Rolling bearing fault sample generation method based on digital twin model

Abstract

The present invention relates to a rolling bearing fault sample generation method based on a digital twin model, and belongs to the technical field of bearing fault diagnosis. The method comprises: S1: collecting fault signal samples of a bearing in a physical space through an accelerated life test bench; S2: for a specific fault, using a multi-degree-of-freedom bearing fault dynamics model to obtain theoretical vibration signals of multiple bearing components, and adding Gaussian white noise of the same intensity thereto; S3: using Fourier transform to calculate the spectrum of the noisy multi-source vibration signal and the measured signal; S4: constructing FBC-GAN and training it; S5: inputting the noise frequency domain into the trained FBC-GAN to generate bearing fault signal samples; S6: obtaining the corresponding time domain bearing fault samples through IFFT; the present invention can effectively improve the imbalance problem that the normal samples in the data sample are far more than the fault samples, and reduce the demand for actual experiments and the cost of sample acquisition.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing fault diagnosis and relates to a method for generating rolling bearing fault samples based on a digital twin model. Background Art

[0002] With the development of modern industrial equipment such as aircraft engines, machine tools, trains, wind turbines, etc., the requirements for their key components are getting higher and higher. As one of the key components, rolling bearings need to work at higher speeds and withstand greater loads as the performance of the equipment improves. Due to harsh working conditions, rolling bearings are prone to failure, which may cause the entire equipment to shut down or even a major accident. Therefore, it is very important to monitor the health status of rolling bearings and diagnose their faults. Existing bearing fault diagnosis methods can be mainly divided into signal processing-based methods and artificial intelligence-based methods. However, these fault diagnosis methods usually require a large number of fault samples.

[0003] In actual engineering, there are a large number of normal bearing samples, while fault samples are scarce, resulting in sample imbalance. Of course, rolling bearing fault samples can also be obtained through experiments, but these experiments usually require huge economic costs and time consumption. Therefore, it is of great value to study data enhancement methods. An obvious method is to use dynamic models to generate fault samples. Shao et al. established a rotor-bearing system dynamics model to generate bearing vibration signals under different states, which were then used to assist the fault diagnosis of actual bearings through generative adversarial networks (GANs). Liu et al. constructed a phenomenological vibration model of the bearing to generate fault samples, and similarly applied it to bearing fault diagnosis through GANs. Nevertheless, there is a significant gap between the fault signals generated by the model-based method and the actual fault signals, which may limit the performance of the diagnosis model. Data generation based on actual signals is another sample enhancement technique. Wang et al. proposed a self-adaptive efficient sub-pixel network (DAESPN) for enhancing fault samples, and then realized intelligent fault diagnosis under speed fluctuation conditions. An et al. established an active imagination data enhancement model for enhanced bearing fault diagnosis. Pei et al. developed an enhanced few-shot Wasserstein autoencoder with meta-learning to enhance rolling bearing data for bearing fault diagnosis. Zhang et al. proposed a self-learning network based on generative adversarial networks to generate bearing fault samples, which can overcome the challenges of small sample fault diagnosis. Li et al. used Gaussian noise, masking noise, signal translation, amplitude offset, and time stretching to increase the orientation samples. However, these data-driven methods usually use a large number of actual samples to train the generative model. In addition, the generated samples have a similar style to the training samples, and the lack of diversity limits the improvement of fault diagnosis accuracy. Therefore, by combining the advantages of the two methods, sample enhancement methods based on digital twins are becoming more and more popular.

