Gear health index construction method based on gaussian mixture model and exponential mixture model

Abstract

The present application relates to a kind of gear health index construction method based on Gaussian mixture model and exponential mixture model, belong to gear health state evaluation technical field.The method includes: the vibration signal of the gear full life cycle under corresponding working condition is collected, and denoising and FFT processing are carried out;Respectively construct and train Gaussian mixture model and exponential mixture model, then respectively select the first S health data after denoising and FFT processing, train Gaussian mixture model and exponential mixture model using EM algorithm, obtain the reference distribution under corresponding model;Secondly, the reference distribution under different models and the distribution of entire life cycle data are used to calculate the distribution coincidence degree value in time domain and frequency domain;Finally, according to the distribution coincidence degree value, obtain the health index in time domain and frequency domain, and adaptively weighted according to the monotonicity of health index to obtain the final gear health index.The present application can improve the applicability of gear health index.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gear health state evaluation, and relates to a gear health index construction method based on a Gaussian mixture model and an exponential mixture model. BACKGROUND

[0002] Gears are the most common mechanical transmission elements, mainly used for transmitting power and torque. They are usually composed of two or more gears matched together to transmit rotary motion through gear meshing. As one of the common parts in mechanical equipment, its health state has an important influence on the normal operation and service life of the entire mechanical equipment. When the gears wear or are damaged, the stability of gear transmission is affected, making the operation of the entire mechanical equipment unstable, the noise increasing, and even causing vibration, thereby affecting the precision and reliability of the mechanical equipment. Secondly, during operation, fatigue cracks and pitting defects may occur on the surface of the gears, which will further expand and eventually cause damage to the gears, seriously affecting the service life and reliability of the mechanical equipment. Therefore, the health state of the gears is crucial to ensure the normal operation of the mechanical equipment and prolong its remaining service life.

[0003] The health state and degradation trend of the gears can be represented by the health index of the gears. The current mainstream health index construction method is to construct the health index in an unsupervised manner. Among them, the Gaussian mixture model can be used to fit the data distribution, and then the distance measurement index is used to measure the difference between the distributions, and the distribution difference obtained is used to construct the health index, thereby representing the health state and degradation trend of the gears. However, the Gaussian mixture model can only estimate the distribution of the monitoring data in the time domain, and constructing the health index only from the time domain cannot comprehensively represent the health state and degradation trend of the gears. Therefore, it is necessary to extract more degradation information from other domains to comprehensively represent the health state of the gears. The degradation information of the gears is not only contained in the time domain signal, but also in the frequency domain signal. If more degradation information can be extracted from the frequency domain to construct the health index, then the health index constructed in the time domain and the health index constructed in the frequency domain can be combined to more comprehensively represent the health state and degradation trend of the gears. Based on this, it is crucial to research a health index construction method that can extract degradation information from the time domain and the frequency domain. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a gear health index construction method based on a Gaussian mixture model and an exponential mixture model to improve the applicability of the gear health index.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0006] A gear health index construction method based on a Gaussian mixture model and an exponential mixture model, specifically comprising the following steps:

[0007] S1: The gear's full life cycle vibration signal under the corresponding working conditions is collected through a data acquisition system. The collected vibration signal is preprocessed to eliminate noise. The preprocessed full life cycle data is Y = (y1, y2, ..., y N ) T , where y i =(y1,y2,…,y n N is the total number of samples throughout the entire lifecycle, and n is the data length of a single sample.

[0008] S2: Perform a Fast Fourier Transform (FFT) on the preprocessed full-lifecycle data to obtain the transformed FFT data. in, m is the data length of a single FFT data sample;

[0009] S3: Construct a Gaussian mixture model (GMM);

[0010] S4: Process the preprocessed full lifecycle data Y = (y1, y2, ..., y...) N ) T The first S health data are input into the GMM, and the EM algorithm is used for iterative training. After multiple iterations and updates, the EM algorithm converges and the baseline distribution P0 is obtained.

