CN111581597A - Wind turbine generator gearbox bearing temperature state monitoring method based on self-organizing kernel regression model - Google Patents

Wind turbine generator gearbox bearing temperature state monitoring method based on self-organizing kernel regression model Download PDF

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CN111581597A
CN111581597A CN202010184781.XA CN202010184781A CN111581597A CN 111581597 A CN111581597 A CN 111581597A CN 202010184781 A CN202010184781 A CN 202010184781A CN 111581597 A CN111581597 A CN 111581597A
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马东
曹力
王明宇
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Huadian Electric Power Research Institute Co Ltd
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Abstract

The invention discloses a wind turbine generator gearbox bearing temperature state monitoring method based on a self-organized kernel regression model, which introduces a self-organized kernel regression modeling method and a sequential probability ratio residual error analysis method into wind turbine generator state monitoring. Selecting variables by adopting a partial least square method, establishing a relation model between the gearbox bearing temperature and the influence variables by adopting a self-organizing kernel regression method, and predicting the gearbox bearing temperature in a monitoring stage by using the model. In order to reduce the false alarm rate and the false alarm rate of the gearbox bearing temperature early warning, the residual error between the predicted value and the actual value of the gearbox bearing temperature calculated by a sequential probability ratio method analysis model is adopted, and when the sequential probability ratio is larger than a set threshold value, the abnormal alarm of the gearbox bearing temperature is sent out. The invention is used for analyzing the temperature data of the bearing of the gear box, accurately realizes the purposes of temperature monitoring and fault early warning of the bearing of the gear box of the wind turbine generator, and verifies the practicability and the universality of the invention.

Description

Wind turbine generator gearbox bearing temperature state monitoring method based on self-organizing kernel regression model
Technical Field
The invention belongs to the field of wind turbine generator gearbox state monitoring, and particularly relates to a wind turbine generator gearbox bearing temperature state monitoring method based on a self-organized kernel regression model.
Background
In recent years, the air environment of partial regions in China is gradually worsened, severe haze weather is frequent, the adjustment of the traditional energy structure mainly based on fossil fuels such as coal and petroleum is urgently needed, and the development of renewable energy sources scientifically and efficiently is urgent. Wind power generation is an important component of renewable energy, the development of the wind power generation is rapid in China, and the accumulated installed capacity and the newly-increased installed capacity are in the top of the world.
The wind turbine generator has severe operating conditions, such as large external temperature difference change, random wind speed change and the like. The fault rate of the wind turbine generator is high due to uncertain external factors, so that the later operation and maintenance cost of the wind power plant is high.
The gearbox is one of the important parts of the wind turbine. The wind turbine generator gearbox has the characteristics of speed change and load change during operation. With the change of the wind speed, the rotating speed and the load of each stage of the gearbox change at any time, which brings great challenges for the application of the traditional state monitoring method to the gearbox of the wind turbine generator.
The traditional gearbox bearing fault diagnosis technology, such as vibration analysis, oil analysis and the like, achieves certain results. The wind speed changes randomly, so that the rotating speed and the load of each stage of bearing of the gearbox of the wind turbine generator set change time instead of the stable working condition that the rotating speed is not changed. The current vibration analysis technology is low in fault diagnosis accuracy and high in false alarm and false alarm rate under the time-varying complex working condition of variable rotating speed and variable load of a gearbox bearing. The gear box oil analysis technology is used for collecting a gear box oil sample during the shutdown of the wind turbine generator, analyzing the water content, the number of metal particles and the diameter of lubricating oil in a laboratory to diagnose the state of a gear box bearing, but the oil analysis can only be used for off-line diagnosis, and the on-line real-time monitoring and diagnosis of the gear box bearing cannot be realized. And a multilayer forward neural network is adopted to model and monitor the temperature of the bearing of the gearbox of the wind turbine generator, but due to the complex structure, multiple model parameters and long training time consumption of the forward neural network, the abnormal change of the temperature of the bearing of the gearbox is difficult to be accurately pre-warned in time.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a wind turbine generator gearbox bearing temperature state monitoring method based on a self-organized kernel regression model. The method introduces a self-organizing kernel regression (AAKR) modeling method and a sequential probability ratio residual error analysis (SPRT) method into the state monitoring of the wind turbine generator. Selecting variables by a Partial Least Squares (PLS) method, establishing a relation model between the gearbox bearing temperature and the influence variables by a self-organizing kernel regression method, and predicting the gearbox bearing temperature in a monitoring stage by using the model. In order to reduce the false alarm rate and the false alarm rate of the gearbox bearing temperature early warning, the residual error between the predicted value and the actual value of the gearbox bearing temperature calculated by a sequential probability ratio method analysis model is adopted, and when the sequential probability ratio is larger than a set threshold value, the abnormal alarm of the gearbox bearing temperature is sent out. The method is used for analyzing the temperature data of the gear box bearing, and accurately achieves the purposes of temperature monitoring and fault early warning of the gear box bearing of the wind turbine generator.
