Automatic detection method and system for bearing failure based on iterative likelihood ratio test

Abstract

The application provides a bearing fault automatic detection method and system based on iterative likelihood ratio test, relates to the technical field of bearing fault periodic signal modeling and period automatic detection, and comprises the following steps: S1, collecting a noisy periodic signal from a fault bearing by using a sensor; S2, constructing a constrained linear model, performing parameter estimation and calculating a likelihood function after segmenting the signal by the constrained linear model; S3, obtaining a likelihood function waveform graph by scanning a period parameter; S4, obtaining an accurate period from the likelihood function waveform graph by iterative likelihood ratio test; and S5, performing fault diagnosis on the bearing by using the period estimation result. The application can make the regression model more stable, the period estimation effect more accurate, effectively eliminate false positives and false negatives of the fault period when the signal is long enough through iterative hypothesis testing.

Description

Technical Field

[0001] This invention relates to the field of bearing fault periodic signal modeling and automatic periodic detection technology, specifically to an automatic bearing fault detection method and system based on iterative likelihood ratio test. Background Technology

[0002] Periodic signals are an essential research object in signal processing and are widely used in various applications such as biomedical signal processing [1], wireless communication [2-3], and vibration signal processing [4-6]. Among them, 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 techniques are based on the time domain and frequency domain information of vibration signals. By extracting and analyzing the relevant features of vibration signals and comparing them with the feature indicators of vibration signals generated in a healthy state, the current operating status of the equipment is analyzed to determine whether there are potential faults. This technology focuses on the periodic fault detection problem caused by single-point bearing faults.

[0003] Typically, if the background noise is sufficiently weak, periodic signals can be processed in the frequency domain to estimate their period. These methods include periodograms [7-10], spectral kurtosis [11-13], wavelet transform [14-15], and multi-signal classification methods [16-17]. However, when the signal is contaminated by strong background noise, the effectiveness of these methods is severely limited, as the spectrum no longer provides effective peaks for localization at the true periodic location due to the strong interference from the background noise [18-19]. Therefore, under strong noise constraints, these traditional methods cannot guarantee accurate identification of fundamental periodic features.

[0004] Another class of methods analyzes periodic signals in the time domain, such as correlation-based methods [20-22] and likelihood-based methods [23-24]. These methods divide the signal into segments, using the parameter with the highest correlation or likelihood at the time of segmentation as the signal period. These methods utilize the statistical properties of periodic signals and have the ability to handle strong background noise. However, these methods assume that two adjacent segments of the signal may be discontinuous, meaning that the last point of one segment may deviate from the first point of the next segment. This assumption of discontinuity violates the experience that most periodic signals (e.g., EEG / ECG and bearing vibration signals) are continuous, therefore two adjacent segments of the segmented signal should also be continuous.

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[0029] For most frequency domain methods, their effectiveness is severely limited when the signal is contaminated by strong background noise. Due to the strong interference from the background noise, the spectrum no longer provides effective peaks for localization at the true periodic positions. Therefore, under strong noise constraints, these traditional methods cannot guarantee accurate identification of fundamental periodic features.

[0030] Time-domain methods for analyzing periodic signals, such as correlation- and likelihood-based methods, are effective at handling strong background noise. However, these methods assume that two adjacent segments of the signal may be discontinuous; that is, the last point of one segment may deviate from the first point of the next segment. This assumption of discontinuity violates the experience that most periodic signals (e.g., EEG / ECG and bearing vibration signals) are continuous, therefore, two adjacent segments of the segmented signal should also be continuous.

[0031] Furthermore, applying the likelihood function of these linear models for period estimation can also encounter a misleading effect: the waveform often has actual peaks located within the true period and misleading peaks with similar or higher amplitudes. This misleading effect often renders traditional maximum likelihood estimation methods ineffective. It is difficult to identify the true peaks using existing optimization techniques because the misleading peaks cause search algorithms to become bogged down by peaks located across multiple periods, hindering these algorithms from automatically finding the true period. This deficiency largely depends on prior human knowledge of the waveform to avoid the misleading effect, making accurate and reliable period estimation extremely difficult and rendering online anomaly detection (such as machine condition monitoring) unreliable. Summary of the Invention

[0032] To address the shortcomings of existing technologies, this invention provides an automatic bearing fault detection method and system based on iterative likelihood ratio testing.

