CN115438301B - Equipment operation trend prediction method based on ICEEMDAN (information and communication technology) secondary decoupling index model - Google Patents

Equipment operation trend prediction method based on ICEEMDAN (information and communication technology) secondary decoupling index model Download PDF

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CN115438301B
CN115438301B CN202211315575.3A CN202211315575A CN115438301B CN 115438301 B CN115438301 B CN 115438301B CN 202211315575 A CN202211315575 A CN 202211315575A CN 115438301 B CN115438301 B CN 115438301B
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田乐
王荟芸
常明煜
郭茂祖
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Beijing University of Civil Engineering and Architecture
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Abstract

The invention provides a device operation trend prediction method based on ICEEMDAN secondary decomposition coupling index model, which comprises the steps of firstly performing VMD decomposition on an original signal; calculating the fuzzy entropy of each component; judging the value of each component fuzzy entropy, if the value is larger than a set threshold, performing ICEEMDAN secondary decomposition, and if the value is smaller than the set threshold, performing wavelet soft threshold denoising; performing cross-correlation function analysis on the components after ICEEMDAN secondary decomposition, removing components with correlation coefficients smaller than a specified threshold, calculating an autocorrelation function on the components meeting the conditions, determining a high-frequency component, and performing wavelet soft and hard threshold combination denoising on the high-frequency component; reconstructing the effective signal; and inputting the reconstruction signal into an index model to obtain a prediction result. The invention solves the problem that the equipment operation process signal recorded by the sensor contains a large amount of noise, so that a prediction result has a large error.

Description

Equipment operation trend prediction method based on ICEEMDAN (information and communication technology) secondary decoupling index model
Technical Field
The invention relates to a device operation trend prediction problem, in particular to a device operation trend prediction method based on an ICEEMDAN secondary decomposition coupling index model.
Background
The equipment operation trend prediction predicts the trend of the equipment operation condition based on the operation states such as equipment vibration and the like, so that equipment maintenance planning, fault risk early warning and the like are facilitated, and the equipment operation trend prediction method is widely used in temporary establishment of facility reliability prediction and equipment reliability and safety prediction in a place. The existing equipment operation trend prediction technology generally adopts an Empirical Mode Decomposition (EMD) method, but has the problems of end-point effect and modal component aliasing. In addition, a transducer model is often adopted in the prior art, and although the transducer model has remarkable performance on capturing long-term dependence compared with RNN, the secondary calculation complexity of a self-focusing mechanism is high; memory bottleneck of stacked layers under long sequence input and low reasoning speed when predicting long output. Therefore, the problems of overlarge signal-to-noise ratio, poor denoising effect and overlarge prediction error of the traditional prediction model exist in the prior art.
Disclosure of Invention
In order to solve the problems of overlarge signal-to-noise ratio, poor denoising effect and overlarge prediction error of a traditional prediction model in the prior art, the invention provides a device operation trend prediction method based on an ICEEMDAN (information and communication technology) quadratic decomposition coupling index model, which comprises the following steps:
s10: VMD decomposition is carried out on the original signal;
s20: calculating the fuzzy entropy of the once decomposed components;
s30: setting a threshold value of fuzzy entropy;
s40: judging the fuzzy entropy value of each component obtained by one-time decomposition, wherein the component A is as follows: the fuzzy entropy value is smaller than a specified threshold, and the B component is as follows: the fuzzy entropy value is larger than a specified threshold value;
s50: if the component of the primary decomposition meets the component A, carrying out wavelet soft threshold denoising on the component to obtain a denoising signal of the primary decomposition;
s60: if the first decomposed component meets the B component, carrying out ICEEMDAN secondary decomposition on the component to obtain a secondary decomposed component;
s70: the correlation coefficient of ICEEMEDAN quadratic decomposed components is calculated, and the X component is: a component with a correlation coefficient smaller than 0.1, and a Y component is a component with a correlation coefficient larger than 0.1;
s80: if the secondarily decomposed component meets the X component, directly eliminating the component;
s90: if the secondarily decomposed component meets the Y component, calculating an autocorrelation function, determining a high-frequency component, and carrying out wavelet soft and hard threshold combined denoising on the high-frequency component to obtain a secondarily decomposed denoising signal;
s100: carrying out waveform reconstruction on the primary decomposed denoising signal and the secondary decomposed denoising signal to obtain a final denoising signal;
s110: and inputting the obtained denoising signal into an index model to obtain prediction data.
