CN112326241A - Nuclear power main pump bearing fault early warning method based on fusion degradation index - Google Patents

Nuclear power main pump bearing fault early warning method based on fusion degradation index Download PDF

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CN112326241A
CN112326241A CN202010958398.5A CN202010958398A CN112326241A CN 112326241 A CN112326241 A CN 112326241A CN 202010958398 A CN202010958398 A CN 202010958398A CN 112326241 A CN112326241 A CN 112326241A
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degradation
data
vibration acceleration
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CN112326241B (en
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申中杰
李盼
宫云杰
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Xi'an Intemax Information Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04B—POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B49/00—Control, e.g. of pump delivery, or pump pressure of, or safety measures for, machines, pumps, or pumping installations, not otherwise provided for, or of interest apart from, groups F04B1/00 - F04B47/00
    • F04B49/10—Other safety measures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis

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Abstract

The invention discloses a nuclear power main pump bearing fault early warning method based on fusion degradation indexes, which comprises the following steps: the vibration acceleration sensor is arranged on the shell of the bearing bush of the nuclear power main pump to acquire vibration acceleration data; cleaning missing points, blank points and outliers in the vibration acceleration data; removing data of an amplitude modulation phenomenon caused by variable rotating speed from the vibration acceleration data to obtain quantized vibration acceleration data; extracting high-dimensional degradation features from the quantized vibration acceleration data; extracting a fusion degradation index for monitoring the fault state of a nuclear power main pump bearing from the high-dimensional degradation characteristic; thresholds for different degradation stages are determined based on the fused degradation indicators.

Description

Nuclear power main pump bearing fault early warning method based on fusion degradation index
Technical Field
The invention belongs to the technical field of nuclear power main pump bearing fault detection, and particularly relates to a nuclear power main pump bearing fault early warning method based on fusion degradation indexes.
Background
Nuclear power plant reactor coolant pumps, commonly referred to as primary pumps, are used to drive the coolant around the reactor coolant system, continuously transferring the heat generated in the core to the steam generator secondary side feedwater, while cooling the core, preventing fuel element burnout or burnout, and are critical equipment of the reactor coolant system and pressure boundary. As the main pump of the heart of the nuclear power plant, the running state of the main pump directly relates to the benefit and the nuclear safety of the whole nuclear power plant. According to incomplete statistics, since the 80 s in the 20 th century, nuclear power plants around the world have been shut down for hundreds of nuclear power plants due to main pump failures, which causes significant economic loss. Therefore, the main pump is monitored in real time, and the running state of the main pump is predicted in advance, which is very necessary!
The vibration performance and the operating state of the bearing serving as the core component of the main pump directly reflect the operating state of the main pump. However, at present, monitoring and diagnosis for a nuclear power main pump bearing are very few, and a temperature overrun alarm or a vibration root mean square value threshold alarm mode is generally adopted. These methods are relatively rare, and hardly play a function of early warning, even if the early warning can be performed, the early warning time is within hours, and the method is not enough for the maintenance of nuclear power equipment. The maintenance of the main pump mainly takes 'after maintenance' and 'timing maintenance' as main parts, and the requirements of the intelligent nuclear power industry are difficult to meet.
The problems are solved to a certain extent by 'after maintenance' and 'timing maintenance', but huge economic losses caused by accidental shutdown cannot be controlled, and even safety accidents which are difficult to imagine cannot be controlled; the alarm based on temperature belongs to indirect monitoring, because the equipment is in failure, the abnormal vibration is firstly shown, and the temperature is increased after the abnormal condition is serious. Alarm based on vibration root mean square value threshold belongs to shallow layer analysis, and a fault can be found only if the fault is serious. The maintenance and early warning modes are difficult to predict faults in advance, so that accidents are avoided, and intelligent operation and maintenance service for the nuclear power industry is further impossible.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a nuclear power main pump bearing fault early warning method based on fusion degradation indexes.
The invention aims to realize the purpose through the following technical scheme, and the nuclear power main pump bearing fault early warning method based on the fusion degradation index comprises the following steps:
in the first step, a vibration acceleration sensor is arranged on a shell of a bearing bush of a nuclear power main pump to acquire vibration acceleration data;
in the second step, cleaning missing points, blank points and outliers in the vibration acceleration data;
in the third step, data of an amplitude modulation phenomenon caused by variable rotating speed is removed from the vibration acceleration data to obtain quantized vibration acceleration data;
in the fourth step, extracting high-dimensional degradation characteristics from the quantized vibration acceleration data;
in the fifth step, extracting a fusion degradation index for monitoring the fault state of the nuclear power main pump bearing from the high-dimensional degradation characteristic;
in the sixth step, thresholds for different degradation stages are determined based on the fused degradation indicators.
In the method, in the second step, the missing point in the vibration acceleration data is cleaned through polynomial fitting, and the sample x with the serial number of 1, 2, …, n before the missing point1，x2，…，xnFitting on the basis of data to solve p (t)i)＝a0+a1ti+a2ti 2+…+anti nAnd make it possible to
Figure BDA0002676894500000021
And is composed of p (t)i) Substitution of deletion points, wherein tiTo fit the data samples, p (t)i) Is tiFitting data of point correspondences, a0，a1，…anAre fitting coefficients.
In the method, in the second step, when the blank point in the vibration acceleration data is cleaned, whether 2 or more continuous points with zero amplitude exist is judged, and x isi＝xi+1…, if present, successive sample points with zero amplitude are removed from the vibration acceleration data.
In the method, in the second step, when the outliers in the vibration acceleration data are cleaned, the normal data xiThe range is as follows:
Figure BDA0002676894500000022
mean value
Figure BDA0002676894500000023
The estimation method comprises the following steps:
Figure BDA0002676894500000024
the standard deviation sigma estimation method comprises the following steps:
Figure BDA0002676894500000025
the outlier determination method is as follows:
Figure BDA0002676894500000026
sample-by-sample judgment of sample xiWhether or not it is in the interval
Figure BDA0002676894500000027
In addition, judgment of βiNot more than 3, or betai> 3, if sample xiCorresponding betaiLess than or equal to 3, then sample xiIs a normal point, otherwise if sample xiCorresponding betai> 3, then sample xiFor outliers, a cleaning process is required.
In the method, the mean value of a plurality of samples adjacent to the outlier is taken to replace the value, and the expression is as follows:
Figure BDA0002676894500000028
where N is an outlier sample xiThe total number of adjacent sample points taken, i is the sample number.
In the method, the data of amplitude modulation phenomenon caused by variable rotating speed is removed from the vibration acceleration data comprises,
for vibration data x containing variable rotating speed working conditioniTaking its Hilbert envelope ei，ei＝|xi+jH(xi) L, where H (x)i) Representing debounce data xiThe Hilbert transform of (1); x is the number ofi+jH(xi) Is a complex number, | xi+jH(xi) | represents taking the complex number xi+jH(xi) The die of (a) is used,
for envelope data eiThe amplitudes of (a) are sorted in descending order, and the mean value μ of the first m maximum amplitude values is obtained:
Figure BDA0002676894500000031
therein, max (e)i)mIndicating packet access data eiThe sum of the first m values with the maximum amplitude values, and the quantized vibration acceleration data x 'after the influence of the rotation speed factors is eliminated'iThe following formula is used to obtain:
Figure BDA0002676894500000032
in the method, in the fourth step, in extracting high-dimensional degradation features from the quantized vibration acceleration data, the high-dimensional degradation features include:
kurtosis characteristic:
Figure BDA0002676894500000033
wherein
Figure BDA0002676894500000034
The waveform index is as follows:
Figure BDA0002676894500000035
kurtosis index:
Figure BDA0002676894500000036
wherein
Figure BDA0002676894500000037
Margin indexes are as follows:
Figure BDA0002676894500000038
frequency domain feature 3:
Figure BDA0002676894500000039
wherein
Figure BDA00026768945000000310
Frequency domain feature 4:
Figure BDA00026768945000000311
wherein
Figure BDA00026768945000000312
Frequency domain characteristics 12:
Figure BDA00026768945000000313
wherein
Figure BDA00026768945000000314
Wherein i is a vibration acceleration data serial number, and n is the total number of data samples; u. ofiRepresenting quantized vibration acceleration data samples; y isjRepresenting quantized vibration acceleration data uiObtaining frequency domain data after FFT; j is quantized vibration acceleration data uiNumber of frequency domainsAccording to yjN denotes quantized vibration acceleration data uiThe total number of samples of the frequency domain data of (a); f. ofjRepresenting frequency domain data yjFrequency components in the frequency spectrum.
