CN113468801A - Method for predicting residual life of gear by estimating nuclear density - Google Patents

Method for predicting residual life of gear by estimating nuclear density Download PDF

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CN113468801A
CN113468801A CN202110631246.9A CN202110631246A CN113468801A CN 113468801 A CN113468801 A CN 113468801A CN 202110631246 A CN202110631246 A CN 202110631246A CN 113468801 A CN113468801 A CN 113468801A
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石慧
康辉
张志壮
任谦力
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Taiyuan University of Science and Technology
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Abstract

A method for predicting the residual life of a gear by estimating the nuclear density belongs to the technical field of mechanical reliability and comprises the following specific implementation steps: 1. monitoring the degradation of an internal gear of the main test gearbox in real time by using an acceleration sensor; 2. extracting the characteristics of the degradation state of the gear, and evaluating the degradation performance of the gear in terms of abrasion; 3. clustering data representing different degradation states in a degradation stage by using a time sequence density peak value clustering algorithm, and dividing different degradation state modes according to a real-time clustering result to realize dynamic transfer of the system degradation state; 4. carrying out nonparametric estimation on the probability density function of the continuous degradation state of the gear by using a kernel density estimation method to obtain the probability density function of the degradation state of the gear; 5. and predicting the residual life of the gear by considering the residual life prediction model of the degradation state transition to obtain the residual life distribution of the gear. The advantages are that: the service life of the gear in gear transmission can be predicted, and the gear failure can be prevented, so that economic loss is caused.

Description

Method for predicting residual life of gear by estimating nuclear density
Technical Field
The invention belongs to the technical field of mechanical reliability, in particular to a method for predicting the residual life of gear nuclear density estimation,
background
The gear is a key component in a mechanical equipment transmission system widely applied in the mechanical industry, when the gear has faults of tooth breakage, tooth surface fatigue, gluing and the like, the catastrophic damage of the whole mechanical equipment is often caused, therefore, a reasonable and effective maintenance scheme provided for the gear becomes an urgent problem to be solved, in the whole maintenance scheme making process, the residual life prediction of the gear is a key and difficult point, with the development of the information sensing technology, the running state of the gear can be monitored in real time, the degradation state and the residual life of the system can be more accurately predicted by using a large amount of received real-time monitoring information, the key information related to the mechanical health state is provided, the occurrence of faults can be identified and managed, the maintenance activities can be planned, and a basis is provided for more reasonably making a maintenance strategy based on the state,
disclosure of Invention
The invention aims to provide a method for predicting the residual life of gear nuclear density estimation, which provides a scientific basis for maintenance and repair, and is implemented as follows, wherein the method is characterized by comprising the following implementation steps of: the implementation steps are shown in figure 1:
step 1, acquiring real-time monitoring data representing the state of an internal gear of a main test gear box through a test bench:
the test bench shown in figure 2 is adopted and is formed by connecting a main test gear box 1 and an auxiliary test gear box 2, the center distance a is 150cm, the test adopts mechanical lever loading, the torque is measured by a torque and rotating speed sensor, the vibration, the acceleration, the temperature and the noise of the main test box body and the auxiliary test box body are monitored in the test process, a pair of gears which are staggered and lapped in the front and the back are arranged in the main test gear box body, the broken tooth state of the gears is equivalent to the failure of the gears,
13 sensors are arranged on the test bench, 1,2, 3 and 4 acceleration sensors 1#, 2#, 3# and 4# are respectively arranged at the radial position of the bearing seat in the main test gear box 1, 7 and 8 acceleration sensors 7# and 8# are respectively arranged at the axial position of the bearing seat in the main test gear box 1, and 5 and 6 acceleration sensors 5# and 6# are respectively arranged at the radial position of the bearing seat in the auxiliary test gear box 2; 9. the No. 10 sound sensors 9# and 10# are respectively hung at the positions 40cm above the main test gear box 1 and the auxiliary test gear box 2; no. 11 temperature sensor 11# is arranged inside the main test gear box; a number 12 rotating speed sensor 12# is arranged at the output end of the driving motor 8; the No. 13 torque sensor 13# is arranged at the coupling shafts of the main and the auxiliary gear boxes 1 and 2,
in the test, eight-stage loads are loaded, wherein the eight-stage loads respectively have 349.5 torque, 430.7 torque, 492.2 torque, 555.6 torque, 612.9 torque, 693.4 torque, 734 torque and 822.7 torque, the running time of each stage of load is 10 hours, tooth breakage occurs during the eighth stage of load, the acceleration data of the gear is recorded by a No. 4 sensor 4#, the residual life prediction selects the acceleration test whole time domain signal from the eighth stage of load to tooth breakage for analysis, and the sampling information is as follows: the sampling frequency is 25.6kHz, each sampling lasts for 60 seconds, and the text sampling is recorded every 9 minutes;
step 2, extracting the characteristic of the degradation state of the gear in the main test gear box, evaluating the degradation performance of the gear abrasion by using mean square amplitude, and expressing the mean square amplitude characteristic value of a sampling signal in each sampling time length as follows:
Figure BDA0003103615790000021
in the formula: Σ is a summation number, n is the number of sampling points per sampling period, yiIs tiMean square amplitude, y, of the state information of the time gearjData for each sampling period of the gear;