[0033] According to the present invention, an automatic bearing fault detection method and system based on iterative likelihood ratio test are provided, the scheme of which is as follows:

[0034] Firstly, an automatic bearing fault detection method based on iterative likelihood ratio test is provided, the method comprising:

[0035] Step S1: Use sensors to collect noisy periodic signals from the faulty bearing;

[0036] Step S2: Construct a constrained linear model, segment the signal using the constrained linear model, estimate the parameters, and calculate the likelihood function;

[0037] Step S3: Obtain the likelihood function waveform by scanning the periodic parameter;

[0038] Step S4: Obtain the accurate period from the likelihood function waveform by iterative likelihood ratio test;

[0039] Step S5: Use the cycle estimation result to diagnose bearing faults.

[0040] Preferably, step S2 includes: adding two continuity constraints to the traditional linear model modeling, the first constraint being:

[0041]

[0042] Ensure realistic fault signals Continuity,

[0043]

[0044] Among them, the actual fault signal Establish a regression model and express it as ,Right now ,in It is a regression function; Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows:

[0045]

[0046]

[0047] in, , For non-decreasing nodes, and These are two important model parameters that control the B-spline basis.

[0048] Preferably, the second constraint is:

[0049]

[0050] Ensure the derivative of the true fault signal Continuity,

[0051]

[0052] In the formula, , .

[0053] Preferably, the parameter estimation and likelihood function calculation in step S2 includes:

[0054] Given signal The log-likelihood of the constrained linear model is written as:

[0055]

[0056] Obeying conditions ,in

[0057]

[0058] When matrix C has linearly dependent rows, i.e. ,use To replace it, ensuring that matrix C is always full rank; log-likelihood function Constraints By order To replace, among which To ensure that the requirement is met, the dimension of matrix D is [missing information]. ,vector Length is .

[0059] For any constraint matrix with full rank There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function:

[0060]

[0061] Maximizing the likelihood function is equivalent to optimizing the following cost function:

[0062]

[0063] Where, the dimension of matrix D is ,vector Length is ; Indicates the number of signal segments; matrix for:

[0064]

[0065] Will Substitution ,get:

[0066]

[0067] By solving the equation ,parameter The estimator is:

[0068]

[0069] in, Indicates signal length; parameters The estimator is substituted into the log-likelihood function In the middle, we get:

[0070]

[0071] By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function.

[0072] Preferably, step S4, which iteratively searches for the true period through an iterative likelihood ratio test, includes:

[0073] Assume the test will be repeated until no new candidate cycles are found, and the steps are as follows:

[0074] 1) init: and

[0075] 2) while: do

[0076] a.

[0077] b. if then

[0078] c.

[0079] end while

[0080] 3) return

[0081] In each iteration, check To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, updating the periodic estimate until no peaks appear in the acceptance domain, at which point the process stops.

[0082] Secondly, an automatic bearing fault detection system based on iterative likelihood ratio test is provided, the system comprising:

[0083] Model M1: Noisy periodic signals are collected from the faulty bearing using sensors;

[0084] Model M2: Construct a constrained linear model, segment the signal using the constrained linear model, estimate the parameters, and calculate the likelihood function;

[0085] Model M3: The likelihood function waveform is obtained by scanning the periodic parameters;

[0086] Model M4: The accurate period is obtained from the likelihood function waveform through iterative likelihood ratio test;

[0087] Model M5: Use the period estimation results to diagnose bearing faults.

[0088] Preferably, module M2 includes: adding two continuity constraints to the traditional linear model modeling, the first constraint being:

[0089]

[0090] Ensure realistic fault signals Continuity,

[0091]

[0092] Among them, the actual fault signal Establish a regression model and express it as ,Right now ,in It is a regression function; Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows:

[0093]

[0094]

[0095] in, , For non-decreasing nodes, and These are two important model parameters that control the B-spline basis.

[0096] Preferably, the second constraint is:

[0097]

[0098] Ensure the derivative of the true fault signal Continuity,

[0099]

[0100] In the formula, , .

