CN116383608A - Small sample equipment fault online prediction method - Google Patents

Small sample equipment fault online prediction method Download PDF

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CN116383608A
CN116383608A CN202310356001.9A CN202310356001A CN116383608A CN 116383608 A CN116383608 A CN 116383608A CN 202310356001 A CN202310356001 A CN 202310356001A CN 116383608 A CN116383608 A CN 116383608A
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张保山
郭基联
周峰
周章文
张明亮
李波
魏圣军
顾金玲
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Air Force Engineering University of PLA
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Abstract

The invention discloses an online prediction method for faults of small sample equipment, which comprises the following prediction steps: s1, data processing: according to the invention, by providing a small sample equipment fault online prediction model and verifying the validity and reliability of the model through rolling bearing life cycle vibration data, the BIC can accurately find out the optimal decomposition layer number of the WTD algorithm, provide a basis for improving WTD model parameter setting, improve WTD model noise reduction effect, ensure fault data reliability, and the MD improved MEST algorithm and dual CSFI algorithm can effectively convert fault signals into fault degree indexes, thereby providing high-quality data guarantee for subsequent fault prediction.

Description

Small sample equipment fault online prediction method
Technical Field
The invention relates to the technical field of equipment fault prediction, in particular to an online small sample equipment fault prediction method.
Background
The fault prediction technology can be based on fault mechanism analysis, a fault occurrence mode is assumed, historical degradation data is utilized, potential fault information is deeply excavated, a prediction model based on physical or data driving is constructed, the prediction of the fault degree is realized, the method is based on equipment health state judgment, residual service life analysis and state maintenance, the equipment degradation presents larger difference, the early-stage faults are difficult to extract characteristics, the later-stage faults are difficult to reflect the current equipment health state, the quantity of fault data at the relatively recent moment is difficult to meet the requirement of fitting precision, the difficulty of fault prediction is increased, and the small-sample, fast-convergence and high-precision fault online prediction technology becomes a hot spot for research in the fault prediction field;
however, the current fault prediction technology has poor adaptability and poor fault prediction effect on equipment with high fault complexity, small sample data size and strong prediction timeliness.
Disclosure of Invention
The invention provides an online fault prediction method for small sample equipment, which can effectively solve the problems of poor adaptability, high fault complexity, small sample data size and poor fault prediction effect of the equipment with strong prediction timeliness of the current fault prediction technology in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions: an online prediction method for faults of small sample equipment comprises the following prediction steps:
s1, data processing: through threshold function optimization in a WTD noise reduction algorithm and introduction of BIC, the influence of the number of decomposition layers on the complexity of the WTD is evaluated, and an improved WTD algorithm is provided for filtering noise in fault signals on line;
s2, fault degree identification: constructing a non-parameter model of a system or equipment through MEST, obtaining an estimated vector through optimal reconstruction estimation of an observed vector and a history memory matrix, reflecting the fault degree by utilizing the difference between the estimated vector and the observed vector, and introducing CSFI to carry out smoothing treatment;
s3, online fault prediction: by a TSFM non-statistical analysis method, accidental variation of data is eliminated, gradient descent on-line updating smoothing factors are introduced, self-adaptive sliding time window is introduced to dynamically intercept time sequence data, and fitting capacity of the TSFM is improved;
s4, experimental analysis: verifying the effectiveness and feasibility of the equipment fault prediction model under the condition of a small sample;
s5, data processing analysis: the complexity of the improved WTD algorithm with different decomposition layers is evaluated through a preset BIC;
s6, fault degree identification analysis: the improved WTD is used for obtaining each wavelet decomposition coefficient as an observation variable of an improved MEST, sampling frequency, health state and degradation state are set for carrying out recognition analysis on fault degree, double CSFI is adopted for processing data, and a 'sharp point' of which the derivative does not exist in a curve is eliminated, so that a fault degree point after smoothing is obtained;
s7, fault online test analysis: the method comprises the steps of presetting an adaptive sliding time window, an adaptive smoothing factor, a learning factor, the maximum training iteration number and the minimum allowable error, and inputting a smoothed bearing fault degree value into a fault online prediction model to obtain an adaptive smoothing factor change trend, an adaptive sliding time window length change trend and a prediction error change trend.
S8, summarizing prediction results: summarizing the effect of online prediction model fault prediction.
2. The online fault prediction method for small sample equipment according to claim 1, wherein in S1, the WTD algorithm is modified to filter noise in a fault signal online, and the principle is as follows:
Figure SMS_1
wherein λ is a threshold value;
ω j,k wavelet coefficients for fault signals;
Figure SMS_2
estimating wavelet coefficients;
j is a decomposition scale, J is more than or equal to 1 and less than or equal to J, and J is a maximum scale;
sgn () is a sign function;
the threshold function has continuity in the wavelet domain when ω j,k →λ - In the time-course of which the first and second contact surfaces,
Figure SMS_3
when omega j,k →λ + In the time-course of which the first and second contact surfaces,
Figure SMS_4
the threshold lambda should be chosen such that:
Figure SMS_5
wherein N represents a signal length;
σ j the standard deviation of the Gaussian white noise of the j layer is expressed as follows:
Figure SMS_6
in the formula, cd j,k A high frequency part which is the decomposition of the j-th layer wavelet;
p is the number of wavelet coefficients at the scale;
WTD considers that a fault signal exists in the low frequency part Ad j,k In which noise exists in the high-frequency portion Cd j,k In (a) and (b);
due to the amplitude of the noise following a gaussian distributionHigh frequency part Cd with maximum number of decomposition layers j,k To evaluate the data of the model complexity, BIC is introduced to evaluate the model complexity:
BIC＝qln(N)-2ln(L)
wherein q is the number of model parameters;
n is the number of samples;
l is the maximum likelihood function obeying gaussian distribution, namely:
Figure SMS_7
according to the above technical solution, in S2, the estimated vector and the observed vector are specifically calculated as follows:
let n interrelated variables in the plant be observed at a certain time t, and this is denoted as observation variable X t I.e.
X t ＝[x t,1 ,x t,2 …x t,n ] T
Wherein x is t,n The observation value of the state variable at the moment t;
constructing a history memory matrix D having m history moments, n associated state variables, i.e
Figure SMS_8
From m observation vectors X in a history memory matrix D obs Can obtain an estimated vector X est I.e.