The technical scheme adopted by the invention for solving the problems is as follows: a wind turbine generator gearbox bearing temperature state monitoring method based on a self-organizing kernel regression model is characterized by comprising the following steps: the method comprises the following steps:
step 1, selecting a temperature modeling variable of a bearing of a gearbox by adopting a Partial Least Squares (PLS) method;
the method comprises the following steps that the temperature of a bearing of a gearbox of the wind turbine generator is influenced by a plurality of parameter variables of the wind turbine generator, in order to determine influence factors of the temperature of the bearing of the gearbox, input modeling variables of a temperature model of the bearing of the gearbox are determined, and the modeling variables are selected from hundreds of operating parameters of the wind turbine generator by a partial least square method; the process is as follows:
an input matrix X and an output gearbox bearing temperature matrix Y are formed by wind turbine generator operation data, and the following formula is as follows:
Figure BDA0002413775810000021
wherein:
n is the number of samples;
m is the number of the original wind turbine generator parameter variables;
normalizing the input matrix X and the output gearbox bearing temperature matrix Y to obtain the following formula:
Figure BDA0002413775810000022
wherein:
X0-input matrix X ∈ RN×MThe normalization matrix of (a);
Y0-output matrix Y ∈ RN×1The normalization matrix of (a);
calculating X0And Y0The first principal axis of (c) is as follows:
Figure BDA0002413775810000023
wherein:
w1——X0a first principal axis of the matrix;
c1——Y0a first principal axis of the matrix;
due to the normalized matrix Y0Is a one-dimensional variable, therefore c11 is ═ 1; solving this optimization problem to obtain w1Obtaining a first main component with the following formula:
Figure BDA0002413775810000031
wherein:
t1——X0a first principal component of the matrix;
u1——Y0a first principal component of the matrix;
the regression coefficient vector is calculated using the following formula:
Figure BDA0002413775810000032
wherein:
p1-principal component t1A vector of regression coefficients of;
r1-principal component u1A vector of regression coefficients of;
finding a regression coefficient vector p1，r1And then, calculating a residual matrix after the first principal component is extracted:
Figure BDA0002413775810000033
wherein:
X1——X0the matrix is extracted with a first principal component t1The residual error matrix after;
Y1——Y0the matrix is extracted with a first principal component u1The residual error matrix after;
by residual matrix X1And Y1Respectively substituted for X0And Y0Calculating the second principal component t2Sequentially determining the number of the final main components according to the following cross validity principle;
cross validation index
Figure BDA0002413775810000034
Figure BDA0002413775810000035
Wherein:
pi-gearbox bearing temperature raw sample points, where i ═ 1,2, …, N;
Figure BDA0002413775810000041
using all sample points and taking t1,t2,…,thFitting values of the ith sample after h component regression modeling;
Figure BDA0002413775810000042
-deleting sample points i and taking h sets during modelingThe fitting value of the ith sample after the fractional regression modeling;
when in use
Figure BDA0002413775810000043
Then, a new principal component t is introducedhThe prediction capability of the model can be obviously improved;
adopting a variable projection Importance index VIP (variable projection in projection) to characterize the interpretability and Importance degree of the independent variable to the dependent variable; the greater the VIP value of the independent variable, the more important the independent variable is to predict the dependent variable, and the formula is as follows:
Figure BDA0002413775810000044
wherein:
m is the number of the original wind turbine generator parameter variables;
Rd(Y；th) -outputs Y and thA correlation coefficient between;
m is the number of main components;
whi——X0principal axis vector w of the matrixhThe ith element of (1);
wh——X0a principal axis vector of the matrix;
calculating variable projection importance indexes of all parameters of the wind turbine generator set aiming at the temperature of a bearing of a gearbox, sorting all parameters from large to small according to the variable projection importance indexes, and selecting the first L sorted parameters to ensure that:
Figure BDA0002413775810000045
wherein:
l is the number of the temperature modeling variables of the bearing of the gearbox;