[0101] Preferably, the parameter estimation and likelihood function calculation in module M2 includes:

[0102] Given signal The log-likelihood of the constrained linear model is written as:

[0103]

[0104] Obeying conditions ,in

[0105]

[0106] When matrix C has linearly dependent rows, i.e. ,use To replace it, ensuring that matrix C is always full rank; log-likelihood function Constraints By order To replace, among which To ensure that the requirement is met, the dimension of matrix D is [missing information]. ,vector Length is .

[0107] For any constraint matrix with full rank There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function:

[0108]

[0109] Maximizing the likelihood function is equivalent to optimizing the following cost function:

[0110]

[0111] Where, the dimension of matrix D is ,vector Length is ; Indicates the number of signal segments; matrix for:

[0112]

[0113] Will Substitution ,get:

[0114]

[0115] By solving the equation ,parameter The estimator is:

[0116]

[0117] in, Indicates signal length; parameters The estimator is substituted into the log-likelihood function In the middle, we get:

[0118]

[0119] By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function.

[0120] Preferably, the module M4 iteratively searches for the true period through an iterative likelihood ratio test, including:

[0121] Assume the test will be repeated until no new candidate cycles are found, and the steps are as follows:

[0122] 1) init: and

[0123] 2) while: do

[0124] a.

[0125] b. if then

[0126] c.

[0127] end while

[0128] 3) return

[0129] In each iteration, check To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, updating the periodic estimate until no peaks appear in the acceptance domain, at which point the process stops.

[0130] Compared with the prior art, the present invention has the following beneficial effects:

[0131] 1. The constrained linear model proposed in this invention considers the continuity constraints between periodic signals compared with traditional methods, making the regression model more stable and the period estimation effect more accurate.

[0132] 2. To fully overcome the misleading effect of periodic peaks, iterative hypothesis testing is used until no more obvious alternative peaks are found. Through iterative hypothesis testing, false alarms and missed alarms during fault cycles can be effectively eliminated when the signal is long enough.

[0133] 3. Compared to traditional methods, this method, based on statistical inference, can more accurately detect periodic components in signals over shorter signal intervals. Furthermore, this invention can use hypothesis testing and statistical inference to select models from a large number of constructed signal models and provide the probabilities of false alarms and false positives. Attached Figure Description

[0134] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0135] Figure 1 This is an overall flowchart of the present invention;

[0136] Figure 2 The waveform of a general B-spline function;

[0137] Figure 3 Comparison of different waveforms generated using the original linear model LM and the constrained linear model CLM;

[0138] Figure 4 An example of the ILRT algorithm for locating the true cycle;

[0139] Figure 5 To improve the accuracy of period estimation as the signal length varies;

[0140] Figure 6 For the period estimation accuracy as the signal-to-noise ratio varies;

[0141] Figure 7 It is a time-domain vibration signal;

[0142] Figure 8 The Fourier spectrum of the time-domain vibration signal;

[0143] Figure 9 The waveform diagram of CLM;

[0144] Figure 10 Waveform diagram of the NRC field for applying ILRT;

[0145] Figure 11 Waveform of the MLPE receiving field for applying ILRT. Detailed Implementation

[0146] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0147] This invention provides an automatic bearing fault detection method based on iterative likelihood ratio testing. The most obvious characteristic of a single-point bearing fault is that the vibration signal exhibits periodicity during uniform rotation, meaning the fault has a certain frequency. This frequency can be calculated using bearing parameters and motor speed. However, due to the overall structure of the equipment and the instability of the rotational speed, and because bearings experience wear over time, actual parameters change, making it impossible to calculate the theoretical fault frequency in practical applications. Therefore, designing an algorithm to capture the bearing fault cycle through vibration signals, extracting the periodic fault components, and performing subsequent diagnosis are essential. (Refer to...) Figure 1 As shown, the specific steps of this method are as follows:

[0148] Step S1: Use a sensor to collect a noisy periodic signal from the faulty bearing.

[0149] Step S2: Construct a constrained linear model, segment the signal using the constrained linear model, estimate the parameters, and calculate the likelihood function.