In the method, in the five steps, the fusion degradation index extracted from the high-dimensional degradation characteristic for monitoring the fault state of the nuclear power main pump bearing comprises,
solving all inter-sample cosine similarity matrix CS and sample cosine similarity mean vector in high-dimensional degraded feature set X
Figure BDA00026768945000000315
According to the cosine similarity matrix CS and the sample cosine similarity mean vector
Figure BDA00026768945000000316
Calculating a similarity matrix S;
calculating to obtain an initial neighborhood parameter K according to the similarity matrix S;
obtaining Euclidean distance D between all samples in high-dimensional degradation feature set XeDistance D from geodesic lineg；
Calculating the local density P and the global density mean value among all samples in the high-dimensional degradation feature set X
Figure BDA0002676894500000041
Calculating the ratio of the local Euclidean distance sum to the local geodesic distance sum to obtain the local popular curvature Q and the global popular curvature
Figure BDA0002676894500000042
Simultaneously calculating the ratio of the Euclidean distance to the geodesic distance to obtain D';
adjusting the initial neighborhood parameter K based on a neighborhood parameter adjusting method to obtain an adjusted neighborhood parameter KcSimultaneously, the Euclidean distance matrix D is updated by the ratio D' of the Euclidean distance to the geodesic distanceeObtaining an updated Euclidean distance matrix De′；
Based onThe adjustment neighborhood parameter KcAnd the updated Euclidean distance matrix DeExtracting low-dimensional characteristics obtained after high-dimensional degradation characteristic mapping through a local linear embedding method, and solving to obtain an objective function through calculating a Lagrange multiplier method: MY (myb disease)T＝λ′YTSolving the formula to obtain the eigenvector Y and eigenvalue lambda 'of the eigenvector matrix M'
Figure BDA0002676894500000043
Is constrained to
Figure BDA0002676894500000044
M＝(Ii-wi)(Ii-wi)T，
Where W represents the set of all sample weight vectors; x is the number ofiAnd xjTwo samples in the high-dimensional degradation characteristic X are respectively; wiIs a sample xiA weight vector of (a); w is aijIs wiThe sample point of (1); i isiRepresenting D-dimensional vectors of all 1; m is a characteristic matrix, and M is a characteristic matrix,
y is a matrix formed by eigenvectors of the feature matrix M, and the eigenvalue decomposition of the matrix M is carried out to obtain a low-dimensional representation Y of the high-dimensional degradation feature X: x → Y ═ Y2，y3，...，yd+1]Wherein y isiI 2, 3., d +1, representing the eigenvectors corresponding to the first d non-zero eigenvalues of the matrix M, and combining the eigenvalues y2The fusion degradation index is used as a fault state monitoring index for the nuclear power main pump bearing.
In the method, the cosine similarity matrix CS is a symmetric matrix, and the solving formula is as follows:
Figure BDA0002676894500000045
in the formula, z is a characteristic dimension serial number, D is a dimension of a high-dimensional degradation characteristic, and i, j are sample serial numbers; CS (i, j) is a sample in the cosine similarity matrix CS; x is the number ofiAnd xjTwo samples in the high-dimensional degradation feature X respectively,
Figure BDA0002676894500000046
and
Figure BDA0002676894500000047
are respectively a sample xiAnd sample xjThe number of sample points in (1) is,
geodesic distance D between all samples of high-dimensional degradation characteristics of bearinggThe iterative expression of (c) is:
dg(i，j)＝min{dg(i，j)，dg(i，m)+dg(m，j)}
in the formula, min is the minimum value; i, j and m are sample serial numbers, and i, j and m are different from each other; n is the total number of samples; dg(i, j) is the geodesic distance DgThe sample of (1).
In the method, in the sixth step, determining the thresholds of different degradation stages based on the fusion degradation indicator includes exponentially fitting a fusion degradation indicator curve to determine threshold intervals of different degradation states: (t) ═ λ + β exp (η t), where: lambda, beta, eta are parameters of the exponential function, and are obtained by fitting the fusion degradation index.
Advantageous effects
According to the method, blank data and outlier data in the complex vibration acceleration data are cleaned through a data cleaning method, and the amplitude modulation phenomenon of the vibration acceleration data generated under the variable-speed working condition is cleaned, so that the reliability of the vibration acceleration data to be analyzed is ensured; based on the cleaned vibration acceleration data, a nuclear power main pump bearing fusion degradation index is extracted through the improved local linear embedding method, the threshold values of different degradation states are determined on the basis, the degradation states of the bearings can be visually depicted in real time based on different threshold value intervals determined by the threshold values, the monitoring reliability of the nuclear power main pump bearing is effectively improved, and early warning is timely carried out on the occurrence of faults.
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Various advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic flow chart of a nuclear power main pump bearing fault early warning method based on fusion degradation indexes, provided by the invention;
FIG. 2 is a nuclear power main pump bearing original vibration acceleration diagram of a nuclear power main pump bearing fault early warning method based on fusion degradation indexes provided by the invention;
FIG. 3 is a vibration acceleration diagram after cleaning of a nuclear power main pump bearing fault early warning method based on fusion degradation indexes provided by the invention;
FIG. 4 is a square root amplitude diagram of 5 rotating speed conditions of a nuclear power main pump bearing of the nuclear power main pump bearing fault early warning method based on fusion degradation indexes provided by the invention;
FIG. 5 is a nuclear power main pump bearing fusion degradation index full-life trend curve, index fitting and threshold interval diagram of the nuclear power main pump bearing fusion degradation index fault early warning method based on the fusion degradation index.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 5. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a flowchart of a nuclear power main pump bearing fault early warning method based on a fusion degradation index, and as shown in fig. 1, the nuclear power main pump bearing fault early warning method based on the fusion degradation index includes the following steps:
in the first step S100, a vibration acceleration sensor is arranged on a shell of a bearing bush of a nuclear power main pump to acquire vibration acceleration data;
in a second step S200, cleaning missing points, blank points and outliers in the vibration acceleration data;
in a third step S300, data of an amplitude modulation phenomenon caused by variable rotating speed is removed from the vibration acceleration data to obtain quantized vibration acceleration data;
in a fourth step S400, extracting high-dimensional degradation features from the quantized vibration acceleration data;
in a fifth step S500, extracting a fusion degradation index for monitoring the fault state of the nuclear power main pump bearing from the high-dimensional degradation characteristics;
in a sixth step S600, thresholds for different degradation stages are determined based on the fused degradation indicators.
In a preferred embodiment of the method, in the second step S200, the missing point in the vibration acceleration data is cleaned by polynomial fitting, and the sample x with the serial number 1, 2, …, n before the missing point1，x2，…，xnFitting on the basis of data to solve p (t)i)＝a0+a1ti+a2ti 2+…+anti nAnd make it possible to
Figure BDA0002676894500000061
And is composed of p (t)i) Substitution of deletion points, wherein tiTo fit the data samples, p (t)i) Is tiFitting data of point correspondences, a0，a1，…anAre fitting coefficients.
In a preferred embodiment of the method, in the second step S200, when the blank point in the vibration acceleration data is cleaned, it is determined whether there are 2 or more continuous points with zero amplitude, xi＝xi+1…, if present, successive sample points with zero amplitude are removed from the vibration acceleration data.
In a preferred embodiment of the method, in the second step S200, when the outliers in the vibration acceleration data are cleaned, the normal data x areiThe range is as follows:
Figure BDA0002676894500000062
mean value
Figure BDA0002676894500000063
The estimation method comprises the following steps:
Figure BDA0002676894500000064
the standard deviation sigma estimation method comprises the following steps:
Figure BDA0002676894500000071
the outlier determination method is as follows:
Figure BDA0002676894500000072
sample-by-sample judgment of sample xiWhether or not it is in the interval
Figure BDA0002676894500000073
In addition, judgment of βiNot more than 3, or betai> 3, if sample xiCorresponding betaiLess than or equal to 3, then sample xiIs a normal point, otherwise if sample xiCorresponding betai> 3, then sample xiFor outliers, a cleaning process is required.
