CN116383750A - Rolling bearing early-stage abnormality detection method based on windowed differential health index - Google Patents
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Abstract
The invention belongs to the technical field of early abnormality detection, and discloses a rolling bearing early abnormality detection method based on windowed differential health indexes. The method comprises the following steps: extracting the time domain and time-frequency domain characteristic parameters of the vibration signals of the rolling bearing; constructing a Markov reference space based on the characteristic parameters; calculating the Marsh distance of a sample space of the rolling bearing; processing the mahalanobis distance based on the cumulative sum method to obtain a health indicator having greater monotonicity and stability; based on a windowing differential health index method, windowing differential operation is carried out on the health index, and early abnormal detection of the rolling bearing is finally realized by combining a given threshold value. The method can effectively filter abnormal information generated by random noise interference in the health index, realize reasonable and effective identification of the early abnormal points of the rolling bearing, and is beneficial to reducing repeated shutdown of equipment caused by false alarm.
Description
Technical Field
The invention relates to the technical field of early-stage abnormality detection, in particular to a rolling bearing early-stage abnormality detection method based on windowed differential health indexes.
Background
Rolling bearings are one of the most widely used key components in rotary machines, and unexpected faults during operation thereof can cause the shutdown of the whole machine, thereby causing great economic losses or casualties. The vibration signal of the early failure of the rolling bearing is weak and is easy to be interfered by external environmental noise, and the problem of false alarm or missing alarm is easy to be caused in the early warning process. Meanwhile, the performance degradation index of the rolling bearing often shows fluctuation and non-monotonicity, so that the abrasion degree of the rolling bearing cannot be comprehensively and accurately estimated. Therefore, the research of the early abnormal accurate identification method of the rolling bearing and the monotonic Health Index (HI) construction method has important significance.
Aiming at the problem of monitoring the state of the rolling bearing, students at home and abroad have made related researches. "Wang Baoxiang, pan Hongxia, yang Wei. Condition monitoring and Performance degradation assessment of Rolling bearing [ J]The method of standard variable is adopted in the Chinese engineering machinery journal 2017 (1): 72-76 to reduce the dimension of various time domain characteristic parameters of the rolling bearing, and then the dimension is reduced by T 2 And Q statistics are used as display indicators to characterize the performance degradation process of the rolling bearing. "Ruijiaoming, hu Xin Rolling bearing life data monitoring analysis and feature extraction [ J ]]The Hua electric technology, 2018,40 (8): 5-10., extracts various time domain characteristic parameters and energy parameters of the vibration signal of the rolling bearing, and uses the characteristic parameters in combination to monitor the performance degradation state of the rolling bearing. In the state monitoring process of the rolling bearing, although the constructed health indexes can reflect the performance degradation trend and the wear severity of the rolling bearing to a certain extent, the health indexes still have certain random fluctuation, and the monotonicity trend is relatively weak, so that the later-stage health management and maintenance work of the rolling bearing, such as the performance degradation stage division, the residual service life prediction and the like of the rolling bearing, have negative effects on the aspect of improving the precision. For the problem of extracting the fault characteristics of the rolling bearing, "dragomiretsky K, zosso D.Variacal mode decomposition [ J ]].IEEE transactions on signal processing,2013,62(3):531Compared with the traditional EMD-based method, the medium variation modal decomposition (Variational Mode Decomposition, VMD) has the characteristics of fast convergence, high robustness and perfect mathematical theory basis. For the problem of multi-characteristic parameter information fusion of rolling bearings, "Chang Z P, li Y W, fatima N.Atheioretical survey on Mahalanobis-Taguchi system [ J ]]The majeldahl distance (Mahalanobis Distance, MD) of the majeldahl system (Mahalanobis Taguchi System, MTS) of measurent, 2019,136:501-510, fuses the multiple feature parameters into a single index that is independent of dimension, and corrects the problem of inconsistent and related dimensions in the euclidean distance independent of the Measurement dimensions. However, the mahalanobis distance fluctuation is obvious, and the effect of changing tiny variables is exaggerated.