[0150] Step S3: Obtain the likelihood function waveform by scanning the periodic parameters.

[0151] Step S4: Obtain the accurate period from the likelihood function waveform by iterative likelihood ratio test.

[0152] Step S5: Use the cycle estimation result to diagnose bearing faults.

[0153] Specifically, step S2 includes: adding two continuity constraints to the traditional linear model modeling, the first constraint being:

[0154]

[0155] Ensure realistic fault signals Continuity,

[0156]

[0157] Among them, the actual fault signal Establish a regression model and express it as ,Right now ,in It is a regression function; Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows:

[0158]

[0159]

[0160] in, , For non-decreasing nodes, and These are two important model parameters that control the B-spline basis.

[0161] The second constraint is:

[0162]

[0163] Ensure the derivative of the true fault signal Continuity,

[0164]

[0165] In the formula, , .

[0166] Parameter estimation and likelihood function calculation include:

[0167] Given signal The log-likelihood of the constrained linear model is written as:

[0168]

[0169] Obeying conditions ,in

[0170]

[0171] When matrix C has linearly dependent rows, i.e. ,use To replace it, ensuring that matrix C is always full rank; log-likelihood function Constraints By order To replace, among which To ensure that the requirement is met, the dimension of matrix D is [missing information]. ,vector Length is .

[0172] For any constraint matrix with full rank There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function:

[0173]

[0174] Maximizing the likelihood function is equivalent to optimizing the following cost function:

[0175]

[0176] Where, the dimension of matrix D is ,vector Length is ; Indicates the number of signal segments; matrix for:

[0177]

[0178] Will Substitution ,get:

[0179]

[0180] By solving the equation ,parameter The estimator is:

[0181]

[0182] in, Indicates signal length; parameters The estimator is substituted into the log-likelihood function In the middle, we get:

[0183]

[0184] By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function.

[0185] Specifically, step S4 iteratively searches for the true period through an iterative likelihood ratio test, including:

[0186] Assume the test will be repeated until no new candidate cycles are found, and the steps are as follows:

[0187] 1) init: and

[0188] 2) while: do

[0189] a.

[0190] b. if then

[0191] c.

[0192] end while

[0193] 3) return

[0194] In each iteration, check To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, updating the periodic estimate until no peaks appear in the acceptance domain, at which point the process stops.

[0195] The present invention will now be described in more detail.

[0196] Periodic pulse signal generated by the operation of a faulty bearing It can be decomposed into real fault signals and background noise ,Right now in .by The sampling frequency and the length of the collection are The signal is represented as:

[0197]

[0198] Here is the signal Divided into each signal segment , of which Each segment is ,when At that time, the signal segment contains There are points, and the last signal segment is represented as... ,Include A point. Here, the symbol... Indicates less than The largest integer, The number of signal points in a signal segment is represented by the actual period of the signal. .

[0199] In this solution, we will use real fault signals Establish a regression model and express it as ,Right now ,in It is a regression function. Therefore, the acquired periodic signal It can be modeled using the following linear model:

[0200]

[0201] in, These are regression coefficients, with a length of [missing information]. The vector and usually with It changes with the changes. Matrix for:

[0202]

[0203] Among the noise components It can be given similarly as

[0204]

[0205] Such a linear model can also be represented in matrix form as follows:

[0206]

[0207] in , It is a block diagonal matrix. .

[0208] when , ,at the same time ,in The dimension is The identity matrix, at the same time The dimension of the matrix is In such cases, the proposed linear model degenerates into the MLPE method (a classic periodic estimator) for estimating speech pitch based on maximum likelihood estimation. However, using the identity matrix as a regression basis is too rigid and has limited practical applicability. Therefore, many researchers have developed other regression bases for modeling periodic signals, such as tunable Q-factor wavelets and Morlet wavelets. However, manually selected dictionaries are not flexible because they typically need to be applied to specific cases based on some prior knowledge.