namely, the first L parameters after VIP index sequencing are selected as modeling variables of the bearing temperature of the gearbox;
step 2, modeling the temperature of the bearing of the gearbox by adopting a self-organizing kernel regression method;
step 2.1, constructing a training sample and a verification sample of the gearbox bearing temperature self-organizing kernel regression model;
in step 1, the number of modeling variables selected by the partial least square method is L, the value of the L modeling variables at the time t is [ x (t,1) x (t,2) … x (t, L) ], and the bearing temperature of the gearbox at the time t is recorded as x (t, L + 1); then at time t, the L modeling variables and the gearbox bearing temperature output constitute an observation vector sample, which is recorded as:
X(t)＝[x(t,1),x(t,2),…,x(t,L),x(t,L+1)]
wherein:
[ x (t,1) x (t,2) … x (t, L) ] -the values of the L modeling variables at time t;
x (t, L +1) -the gearbox bearing temperature value at time t;
selecting the L modeling variables and the temperature of the bearing of the gearbox from each historical data of the normal temperature period of the bearing of the gearbox of the wind turbine generator to form an observation vector sample; all observation vector samples formed by historical data of the bearing temperature of the gearbox in a certain normal period are according to the following ratio of 3: 1, dividing the ratio into a training sample set and a verification sample set;
step 2.2, building a gearbox bearing temperature self-organizing kernel regression model;
in step 2.1, the number of observation vectors in the training sample set is N, and the N observation vectors form a process observation matrix:
Figure BDA0002413775810000051
wherein:
n is the number of observation vectors in the training sample set;
l + 1-number of variables in the observation vector;
for a new observation vector:
Xnew＝[Xnew(1),Xnew(2),…,Xnew(L+1)]；
firstly, a new observation vector and a process observation matrix X are calculatedobsSome observation vector X inobs(i) The Euclidean distance of (a) is as follows:
Figure BDA0002413775810000052
wherein the content of the first and second substances,
di-the euclidean distance between the new observation vector and the ith observation vector in the process observation matrix;
sequentially calculating Euclidean distances between the new observation vector and all observation vectors in the process observation matrix to obtain:
d＝[d1d2…dN]T
wherein:
d-Euclidean distance vectors between the new observation vector and the observation vectors in the process observation matrix;
calculating the weight vector as follows:
Figure BDA0002413775810000061
wherein:
w is weight vector;
h is a bandwidth parameter;
after the weight vector W is obtained, the prediction vector of the new observation vector by the self-organizing kernel regression is as follows:
Figure BDA0002413775810000062
wherein:
Figure BDA0002413775810000063
-a prediction vector of the new observation vector;
wk-the kth dimension component in the weight vector;
Xobs(k) -the kth observation vector in the process observation matrix;
since the L +1 th dimension of the observation vector is the gearbox bearing temperature, the predicted value of the gearbox bearing temperature in the prediction vector of the new observation vector is:
Figure BDA0002413775810000064
wherein:
Figure BDA0002413775810000065
-a predicted value of gearbox bearing temperature;
step 2.3, training a self-organizing kernel regression model by adopting a training sample set to obtain a model parameter h, namely a bandwidth parameter; for observation vector X in all training sample setsobs(k) Calculating the corresponding prediction vector by adopting the step 2.2
Figure BDA0002413775810000066
Minimizing the following objective function by adopting a simulated annealing method and obtaining a value of a bandwidth parameter h; the objective function is:
Figure BDA0002413775810000067
wherein:
j-objective function of the self-organizing kernel regression model;
Figure BDA0002413775810000068
-observation vector XobsThe prediction vector of (a);
n is the number of training samples;
step 3, verifying the self-organizing kernel regression model of the bearing temperature of the gearbox, and calculating the average value and the root mean square of the predicted residual error of the verification data;
after the temperature self-organizing kernel regression model of the bearing of the gearbox is trained, sending a verification sample into the model; verifying that the number of samples is NVGear box bearing temperature model pair NVThe temperature prediction value sequence of each verification sample is
Figure BDA0002413775810000071
Verify the actual gearbox bearing temperature of the sample as