[0004] Digital twin is a new technology in equipment operation and maintenance. The concept of digital twin can be traced back to Professor Greaves' class at the University of Michigan in 2003, and he defined three elements of digital twin, including real space, virtual space and data flow connection. In 2012, NASA defined digital twin as a simulation process that integrates multiple physical fields, scales and probabilities, and has been successfully applied to assist in the design, manufacture, operation and maintenance of aircraft. Tao et al. proposed a prediction and health management (PHM) framework based on digital twin and demonstrated its effectiveness through the example of wind turbines. Piltan et al. proposed a vibration digital twin model for identifying the size of bearing cracks, which combines mechanism modeling with adaptive observers. In order to reveal the degradation law and increase the life cycle samples of rolling bearings, Qin et al. established a life cycle digital twin model of rolling bearings, in which a mapping network based on cycle GAN (CycleGAN) was first proposed to reduce the difference between dynamic response and measurement signals. However, the dynamic model used has only two degrees of freedom, and the mapping capability of CycleGAN needs to be further improved. Lou et al. used GAN to make the simulated signals of the finite element analysis of the faulty bearing close to the measured signals. However, the mapping networks in these models directly generate time domain signals, so the spectral structure of the actual signals cannot be well preserved in the generated signals, and they are easily affected by noise. In addition, the feature extraction capabilities of these networks are not strong enough. Therefore, there is still a certain gap between the measured samples and the samples generated by these networks, which may affect the fault diagnosis accuracy of the rolling bearing. In order to fill this gap, the present invention will develop a new digital twin model of faulty rolling bearings to generate high-quality fault samples. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a rolling bearing fault sample generation method based on a digital twin model, which can be applied to imbalance fault diagnosis, effectively improve the imbalance problem in which normal samples in data samples are far more than fault samples, reduce the need for actual experiments, reduce the cost of sample acquisition, and improve research and economic production efficiency.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for generating rolling bearing fault samples based on a digital twin model specifically comprises the following steps:

[0008] S1: Collect the fault signal samples in the physical space through the bearing accelerated life test bench;

[0009] S2: For a specific fault, the multi-degree-of-freedom bearing fault dynamics model is used to obtain the theoretical vibration signals of multiple bearing components, and Gaussian white noise of the same intensity is added to it to obtain a noisy multi-source vibration signal;

[0010] S3: Calculate the frequency spectrum of the noisy multi-source vibration signal and the measured fault signal using Fourier transform;

[0011] S4: Construct a frequency-domain bidirectional long short-term memory recurrent generative adversarial network (FBC-GAN) and train it;

[0012] S5: Input the noise frequency domain simulation data into the trained FBC-GAN to generate signal samples of bearing faults;

[0013] S6: Obtain the corresponding time domain bearing fault samples through IFFT.

[0014] Further, in step S2, the multi-degree-of-freedom fault bearing dynamics model used is a dynamics model that takes into account the five degrees of freedom of the inner ring of the angular contact ball bearing, the three degrees of freedom of the rolling element and the three degrees of freedom of the cage, and takes into account the interaction between the various components and the high-speed effect;

[0015] The three-degree-of-freedom dynamic model assumes that the outer ring of the rolling bearing is fixed and the inner ring rotates around the z-axis at a speed of ω i Rotation, record the rolling element along the y b Direction and y z The displacement in the y direction is b , z b ; The inner ring of the bearing is in coordinate system o b -x b y b z b The displacement below is y ib ,z ib , the contact angle between the rolling element and the inner and outer rings is obtained as:

[0016]

[0017] Among them, α o is the contact angle, α ij , α oj are the contact angles of the rolling element and the inner and outer rings, h j is an additional half-sine displacement excitation, used to characterize the impact of faults on the vibration of the bearing system; d ib ,d ob They are the distances from the center of curvature of the inner and outer raceways to the center of the rolling element;

[0018] The inner ring of the bearing is in coordinate system o b -x b y b zb The displacement y ib ,z ib for:

[0019]

[0020] Among them, y bj and z bj Represents the coordinate system o b -x b y b z b The jth rolling element in b , z b Displacement in direction; m b Q is the mass of the rolling element; ij and Q oj Respectively represent the contact force with the inner ring and outer ring; F cj and M gj are the centrifugal force and gyroscopic moment of the jth rolling element respectively; ij and λ oj are the inner and outer raceway distribution coefficients respectively, D is the rolling element diameter, and c is the equivalent damping;

