure SMS_353
。
Step 328, determining the new history sequence
Figure SMS_354
Whether or not to waitIn the binarization sequence +.>
Figure SMS_355
If so, go to step 329; if not, go to step 323.
In the embodiment of the invention, in a new history sequence
Figure SMS_356
And binarization sequence->
Figure SMS_357
In the same case, the binarization sequence +.>
Figure SMS_358
After the judgment, the following steps are carried out according to the difference identifier +.>
Figure SMS_359
Calculating signal complexity; in a new history sequence->
Figure SMS_360
And binarization sequence->
Figure SMS_361
In a different case, the binarization sequence is continued +.>
Figure SMS_362
And judging.
Step 329, for the differential identifier
Figure SMS_363
Carrying out normalization treatment to obtain the binarization sequence +.>
Figure SMS_364
Is used for the signal complexity of (a). />
In the embodiment of the invention, the identifier is based on the difference
Figure SMS_365
And difference identifier->
Figure SMS_366
Calculating the ratio of the logarithms of the binarization sequences +.>
Figure SMS_367
Is represented by the following formula (7):
Figure SMS_368
（7）
step 33, using a fast fourier transform function and said post-processing input signal
Figure SMS_369
Calculating the signal length of said post-processed input signal +.>
Figure SMS_370
Is a power spectral density value of (2).
In the embodiment of the invention, the following formula (8) shows:
Figure SMS_371
（8）
in the above-mentioned method, the step of,
Figure SMS_374
is a fast fourier transform;
Figure SMS_375
As a modulo function for post-processing the input signal
Figure SMS_378
Is modulo-extracted at each frequency point to generate a one-dimensional signal matrix +.>
Figure SMS_373
；
Figure SMS_376
Is->
Figure SMS_377
Is a transposed matrix of (a);
Figure SMS_379
For post-processing the input signal +.>
Figure SMS_372
Is used for the signal length of the (c).
In the embodiment of the invention, the frequency points are decomposed according to the target
Figure SMS_380
Lower signal component->
Figure SMS_381
Signal complexity and power spectral density values of (2) to generate the original signal +.>
Figure SMS_382
Complexity spectrum and power spectrum of (a), the complexity spectrum is decomposed with a target frequency point +.>
Figure SMS_383
The change trend of the LZC value along with each decomposition frequency point is shown by taking the abscissa and the LZC value as the ordinate, and the original signal +.>
Figure SMS_384
Complexity variation in a broad frequency band/spectrum; the power spectrum is divided into frequency points by the target>
Figure SMS_385
The abscissa and the ordinate show the variation trend of the power spectrum density value along with each decomposition frequency point, and reflect the original signal +.>
Figure SMS_386
Power variation in a broad frequency band/spectrum.
In the embodiment of the present invention, as shown in fig. 4, the simulation signal a of the present invention is white noise, and as can be seen from fig. 4, compared with EMD, UPEMD obtains the target decomposition frequency point
Figure SMS_387
Signal component +.>
Figure SMS_388
The advantages of relatively narrow band are that the frequency band of the signal obtained by UPEMD decomposition has frequency controllability and narrower bandwidth, and the accuracy is higher than that of EMD, thus being more suitable for obtaining the signal components of different target decomposition frequency points
In the embodiment of the invention, the simulation signal B is a chaotic signal generated by logic map, and the generation of the chaotic signal is shown in the following formula (9):
Figure SMS_389
（9）
in the above-mentioned method, the step of,
Figure SMS_390
for a preset numerical value, determining a generation pattern of the chaotic signal, and determining regularity of an output sequence through polynomial mapping, < >>
Figure SMS_391
For the number of iterations->
Figure SMS_392
. As shown in fig. 5, ->
Figure SMS_393
An initial value of 0.3, with +.>
Figure SMS_394
The value becomes larger and 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.