X est ＝DW＝w 1 X 1 +w 2 X 2 …w m X m
Wherein W= [ W ] 1 ,w 2 ...w m ] T Is an m-dimensional weight vector representing the input observation vector X obs Similarity to the history matrix D, i.e
Figure SMS_9
In the method, in the process of the invention,
Figure SMS_10
is a nonlinear operator used for replacing product operation in a common matrix;
will D T And X is obs The Mahalanobis Distance (MD) between them as a non-linear operator in MEST, i.e
Figure SMS_11
In Sigma -1 An inverse matrix of the multidimensional random variable covariance matrix;
when the two state matrices are more similar, the smaller their MD is;
when the difference of the two state matrixes is larger, the nonlinear operation result is larger;
bringing the equation (9) into the equation (8) can obtain the final expression of the MEST model estimation vector as follows:
Figure SMS_12
by contrasting the observation vector X obs And estimate vector X est The difference value between the two values can obtain a residual error value epsilon of the fault degree of the reaction equipment, namely:
ε＝X est -X obs
the root mean square is selected to reflect the fault degree by comparing the using ranges of various fault indexes;
by taking n dimensions X est And X is obs The root mean square RMSV of the residual epsilon can obtain the fault degree index DR of the reaction equipment:
Figure SMS_13
the equipment fault degree index DR obtained by using the MEST is composed of a plurality of discrete points, a curve formed by the DR comprises a plurality of sharp points with derivatives not existing, and CSFI is introduced for smoothing.
According to the above technical solution, in S3, the expression of TSFM is:
Figure SMS_14
in the formula, DR t Is the original sequence data;
Figure SMS_15
training the adaptive smoothing factor for the ith time of the t+T time of prediction;
Figure SMS_16
is a primary smooth value;
Figure SMS_17
is a secondary smoothed value;
if T represents the predicted time period,
Figure SMS_18
the prediction value of the ith training at the time t+T is represented by the following prediction formula:
Figure SMS_19
wherein:
Figure SMS_20
by comparing the application range of various gradient descent algorithms, random gradient descent (SGD) adaptive updating smoothing factor is selected
Figure SMS_21
Then the ith training adaptive smoothing factor of the t+t prediction +.>
Figure SMS_22
The expression of (2) is:
Figure SMS_23
in the method, in the process of the invention,
Figure SMS_24
training the adaptive smoothing factor for the (i-1) th time of the t+T th time of prediction;
beta is a learning factor;
Figure SMS_25
training predicted values for the ith time of the t+t time of prediction;
DR t+T t+T actual value;
Figure SMS_26
bias of alpha for the ith training loss function predicted at t+t:
Figure SMS_27
in the method, in the process of the invention,
Figure SMS_28
the data length of the ith training time sequence predicted for the t+T time is the self-adaptive sliding time window;
drawing a sliding time window diagram, wherein data_mode_i is training Data of the ith training, data_test_i is test Data of the ith training,
Figure SMS_29
Figure SMS_30
wherein μ is an adjustment factor;
when the time series data does not fully reflect the fault information, i.e. the partial derivatives of the loss function
Figure SMS_31
Always in the same direction, then->
Figure SMS_32
Should continue to grow or decrease, < >>
Figure SMS_33
Maximum according to 1+mu times increase or 1-mu times shortening;
when the time series data can partially reflect fault information, i.e. partial derivatives of the loss function
Figure SMS_34
The non-uniformity is in the same direction, then->
Figure SMS_35
Length is dependent on->
Figure SMS_36
Is (are) direction of->
Figure SMS_37
In order of right->
Figure SMS_38
Length increase, ->
Figure SMS_39
When it is negative, it is added>
Figure SMS_40
The length is shortened;
selecting variance value VARV to represent final prediction error
Figure SMS_41
Where len (T) is the number of index data of the degree of failure of the t+T th prediction.
According to the above technical scheme, in S3, the fault online prediction process is as follows:
step1: ith time of t+t time predictionTraining, the predictive model presets the ith-1 st sliding time window firstly
Figure SMS_42
Dividing the training Data data_mode_i and the test Data data_test_i of the ith training Data into +.>
Figure SMS_43
And
Figure SMS_44
carry-in prediction of the i-th training +.>
Figure SMS_45
A value;
step2: will be
Figure SMS_46
Carrying-in calculation of the loss function of the ith training +.>
Figure SMS_47
If the maximum circulation times maxtrans are met or smaller than the minimum error minerror, training is stopped, and if the conditions are not met, the adaptive smoothing factor +_is updated according to the formula and the formula>
Figure SMS_48
And an adaptive sliding time window->
Figure SMS_49
Step1 is repeated, and the t+t predicted i+1 training is started.
Step3: obtained from Step2
Figure SMS_50
Carrying in to obtain the final ∈>
Figure SMS_51
And calculating a prediction error e according to the formula.
According to the technical scheme, in the step S4, the bearing performance degradation data is taken as a verification object, the sampling frequency is set to be 25.6kHz/min, the radial force is 12kN, the rotating speed is 2100rpm, the operation is 157.44S, and the vibration signal in the horizontal direction is selected to reflect the fault degree of the bearing to be tested.
According to the above technical scheme, in S5, the WTD effects of different hierarchical layers are compared as follows:
when the number of wavelet decomposition layers j=7, the BIC value is minimum;
when the number j of wavelet decomposition layers is less than 7, the effect of improving WTD noise reduction is also enhanced along with the increase of j;
when the number of wavelet decomposition layers j is more than 7, the effect of improving WTD noise reduction is not obvious along with the increase of j;
when j=7, the improved WTD algorithm not only can ensure that the noise reduction effect meets the requirement, but also can effectively prevent the problem of excessive model complexity caused by excessive precision;
taking noise amplitude obeying Gaussian distribution as the basis for evaluating the complexity of the model, so that the high-frequency part Cd with the maximum decomposition layer number is obtained j,k Outputting, drawing a Gaussian white noise amplitude distribution diagram;
when j is less than 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Obeying Gaussian distribution, wherein the improved threshold value in WTD does not destroy the distribution characteristic of Gaussian white noise, namely wavelet decomposition is insufficient;
when j is more than or equal to 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Not obeying Gaussian distribution, the improvement of threshold in WTD destroys the distribution characteristic of Gaussian white noise, namely the wavelet decomposition is sufficient, which illustrates the feasibility of setting BIC to evaluate the decomposition layer number and presets the high-frequency part Cd of the highest Gao Xiaobo decomposition layer number j,k To evaluate the scientificity of the data;
the wavelet decomposition layer number j=7 is set to improve WTD to perform noise reduction processing on the bearing performance degradation data.
