Bearing fault cycle automatic detection method and system

Abstract

The present invention provides a bearing fault cycle automatic detection method and system, including: collecting vibration signals from a faulty bearing through a sensor; dividing and reorganizing the vibration signals to form two sub-signals; processing each sub-signal using an NRC algorithm, and obtaining an EnNRC statistic by weighted summation; constructing a reduced confidence interval; starting from the highest peak of the EnNRC statistic, constructing a peak difference statistic toward the previous peak, and constructing a dynamic confidence interval, checking whether there are other peaks in the interval, and if so, starting the next hypothesis test from the highest peak in the interval, iterating until there are no other peaks in the interval, and the peak at this time is the true fault cycle detected by the algorithm. The present invention compares periodic peaks and other non-periodic peaks with interference effects through iterative hypothesis testing, gradually eliminates the misleading effect of local optimality, and improves the accuracy of period detection.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault detection, and in particular to a method and system for automatically detecting a bearing fault cycle. Background Art

[0002] Bearing fault detection originated from the constant working conditions in the early stage of industrial development, and has accumulated certain results. The research in this field is relatively mature. Most traditional detection technologies are based on the time domain, frequency domain and other information of vibration signals. By extracting and analyzing the relevant characteristics of vibration signals, comparing them with the characteristic indicators of vibration signals generated in a healthy state, the current operating status of the equipment is analyzed to determine whether there is a potential fault.

[0003] In order to overcome the difficulties caused by the masking effect of noise, scholars have designed some benchmark methods in the time domain. Rabiner et al. proposed an autocorrelation function (ACF) to extract the periodic waveform characteristics of periodic signals, and can intuitively identify the period from the time domain transformed signal. Huang et al. proposed an improved version of ACF - weighted average amplitude difference function (AMDF) - for sound wave pitch extraction. The Variability Method and NRC algorithm can overcome the masking effect of strong background noise on the period detection of periodic signals by calculating the correlation of multiple sub-signals. If a sufficiently long signal is provided, the periodic characteristics of the signal under these methods will not be masked by the background noise. Based on these transformed signals in the time domain, some targeted methods for automatically estimating the period have been studied. For example, Martin et al. proposed a method for detecting the period using the AMDF period spectrum, and Antoni et al. proposed a hybrid method combining the ACF and period spectrum methods to automatically identify the period, called the Autoperiod method. Wang et al. also proposed an orthogonal subspace decomposition method to identify the period using the characteristic signal after the Variability Method. There are also some frequency domain methods for identifying periods under moderate background noise, such as periodograms. Transforms based on Ramanujan sums have also been recently designed and used to study frequency domain signals. In order to automatically identify the period of noise signals, some statistical methods using maximum likelihood estimation (ML) have gradually emerged. Wise et al. proposed an ML method with a penalty coefficient, namely maximum likelihood pitch estimation (MLPE), for estimating the pitch period from speech signals. Ramírez et al. proposed an approximate maximum likelihood estimation method with a regularization term for the period estimation of cyclostationary signals. These methods estimate the period by locating the maximum peak of the likelihood function.

[0004] Patent document CN108106838B (application number: CN201611122045.1) discloses a whole-cycle time domain regression and alarm method for precise diagnosis of mechanical faults. It uses a generalized resonance / resonance demodulation method and a speed tracking detection method to detect vibration and impact signals of bearing, gear and other faults. After automatically correcting the number of tracking sampling points per revolution, the original signal is firstly intercepted by a whole cycle according to the analyzed fault type to eliminate the spectrum leakage caused by the limited length of the field data and the non-whole-cycle sampling and its contradiction with the Fourier transform frequency resolution, which can greatly improve the accuracy of spectrum qualitative analysis. Then, the signal is subjected to time domain regression processing, and the energy of other irrelevant signal components will not interfere. Finally, the fault is quantitatively calculated using the differential formula to improve the accuracy of fault classification and quantitative diagnosis.

[0005] Some statistical hypothesis testing methods have also been proposed in existing studies to estimate the signal period. For example, Dandawate et al. proposed a chi-square test method based on cyclic covariance and spectrum to detect the existence of signal cyclostationarity and estimate the signal period. Recently, Horstmann et al. proposed a multiple hypothesis testing method that uses Holm's order rejection test to estimate the period of approximately cyclostationary signals. These hypothesis testing methods are based on an asymptotic generalized likelihood ratio test. The period is estimated by determining the index position of the binary test with the minimum p value. The time domain feature extraction algorithm method mainly provides a feature signal in the time domain that can eliminate the masking effect of background noise, and the period is usually identified by subjective judgment based on manual experience. There are also some methods that determine the period by finding the position of the first peak in the extracted periodic feature, but since the bearing fault signal is interfered by strong background noise, the maximum peak may appear at any multiple period, so this identification method has no stability and persuasiveness. Due to the masking effect of strong background noise, the spectrum of the original signal is easily masked by noise, so the simple judgment method of locating the maximum amplitude spectrum under strong background noise can no longer effectively identify the period. Therefore, the traditional methods designed in the frequency domain are not suitable for some applications where the signal is contaminated by strong background noise. For the method of estimating the period by locating the maximum peak of the likelihood function, the likelihood function has similar statistical properties on the true period and its multiples, and the peaks presented are also similar, which leads to a certain misleading effect on the period identification based on the maximum peak.

[0006] Therefore, simply locating the position with the maximum likelihood estimate to identify the signal period may identify erroneous peaks located at multiple period positions, ultimately leading to misdiagnosis of the period. Methods that estimate the period by determining the index position of the binary test with the minimum p-value are also subject to the interference of the similar statistical properties of period multiples, that is, periodic signals will produce similar p-values ​​at the true period and its multiples. Therefore, hypothesis testing methods may also mistakenly identify multiple periods as the true period of the signal.

[0007] Therefore, the signals after time domain transformation (such as autocorrelation coefficient, likelihood value and p-value) usually have similar visual and statistical characteristics at the real period and its multiples, showing a local optimum phenomenon with misleading effect. The misleading effect of this local optimum phenomenon makes targeted period estimation algorithms, maximum likelihood period estimation algorithms and hypothesis testing methods prone to high false positive and false negative probabilities. In addition, except for hypothesis testing algorithms, the false positive and false negative probabilities of other algorithms are uncontrollable, making period estimation very difficult. Summary of the invention

[0008] In view of the defects in the prior art, an object of the present invention is to provide a method and system for automatically detecting bearing fault cycles.

[0009] The method for automatically detecting bearing fault cycles provided by the present invention comprises:

[0010] Step 1: Collect vibration signals from the faulty bearing through sensors;

[0011] Step 2: Divide the vibration signal, reassemble the odd and even segments respectively, and combine them into two sub-signals;

[0012] Step 3: Use the NRC algorithm to process each sub-signal, and perform weighted summation to obtain the EnNRC statistic;

[0013] Step 4: Use this statistic to further construct the peak difference statistic;

[0014] Step 5: Construct a reduced confidence interval based on the dynamic significance level;

[0015] Step 6: Starting from the highest peak of the EnNRC statistic, construct the peak difference statistic to the previous peak, and build a dynamic confidence interval to check whether there are other peaks in the interval. If there are other peaks, start the next hypothesis test from the highest peak in the interval and iterate until there are no other peaks in the interval. The peak at this time is the true fault cycle detected by the algorithm.

