Bearing health index construction method based on polynomial rotating speed normalization

Abstract

The invention relates to a bearing health index construction method based on polynomial rotating speed normalization, and belongs to the technical field of bearing performance degradation evaluation. According to the method, firstly, a polynomial rotating speed normalization method is adopted to carry out normalization processing on monitoring data, then, a Gaussian mixture model and an index mixture model are utilized to construct time domain and frequency domain health indexes respectively, and finally, the time domain and frequency domain health indexes are linearly weighted to construct a final wind power bearing health index. The method can effectively inhibit the rotation speed interference, thereby achieving the performance degradation evaluation of the bearing under the time-varying rotation speed condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing performance degradation evaluation, and relates to a method for constructing a bearing health index based on polynomial rotational speed normalization. Background Art

[0002] As a core load-bearing component of the transmission system of high-end mechanical equipment, bearings play an irreplaceable role in key fields of the national economy such as national defense, rail transit, and aerospace. Affected by the coupling of multiple uncertain factors such as complex dynamic loads, multi-source lubrication states, assembly tolerances, and material property discreteness, bearings often exhibit the dual characteristics of diverse failure modes and complex failure mechanisms during service. Research shows that under extreme working conditions, its typical failure forms can be systematically classified into four major failure spectra, namely, structural damage type (fatigue spalling, crack propagation, fracture failure), surface degradation type (pitting, wear, scuffing, scoring), material property degradation type (corrosion, indentation), and motion instability type (slipping, burning). It should be noted that the progressive damage evolution of bearings will trigger a chain of fault responses in rotating machinery, which may lead to unplanned shutdowns and damage to core components in the lightest case, and may even trigger catastrophic accidents in the most serious case, posing a serious threat to personnel life safety and major property.

[0003] Based on this, constructing a quantitative evaluation system for bearing performance degradation has become an important research direction in the field of mechanical equipment condition monitoring. By accurately capturing the performance degradation trajectory of components, it can effectively achieve early fault detection and remaining life prediction of mechanical equipment, providing important technical support for ensuring the safe operation of key equipment throughout its life cycle, and having significant social and economic benefits and engineering application values.

[0004] The performance degradation process of bearings can be quantified by constructing health indicators. Among the methods for constructing health indicators of mechanical equipment, most methods establish health indicators under the assumption of stable working conditions. In actual industrial application scenarios, the working conditions of bearings in some mechanical equipment will change continuously with the change of the external environment. The change of working conditions will cause amplitude modulation interference in the collected monitoring data, which will further affect the accurate characterization of the bearing degradation trajectory by the health indicator. Therefore, it is necessary to study a method for constructing a health indicator that suppresses rotational speed interference, so as to realize the performance degradation evaluation of bearings under time-varying rotational speed conditions.

[0005] Existing rotational speed interference suppression methods can eliminate the influence of operating conditions on the amplitude of monitoring data through rotational speed normalization. Currently, researchers, starting from the relationship between centrifugal force and rotational speed, speculate that there is a correlation between the amplitude of the mechanical monitoring signal and the square of the rotational speed. By dividing the amplitude of the original monitoring data by the square of the rotational speed, normalization is implemented to suppress the amplitude modulation interference caused by changes in rotational speed in the monitoring data. However, the amplitude of the actual monitoring data may not be correlated with the square of the rotational speed and may be related to higher orders of the rotational speed. Secondly, changes in rotational speed can also cause changes in signal energy. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method for constructing a bearing health index based on polynomial rotational speed normalization, which can effectively suppress rotational speed interference, thereby realizing the performance degradation assessment of bearings under time-varying rotational speed conditions.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for constructing a bearing health index based on polynomial rotational speed normalization specifically includes the following steps:

[0009] S1: Collect the monitoring data of the bearing and perform preprocessing operations on it to eliminate irrelevant noise interference. The preprocessed monitoring data is x = (x1, x2, …, x N ) T , x i = (x1, x2, …, x n ), where N is the number of samples of the monitoring data, and n is the sample length of a single vibration signal;