[0011] S5: Input the entire lifecycle data into the constructed GMM and use the EM algorithm for iterative training; after multiple iterations and updates, the EM algorithm converges, obtaining the distribution P = (P1, P2, ..., P...). N );

[0012] S6: Using the baseline distribution P0 and the distribution of the entire lifecycle data P = (P1, P2, ..., P...) N To calculate the distribution overlap value in the time domain. The calculation formula is as follows:

[0013]

[0014] Among them, S i Let the baseline distribution P0 and the distribution P be... i The area of ​​the overlapping region between them;

[0015] S7: Using the calculated distribution overlap value To construct health indicators in the time domain

[0016] S8: Construct an exponential mixture model (EMM) with L exponential distribution components;

[0017] S9: Input the first S health data into the EMM, and use the EM algorithm to perform iterative training. After multiple iterations of updating and training, the EM algorithm converges, and the baseline distribution

[0018] S10: Input the entire FFT data into the constructed EMM, and use the EM algorithm to perform iterative training. After multiple iterations of updating and training, the EM algorithm converges, and the distribution of the entire life cycle data is obtained

[0019] S11: Use the baseline distribution and the distribution of the entire FFT data to calculate the distribution overlap value in the frequency domain The calculation formula is as follows:

[0020]

[0021] wherein, is the area of the overlapping region between the baseline distribution and the distribution

[0022] S12: Use the calculated distribution overlap value to construct the health index in the frequency domain as

[0023] S13: Adaptively weight the final gear health index by calculating the monotonicity of the health index in the time domain and the frequency domain respectively.

[0024] Further, in step S3, the probability density function P(x|θ) of the constructed GMM is defined as follows:

[0025]

[0026] wherein, x represents the observation data, K represents the number of Gaussian distributions, α k represents a positive weight coefficient and satisfies

[0027] f(x|θ k ) represents a Gaussian density function, which is defined as follows:

[0028]

[0029] wherein, θ k ​​μk represents the mean of the kth normal distribution component model, k μk represents the mean of the kth normal distribution component model, σk represents the variance of the kth normal distribution component model.

[0030] Further, in step S4, the GMM is trained using the Expectation Maximization (EM) algorithm, the detailed steps are as follows:

[0031] 1) Start iteration with initial values of the GMM model parameters;

[0032] 2) E-step: Calculate the responsibility of component k to the observation data x j according to the current GMM model parameters, The calculation formula is:

[0033]

[0034] 3) M-step: Calculate the GMM model parameters of the next iteration, the calculation formula is:

[0035]

[0036]

[0037]

[0038] 4) Repeat step 2) and step 3) until the EM algorithm converges.

[0039] Further, in step S8, the probability density function P(x|ξ) of the EMM is defined as follows:

[0040]

[0041] Where x represents the observation data, L represents the number of exponential distributions, β l represents a positive weight coefficient and satisfies

[0042] g(x|ξ l ) represents the exponential density function, defined as follows:

[0043]

[0044] Where ξ l = λ l , ξ l represents the parameter set of the lth exponential distribution component model, λ l represents the rate parameter of the lth exponential distribution component model.

[0045] Further, in step S9, the EMM is trained by using an expectation maximization (EM) algorithm, and the specific steps are as follows:

[0046] 1) Start iteration by giving initial values of the EMM model parameters;

[0047] 2) E step: according to the current EMM model parameters, calculate the response degree of the component I to the observation data x j

[0048]

[0049] 3) M step: calculate the model parameters of the next iteration

[0050]

[0051]

[0052] 4) Repeat steps 2) and 3) until the EM algorithm converges.

[0053] Further, in step S13, the calculation formula of the final gear health index is obtained as follows:

[0054]

[0055] Wherein, Mon(·) represents a monotonicity function.

[0056] The beneficial effects of the present application are that the present application is more superior than other unsupervised health index construction methods, and is more suitable for gear health index construction tasks.

[0057] Other advantages, objects and features of the present application will be set forth in part in the following specification, and in part will become apparent to those skilled in the art upon examination of the following specification, or can be learned from practice of the present application. The objects and other advantages of the present application can be realized and attained by the methods and instrumentalities described in the following specification. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred detailed description of the present application will be combined with the drawings, and the drawings are as follows:

[0059] Fig. 1 The flow chart of the gear health index construction method based on the Gaussian mixture model and the exponential mixture model of the present application;

[0060] Fig. 2 The gear contact fatigue test bench;

[0061] Fig. 3 The gear index constructed.​ Detailed Implementation

[0062] The following specific examples illustrate the implementation 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 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 illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0063] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0064] 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 terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0065] Please see Figs. 1-3 This invention improves a method for constructing gear health indicators based on Gaussian mixture models and exponential mixture models, such as... Fig. 1 As shown, the specific steps are as follows:

[0066] Step 1: Collect the gear's full life cycle vibration signal under the corresponding working conditions using a data acquisition system. Preprocess the collected vibration signal to eliminate noise. The preprocessed full life cycle data is Y = (y1, y2, ..., y...). N ) T y i =(y1,y2,…,y n N represents the total number of samples throughout the entire lifecycle, and n represents the data length of a single sample.

