A method for early anomaly detection in rolling bearings based on windowed differential health indicators

Abstract

This invention belongs to the field of early anomaly detection technology and discloses a method for early anomaly detection of rolling bearings based on windowed differential health indicators. It includes the following steps: extracting time-domain and time-frequency domain feature parameters of the rolling bearing vibration signal; constructing a Mahalanobis reference space based on the feature parameters; calculating the Mahalanobis distance of the rolling bearing sample space; processing the Mahalanobis distance using the cumulative sum method to obtain a health indicator with greater monotonicity and stability; and performing windowed differential operation on the health indicator using the windowed differential health indicator method, combined with a given threshold, to finally achieve early anomaly detection of the rolling bearing. This invention can effectively filter out abnormal information caused by random noise interference in the health indicator, enabling reasonable and effective identification of early anomalies in rolling bearings, and helping to reduce multiple equipment downtimes caused by false alarms.

Description

Technical Field

[0001] This invention relates to the field of early anomaly detection technology, and in particular to a method for early anomaly detection of rolling bearings based on windowed differential health indicators. Background Technology

[0002] Rolling bearings are among the most widely used critical components in rotating machinery. Unexpected failures during their operation can cause the entire machine to shut down, resulting in significant economic losses or personal injury. Early-stage rolling bearing failures often produce weak vibration signals that are easily affected by environmental noise, leading to false alarms or missed alarms in early warning systems. Furthermore, rolling bearing performance degradation indicators frequently exhibit fluctuations and non-monotonicity, making it impossible to comprehensively and accurately assess their wear levels. Therefore, researching accurate methods for early anomaly identification in rolling bearings and constructing a monotonic health indicator (HI) is of great significance.

[0003] Regarding the issue of rolling bearing condition monitoring, scholars both domestically and internationally have conducted relevant research. The paper "Wang Baoxiang, Pan Hongxia, Yang Wei. Condition monitoring and performance degradation assessment of rolling bearings [J]. Proceedings of the Chinese Society for Construction Machinery, 2017(1):72-76" uses the method of normalized variables to reduce the dimensionality of various time-domain characteristic parameters of rolling bearings, and then uses T... 2The Q statistic is used as an indicator to characterize the performance degradation process of rolling bearings. "Rui Xiaoming, Hu Xin. Monitoring and Analysis of Rolling Bearing Life-Cycle Data and Feature Extraction [J]. Huadian Technology, 2018, 40(8): 5-10." extracts various time-domain characteristic parameters and energy parameters of rolling bearing vibration signals, and uses these characteristic parameters in combination to monitor the performance degradation state of rolling bearings. In the process of monitoring the condition of rolling bearings, although the health indicators they constructed can reflect the performance degradation trend and wear severity of rolling bearings to a certain extent, their health indicators still have a certain degree of random fluctuation, and the monotonicity trend is relatively weak. This has a negative impact on the accuracy improvement of the later health management and maintenance work of rolling bearings, such as the division of rolling bearing performance degradation stages and the prediction of remaining service life. For the problem of feature extraction of rolling bearing faults, Variational Mode Decomposition (VMD) in "Dragomiretskiy K, Zosso D. Variational mode decomposition[J].IEEE Transactions on Signal Processing, 2013, 62(3):531-544." has the advantages of fast convergence, high robustness and sound mathematical theory compared with traditional EMD-based methods. For the problem of information fusion of multiple feature parameters of rolling bearings, the Mahalanobis Distance (MD) of the Mahalanobis Taguchi System (MTS) in "Chang ZP, Li YW, Fatima N. A theoretical survey on Mahalanobis-Taguchi system[J]. Measurement, 2019, 136:501-510." fuses multiple feature parameters into a single index, which is unaffected by dimensions and independent of the measurement scale, thus correcting the problem of inconsistent and correlated scales in various dimensions in Euclidean distance. However, the Mahalanobis distance exhibits significant fluctuations, exaggerating the effect of small, insignificant variables. Summary of the Invention

[0004] To address the problems of existing technologies, particularly in the early detection of anomalies in rolling bearings, this invention proposes a method for early anomaly detection in rolling bearings based on the Windowed Differential Health Index (WD-HI). The calculated Mahalanobis distance MD is processed using the Cumulative Sum (CUMSUM) method to obtain a more monotonic and stable health index HI. Finally, HI is processed using WD-HI, and combined with a set threshold, robust identification of early anomalies in rolling bearings is achieved. This method enables real-time monitoring of the health status of rolling bearings and exhibits strong adaptability and robustness in early anomaly detection.

