CN111291918A - Rotating machine degradation trend prediction method based on stationary subspace exogenous vector autoregression - Google Patents

Rotating machine degradation trend prediction method based on stationary subspace exogenous vector autoregression Download PDF

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CN111291918A
CN111291918A CN202010010925.XA CN202010010925A CN111291918A CN 111291918 A CN111291918 A CN 111291918A CN 202010010925 A CN202010010925 A CN 202010010925A CN 111291918 A CN111291918 A CN 111291918A
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贾民平
丁鹏
赵孝礼
杨诚
佘道明
许飞云
胡建中
黄鹏
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Abstract

The invention discloses a rotating machine degradation trend prediction method of stationary subspace exogenous vector autoregression, which comprises the following steps: firstly, carrying out primary stationary subspace decomposition on a denoised multi-channel signal to extract a vibration stationary component; extracting time-domain and frequency-domain degradation characteristic quantities and obtaining a high-dimensional degradation index vector group through characteristic fusion; then, performing secondary stationary subspace decomposition and differential operation on the high-dimensional degradation index vector group in the time domain and the frequency domain to extract weak stationary components in the degradation index as the degradation index of the rotary machine; and (3) carrying out stability inspection and impulse response analysis on the degradation indexes, determining endogenous and exogenous variables and model orders, determining vector autoregressive model parameters through maximum likelihood estimation, and finally carrying out degradation trend estimation on the rotating machine at different prediction starting points. The degradation trend prediction model obtained by the method has good generalization capability under the learning of small samples, and is rapid in calculation and strong in interpretability.

Description

Rotating machine degradation trend prediction method based on stationary subspace exogenous vector autoregression
Technical Field
The invention relates to the technical field of degradation trend prediction in rotary mechanical equipment, in particular to a rotary mechanical degradation trend prediction method based on stationary subspace exogenous vector autoregression, and specifically relates to a method for extracting weak stationary vibration degradation indexes through secondary stationary subspace decomposition and differential operation and predicting degradation trends through exogenous vector autoregression.
Background
The continuous aging and growing demand in the operation of rotating machines calls for more advanced fault prediction and health management techniques, where the prediction of degradation trends plays a crucial role in the complex engineering systems that assemble the rotating machines. The accurate degradation trend prediction method can provide state information and health conditions of the machine in advance for predictive maintenance, so that sudden shutdown risks and equipment failures are avoided, and the overall benefits of the industrial production link are improved.
In order to effectively solve the problem of predicting the degradation trend of the rotating machinery, methods based on physical and mechanical models have been widely researched, but the methods need perfect prior knowledge as support, and the methods are difficult to meet and develop in some complex systems. The data-driven solution is another emerging technology, is widely applied to the fault prediction and health management technology of the lithium ion battery, and the large-scale industrial process monitoring and the fault prediction and health management technology of the rotating machinery, and can be used for flexibly modeling an unknown object by directly generating a degradation or service life model through sampling data without prior knowledge. It provides the possibility of accurate prediction and evaluation under complex conditions, such as variable operating conditions and system level prediction. The development of artificial intelligence technology, including deep learning, is rapid in recent years, which greatly promotes the popularization of data driving methods in the field of rotary machine degradation trend prediction, such technology has excellent feature learning and representation capability, and most prediction tasks perform well under abundant and complete marking data. Unfortunately, however, such "learning-generative model" based prediction architectures are more or less dependent on the quality and number of learning samples, and the prediction results are limited by the similarity between the learning and testing data sets. That is, this approach may fail for some high-end application scenarios where data is insufficient. Although the migration learning technique can alleviate this problem to some extent, the lack of an interpretable modeling process and the perfection of the mathematical statistics basis as support remain a troublesome problem.