3, clustering data representing different degradation states at a degradation stage by utilizing a proposed time sequence density peak value clustering algorithm suitable for real-time manifold data clustering according to initial data of the gear in the main test gear box, and dividing different degradation state modes according to a real-time clustering result to realize dynamic transfer of the system degradation state;
according to sample xpK neighbor information of (1), defining sample xpPart ofDensity ppAdaptive truncation distance h in (1)pThe cluster center of the sample is searched, the real distribution information of the data set sample can be reflected better, and the large truncation distance of the place with large sample density is selected, so that the local density of the sample becomes higher, and the cluster center is found accurately; where the density of the sample is small, hpThe value is small, the local density becomes smaller, and outliers are easy to find;
sample xpLocal density p ofpComprises the following steps:
Figure BDA0003103615790000031
wherein d ispqIs a sample xp(x1,y1)，xq(x2,y2) Euclidean distance of (c):
Figure BDA0003103615790000032
sample xpAdaptive truncation distance h ofpComprises the following steps:
hp＝dmax+dmin-dknn(xp) (3)
dmaxand dminIs a set { dknn(xp) 1,2, m } maximum and minimum values, dknn(xp) Represents the average distance to its k nearest neighbors as shown in equation (4):
Figure BDA0003103615790000033
wherein, KNN (x)p)＝{d1(xp),d2(xp),...dk(xp) Is the calculation point xpK-nearest neighbor method of Euclidean distance of each adjacent sample, which is to sample point xpDefining:
d1(xp)≤d2(xp)≤…≤dk(xp) (5)
equation (5) is from sample xpDistance to neighbor in increasing order: d1(xp) Is xpEuclidean distance to nearest neighbor, d2(xp) Is xpEuclidean distance to next neighbor, and so on, k is generally taken as
Figure BDA0003103615790000034
n is the total number of samples;
from the formulas (3) and (4), h is shownpIn the area with high density, the local density is increased by using a large truncation distance; in the area with small density, the local density is reduced by using a small truncation distance, so that the center of the cluster is easier to select;
the transfer distance is the distance between samples determined by the maximum gap in the connecting path between samples, and at least one path exists between every two points in the data set, so that for any two sample points xp,xqDefine a connection path X ═ X with M verticesu1xu2...xuMWherein x isu1＝xp，xuM＝xqAt this time for sample xpAnd sample xqThe distance between is then defined as:
Figure BDA0003103615790000041
any two sample points xp,xqSelecting the maximum gap in each connection path X as the path Xp,xqAt a distance between the connection paths
Figure BDA0003103615790000042
Select each path xp,xqDistance minimum as transfer distance:
Figure BDA0003103615790000043
in the formula
Figure BDA0003103615790000044
Is the transfer distance of the two points,
Figure BDA0003103615790000045
is an arbitrary sample xpAnd sample xqAll connection paths between;
constructing a new transfer matrix to distribute the residual samples, wherein the calculation method of the transfer matrix T comprises the following steps:
1) forming an undirected graph G (X, E) with Euclidean distance as a weight value for all samples of the data, and obtaining the directed graph by adopting a Kruskal minimum spanning tree algorithm
Figure BDA0003103615790000046
Figure BDA0003103615790000047
2) To be provided with
Figure BDA0003103615790000048
Medium maximum transmission distance
Figure BDA0003103615790000049
Cutting apart
Figure BDA00031036157900000410
Can obtain the product
Figure BDA00031036157900000411
And
Figure BDA00031036157900000412
middle arbitrary sample point xpTo
Figure BDA00031036157900000413
Middle arbitrary sample point xqIs defined as the length of the cut edge
Figure BDA00031036157900000414
T is a transfer matrix;
3) repeating the step 2), and cutting
Figure BDA00031036157900000415
And
Figure BDA00031036157900000416
until there is no subtree, then obtaining the transfer matrix T between all sample points;
4) allocating sample points by a transfer matrix;
step 4, the density of the clustered samples is changed, and the smooth parameters of kernel density estimation can be judged according to the local density of the samples, so that the smooth parameters are updated in a self-adaptive mode according to the clustering result to realize the residual life prediction of the degradation state transition;
the kernel density estimation method is a nonparametric estimation method which does not make any assumption on the form of data distribution and researches the data distribution characteristics from the data;
let Δ x1,Δx2,...,ΔxnIs an independent and identically distributed random variable for representing the degradation increment of the system per unit time, and the probability density function is f (delta x), then the function
Figure BDA0003103615790000051
The nuclear density estimate of f (Δ x) is written as:
Figure BDA0003103615790000052
where h is a smoothing parameter, K (-) is a kernel function, n is the number of samples of a random variable, any function can be used as a kernel function in principle when the samples are large enough, and a Gaussian kernel function is generally selected in consideration of the shape influence and smooth weight of the function
Figure BDA0003103615790000053
The smoothing parameter is an important parameter for smoothing the whole estimation in kernel density estimation, and the width of each kernel function can be determined so as to determine the kernel densityThe accuracy of the degree estimate;
the degenerated increments are independently and identically distributed in unit time, then tkThe distribution of the time characteristic degradation amount is [0, t ]k]Distribution of cumulative sums of characteristic degradation increments per unit time, i.e. tkProbability density function of accumulated time characteristic degradation X (t)
Figure BDA0003103615790000054
Is equal to the probability density function of the degradation increment in unit time
Figure BDA0003103615790000055
K-deconvolution of (a), i.e.:
Figure BDA0003103615790000056
then go through tlTime of day, future tk+tlThe characteristic cumulative degradation amount at the time is:
X(tk+tl)＝X(tk)+X(tl) (11)
then tk+tlThe probability density function of the accumulated time characteristic degradation amount is as follows:
Figure BDA0003103615790000057
defining a component first time to failure threshold time TfWith the current time tkThe difference is the remaining life tRULAccording to the nuclear density estimation model of the degradation distribution, a fault time distribution function F (t) is obtained as follows:
Figure BDA0003103615790000058
wherein L is a fault threshold, a remaining life distribution function F can be obtainedk(t) is:
Figure BDA0003103615790000061
probability density function f of real-time residual life can be predictedk(t)：
Figure BDA0003103615790000062
Through the modeling process, the probability density function of the residual life can be predicted in a nuclear density estimation mode after new degradation characteristic incremental data are obtained
Figure BDA0003103615790000063
After clustering, dividing different degradation stages, and setting a smoothing parameter h in formula (9) as degradation increment delta X of each stagenThe function of the surrounding density, the smoothing parameter of the kernel function is adjusted by the distance between the sample point and the nearest neighbor, and is recorded as
Figure BDA0003103615790000064
Taking the average Euclidean distance of m nearest neighbors selected in a new degradation stage after sample clustering as the window width of kernel estimation, namely:
Figure BDA0003103615790000065
wherein d isi(delta x) is the distance from the retrogression incremental sample delta x to the nearest neighbor of the retrogression degraded state of clustering, and in a new degradation stage after clustering, the smoothing parameter adapts to the local density to carry out kernel density estimation, so that the smoothing parameter at the high density part is smaller, the smoothing parameter at the low density part is larger, and smoother estimation is obtained, and therefore, the kernel density estimation is adopted for establishing the self-adapting smoothing parameter degradation incremental probability density function for the data of different degradation states, and the probability density function is as follows:
Figure BDA0003103615790000066
the dynamic transition of the degradation state is realized after the real-time received degradation information is clustered, the degradation information of the last stage selected by the update sample improves the self-adaptive update efficiency of the smooth parameter, and the accuracy of the prediction of the residual life of the system is improved;
new degradation stage after sample clustering, current tkProbability density function with time instant updated to m state degradation increments
Figure BDA0003103615790000067
Can be expressed as:
Figure BDA0003103615790000071
it can be known that the probability density function of the degradation state at the current moment after the sample clustering can be expressed as:
Figure BDA0003103615790000072
it can be known from the formula (18) and the formula (19) that after the system degradation state transition real-time clustering is considered, the kernel density estimation model needs to perform convolution calculation again under different degradation modes, the calculation amount is larger and larger, and therefore the t is passedk-1Estimating the nuclear density of the degradation state at the moment to obtain tkThe kernel density estimation of the dynamic transition of the time degradation state realizes the real-time update of the probability density function of the residual service life, and is very necessary to reduce the calculation complexity;
Figure BDA0003103615790000073
substituting equation (20) into equation (14) can obtain the remaining life distribution and predict the probability density function of the real-time remaining life considering the transition of the degradation state
Figure BDA0003103615790000074
Comprises the following steps:
Figure BDA0003103615790000075
when the m-th sample is received at the current moment, the self-adaptive smoothing parameter of the m-th sample is updated
Figure BDA0003103615790000076
In that
Figure BDA0003103615790000077
Can obtain the real-time residual life distribution at the current moment on the basis
Figure BDA0003103615790000078
Therefore, after new degradation characteristic increment data are continuously obtained, the predicted residual life probability density function is updated in real time, and the calculation complexity is reduced;
and 5, predicting the residual life of the gear by considering the residual life prediction model of the degraded state transition:
finally, the average residual life of the gear is as follows:
Figure BDA0003103615790000081
the invention has the advantages and positive effects that:
the invention is applied to the residual life prediction of the gear, establishes a prediction model, can effectively predict the residual life of the gear,
drawings
FIG. 1 is a flowchart of a method for predicting remaining life of a gear according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a test rig in an embodiment of the present invention;
FIG. 3 is a graph of eigenvalue change with monitoring time in an embodiment of the present invention;
FIG. 4 is a 20-hour regression state T-CFDP clustering in an example of the present invention;
FIG. 5 shows the T-CFDP clustering for 30 hours of degradation in an embodiment of the present invention;
FIG. 6 shows the T-CFDP clustering for 40 hours of degradation in an embodiment of the present invention;
FIG. 7 shows the T-CFDP clustering for 50 hours of degradation in an embodiment of the present invention;
FIG. 8 is a T-CFDP clustering of 60 hours of degradation in accordance with an embodiment of the present invention;
FIG. 9 shows T-CFDP clustering for 70 hours of degradation in an embodiment of the present invention;
FIG. 10 is a graph illustrating predicted remaining life at various monitoring times in accordance with an embodiment of the present invention;
FIG. 11 is a probability density distribution of 30h remaining life in an embodiment of the present invention;
FIG. 12 is a probability density distribution of 60h remaining life in an embodiment of the present invention;
in the figure: 1-a main test gear box, 2-an auxiliary test gear box, 3-a first coupler, 4-a second coupler, 5-a third coupler, 6-a mechanical lever, 7-a detection system, 8-a driving motor, and a-the center distance between the main test gear box and the auxiliary test gear box;
1# -8 # -1 st to 8 th acceleration sensors, 9#, 10# -1 st and 2 nd sound sensors, 11# -temperature sensor, 12# -rotating speed sensor and 13# -torque sensor;