[0005] The technical solution of this invention is: a method for early anomaly detection of rolling bearings based on windowed differential health indicators, comprising the following steps:

[0006] Step 1: Extract the time-domain and time-frequency domain features of the rolling bearing vibration signal;

[0007] Select time-domain characteristic parameters from the rolling bearing vibration signal, including kurtosis, crest factor, margin factor, shape factor, impulse factor, peak value, and root mean square value; extract several IMF components of the rolling bearing vibration signal using the VMD algorithm, and calculate the singular value of each IMF component using the SVD algorithm, as the time-frequency domain characteristic parameters of the rolling bearing vibration signal;

[0008] Step 2: Calculate the Mahalanobis distance of the normal sample during the initial operation of the rolling bearing;

[0009] Based on the time-domain and time-frequency domain characteristic parameters obtained in step 1, the mean and standard deviation of the normal samples during the initial operation of the rolling bearing are calculated:

[0010]

[0011]

[0012] in, It is the mean, s i X represents the standard deviation. ij Let be the i-th feature parameter of the j-th normal sample of the rolling bearing vibration signal, and n be the number of normal samples of the rolling bearing vibration signal.

[0013] Calculation parameters:

[0014]

[0015]

[0016] Among them, Z ij It is a standardized matrix, c ijThese are elements in the correlation matrix C; m represents the normal sample number of the rolling bearing vibration signal, Z im It is the i-th value in the m-th column of Z, Z jm It is the j-th value in the m-th column of Z. The elements in matrix Z are calculated by formula (3).

[0017] Calculate the Mahalanobis distance for a normal sample of rolling bearings:

[0018]

[0019] in, C is the Mahalanobis distance of the j-th normal sample of the rolling bearing vibration signal under normal conditions, k is the number of time-domain and time-frequency domain characteristic parameters of the rolling bearing vibration signal, and C is the distance between the j-th and j-th normal samples of the rolling bearing vibration signal under normal conditions. -1 Z is the inverse of the correlation matrix C. j It consists of all elements corresponding to the j-th normal sample of rolling bearing vibration signal in matrix Z;

[0020] Step 3: Define the samples collected after the n normal samples of rolling bearing vibration signals in Step 2 as degenerate samples, and calculate the Mahalanobis distance of the degenerate sample space;

[0021]

[0022]

[0023] Where, j + This refers to the sequence number corresponding to the degraded sample of the rolling bearing vibration signal. The Mahalanobis distance represents the sample space of the degraded rolling bearings. The normalized matrix representing the degenerate sample space. for The jth + All elements in the column, where l is the number of degraded rolling bearing samples;

[0024] Step 4: Calculate the Mahalanobis distance characterizing the performance degradation process;

[0025] MD = [MD normal (F); MD sample (F)] (8)

[0026] Among them, MD normal MD is calculated using formula (5). sample The Mahalanobis distance MD, calculated by formula (7), characterizes the performance degradation process and represents the Mahalanobis distance corresponding to the rolling bearing during the performance degradation monitoring process. MD is derived from MD normal With MD sample The concatenation yields F, which is the feature parameter matrix, and satisfies F = [f p ;frms ;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, impulse factor, and singular value, respectively.

[0027] Step 5: Construct performance degradation health indicators;

[0028] The Mahalanobis distance MD, which characterizes the performance degradation process, is optimized through an accumulative sum algorithm, and the health index HI is calculated. This is used to overcome the problems of noise interference and poor monotonicity of the Mahalanobis distance in reflecting the performance degradation state of bearings.