In addition to the data-driven research based on the artificial intelligence technology, the data-driven prediction method based on regression analysis is widely researched in the field of rotary machine degradation trend prediction, and the method can provide perfect mathematical and statistical bases and has good interpretability. However, most regression analysis data-driven prediction methods are internally static structures, which greatly limits the extrapolation and generalization from time t to time t + n. The autoregressive theory is widely applied to modeling in the fields of rivers, geography, economy and the like as a prediction and forecast model with a natural extrapolation structure and a perfect mathematical theory basis. The problems generally have certain periodicity and stable data, autoregressive analysis is facilitated, the degradation process of the rotary machine comprises a large number of non-stable and non-linear components, application and popularization of the theory in the field are greatly hindered, and meanwhile, relevant literature reports are rarely found.
In view of the advantages of autoregressive prediction and prediction models and the defects of the autoregressive prediction and prediction models applied to the degradation trend prediction of the rotary machine, how to process vibration non-stationary signals to enable the vibration non-stationary signals to meet the requirements of an autoregressive theory on weak stationarity is a problem to be solved. Based on a subspace decomposition theory, the signal processing is carried out on the vibration degradation signal with non-stability and non-linearity, and the degradation trend prediction is carried out through an exogenous vector autoregressive model.
Disclosure of Invention
The invention aims to provide a rotating machinery degradation trend prediction method of stationary subspace exogenous vector autoregression with exogenous sources (SSVARX). Extracting weak stationary components in time domain and frequency domain degradation indexes as degradation indexes of the rotary machine by applying a twice stationary subspace decomposition method and differential operation; and then carrying out stationarity test and impulse response analysis on the rotary machine, determining endogenous and exogenous variables and a model order, determining vector autoregressive model parameters through maximum likelihood estimation, and finally carrying out degradation trend estimation on the rotary machine at different prediction starting points. The method effectively solves the problems of weak capability of predicting the degradation trend of the rotary machine, long calculation time, black box effect and the like under the condition of small samples at present, and has important economic and social values.
The invention provides a rotating machine degradation trend prediction method of stationary subspace exogenous vector autoregression, which comprises the following steps:
step 1: performing multi-channel signal acquisition on the rotary mechanical sensitive degradation position through a vibration accelerometer, and performing wavelet denoising on the acquired vibration signal to remove high-frequency components in an original signal;
step 2: the method comprises the following steps of carrying out first stationary subspace decomposition on a multi-channel vibration signal subjected to noise reduction to synthesize multi-channel degradation and damage information and extract a vibration weak stationary component, and mainly realizing the first stationary subspace decomposition (SSA) algorithm and the vibration signal subjected to multi-channel noise reduction, namely:
Figure BDA0002357138800000021
in the formula
Figure BDA0002357138800000022
Representing all observed values collected by the channel I;
Figure BDA0002357138800000023
and
Figure BDA0002357138800000024
respectively show weak and steady vibration after decompositionAnd non-stationary components.
And step 3: respectively extracting time domain and frequency domain degradation characteristics from the generated vibration weak stationary components, and performing characteristic fusion on a matrix formed by the degradation characteristics of each domain through principal component analysis to generate a time domain and frequency domain high-dimensional degradation index vector group, wherein the method comprises the following specific steps of: extracting time domain and frequency domain degradation characteristics and fusing the characteristics based on principal component analysis,
step 3.1: the time domain feature extraction adopts a statistical parameter formula as follows: average value:
Figure BDA0002357138800000025
standard deviation:
Figure BDA0002357138800000026
square root amplitude:
Figure BDA0002357138800000027
absolute average value:
Figure BDA0002357138800000028
skewness:
Figure BDA0002357138800000029
kurtosis:
Figure BDA00023571388000000210
variance:
Figure BDA00023571388000000211
maximum value: DF (Decode-feed)8Max | x (n) |, minimum: DF (Decode-feed)9Min | x (n) |, peak mean: DF (Decode-feed)10＝DF8-DF9Root mean square:
Figure BDA00023571388000000212
wave form index:
Figure BDA00023571388000000213
peak index:
Figure BDA00023571388000000214
pulse index:
Figure BDA00023571388000000215
margin index:
Figure BDA00023571388000000216
skewness index:
Figure BDA00023571388000000217
and kurtosis index:
Figure BDA00023571388000000218
the statistical parameter formula adopted by the frequency domain feature extraction is as follows:
Figure BDA00023571388000000219
Figure BDA00023571388000000220
Figure BDA0002357138800000031
and
Figure BDA0002357138800000032
where y (k) is the fast Fourier spectrum of a given signal, fkThen the frequency value, DF, corresponding to the k-th spectrum18Reflecting the vibration energy, DF, in the frequency domain19～DF21、DF23And DF27～DF30Describing the degree of concentration and dispersion of the spectrum, DF22And DF24～DF26Indicating a change in the position of the main band.