Figure BDA0002413775810000072
The model prediction residual of the i-th verification sample is
Figure BDA0002413775810000073
Using mean absolute value errorRMSEThe modeling accuracy of the model is measured as follows:
Figure BDA0002413775810000074
wherein:
NV-verifying the number of samples;
yi-actual gearbox bearing temperature value of the ith validation sample;
Figure BDA0002413775810000075
-gearbox bearing temperature model predicted values for the ith validation sample;
for NVObtaining N by a self-organizing kernel regression model of the temperature of a bearing of the gearbox through an individual verification sampleVA prediction residual; calculating the NVMean and root mean square of the individual prediction residuals:
Figure BDA0002413775810000076
Figure BDA0002413775810000077
wherein:
i-gearbox bearing temperature model prediction residual for the ith validation sample
Figure BDA0002413775810000079
μ0-verifying that the sample prediction residuals are allA value;
σ0-verifying the sample prediction residual root mean square;
step 4, after the steps are completed, switching to a monitoring stage; when the bearing of the gearbox fails or is abnormal, the relationship between the temperature of the bearing of the gearbox and the influence factors of the bearing of the gearbox changes, and the temperature of the bearing of the gearbox deviates from the self-organizing kernel regression model, so that the prediction precision of the model is reduced; the method comprises the steps of collecting operation data of a monitored unit in real time, forming an observation vector sample sequence, sending the observation vector sample sequence into a model for calculation to obtain a predicted value sequence of the bearing temperature of the gear box, and calculating a predicted residual sequence of the model temperature, wherein the predicted value sequence is as follows:
Figure BDA0002413775810000078
wherein:
ymi-monitoring the actual gearbox bearing temperature of the ith sample in the sequence of samples;
Figure BDA0002413775810000081
-monitoring the model of the ith sample in the sequence of samples to predict the gearbox bearing temperature;
mi-monitoring the model prediction residual for the ith sample in the sequence of samples;
m is the number of observation vectors in the monitoring sample sequence;
in order to accurately analyze the abnormal change of the predicted residual error of the bearing temperature model of the gearbox, accurately send out abnormal alarm of the running of the gearbox, reduce the false alarm rate and the false alarm rate, a Sequential Probability Ratio Test (SPRT) method is adopted to analyze the predicted residual error sequence of the monitoring sample.
The SPRT method proposes two hypotheses:
(1) suppose H0: when the gear box operates normally, the mean value of predicted residual errors of a gear box bearing temperature model is mu0Variance is
Figure BDA0002413775810000082
(2) Suppose H1: when the gearbox operates abnormally, the mean value of predicted residual errors of a gearbox bearing temperature model is mu1Variance is
Figure BDA0002413775810000083
Then assume H originally0And alternative hypothesis H1Respectively, under the conditions that the M monitoring samples are sequentially subjected to model prediction residual error sequencesm1,m2,…,mMThe joint probability densities of the random sequences are respectively as follows:
Figure BDA0002413775810000084
Figure BDA0002413775810000085
wherein:
P0Mlet H0Random sequence joint probability density under the condition of establishment;
P1Mlet H1Random sequence joint probability density under the condition of establishment;
the sequential probability ratio is:
Figure BDA0002413775810000086
wherein:
RM-sequential probability ratios;
setting the false alarm rate and the missing alarm rate of abnormal operation monitoring of the gear box as alpha and beta respectively, and obtaining the alarm lower limit and the alarm upper limit of the temperature prediction residual of the bearing of the gear box as follows:
Figure BDA0002413775810000091
wherein:
α -false alarm rate;
beta-leak alarm rate;
a, alarm lower limit of temperature prediction residual error of a gearbox bearing;
b, alarm upper limit of gear box bearing temperature prediction residual error;
(1) when the sequential probability ratio satisfies the inequality: rMA. ltoreq.A, then hypothesis H is accepted0Namely the gear box operates normally;
(2) when the sequential probability ratio satisfies the inequality: rMIf B is greater than or equal to B, the hypothesis H is rejected0Accept hypothesis H1Namely, the gear box runs abnormally, and the alarm of the abnormal temperature of the bearing of the gear box is sent out.