[0010] S2: Use the polynomial rotational speed normalization method to normalize the monitoring data and suppress the amplitude modulation interference of rotational speed on the monitoring data. The normalized monitoring data is On this basis, use the fast Fourier transform to obtain the frequency-domain data corresponding to the monitoring data as where m is the sample length of a single frequency-domain data sample;

[0011] S3: Determine the number of components of the Gaussian distribution in the Gaussian mixture model through the Bayesian information criterion, construct a time-domain mixture model, and obtain a time-domain health index vector based on the distribution coincidence degree value

[0012] Determine the number of components of the exponential distribution in the exponential mixture model through the Bayesian information criterion, construct a frequency-domain mixture model, and obtain a frequency-domain health index vector based on the distribution coincidence degree value Finally, linearly weight the time-domain health index and the frequency-domain health index to obtain the final health index vector H = (H1, H2, …, H N ).

[0013] Further, in step S2, the monitoring data is normalized by using a polynomial speed normalization method, which specifically includes the following steps:

[0014] S21: The collected bearing monitoring data is x = (x1, x2, …, x N ) T , x i = (x1, x2, …, x n ). Apply the variational mode decomposition algorithm to perform signal decomposition on the monitoring data. Use the energy difference method to determine that the decomposition layer number of the variational mode decomposition algorithm is K, and decompose the signal x i into a linear combination of multiple components:

[0015]

[0016] where u k represents the k-th intrinsic mode function;

[0017] S22: Use the energy proportion analysis method to select the decomposition signals strongly correlated with the speed, and calculate the energy proportion α k of each signal component in the total energy, and quantitatively evaluate its relative importance;

[0018] S23: Use the Pearson correlation coefficient to analyze the correlation between the energy proportion of each signal component and the speed;

[0019] S24: Take the l-th component with the largest correlation as the signal strongly correlated with the speed, and reconstruct the monitoring signal by superimposing other components:

[0020]

[0021] Obtain the monitoring data with partial elimination of the speed influence as x′ = (x′1, x′2, …, x′ N ) T ;

[0022] S25: Define the objective function related to the speed, and use the genetic algorithm to optimize and obtain the coefficients of each order in the speed polynomial;

[0023] S26: Divide the monitoring signal x i by the polynomial speed to obtain the monitoring data after speed normalization as follows:

[0024]

[0025] where a0, …, a m represent the polynomial coefficients, m represents the polynomial order, λ represents the relaxation factor for controlling the signal scale, and the monitoring data after polynomial speed normalization is

[0026] Further, in step S22, the calculation formula for the energy magnitude of each decomposed signal component is as follows:

[0027]

[0028] In the formula, E k represents the energy of the k-th signal component, and u i represents the i-th data in the signal component.

[0029] Further, in step S22, the energy ratio α k of each signal component to the total energy is calculated as:

[0030] Further, step S23 specifically includes: for each signal component, the corresponding energy ratio is k = 1, 2, …, K, and the Pearson correlation coefficient is used to analyze the correlation between the energy ratio β k of each signal component and the rotational speed s = (s1, s2, …, s N );

[0031]

[0032] In the formula, r k represents the correlation degree between the energy ratio of the k-th signal component and the rotational speed, is the energy ratio corresponding to the i-th monitoring data; represents the mean value of the energy ratio, represents the mean value of the rotational speed.

[0033] Further, in step S25, the objective function related to the rotational speed is defined as follows:

[0034]

[0035] In the formula, represents the objective function value, No.of dR>0 represents the number of root mean square derivatives greater than 0, No.of dR<0 represents the number of root mean square derivatives greater than 0, R = R1,, R2, …, R N represents the root mean square vector of the data after polynomial rotational speed normalization, represents the mean value of the root mean square vector.