In a preferred embodiment of the method, the value is replaced by the mean value of several samples adjacent to the outlier, expressed as:
Figure BDA0002676894500000074
where N is an outlier sample xiThe total number of adjacent sample points taken, i is the sample number.
In a preferred embodiment of the method, the data for removing the amplitude modulation phenomenon caused by the variable rotation speed from the vibration acceleration data comprises,
for vibration data x containing variable rotating speed working conditioniTaking its Hilbert envelope ei，ei＝|xi+jH(xi) L, where H (x)i) Representing debounce data xiThe Hilbert transform of (1); x is the number ofi+jH(xi) Is a complex number, | xi+jH(xi) | represents taking the complex number xi+jH(xi) The die of (a) is used,
for envelope data eiThe amplitudes of (a) are sorted in descending order, and the mean value μ of the first m maximum amplitude values is obtained:
Figure BDA0002676894500000075
therein, max (e)i)mIndicating packet access data eiThe sum of the first m values with the maximum amplitude values, and the quantized vibration acceleration data x 'after the influence of the rotation speed factors is eliminated'iThe following formula is used to obtain:
Figure BDA0002676894500000076
in a preferred embodiment of the method, in the fourth step S400, in extracting high-dimensional degradation features from the quantized vibration acceleration data, the high-dimensional degradation features include:
kurtosis characteristic:
Figure BDA0002676894500000077
wherein
Figure BDA0002676894500000078
The waveform index is as follows:
Figure BDA0002676894500000079
kurtosis index:
Figure BDA00026768945000000710
wherein
Figure BDA00026768945000000711
Margin indexes are as follows:
Figure BDA0002676894500000081
frequency domain feature 3:
Figure BDA0002676894500000082
wherein
Figure BDA0002676894500000083
Frequency domain feature 4:
Figure BDA0002676894500000084
wherein
Figure BDA0002676894500000085
Frequency domain bitAnd (5) performing characterization:
Figure BDA0002676894500000086
wherein
Figure BDA0002676894500000087
Wherein i is a vibration acceleration data serial number, and n is the total number of data samples; u. ofiRepresenting quantized vibration acceleration data samples; y isjRepresenting quantized vibration acceleration data uiObtaining frequency domain data after FFT; j is quantized vibration acceleration data uiOf frequency domain data yjN denotes quantized vibration acceleration data uiThe total number of samples of the frequency domain data of (a); f. ofjRepresenting frequency domain data yjFrequency components in the frequency spectrum.
In a preferred embodiment of the method, in the fifth step S500, extracting a fusion degradation index for monitoring a fault state of a bearing of the nuclear power main pump from the high-dimensional degradation features includes,
solving all inter-sample cosine similarity matrix CS and sample cosine similarity mean vector in high-dimensional degraded feature set X
Figure BDA0002676894500000088
According to the cosine similarity matrix CS and the sample cosine similarity mean vector
Figure BDA0002676894500000089
Calculating a similarity matrix S;
calculating to obtain an initial neighborhood parameter K according to the similarity matrix S;
obtaining Euclidean distance D between all samples in high-dimensional degradation feature set XeDistance D from geodesic lineg；
Calculating the local density P and the global density mean value among all samples in the high-dimensional degradation feature set X
Figure BDA00026768945000000810
Computing local EuclideanThe ratio of the sum of the distances to the sum of the local geodesic distances is used to obtain the local popular curvature Q and the global popular curvature
Figure BDA00026768945000000811
Simultaneously calculating the ratio of the Euclidean distance to the geodesic distance to obtain D';
adjusting the initial neighborhood parameter K based on a neighborhood parameter adjusting method to obtain an adjusted neighborhood parameter KcSimultaneously, the Euclidean distance matrix D is updated by the ratio D' of the Euclidean distance to the geodesic distanceeObtaining an updated Euclidean distance matrix De′；
Based on the adjustment neighborhood parameter KcAnd the updated Euclidean distance matrix DeExtracting low-dimensional characteristics obtained after high-dimensional degradation characteristic mapping through a local linear embedding method, and solving to obtain an objective function through calculating a Lagrange multiplier method: MY (myb disease)T＝λ′YTSolving the formula to obtain the eigenvector Y and eigenvalue lambda 'of the eigenvector matrix M'
Figure BDA0002676894500000091
Is constrained to
Figure BDA0002676894500000092
M＝(Ii-wi)(Ii-wi)T，
Where W represents the set of all sample weight vectors; x is the number ofiAnd xjTwo samples in the high-dimensional degradation characteristic X are respectively; w is aiIs a sample xiA weight vector of (a); w is aijIs wiThe sample point of (1); i isiIs represented as1A D-dimensional vector of (1); m is a characteristic matrix, and M is a characteristic matrix,
y is a matrix formed by eigenvectors of the feature matrix M, and the eigenvalue decomposition of the matrix M is carried out to obtain a low-dimensional representation Y of the high-dimensional degradation feature X: x → Y ═ Y2，y3，...，yd+1]Wherein y isiI 2, 3., d +1, representing the first d non-zero eigenvalues of the matrix MCorresponding feature vector, feature y2The fusion degradation index is used as a fault state monitoring index for the nuclear power main pump bearing.
In the preferred embodiment of the method, the cosine similarity matrix CS is a symmetric matrix, and the formula is as follows:
Figure BDA0002676894500000093
in the formula, z is a characteristic dimension serial number, D is a dimension of a high-dimensional degradation characteristic, and i, j are sample serial numbers; CS (i, j) is a sample in the cosine similarity matrix CS; x is the number ofiAnd xjTwo samples in the high-dimensional degradation feature X respectively,
Figure BDA0002676894500000094
and
Figure BDA0002676894500000095
are respectively a sample xiAnd sample xjThe number of sample points in (1) is,
geodesic distance D between all samples of high-dimensional degradation characteristics of bearinggThe iterative expression of (c) is:
dg(i，j)＝min{dg(i，j)，dg(i，m)+dg(m，j)}
in the formula, min is the minimum value; i, j and m are sample serial numbers, and i, j and m are different from each other; n is the total number of samples; dg (i, j) is the geodesic distance DgThe sample of (1).
In a preferred embodiment of the method, in the sixth step S600, determining the thresholds of the different degradation stages based on the fused degradation indicator includes exponentially fitting a fused degradation indicator curve to determine the threshold intervals of the different degradation states: (t) ═ λ + β exp (η t), where: lambda, beta, eta are parameters of the exponential function, and are obtained by fitting the fusion degradation index.
In a preferred embodiment, a nuclear power main pump bearing fault early warning method based on fusion degradation indexes comprises the following steps:
s100, collecting vibration acceleration data by a vibration acceleration sensor on a shell of a bearing bush of a nuclear power main pump;
s200, cleaning missing points, blank points and outliers contained in the acquired vibration acceleration data;
s300, eliminating an amplitude modulation phenomenon caused by variable rotating speed from the vibration acceleration data to obtain quantized vibration acceleration data;
s400, extracting high-dimensional degradation features from the quantized vibration acceleration data;
s500, extracting a fusion degradation index from the high-dimensional degradation characteristic, and using the fusion degradation index for monitoring the fault state of the nuclear power main pump bearing;
s600, determining thresholds of different degradation stages based on the fusion degradation indexes.
In step S100, vibration acceleration data x of the nuclear power main pump bearing is measured by using a vibration acceleration sensoriAnd (5) collecting, wherein i is a vibration acceleration data serial number.
In step S201, blank data generally appears in the operation process and the start-stop stage of the main pump, and is collected by the vibration acceleration sensor, and such data may be divided into two types, i.e., single-point missing data and continuous blank invalid data.
1 for single-point missing data, fitting and padding are performed on the basis of a plurality of samples before the missing data by a polynomial fitting method, namely, at sample x with the sequence numbers 1, 2, …, n1，x2，…，xnOn the basis of data, solving a polynomial shown in the following and calculating the polynomial from p (t)i) Instead of the blank spot:
p(ti)＝a0+a1ti+a2ti 2+…+anti nand make it possible to
Figure BDA0002676894500000101
In the formula, tiTo fit data sample numbers, p (t)i) Is tiFitting data of the point correspondences.