Step 3.2: the extracted time domain and frequency domain degradation features respectively form a feature matrix DF1～17，DF18～30Performing feature fusion for principal component analysis;
step 3.3: DF analysis Using principal component analysis1～17And DF18～30Feature fusion is carried out to extract principal components meeting the predetermined contribution rate to form a high-dimensional degradation index vector group, namely
Figure BDA0002357138800000033
Figure BDA0002357138800000034
In the formula
Figure BDA0002357138800000035
And
Figure BDA0002357138800000036
the feature vectors are represented individually by a vector of features,
Figure BDA0002357138800000037
and
Figure BDA0002357138800000038
respectively representing time domain and frequency domain principal components, i.e. high-dimensional degradation indicator vector sets, which meet a predetermined contribution value.
And 4, step 4: performing secondary stationary subspace decomposition on the time domain and frequency domain high-dimensional degradation index vector group, extracting weak stationary components in the degradation index vector group, and performing differential operation based on spectrum analysis to generate time domain and frequency domain degradation indexes meeting weak stationary requirements, wherein the basic steps can be summarized as follows:
step 4.1: and performing secondary stationary subspace decomposition on the high-dimensional degradation index vector group through a stationary subspace decomposition algorithm, namely:
Figure BDA0002357138800000039
Figure BDA00023571388000000310
in the formula
Figure BDA00023571388000000311
Representing the degradation indicator vector at all time instants from the first principal component,
Figure BDA00023571388000000312
and
Figure BDA00023571388000000313
weak stationary and non-stationary components of the time domain high dimensional degradation index vector group are represented;
Figure BDA00023571388000000314
and
Figure BDA00023571388000000315
and weak stationary and non-stationary components of the frequency domain high-dimensional degradation index vector group are represented.
Step 4.2: and calculating a required differential step length through spectral analysis according to the generated time domain and frequency domain high-dimensional degradation index vector group, wherein the differential step length is the reciprocal of the corresponding frequency of the main peak of the spectral analysis, and then performing differential operation to generate a degradation index with periodicity removed so as to input the degradation trend prediction model.
And 5: and finally, inputting the time domain and frequency domain degradation indexes into an exogenous vector autoregressive model to predict the degradation trend of the rotary machine. Comprises the following steps: defining exogenous and endogenous variables, inputting stability test of degradation indexes, determining model orders, analyzing impulse response, estimating parameters and predicting degradation trend, and the basic steps can be summarized as follows:
step 5.1: defining weak and stable components of a high-dimensional degradation index vector group without obvious fluctuation in each degradation stage in a life cycle as endogenous variables, and the rest are exogenous variables to assist in degradation trend prediction;
step 5.2: the stationarity is checked by detecting whether the selected input has a unit root by the augmented disky-fullerene method: h0Assume that as follows:
H0：yt＝c+yt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
H1assume that as follows:
H0：yt＝c+dt+θyt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
in the formula, theta<1,[β1,…,βp]And d is the coefficient of regression term and trend term respectively, epsilontRepresenting random error, and c is a constant term. Then, preliminarily determining the range of the order interval with the stable characteristic by the method: first determine to contain no unit roots, i.e. reject H0All the intervals with proper orders of (1) defineiAnd uiThe upper and lower boundaries of the ith interval are respectively; and then performing intersection operation on all the intervals, namely: [ l1,…,u1]∪,…,∪[li,…,ui]∪,…,∪[ln,…,un]Thereby determining the range of the order interval with the stable characteristic.