According to the above technical solution, in S6, the wavelet decomposition coefficients obtained by improving WTD are used as the observation variables X of the improved MEST t I.e. when j=7, X t ＝[Ca t,7 ,Cd t,7 ,Cd t,6 ,Cd t,5 ,Cd t,4 ,Cd t,3 ,Cd t,2 ,Cd t,1 ]Setting the sampling frequency fs=25600 Hz, i.e. 1 second, setting the bearing performance degradation data 2 seconds beforePut to a healthy state, i.e. history time m=2, history memory matrix d= [ X ] 1 ,X 2 ]The other moments are set to the performance degradation state every 2 seconds, i.e. the observation vector X obs Carrying in bearing performance degradation data, and totally evaluating 77 fault degrees DR;
meanwhile, in order to eliminate the 'sharp point' where a plurality of derivatives do not exist in the DR curve, double CSFI is adopted to process data, the interpolation number is 10 times of the original data quantity, and 7700 fault degree points after smoothing are obtained.
According to the above technical solution, in S7, the initial value of the preset adaptive sliding time window length is 100, the initial value of the adaptive smoothing factor α is 0.05, the learning factor β is 0.5, the maximum training iteration number maxtrans is 1000, and the minimum allowable error is 10 -8 Inputting the smoothed 7700 bearing fault degree DR values into a fault online prediction model, and comparing the change trend of the self-adaptive smoothing factor alpha, the change trend of the self-adaptive sliding time window length and the change trend of the prediction error e.
According to the above technical solution, in S8, the prediction result is summarized as follows:
BIC can accurately find out the optimal decomposition layer number of the WTD algorithm;
the improved WTD algorithm has excellent noise reduction effect;
the MD improved MEST algorithm and the double CSFI algorithm can effectively convert fault signals into fault degree indexes;
the provided online prediction model can realize online prediction of equipment faults.
Compared with the prior art, the invention has the beneficial effects that:
the online fault prediction model of the small sample equipment is provided, the effectiveness and reliability of the model are verified through rolling bearing life cycle vibration data, BIC can accurately find out the optimal decomposition layer number of a WTD algorithm, a basis is provided for improving WTD model parameter setting, the improved WTD algorithm has excellent noise reduction effect, the reliability of fault data is guaranteed, the improved MD MEST algorithm and the double CSFI algorithm can effectively convert fault signals into fault degree indexes, high-quality data guarantee is provided for subsequent fault prediction, the provided online fault prediction model with the self-adaptive intercepting fault data length of a sliding time window and the self-adaptive updating of parameters can continuously mine potential fault degree information in data, online fault prediction of equipment faults is achieved, and the online fault prediction of additional equipment with high fault complexity, small sample data quantity and strong prediction timeliness is met.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a step diagram of an equipment failure online prediction model of the present invention;
FIG. 2 is a schematic diagram of a WTD of the present invention;
FIG. 3 is a schematic diagram of a sliding time window of the present invention;
FIG. 4 is a flow chart of the fault online prediction of the present invention;
FIG. 5 is a block diagram of a bearing fatigue test stand according to the present invention;
FIG. 6 is a graph of an experimental bearing amplitude signal according to the present invention;
FIG. 7 is a chart of BIC value variation according to the present invention;
FIG. 8 is a graph of the WTD effect of different number of decomposition layers according to the present invention;
FIG. 9 is a Gaussian white noise amplitude distribution diagram of the present invention;
FIG. 10 is a graph comparing the effects of various WTD of the present invention;
FIG. 11 is a graph showing the trend of DR values over the life of the bearing of the present invention;
FIG. 12 is a graph of the trend of the adaptive alpha value change according to the present invention;
FIG. 13 is a graph of the trend of the adaptive sliding time window length of the present invention;
FIG. 14 is a graph of the trend of prediction error according to the present invention;
FIG. 15 is a graph of predicted fit effects of the present invention;
fig. 16 is a step diagram of the fault test of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Examples: as shown in fig. 1 and 16, the present invention provides a technical solution, an online prediction method for faults of small sample equipment, which includes the following prediction steps:
s1, data processing:
the common noise reduction algorithms include Empirical Mode Decomposition (EMD) and WTD;
the fundamental principle of EMD is that a fault signal is decomposed into eigenmode functions (IMFs) of each order, and then the characteristics of the fault signal are extracted from the eigenmode functions, but under the background of a large amount of noise, the EMD algorithm has the problems of mode aliasing, end effect and the like;
the WTD mainly comprises a hard threshold noise reduction method and a soft threshold noise reduction method, although the number of wavelet decomposition layers of the WTD is determined empirically, a hard threshold function is discontinuous, oscillation is easy to generate after noise reduction, a soft threshold noise reduction wavelet coefficient has deviation, and the problem of large error of a reconstructed signal is easy to cause, but the WTD and an improved algorithm thereof are widely applied to fault online prediction due to small calculated amount and high noise reduction efficiency, for example, noise in a signal is effectively filtered through improving the wavelet threshold function, the signal to noise ratio of an output signal is improved, but the noise reduction effect is required to be improved and how the number of wavelet decomposition layers is determined;
therefore, by optimizing a threshold function in the WTD and introducing BIC to evaluate the influence of the number of decomposition layers on the complexity of the WTD, an improved WTD algorithm for filtering noise in fault signals on line is provided, and the principle is as follows:
Figure SMS_52
wherein λ is a threshold value;
ω j,k wavelet coefficients for fault signals;
Figure SMS_53
estimating wavelet coefficients;
j is a decomposition scale, J is more than or equal to 1 and less than or equal to J, and J is a maximum scale;
sgn () is a sign function;
the threshold function has continuity in the wavelet domain when ω j,k →λ - In the time-course of which the first and second contact surfaces,
Figure SMS_54
when omega j,k →λ + In the time-course of which the first and second contact surfaces,
Figure SMS_55
the threshold lambda should be chosen such that:
Figure SMS_56
wherein N represents a signal length;
σ j the standard deviation of the Gaussian white noise of the j layer is expressed as follows:
Figure SMS_57
in the formula, cd j,k A high frequency part which is the decomposition of the j-th layer wavelet;
p is the number of wavelet coefficients at the scale;
as shown in fig. 2, WTD considers that a fault signal exists in the low frequency part Ad j,k In which noise exists in the high-frequency portion Cd j,k In (a) and (b);
since the amplitude of the noise follows Gaussian distribution, the layer number high-frequency part Cd is decomposed maximally j,k In order to evaluate the complexity data of the model, BIC is introduced to evaluate the complexity of the model, so that the complexity of the model is effectively reduced under the condition that the noise reduction precision is met
BIC＝q ln(N)-2 ln(L)
Wherein q is the number of model parameters;
n is the number of samples;
l is the maximum likelihood function subject to Gaussian distribution, i.e
Figure SMS_58
S2, fault degree identification:
the method has the core ideas of constructing a non-parameter model of the system or the equipment, obtaining an estimated vector by carrying out optimal reconstruction estimation on an observed vector and a history memory matrix, and reflecting the fault degree of the system or the equipment by utilizing the difference between the estimated vector and the observed vector, wherein compared with a neural network, the method has the advantages of small calculated amount, definite physical meaning of the model and simple structure of the model;
let n interrelated variables in the plant be observed at a certain time t, and this is denoted as observation variable X t I.e.