Detailed Description
The embodiments of the invention will be further explained with reference to the drawings in which:
fig. 2 is a schematic diagram of a test bench for the test application, and the test method comprises the following steps:
step 1, acquiring real-time monitoring data representing the state of an internal gear of a main test gear box through a test bench:
the test bench shown in figure 2 is adopted and is formed by connecting a main test gear box 1 and an auxiliary test gear box 2, the center distance a is 150cm, the test adopts mechanical lever loading, the torque is measured by a torque and rotating speed sensor, the vibration, the acceleration, the temperature and the noise of the main test box body and the auxiliary test box body are monitored in the test process, a pair of gears which are staggered and lapped in the front and the back are arranged in the main test gear box body, the broken tooth state of the gears is equivalent to the failure of the gears,
13 sensors are arranged on the test bench, 1,2, 3 and 4 acceleration sensors 1#, 2#, 3# and 4# are respectively arranged at the radial position of the bearing seat in the main test gear box 1, 7 and 8 acceleration sensors 7# and 8# are respectively arranged at the axial position of the bearing seat in the main test gear box 1, and 5 and 6 acceleration sensors 5# and 6# are respectively arranged at the radial position of the bearing seat in the auxiliary test gear box 2; 9. the No. 10 sound sensors 9# and 10# are respectively hung at the positions 40cm above the main test gear box 1 and the auxiliary test gear box 2; no. 11 temperature sensor 11# is arranged inside the main test gear box; a number 12 rotating speed sensor 12# is arranged at the output end of the driving motor 8; the No. 13 torque sensor 13# is arranged at the coupling shafts of the main and the auxiliary gear boxes 1 and 2,
in the test, eight-stage loads are loaded, wherein the eight-stage loads respectively have 349.5 torque, 430.7 torque, 492.2 torque, 555.6 torque, 612.9 torque, 693.4 torque, 734 torque and 822.7 torque, the running time of each stage of load is 10 hours, tooth breakage occurs during the eighth stage of load, the acceleration data of the gear is recorded by a No. 4 sensor 4#, the residual life prediction selects the acceleration test whole time domain signal from the eighth stage of load to tooth breakage for analysis, and the sampling information is as follows: the sampling frequency is 25.6kHz, each sampling lasts for 60 seconds, and the text sampling is recorded every 9 minutes;
step 2, extracting the characteristic of the degradation state of the gear, evaluating the degradation performance of the gear wear by using mean square amplitude, and expressing the mean square amplitude characteristic value of a sampling signal in each sampling time length as follows:
Figure BDA0003103615790000101
in the formula: Σ is a summation number, n is the number of sampling points per sampling period, yiIs tiStatus information of the time gear, yjData for each sampling period of the gear;
processing the acceleration and noise data by a mean square amplitude method to obtain a graph of the degradation of the gearbox along with the change of monitoring time as shown in figure 3, wherein the threshold value y of the gearbox when a fault occurs is 76.325mm/s2，
And 3, clustering data representing different degradation states in a degradation stage by using the proposed time sequence density peak value clustering algorithm suitable for real-time manifold data clustering, and dividing different degradation state modes according to real-time clustering results to realize dynamic transfer of system degradation states:
according to sample xpK neighbor information of (1), defining sample xpLocal density p ofpAdaptive truncation distance h in (1)pThe cluster center of the sample is searched, the real distribution information of the data set sample can be reflected better, and the large truncation distance of the place with large sample density is selected, so that the local density of the sample becomes higher, and the cluster center is found accurately; where the density of the sample is small, hpThe value is small, the local density becomes smaller, and outliers are easy to find;
sample xpLocal density p ofpComprises the following steps:
Figure BDA0003103615790000102
wherein d ispqIs a sample xp(x1,y1)，xq(x2,y2) Euclidean distance of (c):
Figure BDA0003103615790000103
sample xpAdaptive truncation distance h ofpComprises the following steps:
hp＝dmax+dmin-dknn(xp) (3)
dmaxand dminIs a set { dknn(xp) 1,2, m } maximum and minimum values, dknn(xp) Represents the average distance to its k nearest neighbors as shown in equation (4):
Figure BDA0003103615790000111
wherein, KNN (x)p)＝{d1(xp),d2(xp),...dk(xp) Is the calculation point xpK-nearest neighbor method of Euclidean distance of each adjacent sample, which is to sample point xpDefining:
d1(xp)≤d2(xp)≤…≤dk(xp) (5)
equation (5) is from sample xpDistance to neighbor in increasing order: d1(xp) Is xpEuclidean distance to nearest neighbor, d2(xp) Is xpEuclidean distance to next neighbor, and so on, k is generally taken as
Figure BDA0003103615790000112
n is the total number of samples;
from the formulas (3) and (4), h is shownpIn the area with high density, the local density is increased by using a large truncation distance; in the area with small density, the local density is reduced by using a small truncation distance, so that the center of the cluster is easier to select;
the transfer distance is the distance between samples determined by the maximum gap in the connecting path between samples, and at least one path exists between every two points in the data set, so that for any two sample points xp,xqDefine a connection path X ═ X with M verticesu1xu2…xuMWherein x isu1＝xp，xuM＝xqAt this time for sample xpAnd sample xqThe distance between is then defined as:
Figure BDA0003103615790000113
any two sample points xp,xqSelecting the maximum gap in each connection path X as the path Xp,xqAt a distance between the connection paths
Figure BDA0003103615790000117
Select each path xp,xqDistance minimum as transfer distance:
Figure BDA0003103615790000114
in the formula
Figure BDA0003103615790000115
Is the transfer distance of the two points,
Figure BDA0003103615790000116
is an arbitrary sample xpAnd sample xqAll connection paths between;
constructing a new transfer matrix to distribute the residual samples, wherein the calculation method of the transfer matrix T comprises the following steps:
1) forming an undirected graph G (X, E) with Euclidean distance as a weight value for all samples of the data, and obtaining the directed graph by adopting a Kruskal minimum spanning tree algorithm
Figure BDA0003103615790000121
Figure BDA0003103615790000122
2) To be provided with
Figure BDA0003103615790000123
Medium maximum transmission distance
Figure BDA0003103615790000124
Cutting apart
Figure BDA0003103615790000125
Can obtain the product
Figure BDA0003103615790000126
And
Figure BDA0003103615790000127
all kinds ofThis point xpTo
Figure BDA0003103615790000128
Middle arbitrary sample point xqIs defined as the length of the cut edge
Figure BDA0003103615790000129
T is a transfer matrix;
3) repeating the step 2), and cutting
Figure BDA00031036157900001210
And
Figure BDA00031036157900001211
until there is no subtree, then obtaining the transfer matrix T between all sample points;
4) allocating sample points by a transfer matrix;
finally, obtaining a degradation state cluster map of the system shown in the figures 4-9 at different times;
step 4, the density of the clustered samples is changed, and the smooth parameters of kernel density estimation can be judged according to the local density of the samples, so that the smooth parameters are updated in a self-adaptive mode according to the clustering result to realize the residual life prediction of the degradation state transition;
the kernel density estimation method is a nonparametric estimation method which does not make any assumption on the form of data distribution and researches the data distribution characteristics from the data;
let Δ x1,Δx2,...,ΔxnIs an independent and identically distributed random variable for representing the degradation increment of the system per unit time, and the probability density function is f (delta x), then the function
Figure BDA00031036157900001212
The nuclear density estimate of f (Δ x) is written as:
Figure BDA00031036157900001213
wherein h is a smoothing parameter and K (-) isKernel function, n is the number of samples of random variables, when the samples are large enough, in principle any function can be used as kernel function, and the Gaussian kernel function is generally selected in consideration of the shape influence and smooth weight
Figure BDA00031036157900001214
The smoothing parameter is an important parameter for smoothing the whole estimation in the kernel density estimation, and the width of each kernel function can be determined so as to determine the accuracy of the kernel density estimation;
the degenerated increments are independently and identically distributed in unit time, then tkThe distribution of the time characteristic degradation amount is [0, t ]k]Distribution of cumulative sums of characteristic degradation increments per unit time, i.e. tkProbability density function of accumulated time characteristic degradation X (t)
Figure BDA0003103615790000131
Is equal to the probability density function of the degradation increment in unit time
Figure BDA0003103615790000132
K deconvolution of (i), i.e.
Figure BDA0003103615790000133
Then go through tlTime of day, future tk+tlThe characteristic cumulative degradation amount at the time is:
X(tk+tl)＝X(tk)+X(tl) (11)
then tk+tlThe probability density function of the accumulated time characteristic degradation amount is as follows:
Figure BDA0003103615790000134
defining a component first time to failure threshold time TfWith the current time tkThe difference is the remaining life tRULThe fault can be obtained according to the nuclear density estimation model of the degradation distributionThe time distribution function F (t) is:
Figure BDA0003103615790000135
wherein L is a fault threshold, a remaining life distribution function F can be obtainedk(t) is:
Figure BDA0003103615790000136
probability density function f of real-time residual life can be predictedk(t)：
Figure BDA0003103615790000137
Through the modeling process, the probability density function of the residual life can be predicted in a nuclear density estimation mode after new degradation characteristic incremental data are obtained
Figure BDA0003103615790000138
After clustering, dividing different degradation stages, and setting a smoothing parameter h in formula (9) as degradation increment delta X of each stagenThe function of the surrounding density, the smoothing parameter of the kernel function is adjusted by the distance between the sample point and the nearest neighbor, and is recorded as
Figure BDA0003103615790000139
Figure BDA00031036157900001310
Taking the average Euclidean distance of m nearest neighbors selected in a new degradation stage after sample clustering as the window width of kernel estimation, namely:
Figure BDA0003103615790000141
wherein d isi(Δ x) is the cluster degradation stateAnd transferring a retrogression incremental sample delta x to the nearest neighbor distance of the retrogression incremental sample delta x, and in a new degradation stage after clustering, adapting the smoothing parameters to local density to carry out kernel density estimation, so that the local smoothing parameters with high density are smaller, the local smoothing parameters with low density are larger, and smoother estimation is obtained, and thus, adopting kernel density estimation to establish a self-adaptive smoothing parameter degradation incremental probability density function for data in different degradation states:
Figure BDA0003103615790000142
the dynamic transition of the degradation state is realized after the real-time received degradation information is clustered, the degradation information of the last stage selected by the update sample improves the self-adaptive update efficiency of the smooth parameter, and the accuracy of the prediction of the residual life of the system is improved;
new degradation stage after sample clustering, current tkProbability density function with time instant updated to m state degradation increments
Figure BDA0003103615790000143
Can be expressed as:
Figure BDA0003103615790000144
it can be known that the probability density function of the degradation state at the current moment after the sample clustering can be expressed as:
Figure BDA0003103615790000145