[0067] Step 2, the pre-processed vibration signal is subjected to fast Fourier transform (FFT) to obtain transformed FFT data m is the data length of a single FFT data sample.

[0068] Step 3, a Gaussian mixture model (GMM) is constructed, and the number of Gaussian distribution components is K.

[0069] The GMM is constructed as follows:

[0070] As a commonly used probability model, the Gaussian mixture model can fit the unknown data distribution through a weighted combination of multiple Gaussian distributions. The probability density function of the Gaussian mixture model is defined as follows:

[0071]

[0072] In the formula, x represents the observation data, K represents the number of Gaussian distributions, α k represents a positive weight coefficient and satisfies f(x|θ k ) represents the Gaussian density function, which is defined as follows:

[0073]

[0074] For parameter estimation of the Gaussian mixture model, the expectation maximization (EM) algorithm is used for parameter estimation, and the specific parameter estimation steps are as follows:

[0075] (1) Start iteration with the initial value of the model parameters;

[0076] (2) E step: according to the current model parameters, calculate the response degree of component k to the observation data x j :

[0077]

[0078] (3) M step: calculate the model parameters

[0079]

[0080]

[0081]

[0082] (4) Repeat steps (2) and (3) until convergence.

[0083] Step 4, the pre-processed full life cycle data Y=(y1, y2, …, y N ) TThe first S health data are input into the GMM, and the EM algorithm is used for iterative training. After multiple iterations of updating and training, the EM algorithm converges, and the baseline distribution P0 is obtained.

[0084] Step 5, the full life cycle data is also input into the constructed GMM, and the EM algorithm is used for iterative training. After multiple iterations of updating and training, the EM algorithm converges, and the distribution P of the entire life cycle data (P1, P2, …, P N ) is obtained.

[0085] Step 6, the baseline distribution P0 and the distribution P of the entire life cycle data (P1, P2, …, P N ) are used to calculate the distribution coincidence value in the time domain The calculation formula is as follows:

[0086]

[0087] In the formula, S i is the area of the overlapping region between the baseline distribution P0 and the distribution P i .

[0088] Step 7, the distribution coincidence value calculated is used to construct the health index in the time domain, and the constructed health index is

[0089] Step 8, an exponential mixture model (EMM) is constructed, and the number of exponential distribution components is L.

[0090] The EMM is constructed as follows:

[0091] The exponential mixture model can fit the unknown data distribution through the weighted combination of multiple exponential distributions. The probability density function of the exponential mixture model is defined as follows:

[0092]

[0093] In the formula, x represents the observation data, L represents the number of exponential distributions, β l represents a positive weight coefficient and satisfies ξ l = λ l , g(x|ξ l ) represents an exponential density function, which is defined as follows:

[0094]

[0095] For parameter estimation of the exponential mixture model, the expectation maximization (EM) algorithm is used for parameter estimation, and the specific parameter estimation steps are as follows:

[0096] (1) Start iterating with initial values ​​for the model parameters;

[0097] (2) Step E: Based on the current model parameters, calculate component l in relation to the observed data x. j Response rate:

[0098]

[0099] (3) M-step: Calculate the model parameters for the next iteration.

[0100]

[0101]

[0102] (4) Repeat steps (2) and (3) until convergence.

[0103] Step 9: Transfer the FFT data The first S health data points are input into the EMM, and the EM algorithm is used for iterative training. After multiple iterations and updates, the EM algorithm converges, obtaining the baseline distribution.

[0104] Step 10: Input the entire FFT data into the constructed EMM and perform iterative training using the EM algorithm. After multiple iterations and updates, the EM algorithm converges, yielding the distribution of the entire lifecycle data.