2 for connectingBlank-continuing invalid points are determined by judging whether continuous 2 and more than 2 points with zero amplitude, i.e. xi＝xi+1…, if present, successive sample points with zero amplitude are removed from the vibration acceleration data.
In step S202, due to the non-stationarity of the vibration data, the normal vibration data contains many outliers, and the cleaning of the outliers is determined by the following improved ralay criterion, and the detailed steps are as follows:
1 estimating the Normal data amplitude Range
The present disclosure is based on an improved method of Laviand's criterion to determine the range of normal data. Due to the existence of noise and outliers in the vibration data, the true mean and standard deviation of the bearing vibration data are unknown and need to be estimated by statistical methods as shown below:
normal data xiThe range is as follows:
Figure BDA0002676894500000111
mean value
Figure BDA0002676894500000112
The estimation method comprises the following steps:
Figure BDA0002676894500000113
the standard deviation sigma estimation method comprises the following steps:
Figure BDA0002676894500000114
2 the outlier judgment method is as follows:
Figure BDA0002676894500000115
sample by sample, judge sample xiWhether or not it is in the interval
Figure BDA0002676894500000116
Other than, i.e. determining βiNot more than 3, or betai> 3, if sample xiCorresponding betaiLess than or equal to 3, then sample xiIs a normal point, otherwise if sample xiCorresponding betai> 3, then sample xiFor outliers, a cleaning process is needed, and in order to ensure the reliability of the substitute data as much as possible, the mean value of several samples adjacent to the substitute data can be used to substitute the value, and the expression is:
Figure BDA0002676894500000117
wherein N is an outlier sample xiThe total number of adjacent sample points taken, i is the sample number.
In step S300, for the vibration data amplitude modulation phenomenon caused by the variable rotation speed condition, the cleaning method is as follows:
for vibration data x containing variable rotating speed working conditioniTaking its Hilbert envelope eiThe formula is shown as follows:
ei＝|xi+jH(xi)|
in the formula, H (x)i) Representing debounce data xiThe Hilbert transform of (1); x is the number ofi+jH(xi) Is a complex number, | xi+jH(xi) | represents taking the complex number xi+jH(xi) The die of (1).
For envelope data eiThe amplitudes of (a) are sorted in descending order, and the mean value μ of the first m maximum amplitude values is obtained:
Figure BDA0002676894500000118
in the formula, max (e)i)mIndicating packet access data eiThe sum of the first m maximum amplitude values of (a) is used to reduce the interference caused by non-stationary factors in the vibration data by averaging the plurality of amplitude values.
Quantized vibration acceleration data x after eliminating influence of rotating speed factorsiThe following formula is used to obtain:
Figure BDA0002676894500000121
in step S400, high-dimensional degradation features are extracted. Vibration acceleration data in three directions can be collected through a triaxial vibration acceleration sensor, and after the cleaning in the steps S200-S300, a 15-dimensional high-dimensional degradation feature X [ X ] shown in the specification can be extracted1，X2，X3，…，X15]：
Reference numerals Feature(s) Reference numerals Feature(s)
X1 Characteristic of kurtosis of x-axis X9 y-axis waveform index
X2 x-axis waveform index X10 y-axis kurtosis index
X3 Kurtosis index of x-axis X11 Frequency domain feature 3 of the y-axis
X4 Margin index of x-axis X12 Frequency domain feature 4 of the y-axis
X5 Frequency domain feature 3 of the x-axis X13 z-axis waveform index
X6 Frequency domain feature 4 of the x-axis X14 z-axis frequency domain feature 3
X7 Frequency domain feature 12 of the x-axis X15 z-axis frequency domain feature 4
X8 Kurtosis feature of y-axis
The features in the table above are represented as follows:
kurtosis characteristic:
Figure BDA0002676894500000122
wherein
Figure BDA0002676894500000123
The waveform index is as follows:
Figure BDA0002676894500000124
kurtosis index:
Figure BDA0002676894500000125
wherein
Figure BDA0002676894500000126
Margin indexes are as follows:
Figure BDA0002676894500000127
frequency domain feature 3:
Figure BDA0002676894500000128
wherein
Figure BDA0002676894500000129
Frequency domain feature 4:
Figure BDA0002676894500000131
wherein
Figure BDA0002676894500000132
Frequency domain characteristics 12:
Figure BDA0002676894500000133
wherein
Figure BDA0002676894500000134
In the above calculation expression, i is a vibration acceleration data serial number, and n is a total number of data samples; u. ofiRepresenting a vibration acceleration data sample; y isjRepresenting vibration acceleration data uiObtaining frequency domain data after FFT; j is vibration acceleration data uiOf frequency domain data yjN denotes vibration acceleration data uiOf the frequency domain dataTotal number of samples of (a); f. ofjRepresenting frequency domain data yjFrequency components in the frequency spectrum.
In particular, when the vibration acceleration sensor is uniaxial, the degradation feature X can be extracted1～X77 degradation features in total are taken as high-dimensional degradation features; when the vibration acceleration sensor is in two axial directions, the degradation characteristic X can be extracted1～X12A total of 7 degradation features are taken as high-dimensional degradation features.
In step S500, fusion degradation indexes are extracted from the high-dimensional degradation characteristics, and the fusion degradation indexes are used for monitoring the fault state of a bearing of a transmission system of the wind driven generator, and the specific process is as follows:
s510, setting initial neighborhood parameters, the general steps are as follows:
s511, solving all inter-sample cosine similarity matrix CS and sample cosine similarity mean vector in the high-dimensional degradation feature set X
Figure BDA0002676894500000135
S512, according to the cosine similarity matrix CS and the sample cosine similarity mean vector in the step S511
Figure BDA0002676894500000136
Calculating a similarity matrix S;
and S513, calculating to obtain an initial neighborhood parameter K according to the similarity matrix S obtained in the step S512.
More specifically, in step S511, the cosine similarity matrix CS is a symmetric matrix, and the solving formula is as follows:
Figure BDA0002676894500000137
in the formula, z is a characteristic dimension serial number, D is a dimension of a high-dimensional degradation characteristic, and i, j are sample serial numbers; CS (i, j) is a sample in the cosine similarity matrix CS; x is the number ofiAnd xjTwo samples in the high-dimensional degradation feature X respectively,
Figure BDA0002676894500000138
and
Figure BDA0002676894500000139
are respectively a sample xiAnd sample xjSample point(s) in (c).
More specifically, in step S512, the initial neighborhood parameter matrix S may be set as:
Figure BDA0002676894500000141
in the formula, i and j are sample serial numbers, and n is the total number of samples;
Figure BDA0002676894500000142
the mean value of cosine similarity of the ith sample and all other samples; s (i, j) is the sample in the initial neighborhood parameter matrix S.
If sample xiAnd sample xjThe cosine similarity between them is larger than the mean value of the cosine similarities between all the adjacent samples
Figure BDA0002676894500000143
I.e. consider sample xiAnd sample xjGreater similarity, sample xjAt sample xiNeighbor position, otherwise sample xjNot sample xiIs close to (2).
More specifically, in step S513, sample xiThe neighborhood parameter matrix K of (a) may be expressed as:
Figure BDA0002676894500000144
in the formula, i and j are sample serial numbers, and n is the total number of samples; s (i, j) is a sample in the initial neighborhood parameter matrix S; k is a radical ofiFor a sample in the neighborhood parameter matrix K, a sample x is representediThe initial neighborhood parameter of.
By the method, the initial neighborhood parameter K of all samples can be obtained[k1，k2，...，kn]。
S520, neighborhood parameter adjustment:
the density distribution condition of the high-dimensional degradation features has a large influence on the setting of neighborhood parameters, if the density of the local range of the sample is large, the Euclidean distance between the sample point and other points in the neighborhood range is small, the similarity is high, and otherwise, the similarity between the sample point and other points in the neighborhood range is low. Meanwhile, the size of the intrinsic prevalence curvature of the high-dimensional degradation feature also has a large influence on the neighborhood parameters, for example, at the position of the large prevalence curvature, in order to ensure that the correct low-dimensional feature is extracted, a small parameter value should be set for the neighborhood parameters. The estimation of the local popular curvature is estimated by adopting the ratio of the Euclidean distance between two samples and the geodesic distance, and the popular curvature is smaller when the ratio is larger, and the popular curvature is larger otherwise. Therefore, for the adjustment of the initial neighborhood parameters, it is necessary to consider the density distribution of the high-dimensional degradation features and the intrinsic prevalence curvature of the high-dimensional degradation features. According to the method, the distribution density of the high-dimensional degradation characteristic sample and the intrinsic prevalence curvature of the high-dimensional degradation characteristic are estimated, so that the neighborhood parameters are adjusted more accurately.