[0016] Preferably, the collected periodic pulse signal y(t) generated by the operation of the faulty bearing is decomposed into the real fault signal x(t) and the background noise ∈(t), then: y(t)=x(t)+∈(t), where ∈(t)~N(0,σ 2 );

[0017] Define the time series y = [y(1), y(2), ..., y(l)] T is the discrete observation value of y(t), l is the total number of samples; x = [x(1), x(2), ..., x(l)] T ,∈=[∈(1),∈(2),...,∈(l)] T ;

[0018] Then the signal y is expressed as: y = x + ∈, ∈ ~ N (0, σ 2 I l ), I l is the identity matrix of size l×l;

[0019] Assume the period of the fault signal x(t) is T0, T0 = p0 / f s , where p0>1 is the number of samples in one cycle, f s is the sampling frequency;

[0020] The signal y is divided into Segment, the kth signal segment y k =[y((k-1)n+1), ..., y(kn)], where k = 1, 2, ..., m; n is the number of samples in each signal segment;

[0021] Then the EnNRC statistic is expressed as:

[0022]

[0023] Where i and j are sequence numbers; if l%n≠0, the signal is divided into 2m+1 segments;

[0024] The length of the signal segment of the odd segment is: n1 = l-mn, where

[0025] The signal segment length of the even-numbered segment is: n2=n-n1;

[0026] Reassemble the odd-numbered signal segments into new sub-signals:

[0027] Reassemble the even-numbered signal into a new sub-signal:

[0028] In y o and eConstruct NRC functions respectively, and get:

[0029]

[0030] in,

[0031] The EnNRC statistic is and The weighted sum of The expression is:

[0032]

[0033] Among them, ω o =o n n1 / l,ω e =e n n2 / l.

[0034] Preferably, the expression of EnNRC statistic is:

[0035]

[0036] Define l%n=0 when y j，1 Empty, y j，2 =y j , and the inner product of two empty vectors is 0, for all i and j, Therefore, for any l, the EnNRC statistic is unified as:

[0037]

[0038] The expression of is rewritten into matrix form: in, is a matrix of size l×l:

[0039]

[0040] Among them, M n By O n and E n The block diagonal matrix is ​​formed by and:

[0041]

[0042]

[0043] The signal is divided in the same way on the real signal x and the background noise ∈ and the EnNRC statistic is constructed:

[0044]

[0045] thereby Rewritten as:

[0046]

[0047]

[0048] The mean and variance of are:

[0049]

[0050]

[0051]

[0052]

[0053] The expectation is no greater than the average energy of the true signal x According to the Cauchy-Schwarz inequality:

[0054]

[0055] in, The equation holds true if and only if n∈N; when l tends to infinity, Converges to

[0056] Preferably, the highest peak occurs at the fault true cycle The probability of and its multiples converges to 1 as the signal length l→∞, and the expression is:

[0057]

[0058] in, For any n≤K and As l→∞, the probability expression is:

[0059]

[0060] Noise term Any peak p to be detected and any candidate peak q obey an approximate normal distribution, and the expression is:

[0061]

[0062]

[0063] when When the hypothesis test statistic is is related to the unknown signal x; and for any p and q, the peak difference are all bounded, and the expression is:

[0064]

[0065] is the real cycle peak of the fault; is the target period peak, and the equality holds if and only if q∈N;

[0066] According to this inequality, we construct a bounded acceptance region for the null hypothesis at any q value:

[0067]

[0068] Among them, δ is a parameter that controls the size of the receptive field;

[0069] The reduced acceptance region for constructing the null hypothesis for any q value is:

[0070]

[0071] The reduced receptive field is obtained by the following formula, for all p and q, we have:

[0072]

[0073] The equivalent expression is:

[0074] Tr(C p C p +C q C q -2C p C q )≥Tr(C p C p -C q C q )

[0075] The equality holds if and only if p%q=0. Verifying this inequality is equivalent to verifying the inequality:

[0076] Tr(C p C q )≤Tr(C q C q )

[0077] The equality holds if and only if p%q=0;

[0078] Each column vector of is a periodic sequence with period n, and when p%q=0, we have:

[0079]

[0080] therefore:

[0081]

[0082] So when p%q=0, we have:

[0083] Tr((C p -C q )C q )=Tr(-(C p -C q )D q )=0

[0084] The condition for the equation to hold in the inequality is p%q=0, and when p%q≠0, we get:

[0085] Tr(C p C q )<Tr(C k C q )=Tr(C q C q )

[0086] Here, k is a common multiple of p and q.

[0087] Preferably, when there are multiple significant peaks in the acceptance domain, the one with the largest p-value is selected. The expression is:

[0088]

[0089] make Iterate until:

[0090]

[0091] when When the receiving domain There is no new peak

[0092] The noise estimation method in the NRC algorithm is used to estimate σ 2 To estimate, the expression is:

[0093]

[0094] Designing iterative hypothesis testing based on dynamic significance level IHTDSL for automatic detection of fault cycles, the acceptance domain of IHTDSL Iterative learning is performed from the fault signal, and the confidence level δ is dynamically estimated in each iteration according to the following formula:

[0095]

[0096] Among them, γ∈(0,1), is the peak to be detected in this hypothesis test;

[0097] The termination condition is simplified to:

[0098]

[0099] By estimating the δ value in IHTDSL to dynamically control the significance level, the adaptive receptive field in each iteration achieves a balance between the first type error and the second type error, so that both converge to 0, which is manifested in that both the misjudgment and omission of the fault cycle disappear when the signal is long enough.

[0100] The bearing fault cycle automatic detection system provided by the present invention comprises:

[0101] Module M1: collects vibration signals from the faulty bearing through sensors;

[0102] Module M2: divides the vibration signal, recombines the odd and even segments respectively, and combines them into two sub-signals;

[0103] Module M3: Process each sub-signal using the NRC algorithm and perform weighted summation to obtain the EnNRC statistic;

[0104] Module M4: Use this statistic to further construct the peak difference statistic;

[0105] Module M5: Constructing reduced confidence intervals based on dynamic significance levels;

[0106] Module M6: Starting from the highest peak of the EnNRC statistic, construct the peak difference statistic to the previous peak, and build a dynamic confidence interval to check whether there are other peaks in the interval. If there are other peaks, start the next hypothesis test from the highest peak in the interval and iterate until there are no other peaks in the interval. The peak at this time is the real fault cycle detected by the algorithm.