Preferably, the VMD decomposition algorithm in S10 is:
wherein, S11: initialization of
Figure SMS_1
，/>
Figure SMS_2
，/>
Figure SMS_3
and />
Figure SMS_4
；
Wherein, S12: execution cycle:
Figure SMS_5
;
wherein, S13: when (when)
Figure SMS_6
When, update according to the following formula>
Figure SMS_7
：
Figure SMS_8
Wherein, S14: updating
Figure SMS_9
：
Figure SMS_10
Wherein, S15: updating
Figure SMS_11
：
Figure SMS_12
Wherein, S16: steps S12 to S15 are repeated until the iteration stop condition is satisfied.
Figure SMS_13
in the formula ,
Figure SMS_16
representing the disassembled IMF component, +.>
Figure SMS_19
Representing the center frequencies of the components. />
Figure SMS_23
Represents the Lagrangian multiplier, +.>
Figure SMS_15
Representing a second order penalty factor>
Figure SMS_21
Representing frequency, & lt>
Figure SMS_24
，/>
Figure SMS_26
，/>
Figure SMS_14
Respectively corresponding to->
Figure SMS_18
，/>
Figure SMS_22
，/>
Figure SMS_25
Is a fourier transform of (a). />
Figure SMS_17
Is->
Figure SMS_20
And the residual quantity after wiener filtering.
Preferably, the fuzzy entropy calculation method in S20 is as follows:
wherein, S21: definition for an M-point sampling sequence:
Figure SMS_27
wherein, S22: reconstructing in sequential order of sequence numbers to generate a set of n-dimensional vectors,
Figure SMS_28
wherein
Figure SMS_29
Represents the value of n consecutive u starting at the j-th point,/>
Figure SMS_30
Mean value is expressed in the formula
Figure SMS_31
Wherein, S23: defining two n-dimensional vectors
Figure SMS_32
and />
Figure SMS_33
Distance between->
Figure SMS_34
For the largest difference between the two corresponding elements, i.e
Figure SMS_35
Figure SMS_36
Wherein, S24: by fuzzy functions
Figure SMS_37
Defining two vectors +.>
Figure SMS_38
and />
Figure SMS_39
Similarity between->
Figure SMS_40
I.e.
Figure SMS_41
In the above, the function
Figure SMS_42
And m and r are the gradient and the width of the boundary of the exponential function respectively.
Wherein, S25: definition of a function
Figure SMS_43
Wherein, S26: repeating the steps S22-S25, reconstructing a group of n+1-dimensional vectors according to the sequence number sequence, wherein the function is defined as follows:
Figure SMS_44
wherein, S27: the fuzzy entropy is defined as:
Figure SMS_45
when the M value is a finite value, estimating fuzzy entropy when the sequence number length obtained according to the seven steps is M
Figure SMS_46
Preferably, the threshold formula of the wavelet soft threshold denoising in S50 is:
Figure SMS_47
the wavelet base is cB10, and the number of wavelet layers is set to 3;
Figure SMS_48
is the detail coefficient of the first layer decomposition, N is the data length, j is the decomposition layer number.
Preferably, the ICEEMDAN decomposition algorithm in S60 is:
wherein, S61: adding a set of white noise to the original sequence
Figure SMS_49
Construction sequence->
Figure SMS_50
Obtaining a first set of residuals->
Figure SMS_51
Wherein, S62: computing a first modal component
Figure SMS_52
Wherein, S63: continuing to add white noise, calculating a second set of residuals using local mean decomposition
Figure SMS_53
Define the second modality component->
Figure SMS_54
：
Figure SMS_55
Wherein, S64: calculate the Kth residual
Figure SMS_56
And modality component->
Figure SMS_57
；
Wherein, S65: and (5) until the calculation and decomposition are finished, obtaining all modes and residual numbers.
x is the signal to be decomposed and,
Figure SMS_58
representing k-order modal components resulting from EMD decomposition, < >>
Figure SMS_59
Representing the local mean of the generated signal,/->
Figure SMS_60
Representing gaussian white noise.