it can be known from the formula (18) and the formula (19) that after the system degradation state transition real-time clustering is considered, the kernel density estimation model needs to perform convolution calculation again under different degradation modes, the calculation amount is larger and larger, and therefore the t is passedk-1Estimating the nuclear density of the degradation state at the moment to obtain tkThe kernel density estimation of the dynamic transition of the time degradation state realizes the real-time update of the probability density function of the residual service lifeAnd it is very necessary to reduce the computational complexity;
Figure BDA0003103615790000151
substituting equation (20) into equation (14) can obtain the remaining life distribution and predict the probability density function of the real-time remaining life considering the transition of the degradation state
Figure BDA0003103615790000152
Comprises the following steps:
Figure BDA0003103615790000153
when the m-th sample is received at the current moment, the self-adaptive smoothing parameter of the m-th sample is updated
Figure BDA0003103615790000154
In that
Figure BDA0003103615790000155
Can obtain the real-time residual life distribution at the current moment on the basis
Figure BDA0003103615790000156
Therefore, after new degradation characteristic increment data are continuously obtained, the predicted residual life probability density function is updated in real time, and the calculation complexity is reduced;
and 5, predicting the residual life of the gear by considering the residual life prediction model of the degraded state transition:
finally, the average residual life of the gear in 70 hours is as follows:
Figure BDA0003103615790000157
hours;
the predicted value result of the residual life of the dynamic transfer gear considering the degradation state shown in fig. 10 is finally obtained:
the comparison error between the predicted value and the actual value of the residual life of the gear for the dynamic transition considering the degradation state and the dynamic transition not considering the degradation state under the same parameter is shown in table 1:
TABLE 1 dynamic transition with degradation state considered and dynamic transition model with degradation state not considered error comparison of predicted values to true values
Figure BDA0003103615790000158
Figure BDA0003103615790000161
Comparing the data in the table 1, it can be found that as the operation time of the system increases, the state monitoring information increases, the absolute error between the predicted value and the actual value of the residual life is gradually reduced, meanwhile, the prediction of the residual life considering the dynamic transition of the degradation state is closer to the true value, which shows that the prediction value of the real-time residual life is more accurate by considering the adaptive kernel density estimation of the dynamic transition of the degradation state, which shows that the method provided by the invention can well predict the residual life in real time,
in order to further verify the effectiveness of the method provided by the invention, residual life of the gearbox is predicted by adopting a residual life prediction method based on Gamma distribution on the residual life of the same monitoring point under the same initial sample, and the two predicted values are compared to obtain the results of the graphs in FIGS. 11 and 12;
from fig. 11 and fig. 12, it can be seen that the variance of the residual life probability density function predicted by the kernel density estimation method is smaller than that of the residual life probability density function predicted based on the Gamma distribution model, and the predicted value of the residual life is closer to the actual value, which indicates that the residual life prediction predicted based on the kernel density estimation method is more accurate than that based on the Gamma distribution model, and meanwhile, as the monitoring time increases, the performance of the gearbox deteriorates continuously, the data representing the state degradation of the gearbox increases continuously, so that the variance of the residual life probability density function becomes smaller gradually, the predicted value of the residual life is closer to the actual value gradually, which indicates that the predicted residual life value is more accurate;
fig. 11 shows the probability density distribution of the remaining lifetime of 30h, and it can be seen that the variance of the probability density distribution of the dynamic transition without considering the degradation state and the probability density distribution of the kernel density estimation with considering the degradation state are approximately the same, but the kernel density estimation with considering the degradation state is closer to the true value, fig. 12 shows the probability density distribution of the remaining lifetime of 60h, the absolute error of the kernel density estimation result of the dynamic transition without considering the degradation state is large, and the variance is small because all data at the current time and before are selected, the possible mutation and the possible degradation acceleration in the degradation process are not considered, the error of the predicted lifetime obtained by considering the kernel density estimation method of the dynamic transition with the degradation state is small, but the variance is large, because the dynamic transition of the degradation state is considered in clustering, the degradation data after the state transition at the new degradation acceleration stage is selected, and the predicted average remaining lifetime is more accurate, is closer to the true value of the image,
in conclusion, the invention provides a method for predicting the residual life of gear nuclear density estimation, which clusters data representing different degradation states in a degradation stage by using a time sequence density peak value clustering algorithm, divides different degradation state modes according to a real-time clustering result and realizes dynamic transfer of a system degradation state; carrying out nonparametric estimation on the probability density function of the continuous degradation state of the gear by using a kernel density estimation method to obtain the probability density function of the degradation state of the gear; and finally, adaptively updating smooth parameters according to the sample density, and simultaneously considering the problem of high calculation complexity in the real-time prediction process, establishing an adaptive kernel density estimation real-time residual life prediction recurrence model of the dynamic transition of the degradation state to obtain the residual life distribution of the gear.