[0107] Preferably, the collected periodic pulse signal y(t) generated by the operation of the faulty bearing is decomposed into the real fault signal x(t) and the background noise ∈(t), then: y(t)=x(t)+∈(t), where ∈(t)~N(0,σ 2 );

[0108] Define the time series y = [y(1), y(2), ..., y(l)] T is the discrete observation value of y(t), l is the total number of samples; x = [x(1), x(2), ..., x(l)] T ,∈=[∈(1),∈(2),...,∈(l)] T ;

[0109] Then the signal y is expressed as: y = x + ∈, ∈ ~ N (0, σ2 I l ), I l is the identity matrix of size l×l;

[0110] Assume the period of the fault signal x(t) is T0, T0 = p0 / f s , where p0>1 is the number of samples in one cycle, f s is the sampling frequency;

[0111] The signal y is divided into Segment, the kth signal segment y k =[y((k-1)n+1), ..., y(kn)], where k = 1, 2, ..., m; n is the number of samples in each signal segment;

[0112] Then the EnNRC statistic is expressed as:

[0113]

[0114] Where i and j are sequence numbers; if l%n≠0, the signal is divided into 2m+1 segments;

[0115] The length of the signal segment of the odd segment is: n1 = l-mn, where

[0116] The signal segment length of the even-numbered segment is: n2=n-n1;

[0117] Reassemble the odd-numbered signal segments into new sub-signals:

[0118] Reassemble the even-numbered signal into a new sub-signal:

[0119] In y o and e Construct NRC functions respectively, and get:

[0120]

[0121] in,

[0122] The EnNRC statistic is and The weighted sum of The expression is:

[0123]

[0124] Among them, ω o =o n n1 / l,ω e =e nn2 / l.

[0125] Preferably, the expression of EnNRC statistic is:

[0126]

[0127] Define l%n=0 when y j，1 Empty, y j，2 =y j , and the inner product of two empty vectors is 0, for all i and j, Therefore, for any l, the EnNRC statistic is unified as:

[0128]

[0129] The expression of is rewritten into matrix form: in, is a matrix of size l×l:

[0130]

[0131] Among them, M n By O n and E n The block diagonal matrix is ​​formed by and:

[0132]

[0133]

[0134] The signal is divided in the same way on the real signal x and the background noise ∈ and the EnNRC statistic is constructed:

[0135]

[0136] thereby Rewritten as:

[0137]

[0138]

[0139] The mean and variance of are:

[0140]

[0141]

[0142]

[0143]

[0144] The expectation is no greater than the average energy of the true signal x According to the Cauchy-Schwarz inequality:

[0145]

[0146] in, The equation holds true if and only if n∈N; when l tends to infinity, Converges to

[0147] Preferably, the highest peak occurs at the fault true cycle The probability of and its multiples converges to 1 as the signal length l→∞, and the expression is:

[0148]

[0149] in, For any n≤K and As l→∞, the probability expression is:

[0150]

[0151] Noise term Any peak p to be detected and any candidate peak q obey an approximate normal distribution, and the expression is:

[0152]

[0153]

[0154] when When the hypothesis test statistic is is related to the unknown signal x; and for any p and q, the peak difference are all bounded, and the expression is:

[0155]

[0156] is the real cycle peak of the fault; is the target period peak, and the equality holds if and only if q∈N;

[0157] According to this inequality, we construct a bounded acceptance region for the null hypothesis at any q value:

[0158]

[0159] Among them, δ is a parameter that controls the size of the receptive field;

[0160] The reduced acceptance region for constructing the null hypothesis for any q value is:

[0161]

[0162] The reduced receptive field is obtained by the following formula, for all p and q, we have:

[0163]

[0164] The equivalent expression is:

[0165] Tr(C p C p +C q C q -2C p C q )≥Tr(C p C p -C q C q )

[0166] The equality holds if and only if p%q=0. Verifying this inequality is equivalent to verifying the inequality:

[0167] Tr(C p C q )≤Tr(C q C q )

[0168] The equality holds if and only if p%q=0;

[0169] Each column vector of is a periodic sequence with period n, and when p%q=0, we have:

[0170]

[0171] therefore:

[0172]

[0173] So when p%q=0, we have:

[0174] Tr((C p -C q )C q )=Tr(-(C p -C q )D q )=0

[0175] The condition for the equation to hold in the inequality is p%q=0, and when p%q≠0, we get:

[0176] Tr(C p C q)<Tr(C k C q )=Tr(C q C q )

[0177] Here, k is a common multiple of p and q.

[0178] Preferably, when there are multiple significant peaks in the acceptance domain, the one with the largest p-value is selected. The expression is:

[0179]

[0180] make Iterate until:

[0181]

[0182] when When the receiving domain There is no new peak

[0183] The noise estimation method in the NRC algorithm is used to estimate σ 2 To estimate, the expression is:

[0184]

[0185] Designing iterative hypothesis testing based on dynamic significance level IHTDSL for automatic detection of fault cycles, the acceptance domain of IHTDSL Iterative learning is performed from the fault signal, and the confidence level δ is dynamically estimated in each iteration according to the following formula:

[0186]

[0187] Among them, γ∈(0,1), is the peak to be detected in this hypothesis test;

[0188] The termination condition is simplified to:

[0189]

[0190] By estimating the δ value in IHTDSL to dynamically control the significance level, the adaptive receptive field in each iteration achieves a balance between the first type error and the second type error, so that both converge to 0, which is manifested in that both the misjudgment and omission of the fault cycle disappear when the signal is long enough.

[0191] Compared with the prior art, the present invention has the following beneficial effects:

[0192] (1) The present invention balances the first and second type errors in the hypothesis testing process through dynamic confidence intervals, and can also eliminate false positives and false negatives of the fault cycle when the signal is long enough;

[0193] (2) The present invention compares periodic peaks and other non-periodic peaks with interference effects through iterative hypothesis testing, gradually eliminating the misleading effect of local optimality, and improving the accuracy of period detection;

[0194] (3) The present invention can apply the algorithm to other applications that are essentially periodic detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0195] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0196] Figure 1 Implement a flowchart for the algorithm;

[0197] Figure 2 This is a typical ACF waveform diagram;

[0198] Figure 3 This is a typical waveform diagram of NRC;

[0199] Figure 4 This is a schematic diagram of EnNRC signal division method;

[0200] Figure 5 Schematic diagram of bounded and reduced receptive regions for the first step of iterative hypothesis testing (δ=3);

[0201] Figure 6 Schematic diagram of bounded and reduced receptive regions for the last step of iterative hypothesis testing (δ=3);

[0202] Figure 7a and Figure 7b They are schematic diagrams of simulation signals x(n) and y(n), respectively;

[0203] Figure 8 Schematic diagram of bearing vibration signal fault period detection accuracy (CWRU experiment). DETAILED DESCRIPTION

[0204] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0205] Example:

[0206] The most obvious feature of a single-point failure in a bearing is that when it rotates at a constant speed, the vibration signal will show periodic characteristics, that is, the fault has a certain frequency. This frequency can be calculated using the bearing parameters and the motor speed. However, due to the integrity of the equipment and the instability of the speed, and the fact that the bearing will wear out over time, the actual parameters will change, and the theoretical fault frequency in actual applications cannot be calculated in this way. Therefore, it is necessary to design an algorithm to capture the bearing failure cycle in a timely manner through the vibration signal, and to extract the bearing periodic fault components and conduct subsequent diagnosis.

[0207] The periodic pulse signal y(t) generated by the operation of the faulty bearing can be decomposed into the real fault signal x(t) and the background noise ∈(t), that is:

[0208] y(t)=x(t)+∈(t)

[0209] Among them, ∈(t)~N(0,σ 2 ).