Compared with the prior art, the invention has the following advantages and effects:
1) the self-organized nuclear regression modeling method is applied to monitoring the temperature state of the bearing of the gearbox of the wind turbine generator, has only one model parameter, is short in model training time and is suitable for on-line monitoring of the gearbox of the wind turbine generator;
2) the partial least square method is applied to the modeling variable selection of the bearing temperature of the gearbox, and the modeling precision is improved;
3) in order to reduce the false alarm rate and the false alarm rate of the temperature monitoring alarm of the gearbox bearing, a sequential probability ratio method capable of analyzing the abnormal change of a weak signal is introduced into the prediction residual error analysis of the gearbox bearing temperature model, so that the abnormal change of the gearbox bearing temperature can be timely and accurately found.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph of predicted versus actual temperature values for a validation sample of a self-organizing nuclear regression model.
FIG. 3 is a graph of predicted residuals for a validation sample of the self-organizing kernel regression model.
FIG. 4 is a graph of predicted versus actual values of model temperature for monitored samples.
Fig. 5 is a graph of model prediction residuals for monitored samples.
FIG. 6 is a graph of monitored sample sequential probability ratios and gearbox bearing temperature anomaly alarms.
Detailed Description
The present invention will be described in further detail below by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and are not to be construed as limiting the present invention.
Examples are given.
With a gearbox of a single 1.5MW unit in a certain wind farm as a research object, selecting operation data recorded by an SCADA system of the unit at a level of 1 minute, as shown in fig. 1, in this embodiment, a method for monitoring a temperature state of a bearing of a gearbox of a wind turbine based on a self-organized nuclear regression model includes the following steps:
step 1, selecting 10 variables meeting the requirements by a partial least square method, which is specifically shown in the following table 1.
Table 1: selecting variables for gearbox bearing temperature modeling
Serial number Wind turbine state parameter
T1 High speed shaft side temperature of gear box
T2 Low speed shaft side temperature of gear box
T3 Gear box oil temperature
T4 Cabin temperature
T5 Gear case cooling water temperature
T6 Temperature of hydraulic oil
T7 Control cabinet temperature
T8 Temperature of frequency conversion controller
V Wind speed
P Active power
And 2, constructing a training sample and a verification sample from the historical operating data of the wind turbine generator. The ratio of training samples to validation samples was 3: 1. and adopting the observation vectors in the training samples to form a process observation matrix. And training by using a training sample and a simulated annealing method to obtain a unique model parameter, namely a bandwidth parameter h is 0.0193, and finishing modeling.
Step 3, verifying the self-organizing kernel regression model of the bearing temperature of the gearbox, and calculating the mean value mu of the predicted residual error of the verification data model0And root mean square σ0。
The 300 gearbox bearing temperature verification samples are sent into a self-organizing kernel regression model, and the predicted values and the predicted residuals of the obtained verification samples are respectively shown in fig. 2 and fig. 3. As can be seen from FIGS. 2 and 3, the self-organized kernel regression model has very high prediction accuracy on the bearing temperature of the gearbox, the absolute maximum value of the prediction residual is only 1.02 degrees, and the model accuracyRMSE1.96 percent. Calculating the mean and standard deviation of the prediction residuals of 300 verification samples as follows:
μ0＝0.0294，σ0＝0.2288。
and 4, in the monitoring stage, 300 samples of abnormal bearing temperature of the gearbox are sent to the self-organizing kernel regression model. The model calculates the bearing temperature prediction values and residuals of the monitored samples, as shown in fig. 4 and 5. In fig. 4, the temperature of the gear box bearing abnormally increases due to the failure thereof. The predicted value and the actual value of the model of the monitoring sample gradually deviate obviously after the 200 th sample. In fig. 5, the self-organizing kernel regression model temperature prediction residuals are increasing.
The gearbox bearing temperature prediction residual in fig. 5 is analyzed by a sequential probability ratio method. Suppose H0And hypothesis H1The mean and variance settings of (a) are shown in table 2, respectively.