[0021] Similarly, the dynamic equations of the cage and inner ring can be obtained as follows:

[0022]

[0023] Among them, m c and I c Respectively represent the mass and moment of inertia of the cage; y c and z c is the displacement of the cage along the Y and Z directions in the coordinate system o-xyz; d m Indicates the median diameter of the rolling bearing, ω c Indicates the rotational speed of the cage, f cbj Indicates the tangential friction between the rolling element and the cage pocket, N b represents the number of rolling elements; x, y, z are the displacements of the inner ring along the X, Y, and Z directions; m represents the mass of the inner ring; c i is the damping coefficient of the inner ring; Q ix ,Q iy ,Q iz is the contact force along the X, Y, and Z directions; F x ,F y ,F z is the loading force in three directions; ω i is the inner ring speed; I x and I y are the moments of inertia about the x-axis and y-axis respectively; θ ix and θ iyare the angular displacements of the inner ring around the x-axis and y-axis respectively; M ix and M iy They represent the torque of the inner ring around the x-axis and y-axis respectively.

[0024] The theoretical vibration responses of different components of rolling bearings can be obtained by the fourth-order Runge-Kutta method.

[0025] Furthermore, in step S2, when adding noise, the Gaussian white noise added in each training is only the same in noise level (ie, signal-to-noise ratio), and the noise added each time is random, which ensures the diversity of generated samples.

[0026] Further, in step S4, the constructed FBC-GAN includes two GAN networks with opposite mapping directions; each GAN network includes a generator and a discriminator; the generator includes a Bi-LSTM layer, two convolutional layers (downsampling), four residual blocks and a deconvolution layer (upsampling); the discriminator includes four consecutive convolutional layers (downsampling), and the whole is a fully convolutional neural network structure.

[0027] Furthermore, in step S4, during the FBC-GAN training process, in order to ensure the approximate analyticity of the generated frequency domain data, that is, the real and imaginary parts of the generated signal approximately satisfy the relationship of the Hilbert transform pair, a spectrum constraint loss is proposed. At the same time, in order to ensure the mapping and alternating training of the two GANs, adversarial loss, cycle consistency loss and identity mapping loss are also required. The purpose of the adversarial loss is to make the generator and discriminator of the GAN confront each other, so as to generate samples that follow the target distribution.

[0028] The loss function during FBC-GAN training is:

[0029] L=L adv (G X→Y ,D Y )+L adv (G Y→X ,D X )+λ cyc L cyc (G X→Y ,G Y→X )

[0030] +λ identity L identity (G X→Y ,G Y→X )+λ sp [L sp (G X→Y )+L sp (G Y→X )]

[0031] Among them, λ cyc ,λidentity ,λ sp is the weight value; G X→Y The forward generator, G, represents the forward mapping from input sample X to generated sample Y. Y→X The inverse generator represents the inverse mapping from input sample Y to generated sample X; D X , D Y They represent the discriminator of forward mapping and the discriminator of reverse mapping respectively;

[0032] L sp (G X→Y ) represents the spectrum constraint loss, which is used to constrain the relationship between the real and imaginary parts of the spectrum and is defined as follows:

[0033]

[0034] Where real(y) and imag(y) represent the real and imaginary parts of the measured spectrum respectively; real[G X→Y (x)] and imag[G X→Y (x)] represent the real and imaginary parts of the generated data, respectively;

[0035] L adv (G X→Y ,D Y ) represents the adversarial loss, which aims to make the generator and discriminator of GAN confront each other so as to generate samples that follow the target distribution. It is defined as:

[0036]

[0037] Under the action of adversarial loss, the discriminator D Y Trying to find the best decision boundary between real samples and generated samples by minimizing the loss, while the generator G X→Y Try to generate a model that can fool the discriminator D by minimizing the loss Y of the sample.