[0210] Time series y = [y(1), y(2), ..., y(Ll)] T is the discrete observation value of y(t), that is, the signal form that the vibration sensor can collect on the bearing, where l is the total number of samples. Similarly, define x = [x(1), x(2), ..., x(l)] T , and ∈ = [∈(1), ∈(2), ..., ∈(l)] T The signal y can be expressed as:

[0211] y=x+∈

[0212] Among them, ∈~N(0,σ 2 I l ), I l is a unit matrix of size l×l. Assume that the period of the fault signal x(t) is T0, T0=p0 / f s , where p0>1 is the number of samples in one cycle, f s is the sampling frequency. The present invention also assumes that the average energy of the fault signal x is bounded.

[0213] Most autocorrelation functions can be written as follows:

[0214]

[0215] Among them, C n is a matrix of size l×l. If C n If it is not a symmetric matrix, you can use To replace C n , so without loss of generality, we can assume that Cn is a symmetric matrix. For example, the ACF algorithm proposed by Rabiner et al. can be expressed as:

[0216]

[0217] where l≥n. This equation can be further rewritten into quadratic form:

[0218]

[0219]

[0220] R n is an l×l matrix, which has unit elements at the nth non-diagonal line and all other elements are 0. The typical waveform of ACF is shown in Figure 2 shown.

[0221] The NRC algorithm divides the signal y into Segment, the kth signal segment y k =[y((k-1)n+1), ..., y(kn)], where k = 1, 2, ..., m, n is the number of samples in each signal segment. NRC is also a statistic designed based on the autocorrelation algorithm, expressed as:

[0222]

[0223] It can be seen that the NRC statistic does not take into account the residual segment with a length of n1=l-mn after the signal segmentation, so NRC does not fully utilize all the information in the original fault vibration signal to a certain extent. Similarly, the NRC statistic can be rewritten as a quadratic form:

[0224]

[0225]

[0226] Among them, I n is the n×n identity matrix, 0 n is an n×n zero matrix, is a zero matrix of n1×n. The typical waveform of NRC is as follows Figure 3 shown.

[0227] Due to the periodic characteristics of signal y, The waveform of usually has obvious peaks at the period position, that is, When n∈N, N={p0,2p0,3p0,…}, a local optimum appears. The peak of the wave is called the cycle peak, and The peaks that appear when the peaks are called non-periodic peaks. However, the similarity of the statistical properties of these periodic peaks makes the period estimation algorithm prone to false positives and false negatives, because the algorithm may be misled by these local optimal periodic peaks. Therefore, it is quite difficult to identify the true period where the correct peak is located. Specifically, traditional optimization algorithms are good at finding the highest peak in the search area [1, K] by:

[0228]

[0229] Among them, K>2p0, It is the highest peak The coordinates of. When n≤≤K, if If there are two identical maximum peaks, the position of the peak with smaller coordinates is returned, that is, the position of the first maximum peak is returned.

[0230] Found in this way Figure 2 and 3 The highest peak in is not the location of the real period of the signal, but may be a multiple of the real period of the signal.

[0231] The likelihood function proposed in MLPE can also be written in quadratic form. The waveform of this likelihood function is very similar to the NRC function, showing periodic peaks. Although a penalty term is used to enhance periodic peaks with smaller coordinates, these periodic peaks presented by the MLPE statistic are still quite misleading. Therefore, due to the misleading effect of the periodic peaks, it is also quite difficult to correctly identify the peaks at the true period of the likelihood function.

[0232] This misleading effect makes many actual bearing fault detection applications rely heavily on domain knowledge and subjective judgment to identify the fault cycle, and the feedback information is not timely and reliable. In order to meet the urgent need for accurate and rapid estimation of bearing fault cycles in actual production rather than manual participation in cycle identification, it is crucial and urgent to design a robust cycle estimation method to solve the misleading effect caused by the above local optimum, so as to determine the true cycle.

[0233] Simply identifying the maximum peak may result in multiple cycle errors, since the true peak may be located at The previous position (i.e. ). To determine the highest peak Whether it is a peak at the real cycle, it is necessary to compare the peak with the previous peak, otherwise it is easy to cause a high false detection rate. Therefore, in order to reduce the false detection rate, it is necessary to compare the maximum peak with any preceding crest Make statistical comparisons.

[0234] Statistically comparing two peaks can be accomplished using statistical hypothesis testing. The present invention proposes the following hypothesis testing:

[0235]

[0236] To compare the peak to be detected With other alternative crests If all are significantly smaller than It can be determined is the true period of the fault. If there is a significant The crest You can refuse The hypothesis is located at the true cycle and the hypothesis testing process is repeated to verify Whether it is the target cycle peak. Figure 2 The two marked peaks are statistically considered to be significantly equal, which indicates that the maximum peak found in the first step is Probably not the correct cycle peak.

[0237] The present invention compares two candidate peaks of the fault feature statistics that may be located at the cycle to eliminate the misleading effect of the peaks of multiple cycles. Construct a new statistic:

[0238]

[0239] That is, the difference between the two peaks. Based on this statistic, an iterative hypothesis testing method can be used to statistically find the true cycle.

[0240] The present invention intends to design the Enhanced Noise Resistant Correlation (EnNRC) algorithm to extract the bearing fault characteristics. This step is to preliminarily weaken the masking effect of the background noise and enhance the fault characteristics. It not only has statistical properties similar to NRC, but also has special statistical properties that are convenient for constructing iterative hypothesis tests. Similar to NRC, EnNRC also divides the vibration signal collected by the sensor into several signal segments. If the signal can be divided into m segments, each signal segment has n points (i.e., l%n=0), the construction method of the EnNRC function is exactly the same as that of NRC. In this case, the EnNRC statistic can be expressed as:

[0241]

[0242] If the signal cannot be divided exactly (ie, l%n≠0), the signal is divided into 2m+1 segments. Figure 4 The specific division method of the signal in this case is shown in the figure. As can be seen from the figure, the length of the signal segment of the odd segment is n1=l-mn, where The length of the even-numbered signal segment is n2=n-n1.

[0243] Reassemble the odd-numbered signal segments into new sub-signals:

[0244]

[0245] And reassemble the even-numbered signal into:

[0246]

[0247] In y o and e Construct NRC functions respectively, and get:

[0248]

[0249] in, (the smallest integer not less than l / n), The EnNRC statistic is and The weighted sum of Right now:

[0250]

[0251] Among them, ω o =o n n1 / l,ω e =e n n2 / l. Under this weight, EnNRC will have some special statistical properties, which will be discussed in detail in the next section.