[0209] Similar to the regression basis used in the separable sparse representation model, this study also uses B-spline basis functions as the regression basis because they more closely approximate the true signal. The flexibility. The regression basis function is:

[0210]

[0211] Where k = 0, 1, 2, ..., n-1, It means k mod p, and at the same time Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows:

[0212]

[0213]

[0214] in, , These are non-decreasing nodes. For example, a commonly used node sequence is: ,in In the interval Medium-distance distribution.

[0215] In such a model, and These are two important model parameters that control the B-spline basis. These are the degrees of freedom of a B-spline function with non-negative integer values. By appropriately selecting the corresponding nodes when d = 0, this basis function can also obtain the same regression matrix as proposed in MLPE. However, when When using large integers, the linear model can become very complex, potentially leading to overfitting. Therefore, we recommend choosing d=2, 3, or 4 in practical applications. It is less than or equal to But greater than The number of B-spline control points within the segment, i.e. It is important to note that, Should follow The corresponding changes occur because longer signal segments should ideally be modeled using B-splines with more control points. A linear relationship is recommended here. and .

[0216] However, using only such a model has certain drawbacks. Traditional linear models struggle to guarantee the continuity of the signal and its derivatives between two adjacent periods because they ignore the constraint that start and end points with the same period should have similar values. On the contrary, such signal modeling can sometimes result in significant jumps between two adjacent periods. . Reference Figure 2 The step portion of the solid line indicates that it does not consider the continuity constraint, and the dashed line also ignores this constraint because its first derivative is discontinuous, resulting in a lack of smoothness.

[0217] To address this shortcoming, we added two continuity constraints to the traditional linear model. The first constraint is:

[0218]

[0219] Ensure signal The continuity, in which

[0220]

[0221] The second constraint is:

[0222]

[0223] Ensure signal derivative The continuity. Among them,

[0224]

[0225] In the formula , Linear constraints allow us to... The information is combined as a continuous cyclic function. Therefore, we call this modified linear model a constrained linear model (CLM).

[0226] Therefore, given signal The log-likelihood of a constrained linear model can be written as:

[0227]

[0228] Obeying conditions ,in

[0229]

[0230] When matrix C has linearly dependent rows, i.e. We use Instead, this simplified form ensures that matrix C is always full rank. (Log-likelihood function) Constraints It can be made To replace, among which This will ensure that the D matrix dimension is satisfied. ,vector Length is Matrix D can be obtained by performing singular value decomposition on matrix C, a property that will be proven by the following theorem.

[0231] Theorem: For any constraint matrix with full rank... There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function:

[0232]

[0233] According to singular value decomposition:

[0234]

[0235] Proof: Because at the same time It can be concluded that ,in yes A matrix. Then there exists a matrix. , such that for any , Established. Substituting into this equation, we can obtain For any All Therefore, for any You can get This indicates that the constraint This is true. Therefore, the original constrained log-likelihood function can be replaced by the unconstrained log-likelihood function as described above.

[0236] According to the theorem, maximizing the likelihood function is equivalent to optimizing the following cost function:

[0237]

[0238] Therefore, Substitution We can obtain:

[0239]

[0240] By solving the equation ,parameter The estimator is:

[0241]

[0242] parameters The estimator is substituted into the log-likelihood function From this, we can obtain:

[0243]

[0244] By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function. For example... Figure 3As shown, the original LM model encounters a significant jump between two signal segments because the control points in the B-spline basis can only guarantee smoothness within the signal segment. Without continuity constraints, LM leads to low period estimation accuracy and unsmooth signal reconstruction. In contrast, the Constrained Linear Model (CLM) avoids these drawbacks, producing continuous... The periodicity is also smooth over two adjacent segments. This characteristic improves the stability of the periodicity estimation.

[0245] In periodic signal modeling, traditional methods typically use the scan period parameter. The method to estimate the accurate period is when the likelihood function When the peak is reached, that is The period estimation results are obtained. However, the likelihood function waveform under the linear model framework usually has not only one peak at the exact period, but also multiple similar peaks at multiples of the period. , in Furthermore, this likelihood function waveform tends to drift upwards because of the degree of freedom. Typically, the likelihood increases with p. Although some methods propose a penalty term to eliminate this increasing trend, the penalized likelihood waveform of traditional linear models (such as MLPE) still exhibits misleading peaks at the true period and its multiples, also known as the misleading effect. The appearance of these peaks will greatly affect the accuracy of period estimation and hinder automatic period detection, because the highest peak may not be within the true period.