[0105] Step 11: Using the baseline distribution and the distribution of the entire FFT data To calculate the distribution overlap value in the frequency domain The calculation formula is as follows:

[0106]

[0107] In the formula, As a baseline distribution and distribution The area of ​​the overlapping region between them.

[0108] Step 12: Use the calculated distribution overlap value to construct a health index in the frequency domain. The constructed health index is...

[0109] Step 13: Obtain the final gear health index by adaptively weighting the monotonicity of the health index in the time and frequency domains respectively. The calculation formula is as follows:

[0110]

[0111] The effectiveness of the method of the present invention will be demonstrated through specific experiments below.

[0112] The gear full life cycle vibration signal data used in this experiment comes from the variable center distance gear contact fatigue test bench manufactured by Strama-MPS Company in Germany. The gear box structure diagram of the test bench is shown in Fig. 2 The gear contact fatigue test bench mainly consists of a hydraulic cooling system, a torque control system, a test operation platform, and a gear test platform. The gear test platform includes a motor, a hydraulic loader, a test gear box, and a matching gear box. The test bench has a power closed structure, and the power of the motor is mainly used to supplement the torque. There is a torque sensor on the driven shaft, and the motor only needs to follow the set working torque, and the torque can be supplemented according to the sensor data.

[0113] Three groups of full life cycle data collected in the experiment are used to construct the health index of the gear. In the first group of data, the sampling rate of the gear vibration signal is 50 kHz, the sampling time is 5 s, the sampling interval time is 30 s, the rotating speed is 500 rpm, and the torque is 1400 Nm. In the second and third groups of data, the sampling rate of the gear vibration signal is 50 kHz, the sampling time is 10 s, the sampling interval time is 60 s, the rotating speed is 1000 rpm, and the torque is 1300 Nm. For the three groups of data, the first two sample data are selected as the health data sample to estimate the baseline distribution, and then the health index of the gear is obtained by using the proposed health index construction method. As shown in Fig. 3 From Fig. 3 it can be seen that the health index constructed based on the proposed method has a monotonous rising trend, which can effectively reflect the degradation trend over time. In the initial stage, the value of the health index is close to zero, which indicates that the distribution difference between the current data and the health data is small, and the gear is running in a healthy state, and no failure is observed on the tooth surface of the measured gear. As the running time increases, the value of the health index gradually becomes larger, which indicates that the distribution difference is also getting larger, and some failures will occur on the tooth surface of the measured gear. Finally, the value of the health index reaches the maximum, which indicates that it cannot work normally due to some serious failures.

[0114] Comparison test:

[0115] In order to fully prove the superiority of the method, the monotonousness (Mon), correlation (Cor), robustness (Rob), and comprehensive evaluation index (CI) are used to compare with other unsupervised health index construction methods. In order to calculate these evaluation indexes, the health index (Health indicator, HI) needs to be decomposed into a trend item and a random item:

[0116] H(t m )=H T (t m )+H R (tm )

[0117] In the formula, H(t m ) represents the health index value at t m , H T (t m ) is a trend item thereof, and H R (t m ) is a random item. Based on the obtained trend item and random item, the calculation formula of monotonicity, correlation, robustness and comprehensive index is as follows:

[0118] 1) Monotonicity:

[0119]

[0120] 2) Correlation:

[0121]

[0122] 3) Robustness:

[0123]

[0124] In the formula, dH T is the derivative of H T , M is the number of health indexes, and the parameter λ is a relaxation factor for controlling robustness.

[0125] 4) Comprehensive evaluation index:

[0126] CI = θ1*Mon + θ2*Cor + θ3*Rob

[0127] In the formula, θ i is a positive number and satisfies Here, θ1, θ2 and θ3 are respectively set as 0.4, 0.3 and 0.3.

[0128] Here, the second group of gear data is selected for comparative analysis, and the comparison results are shown in Table 1. As can be seen from Table 1, the health index construction method based on the Gaussian mixture model and the exponential mixture model is more superior than other unsupervised health index construction methods, and the method is more suitable for the health index construction task of gears.

[0129] Table 1 Evaluation results of different health index construction methods

[0130]

[0131] Finally, it is to be explained that the above embodiments are only used to illustrate the technical solutions of the present application but not to limit the present application. Although the present application is described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions, and all should be covered in the scope of the claims of the present application.