[0252] The full form of the EnNRC statistic is:

[0253]

[0254] For the convenience of expression, define y as l%n=0 j，1 Empty, y j，2 =y j , and the inner product of two empty vectors is 0, that is, for all i and j, Therefore, for any l, the EnNRC statistic can be uniformly written as:

[0255]

[0256] The expression can also be rewritten in matrix form:

[0257] in, is a matrix of size l×l:

[0258]

[0259] Among them, M n By O n and E n The block diagonal matrix is ​​formed by and:

[0260]

[0261]

[0262] The same method can be used to divide the signal and construct the EnNRC statistic on the real signal x and background noise ∈:

[0263]

[0264] thereby It can be further written as:

[0265]

[0266]

[0267] The mean and variance of are:

[0268]

[0269]

[0270]

[0271]

[0272] Although compared to Q n , C n Although the matrix structure is more complex, the EnNRC statistic still has similar statistical properties to the NRC statistic. The expectation is no greater than the average energy of the true signal x That is, according to the Cauchy-Schwarz inequality:

[0273]

[0274] in, The equation holds true if and only if n∈N. When l tends to infinity (i.e. l→∞), Converges to

[0275] Similar to the NRC statistic, the fault features extracted by the EnNRC statistic will also show some prominent peaks. The probability that the highest peak appears at the fault true cycle and its multiples converges to 1 as the signal length l→∞, that is:

[0276]

[0277] in, For any n≤K and As l→∞, we have:

[0278]

[0279] This indicates that the maximum peak is one of the periodic peaks. However, the maximum peak may not be located at p0 because all periodic peaks have the same expected value, namely:

[0280]

[0281] And the variance caused by background noise may cause the maximum peak to appear at any position. This statistically misleading similarity property shows that simply locating the largest peak without comparing it with the previous peaks will have a low reliability in identifying the cycle, which can easily lead to false positives and false negatives of fault cycles.

[0282] Considering that the true fault signal x is unknown, it is very difficult to statistically compare the peaks of any statistics based on the correlation function (e.g. and ), which makes it almost impossible to parse the rejection region or acceptance region of hypothesis testing. However, from another perspective, the EnNRC statistic can solve this problem well, because for any p, q∈N, we have:

[0283]

[0284] This shows that for p,q∈N, and The difference between these two peaks is only determined by the background noise, and the background noise of the fault signal can be estimated by a certain method. Therefore, when p, q∈N, only Rather than research The present invention will construct a special acceptance domain for comparing the peaks to be detected in hypothesis testing. and alternative peaks

[0285] The exact probability distribution of can be calculated using a variety of methods, however, these methods will have problems such as poor interpolation effect when l is large. In addition, in order to overcome the masking effect of background noise, in practical applications, signals that are long enough are generally collected to detect faults. If these methods use numerical integration to accurately calculate the distribution, it will take a lot of computing time and cannot be used for online fault detection.

[0286] The present invention proposes a The approximate probability distribution calculation method can solve these problems. For any p and q, it obeys an approximate normal distribution, that is:

[0287]

[0288]

[0289] However, when When the hypothesis test statistic is It is still inevitably related to the unknown signal x, so it is impossible to construct an accurate rejection region or acceptance region. For any p and q, the peak difference are all bounded, that is:

[0290]

[0291] The equality holds if and only if q∈N.

[0292] Based on this inequality, we can construct a bounded acceptance region for the null hypothesis at any q value:

[0293]

[0294] Where δ is a parameter that controls the size of the receptive field. Figure 5 As shown, the area in the figure is the bounded acceptance region of the hypothesis test.

[0295] Compared with the exact acceptance domain, the bounded acceptance domain has some special and important statistical properties. First, when using the bounded acceptance domain for hypothesis testing, when q∈N, since the acceptance domain size remains unchanged, the first and second error rates remain unchanged. The first error is The null hypothesis is incorrectly rejected when , while the second type of error is Secondly, when When , since the bounded acceptance region is narrower than the exact acceptance region, using the bounded acceptance region for hypothesis testing will increase the first type error rate and reduce the second type error rate. It is worth noting that due to The peaks that appear when are all interference peaks at non-periodic locations. Therefore, increasing the first type error rate can effectively reduce the receptive field of non-periodic peaks, that is, increasing The rejection rate can reduce the false alarm rate of fault detection. Therefore, these two properties show that using bounded acceptance region for hypothesis testing helps to overcome the interference of non-periodic peaks caused by background noise pollution, thus achieving higher fault cycle detection accuracy than the exact acceptance region.

[0296] However, computing the bounded receptive field is very time-consuming and memory-intensive since the signal length l is usually quite large. Therefore, this study further proposes to reduce the receptive field, such as Figure 5 The reduced acceptance region of the null hypothesis for any value of q is:

[0297]

[0298] The reduced receptive field is mainly obtained by the following formula: For all p and q, there is:

[0299]

[0300] Or equivalently:

[0301] Tr(C p C p +C q C q -2C p C q )≥Tr(C p C p -C q C q )

[0302] The equality holds if and only if p%q = 0. Verifying this inequality is equivalent to verifying the inequality:

[0303] Tr(C p C q )≤Tr(C q C q )

[0304] The equality holds if and only if p%q=0. It can be seen that Each column vector of is a periodic sequence with period n, and when p%q=0, we have:

[0305]

[0306] therefore:

[0307]

[0308] So when p%q=0, we have:

[0309] Tr((C p -C q )C q )=Tr(-(C p -C q )D q )=0

[0310] That is, the condition for the equation in the inequality to hold is p%q=0. When p%q≠0, we can get:

[0311] Tr(C p C q )<Tr(C k C q )=Tr(C q C q )

[0312] where k is a common multiple of p and q. This inequality holds because C k The non-zero elements of C p The element at the corresponding position is larger. The equality condition of the inequality shows that the hypothesis test based on the reduced acceptance domain is This conclusion means that at least when q = p0, the hypothesis test still maintains the same false alarm rate, because That is, the probability of accepting a true cycle peak of a fault remains unchanged when using a reduced acceptance region. Another benefit of using a reduced acceptance region is that it reduces the probability of other unsatisfactory The cycle peak The acceptance rate of , to some extent, weakens the misleading effect of the multiple period peak. In addition, similar to the bounded acceptance field, When the hypothesis test based on reduced receptive field uses a narrower receptive field, the masking effect of background noise can be alleviated to a great extent. Figure 5 As shown, both the bounded receptive field and the reduced receptive field can cover the peaks at the real period, but the non-periodic peaks covered by the reduced receptive field are much less than those of the bounded receptive field, thereby improving the judgment and calculation efficiency.

[0313] However, there may be more than one like Figure 4 As shown, there are 3 significant peaks in the acceptance region. In this case, the one with the largest p-value is selected.

[0314]

[0315] Similar to the traditional method of determining the period by simply optimizing indicators such as likelihood or p-value, the above formula gives may not be the true cycle, which is caused by the misleading effect of the cycle peak. Therefore, this one-shot algorithm of locating the maximum value of the statistic to identify the cycle cannot effectively overcome the misleading effect. To further solve this problem, the newly found peak It should also continue to be compared with its previous peak, so it is necessary to repeat the hypothesis testing process proposed in the previous section and regard this peak as the new maximum peak, that is, Iterate until:

[0316]

[0317] That is Time Receptive Field There is no new peak Table 1 gives the detailed steps of the iterative hypothesis testing process. Figure 6 It is the acceptance region of the last hypothesis test when the termination condition in the above formula is met. As can be seen from the figure, before the last peak found, there is no other peak in the acceptance region, then the peak is in the true cycle of the fault, and the iterative hypothesis testing process can effectively overcome the misleading effect of multiple cycle peaks.