[0029] HI = max(0, MD) τ -(μ0+ρ)+CM τ-1 (9)

[0030] Among them, CM τ =max(0,MD) τ -(μ0+ρ)+CM τ-1 ), CM0=0, μ0 is the target value, obtained from the mean Mahalanobis distance of normal rolling bearing samples; ρ is the error value, which is half the standard deviation of the Mahalanobis distance of normal rolling bearing samples; MD τ Let τ be the τth value of the Mahalanobis distance in formula (8) that characterizes the performance degradation process;

[0031] Step 6: Early anomaly detection based on windowed difference health indicators;

[0032] Solve for the first-order difference dHI corresponding to the health index HI:

[0033]

[0034] Where HI(t) is the value of HI at time t;

[0035] Windowing is applied to dHI:

[0036] D(t)=min(dHI(t-L+1:t)) (11) where L is the window length, t is the end position of the window, and D(t) is the result corresponding to the t-th value after windowing; early anomaly identification time:

[0037] T e =inf{t|D(t)>e T}, (12)

[0038] Where inf{·} represents the infimum, eT T is the threshold for setting early anomalies. e This represents the time when early anomalies were identified.

[0039] The health index HI calculated for rolling bearings was subjected to windowed differential processing. The processed data was then combined with a given threshold for robust detection of early anomalies in the rolling bearing degradation process.

[0040] The beneficial effects of this invention are as follows: This invention proposes an early anomaly detection method for rolling bearings based on windowed differential health index. It monitors the condition of rolling bearings based on real-time data during the performance degradation process and uses the WD-HI method to detect early anomalies in rolling bearings. It has the characteristics of strong anti-noise interference capability and strong robustness. Attached Figure Description

[0041] Figure 1 This is a flowchart of an early anomaly detection method for rolling bearings based on windowed differential health indicators provided by the present invention;

[0042] Figure 2 These are the original vibration data of the rolling bearing throughout its entire lifespan in this embodiment of the invention;

[0043] Figure 3 It is the Martens distance MD of the rolling bearing in the embodiment of the present invention;

[0044] Figure 4 This refers to the rolling bearing health index HI in this embodiment of the invention.

[0045] Figure 5 This refers to the early abnormality point of the rolling bearing identified based on WD-HI in this embodiment of the invention. Detailed Implementation

[0046] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0047] This embodiment presents a method for early anomaly detection in rolling bearings based on windowed differential health indicators. Figure 1 This flowchart illustrates the early anomaly detection method for rolling bearings, including the following steps:

[0048] Step 1: Extract time-domain features and time-frequency domain features of the sample;

[0049] Acquire real-time acceleration and vibration signal data during the operation of rolling bearings, such as Figure 2As shown; specifically, the rolling bearing dataset used in this embodiment comes from the PRONOSTIA test platform; combined with the collected rolling bearing acceleration vibration signal data, the time-domain feature parameters of the rolling bearing are extracted, including kurtosis, crest factor, margin factor, shape factor and impulse factor, peak value, and root mean square value; at the same time, several IMF components of the original vibration signal of the bearing are extracted by the VMD algorithm, and the singular value of each component is calculated by the SVD algorithm as the time-frequency domain feature parameters of the rolling bearing vibration signal;

[0050] Step 2: Construct the Markov reference space;

[0051] Using the time-domain and time-frequency domain characteristic parameters obtained in step 1, a Mahalanobis reference space is constructed; the mean and standard deviation of normal samples during the initial operation of the rolling bearing are calculated.

[0052]

[0053]

[0054] in, It is the mean, s i X represents the standard deviation. ij Let be the i-th feature parameter of the j-th normal sample of the rolling bearing vibration signal, and n be the number of normal samples of the rolling bearing vibration signal.

[0055] Calculate the relevant parameters:

[0056]

[0057]

[0058] Among them, Z ij It is a standardized matrix, c ij These are elements in the correlation matrix C; m represents the normal sample number of the rolling bearing vibration signal, Z im It is the i-th value in the m-th column of Z, Z jm It is the j-th value in the m-th column of Z. The elements in matrix Z are calculated by formula (15).