TABLE 2 assumptions parameters
Suppose that Temperature state of gearbox bearing Mean value Root mean square
H0 Is normal μ0＝0.0294 σ0＝0.2288
H1 Abnormality (S) μ1＝3μ0 σ1＝2σ0
Setting the false alarm rate and the false alarm rate to be 0.05, and calculating to obtain an alarm lower limit and an alarm upper limit which are respectively as follows:
A＝0.053，B＝19；
in FIG. 6(A), the model prediction residual sequential probabilities are all less than the alarm threshold ceiling B before the 205 th sample; at sample 205, the sequential probability ratio exceeds the upper alarm limit. In FIG. 6(B), at sample 205, the sequential probability ratio exceeds the upper alarm limit, and a gearbox anomaly alarm is issued.
Those not described in detail in this specification are well within the skill of the art.
Although the present invention has been described with reference to the above embodiments, it should be understood that the scope of the present invention is not limited thereto, and that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the present invention.

Claims (1)

1. A wind turbine generator gearbox bearing temperature state monitoring method based on a self-organizing kernel regression model is characterized by comprising the following steps: the method comprises the following steps:
step 1, selecting a temperature modeling variable of a bearing of a gearbox by adopting a Partial Least Squares (PLS) method;
the method comprises the following steps that the temperature of a bearing of a gearbox of the wind turbine generator is influenced by a plurality of parameter variables of the wind turbine generator, in order to determine influence factors of the temperature of the bearing of the gearbox, input modeling variables of a temperature model of the bearing of the gearbox are determined, and the modeling variables are selected from hundreds of operating parameters of the wind turbine generator by a partial least square method; the process is as follows:
an input matrix X and an output gearbox bearing temperature matrix Y are formed by wind turbine generator operation data, and the following formula is as follows:
Figure FDA0002413775800000011
wherein:
n is the number of samples;
m is the number of the original wind turbine generator parameter variables;
normalizing the input matrix X and the output gearbox bearing temperature matrix Y to obtain the following formula:
Figure FDA0002413775800000012
wherein:
X0-input matrix X ∈ RN×MThe normalization matrix of (a);
Y0-output matrix Y ∈ RN×1The normalization matrix of (a);
calculating X0And Y0The first principal axis of (c) is as follows:
Figure FDA0002413775800000013
wherein:
w1——X0a first principal axis of the matrix;
c1——Y0a first principal axis of the matrix;
due to the normalized matrix Y0Is a one-dimensional variable, therefore c11 is ═ 1; solving this optimization problem to obtain w1Obtaining a first main component with the following formula:
Figure FDA0002413775800000021
wherein:
t1——X0a first principal component of the matrix;
u1——Y0a first principal component of the matrix;
the regression coefficient vector is calculated using the following formula:
Figure FDA0002413775800000022
wherein:
p1-principal component t1A vector of regression coefficients of;
r1-principal component u1A vector of regression coefficients of;
finding a regression coefficient vector p1，r1And then, calculating a residual matrix after the first principal component is extracted:
Figure FDA0002413775800000023
wherein:
X1——X0the matrix is extracted with a first principal component t1The residual error matrix after;
Y1——Y0the matrix is extracted with a first principal component u1The residual error matrix after;
by residual matrix X1And Y1Respectively substituted for X0And Y0Calculating the second principal component t2Sequentially determining the number of the final main components according to the following cross validity principle;
cross validation index
Figure FDA0002413775800000024
Figure FDA0002413775800000025
Wherein:
pi-gearbox bearing temperature raw sample points, where i ═ 1,2, …, N;
Figure FDA0002413775800000026
using all sample points and taking t1,t2,…,thFitting values of the ith sample after h component regression modeling;
Figure FDA0002413775800000031
deleting the sample point i during modeling, and taking a fitting value of h components to the ith sample after regression modeling;
when in use
Figure FDA0002413775800000032
Then, a new principal component t is introducedhThe prediction capability of the model is obviously improved;
representing the interpretability and the importance degree of the independent variable to the dependent variable by adopting a variable projection importance index VIP; the greater the VIP value of the independent variable, the more important the independent variable is to predict the dependent variable, and the formula is as follows:
Figure FDA0002413775800000033
wherein:
m is the number of the original wind turbine generator parameter variables;
Rd(Y；th) -outputs Y and thA correlation coefficient between;
m is the number of main components;