[0318] Table 1 Iterative hypothesis testing algorithm flow

[0319]

[0320] Generally speaking, when determining the confidence interval, the parameter δ is fixed, such as δ = 3, because the statistic to be measured generally obeys a normal distribution. The iterative hypothesis testing method using a fixed confidence level (fixed δ value) is called IHTFSL (Iterative Hypothesis Testing on Fixed Significance Level). 2 is unknown, so refer to the noise estimation method in the NRC algorithm to estimate σ 2 :

[0321]

[0322] Using the estimated σ 2 , the receptive field can be calculated when executing IHTFSL.

[0323] However, using a fixed significance level inevitably leads to a fixed type I error rate, even if the signal is long enough. When the signal length is short, a smaller significance level leads to a higher type II error rate, and vice versa. In addition, it is almost impossible to reduce both type I and type II errors at the same time, because a reduction in one error will almost certainly increase the other error when l remains constant. These contradictions suggest that finding a better balance between type I and type II errors can effectively reduce false positive and false negative rates.

[0324] In order to overcome this contradiction, the present invention improves the commonly used hypothesis test with fixed confidence interval and designs iterative hypothesis test (IHTDSL) based on dynamic significance level for automatic detection of fault cycle. Iterative learning from the fault signal, where δ is dynamically estimated in each iteration according to the following formula:

[0325]

[0326] where γ∈(0,1), is the peak to be detected in this hypothesis test. A large number of simulation and experimental studies have shown that in most cases, the non-periodic peak when q < p0 The expected value is usually less than Therefore, it is completely reasonable to select γ≤0.5 in the iterative hypothesis testing process. Simulation and experimental research results also show that IHTDSL usually has higher fault cycle detection accuracy when γ=0.5.

[0327] The termination condition can be simplified to:

[0328]

[0329] It can be seen that the termination condition at this time no longer depends on the unknown σ 2 , which is the first advantage of IHTDSL over IHTFSL. The second advantage is that as the signal length tends to infinity, both the first and second error rates of period detection converge to 0. Increasing the number of data samples in traditional hypothesis testing methods usually helps to reduce the second error, while the manually specified first error rate remains unchanged. However, by estimating the δ value in IHTDSL to dynamically control the significance level, the adaptive receptive field in each iteration can achieve a good balance between the first and second errors, so that both converge to 0, which is manifested as the misjudgment and omission of fault cycles disappear when the signal is long enough.

[0330] The algorithm construction process is as follows Figure 1 As shown, the steps are as follows:

[0331] 1. Use sensors to collect vibration signals y(t) from the faulty bearing;

[0332] 2. Figure 4 The signal is redivided in the manner shown, and the odd and even segments are reassembled separately to form two sub-signals;

[0333] 3. Use the NRC algorithm to process each sub-signal and perform weighted summation to obtain the EnNRC statistic;

[0334] 4. Use this statistic to further construct the peak difference statistic;

[0335] 5. Construct a reduced confidence interval based on the dynamic significance level, and set γ = 0.5;

[0336] 6. Starting from the highest peak of the EnNRC statistic, construct the peak difference statistic to the previous peak, and build a dynamic confidence interval to check whether there are other peaks in the interval;

[0337] If there are other peaks, the next hypothesis test starts from the highest peak in the interval and iterates until there are no other peaks in the interval. The peak at this time can be considered as the real cycle of the fault detected by the algorithm.

[0338] Preferably, the present invention further comprises: simulation verification;

[0339] This section compares the performance of the proposed IHTDSL and IHTFSL using a periodic transient signal to simulate a periodic signal x:

[0340]

[0341] Where ζ=0.01 is the damping ratio, f=10Hz is the natural frequency, p0=400 is the number of sample points in one cycle, and f s = 200 Hz is the sampling frequency. In addition, a strength of σ is added 2 =4 background noise, synthesize the signal y(n) contaminated by the background noise, the waveform is as follows Figure 7a and Figure 7b The signal-to-noise ratio of this signal is about -19dB.

[0342] The length of the synthetic simulation signal varies from 10,000 to 150,000 points. Each length of the signal is tested 200 times, and the period recognition interval of each method is [1, 2500], that is, K = 2500. According to the correct number of period detection in 200 tests, The period detection accuracy under each signal length is calculated, and the results are shown in Table 2.

[0343] Table 2 Period detection accuracy of IHTDSL, IHTFSL, NRCPE and MLPE under different γ and l combinations

[0344]

[0345]

[0346] From the results in Table 2, it can be seen that when the value of γ is large, IHTDSL has a higher period detection accuracy. As the signal length increases, the accuracy of IHTDSL converges to 1 for all γ values, which further proves that the false detection rate will converge to 0 when the signal length tends to infinity. The speed at which the period detection accuracy converges to 1 increases with the increase of γ value, and the convergence speed will not continue to increase when γ ≥ 0.5, which also explains why the convergence speed of period detection accuracy when γ = 0.5 is not as fast as when γ = 0.4. In general, since the period detection accuracy of γ = 0.5 is sufficient in most application scenarios, it is recommended to select γ = 0.5 when using the IHTDSL method.

[0347] Similarly, if the δ value remains unchanged, IHTFSL has higher period detection accuracy when processing longer signals, because increasing the signal length can effectively reduce the type II error rate. However, IHTFSL uses a fixed significance level, so even if the signal is long enough, the type I error rate is always fixed. As shown in Table 2, when δ = 2, the period detection accuracy of IHTFSL still fluctuates around a certain level when the signal length is long enough. This fluctuation decreases as the δ value increases, because the increase in the δ value reduces the type I error rate.

[0348] When the signal length is fixed, increasing δ does not necessarily improve the period detection accuracy. For example, when the signal length is long enough (l ≥ 30000), the period detection accuracy increases with the increase of δ, because in this case the second type error rate is much smaller than the first type error rate. However, when the signal length is short (l ≤ 20000), the second type error rate is relatively large. At this time, the period detection accuracy is not only dominated by the first type error rate, but the two are affected together. As δ increases, the period detection accuracy first increases and then decreases, and does not show an obvious upward trend. The non-increasing trend of period detection accuracy at different δ values ​​shows that dynamically selecting the appropriate δ according to different situations, that is, adaptively balancing the first and second type errors, can reduce the false alarm rate of period detection.

[0349] Experimental verification - bearing failure cycle detection

[0350] Bearings are key components of rotating machinery. When a bearing fails, the signal collected from the faulty bearing will show periodic characteristics, so the signal can be analyzed periodically to detect the fault. This experiment uses CWRU bearing experimental data to compare the fault cycle detection effect of IHTDSL and IHTFSL bearings, with a sampling frequency of 48kHz for drive-end bearing experiments. The test fault bearing used in the experiment is a 62052RS JEM SKF deep groove ball bearing. The outer ring fault diameter of the bearing is 0.007 inches, and this single-point fault is generated by electrospark machining. The specific operating parameters of the bearing are shown in Table 3. The bearing fault cycle is calculated to be approximately 9.3ms, that is, there are approximately 446 sample points in one cycle.

[0351] Table 3 Test bearing 62052RS JEM SKF working parameters

[0352]

[0353]

[0354] Table 3 (continued) Test bearing 62052RS JEM SKF operating parameters

[0355]

[0356] This case study randomly extracts sub-signals of length l from the collected vibration signal, where l = 2500, 3000, 3500, ..., 6000. 200 sub-signals of each length are randomly extracted to test the period detection accuracy of IHTDSL and IHTFSL at different lengths. The period detection range is set to [1, 1200], that is, K = 1200. The period detection accuracy of each method (i.e., satisfying )like Figure 8 shown.