Step 5.3: calculating an Akaike information criterion value in an order interval with a stable characteristic, namely:
Figure BDA0002357138800000041
searching the order corresponding to the minimum value of the above formula, and defining the order as a model order;
step 5.4: further analyzing the endogenous variables by using impulse response analysis, namely the influence of time domain and frequency domain degradation indexes on the interference of a vector autoregressive model lag structure, and checking the influence of impact on all the endogenous variables from a short-term or long-term angle;
step 5.5: and performing parameter estimation on the external source vector autoregressive model by utilizing maximum likelihood estimation, and then using the model for the degradation trend prediction at different starting points to test the generalization capability of the model.
The invention has the beneficial effects that:
1. the method for predicting the degradation trend based on the SSVARX is the first attempt of applying the vector autoregressive theory to the field of rotating machinery, and provides a perfect mathematical theoretical basis for prediction and forecast research under data drive;
2. the degradation trend prediction method provided by the invention not only has a natural extrapolation structure and high calculation speed, but also provides a high-precision prediction result under the condition of a small sample, and is very suitable for high-end application scenes with rare state data;
3. the degradation trend prediction method provided by the invention provides a feasible way for converting a non-stationary vibration signal into a weak stationary degradation index, and simultaneously considers potential causal relationships and relationships among endogenous variables from different fields, thereby further improving the degradation trend prediction precision.
Drawings
FIG. 1 is a flow chart of an embodiment of the method of the present invention.
Fig. 2 is a multi-channel vibration raw signal acquired in the present invention.
Fig. 3 is a first stationary subspace decomposition component obtained by the method of the present invention.
FIG. 4 is a time domain and frequency domain feature extraction of weak stationary components of a vibration signal in the present invention.
FIG. 5 shows HDDIVs in the time domain and frequency domain in the present invention.
FIG. 6 is a degradation indicator after the second stationary subspace decomposition and difference operation obtained by the method of the present invention.
Fig. 7 is a result of impulse response analysis between degradation indicators in the present invention.
FIG. 8 shows the results of the prediction of the rolling bearing degradation trend at different actual prediction points obtained by the method of the present invention.
FIG. 9 is a graph comparing the predicted degradation trend obtained by the method of the present invention with comparative tests A, B, and C.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The flow of a rotating machine degradation trend prediction method based on stationary subspace exogenous vector autoregression is shown in fig. 1, and the steps can be summarized as follows:
step 1, adopting an HRB6308 rolling bearing in the embodiment, and matching with an ABLT-1A type bearing life strengthening testing machine to perform a full-life fatigue acceleration test. Firstly, performing two-channel signal acquisition on a rotary mechanical sensitive degradation position by matching a PCB 608A11 vibration accelerometer with a National Instruments 9234 data acquisition card, wherein an original signal refers to FIG. 2, and performing wavelet denoising on the acquired vibration signal to remove high-frequency components in the original signal;
and 2, performing first stationary subspace decomposition on the denoised multi-channel vibration signal through a Stationary Subspace Analysis (SSA) algorithm and the denoised multi-channel vibration signal, integrating multi-channel degradation and damage information and extracting a weak stationary component of vibration, and particularly referring to FIG. 3. Namely:
Figure BDA0002357138800000051
in the formula
Figure BDA0002357138800000052
Representing all observed values collected by the channel I;
Figure BDA0002357138800000053
and
Figure BDA0002357138800000054
respectively representing weak stationary and non-stationary components of the vibration after decomposition.