[0246] Generally, the traditional maximum likelihood method is used. An estimate of the cycle can be provided. However, the method estimates... It is usually located at multiple cycle points (rather than exact cycle points). Therefore, in All previous likelihoods ,Right now It should be carefully examined for testing. Any previous period This relates to the possibility of a true periodicity. To address the misleading effect, an Iterative Likelihood Ratio Test (ILRT) is proposed to statistically detect the true periodicity. To obtain more accurate cycle estimation results.

[0247] Based on the linear model framework, These are the model parameters, and the number of parameters varies with the period. It changes with the change. Therefore, the corresponding value for each point in the likelihood function is... The total will constitute a parameter space To distinguish the peaks at true periodic points from other misleading peaks, we define a subparameter space. ,in ,at the same time .

[0248] In this case, we propose the following hypothesis test:

[0249]

[0250] According to Wilk's theorem, the test statistic for the proposed hypothesis test can be constructed using the likelihood ratio, as follows:

[0251]

[0252] in, This is the currently estimated period. Indicates the alternative real period. Under the null hypothesis... The likelihood ratio between the original model and the candidate model follows a chi-square distribution:

[0253]

[0254] in It is the difference in degrees of freedom between the zero model and the alternative models, i.e.

[0255]

[0256] Given a significance level The chi-square distribution described above can be used to generate log-likelihood. The accepting domain. If If it falls into the accepting domain, then By updating The new candidate period is accepted as a new candidate. Similarly, the new candidate period may still not be the true period because there may still be other candidate periods ahead, so another hypothesis needs to be made. Therefore, we propose an iterative likelihood ratio test (ILRT) to iteratively search for the true period. The hypothesis test will be repeated until no new candidate period can be found. The steps of the algorithm are as follows:

[0257] 1) init: and

[0258] 2) while: do

[0259] a.

[0260] b. if then

[0261] c.

[0262] end while

[0263] 3) return

[0264] The proposed hypothesis testing involves three iterations, as follows: Figure 4 As shown. The shaded area is The acceptance region is calculated based on the chi-square distribution. In each iteration, the following is checked: To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, thus the proposed ILRT algorithm can update its periodic estimate until no peaks appear in the acceptance region. It can usually be set to 0.05.

[0265] By applying this ILRT algorithm, the drift problem present in waveforms using likelihood functions can be solved. It should also be noted that this algorithm is not limited to our proposed CLM model. It can also be applied to other conventional methods, such as MLPE, to address the misleading effect problem. Furthermore, traditional period detection tasks provide a frequency or time domain plot, requiring further visual judgment to identify the period. However, the algorithm proposed in this paper can automatically detect the true period with high accuracy, making online detection feasible and reliable.

[0266] The invention will be further described below with reference to examples:

[0267] 1. Simulation verification

[0268] This section compares the period estimation performance of the proposed constrained linear models CLM and ILRT with that of the original linear models LM and ILRT, the noise-resistant correlation method (NRC), and the maximum likelihood fundamental frequency estimation (MLPE), using periodic transient signals:

[0269]

[0270] To simulate periodic signals ,in For the damping ratio, Hz is the natural frequency. The number of sample points within one period. Hz is the sampling frequency. Additionally, Gaussian white noise is added to obtain the noise signal. .

[0271] Two simulations were performed: (a) signal length (a) The signal length changes from 5 seconds to 40 seconds in increments of 5 seconds, with the SNR (signal-to-noise ratio) set to -20 dB; (b) The SNR changes from -20 dB to -11 dB in increments of 1 dB. The time limit is set to 10 seconds. For each of the two guidelines, 100 trials are repeated, with signals generated independently in each trial. This simulation aims to investigate the period estimation performance of various methods with different signal lengths and SNRs.

[0272] The comparison results of the two simulations in terms of period estimation accuracy are as follows: Figure 5 and Figure 6 As shown in the figure. In both simulations, LM and CLM both showed superior performance compared to their competitors NRC and MLPE. This is because LM and CLM use more complex periodic structures to model the signal, and the ILRT algorithm can resolve misleading effects by statistically comparing suspicious peaks.