Based on the relevant parameters found in the step S510, the neighborhood parameter adjustment method provided by the present invention includes the following steps:
s521, solving the Euclidean distance D between all samples in the high-dimensional degradation feature set XeDistance D from geodesic lineg；
S522, solving the local density P and the global density mean value among all samples in the high-dimensional degradation feature set X
Figure BDA0002676894500000151
S523, calculating the ratio of the sum of the local Euclidean distances to the sum of the local geodesic distances to obtain a local popular curvature Q and a global popular curvature
Figure BDA0002676894500000152
Simultaneously calculating the ratio of the Euclidean distance to the geodesic distance to obtain D';
s524, adjusting the initial neighborhood parameter K by a neighborhood parameter adjusting method to obtain KcSimultaneously, the Euclidean distance matrix D is updated by the ratio D' of the Euclidean distance to the geodesic distanceeObtaining an updated Euclidean distance matrix De。
In the step of S521,
the geodesic distance D between all samples of the high-dimensional degradation characteristics of the bearinggThe iterative expression of (c) is:
dg(i，j)＝min{dg(i，j)，dg(i，m)+dg(m，j)}
in the formula, min is the minimum value; i, j and m are sample serial numbers, and i, j and m are different from each other; n is the total number of samples; dg (i, j) is the geodesic distance DgThe sample of (1).
More specifically, in step S522, sample xiThe local density vector p, based on the gaussian kernel probability density estimation, is given by the following formula:
Figure BDA0002676894500000153
in the formula, n is the total number of samples, i, j is the serial number of the samples; p is a radical ofiSamples in the local density vector P; k is a radical ofiIs a sample in the preliminary neighborhood parameter K; dc(i, j) is sample xiAnd sample xjThe euclidean distance between them.
Global density of high dimensional degradation features, mean estimated from Gaussian kernel probability density
Figure BDA0002676894500000154
Represented by the formula:
Figure BDA0002676894500000155
in the formula, n is the total number of samples, and i is the serial number of the sample point; p is a radical ofiSamples in the local density vector P.
Based on heightLocal density vector P and global density obtained by Gaussian kernel probability density estimation method
Figure BDA0002676894500000156
The comparison of (a) may be performed to adjust the preliminary adaptive neighborhood parameters.
More specifically, in step S523, the local prevalence curvature matrix Q of the high-dimensional degradation feature is a ratio of a sum of euclidean distances and a sum of geodesic distances in the sample neighborhood range, and an expression is as follows:
Figure BDA0002676894500000161
in the formula, i and j are sample serial numbers; de(i, j) and dg(i, j) are Euclidean distance matrices D, respectivelyeDistance matrix D from geodesic linegThe sample of (1); k is a radical ofiIs a sample in the preliminary neighborhood parameter K; q. q.siAre samples in the local prevalence curvature matrix Q.
Global prevalence curvature, as follows:
Figure BDA0002676894500000162
in the formula, i is a sample serial number, and n is the total number of samples; q (i) are samples in the local prevalence curvature matrix Q.
The local popular curvature can be estimated by calculating the ratio of the sum of the local Euclidean distances to the sum of the local geodesic distances, and the ratio of the local popular curvature to the global popular curvature obtained by the method can be used for adjusting the initial self-adaptive neighborhood parameters.
Meanwhile, the ratio of the Euclidean distance corresponding to each sample to the geodesic distance is obtained to obtain D ', and the formula is D' (i, j) ═ De(i，j)/dg(i, j), if the ratio d' (i, j) is greater than a constant γ, the sample x is considered to beiAnd sample xjSample d in Euclidean distance matrix on the same local popular surface with smaller folding surfacee(i, j) the value is unchanged; if the ratio d' (i, j) is less than a constant gamma, the sample x is considered to beiAnd sample xjOn two popular surfaces with larger folding surfaces, in this case deUpdating Euclidean distance matrix D when (i, j) ∞eI.e. the sample x can be excludediAnd sample xjThe probability of becoming a neighborhood is effectively ensured by the method, the extracted low-dimensional features do not coincide with samples at the position where the curvature of the streamline is large, and the value of gamma is set by experience.
More specifically, in step S524, based on the obtained parameters, the neighborhood parameter adjusting method includes the following steps:
Figure BDA0002676894500000163
in the formula, i is a sample serial number; k is a radical ofiIs a sample in the preliminary neighborhood parameter K;
Figure BDA0002676894500000164
is the adjusted neighborhood parameter KcThe sample of (1); floor (·) denotes round down; q. q.siAre samples in the local prevalence curvature matrix Q; p is a radical ofiSamples in the local density vector P.
S530 fusion degradation index extraction:
adjusting neighborhood parameter K obtained based on part S520cAnd updating the Euclidean distance De' extracting low-dimensional features obtained after mapping of high-dimensional degradation features by a local linear embedding method. Under the following loss function and weight constraint conditions, solving to obtain an objective function by calculating a Lagrange multiplier method: MY (myb disease)TThis equation is solved to obtain an eigenvector Y and eigenvalue λ 'of the eigenvector matrix M'
Figure BDA0002676894500000171
Is constrained to
Figure BDA0002676894500000172
M＝(Ii-wi)(Ii-wi)T
Where W represents the set of all sample weight vectors; x is the number ofiAnd xjTwo samples in the high-dimensional degradation characteristic X are respectively; w is aiIs a sample xiA weight vector of (a); w is aijIs wiThe sample point of (1); i isiRepresenting D-dimensional vectors of all 1; m is a feature matrix.
And Y is a matrix formed by eigenvectors of the feature matrix M, in order to reduce the high-dimensional data to d dimensions, the eigenvectors corresponding to the minimum d non-zero eigenvalues of M are taken, and eigenvalue decomposition is carried out on the matrix M to obtain the low-dimensional representation Y of the high-dimensional degradation feature X: x → Y ═ Y2，y3，...，yd+1]Wherein y isiI is 2, 3, …, d +1, represents the eigenvector corresponding to the first d non-zero eigenvalues of the matrix M, and combines the eigenvalues y with the eigenvalues y2The fusion degradation index extracted by the method is used for monitoring the fault state of the nuclear power main pump bearing.
Step S600, exponentially fitting and fusing degradation index curves, and determining different degradation state threshold intervals according to experience:
f(t)＝λ+βexp(ηt)
in the formula: lambda, beta, eta are parameters of the exponential function, and are obtained by fitting the fusion degradation index.
Empirically determining four degradation stages marked S of different degradation states of the bearing1、S2、S3、S4Wherein S is1In the normal operation stage, the normal wear period with the longest operation time is adopted; s2、S3In the weak fault stage and the deep fault development stage, maintenance personnel need to provide proper maintenance to prevent the bearing from being damaged more seriously; s4In the failure stage, the bearing can not work normally because the fault degree is too serious, and the division threshold is marked as x1、χ2、χ3. The corresponding relationship is shown in the following table:
the corresponding interval thresholds are shown in the following table.
Degradation phase and threshold interval
Figure BDA0002676894500000173
Example 1 to facilitate an understanding of the disclosed embodiments
In the step S100, vibration acceleration data are collected, and the data duration of the vibration acceleration data of a section of acceleration life test collected on a certain type of nuclear power main pump bearing is about 150 hours. As shown in fig. 2, there are many blank data and a large number of outliers in the segment of data, which need to be cleaned.
In step S200, deletion, blank spot, outlier cleaning:
step S201, cleaning missing data and blank invalid data:
1, for single-point missing data, performing polynomial fitting on the basis of a plurality of samples before the missing data by a polynomial fitting method, and filling the missing data. In this embodiment, the first 30 samples of the missing data are taken for polynomial fitting, i.e. the following polynomial is solved, and p (t) is used as a basisi) Substitution deletion points:
p(ti)＝a0+a1ti+a2ti 2+…+anti nand make it possible to
Figure BDA0002676894500000181
Wherein t isiTo fit data sample numbers, p (t)i) Is tiFitting data of the point correspondences.