Step 3, respectively extracting 17 time domains DF from the generated vibration weak stationary components1-1713 frequency domain degradation features DF18-30The normalized features are shown in fig. 4. And then, forming a matrix for the degradation characteristics of each domain through principal component analysis, namely: [ DF)1，DF2，...，DF17]And [ DF ]18，DF19，...，DF30]And performing feature fusion, wherein the contribution rate threshold value is set to be 98% so as to ensure that the degeneration and damage information is covered to a greater extent. Fig. 5 shows the generated time-domain and frequency-domain high-dimensional degradation indicator vectors (HDDIVs). The method specifically comprises the following steps: extracting time domain and frequency domain degradation characteristics and fusing the characteristics based on principal component analysis,
step 3.1, statistics for time domain feature extractionThe parameter formula is as follows: average value:
Figure BDA0002357138800000055
standard deviation:
Figure BDA0002357138800000056
square root amplitude:
Figure BDA0002357138800000057
absolute average value:
Figure BDA0002357138800000058
skewness:
Figure BDA0002357138800000061
kurtosis:
Figure BDA0002357138800000062
variance:
Figure BDA0002357138800000063
maximum value: DF (Decode-feed)8Max | x (n) |, minimum: DF (Decode-feed)9Min | x (n) |, peak mean: DF (Decode-feed)10＝DF8-DF9Root mean square:
Figure BDA0002357138800000064
wave form index:
Figure BDA0002357138800000065
peak index:
Figure BDA0002357138800000066
pulse index:
Figure BDA0002357138800000067
margin index:
Figure BDA0002357138800000068
skewness index:
Figure BDA0002357138800000069
harmony peakDegree index:
Figure BDA00023571388000000610
the statistical parameter formula adopted by the frequency domain feature extraction is as follows:
Figure BDA00023571388000000611
Figure BDA00023571388000000612
Figure BDA00023571388000000613
and
Figure BDA00023571388000000614
where y (k) is the fast Fourier spectrum of a given signal, fkThen the frequency value, DF, corresponding to the k-th spectrum18Reflecting the vibration energy, DF, in the frequency domain19～DF21、DF23And DF27～DF30Describing the degree of concentration and dispersion of the spectrum, DF22And DF24～DF26Indicating a change in the position of the main band.
Step 3.2, the extracted time domain and frequency domain degradation features respectively form a feature matrix DF1～17，DF18～30Performing feature fusion for principal component analysis;
step 3.3, DF analysis Using principal component analysis1～17And DF18～30Feature fusion is carried out to extract principal components meeting the predetermined contribution rate to form a high-dimensional degradation index vector group, namely
Figure BDA00023571388000000615
Figure BDA00023571388000000616
In the formula
Figure BDA00023571388000000617
And
Figure BDA00023571388000000618
the feature vectors are represented individually by a vector of features,
Figure BDA00023571388000000619
and
Figure BDA00023571388000000620
respectively representing time domain and frequency domain principal components, i.e. high-dimensional degradation indicator vector sets, which meet a predetermined contribution value.
Step 4, carrying out secondary stationary subspace decomposition on the time domain and frequency domain high-dimensional degradation index vector group, and extracting the weak stationary component DI in the degradation index vector groupTimeAnd DIFrequencyAnd carrying out differential operation based on spectrum analysis to generate time domain and frequency domain degradation indexes meeting weak and stable requirements. The basic steps can be summarized as follows:
step 4.1, performing secondary stationary subspace decomposition on the high-dimensional degradation index vector group through a stationary subspace decomposition algorithm, namely:
Figure BDA00023571388000000621
Figure BDA0002357138800000071
in the formula
Figure BDA0002357138800000072
Representing the degradation indicator vector at all time instants from the first principal component,
Figure BDA0002357138800000073
and
Figure BDA0002357138800000074
weak stationary and non-stationary components of the time domain high dimensional degradation index vector group are represented;
Figure BDA0002357138800000075
and
Figure BDA0002357138800000076
and weak stationary and non-stationary components of the frequency domain high-dimensional degradation index vector group are represented.
And 4.2, calculating a required differential step length through spectral analysis according to the generated time domain and frequency domain high-dimensional degradation index vector group, wherein the differential step length is the reciprocal of the corresponding frequency of the main peak of the spectral analysis, then performing differential operation to generate a degradation index with periodicity removed, and inputting the degradation index into a subsequent degradation trend prediction model.