Preferably, the correlation coefficient calculation formula in S70 is as follows:
Figure SMS_61
wherein ,
Figure SMS_62
，/>
Figure SMS_63
the function of mean is to average the columns, a representing the original signal and B representing the decomposed component.
Preferably, the formula of the autocorrelation function calculated in S90 is:
Figure SMS_64
wherein T is a signal
Figure SMS_65
Is->
Figure SMS_66
Is->
Figure SMS_67
and />
Figure SMS_68
Correlation between them.
Preferably, the wavelet soft and hard threshold denoising algorithm in S90 is:
wherein, S91: wavelet decomposition is performed on the noisy signal. And selecting sym8 wavelet base, setting the wavelet layer number to be 5, and carrying out wavelet decomposition to obtain a group of wavelet coefficients.
Wherein, S92: threshold quantization processing is carried out on each layer of high-frequency coefficient of wavelet decomposition, and an estimated value of the wavelet coefficient is obtained:
Figure SMS_69
wherein ,
Figure SMS_70
for the detail coefficients of the first layer decomposition, +.>
Figure SMS_71
Is the data length.
Wherein, S93: and carrying out inverse wavelet transformation on the wavelet coefficient subjected to threshold quantization processing to reconstruct a signal, and obtaining a denoising signal.
Preferably, the encoder of the index model in S110 receives a long-sequence input, and obtains the characteristic representation through a probspark self-attention module and a self-attention distillation module. The probspark Self-attention mechanism replaces the original attention matrix with a sparse matrix, greatly reduces the calculation force requirement, maintains good performance, and effectively processes overlong input sequences by halving the cascade layer input to highlight the dominant factors in Self-attention. The decoder receives long sequence inputs, interacts with the encoded features through multi-head attention, and finally predicts the output target portion directly.
The invention provides an optimized device operation trend prediction method based on an ICEEMDAN secondary decomposition coupling index model, which combines VMD and fuzzy entropy to process facility vibration signals acquired by a sensor, uses a wavelet soft threshold method to denoise high-frequency noise, ensures the effectiveness of decomposed components, combines ICEEMDAN and autocorrelation coefficients to screen the high-frequency noise, uses a wavelet soft and hard threshold combination method to denoise the high-frequency noise, and improves the task operation integrity and prediction accuracy; and the processed data is predicted by adopting an index model, so that the prediction error is reduced, the model operation efficiency is improved, and the prediction precision is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It will be apparent to those of ordinary skill in the art that the drawings in the following description are exemplary only and that other implementations can be obtained from the extensions of the drawings provided without inventive effort.
FIG. 1 is a schematic diagram of a workflow provided by the present invention;
FIG. 2 is a block diagram of an inventive index model.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, in the case of no conflict, the embodiments of the present application and the features in the embodiments may be combined with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
The embodiment provides a method for predicting the running trend of equipment based on an ICEEMDAN secondary decoupling index model, which is shown in fig. 1, and specifically comprises the following steps:
step S10: VMD decomposition is performed on the original signal.
The decomposition algorithm is as follows:
step S11: initialization of
Figure SMS_72
，/>
Figure SMS_73
，/>
Figure SMS_74
and />
Figure SMS_75
；
Step S12: execution cycle:
Figure SMS_76
;
step S13: when (when)
Figure SMS_77
When, update according to the following formula>
Figure SMS_78
Figure SMS_79
Step S14: updating
Figure SMS_80
Figure SMS_81
Step S15: updating
Figure SMS_82
Figure SMS_83
Step S16: steps S12 to S15 are repeated until the iteration stop condition is satisfied.
Figure SMS_84
in the formula ,
Figure SMS_87
representing the scoreThe resolved IMF component>
Figure SMS_92
Representing the center frequencies of the components. />
Figure SMS_95
Represents the Lagrangian multiplier, +.>
Figure SMS_88
Representing a second order penalty factor->
Figure SMS_90
Representing frequency, & lt>
Figure SMS_94
，/>
Figure SMS_97
，/>
Figure SMS_85
Respectively corresponding to->
Figure SMS_89
，/>
Figure SMS_93
，/>
Figure SMS_96
Is a fourier transform of (a). />
Figure SMS_86
Is->
Figure SMS_91
And the residual quantity after wiener filtering.