Disclosure of Invention
In order to solve the problems existing in the prior art and relate to the problem of early abnormality detection of a rolling bearing, the invention provides a rolling bearing early abnormality detection method based on windowed differential health indexes (Windowed Differential HI, WD-HI). And processing the calculated mahalanobis distance MD by using a cumulative sum (CUMSUM) to obtain a health index HI with more monotonicity and stability, and finally performing WD-HI processing on the HI, and combining a set threshold value to realize the robust identification of the early abnormality of the rolling bearing. The method can monitor the health state of the rolling bearing in real time, and has the characteristics of strong adaptability and good robustness in early abnormal detection.
The technical scheme of the invention is as follows: a rolling bearing early-stage abnormality detection method based on windowed differential health indexes comprises the following steps:
step 1: extracting time domain features and time-frequency domain features of vibration signals of the rolling bearing;
selecting time domain characteristic parameters in a rolling bearing vibration signal, wherein the time domain characteristic parameters comprise kurtosis, crest factor, margin factor, shape factor, pulse coefficient, peak value and root mean square value; extracting a plurality of IMF components of the rolling bearing vibration signal by using a VMD algorithm, and calculating singular values of each IMF component by using an SVD algorithm to serve as time-frequency domain characteristic parameters of the rolling bearing vibration signal;
step 2: calculating the mahalanobis distance of a normal sample at the initial running stage of the rolling bearing;
calculating the mean value of normal samples and the standard deviation of the normal samples in the initial stage of running of the rolling bearing based on the time domain characteristic parameters and the time-frequency domain characteristic parameters obtained in the step 1:
wherein,,
is the mean value, s i Is standard deviation, X ij The characteristic parameter is the ith characteristic parameter of the normal sample of the vibration signal of the jth rolling bearing, and n is the number of the normal samples of the vibration signal of the rolling bearing;
calculating parameters:
wherein Z is ij Is a standardized matrix, c ij Is an element in the correlation matrix C; m represents the serial number of a normal sample of a vibration signal of the rolling bearing, Z im Is the i value of the m-th column in Z, Z jm Is the j value of the m-th column in Z, and the elements in the matrix Z are calculated by the formula (3);
calculating the mahalanobis distance of a normal sample of the rolling bearing:
wherein,,
is the Marshall distance of the normal sample of the j-th rolling bearing vibration signal in the normal state of the rolling bearing, k is the number of the time domain characteristic parameters and the time-frequency domain characteristic parameters of the rolling bearing vibration signal, and C -1 Is the inverse of the correlation matrix C, Z j All elements corresponding to the normal sample of the vibration signal of the jth rolling bearing in the matrix Z;
step 3: defining samples acquired after n rolling bearing vibration signals are normal samples in the step 2 as degradation samples, and calculating the mahalanobis distance of a degradation sample space;
wherein j is + For the serial number corresponding to the rolling bearing vibration signal degradation sample,
mahalanobis distance, indicative of the degraded sample space of the rolling bearing>
Normalized matrix representing degraded sample space, +.>
Is->
J of (j) + All elements of the column, l, are the number of rolling bearing degradation samples;
step 4: calculating a mahalanobis distance for characterizing the performance degradation process;
MD＝[MD normal (F)；MD sample (F)] (8)
wherein,,MD normal calculated by the formula (5), MD sample Calculated by a formula (7), wherein the Marshall distance MD representing the performance degradation process represents the Marshall distance corresponding to the rolling bearing in the performance degradation monitoring process, and the MD is calculated by the MD normal With MD sample Splicing to obtain; f is a characteristic parameter matrix and satisfies F= [ F p ；f rms ；f kur ；f crest ；f clc ；f shape ；f imp ；f sv ]The elements contained in F are peak value, root mean square value, kurtosis, crest factor, margin factor, shape factor, pulse factor and singular value respectively;
step 5: constructing performance degradation health indexes;
the Marshall distance MD representing the performance degradation process is optimized through accumulation and algorithm, and a health index HI is obtained through calculation, so that the problem that noise interference and monotonicity are poor in a state of reflecting the performance degradation of the bearing in the Marshall distance representing the performance degradation process is solved:
HI＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 ) (9)
wherein CM is τ ＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 )，CM 0 ＝0，μ 0 The mean value of the mahalanobis distance of the normal sample of the rolling bearing is used as a target value; ρ is an error value which is half of the standard deviation of the mahalanobis distance of a normal sample of the rolling bearing; MD (machine direction) device τ A τ value representing a mahalanobis distance of the performance degradation process for formula (8);
step 6: early anomaly detection based on windowed differential health indicators;
solving a first-order difference dHI corresponding to the health index HI:
wherein HI (t) is the value of HI at time t;
windowing dHI:
d (t) =min (dHI (t-l+ 1:t)) (11), where L is the window length, t is the window end position, and D (t) is the result corresponding to the t-th value after windowing; identifying early anomaly time:
T e ＝inf{t|D(t)＞e T }, (12)
wherein inf {.cndot.j represents the infinitum, e T To set early abnormality threshold, T e Representing the identified early anomaly time.