[0357] from Figure 8 It can be seen that when the length of the signal to be tested is short, the period detection accuracy of all methods is relatively low, mainly due to the strong background noise masking effect of short signals. If the randomly generated non-periodic peaks have a similar height to the real periodic peaks (or even higher than the real periodic peaks), it is almost impossible to identify the real periodic peaks, resulting in period false alarms. However, in this case, the IHTDSL method proposed in this chapter is still better than the traditional methods.

[0358] As the signal length increases, the period detection accuracy of the IHTDSL method increases steadily when γ = 0.4 and γ = 0.5, and is significantly better than other methods. In contrast, the performance of IHTFSL depends largely on the choice of δ. The IHTFSL with δ = 3 has the lowest accuracy, while when δ is set to 30, the accuracy of IHTFSL is significantly improved, indicating that simply fixing the δ value cannot adapt well to signals with different noise conditions.

[0359] The relatively poor performance of IHTFSL may be due to the fact that the detected signal may not be strictly periodic, and the difference between two periodic peaks may be affected by periodic fluctuations. Therefore, the theoretical acceptance domain is too narrow to cover the true periodic peaks, resulting in a rather high type I error rate. This can also explain why increasing δ to 30 greatly improves the accuracy of period detection. This result shows that it is necessary to use dynamic confidence intervals in hypothesis testing, because it is quite difficult to manually determine the appropriate significance level in different application contexts.

[0360] The present invention designs a statistical method that can compare and gradually eliminate local optimal values, which is an important idea and urgent need to reduce the misdiagnosis rate of bearing fault cycle estimation. In order to fill the research gap of this idea in existing achievements, this technology will first borrow a similar idea of ​​NRC to design an enhanced anti-noise correlation (EnNRC) function to resist the masking effect of strong background noise. On this basis, an iterative hypothesis testing method is designed to gradually compare the two peaks of the proposed EnNRC statistic. The acceptance region is dynamically calculated in each step of the iterative hypothesis test, thereby greatly reducing the false alarm and omission rates. This method dynamically compares the alternative optimal value with other local optimal values ​​through iterative hypothesis testing, and ultimately eliminates the misleading of local optimality, eliminates false alarms and omissions of fault cycles, and correctly locates the cycle.

[0361] The present invention proposes an iterative hypothesis testing method with a dynamic significance level for the periodic automatic detection of bearing single-point fault signals. First, an EnNRC function designed based on an autocorrelation function is proposed for extracting signal features. Due to the special statistical properties of the peak difference of the EnNRC characteristic signal, this statistic is used as a test statistic for hypothesis testing, and the acceptance domain of the null hypothesis is specially designed using its statistical properties. In order to fully overcome the misleading effect of the periodic peak, the dynamically learned significance level is used to repeatedly perform iterative hypothesis testing until there are no obvious alternative peaks. Through iterative hypothesis testing, IHTDSL achieves a balance between type I errors and type II errors, and eliminates false alarms and missed alarms of fault cycles when the signal is long enough.

[0362] As an improved algorithm of NRC, the peak difference statistic and IHTDSL method designed based on EnNRC statistic are also applicable to NRC algorithm, and due to the similarity of the statistical structure of autocorrelation algorithm, the IHTDSL algorithm can be generalized and applied to the improvement of this type of algorithm through simple adaptation. Therefore, the IHTDSL proposed in the present invention has a certain universality, and provides theoretical support and research direction for the design of period automatic detection algorithm of autocorrelation feature extraction algorithm.

[0363] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0364] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for automatically detecting bearing fault cycles, characterized in that: include: Step 1: Collect vibration signals from the faulty bearing through sensors; Step 2: Divide the vibration signal, reassemble the odd and even segments respectively, and combine them into two sub-signals; Step 3: Use the NRC algorithm to process each sub-signal, and perform weighted summation to obtain the EnNRC statistic; Step 4: Use this statistic to further construct the peak difference statistic; Step 5: Construct a reduced confidence interval based on the dynamic significance level; Step 6: Starting from the highest peak of the EnNRC statistic, construct the peak difference statistic to the previous peak, and build a dynamic confidence interval to check whether there are other peaks in the interval. If there are other peaks, start the next hypothesis test from the highest peak in the interval and iterate until there are no other peaks in the interval. The peak at this time is the true fault cycle detected by the algorithm.

2. The method for automatic detection of bearing fault cycles according to claim 1, characterized in that: The collected periodic pulse signal y(t) generated by the operation of the faulty bearing is decomposed into the real fault signal x(t) and the background noise ∈(t), then: y(t) = x(t) + ∈(t), where ∈(t) ~ N(0, σ 2 ); Define the time series y = [y(1), y(2), ..., y(l)] T is the discrete observation value of y(t), l is the total number of samples; x = [x(1), x(2), ..., x(l)] T ,∈=[∈(1),∈(2),...,∈(l)] T ; Then the signal y is expressed as: y = x + ∈, ∈ ~ N (0, σ 2 I l ), I l is the identity matrix of size l×l; Assume the period of the fault signal x(t) is T0, T0 = p0 / f s , where p0>1 is the number of samples in one cycle, f s is the sampling frequency; The signal y is divided into Segment, the kth signal segment y k =[y((k-1)n+1), ..., y(kn)], where k = 1, 2, ..., m; n is the number of samples in each signal segment; Then the EnNRC statistic is expressed as: Where i and j are sequence numbers; if l%n≠0, the signal is divided into 2m+1 segments; The length of the signal segment of the odd segment is: n1 = l-mn, where The signal segment length of the even-numbered segment is: n2 = n - n1; Reassemble the odd-numbered signal segments into new sub-signals: Reassemble the even-numbered signal into a new sub-signal: In y o and e Construct NRC functions respectively, and get: in, The EnNRC statistic is and The weighted sum of The expression is: Among them, ω o =o n n1 / l,ω e =e n n2 / l.

3. The method for automatically detecting bearing fault cycles according to claim 2, characterized in that: The expression of EnNRC statistic is: Define y when 1%n=0 j，1 Empty, y j，2 =y j , and the inner product of two empty vectors is 0, for all i and j, Therefore, for any l, the EnNRC statistic is unified as: The expression is rewritten into matrix form: in, is a matrix of size l×l: Among them, M n By O n and E n The block diagonal matrix is ​​formed by and: The signal is divided in the same way on the real signal x and the background noise ∈ and the EnNRC statistic is constructed: thereby Rewritten as: The mean and variance of are: The expectation is no greater than the average energy of the true signal x According to the Cauchy-Schwarz inequality: in, The equation holds true if and only if n∈N; when l tends to infinity, Converges to 4. The method for automatically detecting bearing fault cycles according to claim 3 is characterized in that: The highest peak appears at the actual fault cycle The probability of and its multiples converges to 1 as the signal length l→∞, and the expression is: in, For any n≤K and As l→∞, the probability expression is: Noise term Any peak p to be detected and any candidate peak q obey an approximate normal distribution, and the expression is: when When the hypothesis test statistic is is related to the unknown signal x; and for any p and q, the peak difference are all bounded, and the expression is: is the actual cycle peak of the fault; is the target period peak, and the equality holds if and only if q∈N; According to this inequality, we construct a bounded acceptance region for the null hypothesis at any q value: Among them, δ is a parameter that controls the size of the receptive field; The reduced acceptance region for constructing the null hypothesis for any q value is: The reduced receptive field is obtained by the following formula, for all p and q, we have: The equivalent expression is: The equality holds if and only if p%q=0. Verifying this inequality is equivalent to verifying the inequality: T(C) p C q )≤Tr(C q C q ) The equality holds if and only if p%q=0; Each column vector of is a periodic sequence with period n, and when p%q=0, we have: therefore: So when p%q=0, we have: T((C) p —C q )C q )=Tr(-(C p —C q )D q )=0 The condition for the equation to hold in the inequality is p%q=0, and when p%q≠0, we get: T(C) p C q )<Tr(C k C q )=Tr(C q C q ) Here, k is a common multiple of p and q.