[0038] In order to ensure that the characteristics of the input samples can be preserved during the mapping process, a cycle consistency loss L is required. cyc and the identity mapping loss L identity . The following are two loss functions:

[0039] L cyc (G X→Y ,G Y→X ) represents the cycle consistency loss, and the calculation formula is:

[0040]

[0041] L identity (GX→Y ,G Y→X ) represents the identity mapping loss, which is calculated as:

[0042]

[0043] in, They respectively represent the expected values ​​of the results after the data in the two domains are involved in the calculation.

[0044] Further, in step S4, during the training process of FBC-GAN, the present invention trains the network by alternately training each part. For the forward mapping from X to Y, the generator G X→Y The input sample X of G consists of three vectors, which are the frequency spectra of the three components of the faulty bearing (inner ring, cage, rolling element). X→Y The output of is the generated signal Y. During the training phase, the generated Y and the real bearing fault data are fed into the discriminator D. Y , to determine whether the generated data is real. X→Y In the fixed case, the discriminator D is trained by maximizing the probability of assigning the correct labels to real data and generated data (i.e., adversarial loss). Y The generator G is then trained by minimizing the adversarial loss X→Y . Then, the reverse GAN network for mapping from Y to X is trained in a similar way. Then, the forward GAN network for mapping from X to Y is trained. FBC-GAN is trained by alternately optimizing the two GANs.

[0045] The beneficial effects of the present invention are that the present invention can effectively improve the imbalance problem in which normal samples outnumber faulty samples in data samples, while greatly reducing the need for actual experiments, reducing the time and economic cost of sample acquisition, and improving the efficiency of research and economic production.

[0046] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0048] Figure 1 is the rolling bearing coordinate system;

[0049] Figure 2 For the force analysis of the rolling elements of the bearing;

[0050] Figure 3 It is the overall structure of FBC-GAN;

[0051] Figure 4 is the spectrum of the input signal. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways 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 only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] See also Figure 1 to Figure 4 The present invention provides a process step for applying a faulty rolling bearing digital twin model constructed in unbalance fault diagnosis:

[0054] Step 1: Collect the fault signal samples in the physical space through the bearing accelerated life test bench, such as Figure 4 The bearing speed in the experiment is 20000rpm, and the bearing fault is a pitting located on the outer ring of the bearing, and its fault characteristic frequency is expected to be 3.5khz.

[0055] Step 2: For the pitting of the outer ring of the bearing, the multi-degree-of-freedom bearing fault dynamics model is used to obtain the theoretical vibration signals of the inner ring, cage and rolling element of the bearing. The dynamic model formula used is as follows

[0056]

[0057] Among them, α o is the contact angle, α ij , α oj are the contact angles of the rolling element and the inner and outer rings respectively; h j It is an additional half-sine displacement excitation used to characterize the impact of faults on the vibration of the bearing system. ib d ob They are the distances from the center of curvature of the inner and outer raceways to the center of the rolling element. b , z b The rolling element moves along the y axis under the action of external load. b Direction and y z The displacement of the bearing inner ring in the coordinate system o b -x b y b zb The displacement y ib ,z ib for:

[0058]

[0059] Among them, y bj and z bj Represents the coordinate system o b -x b y b z b The jth rolling element in the b , z b Displacement in direction; m b Q is the mass of the rolling element; ij and Q oj Represents the contact force with the inner ring and outer ring respectively; F cj and M gj are the centrifugal force and gyroscopic moment of the jth rolling element respectively; ij and λ oj are the inner and outer raceway distribution coefficients respectively, D is the rolling element diameter, and c is the equivalent damping.

[0060] Similarly, the dynamic equations of the cage and inner ring can be obtained as follows:

[0061]

[0062] Among them, m c ,I c Respectively represent the mass and moment of inertia of the cage; y c ,z c is the displacement of the cage along the Y and Z directions in the coordinate system o-xyz; d m Indicates the median diameter of the rolling bearing, ω c represents the rotation speed of the cage, c is the equivalent damping, f cbj Indicates the tangential friction between the rolling element and the cage pocket, N b represents the number of rolling elements; x, y, z are the displacements of the inner ring along the X, Y, and Z directions; m represents the mass of the inner ring; c i is the damping coefficient of the inner ring; Q ix ,Q iy ,Q iz is the contact force along the X, Y, and Z directions; F x ,F y ,F z is the loading force in three directions; ω i is the inner ring speed; I x ,I y are the moments of inertia about the x-axis and y-axis respectively; θ ix ,θ iyare the angular displacements of the inner ring around the two axes; M ix ,M iy Respectively represent the torque of the inner ring around the two axes.