VMD (Variational mode decomposition) is a method of adaptive, completely non-recursive modal variation and signal processing. The method has the advantages that the number of modal decomposition can be determined, the adaptivity is represented by determining the number of modal decomposition of a given sequence according to actual conditions, the optimal center frequency and the limited bandwidth of each modal can be adaptively matched in the subsequent searching and solving process, the effective separation of inherent modal components (IMFs), the frequency domain division of signals and further the effective decomposition components of the given signals can be realized, and finally the optimal solution of the variation problem is obtained. The method solves the problems of end effect and modal component aliasing of the EMD method, has firmer mathematical theory basis, can reduce the time sequence non-stationarity with high complexity and strong nonlinearity, and is suitable for the non-stationarity sequence by decomposing to obtain a relatively stable subsequence containing a plurality of different frequency scales. The ICEEMDAN method is an improved algorithm of the CEEMDAN method, gaussian white noise which corresponds to the modal order after being decomposed by the EMD method is added into the original sequence, so that the problem of modal aliasing existing in the EMD method can be effectively solved, and interference of other signals is prevented.
Step S20: the fuzzy entropy of the once decomposed components is calculated.
The fuzzy entropy calculation formula is:
step S21: definition for an M-point sampling sequence:
Figure SMS_98
step S22: reconstructing in sequential order of sequence numbers to generate a set of n-dimensional vectors,
Figure SMS_99
wherein
Figure SMS_100
Represents the value of n consecutive u starting at the j-th point,/>
Figure SMS_101
Mean value is expressed in the formula
Figure SMS_102
Step S23: defining two n-dimensional vectors
Figure SMS_103
and />
Figure SMS_104
Distance between->
Figure SMS_105
For the largest difference between the two corresponding elements, i.e
Figure SMS_106
Figure SMS_107
Step S24: by fuzzy functions
Figure SMS_108
Defining two vectors +.>
Figure SMS_109
and />
Figure SMS_110
Similarity between->
Figure SMS_111
I.e.
Figure SMS_112
In the above, the function
Figure SMS_113
And m and r are the gradient and the width of the boundary of the exponential function respectively.
Step S25: definition of a function
Figure SMS_114
Step S26: repeating steps S22-S25, reconstructing a group of n+1 dimension vectors according to the sequence number sequence, wherein the function is defined as follows:
Figure SMS_115
step S27: the fuzzy entropy is defined as:
Figure SMS_116
when the M value is a finite value, estimating fuzzy entropy when the sequence number length obtained according to the seven steps is M:
Figure SMS_117
step S30: a prescribed threshold value of the blurring entropy is set. The prescribed threshold may be set to 0.05.
Step S40: judging the fuzzy entropy value of each component obtained by one-time decomposition, wherein the component A is as follows: the fuzzy entropy value is smaller than a specified threshold, and the B component is as follows: the fuzzy entropy value is greater than a prescribed threshold.
Step S50: and if the component subjected to primary decomposition meets the component A, carrying out wavelet soft threshold denoising on the component to obtain a primary decomposed denoising signal.
The wavelet soft threshold denoising algorithm is as follows:
step S51: wavelet decomposition is performed on the noisy signal. And (3) selecting a cB10 wavelet base, setting the wavelet layer number to be 3, and carrying out wavelet decomposition to obtain a group of wavelet coefficients.
Step S52: threshold quantization processing is carried out on each layer of high-frequency coefficient of wavelet decomposition to obtain an estimated value of the wavelet coefficient, and a threshold formula is as follows:
Figure SMS_118
wherein ,
Figure SMS_119
is the detail coefficient of the first layer decomposition, N is the data length, j is the decomposition layer number.
Step S53: and carrying out inverse wavelet transformation on the wavelet coefficient subjected to threshold quantization processing to reconstruct a signal, and obtaining a denoising signal.