[0036] Further, in step S3, to construct the frequency domain hybrid model, it specifically includes: the parameters of the Gaussian mixture model are initialized by the K-means algorithm and iteratively updated by the expectation maximization algorithm; the reference distribution is estimated using the first L healthy data samples and the constructed hybrid model monitoring data the corresponding data distribution It is also estimated by the Gaussian mixture model; according to the reference distribution and the data distribution Calculate the distribution coincidence degree between the reference distribution and different data distributions in the time domain :

[0037]

[0038] In the formula, represents and The area of the overlapping region between them can be calculated by the following formula:

[0039]

[0040] Based on the distribution coincidence degree value, the time-domain health index vector is obtained as

[0041] Furthermore, in step S3, a frequency-domain mixture model is constructed, specifically including: estimating the reference distribution based on the first L healthy frequency-domain data and the constructed exponential mixture model and the frequency-domain data The data distribution of Calculate the distribution coincidence degree between the reference distribution and different data distributions in the frequency domain :

[0042]

[0043] In the formula, is and The area of the overlapping region between them can be calculated by the following formula:

[0044]

[0045] Based on the distribution coincidence degree value, the frequency-domain health index vector is obtained

[0046] The beneficial effects of the present invention are as follows:

[0047] (1) Effectively suppress rotational speed interference and improve degradation characterization performance: By using variational mode decomposition to screen out components strongly correlated with rotational speed and reconstruct the signal, combined with a polynomial rotational speed normalization model optimized by a genetic algorithm, the modulation effect of time-varying rotational speed on the amplitude of monitoring data is accurately eliminated.

[0048] (2)Enhanced robustness through multi - dimensional hybrid modeling: Innovatively combine the time - domain Gaussian mixture model and the frequency - domain exponential mixture model. Adaptively determine the number of components based on the Bayesian information criterion, and calculate the distribution coincidence index between the reference distribution and the real - time data distribution. This dual - domain joint modeling strategy overcomes the problem of insufficient sensitivity of single degradation features and maintains high robustness in complex noise environments.

[0049] (3)Outstanding engineering practical value: The method of the present invention can successfully capture the progressive performance degradation evolution trajectory of the bearing from the normal state to the faulty degradation state. Normalization processing makes the amplitude of the monitoring data independent of the rotational speed, solves the problem of variable - working - condition monitoring of wind power equipment, and provides a highly sensitive quantitative basis for its health monitoring.

[0050] Other advantages, objectives, and features of the present invention will, to some extent, be described in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. Brief Description of the Drawings

[0051] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0052] Figure 1 It is a flowchart of the method for constructing the bearing health index based on polynomial rotational speed normalization;

[0053] Figure 2 They are the bearing health indexes of two wind power generators. Detailed Embodiment

[0054] The following specific examples illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention schematically. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0055] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be construed as a limitation to the present invention; for better illustrating the embodiments of the present invention, some components in the drawings will be omitted, enlarged, or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well - known structures and their descriptions in the drawings may be omitted.

[0056] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the accompanying drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the accompanying drawings are only for illustrative purposes and should not be construed as a limitation of the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0057] Please refer to Figure 1 , an embodiment of the present invention provides a method for constructing a bearing health index based on polynomial speed normalization, and the steps are as follows:

[0058] 1) Collect the original vibration signal of the bearing by installing an acceleration sensor, and perform preprocessing operations on the monitoring data to eliminate irrelevant noise interference. The preprocessed monitoring data is x = (x1, x2,..., x N ) T , x i = (x1, x2,..., x n ), where N is the number of samples of the monitoring data, and n is the sample length of a single vibration signal.

[0059] 2) Implement normalization processing on the monitoring data using the polynomial speed normalization method to suppress the modulation interference of the speed on the amplitude of the monitoring data. The normalized monitoring data is On this basis, use the fast Fourier transform to obtain the frequency-domain data corresponding to the monitoring data as where m is the sample length of a single frequency-domain data sample.