X t ＝[x t,1 ,x t,2 …x t,n ] T
Wherein x is t,n The observation value of the state variable at the moment t;
constructing a history memory matrix D having m history moments, n associated state variables, i.e
Figure SMS_59
From m observation vectors X in a history memory matrix D obs Can obtain an estimated vector X est I.e.
X est ＝DW＝w 1 X 1 +w 2 X 2 …w m X m
Wherein W= [ W ] 1 ,w 2 …w m ] T Is an m-dimensional weight vector representing the input observation vector X obs Similarity to the history matrix D, i.e
Figure SMS_60
In the method, in the process of the invention,
Figure SMS_61
is a nonlinear operator used for replacing product operation in a common matrix to avoid +.>
Figure SMS_62
The irreversible phenomenon generated expands the application range;
to improve the multidimensional data processing capacity of the MEST algorithm, D is adopted T And X is obs The Mahalanobis Distance (MD) between them as a non-linear operator in MEST, i.e
Figure SMS_63
In Sigma -1 As the inverse matrix of the multidimensional random variable covariance matrix, it can be seen intuitively that the smaller the MD is when the two state matrices are more similar;
when the difference of the two state matrixes is larger, the nonlinear operation result is larger;
bringing the expression (9) into the expression (8) can obtain the final expression of the MEST model estimation vector as follows
Figure SMS_64
By contrasting the observation vector X obs And estimate vector X est The difference value between the two values can intuitively obtain the residual error value epsilon of the fault degree of the reaction equipment, namely
ε＝X est -X obs
By comparing the use ranges of various fault indexes, the root mean square is selected to reflect the fault degree, as shown in table 1:
TABLE 1 error indicator table
Figure SMS_65
Wherein VARV is a variance value;
RMSV is root mean square;
SF is a form factor;
MF is a marginal factor;
e is energy;
SE is shannon entropy;
RE is kernel entropy;
TE is the Morse entropy;
by taking n dimensions X est And X is obs RMSV of residual epsilon, the reaction equipment failure degree index DR can be obtained:
Figure SMS_66
because the equipment fault degree index DR obtained by using the MEST is formed by a plurality of discrete points, the curve formed by the DR inevitably comprises a plurality of sharp points with no derivative, the difficulty of fault prediction is greatly increased, the CSFI can directly construct a relation by using the smoothness and the connection condition of the joints of each node, the undetermined coefficient is determined, an interpolation polynomial is constructed, and the operation of smoothing the curve with the sharp points is completed.
S3, online fault prediction:
the TSFM is a non-statistical analysis method, can eliminate accidental variation of data, improves importance degree of recent data in prediction, accords with objective rules of the data in fault prediction, is particularly suitable for short-term or medium-long term fault online prediction due to small data demand, simple calculation process and convenient model construction, but severely limits effect of fault prediction due to lack of discrimination capability of data turning points and excessive subjectivity of selection of smoothing factors, so that gradient descent online updating of the smoothing factors is introduced, adaptive sliding time window dynamic interception of time sequence data is introduced, fitting capability of the TSFM is improved, and TSFM expression is as follows:
Figure SMS_67
in the formula, DR t Is the original sequence data;
Figure SMS_68
training the adaptive smoothing factor for the ith time of the t+T time of prediction;
Figure SMS_69
is a primary smooth value;
Figure SMS_70
is a secondary smoothed value;
if T represents the predicted time period,
Figure SMS_71
the prediction value of the ith training at the time t+T is represented by the following prediction formula:
Figure SMS_72
wherein:
Figure SMS_73
by comparing the application range of various gradient descent algorithms, random gradient descent (SGD) adaptive updating smoothing factor is selected
Figure SMS_74
As shown in table 2:
table 2 gradient descent algorithm comparison table
Figure SMS_75
Wherein, BGD is Batch Gradient Descent (BGD), momentum-SGD is random gradient descent with Momentum (SGDM);
then the ith training adaptive smoothing factor of the t+t prediction
Figure SMS_76
The expression of (2) is:
Figure SMS_77
in the method, in the process of the invention,
Figure SMS_78
training the adaptive smoothing factor for the (i-1) th time of the t+T th time of prediction;
beta is a learning factor;
Figure SMS_79
training predicted values for the ith time of the t+t time of prediction;
DR t+T t+T actual value;
Figure SMS_80
bias of alpha for the ith training loss function predicted at t+t:
Figure SMS_81
as shown in fig. 3, in the formula,
Figure SMS_82
the data length of the ith training time sequence predicted for the t+T time is the self-adaptive sliding time window;
in fig. 6, data_mode_i refers to training Data of the ith training, data_test_i refers to test Data of the ith training,
Figure SMS_83
Figure SMS_84
wherein μ is an adjustment factor;
is readily available by the sum (18), when the time series data does not fully reflect the fault information, i.e. the bias of the loss functionGuide rail
Figure SMS_85
Always in the same direction, then->
Figure SMS_86
Should continue to grow or decrease to meet the need for extracting fault information,/or->
Figure SMS_87
Maximum according to 1+mu times increase or 1-mu times shortening; />
When the time series data can partially reflect fault information, i.e. partial derivatives of the loss function
Figure SMS_88
The non-uniformity is in the same direction, then->
Figure SMS_89
Length is dependent on->
Figure SMS_90
Is (are) direction of->
Figure SMS_91
In order of right->
Figure SMS_92
Length increase, ->
Figure SMS_93
When it is negative, it is added>
Figure SMS_94
The length is shortened.