5. The method for automatically detecting bearing fault cycles according to claim 4, characterized in that: When there are multiple significant peaks in the acceptance domain, the one with the largest p-value is selected. The expression is: make Iterate until: when When the receiving domain There is no new peak The noise estimation method in the NRC algorithm is used to estimate σ 2 To estimate, the expression is: Designing iterative hypothesis testing based on dynamic significance level IHTDSL for automatic detection of fault cycles, the acceptance domain of IHTDSL Iterative learning is performed from the fault signal, and the confidence level δ is dynamically estimated in each iteration according to the following formula: Among them, γ∈(0,1), is the peak to be detected in this hypothesis test; The termination condition is simplified to: By estimating the δ value in IHTDSL to dynamically control the significance level, the adaptive receptive field in each iteration achieves a balance between the first type error and the second type error, so that both converge to 0, which is manifested in that both the misjudgment and omission of the fault cycle disappear when the signal is long enough.

6. A bearing fault cycle automatic detection system, characterized in that: include: Module M1: collects vibration signals from the faulty bearing through sensors; Module M2: divides the vibration signal, recombines the odd and even segments respectively, and combines them into two sub-signals; Module M3: Process each sub-signal using the NRC algorithm and perform weighted summation to obtain the EnNRC statistic; Module M4: Use this statistic to further construct the peak difference statistic; Module M5: Constructing reduced confidence intervals based on dynamic significance levels; Module M6: Starting from the highest peak of the EnNRC statistic, construct the peak difference statistic to the previous peak, and build a dynamic confidence interval to check whether there are other peaks in the interval. If there are other peaks, start the next hypothesis test from the highest peak in the interval and iterate until there are no other peaks in the interval. The peak at this time is the real fault cycle detected by the algorithm.

7. The bearing fault cycle automatic detection system according to claim 6, characterized in that: The collected periodic pulse signal y(t) generated by the operation of the faulty bearing is decomposed into the real fault signal x(t) and the background noise ∈(t), then: y(t) = x(t) + ∈(t), where ∈(t) ~ N(0, σ 2 ); Define the time series y = [y(1), y(2), ..., y(l)] T is the discrete observation value of y(t), l is the total number of samples; x = [x(1), x(2), ..., x(l)] T ,∈=[∈(1),∈(2),...,∈(l)] T ; Then the signal y is expressed as: y = x + ∈, ∈ ~ N (0, σ 2 I l ), I l is the identity matrix of size l×l; Assume the period of the fault signal x(t) is T0, T0 = p0 / f s , where p0>1 is the number of samples in one cycle, f s is the sampling frequency; The signal y is divided into Segment, the kth signal segment y k =[y((k-1)n+1), ..., y(kn)], where k = 1, 2, ..., m; n is the number of samples in each signal segment; Then the EnNRC statistic is expressed as: Where i and j are sequence numbers; if 1%n≠0, the signal is divided into 2m+1 segments; The length of the signal segment of the odd segment is: n1 = l-mn, where The signal segment length of the even-numbered segment is: n2 = n - n1; Reassemble the odd-numbered signal segments into new sub-signals: Reassemble the even-numbered signal into a new sub-signal: In y o and e Construct NRC functions respectively, and get: in, The EnNRC statistic is and The weighted sum of The expression is: Among them, ω o =o n n1 / l,ω e =e n n2 / l.

8. The bearing fault cycle automatic detection system according to claim 7, characterized in that: The expression of EnNRC statistic is: Define l%n=0 when y j，1 Empty, y j，2 =y j , and the inner product of two empty vectors is 0, for all i and j, Therefore, for any l, the EnNRC statistic is unified as: The expression of is rewritten into matrix form: in, is a matrix of size l×l: Among them, M n By O n and E n The block diagonal matrix is ​​formed by and: The signal is divided in the same way on the real signal x and the background noise ∈ and the EnNRC statistic is constructed: thereby Rewritten as: The mean and variance of are: The expectation is no greater than the average energy of the true signal x According to the Cauchy-Schwarz inequality: in, The equation holds true if and only if n∈N; when l tends to infinity, Converges to 9. The bearing fault cycle automatic detection system according to claim 8, characterized in that: The highest peak appears at the actual fault cycle The probability of and its multiples converges to 1 as the signal length l→∞, and the expression is: in, For any n≤K and As l→∞, the probability expression is: Noise term Any peak p to be detected and any candidate peak q obey an approximate normal distribution, and the expression is: when When the hypothesis test statistic is is related to the unknown signal x; and for any p and q, the peak difference are all bounded, and the expression is: is the actual cycle peak of the fault; is the target period peak, and the equality holds if and only if q∈N; According to this inequality, we construct a bounded acceptance region for the null hypothesis at any q value: Among them, δ is a parameter that controls the size of the receptive field; The reduced acceptance region for constructing the null hypothesis for any q value is: The reduced receptive field is obtained by the following formula, for all p and q, we have: The equivalent expression is: The equality holds if and only if p%q=0. Verifying this inequality is equivalent to verifying the inequality: The equality holds if and only if p%q=0; Each column vector of is a periodic sequence with period n, and when p%q=0, we have: therefore: So when p%q=0, we have: The condition for the equation to hold in the inequality is p%q=0, and when p%q≠0, we get: T(C) p C q )<Tr(C k C q )=Tr(C q C q ) Here, k is a common multiple of p and q.

10. The bearing fault cycle automatic detection system according to claim 9, characterized in that: When there are multiple significant peaks in the acceptance domain, the one with the largest p-value is selected. The expression is: make Iterate until: when When the receiving domain There is no new peak The noise estimation method in the NRC algorithm is used to estimate σ 2 To estimate, the expression is: Designing iterative hypothesis testing based on dynamic significance level IHTDSL for automatic detection of fault cycles, the acceptance domain of IHTDSL Iterative learning is performed from the fault signal, and the confidence level δ is dynamically estimated in each iteration according to the following formula: Among them, γ∈(0,1), is the peak to be detected in this hypothesis test; The termination condition is simplified to: By estimating the δ value in IHTDSL to dynamically control the significance level, the adaptive receptive field in each iteration achieves a balance between the first type error and the second type error, so that both converge to 0, which is manifested in that both the misjudgment and omission of the fault cycle disappear when the signal is long enough.

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