Claims (1)

1. A method for predicting the residual life of gear nuclear density estimation is characterized by comprising the following implementation steps:
step 1, acquiring real-time monitoring data representing the state of an internal gear of a main test gear box through a test bench:
the adopted test bench is formed by connecting a main test gear box (1) and an auxiliary test gear box (2), the center distance a is 150cm, the test adopts mechanical lever loading, the torque is measured by a torque and rotation speed sensor, the vibration, acceleration, temperature and noise of the main test box body and the auxiliary test box body are monitored in the test process, a pair of gears which are staggered and lapped in the front and the back are arranged in the main test gear box, and the broken tooth state of the gears is equivalent to the failure of the gears;
13 sensors are arranged on the test bench, 1,2, 3 and 4 acceleration sensors (1#, 2#, 3#, and 4#) are respectively arranged at the radial direction of the inner bearing seat of the main test gear box (1), 7 and 8 acceleration sensors (7#, 8#) are respectively arranged at the axial direction of the inner bearing seat of the main test gear box (1), and 5 and 6 acceleration sensors (5#, 6#) are respectively arranged at the radial direction of the inner bearing seat of the auxiliary test gear box (2); 9. the No. 10 sound sensors (9#, 10#) are respectively hung at the positions 40cm above the main test gear box (1) and the auxiliary test gear box (2); the No. 11 temperature sensor (11#) is arranged inside the main test gear box; a No. 12 rotating speed sensor (12#) is arranged at the output end of the driving motor; the No. 13 torque sensor (13#) is arranged at the connecting shafts of the main and auxiliary gear boxes (1, 2);
in the test, eight-stage loads are loaded, wherein the eight-stage loads respectively have 349.5 torque, 430.7 torque, 492.2 torque, 555.6 torque, 612.9 torque, 693.4 torque, 734 torque and 822.7 torque, the running time of each stage of load is 10 hours, tooth breakage occurs during the eighth stage of load, a No. 4 sensor (4#) is used for recording the acceleration data of the gear, the residual life prediction selects the acceleration from the eighth stage of loading to the tooth breakage to test the whole time domain signal for analysis, and the sampling information is as follows: the sampling frequency is 25.6kHz, each sampling lasts for 60 seconds, and the text sampling is recorded every 9 minutes;
step 2, extracting the characteristic of the degradation state of the gear in the main test gear box, evaluating the degradation performance of the gear abrasion by using mean square amplitude, and expressing the mean square amplitude characteristic value of a sampling signal in each sampling time length as follows:
Figure FDA0003103615780000021
in the formula: sigma being a sum number and n being per sampling periodNumber of sampling points, yiIs tiMean square amplitude, y, of the state information of the time gearjData for each sampling period of the gear;
3, clustering data representing different degradation states at a degradation stage by utilizing a proposed time sequence density peak value clustering algorithm suitable for real-time manifold data clustering according to initial data of the gear in the main test gear box, and dividing different degradation state modes according to a real-time clustering result to realize dynamic transfer of the system degradation state;
according to sample xpK neighbor information of (1), defining sample xpLocal density p ofpAdaptive truncation distance h in (1)pThe cluster center of the sample is searched, the real distribution information of the data set sample can be reflected better, and the large truncation distance of the place with large sample density is selected, so that the local density of the sample becomes higher, and the cluster center is found accurately; where the density of the sample is small, hpThe value is small, the local density becomes smaller, and outliers are easy to find;
sample xpLocal density p ofpComprises the following steps:
Figure FDA0003103615780000022
wherein d ispqIs a sample xp(x1,y1)，xq(x2,y2) Euclidean distance of (c):
Figure FDA0003103615780000023
sample xpAdaptive truncation distance h ofpComprises the following steps:
hp＝dmax+dmin-dknn(xp) (3)
dmaxand dminIs a set { dknn(xp) 1,2, m } maximum and minimum values, dknn(xp) Represents the average distance to its k nearest neighbors as shown in equation (4):
Figure FDA0003103615780000024
wherein, KNN (x)p)＝{d1(xp),d2(xp),...dk(xp) Is the calculation point xpK-nearest neighbor method of Euclidean distance of each adjacent sample, which is to sample point xpDefining:
d1(xp)≤d2(xp)≤…≤dk(xp) (5)
equation (5) is from sample xpDistance to neighbor in increasing order: d1(xp) Is xpEuclidean distance to nearest neighbor, d2(xp) Is xpEuclidean distance to next neighbor, and so on, k is generally taken as
Figure FDA0003103615780000031
n is the total number of samples;
from the formulas (3) and (4), h is shownpIn the area with high density, the local density is increased by using a large truncation distance; in the area with small density, the local density is reduced by using a small truncation distance, so that the center of the cluster is easier to select;
the transfer distance is the distance between samples determined by the maximum gap in the connecting path between samples, and at least one path exists between every two points in the data set, so that for any two sample points xp,xqDefine a connection path X ═ X with M verticesu1xu2…xuMWherein x isu1＝xp，xuM＝xqAt this time for sample xpAnd sample xqThe distance between is then defined as:
Figure FDA0003103615780000032
any twoA sample point xp,xqSelecting the maximum gap in each connection path X as the path Xp,xqAt a distance between the connection paths
Figure FDA0003103615780000033
Select each path xp,xqDistance minimum as transfer distance:
Figure FDA0003103615780000034
in the formula
Figure FDA0003103615780000035
Is the transfer distance of the two points,
Figure FDA0003103615780000036
is an arbitrary sample xpAnd sample xqAll connection paths between;
constructing a new transfer matrix to distribute the residual samples, wherein the calculation method of the transfer matrix T comprises the following steps:
1) forming an undirected graph G (X, E) with Euclidean distance as a weight value for all samples of the data, and obtaining the directed graph by adopting a Kruskal minimum spanning tree algorithm
Figure FDA0003103615780000037
Figure FDA0003103615780000038
2) To be provided with
Figure FDA0003103615780000041
Medium maximum transmission distance
Figure FDA0003103615780000042
Cutting apart
Figure FDA0003103615780000043
Can obtain the product
Figure FDA0003103615780000044
And
Figure FDA0003103615780000045
middle arbitrary sample point xpTo
Figure FDA0003103615780000046
Middle arbitrary sample point xqIs defined as the length of the cut edge
Figure FDA0003103615780000047
T is a transfer matrix;
3) repeating the step 2), and cutting
Figure FDA0003103615780000048
And
Figure FDA0003103615780000049