The selected VARV represents the final prediction error
Figure SMS_95
Where len (T) is the number of index data of the degree of failure of the t+T th prediction.
As shown in fig. 4, step1: ith training of t+T prediction, when the predictive model slides the ith-1 th presetWindow
Figure SMS_96
Dividing the training Data data_mode_i and the test Data data_test_i of the ith training Data into +.>
Figure SMS_97
And->
Figure SMS_98
Carry-in prediction of the i-th training +.>
Figure SMS_99
A value;
step2: will be
Figure SMS_100
Carrying-in calculation of the loss function of the ith training +.>
Figure SMS_101
If the maximum circulation times maxtrans are met or smaller than the minimum error minerror, training is stopped, and if the conditions are not met, the adaptive smoothing factor +_is updated according to the formula and the formula>
Figure SMS_102
And an adaptive sliding time window->
Figure SMS_103
Repeating Step1, and starting the i+1 training of the t+T prediction;
step3: obtained from Step2
Figure SMS_104
Carrying in to obtain the final ∈>
Figure SMS_105
And calculating a prediction error e according to the formula.
S4, experimental analysis:
in order to verify the effectiveness and feasibility of the equipment failure prediction model under the condition of a small sample in one step, the rolling bearing performance degradation data is utilized for analysis and verification;
as shown in fig. 5, in order to obtain bearing fault data with the model LDK UER204, two PCB 352C33 accelerometers are placed on the housing of the bearing to be tested, with an included angle of 90 ° therebetween, i.e. one is placed on the horizontal axis, the other is placed on the vertical axis, the sampling frequency is set to 25.6kHz/min, the radial force is 12kN, the rotation speed is 2100rpm, and the operation is 157.44s, because the load is applied in the horizontal direction, the accelerometer in this direction can more accurately reflect the degradation information of the bearing to be tested, so that the vibration signal in the horizontal direction is selected to reflect the fault degree of the bearing to be tested;
as shown in fig. 6, in the early stage of the bearing performance degradation experiment, the amplitude change is not large, and the bearing is in the normal operation stage, namely before the point a, but contains a large amount of noise signals at the moment;
in the later stage of performance degradation experiment, the bearing amplitude increases along with the increase of working time, the bearing is in the performance degradation stage, namely, between the point a and the point c, and the detected signal contains a large amount of bearing performance degradation signals and noise signals;
at the end of the performance degradation experiment, the amplitude of the bearing is suddenly increased, and the bearing is in a fault stage, namely after the point c;
therefore, whether the influence of noise signals can be removed or not, the bearing performance degradation time a and the failure time c are accurately judged, the trend of the bearing degradation performance is truly reflected, and ensuring higher prediction precision and shorter prediction time is the key point for verifying the proposed model.
S5, data processing analysis:
as shown in fig. 7 and 8, the complexity of the improved WTD algorithm with different decomposition levels is evaluated by preset BIC;
when the number of wavelet decomposition layers j=7, the BIC value is minimum;
when the number j of wavelet decomposition layers is less than 7, the effect of improving WTD noise reduction is also enhanced along with the increase of j;
when the number of wavelet decomposition layers j is more than 7, the effect of improving WTD noise reduction is not obvious along with the increase of j;
therefore, when j=7, the improved WTD algorithm not only can ensure that the noise reduction effect meets the requirement, but also can effectively prevent the problem of excessive model complexity caused by excessive precision;
as shown in FIG. 9, the noise amplitude obeys Gaussian distribution and is used as the basis for evaluating the complexity of the model, so that the maximum decomposition layer number high-frequency part Cd j,k Outputting;
when j is less than 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Obeying Gaussian distribution, wherein the improved threshold value in WTD does not destroy the distribution characteristic of Gaussian white noise, namely wavelet decomposition is insufficient;
when j is more than or equal to 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Not obeying the gaussian distribution, at this time, improving the threshold in WTD destroys the distribution characteristics of gaussian white noise, i.e. wavelet decomposition is sufficient;
thus, the feasibility of setting the BIC evaluation decomposition level and the high frequency part Cd of presetting the maximum Gao Xiaobo decomposition level are illustrated j,k To evaluate the scientificity of the data;
as shown in fig. 10, the wavelet decomposition level j=7 is set to propose an improved WTD and an improved WTD (referred to simply as an improved WTD) to perform noise reduction processing on the bearing performance degradation data;
in fig. 10, (1), (4), (2), (5), (3), (6) are respectively an original time domain diagram of bearing performance degradation, an original spectrogram, a time domain diagram after WTD noise reduction, a spectrogram after WTD noise reduction, a time domain diagram after WTD noise reduction, and a frequency domain diagram after WTD noise reduction;
the noise reduction effect of the improved WTD algorithm is superior to that of the quoted improved WTD algorithm, the influence of noise in the normal operation stage can be greatly restrained, the bearing fault degree information in the performance degradation stage and the fault stage can be reserved, and the starting time of the performance degradation stage and the fault generation stage can be accurately judged.
S6, fault degree identification analysis:
as shown in FIG. 11, each wavelet decomposition coefficient obtained by modifying WTD is used as an observation variable X of modified MEST t I.e. when j=7, X t ＝[Ca t,7 ,Cd t,7 ,Cd t,6 ,Cd t,5 ,Cd t,4 ,Cd t,3 ,Cd t,2 ,Cd t,1 ]Setting a sampling frequencyfs=25600 Hz, i.e. 1 second, the first 2 seconds of the bearing performance degradation data is set to a healthy state, i.e. the history time m=2, the history memory matrix d= [ X 1 ,X 2 ]The other moments are set to the performance degradation state every 2 seconds, i.e. the observation vector X obs Carrying in bearing performance degradation data, and totally evaluating 77 fault degrees DR;
meanwhile, in order to eliminate the 'sharp point' where a plurality of derivatives do not exist in the DR curve, double CSFI is adopted to process data, the interpolation number is 10 times of the original data quantity, and 7700 fault degree points after smoothing are obtained;
fig. 11 (1), (2), and (3) are graphs of degradation of bearing performance, a failure degree DR, and a post-smoothing failure degree DR, respectively;
as can be seen from fig. 11 (1) and (2), when the performance of the bearing is degraded at the point a, the fault degree DR is increased at the same time, the improved MEST model can accurately determine the starting time of the performance degradation stage, and can increase the value of the fault degree DR immediately before the fault occurrence point c and at the fault occurrence point b, and give an early warning signal;
as can be seen from fig. 11 (2) and (3), the adopted dual CSFI algorithm can eliminate the sharp points in the curve, where the derivative does not exist, without changing the trend of the original fault degree DR curve, so as to enhance the predictability of the data.