And 5, finally, inputting the time domain and frequency domain degradation indexes after difference into an exogenous vector autoregressive model to predict the degradation trend of the rotary machine. Comprises the following steps: defining exogenous and endogenous variables, inputting stability test of degradation indexes, determining model orders, analyzing impulse response, estimating parameters and predicting degradation trend, and the basic steps can be summarized as follows:
step 5.1, defining weak stationary components of a high-dimensional degradation index vector group without remarkable fluctuation in each degradation stage in a life cycle as endogenous variables, specifically as shown in fig. 6, and the rest are exogenous variables for assisting degradation trend prediction;
and 5.2, detecting whether the selected input quantity has a unit root by an augmented Diety-Fuller method to check the stability: h0Assume that as follows:
H0：yt＝c+yt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
H1assume that as follows:
H0：yt＝c+dt+θyt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
in the formula, theta<1,[β1,…,βp]And d is the coefficient of regression term and trend term respectively, epsilontRepresenting random error, and c is a constant term. Then, the order interval range with stable characteristic is preliminarily determined by the method: first determine to contain no unit roots, i.e. reject H0All the intervals with proper orders of (1) defineiAnd uiThe upper and lower boundaries of the ith interval are respectively; and then performing intersection operation on all the intervals, namely: [ l1,…,u1]∪,…,∪[li,…,ui]∪,…,∪[ln,…,un]Thereby determining the range of the order interval with the stable characteristic.
Step 5.3, calculating an Akaike information criterion value in the order interval with the stable characteristic, namely:
Figure BDA0002357138800000077
searching the order corresponding to the minimum value of the above formula to define the order of the model, wherein the unit root test result is shown in table 1;
TABLE 1 Unit root test results of time-domain and frequency-domain degradation indicators
Variables of t-statistic Number of delay steps 1% critical value Critical value of 5% 10% critical value Conclusion
DITime -3.6143 60 -2.5695 -1.9415 -1.6166 Stability of
DIFrequency -2.9781 60 -2.5695 -1.9415 -1.6166 Stability of
Step 5.4, further analyzing the endogenous variables by using impulse response analysis, namely the influence of time domain and frequency domain degradation indexes on the interference of a lag structure of the vector autoregressive model, and checking the influence of impact on all the endogenous variables from a short-term or long-term angle, wherein the specific result is shown in fig. 7;
and 5.5, performing parameter estimation on the exogenous vector autoregressive model by utilizing maximum likelihood estimation, wherein the model for predicting the stationary subspace exogenous vector autoregressive degradation trend provided by the invention is as follows. The model is then used for the degradation trend prediction at different starting points, and the generalization capability of the model is tested, and the prediction result is shown in FIG. 8.
Figure BDA0002357138800000081
Step 6, in order to highlight the effectiveness and the necessity of the method, a contrast test is constructed: a, the absence of a first stationary subspace decomposition; and B, the degradation trend prediction under 20 different prediction starting points is respectively carried out on the three-time comparison test based on the classical autoregressive model and the lack of the secondary stationary subspace decomposition in the method disclosed by the invention. As can be seen from fig. 9 and table 2: the secondary stationary subspace decomposition and vector autoregressive modeling method in the method provided by the invention can effectively improve the degradation trend precision, and has significant engineering application value.
TABLE 2 comparative testing of the process of the invention
Average prediction error of twenty predictions
Comparative experiment A 0.2402
Comparative test B 0.1052
Comparative test C 0.4104
The method of the invention 0.1038
Step 7, to highlight the advantages of the method of the present invention compared with other existing prediction technologies, the prediction conditions of the Long Short-Term Memory network (LSTM) and the Gated Recirculation Unit (GRU) at different prediction starting points are respectively constructed, as shown in table 3: the method has low prediction error under different prediction starting points and is far lower in calculation time than LSTM and GRU models.
TABLE 3 comparison of the Process of the invention with other Processes
Figure BDA0002357138800000083
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A rotating machine degradation trend prediction method based on stationary subspace exogenous vector autoregression is characterized by comprising the following steps:
step 1: carrying out multi-channel signal acquisition on the rotary mechanical sensitive degradation position through a vibration accelerometer, and carrying out noise reduction processing on the acquired vibration signal;
step 2: performing primary stationary subspace decomposition on the denoised multi-channel vibration signal to synthesize multi-channel degradation and damage information and extract a weak stationary component of vibration;
and step 3: respectively extracting time domain and frequency domain degradation characteristics from the generated vibration weak and stable components, and performing characteristic fusion on a matrix formed by the degradation characteristics of each domain through principal component analysis to generate a time domain and frequency domain high-dimensional degradation index vector group;
and 4, step 4: performing secondary stationary subspace decomposition on the time domain and frequency domain high-dimensional degradation index vector group, extracting weak stationary components in the degradation index vector group, and performing differential operation based on spectral analysis to generate time domain and frequency domain degradation indexes meeting weak stationary requirements;
and 5: and finally, inputting the time domain and frequency domain degradation indexes into an exogenous vector autoregressive model to predict the degradation trend of the rotary machine.