Step S60: if the first decomposed component meets the B component, carrying out ICEEMDAN (information and energy conservation) secondary decomposition on the component to obtain a second decomposed component, wherein the ICEEMDAN decomposition algorithm is as follows:
step S61: adding a set of white noise to the original sequence
Figure SMS_120
Construction sequence->
Figure SMS_121
Obtaining a first set of residuals->
Figure SMS_122
Step S62: computing a first modal component
Figure SMS_123
Step S63: continuing to add white noise, calculating a second set of residuals using local mean decomposition
Figure SMS_124
Define the second modality component->
Figure SMS_125
。
Figure SMS_126
Step S64: calculate the Kth residual
Figure SMS_127
And modality component->
Figure SMS_128
Step S65: and (5) until the calculation and decomposition are finished, obtaining all modes and residual numbers.
x is the signal to be decomposed and,
Figure SMS_129
representing k-order modal components resulting from EMD decomposition, < >>
Figure SMS_130
Representing the local mean of the generated signal,/->
Figure SMS_131
Representing gaussian white noise.
Step S70: the correlation coefficient of the ICEEMEDAN quadratic decomposed component is calculated. The X component is as follows: the component with the correlation coefficient smaller than 0.1, and the Y component is the component with the correlation coefficient larger than 0.1.
In step S70, the correlation coefficient calculation formula is:
Figure SMS_132
wherein ,
Figure SMS_133
the function of mean is to average the columns, a representing the original signal and B representing the decomposed component.
Step S80: if the twice decomposed component satisfies the X component, the component is directly removed.
Step S90: if the secondarily decomposed component meets the Y component, an autocorrelation function is calculated, a high-frequency component is determined, and wavelet soft and hard threshold combination denoising is performed on the high-frequency component to obtain a secondarily decomposed denoising signal.
The formula of the autocorrelation function calculated in step S90 is:
Figure SMS_134
wherein T is a signal
Figure SMS_135
Is->
Figure SMS_136
Is->
Figure SMS_137
and />
Figure SMS_138
Correlation between them.
The wavelet soft and hard threshold denoising algorithm in step S90 is:
step S91: wavelet decomposition is performed on the noisy signal. And selecting sym8 wavelet base, setting the wavelet layer number to be 5, and carrying out wavelet decomposition to obtain a group of wavelet coefficients.
Step S92: threshold quantization processing is carried out on each layer of high-frequency coefficient of wavelet decomposition, and an estimated value of the wavelet coefficient is obtained:
Figure SMS_139
wherein ,
Figure SMS_140
for the detail coefficients of the first layer decomposition, +.>
Figure SMS_141
Is the data length.
Step S93: and carrying out inverse wavelet transformation on the wavelet coefficient subjected to threshold quantization processing to reconstruct a signal, and obtaining a denoising signal.
Step S100: and carrying out waveform reconstruction on the primary decomposed denoising signal and the secondary decomposed denoising signal to obtain a final denoising signal.
Step S110: and inputting the obtained denoising signal into an index model to obtain prediction data.
The inventive index model is shown in fig. 2, where the encoder receives long sequence inputs and obtains a feature representation via the probspark self-attention module and the self-attention distillation module. The probspark Self-attention mechanism replaces the original attention matrix with a sparse matrix, greatly reduces the computational power requirements while maintaining good performance, and effectively handles lengthy input sequences by halving the cascade layer input to highlight the dominant factors in the Self-attention mechanism (Self-attention). The decoder receives long sequence inputs, interacts with the encoded features through multi-head attention, and finally predicts the output target portion directly. The remaining non-illustrated portions are conventional arrangements of an index model itself, and are not described in detail herein.
The ProbSparse autocorrelation mechanism of the Informier model of the invention ensures that the time complexity and the memory utilization rate reach
Figure SMS_142
The method comprises the steps of carrying out a first treatment on the surface of the The autocorrelation distillation operation highlights features of high score of interest over J stacked layers and greatly reduces spatial complexity, which helps the model receive long sequence inputs; the generation type decoder (decoder) directly predicts in one step and multiple steps, avoids error accumulation generated by single-step prediction, improves prediction precision and reduces prediction time.