S7, online fault prediction analysis:
the experimental hardware CPU is i7-10875H, the running memory is 32GB, the display card is RTX2060, the preset self-adaptive sliding time window length initial value is 100, the self-adaptive smoothing factor alpha initial value is 0.05, the learning factor beta is 0.5, the maximum training iteration number maxtrans is 1000 times, and the minimum allowable error is 10 -8 Inputting the smoothed 7700 bearing fault degree DR values into a fault online prediction model, and then adapting to the change trend of the smoothing factor alpha, the change trend of the length of the self-adapting sliding time window length and the change trend of the prediction error e.
As shown in fig. 12, in the normal operation stage, that is, before point a, the variation amplitude of the DR value of the bearing failure degree is small, and the adaptive smoothing factor α in this stage is quickly stabilized to operate around 0.5 except for the short adjustment in the early stage;
after the performance degradation stage, namely point a, the self-adaptive smoothing factor alpha changes obviously along with the increase of the fault degree DR, and the self-adaptive smoothing factor alpha is adjusted more severely at the moment b when the bearing is detected to be in fault, which shows that the proposed self-adaptive smoothing factor alpha can change along with the fault degree DR in real time, accurately judges the point a of the performance degradation moment and the moment b of the complete fault, has strong optimizing capability and meets the requirement of online prediction of the fault.
As shown in fig. 13, in the normal operation stage, that is, before point a, the variation amplitude of the bearing failure degree DR value is small, and the adaptive sliding time window length in this stage is stabilized at about an initial value of 100;
after the performance degradation stage, namely the point a, the performance degradation data in the normal operation stage cannot represent the failure degree of the bearing at the moment and even generate a negative effect along with the increase of the failure degree DR, so that the length of the self-adaptive sliding time window length is rapidly shortened, and small-range fluctuation begins to be generated at the point b when the bearing is detected to be failed, which indicates that the proposed self-adaptive sliding time window length can be changed along with the failure degree DR in real time, the sliding time window length is kept stable in the stable stage, the sliding time window length is rapidly adjusted in the severe change stage, the point a of the performance degradation moment and the point b of the failure moment can be accurately judged, and the requirement of online failure prediction is met;
as shown in fig. 14 and 15, the variation trend of the prediction error e is similar to the variation trend of the bearing fault degree DR, that is, the error gradually increases along with the complexity of the variation trend of the fault degree DR, the increase of the error at the point b at the moment of impending fault is obvious, the variation trend of the adaptive smoothing factor α and the adaptive sliding time window length is met, the prediction value almost coincides with the actual value, the final prediction error e=0.068%, the fitting precision is high, and the requirement of online fault prediction is met.
Under the experimental condition, the single average prediction time is about 0.0277s, the single average prediction time is about 1.385% of the interval time of the two fault degrees DR, namely, the model can give the prediction result of the equipment fault degree in a shorter time, the prediction time is shorter, and the requirement of fault prediction is met.
S8, summarizing prediction results:
aiming at the equipment fault prediction problems of high fault complexity, small sample data size and strong prediction timeliness, a small sample equipment fault online prediction model is provided, the effectiveness and reliability of the model are verified through rolling bearing life cycle vibration data, and the prediction results are summarized as follows:
(1) The BIC can accurately find out the optimal decomposition layer number of the WTD algorithm, and provides a basis for improving the parameter setting of the WTD model;
(2) The improved WTD algorithm has excellent noise reduction effect, and the reliability of fault data is ensured;
(3) The MD improved MEST algorithm and the double CSFI algorithm can effectively convert fault signals into fault degree indexes, and high-quality data guarantee is provided for subsequent fault prediction;
(4) The provided fault online prediction model with the sliding time window self-adaptive intercepting fault data length and parameter self-adaptive updating can continuously mine potential fault degree information in the data, and realize online prediction of equipment faults.
Finally, it should be noted that: the foregoing is merely a preferred example of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. 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 (10)

1. An online prediction method for faults of small sample equipment is characterized by comprising the following steps of: the method comprises the following prediction steps:
s1, data processing: through threshold function optimization in a WTD noise reduction algorithm and introduction of BIC, the influence of the number of decomposition layers on the complexity of the WTD is evaluated, and an improved WTD algorithm is provided for filtering noise in fault signals on line;
s2, fault degree identification: constructing a non-parameter model of a system or equipment through MEST, obtaining an estimated vector through optimal reconstruction estimation of an observed vector and a history memory matrix, reflecting the fault degree by utilizing the difference between the estimated vector and the observed vector, and introducing CSFI to carry out smoothing treatment;
s3, online fault prediction: by a TSFM non-statistical analysis method, accidental variation of data is eliminated, gradient descent on-line updating smoothing factors are introduced, self-adaptive sliding time window is introduced to dynamically intercept time sequence data, and fitting capacity of the TSFM is improved;
s4, experimental analysis: verifying the effectiveness and feasibility of the equipment fault prediction model under the condition of a small sample;
s5, data processing analysis: the complexity of the improved WTD algorithm with different decomposition layers is evaluated through a preset BIC;
s6, fault degree identification analysis: the improved WTD is used for obtaining each wavelet decomposition coefficient as an observation variable of an improved MEST, sampling frequency, health state and degradation state are set for carrying out recognition analysis on fault degree, double CSFI is adopted for processing data, and a 'sharp point' of which the derivative does not exist in a curve is eliminated, so that a fault degree point after smoothing is obtained;
s7, fault online test analysis: the method comprises the steps of presetting an adaptive sliding time window, an adaptive smoothing factor, a learning factor, the maximum training iteration number and the minimum allowable error, and inputting a smoothed bearing fault degree value into a fault online prediction model to obtain an adaptive smoothing factor change trend, an adaptive sliding time window length change trend and a prediction error change trend.