whi——X0principal axis vector w of the matrixhThe ith element of (1);
wh——X0a principal axis vector of the matrix;
calculating variable projection importance indexes of all parameters of the wind turbine generator set aiming at the temperature of a bearing of a gearbox, sorting all parameters from large to small according to the variable projection importance indexes, and selecting the first L sorted parameters to ensure that:
Figure FDA0002413775800000034
wherein:
l is the number of the temperature modeling variables of the bearing of the gearbox;
namely, the first L parameters after VIP index sequencing are selected as modeling variables of the bearing temperature of the gearbox;
step 2, modeling the temperature of the bearing of the gearbox by adopting a self-organizing kernel regression method;
step 2.1, constructing a training sample and a verification sample of the gearbox bearing temperature self-organizing kernel regression model;
in step 1, the number of modeling variables selected by the partial least square method is L, the value of the L modeling variables at the time t is [ x (t,1) x (t,2) … x (t, L) ], and the bearing temperature of the gearbox at the time t is recorded as x (t, L + 1); then at time t, the L modeling variables and the gearbox bearing temperature output constitute an observation vector sample, which is recorded as:
X(t)＝[x(t,1),x(t,2),…,x(t,L),x(t,L+1)]
wherein:
[ x (t,1) x (t,2) … x (t, L) ] -the values of the L modeling variables at time t;
x (t, L +1) -the gearbox bearing temperature value at time t;
selecting the L modeling variables and the temperature of the bearing of the gearbox from each historical data of the normal temperature period of the bearing of the gearbox of the wind turbine generator to form an observation vector sample; all observation vector samples formed by historical data of the bearing temperature of the gearbox in a certain normal period are according to the following ratio of 3: 1, dividing the ratio into a training sample set and a verification sample set;
step 2.2, building a gearbox bearing temperature self-organizing kernel regression model;
in step 2.1, the number of observation vectors in the training sample set is N, and the N observation vectors form a process observation matrix:
Figure FDA0002413775800000041
wherein:
n is the number of observation vectors in the training sample set;
l + 1-number of variables in the observation vector;
for a new observation vector:
Xnew＝[Xnew(1),Xnew(2),…,Xnew(L+1)]；
firstly, a new observation vector and a process observation matrix X are calculatedobsSome observation vector X inobs(i) The Euclidean distance of (a) is as follows:
Figure FDA0002413775800000042
wherein the content of the first and second substances,
di-the euclidean distance between the new observation vector and the ith observation vector in the process observation matrix;
sequentially calculating Euclidean distances between the new observation vector and all observation vectors in the process observation matrix to obtain:
d＝[d1d2…dN]T
wherein:
d-Euclidean distance vectors between the new observation vector and the observation vectors in the process observation matrix;
calculating the weight vector as follows:
Figure FDA0002413775800000043
wherein:
w is weight vector;
h is a bandwidth parameter;
after the weight vector W is obtained, the prediction vector of the new observation vector by the self-organizing kernel regression is as follows:
Figure FDA0002413775800000051
wherein:
Figure FDA0002413775800000052
-a prediction vector of the new observation vector;
wk-the kth dimension component in the weight vector;
Xobs(k) -the kth observation vector in the process observation matrix;
since the L +1 th dimension of the observation vector is the gearbox bearing temperature, the predicted value of the gearbox bearing temperature in the prediction vector of the new observation vector is:
Figure FDA0002413775800000053
wherein:
Figure FDA0002413775800000054
-a predicted value of gearbox bearing temperature;
step 2.3, training a self-organizing kernel regression model by adopting a training sample set to obtain a model parameter h, namely a bandwidth parameter; for observation vector X in all training sample setsobs(k) Calculating the corresponding prediction vector by adopting the step 2.2
Figure FDA0002413775800000055
Minimizing the following objective function by adopting a simulated annealing method and obtaining a value of a bandwidth parameter h; the objective function is:
Figure FDA0002413775800000056
wherein:
j-objective function of the self-organizing kernel regression model;
Figure FDA0002413775800000057
-observation vector XobsThe prediction vector of (a);
n is the number of training samples;
step 3, verifying the self-organizing kernel regression model of the bearing temperature of the gearbox, and calculating the average value and the root mean square of the predicted residual error of the verification data;