2. The method for predicting the degradation trend of rotating machinery by stationary subspace exogenous vector autoregression as claimed in claim 1, wherein: in the step 1, the noise reduction processing is performed on the acquired vibration signals, namely, high-frequency components in the original signals are removed through wavelet noise reduction.
3. The method for predicting the degradation trend of rotating machinery by stationary subspace exogenous vector autoregression as claimed in claim 1, wherein: the first stationary subspace decomposition in the step 2 is realized by a stationary subspace analysis algorithm and a noise-reduced multi-channel vibration signal, that is:
Figure RE-FDA0002486728530000011
in the formula
Figure RE-FDA0002486728530000012
Representing all observed values collected by the channel I;
Figure RE-FDA0002486728530000013
and
Figure RE-FDA0002486728530000014
respectively representing weak stationary and non-stationary components of the vibration after decomposition.
4. The method for predicting the degradation trend of rotating machinery by stationary subspace exogenous vector autoregression as claimed in claim 1, wherein: the construction of the time domain and frequency domain high-dimensional degradation index vector group in the step 3 comprises the following specific steps: extracting time domain and frequency domain degradation characteristics and fusing the characteristics based on principal component analysis,
step 3.1: the time domain feature extraction adopts a statistical parameter formula as follows: average value:
Figure RE-FDA0002486728530000015
standard deviation:
Figure RE-FDA0002486728530000016
square root amplitude:
Figure RE-FDA0002486728530000017
absolute average value:
Figure RE-FDA0002486728530000018
skewness:
Figure RE-FDA0002486728530000019
kurtosis:
Figure RE-FDA00024867285300000110
variance:
Figure RE-FDA00024867285300000111
maximum value: DF (Decode-feed)8Max | x (n) |, minimum: DF (Decode-feed)9Min | x (n) |, peak mean: DF (Decode-feed)10＝DF8-DF9Root mean square:
Figure RE-FDA00024867285300000112
wave form index:
Figure RE-FDA00024867285300000113
peak index:
Figure RE-FDA00024867285300000114
pulse index:
Figure RE-FDA00024867285300000115
margin index:
Figure RE-FDA00024867285300000116
skewness index:
Figure RE-FDA00024867285300000117
and kurtosis index:
Figure RE-FDA00024867285300000118
the statistical parameter formula adopted by the frequency domain feature extraction is as follows:
Figure RE-FDA00024867285300000119
Figure RE-FDA0002486728530000021
Figure RE-FDA0002486728530000022
and
Figure RE-FDA0002486728530000023
where y (k) is the fast Fourier spectrum of a given signal, fkThen the frequency value, DF, corresponding to the k-th spectrum18Reflecting the vibration energy, DF, in the frequency domain19～DF21、DF23And DF27～DF30Describing the degree of concentration and dispersion of the spectrum, DF22And DF24～DF26Indicating a change in the position of the main band.
Step 3.2: the extracted time domain and frequency domain degradation features respectively form a feature matrix DF1～17，DF18～30Performing feature fusion for principal component analysis;
step 3.3: DF analysis Using principal component analysis1～17And DF18～30Feature fusion is carried out to extract principal components meeting the predetermined contribution rate to form a high-dimensional degradation index vector group, namely
Figure RE-FDA0002486728530000024
Figure RE-FDA0002486728530000025
In the formula
Figure RE-FDA0002486728530000026
And
Figure RE-FDA0002486728530000027
the feature vectors are represented individually by a vector of features,
Figure RE-FDA0002486728530000028
and
Figure RE-FDA0002486728530000029
respectively representing time domain and frequency domain principal components, i.e. high-dimensional degradation indicator vector sets, which meet a predetermined contribution value.