The invention processes facility vibration signals collected by the sensor by combining VMD and fuzzy entropy, uses a wavelet soft threshold method to denoise high-frequency noise, ensures the effectiveness of the decomposed components, screens the high-frequency noise by combining ICEEMDAN and autocorrelation coefficients, uses a wavelet soft and hard threshold combination method to denoise the high-frequency noise, and improves the task running integrity and the prediction accuracy; and creatively combines adopting an index model to predict the processed data, reduces prediction errors, improves model operation efficiency and improves prediction accuracy. Therefore, the invention solves the problem that the equipment operation process signal recorded by the sensor contains a large amount of noise, so that a prediction result has a large error. The invention improves the accuracy of the prediction task, reduces errors caused by noise and improves the prediction accuracy.
The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the embodiments. However, it will be apparent to one skilled in the art that the embodiments may be practiced without the specific details. Thus, the foregoing descriptions of specific embodiments described herein are presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the embodiments to the precise form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art in light of the above teachings. Additionally, as used herein to refer to the position of a component, the terms above and below or their synonyms do not necessarily refer to absolute positions relative to external references, but rather to relative positions of components with reference to the figures.
Furthermore, the foregoing figures and description include many concepts and features that can be combined in various ways to achieve various benefits and advantages. Thus, features, components, elements, and/or concepts from the various figures may be combined to produce embodiments or implementations that are not necessarily shown or described in this specification. Furthermore, not all of the features, components, elements, and/or concepts illustrated in the drawings or description may be required in any particular embodiment and/or implementation. It should be understood that such embodiments and/or implementations fall within the scope of the present description.

Claims (9)

1. An equipment operation trend prediction method based on an ICEEMDAN secondary decoupling index model is characterized by comprising the following steps of:
step S10: VMD decomposition is carried out on an original signal, wherein the original signal is a facility vibration signal acquired by a sensor;
step S20: calculating the fuzzy entropy of the once decomposed components;
step S30: setting a specified threshold of fuzzy entropy;
step S40: judging the fuzzy entropy value of each component obtained by one-time decomposition, wherein the component A is as follows: the fuzzy entropy value is smaller than a specified threshold, and the B component is as follows: the fuzzy entropy value is larger than a specified threshold value;
step S50: if the component of the primary decomposition meets the component A, carrying out wavelet soft threshold denoising on the component to obtain a denoising signal of the primary decomposition;
step S60: if the first decomposed component meets the B component, carrying out ICEEMDAN secondary decomposition on the component to obtain a secondary decomposed component;
step S70: calculating the correlation coefficient of the components of ICEEMDAN secondary decomposition, wherein the X component is a component with the correlation coefficient smaller than 0.1, and the Y component is a component with the correlation coefficient larger than 0.1;
step S80: if the secondarily decomposed component meets the X component, directly eliminating the component;
step S90: if the secondarily decomposed component meets the Y component, calculating an autocorrelation function, determining a high-frequency component, and carrying out wavelet soft and hard threshold combined denoising on the high-frequency component to obtain a secondarily decomposed denoising signal;
step S100: carrying out waveform reconstruction on the primary decomposed denoising signal and the secondary decomposed denoising signal to obtain a final denoising signal;
step S110: and inputting the final denoising signal into an index model to obtain prediction data.
2. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the fuzzy entropy calculation method in step S20 is as follows:
step S21: definition for an M-point sampling sequence:
Figure QLYQS_1
，
step S22: reconstructing in sequential order of sequence numbers to generate a set of n-dimensional vectors,
Figure QLYQS_2
wherein
Figure QLYQS_3
Represents the j-th point beginning n consecutive +.>
Figure QLYQS_4
Value of->
Figure QLYQS_5
Mean value->
Figure QLYQS_6
The calculation is as follows:
Figure QLYQS_7
step S23: defining two n-dimensional vectors
Figure QLYQS_8
and />
Figure QLYQS_9
Distance between->
Figure QLYQS_10
For the largest difference between the two corresponding elements, i.e
Figure QLYQS_11
Figure QLYQS_12
Step S24: by fuzzy functions
Figure QLYQS_13
Defining two vectors +.>
Figure QLYQS_14
and />
Figure QLYQS_15
Similarity between->
Figure QLYQS_16
I.e.