[0059] Calculate the Mahalanobis distance for a normal sample of rolling bearings:

[0060]

[0061] in, C is the Mahalanobis distance of the j-th normal sample of the rolling bearing vibration signal under normal conditions, k is the number of time-domain and time-frequency domain characteristic parameters of the rolling bearing vibration signal, and C is the distance between the j-th and j-th normal samples of the rolling bearing vibration signal under normal conditions. -1 Z is the inverse of the correlation matrix C. jIt consists of all elements corresponding to the j-th normal sample of rolling bearing vibration signal in matrix Z;

[0062] Step 3: Define the samples collected after the n normal samples of rolling bearing vibration signals in Step 2 as degenerate samples, and calculate the Mahalanobis distance of the degenerate sample space;

[0063]

[0064]

[0065] Where, j + This refers to the sequence number corresponding to the degraded sample of the rolling bearing vibration signal. The Mahalanobis distance represents the sample space of the degraded rolling bearings. The normalized matrix representing the degenerate sample space. for The jth + All elements in the column, where l is the number of degraded rolling bearing samples;

[0066] Step 4: Calculate the Mahalanobis distance characterizing the performance degradation process;

[0067] MD = [MD normal (F); MD sample (F)] (18)

[0068] Among them, MD normal MD is calculated using formula (5). sample The Mahalanobis distance, characterizing the performance degradation process, is calculated using formula (7). MD represents the Mahalanobis distance corresponding to the rolling bearing during performance degradation monitoring. MD is derived from MD normal With MD sample The concatenation yields F, which is the feature 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, impulse factor, and singular value; the Mahalanobis distance of the performance degradation process is as follows: Figure 3 As shown;

[0069] Step 5: Construct performance degradation health indicators;

[0070] To overcome the problems of noise interference and poor monotonicity of Mahalanobis distance in reflecting bearing performance degradation, a cumulative sum (CUSUM) algorithm is introduced to optimize the Mahalanobis distance MD, which characterizes the performance degradation process, and the health index HI is calculated.

[0071] HI = max(0, MD) τ -(μ0+ρ)+CM τ-1 ), (19)

[0072] Among them, CM τ =max(0,MD) τ -(μ0+ρ)+CM τ-1 ), CM0=0, μ0 is the target value, which can be obtained from the mean Mahalanobis distance of normal rolling bearing samples. ρ is the error value, which is half the standard deviation of the Mahalanobis distance of normal rolling bearing samples; the health indicators of rolling bearings are as follows: Figure 4 As shown;

[0073] Step 6: Early anomaly detection based on WD-HI;

[0074] Solve for the first-order difference dHI corresponding to the health index HI:

[0075]

[0076] Where Δt=1, HI(t) is the value of HI at time t;

[0077] Windowing is applied to dHI:

[0078] In D(t)=min(dHI(t-L+1:t)), (21), L is the window length, t is the end position of the window, and D(t) is the result corresponding to the t-th value after windowing; early anomaly identification time:

[0079] T e =inf{t|D(t)>e T},(twenty two)

[0080] Where inf{·} represents the infimum, e T T is a pre-set threshold for early anomalies. e Represents the early anomaly time of identification; detection results of early anomalies in the rolling bearing performance degradation process are as follows: Figure 5 As shown.

[0081] Specifically, from Figure 2-3 As shown by the black curve circled area, the time-domain data of the original vibration signal of the rolling bearing and its corresponding Mahalanobis distance exhibit fluctuations or random noise interference in the early stages of performance degradation. This causes a significant anomaly in the corresponding health indicator HI near the 1300th sampling point. Figure 4 The area circled by the black curve in the image; however, considering the entire lifespan degradation process of this rolling bearing, this area circled by the black HI curve is not suitable as an early anomaly point, because the performance degradation of this bearing begins later than this point; by applying windowed difference processing to the health index HI using the WD-HI method, the following results are obtained: Figure 5 The bearing early anomaly shown is the 2758th sampling point. This can effectively filter out abnormal fluctuation information caused by random noise interference from the original vibration signal, realize reasonable and effective identification of early anomaly points of rolling bearings, and thus reduce multiple equipment shutdowns caused by false alarms.