And carrying out windowing differential processing on the health index HI calculated by the rolling bearing, and combining the processed data with a given threshold value for detecting the robustness of early abnormality of the rolling bearing degradation process.
The beneficial effects of the invention are as follows: the invention provides a rolling bearing early-stage abnormality detection method based on windowed differential health indexes, which is used for carrying out state monitoring according to real-time data in the rolling bearing performance degradation process, and detecting the rolling bearing early-stage abnormality by adopting a WD-HI method, and has the characteristics of strong noise interference resistance and strong robustness.
Drawings
FIG. 1 is a flow chart of a rolling bearing early-stage abnormality detection method based on windowed differential health indexes;
FIG. 2 is raw vibration data of a rolling bearing in an embodiment of the invention over its life;
FIG. 3 is a rolling bearing Marsh distance MD in an embodiment of the present invention;
FIG. 4 is a rolling bearing health index HI in an embodiment of the invention;
FIG. 5 is an early outlier of a rolling bearing based on WD-HI recognition in an embodiment of the present invention.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical scheme and the accompanying drawings.
In this embodiment, fig. 1 shows a flowchart of a method for detecting early anomalies of a rolling bearing based on windowed differential health indexes, which includes the following steps:
step 1: extracting sample time domain characteristics and time-frequency domain characteristic parameters;
acquiring real-time acceleration vibration signal data in the running process of the rolling bearing, as shown in fig. 2; specifically, the rolling bearing data set employed in the present embodiment is from the procostia test platform; extracting time domain characteristic parameters of the rolling bearing, including kurtosis, crest factor, margin factor, shape factor, pulse coefficient, peak value and root mean square value, according to the acquired rolling bearing acceleration vibration signal data; meanwhile, extracting a plurality of IMF components of an original vibration signal of the bearing through a VMD algorithm, and calculating singular values of each component by adopting an SVD algorithm to serve as time-frequency domain characteristic parameters of the vibration signal of the rolling bearing;
step 2: constructing a Markov reference space;
constructing a Markov reference space by adopting the time domain and time-frequency domain characteristic parameters obtained by calculation in the step 1; calculating the average value and standard deviation of normal samples in the initial running stage of the rolling bearing:
wherein,,
is the mean value, s i Is standard deviation, X ij The characteristic parameter is the ith characteristic parameter of the normal sample of the vibration signal of the jth rolling bearing, and n is the number of the normal samples of the vibration signal of the rolling bearing;
calculating relevant parameters:
wherein Z is ij Is a standardized matrix, c ij Is an element in the correlation matrix C; m represents the serial number of a normal sample of a vibration signal of the rolling bearing, Z im Is the i value of the m-th column in Z, Z jm Is the j value of the m-th column in Z, and the elements in the matrix Z are calculated by the formula (15);
calculating the mahalanobis distance of a normal sample of the rolling bearing:
wherein,,
is the Marshall distance of the normal sample of the j-th rolling bearing vibration signal in the normal state of the rolling bearing, k is the number of the time domain characteristic parameters and the time-frequency domain characteristic parameters of the rolling bearing vibration signal, and C -1 Is the inverse of the correlation matrix C, Z j All elements corresponding to the normal sample of the vibration signal of the jth rolling bearing in the matrix Z;
step 3: defining samples acquired after n rolling bearing vibration signals are normal samples in the step 2 as degradation samples, and calculating the mahalanobis distance of a degradation sample space;