after the temperature self-organizing kernel regression model of the bearing of the gearbox is trained, sending a verification sample into the model; verifying that the number of samples is NVGear box bearing temperature model pair NVThe temperature prediction value sequence of each verification sample is
Figure FDA0002413775800000058
Verify the actual gearbox bearing temperature of the sample as
Figure FDA0002413775800000059
The model prediction residual of the i-th verification sample is
Figure FDA00024137758000000510
Using mean absolute value errorRMSEThe modeling accuracy of the model is measured as follows:
Figure FDA0002413775800000061
wherein:
NV-verifying the number of samples;
yi-actual gearbox bearing temperature value of the ith validation sample;
Figure FDA0002413775800000062
-gearbox bearing temperature model predicted values for the ith validation sample;
for NVObtaining N by a self-organizing kernel regression model of the temperature of a bearing of the gearbox through an individual verification sampleVA prediction residual; calculating the NVMean and root mean square of the individual prediction residuals:
Figure FDA0002413775800000063
Figure FDA0002413775800000064
wherein:
i-gearbox bearing temperature model prediction residual for the ith validation sample
Figure FDA0002413775800000065
μ0-verifying the samplePredicting a residual mean value;
σ0-verifying the sample prediction residual root mean square;
step 4, after the steps are completed, switching to a monitoring stage; when the bearing of the gearbox fails or is abnormal, the relationship between the temperature of the bearing of the gearbox and the influence factors of the bearing of the gearbox changes, and the temperature of the bearing of the gearbox deviates from the self-organized kernel regression model, so that the prediction accuracy of the model is reduced; the method comprises the steps of collecting operation data of a monitored unit in real time, forming an observation vector sample sequence, sending the observation vector sample sequence into a model for calculation to obtain a predicted value sequence of the bearing temperature of the gear box, and calculating a predicted residual sequence of the model temperature, wherein the predicted value sequence is as follows:
Figure FDA0002413775800000066
wherein:
ymi-monitoring the actual gearbox bearing temperature of the ith sample in the sequence of samples;
Figure FDA0002413775800000067
-monitoring the model of the ith sample in the sequence of samples to predict the gearbox bearing temperature;
mi-monitoring the model prediction residual for the ith sample in the sequence of samples;
m is the number of observation vectors in the monitoring sample sequence;
in order to accurately analyze the abnormal change of the predicted residual error of the bearing temperature model of the gearbox, accurately send out abnormal alarm of the running of the gearbox, reduce the false alarm rate and the false alarm rate, a Sequential Probability Ratio Test (SPRT) method is adopted to analyze the predicted residual error sequence of the monitoring sample.
The SPRT method proposes two hypotheses:
(1) suppose H0: when the gear box operates normally, the mean value of predicted residual errors of a gear box bearing temperature model is mu0Variance is
Figure FDA0002413775800000071
(2) Suppose H1: when the gearbox operates abnormally, the mean value of predicted residual errors of a gearbox bearing temperature model is mu1Variance is
Figure FDA0002413775800000072
Then assume H originally0And alternative hypothesis H1Respectively, under the conditions that the M monitoring samples are sequentially subjected to model prediction residual error sequencesm1,m2,…,mMThe joint probability densities of the random sequences are respectively as follows:
Figure FDA0002413775800000073
Figure FDA0002413775800000074
wherein:
P0Mlet H0Random sequence joint probability density under the condition of establishment;
P1Mlet H1Random sequence joint probability density under the condition of establishment;
the sequential probability ratio is:
Figure FDA0002413775800000075
wherein:
RM-sequential probability ratios;
setting the false alarm rate and the missing alarm rate of abnormal operation monitoring of the gear box as alpha and beta respectively, and obtaining the alarm lower limit and the alarm upper limit of the temperature prediction residual of the bearing of the gear box as follows:
Figure FDA0002413775800000076
wherein:
α -false alarm rate;
beta-leak alarm rate;
a, alarm lower limit of temperature prediction residual error of a gearbox bearing;
b, alarm upper limit of gear box bearing temperature prediction residual error;
(1) when the sequential probability ratio satisfies the inequality: rMA. ltoreq.A, then hypothesis H is accepted0Namely the gear box operates normally;
(2) when the sequential probability ratio satisfies the inequality: rMIf B is greater than or equal to B, the hypothesis H is rejected0Accept hypothesis H1Namely, the gear box runs abnormally, and the alarm of the abnormal temperature of the bearing of the gear box is sent out.
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