[0273] In both simulations, CLM significantly outperformed LM in period estimation, especially when the signal length was short or the signal-to-noise ratio was low. CLM's superior performance demonstrates that adding continuity constraints can significantly improve period estimation accuracy because the linearity in CLM takes into account more information contained in the signal. On the other hand, LM encounters anomalous discontinuities between two signal segments. This instability hinders the accuracy of period estimation, especially for short signals with low signal-to-noise ratios.

[0274] 2. Experimental Verification – Bearing Failure Cycle Detection

[0275] Bearings are critical components of rotating machinery. When a bearing fails, the signal collected from the faulty bearing exhibits periodic characteristics, thus periodic analysis can be performed to detect the fault. This experiment uses experimental data from a self-made bearing to compare the bearing fault periodic detection effect of the proposed method. The sampling frequency of the experimental setup was 51.2 kHz, used for the drive-end bearing experiment. The faulty bearing used in the experiment was an NJ208 TMB deep groove ball bearing. Its operating parameters are shown in Table 1 below:

[0276] Table 1. Operating parameters of bearing NJ208 TMB tested.

[0277]

[0278] Table 1 (continued) Operating parameters of bearing NJ208 TMB

[0279]

[0280] The vibration signal with a time domain length of 0.195s (N=10000 sampling points) and its Fourier spectrum are as follows: Figure 7 and Figure 8 As shown, the time-domain vibration signal only exhibits some fuzzy periodic structures, with a fault characteristic period (T=7pm0.07ms, i.e.) This type of vibration signal is difficult to detect due to interference from other periodic components and background noise. Furthermore, traditional Fourier spectra fail to reveal the fault frequency. In this case, the fault characteristic frequency is obscured by high-frequency periodic components. Therefore, the proposed CLM combined with ILRT can be used to analyze such vibration signals. The search range of p in ILRT is designed as follows: ,Right now Model parameters and Set to 2 and The experimental results are as follows: Figure 9 , 10 As shown in Figure 11.

[0281] Figure 9 This indicates that the likelihood waveform of the CLM can be observed during the fault characteristic period ( The peaks at and multiples thereof are clearly visible. However, only blurred peaks can be observed in the waveforms obtained using the NRC and MLPE methods. Figure 10 As shown in Figure 11, the true period is difficult to obtain directly due to numerous misleading peaks around the true period and double period points. This reduces the reliability of these methods in practical applications due to strong noise interference. In contrast, the likelihood waveform of CLM is clearer, the true peak is easily identified, and other points are suppressed to low amplitude. Although the second peak of the CLM likelihood is higher than the true peak, the ILRT algorithm can bypass the highest peak because... The peak value falls within its acceptance region, as shown by the shaded area in the figure. Combining CLM with ILRT allows for accurate and automatic estimation of fault characteristic cycles, suitable for online automated detection without human intervention. This experiment demonstrates the superiority of the proposed method over traditional methods and its ability to automatically detect bearing faults from numerous misleading peak values.

[0282] This invention provides an automatic bearing fault detection method and system based on iterative likelihood ratio test. It proposes a continuity constraint in the construction of the signal regression model; by comparing periodic peaks with interference effects and other non-periodic peaks through iterative hypothesis testing, it gradually eliminates the misleading effect of local optima, thereby improving the accuracy of periodic detection; it uses statistical inference for model selection, providing the probability of false alarms; and it applies this algorithm to other applications that are essentially periodic detection (including applications such as audio main frequency recognition).