wherein j is + For the serial number corresponding to the rolling bearing vibration signal degradation sample,
mahalanobis distance, indicative of the degraded sample space of the rolling bearing>
Standard representing degraded sample spaceMatrix formation, I->
Is->
J of (j) + All elements of the column, l, are the number of rolling bearing degradation samples;
step 4: calculating a mahalanobis distance for characterizing the performance degradation process;
MD＝[MD normal (F)；MD sample (F)] (18)
wherein MD is normal Calculated by the formula (5), MD sample Calculated by a formula (7), representing the mahalanobis distance of the performance degradation process, wherein MD represents the mahalanobis distance corresponding to the rolling bearing in the performance degradation monitoring process, and MD is calculated by MD normal With MD sample Splicing to obtain; f is a characteristic parameter matrix and satisfies F= [ F p ；f rms ；f kur ；f crest ；f clc ；f shape ；f imp ；f sv ]The elements contained in F are peak value, root mean square value, kurtosis, crest factor, margin factor, shape factor, pulse factor and singular value respectively; the mahalanobis distance of the performance degradation process is shown in fig. 3;
step 5: constructing performance degradation health indexes;
in order to overcome the problem that the March distance is poor in noise interference and monotonicity in a state reflecting the performance degradation of the bearing, a cumulative sum (CUSUM) algorithm is introduced to optimize the March distance MD representing the performance degradation process and calculate to obtain a health index HI:
HI＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 ), (19)
wherein CM is τ ＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 )，CM 0 ＝0，μ 0 The target value can be obtained by the mean value of the mahalanobis distance of a normal sample of the rolling bearing. ρ is an error value which is half of the standard deviation of the mahalanobis distance of a normal sample of the rolling bearing; the health index of the rolling bearing is shown in fig. 4;
step 6: early detection of anomalies based on WD-HI;
solving a first-order difference dHI corresponding to the health index HI:
where Δt=1, HI (t) is the value of HI at time t;
windowing dHI:
d (t) =min (dHI (t-l+ 1:t)), (21) L is the window length, t is the window end position, and D (t) is the result corresponding to the t-th value after windowing; identifying early anomaly time:
T e ＝inf{t|D(t)＞e T },(22)
wherein inf {.cndot.j represents the infinitum, e T To set early abnormality threshold in advance, T e Representing the identified early anomaly time; the detection result of the early abnormality of the rolling bearing performance degradation process is shown in fig. 5.
Specifically, as can be seen from the area of the black curve coil shown in fig. 2-3, the rolling bearing original vibration signal time domain data has a certain fluctuation or random noise interference at the early stage of the performance degradation process from the corresponding mahalanobis distance, which causes the corresponding health index HI to appear as a distinct abnormal point near the 1300 th sampling point, such as the area of the black curve coil shown in fig. 4; however, from the viewpoint of the life-time degradation process of the rolling bearing, the HI black curve-coiled region is not suitable as an early abnormal point, since the performance degradation of the bearing starts later than this point; the health index HI is subjected to windowing differential processing by a WD-HI method to obtain 2758 th sampling points of early anomalies of the bearing as shown in FIG. 5, so that abnormal fluctuation information caused by random noise interference of an original vibration signal can be effectively filtered, the early anomalies of the rolling bearing can be reasonably and effectively identified, and multiple machine halt of equipment caused by false alarm is reduced.
It should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the present invention, and should not be construed as limiting the present invention, and those skilled in the art may modify and replace the above-mentioned embodiments within the scope of the present invention without departing from the principle and spirit of the present invention.