[0060] Among them, the detailed steps of the polynomial speed normalization method are as follows:

[0061] (1) The collected bearing monitoring data is x(x1, x2,..., x N ) T , x i = (x1, x2,..., x n ). Apply the variational mode decomposition algorithm to perform signal decomposition on the monitoring data, and use the energy difference method to determine that the decomposition layer number of the variational mode decomposition algorithm is K. Decompose the signal x i into a linear combination of multiple components:

[0062]

[0063] In the formula, u k represents the kth intrinsic mode function.

[0064] (2) Select the decomposition signals strongly correlated with the rotational speed using the energy ratio analysis method. The energy of each decomposition signal component is calculated as follows:

[0065]

[0066] In the formula, E k represents the energy of the k-th signal component. Calculate the energy ratio α k of each signal component to the total energy, and quantitatively evaluate its relative importance. The calculation formula of the energy ratio α k is as follows:

[0067]

[0068] (3) The energy ratio corresponding to each signal component is k = 1, 2,..., K. Use the Pearson correlation coefficient to analyze the energy ratio β k of each signal component and the rotational speed s = (s1, s2,..., s N ) as follows:

[0069]

[0070] (4) Take the l-th component with the largest correlation as the signal strongly correlated with the rotational speed, and superimpose other components to reconstruct the monitoring signal:

[0071]

[0072] Obtain the monitoring data with partially eliminated rotational speed influence as x′ = (x′1, x′2,..., x′ N ) T .

[0073] (5) Set the objective function related to the rotational speed, and use the genetic algorithm to optimize and obtain the coefficients of each order in the rotational speed polynomial. The objective function is defined as follows:

[0074]

[0075] In the formula, R represents the root mean square vector of the normalized data of the polynomial rotational speed.

[0076] (6) Divide the monitoring signal x i by the polynomial rotational speed to obtain the monitoring data after rotational speed normalization as follows:

[0077]

[0078] In the formula, a0,..., a mdenotes the polynomial coefficient, m denotes the polynomial order, λ denotes the relaxation factor for controlling the signal scale, and the monitored data after polynomial speed normalization is

[0079] 3) Determine the number of components of the Gaussian distribution in the Gaussian mixture model through the Bayesian information criterion, and construct the time-domain mixture model. The parameters of the Gaussian mixture model are initialized by the K-means algorithm and iteratively updated by the expectation-maximization algorithm. Use the first L healthy data samples and the constructed mixture model to estimate the reference distribution Monitored data The corresponding data distribution is also estimated by the Gaussian mixture model. According to the reference distribution and the data distribution Calculate the distribution overlap degree between the reference distribution and different data distributions in the time domain :

[0080]

[0081] In the formula, denotes and the area of the overlapping region between them, which can be calculated by the following formula:

[0082]

[0083] Based on the distribution overlap degree value, obtain the time-domain health index vector as

[0084] Similarly, use the Bayesian information criterion to determine the number of components of the exponential distribution in the exponential mixture model, and construct the frequency-domain mixture model. Based on the first L healthy frequency-domain data and the constructed exponential mixture model, estimate the reference distribution and the frequency-domain data The data distribution Calculate the distribution overlap degree between the reference distribution and different data distributions in the frequency domain :

[0085]

[0086] In the formula, is and the area of the overlapping region between them. It can be calculated by the following formula:

[0087]

[0088] Based on the distribution overlap degree value, obtain the frequency-domain health index vector

[0089] Finally, linearly weight the time-domain health index and the frequency-domain health index to obtain the final health index vector H=(H1, H2, …, H N ).

[0090] The above is the method for constructing a bearing health index based on polynomial speed normalization proposed by the present invention. The following is to illustrate the effectiveness of the method through specific experiments.