until there is no subtree, then obtaining the transfer matrix T between all sample points;
4) allocating sample points by a transfer matrix;
step 4, the density of the clustered samples is changed, and the smooth parameters of kernel density estimation can be judged according to the local density of the samples, so that the smooth parameters are updated in a self-adaptive mode according to the clustering result to realize the residual life prediction of the degradation state transition;
the kernel density estimation method is a nonparametric estimation method which does not make any assumption on the form of data distribution and researches the data distribution characteristics from the data;
let Δ x1,Δx2,...,ΔxnIs an independent and identically distributed random variable for representing the degradation increment of the system per unit time, and the probability density function is f (delta x), then the function
Figure FDA00031036157800000410
The nuclear density estimate of f (Δ x) is written as:
Figure FDA00031036157800000411
where h is a smoothing parameter, K (-) is a kernel function, n is the number of samples of a random variable, any function can be used as a kernel function in principle when the samples are large enough, and a Gaussian kernel function is generally selected in consideration of the shape influence and smooth weight of the function
Figure FDA00031036157800000412
The smoothing parameter is an important parameter for smoothing the whole estimation in the kernel density estimation, and the width of each kernel function can be determined so as to determine the accuracy of the kernel density estimation;
the degenerated increments are independently and identically distributed in unit time, then tkThe distribution of the time characteristic degradation amount is [0, t ]k]Distribution of cumulative sums of characteristic degradation increments per unit time, i.e. tkProbability density function of accumulated time characteristic degradation X (t)
Figure FDA00031036157800000413
Is equal to the probability density function of the degradation increment in unit time
Figure FDA00031036157800000414
K-deconvolution of (a), i.e.:
Figure FDA0003103615780000051
then go through tlTime of day, future tk+tlThe characteristic cumulative degradation amount at the time is:
X(tk+tl)＝X(tk)+X(tl) (11)
then tk+tlTime of day characteristicsThe probability density function for the cumulative amount of degradation is:
Figure FDA0003103615780000052
defining a component first time to failure threshold time TfWith the current time tkThe difference is the remaining life tRULAccording to the nuclear density estimation model of the degradation distribution, a fault time distribution function F (t) is obtained as follows:
Figure FDA0003103615780000053
wherein L is a fault threshold, a remaining life distribution function F can be obtainedk(t) is:
Figure FDA0003103615780000054
probability density function f of real-time residual life can be predictedk(t)：
Figure FDA0003103615780000055
Through the modeling process, the probability density function of the residual life can be predicted in a nuclear density estimation mode after new degradation characteristic incremental data are obtained
Figure FDA0003103615780000056
After clustering, dividing different degradation stages, and setting a smoothing parameter h in formula (9) as degradation increment delta X of each stagenThe function of the surrounding density, the smoothing parameter of the kernel function is adjusted by the distance between the sample point and the nearest neighbor, and is recorded as
Figure FDA0003103615780000057
Figure FDA0003103615780000058
Taking the average Euclidean distance of m nearest neighbors selected in a new degradation stage after sample clustering as the window width of kernel estimation, namely:
Figure FDA0003103615780000059
wherein d isi(delta x) is the distance from the retrogression incremental sample delta x to the nearest neighbor of the retrogression degraded state of clustering, and in a new degradation stage after clustering, the smoothing parameter adapts to the local density to carry out kernel density estimation, so that the smoothing parameter at the high density part is smaller, the smoothing parameter at the low density part is larger, and smoother estimation is obtained, and therefore, the kernel density estimation is adopted for establishing the self-adapting smoothing parameter degradation incremental probability density function for the data of different degradation states, and the probability density function is as follows:
Figure FDA0003103615780000061
the dynamic transition of the degradation state is realized after the real-time received degradation information is clustered, the degradation information of the last stage selected by the update sample improves the self-adaptive update efficiency of the smooth parameter, and the accuracy of the prediction of the residual life of the system is improved;
new degradation stage after sample clustering, current tkProbability density function with time instant updated to m state degradation increments
Figure FDA0003103615780000062
Can be expressed as:
Figure FDA0003103615780000063
it can be known that the probability density function of the degradation state at the current moment after the sample clustering can be expressed as:
Figure FDA0003103615780000064
it can be known from the formula (18) and the formula (19) that after the system degradation state transition real-time clustering is considered, the kernel density estimation model needs to perform convolution calculation again under different degradation modes, the calculation amount is larger and larger, and therefore the t is passedk-1Estimating the nuclear density of the degradation state at the moment to obtain tkThe kernel density estimation of the dynamic transition of the time degradation state realizes the real-time update of the probability density function of the residual service life, and is very necessary to reduce the calculation complexity;
Figure FDA0003103615780000071
substituting equation (20) into equation (14) can obtain the remaining life distribution and predict the probability density function of the real-time remaining life considering the transition of the degradation state
Figure FDA0003103615780000072
Comprises the following steps:
Figure FDA0003103615780000073
when the m-th sample is received at the current moment, the self-adaptive smoothing parameter of the m-th sample is updated
Figure FDA0003103615780000074
In that
Figure FDA0003103615780000075
Can obtain the real-time residual life distribution at the current moment on the basis
Figure FDA0003103615780000076
Thereby continuously obtaining new degradation characteristic incrementThen, the predicted residual life probability density function is updated in real time, and the calculation complexity is reduced;
and 5, predicting the residual life of the gear by considering the residual life prediction model of the degraded state transition:
finally, the average residual life of the gear is as follows:
Figure FDA0003103615780000077
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