In the generated complexity spectrum and power spectrum, for better display effect, decomposing the frequency point according to a preset signal threshold
Figure SMS_395
Screening the signal components of the target decomposition frequency point +.>
Figure SMS_396
Whether each signal component of the (a) needs to be ignored or not, forming the screened signal components into a post-processing input signal, calculating the signal complexity and the power spectral density value of the screened post-processing input signal, and generating a complexity spectrum and a power spectrum. The signal threshold can be debugged according to signal characteristics of different application scenes. For example, in fig. 6 (b), the signal threshold is 0.08, and as can be seen from the LZC spectrum of the logic-element mapping in fig. 6 (a) and fig. 6 (b), after the threshold screening is performed on the signal component obtained by the logic-element mapping through UPEMD decomposition, the obtained LZC spectrum is more stable than the LZC spectrum without the threshold screening, the greater the LZC value indicates the higher the complexity, and the non-screened LZC spectrum in fig. 6 (a) corresponds to the periodic outputRJitter appears at the value indicating that it lacks the ability to select signals resulting from UPEMD decomposition. Wherein, in the process of generating LZC spectrum, the target decomposition frequency point +.>
Figure SMS_397
The LZC value of the signal component that does not satisfy the signal threshold among the lower signal components is set to 0.01, indicating its existence but is negligible.
As shown in fig. 7 (a) and 7 (C), the simulation signal C of the present invention is a linear signal superimposed by a 10Hz and 90Hz sinusoidal signal; as shown in fig. 7 (b) and 7 (D), the simulation signal D of the present invention is a nonlinear signal formed by splicing 10Hz and 90Hz sinusoidal signals. As can be seen from comparison of the simulation signal C and the simulation signal D, based on the complexity of uniform phase modal decomposition and the advantages of the power dual spectrum in nonlinear signal analysis, harmonic components appear in the power spectrum of the nonlinear signal in the figure, but the UPEMD power spectrum cannot fully embody the visual advantages of the UPEMD power spectrum in the nonlinear signal.
Fig. 8 is a schematic diagram of main modules of a system for generating a complexity and power bispectrum based on uniform phase modal decomposition according to an embodiment of the present invention, as shown in fig. 8, the system for generating a complexity and power bispectrum based on uniform phase modal decomposition of the present invention includes:
UPEMD decomposition module for setting multiple target decomposition frequency points
Figure SMS_398
For the original signal->
Figure SMS_399
Performing UPEMD decomposition to obtain the original signal +.>
Figure SMS_400
At the target decomposition frequency point->
Figure SMS_401
Lower signal component->
Figure SMS_402
。
A complexity module for calculating the target decomposition frequency point
Figure SMS_403
Signal component +.>
Figure SMS_404
Generates a complexity spectrum.
A power module for calculating the target decomposition frequency point
Figure SMS_405
Signal component +.>
Figure SMS_406
Is used to generate a power spectrum.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. The method for generating the complexity and power dual spectrum based on uniform phase modal decomposition is characterized by comprising the following steps:
setting a plurality of target decomposition frequency points f d UPEMD decomposition is carried out on the original signal x (t), and the original signal x (t) is obtained at the target decomposition frequency point f d Lower signal component C mfd (t)；
Calculating the target decomposition frequency point f d Signal component C of (2) mfd Signal complexity and power spectral density values of (t), generating a complexity spectrum and a power spectrum, comprising:
decomposing the target frequency point f d Lower signal component C mfd (t) as post-processing input signal x u (t)；
For the post-processing input signal x u (t) performing LZC processing to obtain the post-processed input signal x u The signal complexity of (t), comprising:
according to the binarization threshold T h For the post-processing input signal x u (t) performing binarization processing to obtain a binarization sequence b (E); setting a historical sequence P and a current sequence Q of the binarization sequence b (E); increasing the element sequence number j of the last element of the history sequence P, and adding the sequence element b corresponding to the element sequence number (j+1) after the history sequence P is increased in the binarization sequence b (E) j+1 Added to the current sequence Q; splicing the historical sequence P with the current sequence Q, and removing last element to obtain a combined sequence PQgamma; determining whether the current sequence Q is present in the combined sequence PQγ, if not, incrementing a difference identifier n d Splicing the current sequence Q and the historical sequence P to be used as a new historical sequence P=P-Q, and updating the current sequence Q into an empty set; determining whether the new history sequence P is equal to the binarized sequence b (E), if so, for the difference identifier n d Performing normalization processing to obtain the signal complexity of the binarized sequence b (E)
Figure FDA0004151622540000011
Using a fast fourier transform function and said post-processing input signal x u (t) calculating the signal length of the post-processed input signal x u The power spectral density value of (t).