Claims (2)
1. The rolling bearing early-stage abnormality detection method based on the windowed differential health index is characterized by comprising the following steps of:
step 1: extracting time domain features and time-frequency domain features of vibration signals of the rolling bearing;
selecting time domain characteristic parameters in a rolling bearing vibration signal, wherein the time domain characteristic parameters comprise kurtosis, crest factor, margin factor, shape factor, pulse coefficient, peak value and root mean square value; extracting a plurality of IMF components of the rolling bearing vibration signal by using a VMD algorithm, and calculating singular values of each IMF component by using an SVD algorithm to serve as time-frequency domain characteristic parameters of the rolling bearing vibration signal;
step 2: calculating the mahalanobis distance of a normal sample at the initial running stage of the rolling bearing;
calculating the mean value of normal samples and the standard deviation of the normal samples in the initial stage of running of the rolling bearing based on the time domain characteristic parameters and the time-frequency domain characteristic parameters obtained in the step 1:
wherein,,
is the mean value, s i Is standard deviation, X ij The characteristic parameter is the ith characteristic parameter of the normal sample of the vibration signal of the jth rolling bearing, and n is the number of the normal samples of the vibration signal of the rolling bearing;
calculating parameters:
wherein Z is ij Is a standardized matrix, c ij Is an element in the correlation matrix C; m represents the serial number of a normal sample of a vibration signal of the rolling bearing, Z im Is the i value of the m-th column in Z, Z jm Is the j value of the m-th column in Z, and the elements in the matrix Z are calculated by the formula (3);
calculating the mahalanobis distance of a normal sample of the rolling bearing:
wherein,,
is the Marshall distance of the normal sample of the j-th rolling bearing vibration signal in the normal state of the rolling bearing, k is the number of the time domain characteristic parameters and the time-frequency domain characteristic parameters of the rolling bearing vibration signal, and C -1 Is the inverse of the correlation matrix C, Z j All elements corresponding to the normal sample of the vibration signal of the jth rolling bearing in the matrix Z;
step 3: defining samples acquired after n rolling bearing vibration signals are normal samples in the step 2 as degradation samples, and calculating the mahalanobis distance of a degradation sample space;
wherein j is + For the serial number corresponding to the rolling bearing vibration signal degradation sample,
mahalanobis distance, indicative of the degraded sample space of the rolling bearing>
Normalized matrix representing degraded sample space, +.>
Is->
J of (j) + All elements of the column, l, are the number of rolling bearing degradation samples;
step 4: calculating a mahalanobis distance for characterizing the performance degradation process;
MD＝[MD normal (F)；MD sample (F)](8) Wherein MD is normal Calculated by the formula (5), MD sample Calculated by a formula (7), representing the mahalanobis distance of the performance degradation process, wherein MD represents the mahalanobis distance corresponding to the rolling bearing in the performance degradation monitoring process, and MD is calculated by MD normal With MD sample Splicing to obtain; f is a characteristic parameter matrix and satisfies F= [ F p ；f rms ；f kur ；f crest ；f clc ；f shape ；f imp ；f sv ]The elements contained in F are peak value, root mean square value, kurtosis, crest factor, margin factor, shape factor, pulse factor and singular value respectively;
step 5: constructing performance degradation health indexes;
the Marshall distance MD representing the performance degradation process is optimized through accumulation and algorithm, and a health index HI is obtained through calculation, so that the problem that noise interference and monotonicity are poor in a state of reflecting the performance degradation of the bearing in the Marshall distance representing the performance degradation process is solved:
HI＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 ) (9)
wherein CM is τ ＝max(0,MD τ -(μ 0 +ρ)+CM τ-1 )，CM 0 ＝0，μ 0 The mean value of the mahalanobis distance of the normal sample of the rolling bearing is used as a target value; ρ is an error value which is half of the standard deviation of the mahalanobis distance of a normal sample of the rolling bearing; MD (machine direction) device τ A τ value representing a mahalanobis distance of the performance degradation process for formula (8);
step 6: early anomaly detection based on windowed differential health indicators;
solving a first-order difference dHI corresponding to the health index HI:
wherein HI (t) is the value of HI at time t;
windowing dHI:
D(t)＝min(dHI(t-L+1:t)) (11)
wherein L is the length of the window, t is the position of the tail end of the window, and D (t) is the result corresponding to the t-th value after windowing;
identifying early anomaly time:
T e ＝inf{t|D(t)＞e T }, (12)
wherein inf {.cndot.j represents the infinitum, e T To set early abnormality threshold, T e Representing the identified early anomaly time.
2. The rolling bearing early abnormality detection method based on the windowed differential health index according to claim 1, characterized in that the health index HI calculated by the rolling bearing is windowed differential processed, and the processed data is combined with a given threshold value for robust detection of early abnormalities in the rolling bearing degradation process.
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| CN117743836A (en) * | 2024-02-21 | 2024-03-22 | 聊城市产品质量监督检验所 | Abnormal vibration monitoring method for bearing |
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| CN117743836A (en) * | 2024-02-21 | 2024-03-22 | 聊城市产品质量监督检验所 | Abnormal vibration monitoring method for bearing |
| CN117743836B (en) * | 2024-02-21 | 2024-05-03 | 聊城市产品质量监督检验所 | Abnormal vibration monitoring method for bearing |
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