[0283] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0284] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. An automatic bearing fault detection method based on iterative likelihood ratio test, characterized in that, include: Step S1: Use sensors to collect noisy periodic signals from the faulty bearing; Step S2: Construct a constrained linear model, segment the signal using the constrained linear model, estimate the parameters, and calculate the likelihood function; Step S3: Obtain the likelihood function waveform by scanning the periodic parameter; Step S4: Obtain the accurate period from the likelihood function waveform by iterative likelihood ratio test; Step S5: Use the cycle estimation result to diagnose bearing faults; Step S2 includes: adding two continuity constraints to the traditional linear model modeling, the first constraint being: Ensure realistic fault signals Continuity, Among them, the actual fault signal Establish a regression model and express it as ,Right now ,in It is a regression function; Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows: in, , For non-decreasing nodes, and These are two important model parameters that control the B-spline basis; The second constraint is: Ensure the derivative of the true fault signal Continuity, In the formula, , ; Step S4, which iteratively searches for the true period through an iterative likelihood ratio test, includes: Assume the test will be repeated until no new candidate cycles are found, and the steps are as follows: 1) init: and 2) while: do a. b. if then c. end while 3) return In each iteration, check To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, updating the periodic estimate until no peaks appear in the acceptance domain, at which point the process stops.

2. The automatic bearing fault detection method based on iterative likelihood ratio test according to claim 1, characterized in that, The parameter estimation and likelihood function calculation in step S2 include: Given signal The log-likelihood of the constrained linear model is written as: Obeying conditions ,in When matrix C has linearly dependent rows, i.e. ,use To replace it, ensuring that matrix C is always full rank; log-likelihood function Constraints By order To replace, among which To ensure that the requirement is met, the dimension of matrix D is [missing information]. ,vector Length is ; For any constraint matrix with full rank There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function: Maximizing the likelihood function is equivalent to optimizing the following cost function: Where, the dimension of matrix D is ,vector Length is ; Indicates the number of signal segments; matrix for: Will Substitution ,get: By solving the equation ,parameter The estimator is: in, Indicates signal length; parameters The estimator is substituted into the log-likelihood function In the middle, we get: By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function.

3. An automatic bearing fault detection system based on iterative likelihood ratio test, characterized in that, include: Module M1: Uses sensors to collect noisy periodic signals from the faulty bearing; Module M2: Constructs a constrained linear model, segments the signal using the constrained linear model, estimates the parameters, and calculates the likelihood function; Module M3: Obtains the likelihood function waveform by scanning the periodic parameters; Module M4: Obtains the accurate period from the likelihood function waveform through iterative likelihood ratio test; Module M5: Uses the cycle estimation results to diagnose bearing faults; Module M2 includes: adding two continuity constraints to the traditional linear model modeling, the first constraint being: Ensure realistic fault signals Continuity, Among them, the actual fault signal Establish a regression model and express it as ,Right now ,in It is a regression function; Let d denote the B-spline basis function with d degrees of freedom, and its specific definition is as follows: in, , For non-decreasing nodes, and These are two important model parameters that control the B-spline basis; The second constraint is: Ensure the derivative of the true fault signal Continuity, In the formula, , ; The module M4 iteratively searches for the true period through an iterative likelihood ratio test, including: Assume the test will be repeated until no new candidate cycles are found, and the steps are as follows: 1) init: and 2) while: do a. b. if then c. end while 3) return In each iteration, check To test Whether it falls within the acceptance domain, in which, It is a chi-square distribution The top quantile; if any Make ,renew The hypothesis testing continues, updating the periodic estimate until no peaks appear in the acceptance domain, at which point the process stops.

4. The automatic bearing fault detection system based on iterative likelihood ratio test according to claim 3, characterized in that, The parameter estimation and likelihood function calculation in module M2 include: Given signal The log-likelihood of the constrained linear model is written as: Obeying conditions ,in When matrix C has linearly dependent rows, i.e. ,use To replace it, ensuring that matrix C is always full rank; log-likelihood function Constraints By order To replace, among which To ensure that the requirement is met, the dimension of matrix D is [missing information]. ,vector Length is ; For any constraint matrix with full rank There exists a matrix This makes the original log-constrained likelihood function the same as the following unconstrained likelihood function: Maximizing the likelihood function is equivalent to optimizing the following cost function: Where, the dimension of matrix D is ,vector Length is ; Indicates the number of signal segments; matrix for: Will Substitution ,get: By solving the equation ,parameter The estimator is: in, Indicates signal length; parameters The estimator is substituted into the log-likelihood function In the middle, we get: By incorporating these continuity constraints into a B-spline-based linear model, the recovered signal... It is a continuous, smooth, periodic function.

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