Claims

1. A method for constructing a gear health indicator based on a Gaussian mixture model and an exponential mixture model, characterized in that, The method specifically comprises the following steps: S1: Collect the vibration signals of the gear in the whole life cycle under the corresponding working conditions through the data acquisition system, and preprocess the collected vibration signals to eliminate the noise in the vibration signals. The preprocessed whole life cycle data is Y=(y1, y2, …, y N ) T , wherein y i =(y1, y2, …, y n ), N is the sample number of the whole life cycle, and n is the data length of a single sample. S2: performing FFT on the preprocessed full life cycle data to obtain transformed FFT data wherein, m is the data length of a single FFT data sample; S3: constructing a Gaussian mixture model GMM; S4: input the preprocessed full life cycle data Y = (y1, y2, …, y N ) T the first S health data into the GMM, and perform iterative training using the EM algorithm; after multiple iterations of updating and training, the EM algorithm converges, and a baseline distribution P0 is obtained; S5: the whole life cycle data is also input into the built GMM, and the EM algorithm is used for iterative training; after multiple iterations of updating training, the EM algorithm converges, and the distribution P=(P1, P2, …, P N ) of the whole life cycle data is obtained. S6: Calculate the distribution coincidence value in the time domain using the reference distribution P0 and the distribution P = (P1, P2,..., P N ) of the entire life cycle data The calculation formula is as follows: where S i is the area of the overlap between the reference distribution P0 and the distribution P i . S7: using the calculated distribution coincidence value to construct the health index in the time domain as S8: constructing an exponential mixture model EMM; S9: input the first S health data of FFT data into the EMM, and perform iterative training by using the EM algorithm; after multiple iterative update training, the EM algorithm converges, and the reference distribution is obtained S10: input the entire FFT data into the built EMM, and use the EM algorithm for iterative training; after multiple iterations of updating and training, the EM algorithm converges, and the distribution of the entire life cycle data is obtained S11: Calculate the distribution coincidence value in the frequency domain using the reference distribution and the distribution of the entire FFT data The calculation formula is as follows:​ wherein is the area of the overlap region between the reference distribution and the distribution and the distribution S12: Constructing the health index in the frequency domain by using the calculated distribution coincidence value ​ S13: obtaining the final gear health index by adaptively weighting through calculating the monotonicity of the health index in time domain and frequency domain respectively.

2. The method of claim 1, wherein, In step S3, the probability density function P(x|θ) of the constructed GMM is defined as follows: where x represents observation data, K represents the number of Gaussian distributions, a k represents a positive weight coefficient and satisfies f(x | 0 k ) denotes a Gaussian density function, defined as follows: wherein, θ k denotes a parameter set of the k-th normal distribution component model, μ k denotes a mean value of the k-th normal distribution component model, denotes a variance of the k-th normal distribution component model.

3. The method according to claim 2, wherein, In step S4, the EM algorithm is used to train the GMM, and the specific steps are as follows: 1) Start iteration by giving the initial value of the GMM model parameter; 2) Step E: Compute the component k's response to the observation data x given the current GMM model parameters j Responsiveness The formula is: 3) M step: calculate the GMM model parameter of the next iteration, and the calculation formula is: 4) Repeat step 2) and step 3) until the EM algorithm converges.

4. The method of claim 1, wherein, In step S8, the probability density function P(x|ξ) of the constructed EMM is defined as follows: where x represents observation data, L represents the number of exponential distributions, β l represents a positive weight coefficient and satisfies g(x | ξ l ) denotes the exponential density function, defined as follows: wherein ξ l = λ l , ξ l denotes the parameter set of the l-th exponential distribution submodel, λ l denotes the rate parameter of the l-th exponential distribution submodel.

5. The method according to claim 4, wherein, In step S9, the EM algorithm is used to train the EMM, and the specific steps are as follows: 1) Start iteration by giving the initial value of the EMM model parameter; 2) Step E: Compute the response of component / to the observed data x given the current EMM model parameters j Responsiveness 3) M step: calculate the model parameter of the next iteration 4) Repeat step 2) and step 3) until the EM algorithm converges.

6. The method of claim 1, wherein, In step S13, the calculation formula of the final gear health index is: Wherein, Mon(·) represents the monotonicity function.

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