2 for continuous blank invalid points, judging whether continuous 2 and more than 2 points with zero amplitude exist, namely xi＝xi+1…, if present, successive null sample points with zero amplitude are removed from the vibration acceleration data.
Step S202, outlier cleaning:
1 estimating the Normal data amplitude Range
For vibration acceleration data x with outliersiDetermining the range of normal data based on the Laplace criterion:
normal data xiThe range is as follows:
Figure BDA0002676894500000182
wherein the mean value
Figure BDA0002676894500000183
Standard deviation of
Figure BDA0002676894500000184
n is vibration acceleration data xiThe number of samples of (1).
2 the outlier judgment method is as follows:
Figure BDA0002676894500000185
judging whether each sample is in the interval or not one by one
Figure BDA0002676894500000186
Within, i.e. determining betaiNot more than 3, or betai> 3, if sample xiCorresponding betaiLess than or equal to 3, then sample xiIs a normal point, otherwise if sample xiCorresponding betai> 3, then sample xiFor outliers, a cleaning process is needed, and in order to guarantee the reliability of the substitute data as much as possible, the present disclosure replaces the value with the mean value of its neighboring 6 samples, where the expression is:
Figure BDA0002676894500000191
the vibration acceleration data after cleaning is shown in fig. 3, the outliers and blank invalid points contained in the data are effectively cleaned, and the data quality is improved.
Example 2
In step S300, for the amplitude modulation phenomenon of vibration acceleration data caused by the variable-speed working condition, the fault simulation data extracted by the fault simulation experiment of the bearing of the nuclear power main pump under different speed working conditions are used as analysis data, the speed working conditions are 600RPM, 800RPM, 1000RPM, 1200RPM and 1400RPM, the sample length of each speed data is 100, and the specific analysis is as follows:
for vibration data x containing variable rotating speed working conditioniTaking its Hilbert envelope eiAs shown in the following formula:
ei＝|xi+jH(xi)|
in the formula, H (x)i) Representing debounce data xiThe Hilbert transform of (1); x is the number ofi+jH(xi) Is a complex number, | xi+jH(xi) | represents taking the complex number xi+jH(xi) The die of (1).
For envelope data eiThe amplitudes of (a) are sorted in descending order, and the mean value μ of the first m maximum amplitude values is obtained:
Figure BDA0002676894500000192
in the formula, max (e)i)mIndicating packet access data eiThe sum of the first m maximum amplitude values of (a) is used to reduce the interference caused by non-stationary factors in the vibration data by averaging the plurality of amplitude values.
Quantized vibration acceleration data u after eliminating influence of rotating speed factorsiThe following formula is used to obtain:
Figure BDA0002676894500000193
as shown in fig. 4, a time domain square root amplitude diagram extracted from a certain nuclear power main pump bearing fault simulation experiment data under 5 rotation speed conditions shows that amplitude fluctuation caused by the influence of rotation speed on square root amplitude characteristics extracted from processed vibration acceleration data is greatly reduced under different rotation speeds.
In step S400, high-dimensional degenerate features are extractedAnd (5) carrying out characterization. A section of bearing life data of gathering in certain nuclear power main pump bearing accelerated life experiment, data sample length n is 5750, and data are long for about 150 hours. Vibration acceleration data in three directions can be collected through a triaxial vibration acceleration sensor, and after the cleaning in the steps S200-S300, a 15-dimensional high-dimensional degradation feature X [ X ] shown in the specification can be extracted1，X2，X3，…，X15]：
Reference numerals Feature(s) Reference numerals Feature(s)
X1 Characteristic of kurtosis of x-axis X9 y-axis waveform index
X2 x-axis waveform index X10 y-axis kurtosis index
X3 Kurtosis index of x-axis X11 Frequency domain feature 3 of the y-axis
X4 Margin index of x-axis X12 Frequency domain feature 4 of the y-axis
X5 Frequency domain feature 3 of the x-axis X13 z-axis waveform index
X6 Frequency domain feature 4 of the x-axis X14 z-axis frequency domain feature 3
X7 Frequency domain feature 12 of the x-axis X15 z-axis frequency domain feature 4
X8 Kurtosis feature of y-axis
The features of the above table are shown below
Kurtosis characteristic:
Figure BDA0002676894500000201
wherein
Figure BDA0002676894500000202
The waveform index is as follows:
Figure BDA0002676894500000203
kurtosis index:
Figure BDA0002676894500000204
wherein
Figure BDA0002676894500000205
Margin indexes are as follows:
Figure BDA0002676894500000206
frequency domain feature 3:
Figure BDA0002676894500000207
wherein
Figure BDA0002676894500000208
Frequency domain feature 4:
Figure BDA0002676894500000209
wherein
Figure BDA00026768945000002010
Frequency domain features 12
Figure BDA00026768945000002011
Wherein
Figure BDA00026768945000002012
In the above calculation expression, i is a vibration acceleration data serial number, n is a total number of data samples, and n is 5750; u. ofiRepresenting a vibration acceleration data sample; y isjRepresenting vibration acceleration data uiObtaining frequency domain data after FFT; j is vibration acceleration data uiOf frequency domain data yjN denotes vibration acceleration data uiN is 5750; f. ofjRepresenting frequency domain data yjFrequency components in the frequency spectrum.
In particular, when the vibration acceleration sensor is uniaxial, the degradation feature X can be extracted1～X77 degradation features in total are taken as high-dimensional degradation features; when the vibration acceleration sensor is in two axial directions, the degradation characteristic X can be extracted1～X12A total of 7 degradation features are taken as high-dimensional degradation features.
In step S500, fusion degradation indexes are extracted from the high-dimensional degradation characteristics, and the fusion degradation indexes are used for monitoring the fault state of a bearing of a transmission system of the wind driven generator, and the specific process is as follows:
s510, setting initial neighborhood parameters, the general steps are as follows:
s511, solving all inter-sample cosine similarity matrix CS and sample cosine similarity mean vector in the high-dimensional degradation feature set X
Figure BDA0002676894500000216
S512, according to the cosine similarity matrix CS and the sample cosine similarity mean vector in the step S511
Figure BDA0002676894500000217
Calculating a similarity matrix S;
and S513, calculating to obtain an initial neighborhood parameter K according to the similarity matrix S obtained in the step S512.
More specifically, in step S511, the cosine similarity matrix CS is a symmetric matrix, and the solving formula is as follows:
Figure BDA0002676894500000211
in the formula, z is a characteristic dimension serial number, D is a dimension of a high-dimensional degradation characteristic, and i, j are sample serial numbers; CS (i, j) is a sample in the cosine similarity matrix CS; x is the number ofiAnd xjTwo samples in the high-dimensional degradation feature X respectively,
Figure BDA0002676894500000212
and
Figure BDA0002676894500000213
are respectively a sample xiAnd sample xjSample point(s) in (c).
More specifically, in step S512, the initial neighborhood parameter matrix S may be set as:
Figure BDA0002676894500000214
in the formula, i and j are sample serial numbers, and n is the total number of samples;
Figure BDA0002676894500000215
the mean value of cosine similarity of the ith sample and all other samples; s (i, j) is the sample in the initial neighborhood parameter matrix S.
If sample xiAnd sample xjThe cosine similarity between them is larger than the mean value of the cosine similarities between all the adjacent samples
Figure BDA0002676894500000221
I.e. consider sample xiAnd sample xjGreater similarity, sample xjAt sample xiNeighbor position, otherwise sample xjNot sample xiIs close to (2).
More specifically, in step S513, sample xiThe neighborhood parameter matrix K of (a) may be expressed as:
Figure BDA0002676894500000222
in the formula, i and j are sample serial numbers, and n is the total number of samples; s (i, j) is a sample in the initial neighborhood parameter matrix S; k is a radical ofiFor a sample in the neighborhood parameter matrix K, a sample x is representediThe initial neighborhood parameter of.