[0091] The bearing data used in this experiment comes from a wind turbine in a real large-scale wind farm in the northern plain of China. The monitoring data is collected from the generator drive-end bearing of the wind turbine, and is collected and stored through a multi-channel data acquisition module. The sampling frequency is 25.6 kHz, the sampling interval time is 24 h, and the sampling time is 1.0 s. The monitoring data of the generator drive-end bearings of two wind turbines are used to construct the health index. First, use the proposed polynomial speed normalization method to normalize the monitoring data, then use the Gaussian mixture model and the exponential mixture model to construct the time-domain and frequency-domain health indexes respectively, and finally linearly weight the time-domain and frequency-domain health indexes to construct the final wind power bearing health index. The constructed wind power generator bearing health index is as Figure 2 shown. It can be seen from Figure 2 that the values of the constructed health index are restricted within the range of [0, 1], and can quantitatively characterize the dynamic degradation process of the wind power generator bearing under time-varying speed. During the normal operation stage of the wind power generator bearing, the value of the health index is relatively small, indicating that the data distribution of the monitoring data is similar to the reference distribution at this time, and the bearing has no defect faults; during the degradation stage of the wind power generator bearing, the value of the health index is higher than that in the normal stage, indicating that there is a large difference between the data distribution of the monitoring data and the reference distribution at this time, and obvious defect faults have occurred in the bearing. From the above analysis, it can be seen that the health index construction method based on polynomial speed normalization can effectively generate health indexes to describe the performance degradation evolution process of the wind power generator bearing.

[0092] Comparative experiment:

[0093] To fully verify the superior performance of the health index construction method based on polynomial speed normalization (PSN) in performance degradation assessment, the monotonicity, correlation, robustness, comprehensive index, and the improvement rate of the proposed method compared with the comparative methods in terms of the comprehensive index are used for comparative analysis. The comparative methods include root mean square (RMS), kurtosis, Gini index (GI), negative entropy (NE), approximate entropy (ApEn), L2 / L1 norm, Hoyer measure (HM), principal component analysis method (PCA), kernel principal component analysis method (KPCA), isometric mapping method (ISOMAP), health index construction method based on Gaussian mixture model (GMM), health index construction method based on exponential mixture model (EMM), health index construction method based on Gaussian mixture model and confidence value (GCV), health index construction method without speed normalization (WSN), and health index construction method based on square speed normalization (SSN).

[0094] Considering two wind turbine generator bearing datasets, the comprehensive evaluation results are shown in Table 1. It can be seen from Table 1 that the health index construction method based on polynomial speed normalization proposed in the present invention is more superior than other health index construction methods, and the proposed method is more suitable for the health index construction task of wind power bearings under time-varying speeds.

[0095] Table 1 Evaluation results of different health index construction methods

[0096]

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for constructing a bearing health index based on polynomial rotational speed normalization, characterized in that The method specifically includes the following steps: S1: Collect the monitoring data of the bearing and preprocess it. The preprocessed monitoring data is \(x=(x_1,x_2,\cdots,x\) N ) T ,x i =(x_1,x_2,\cdots,x\) n ), where \(N\) is the sample number of the monitoring data and \(n\) is the sample length of a single vibration signal; S2: Normalize the monitoring data using the polynomial speed normalization method, and the normalized monitoring data is Obtain the frequency-domain data corresponding to the monitoring data by using the fast Fourier transform as m is the sample length of a single frequency-domain data sample; S3: Determine the number of components of the Gaussian distribution in the Gaussian mixture model through the Bayesian information criterion, construct a time-domain mixture model, and obtain a time-domain health index vector based on the distribution coincidence degree value The Bayesian information criterion is used to determine the number of components of the exponential distribution in the exponential mixture model, construct the frequency-domain mixture model, and obtain the frequency-domain health index vector based on the distribution coincidence degree value. Finally, linearly weight the time-domain health index and the frequency-domain health index to obtain the final health index vector H = (H1, H2, …, H N ).