S8, summarizing prediction results: summarizing the effect of online prediction model fault prediction.
2. The online fault prediction method for small sample equipment according to claim 1, wherein in S1, the WTD algorithm is modified to filter noise in a fault signal online, and the principle is as follows:
Figure FDA0004163289550000021
wherein λ is a threshold value;
ω j,k wavelet coefficients for fault signals;
Figure FDA0004163289550000022
estimating wavelet coefficients;
j is a decomposition scale, J is more than or equal to 1 and less than or equal to J, and J is a maximum scale;
sgn () is a sign function;
the threshold function has continuity in the wavelet domain when ω j,k →λ - In the time-course of which the first and second contact surfaces,
Figure FDA0004163289550000023
when omega j,k →λ + In the time-course of which the first and second contact surfaces,
Figure FDA0004163289550000024
the threshold lambda should be chosen such that:
Figure FDA0004163289550000025
wherein N represents a signal length;
σ j the standard deviation of the Gaussian white noise of the j layer is expressed as follows:
Figure FDA0004163289550000026
in the formula, cd j,k A high frequency part which is the decomposition of the j-th layer wavelet;
p is the number of wavelet coefficients at the scale;
WTD considers that a fault signal exists in the low frequency part Ad j,k In which noise exists in the high-frequency portion Cd j,k In (a) and (b);
since the amplitude of the noise follows a gaussian distribution,high frequency part Cd with maximum decomposition layer number j,k To evaluate the data of the model complexity, BIC is introduced to evaluate the model complexity:
BIC＝qln(N)-2ln(L)
wherein q is the number of model parameters;
n is the number of samples;
l is the maximum likelihood function obeying gaussian distribution, namely:
Figure FDA0004163289550000031
3. the online prediction method of small sample equipment faults according to claim 1, wherein in the step S2, an estimated vector and an observed vector are specifically calculated as follows:
let n interrelated variables in the plant be observed at a certain time t, and this is denoted as observation variable X t I.e.
X t ＝[x t,1 ,x t,2 …x t,n ] T
Wherein x is t,n The observation value of the state variable at the moment t;
constructing a history memory matrix D having m history moments, n associated state variables, i.e
Figure FDA0004163289550000032
From m observation vectors X in a history memory matrix D obs Can obtain an estimated vector X est I.e.
X est ＝DW＝w 1 X 1 +w 2 X 2 …w m X m
Wherein W= [ W ] 1 ,w 2 …w m ] T Is an m-dimensional weight vector representing the input observation vector X obs Similarity to the history matrix D, i.e
Figure FDA0004163289550000041
In the method, in the process of the invention,
Figure FDA0004163289550000042
is a nonlinear operator used for replacing product operation in a common matrix;
will D T And X is obs The Mahalanobis Distance (MD) between them as a non-linear operator in MEST, i.e
Figure FDA0004163289550000043
In Sigma -1 An inverse matrix of the multidimensional random variable covariance matrix;
when the two state matrices are more similar, the smaller their MD is;
when the difference of the two state matrixes is larger, the nonlinear operation result is larger;
bringing the equation (9) into the equation (8) can obtain the final expression of the MEST model estimation vector as follows:
Figure FDA0004163289550000044
by contrasting the observation vector X obs And estimate vector X est The difference value between the two values can obtain a residual error value epsilon of the fault degree of the reaction equipment, namely:
ε＝X est -X obs
the root mean square is selected to reflect the fault degree by comparing the using ranges of various fault indexes;
by taking n dimensions X est And X is obs The root mean square RMSV of the residual epsilon can obtain the fault degree index DR of the reaction equipment:
Figure FDA0004163289550000045
the equipment fault degree index DR obtained by using the MEST is composed of a plurality of discrete points, a curve formed by the DR comprises a plurality of sharp points with derivatives not existing, and CSFI is introduced for smoothing.
4. The online small sample equipment fault prediction method according to claim 1, wherein in S3, the TSFM expression is:
Figure FDA0004163289550000051
in the formula, DR t Is the original sequence data;
Figure FDA0004163289550000052
training the adaptive smoothing factor for the ith time of the t+T time of prediction;
Figure FDA0004163289550000053
is a primary smooth value;
Figure FDA0004163289550000054
is a secondary smoothed value;
if T represents the predicted time period,
Figure FDA0004163289550000055
the prediction value of the ith training at the time t+T is represented by the following prediction formula:
Figure FDA0004163289550000056
wherein:
Figure FDA0004163289550000057
by comparing the application range of various gradient descent algorithms, random gradient descent (SGD) adaptive updating smoothing factor is selected
Figure FDA0004163289550000058
Then the ith training adaptive smoothing factor of the t+t prediction +.>
Figure FDA0004163289550000059
The expression of (2) is:
Figure FDA00041632895500000510
in the method, in the process of the invention,
Figure FDA00041632895500000511
training the adaptive smoothing factor for the (i-1) th time of the t+T th time of prediction;
beta is a learning factor;
Figure FDA00041632895500000512
training predicted values for the ith time of the t+t time of prediction;
DR t+T t+T actual value;
Figure FDA0004163289550000061
bias of alpha for the ith training loss function predicted at t+t:
Figure FDA0004163289550000062
in the method, in the process of the invention,
Figure FDA0004163289550000063
the data length of the ith training time sequence predicted for the t+T time is the self-adaptive sliding time window;
drawing a sliding time window diagram, wherein data_mode_i is training Data of the ith training, data_test_i is test Data of the ith training,
Figure FDA0004163289550000064
Figure FDA0004163289550000065
wherein μ is an adjustment factor;
when the time series data does not fully reflect the fault information, i.e. the partial derivatives of the loss function
Figure FDA0004163289550000066
Always in the same direction, then
Figure FDA0004163289550000067
Should continue to grow or decrease, < >>
Figure FDA0004163289550000068
Maximum according to 1+mu times increase or 1-mu times shortening;
when the time series data can partially reflect fault information, i.e. partial derivatives of the loss function
Figure FDA0004163289550000069
Non-uniform in the same direction, then
Figure FDA00041632895500000610
Length is dependent on->
Figure FDA00041632895500000611
Is (are) direction of->
Figure FDA00041632895500000612
In order of right->
Figure FDA00041632895500000613
Length increase, ->
Figure FDA00041632895500000614
When the value of the voltage is negative, the voltage is higher,
Figure FDA00041632895500000615
the length is shortened;
selecting variance value VARV to represent final prediction error
Figure FDA00041632895500000616
Where len (T) is the number of index data of the degree of failure of the t+T th prediction.