By the method, the initial neighborhood parameter K [ K ] of all samples can be obtained1，k2，...，kn]。
S520, neighborhood parameter adjustment:
based on the relevant parameters found in the step S510, the neighborhood parameter adjustment method provided by the present invention includes the following steps:
s521, solving the Euclidean distance D between all samples in the high-dimensional degradation feature set XeDistance D from geodesic lineg；
S522, solving the local density P and the global density mean value among all samples in the high-dimensional degradation feature set X
Figure BDA0002676894500000223
S523, calculating the ratio of the sum of the local Euclidean distances to the sum of the local geodesic distances to obtain a local popular curvature Q and a global popular curvature
Figure BDA0002676894500000224
Simultaneously calculating the ratio of the Euclidean distance to the geodesic distance to obtain D';
s524, adjusting the initial neighborhood parameter K by a neighborhood parameter adjusting method to obtain KcSimultaneously, the Euclidean distance matrix D is updated by the ratio D' of the Euclidean distance to the geodesic distanceeObtaining an updated Euclidean distance matrix De′。
More specifically, in step S521, the geodesic distance matrix DgThe distance between the geodesic lines is calculated by an isometric feature mapping (ISOMAP) algorithm;
the geodesic distance D between all samples of the high-dimensional degradation characteristics of the bearinggThe iterative expression of (c) is:
dg(i，j)＝min{dg(i，j)，dg(i，m)+dg(m，j)}
in the formula, min is the minimum value; i, j and m are sample serial numbers, and i, j and m are different from each other; n is the total number of samples; dg (i, j) is the geodesic distance DgThe sample of (1).
Euclidean distance matrix DeThe following formula is used to obtain:
Figure BDA0002676894500000231
in the formula, D is a degradation characteristic dimension, z is a characteristic dimension serial number, and i, j are sample serial numbers;
Figure BDA0002676894500000232
and
Figure BDA0002676894500000233
are respectively a sample xiAnd xjThe sample point of (1); de(i, j) is Euclidean distance matrix DeThe sample of (1).
More specifically, in step S522, sample xiThe local density vector p, based on the gaussian kernel probability density estimation, is given by the following formula:
Figure BDA0002676894500000234
in the formula, n is the total number of samples, i, j is the serial number of the samples; p is a radical ofiSamples in the local density vector P; k is a radical ofiIs a sample in the preliminary neighborhood parameter K; de(i, j) is sample xiAnd sample xjThe euclidean distance between them.
Global density of high dimensional degradation features, mean estimated from Gaussian kernel probability density
Figure BDA0002676894500000235
Represented by the formula:
Figure BDA0002676894500000236
in the formula, n is the total number of samples, and i is the serial number of the sample point; p is a radical ofiSamples in the local density vector P.
Local density vector P and global density obtained based on Gaussian kernel probability density estimation method
Figure BDA0002676894500000237
The comparison of (a) may be performed to adjust the preliminary adaptive neighborhood parameters.
More specifically, in step S523, the local prevalence curvature matrix Q of the high-dimensional degradation feature is a ratio of a sum of euclidean distances and a sum of geodesic distances in the sample neighborhood range, and an expression is as follows:
Figure BDA0002676894500000238
in the formula, i and j are sample serial numbers; de(i, j) and dg(i, j) are Euclidean distance matrices D, respectivelyeDistance matrix D from geodesic linegThe sample of (1); k is a radical ofiIs a sample in the preliminary neighborhood parameter K; q. q.siAre samples in the local prevalence curvature matrix Q.
Global prevalence curvature, as follows:
Figure BDA0002676894500000241
in the formula, i is a sample serial number, and n is the total number of samples; q (i) are samples in the local prevalence curvature matrix Q.
The local popular curvature can be estimated by calculating the ratio of the sum of the local Euclidean distances to the sum of the local geodesic distances, and the ratio of the local popular curvature to the global popular curvature obtained by the method can be used for adjusting the initial self-adaptive neighborhood parameters.
Meanwhile, the ratio of the Euclidean distance corresponding to each sample to the geodesic distance is obtained to obtain D ', and the formula is D' (i, j) ═ De(i，j)/dg(i, j), if the ratio d' (i, j) is greater than a constant γ, the sample x is considered to beiAnd sample xjSample d in Euclidean distance matrix on the same local popular surface with smaller folding surfacee(i, j) the value is unchanged; if the ratio d' (i, j) is less than a constant gamma, the sample x is considered to beiAnd sample xjOn two popular surfaces with larger folding surfacesWhen d is at this timeeUpdating Euclidean distance matrix D when (i, j) ∞eI.e. the sample x can be excludediAnd sample xjThe probability of becoming a neighborhood is effectively ensured by the method, the extracted low-dimensional features do not coincide with samples at the position where the curvature of the streamline is large, and the value of gamma is set by experience.
More specifically, in step S524, based on the obtained parameters, the neighborhood parameter adjusting method includes the following steps:
Figure BDA0002676894500000242
in the formula, i is a sample serial number; k is a radical ofiIs a sample in the preliminary neighborhood parameter K;
Figure BDA0002676894500000243
is the adjusted neighborhood parameter KcThe sample of (1); floor (·) denotes round down; q. q.siAre samples in the local prevalence curvature matrix Q; p is a radical ofiSamples in the local density vector P.
S530 fusion degradation index extraction:
adjusting neighborhood parameter K obtained based on part S520cAnd updating the Euclidean distance De' extracting low-dimensional features obtained after mapping of high-dimensional degradation features by a local linear embedding method. Under the following loss function and weight constraint conditions, solving to obtain an objective function by calculating a Lagrange multiplier method: MY (myb disease)T＝λ′YTSolving the formula to obtain the eigenvector Y and eigenvalue lambda 'of the eigenvector matrix M'
Figure BDA0002676894500000244
Is constrained to
Figure BDA0002676894500000245
M＝(Ii-wi)(Ii-wi)T
Where W represents the set of all sample weight vectors; x is the number ofiAnd xjTwo samples in the high-dimensional degradation characteristic X are respectively; w is aiIs a sample xiA weight vector of (a); w is aijIs wiThe sample point of (1); i isiRepresenting D-dimensional vectors of all 1; m is a feature matrix.
And Y is a matrix formed by eigenvectors of the feature matrix M, in order to reduce the high-dimensional data to d dimensions, the eigenvectors corresponding to the minimum d non-zero eigenvalues of M are taken, and eigenvalue decomposition is carried out on the matrix M to obtain the low-dimensional representation Y of the high-dimensional degradation feature X: x → Y ═ Y2，y3，...，yd+1]Wherein y isiI is 2, 3, …, d +1, represents the eigenvector corresponding to the first d non-zero eigenvalues of the matrix M, and combines the eigenvalues y with the eigenvalues y2The fusion degradation index extracted by the method is used for monitoring the fault state of the nuclear power main pump bearing.
In step S600, a degradation trend curve is exponentially fitted, and different degradation state threshold intervals are determined:
f(t)＝λ+βexp(ηt)
in the formula: lambda, beta, eta are parameters of the exponential function, and are obtained by fitting the fusion degradation index.
The fusion degradation index and exponential fitting curve is shown in FIG. 5, and four degradation stages marked as S in different degradation states of the bearing are determined empirically1、S2、S3、S4Wherein S is1In the normal operation stage, the normal wear period with the longest operation time is adopted; s2、S3In the weak fault stage and the deep fault development stage, maintenance personnel need to provide proper maintenance to prevent the bearing from being damaged more seriously; s4In the failure stage, the bearing cannot work normally due to the too serious fault degree, and the corresponding interval threshold is shown in the following table.
TABLE 1 degradation stages and threshold intervals
Figure BDA0002676894500000251
Although embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and applications, which are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (10)

1. A nuclear power main pump bearing fault early warning method based on fusion degradation indexes comprises the following steps:
in the first step (S100), a vibration acceleration sensor is arranged on a shell of a bearing bush of a nuclear power main pump to acquire vibration acceleration data;
in a second step (S200), cleaning missing points, blank points, and outliers in the vibration acceleration data;
in the third step (S300), data of an amplitude modulation phenomenon caused by variable rotating speed is removed from the vibration acceleration data to obtain quantized vibration acceleration data;
in a fourth step (S400), extracting high-dimensional degradation features from the quantized vibration acceleration data;
in the fifth step (S500), extracting a fusion degradation index for monitoring the fault state of the nuclear power main pump bearing from the high-dimensional degradation characteristic;
in a sixth step (S600), thresholds for different degradation stages are determined based on the fused degradation indicators.