2. The method for constructing a bearing health index according to claim 1, wherein In step S2, the monitoring data is normalized by using the polynomial speed normalization method, which specifically includes the following steps: S21: The collected bearing monitoring data is \(x=(x_1,x_2,\cdots,x\) N ) T , \(x\) i =(x_1,x_2,\cdots,x\) n ). Apply the variational mode decomposition algorithm to perform signal decomposition on the monitoring data, and use the energy difference method to determine that the decomposition layer number of the variational mode decomposition algorithm is \(K\). Decompose the signal \(x\) i into a linear combination of multiple components: where u k represents the k-th intrinsic mode function; S22: Select the decomposition signals strongly correlated with the rotational speed using the energy ratio analysis method, and calculate the energy ratio α of each signal component to the total energy k ; S23: Analyze the correlation between the energy ratio of each signal component and the speed by using the Pearson correlation coefficient; S24: Take the l-th component with the largest correlation as the signal strongly correlated with the speed, and reconstruct the monitoring signal by superimposing other components; The monitored data with partial elimination of the influence of rotational speed is x′=(x′1,x′2,…,x′ N ) T ; S25: Define the objective function related to the speed, and use the genetic algorithm to optimize and obtain the coefficients of each order in the speed polynomial; S26: Divide the monitoring signal x i by the polynomial rotational speed to obtain the following monitoring data after rotational speed normalization: where a0, …, a m represent polynomial coefficients, m represents the polynomial order, λ represents the relaxation factor for controlling the signal scale, and the monitored data after polynomial speed normalization is 3. The method for constructing a bearing health index according to claim 2, wherein, In step S22, the calculation formula for the energy size of each decomposed signal component is as follows: where E k represents the energy of the k-th signal component, and u i represents the i-th data in the signal component.

4. The method for constructing a bearing health index according to claim 3, wherein In step S22, the energy ratio α of each signal component to the total energy k is calculated by the formula:

5. The method for constructing a bearing health index according to claim 4, wherein Step S23 specifically includes: the energy ratio corresponding to each signal component is using the Pearson correlation coefficient to analyze the energy ratio β of each signal component k with the rotational speed s = (s1, s2, …, s N ) for correlation; where r k represents the correlation between the energy ratio of the k-th signal component and the rotational speed, is the energy ratio corresponding to the i-th monitoring data; represents the mean value of the energy ratio, represents the mean value of the rotational speed.

6. The method for constructing a bearing health index according to claim 5, characterized in that In step S25, the objective function related to the speed is defined as follows: In the formula, represents the objective function value, No.of dR>0 represents the number of root mean square derivatives greater than 0, No.of dR<0 represents the number of root mean square derivatives greater than 0, and R = R1, R2, …, R N represents the root mean square vector of the data after polynomial speed normalization, represents the mean value of the root mean square vector.

7. The method for constructing a bearing health index according to claim 1, wherein In step S3, a frequency-domain hybrid model is constructed, which specifically includes: the parameters of the Gaussian mixture model are initialized by the K-means algorithm and iteratively updated by the expectation-maximization algorithm; the reference distribution is estimated using the first L healthy data samples and the constructed hybrid model. Monitoring data The corresponding data distribution Is estimated by the Gaussian mixture model; according to the reference distribution And the data distribution Calculate the distribution coincidence degree between the reference distribution and different data distributions in the time domain In the formula, represents and the area of the overlapping region between them, which is obtained by the following formula: Based on the distribution coincidence degree value, the time-domain health index vector is obtained as 8. The method for constructing a bearing health index according to claim 1, wherein In step S3, a frequency-domain hybrid model is constructed, specifically including: estimating a reference distribution based on the first L healthy frequency-domain data and the constructed exponential hybrid model and the frequency-domain data data distribution Calculate the distribution overlap degree between the reference distribution and different data distributions in the frequency domain In the formula, is and the area of the overlapping region between them, which is calculated by the following formula: Based on the distribution coincidence degree value, a frequency-domain health index vector is obtained

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