5. The online fault prediction method for small sample equipment according to claim 4, wherein in S3, the flow of online fault prediction is as follows:
step1: ith training of t+T prediction, the predictive model first presets the ith-1 th sliding time window
Figure FDA0004163289550000071
Dividing the training Data data_mode_i and the test Data data_test_i of the ith training Data into +.>
Figure FDA0004163289550000072
And->
Figure FDA0004163289550000073
Carry-in prediction of the i-th training +.>
Figure FDA0004163289550000074
A value;
step2: will be
Figure FDA0004163289550000075
Carrying-in calculation of the loss function of the ith training +.>
Figure FDA0004163289550000076
If the maximum circulation times maxtrans are met or smaller than the minimum error minerror, training is stopped, and if the conditions are not met, the adaptive smoothing factor +_is updated according to the formula and the formula>
Figure FDA0004163289550000077
And an adaptive sliding time window->
Figure FDA0004163289550000078
Step1 is repeated, and the t+t predicted i+1 training is started.
Step3: obtained from Step2
Figure FDA0004163289550000079
Carrying in to obtain the final ∈>
Figure FDA00041632895500000710
And calculating a prediction error e according to the formula.
6. The online prediction method of small sample equipment faults according to claim 1, wherein in the step S4, bearing performance degradation data is taken as a verification object, the sampling frequency is set to be 25.6kHz/min, the radial force is set to be 12kN, the rotating speed is set to be 2100rpm, the operation is carried out for 157.44S, and the vibration signal in the horizontal direction is selected to reflect the fault degree of the detected bearing.
7. The online prediction method of small sample equipment faults according to claim 1, wherein in the step S5, WTD effects of different hierarchical layers are compared as follows:
when the number of wavelet decomposition layers j=7, the BIC value is minimum;
when the number j of wavelet decomposition layers is less than 7, the effect of improving WTD noise reduction is also enhanced along with the increase of j;
when the number of wavelet decomposition layers j is more than 7, the effect of improving WTD noise reduction is not obvious along with the increase of j;
when j=7, the improved WTD algorithm not only can ensure that the noise reduction effect meets the requirement, but also can effectively prevent the problem of excessive model complexity caused by excessive precision;
taking noise amplitude obeying Gaussian distribution as the basis for evaluating the complexity of the model, so that the high-frequency part Cd with the maximum decomposition layer number is obtained j,k Outputting, drawing a Gaussian white noise amplitude distribution diagram;
when j is less than 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Obeying Gaussian distribution, wherein the improved threshold value in WTD does not destroy the distribution characteristic of Gaussian white noise, namely wavelet decomposition is insufficient;
when j is more than or equal to 7, improving the high-frequency part Cd of the maximum decomposition layer number of WTD j,k Not obeying Gaussian distribution, the improvement of threshold in WTD destroys the distribution characteristic of Gaussian white noise, namely the wavelet decomposition is sufficient, which illustrates the feasibility of setting BIC to evaluate the decomposition layer number and presets the high-frequency part Cd of the highest Gao Xiaobo decomposition layer number j,k To evaluate the scientificity of the data;
the wavelet decomposition layer number j=7 is set to improve WTD to perform noise reduction processing on the bearing performance degradation data.
8. The online small sample equipment fault prediction method according to claim 1, wherein in S6, each wavelet decomposition coefficient obtained by improving WTD is used as an observation variable X of improving MEST t I.e. when j=7, X t ＝[Ca t,7 ,Cd t,7 ,Cd t,6 ,Cd t,5 ,Cd t,4 ,Cd t,3 ,Cd t,2 ,Cd t,1 ]Setting the sampling frequency fs=25600 Hz, i.e. 1 second, setting the bearing performance degradation data to a healthy state for the first 2 seconds, i.e. the history time m=2, the history memory matrix d= [ X 1 ,X 2 ]Other times set to every 2 secondsState of performance degradation, i.e. observation vector X obs Carrying in bearing performance degradation data, and totally evaluating 77 fault degrees DR;
meanwhile, in order to eliminate the 'sharp point' where a plurality of derivatives do not exist in the DR curve, double CSFI is adopted to process data, the interpolation number is 10 times of the original data quantity, and 7700 fault degree points after smoothing are obtained.
9. The online prediction method of small sample equipment faults according to claim 1, wherein in the step S7, an initial value of a preset adaptive sliding time window length is 100, an initial value of an adaptive smoothing factor alpha is 0.05, a learning factor beta is 0.5, the maximum training iteration number maxtrans is 1000, and a minimum allowable error is 10 -8 Inputting the smoothed 7700 bearing fault degree DR values into a fault online prediction model, and comparing the change trend of the self-adaptive smoothing factor alpha, the change trend of the self-adaptive sliding time window length and the change trend of the prediction error e.
10. The online small sample equipment fault prediction method according to claim 1, wherein in S8, the prediction results are summarized as follows:
BIC can accurately find out the optimal decomposition layer number of the WTD algorithm;
the improved WTD algorithm has excellent noise reduction effect;
the MD improved MEST algorithm and the double CSFI algorithm can effectively convert fault signals into fault degree indexes;
the provided online prediction model can realize online prediction of equipment faults.
CN202310356001.9A 2023-04-06 2023-04-06 Small sample equipment fault online prediction method Pending CN116383608A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116592951A (en) * 2023-07-17 2023-08-15 陕西西特电缆有限公司 Intelligent cable data acquisition method and system
CN117330816A (en) * 2023-12-01 2024-01-02 南京中旭电子科技有限公司 Monitoring data optimization method for Hall current sensor

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116592951A (en) * 2023-07-17 2023-08-15 陕西西特电缆有限公司 Intelligent cable data acquisition method and system
CN116592951B (en) * 2023-07-17 2023-09-08 陕西西特电缆有限公司 Intelligent cable data acquisition method and system
CN117330816A (en) * 2023-12-01 2024-01-02 南京中旭电子科技有限公司 Monitoring data optimization method for Hall current sensor
CN117330816B (en) * 2023-12-01 2024-01-26 南京中旭电子科技有限公司 Monitoring data optimization method for Hall current sensor

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