2. The method according to claim 1, wherein preferably in a second step (S200) missing points in the vibration acceleration data are cleaned by polynomial fitting, sample x with serial number 1, 2, …, n preceding the missing points1，x2，…，xnFitting on the basis of data to solve p (t)i)＝a0+a1ti+a2ti 2+…+anti nAnd make it possible to
Figure FDA0002676894490000011
And is composed of p (t)i) Substitution of deletion points, wherein tiTo fit the data samples, p (t)i) Is tiFitting data of point correspondences, a0，a1，…anAre fitting coefficients.
3. The method according to claim 1, wherein in the second step (S200), when the blank spots in the vibration acceleration data are cleaned, it is determined whether there are 2 and 2 or more continuous spots with zero amplitude, xi＝xi+1…, if present, successive sample points with zero amplitude are removed from the vibration acceleration data.
4. The method according to claim 1, wherein in a second step (S200), normal data x while cleaning outliers in the vibration acceleration dataiThe range is as follows:
Figure FDA0002676894490000012
mean value
Figure FDA0002676894490000013
The estimation method comprises the following steps:
Figure FDA0002676894490000014
the standard deviation sigma estimation method comprises the following steps:
Figure FDA0002676894490000015
the outlier determination method is as follows:
Figure FDA0002676894490000016
sample-by-sample judgment of sample xiWhether or not it is in the interval
Figure FDA0002676894490000017
In addition, judgment of βiNot more than 3, or betai> 3, if sample xiCorresponding betaiLess than or equal to 3, then sample xiIs a normal point, otherwise if sample xiCorresponding betai> 3, then sample xiFor outliers, a cleaning process is required.
5. The method of claim 4, wherein the value is replaced by an average of a number of samples adjacent to the outlier, expressed as:
Figure FDA0002676894490000018
where N is an outlier sample xiThe total number of adjacent sample points taken, i is the sample number.
6. The method of claim 1, wherein the removing of the data of amplitude modulation phenomena caused by the varying speed from the vibration acceleration data comprises,
for vibration data x containing variable rotating speed working conditioniTaking its Hilbert envelope ei，ei＝|xi+jH(xi) L, where H (x)i) Representing debounce data xiThe Hilbert transform of (1); x is the number ofi+jH(xi) Is a complex number, | xi+jH(xi) | represents taking the complex number xi+jH(xi) The die of (a) is used,
for envelope data eiThe amplitudes of (a) are sorted in descending order, and the mean value μ of the first m maximum amplitude values is obtained:
Figure FDA0002676894490000021
therein, max (e)i)mIndicating packet access data eiThe sum of the first m values with the maximum amplitude values, and the quantized vibration acceleration data x 'after the influence of the rotation speed factors is eliminated'iThe following formula is used to obtain:
Figure FDA0002676894490000022
7. the method of claim 1, wherein in the fourth step (S400), extracting high-dimensional degradation features from the quantized vibration acceleration data, the high-dimensional degradation features comprise:
kurtosis characteristic:
Figure FDA0002676894490000023
wherein
Figure FDA0002676894490000024
The waveform index is as follows:
Figure FDA0002676894490000025
kurtosis index:
Figure FDA0002676894490000026
wherein
Figure FDA0002676894490000027
Margin indexes are as follows:
Figure FDA0002676894490000028
frequency domain feature 3:
Figure FDA0002676894490000029
wherein
Figure FDA00026768944900000210
Frequency domain feature 4:
Figure FDA00026768944900000211
wherein
Figure FDA00026768944900000212
Frequency domain characteristics 12:
Figure FDA00026768944900000213
wherein
Figure FDA00026768944900000214
Wherein i is a vibration acceleration data serial number, and n is the total number of data samples; u. ofiRepresenting quantized vibration acceleration data samples; y isjRepresenting quantized vibration acceleration data uiObtaining frequency domain data after FFT; j is quantized vibration acceleration data uiOf frequency domain data yjN denotes quantized vibration acceleration data uiThe total number of samples of the frequency domain data of (a); f. ofjRepresenting frequency domain data yjFrequency components in the frequency spectrum.
8. The method of claim 1, wherein in the fifth step (S500), extracting a fused degradation index for nuclear power main pump bearing fault condition monitoring from the high-dimensional degradation features comprises,
solving all inter-sample cosine similarity matrix CS and sample cosine similarity mean vector in high-dimensional degraded feature set X
Figure FDA0002676894490000031
According to the cosine similarity matrix CS and the sample cosine similarity mean vector
Figure FDA0002676894490000032
Calculating a similarity matrix S;
calculating to obtain an initial neighborhood parameter K according to the similarity matrix S;
obtaining Euclidean distance D between all samples in high-dimensional degradation feature set XeDistance D from geodesic lineg；
Calculating the local density P and the global density mean value among all samples in the high-dimensional degradation feature set X
Figure FDA0002676894490000033
Calculating the ratio of the local Euclidean distance sum to the local geodesic distance sum to obtain the local popular curvature Q and the global popular curvature
Figure FDA0002676894490000034
Simultaneously calculating the ratio of the Euclidean distance to the geodesic distance to obtain D';
adjusting the initial neighborhood parameter K based on a neighborhood parameter adjusting method to obtain an adjusted neighborhood parameter KcSimultaneously, the Euclidean distance matrix D is updated by the ratio D' of the Euclidean distance to the geodesic distanceeObtaining an updated Euclidean distance matrix De′；
Based on the adjustment neighborhood parameter KcAnd the updated Euclidean distance matrix DeExtracting low-dimensional characteristics obtained after high-dimensional degradation characteristic mapping through a local linear embedding method, and solving to obtain an objective function through calculating a Lagrange multiplier method: MY (myb disease)T＝λ′YTSolving the formula to obtain the eigenvector Y and eigenvalue lambda 'of the eigenvector matrix M'
Figure FDA0002676894490000035
Is constrained to
Figure FDA0002676894490000036
M＝(Ii-wi)(Ii-wi)T，
Where W represents the set of all sample weight vectors; xiAnd XjTwo samples in the high-dimensional degradation characteristic X are respectively; wiIs a sample XiA weight vector of (a); w is aijIs WiThe sample point of (1); i isiRepresenting D-dimensional vectors of all 1; m is a characteristic matrix, and M is a characteristic matrix,
y is a matrix formed by eigenvectors of the feature matrix M, and the eigenvalue decomposition of the matrix M is carried out to obtain the low-dimensional representation of the high-dimensional degradation feature XY：X→Y＝[y2，y3，...，yd+1]Wherein y isiI 2, 3., d +1, representing the eigenvectors corresponding to the first d non-zero eigenvalues of the matrix M, and combining the eigenvalues y2The fusion degradation index is used as a fault state monitoring index for the nuclear power main pump bearing.
9. The method of claim 7, wherein the cosine similarity matrix CS is a symmetric matrix, and the formula is as follows:
Figure FDA0002676894490000041
in the formula, z is a characteristic dimension serial number, D is a dimension of a high-dimensional degradation characteristic, and i, j are sample serial numbers; CS (i, j) is a sample in the cosine similarity matrix CS; xiAnd XjTwo samples in the high-dimensional degradation feature X respectively,
Figure FDA0002676894490000042
and
Figure FDA0002676894490000043
are respectively a sample XiAnd sample XjThe number of sample points in (1) is,
geodesic distance D between all samples of high-dimensional degradation characteristics of bearinggThe iterative expression of (c) is:
dg(i，j)＝min{dg(i，j)，dg(i，m)+dg(m，j)}
in the formula, min is the minimum value; i, j and m are sample serial numbers, and i, j and m are different from each other; n is the total number of samples; dg(i, j) is the geodesic distance DgThe sample of (1).
10. The method according to claim 1, wherein in the sixth step (S600), determining thresholds for different degradation phases based on the fused degradation indicator comprises exponentially fitting a fused degradation indicator curve to determine different degradation state threshold intervals: (t) ═ λ + β exp (η t), where: lambda, beta, eta are parameters of the exponential function, and are obtained by fitting the fusion degradation index.
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