2. The method of claim 1, wherein the UPEMD decomposition is performed on the original signal x (t) to obtain the original signal x (t) at the target decomposition frequency point f d Lower signal component C mfd (t) comprising:
for each of the target decomposition frequency points f d Constructing a one-dimensional frequency matrix D;
for the frequency matrix D, the last matrix element D n-1 Is input to the input signal of (a)
Figure FDA0004151622540000021
And Modal resolution Signal->
Figure FDA00041516225400000213
The difference value as the next matrix element D n Input signal +.>
Figure FDA0004151622540000022
Sequentially for each matrix element D i Input signal +.>
Figure FDA0004151622540000023
Performing modal decomposition until the target decomposition frequency point f is obtained d Signal component C of (2) mfd (t)。
3. The method of claim 2, wherein the sequence is for each matrix element D i Is input to the input signal of (a)
Figure FDA0004151622540000024
Performing modal decomposition, comprising:
dividing the phase of the original signal x (t) to generate the matrix elements D at different phases v i Mask signal y of (2) M,v (t)；
Respectively applying the mask signals y in each phase M,v (t) adding the matrix element D i Is input to the input signal of (a)
Figure FDA00041516225400000214
Obtaining the matrix element D i Decomposing the input signal in the respective phase +.>
Figure FDA0004151622540000025
Using the decomposition of the input signal at different phases
Figure FDA0004151622540000026
For the decomposed input signal
Figure FDA0004151622540000027
Decomposing to obtain the matrix element D i Modal decomposition signal->
Figure FDA0004151622540000028
4. The method of claim 3, wherein the decomposing the input signal with different phases
Figure FDA0004151622540000029
Is added to the decomposed input signal +.>
Figure FDA00041516225400000210
Decomposing to obtain the matrix element D i Modal decomposition signal->
Figure FDA00041516225400000211
Comprising the following steps:
decomposing the input signal
Figure FDA00041516225400000212
As signal y to be decomposed v (t)；
Identifying the signal y to be decomposed v Fitting a plurality of extreme points of (t) through a cubic spline interpolation method to obtain an upper envelope line U (t) and a lower envelope line L (t) of the extreme points, averaging the upper envelope line U (t) and the lower envelope line L (t), and determining an average envelope line m (t) = (U (t) +L (t))/2 of the extreme points;
for the signal y to be decomposed v Performing difference operation on the (t) and the average envelope m (t) to obtain an intermediate signal h (t);
judging whether the intermediate signal h (t) has a negative local maximum value and a positive local minimum value, if not, determining that the intermediate signal h (t) meets an Intrinsic Mode Function (IMF) standard, and obtaining a qualified IMF signal
Figure FDA0004151622540000031
From said decomposed input signal
Figure FDA0004151622540000032
Removing said qualified IMF signal +.>
Figure FDA0004151622540000033
Judging residual signal->
Figure FDA0004151622540000034
Whether it is constant or monotonous, if so, extracting the first qualified IMF signal in the decomposition results of different phases>
Figure FDA0004151622540000035
The matrix element D is obtained after the averaging process i Modal decomposition signal->
Figure FDA0004151622540000036
5. The method of claim 4, wherein the target decomposition frequency point f d Is the last matrix element D of the frequency matrix D n+1 ＝f d The decomposition result of (a), i.e
Figure FDA0004151622540000037
6. The method of claim 4, wherein the extremum points comprise local maxima and local minima; fitting the extreme points through a cubic spline interpolation method to obtain an upper envelope line U (t) and a lower envelope line L (t) of the extreme points, wherein the fitting comprises the following steps:
according to the signal y to be decomposed v Fitting the local maxima of (t) to obtain the upper envelope U (t) by using a cubic spline interpolation method;
according to the signal y to be decomposed v Fitting a plurality of the local minima of (t) to obtain the lower envelope L (t) by using cubic spline interpolation.
7. The method according to claim 1, characterized in that in case the current sequence Q is not present in the combined sequence pqγ, a next sequence element of the binarized sequence b (E) corresponding to a last element of the current sequence Q is added to the current sequence Q.
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