Figure QLYQS_17
In the above, the function
Figure QLYQS_18
M and r are the gradient and width of the boundary of the exponential function respectively;
step S25: definition of a function
Figure QLYQS_19
Step S26: repeating steps S22-S25, reconstructing a group of n+1 dimension vectors according to the sequence number sequence, wherein the function is defined as follows:
Figure QLYQS_20
step S27: the fuzzy entropy is defined as:
Figure QLYQS_21
when the M value is a finite value, estimating fuzzy entropy when the sequence number length obtained in the steps S21-S27 is M:
Figure QLYQS_22
。
3. the method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the prescribed threshold value is set to 0.05 in step S30.
4. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the wavelet soft threshold denoising algorithm in step S50 is:
step S51: performing wavelet decomposition on the noise-containing signal, selecting a cB10 wavelet basis, setting the wavelet layer number to be 3, and performing wavelet decomposition to obtain a group of wavelet coefficients;
step S52: performing wavelet soft threshold quantization processing on each layer of high-frequency coefficients of wavelet decomposition to obtain an estimated value of the wavelet coefficients, wherein a wavelet soft threshold formula is as follows:
Figure QLYQS_23
wherein ,
Figure QLYQS_24
is the detail coefficient of the first layer decomposition, N is the data length, j is the decomposition layer number;
step S53: and carrying out inverse wavelet transformation on the wavelet coefficient subjected to wavelet soft threshold quantization processing to reconstruct a signal, thereby obtaining a denoising signal.
5. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the ICEEMDAN quadratic decomposition algorithm in the step S60 is as follows:
step S61: adding a set of white noise to the original sequence
Figure QLYQS_25
，
Construction sequence
Figure QLYQS_26
Obtaining a first set of residuals->
Figure QLYQS_27
，
Step S62: computing a first modal component
Figure QLYQS_28
，
Step S63: continuing to add white noise, calculating a second set of residuals using local mean decomposition
Figure QLYQS_29
Define the second modality component->
Figure QLYQS_30
，
Figure QLYQS_31
Step S64: calculate the kth residual
Figure QLYQS_32
And modality component->
Figure QLYQS_33
，
Step S65: obtaining all modes and residual numbers until the calculation decomposition is finished;
wherein x is a signal to be decomposed,
Figure QLYQS_34
representing k-order modal components resulting from EMD decomposition, < >>
Figure QLYQS_35
Representing the local mean of the generated signal,/->
Figure QLYQS_36
Representing gaussian white noise.
6. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the correlation coefficient threshold is defined as 0.1.
7. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: the formula of the autocorrelation function calculated in step S90 is:
Figure QLYQS_37
wherein T is a signal
Figure QLYQS_38
Is->
Figure QLYQS_39
Is->
Figure QLYQS_40
and />
Figure QLYQS_41
Correlation between them.
8. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of: in the step S90, the denoising is performed by combining the wavelet soft and hard thresholds on the high-frequency component to obtain a denoised signal of the secondary decomposition, which includes:
step S91: performing wavelet decomposition on the noise-containing signal, selecting sym8 wavelet basis, setting the wavelet layer number to be 5, and performing wavelet decomposition to obtain a group of wavelet coefficients;
step S92: threshold quantization processing is carried out on each layer of high-frequency coefficient of wavelet decomposition to obtain an estimated value of the wavelet coefficient, and a threshold formula is as follows:
Figure QLYQS_42
wherein ,
Figure QLYQS_43
for the detail coefficients of the first layer decomposition, +.>
Figure QLYQS_44
Data length;
step S93: and carrying out inverse wavelet transformation on the wavelet coefficient subjected to threshold quantization processing to reconstruct a signal, and obtaining a denoising signal.
9. The method for predicting the running trend of the equipment based on the ICEEMDAN quadratic decoupling index model according to claim 1, wherein the method comprises the following steps of:
the step S110 of inputting the final denoising signal into an index model to obtain prediction data includes:
the encoder of the index model receives long-sequence input, and obtains characteristic representation through a ProbSparse self-attention module and a self-attention distillation module;
the probspark Self-attention module replaces the attention matrix with a sparse matrix and highlights the dominant factor in Self-attention by halving the cascade layer input;
the decoder receives long sequence inputs, interacts with the encoded features through multi-head attention, and finally predicts the output target portion directly.
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