5. The method for predicting the degradation trend of rotating machinery by stationary subspace exogenous vector autoregression as claimed in claim 1, wherein: the second stationary subspace decomposition in the step 4 is realized by a stationary subspace decomposition algorithm and a high-dimensional degradation index vector set, and the basic steps are as follows:
step 4.1: and performing secondary stationary subspace decomposition on the high-dimensional degradation index vector group through a stationary subspace decomposition algorithm, namely:
Figure RE-FDA00024867285300000210
Figure RE-FDA00024867285300000211
in the formula
Figure RE-FDA00024867285300000212
Representing the degradation indicator vector at all time instants from the first principal component,
Figure RE-FDA00024867285300000213
and
Figure RE-FDA00024867285300000214
weak stationary and non-stationary components of the time domain high dimensional degradation index vector group are represented;
Figure RE-FDA00024867285300000215
and
Figure RE-FDA00024867285300000216
and weak stationary and non-stationary components of the frequency domain high-dimensional degradation index vector group are represented.
Step 4.2: and calculating the required difference step length through spectral analysis according to the generated time domain and frequency domain high-dimensional degradation index vector group, and performing difference operation to generate the degradation index with periodicity removed so as to input the degradation trend prediction model.
6. The method for predicting the degradation trend of a rotating machine based on stationary subspace exogenous vector autoregressive, as claimed in claim 5, wherein: and 4.2, the difference step length is the reciprocal of the frequency corresponding to the main peak of the spectrum analysis.
7. The method for predicting the degradation trend of rotating machinery by stationary subspace exogenous vector autoregression as claimed in claim 1, wherein: the construction of the extrinsic vector autoregressive degradation trend prediction model in the step 5 comprises the following steps: defining exogenous and endogenous variables, inputting stability test of degradation indexes, determining model orders, analyzing impulse response, estimating parameters and predicting degradation trend, and basically comprising the following steps of:
step 5.1: defining weak and stable components of a high-dimensional degradation index vector group without obvious fluctuation in each degradation stage in a life cycle as endogenous variables, and the rest are exogenous variables to assist in degradation trend prediction;
step 5.2: the stationarity is checked by detecting whether the selected input has a unit root by the augmented disky-fullerene method: h0Assume that as follows:
H0：yt＝c+yt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
H1assume that as follows:
H0：yt＝c+dt+θyt-1+β1Δyt-1+β2Δyt-2+…+βpΔyp-1+εt
in the formula, theta<1,[β1,…,βp]And d is the coefficient of regression term and trend term respectively, epsilontRepresenting random error, and c is a constant term. Then, preliminarily determining an order interval range with stable characteristics by the method;
step 5.3: calculating an Akaike information criterion value in an order interval with a stable characteristic, namely:
Figure RE-FDA0002486728530000031
searching the order corresponding to the minimum value of the above formula, and defining the order as a model order;
step 5.4: further analyzing the endogenous variables by using impulse response analysis, namely the influence of time domain and frequency domain degradation indexes on the interference of a vector autoregressive model lag structure, and checking the influence of impact on all the endogenous variables from a short-term or long-term angle;
step 5.5: and performing parameter estimation on the external source vector autoregressive model by utilizing maximum likelihood estimation, and then using the model for the degradation trend prediction at different starting points to test the generalization capability of the model.
8. The method for predicting the degradation trend of a rotating machine based on stationary subspace exogenous vector autoregressive, as claimed in claim 7, wherein: the order interval determination method with the stable characteristic in the step 5.2 is as follows: first determine to contain no unit roots, i.e. reject H0All the intervals with proper orders of (1) defineiAnd uiThe upper and lower boundaries of the ith interval are respectively; and then performing intersection operation on all the intervals, namely: [ l1,…,u1]∪,…,∪[li,…,ui]∪,…,∪[ln,…,un]Thereby determining the range of the order interval with the stable characteristic.
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