[0082] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and should not be construed as limiting the present invention. Those skilled in the art can make modifications and substitutions to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for early abnormality detection of a rolling bearing based on windowed differential health indicators, characterized in that, The method comprises the following steps: Step 1: extracting time domain features and time-frequency domain features of the rolling bearing vibration signal; Selecting time domain feature parameters in the rolling bearing vibration signal, including kurtosis, peak factor, margin factor, shape coefficient, pulse coefficient, peak value and root mean square value; extracting several IMF components of the rolling bearing vibration signal through the VMD algorithm, and calculating singular values of each IMF component through the SVD algorithm as time-frequency domain feature parameters of the rolling bearing vibration signal; Step 2: calculating Mahalanobis distance of normal samples in the initial stage of rolling bearing operation; Based on the time domain feature parameters and the time-frequency domain feature parameters obtained in step 1, the mean of the normal samples in the initial stage of rolling bearing operation and the standard deviation of the normal samples are calculated: wherein, is the mean, s i is the standard deviation, X ij is the i-th feature parameter of the j-th normal sample of the rolling bearing vibration signal, and n is the number of normal samples of the rolling bearing vibration signal. Calculation parameters: wherein Z ij is a standardized matrix, c ij is an element in the correlation matrix C; m represents the normal sample serial number of the rolling bearing vibration signal, Z im is the i-th value of the m-th column in Z, Z jm is the j-th value of the m-th column in Z, and the elements in the matrix Z are calculated by formula (3): wherein Z ij is a standardized matrix, c ij is an element in the correlation matrix C; m represents the normal sample serial number of the rolling bearing vibration signal, Z im is the i-th value of the m-th column in Z, Z jm is the j-th value of the m-th column in Z, and the elements in the matrix Z are calculated by formula (3): wherein Z ij The Mahalanobis distance of the normal samples of the rolling bearing is calculated: wherein, is the Mahalanobis distance of the jth normal sample of the rolling bearing vibration signal under normal state, k is the number of time domain characteristic parameters and time-frequency domain characteristic parameters of the rolling bearing vibration signal, C -1 is the inverse of the correlation matrix C, Z j is all elements corresponding to the jth normal sample of the rolling bearing vibration signal in the matrix Z; Step 3: defining the samples collected after the n rolling bearing vibration signal normal samples in step 2 as degradation samples, and calculating the Mahalanobis distance of the degradation sample space; wherein j + is the serial number corresponding to the rolling bearing vibration signal degradation sample, represents the Mahalanobis distance of the rolling bearing degradation sample space, represents the standardization matrix of the degradation sample space, is the j + th column of all elements, and l is the number of rolling bearing degradation samples; Step 4: calculating the Mahalanobis distance representing the performance degradation process; MD = [MD normal (F) ; MD sample (F)] (8) wherein, MD normal MD is calculated by formula (5), MD sample The Mahalanobis distance representing the performance degradation process is calculated by formula (7), MD represents the corresponding Mahalanobis distance of the rolling bearing in the performance degradation monitoring process, MD is obtained by MD normal MD is obtained by MD sample Splicing is obtained; F is a feature 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, wave crest factor, margin factor, shape coefficient, pulse coefficient and singular value respectively; Step 5: constructing a performance degradation health index; The Mahalanobis distance representing the performance degradation process MD is optimized through the cumulative sum algorithm, and a health index HI is calculated to overcome the problems of noise interference and monotony in reflecting the bearing performance degradation state: HI = max(0, MD τ -(μ0+ρ) + CM τ-1 ) (9) where CM τ = max(0, MD τ - (μ0+ ρ) + CM τ-1 ), CM0= 0, μ0is a target value obtained by Mahalanobis distance mean of normal samples of rolling bearings; ρ is an error value, which is half of the Mahalanobis distance standard deviation of normal samples of rolling bearings; MD τ is the τth value of the Mahalanobis distance representing the performance degradation process in formula (8). Step 6: early anomaly detection based on windowed difference health index; Solving the 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 window length, t is the window end position, and D(t) is the result corresponding to the tth value after windowing. Identifying early anomaly time: T e = inf {t | D(t) > e T}, (12) where inf{•} denotes the infimum, e T Tearlyabnormal is the set early abnormal threshold, T e represents the identified early abnormal time.

2. The early abnormality detection method of the rolling bearing based on the windowed differential health index according to claim 1, characterized in that, The health index HI calculated by the rolling bearing is subjected to windowed difference processing, the processed data is combined with a given threshold, and the rolling bearing degradation process early anomaly robustness detection is realized.

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