[0063] The theoretical vibration responses of different components of rolling bearings can be obtained by the fourth-order Runge-Kutta method.

[0064] Step 3: Use Fourier transform to calculate the frequency spectrum of the noisy multi-source vibration signal and the measured signal. In this process, after the fast Fourier transform, the real and imaginary parts of the spectrum should be completely retained instead of calculating the final modulus value to retain the corresponding signal phase information.

[0065] Step 4: Construct a frequency domain bidirectional long short-term memory recurrent generative adversarial network (FBC-GAN), and train the FBC-GAN with the simulated frequency domain vibration data and actual frequency domain vibration data obtained by the dynamic model. During the training process, the optimizer used is the adam optimizer, and the loss function used is

[0066] L=L adv (G X→Y ,D Y )+L adv (G Y→X ,D X )+λ cyc L cyc (G X→Y ,G Y→X )

[0067] +λ identity L identity (G X→Y ,G Y→X )+λ sp [L sp (G X→Y )+L sp (G Y→X )]

[0068] Among them, λ cyc ,λ identity ,λ sp is the weight value, and the specific formula of the loss function of each part is as follows:

[0069]

[0070] Where real(y) and imag(y) represent the real and imaginary parts of the measured spectrum respectively; real[G X→Y (x)] and imag[G X→Y (x)] represent the real and imaginary parts of the generated data, respectively.

[0071]

[0072]

[0073]

[0074] During the training process, the network is trained by alternating the training of each part. For the forward mapping from X to Y, the generator G X→Y The input sample X of G consists of three vectors, which are the frequency spectra of the three components of the faulty bearing (inner ring, cage, rolling element). X→Y The output of is the generated signal Y. During the training phase, the generated Y and the real bearing fault data are fed into the discriminator D. Y , to determine whether the generated data is real. X→Y In the fixed case, the discriminator D is trained by maximizing the probability of assigning the correct labels to real data and generated data (i.e., adversarial loss). Y The generator G is then trained by minimizing the adversarial loss X→Y . Then, the reverse GAN network for mapping from Y to X is trained in a similar way. Then, the forward GAN network for mapping from X to Y is trained. FBC-GAN is trained by alternately optimizing the two GANs.

[0075] Step 5: Input the noise frequency domain simulation data into the trained FBC-GAN to generate signal samples of bearing faults. In different training cycles, the added Gaussian noise should be of the same level, and the Gaussian white noise generated each time should be different to generate a variety of bearing fault samples.

[0076] Step 6: Obtain the corresponding time domain bearing fault samples through IFFT.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A rolling bearing fault sample generation method based on a digital twin model, characterized in that: The method specifically comprises the following steps: S1: Collect the fault signal samples in the physical space through the bearing accelerated life test bench; S2: For a specific fault, the multi-degree-of-freedom bearing fault dynamics model is used to obtain the theoretical vibration signals of multiple bearing components, and Gaussian white noise of the same intensity is added to it to obtain a noisy multi-source vibration signal; S3: Calculate the frequency spectrum of the noisy multi-source vibration signal and the measured fault signal using Fourier transform; S4: construct an FBC-GAN and train it, where FBC-GAN stands for frequency-domain bidirectional long short-term memory recurrent generative adversarial network; the constructed FBC-GAN includes two GAN networks with opposite mapping directions; each GAN network includes a generator and a discriminator; the generator includes a Bi-LSTM layer, two convolutional layers, four residual blocks and a deconvolutional layer; the discriminator includes four consecutive convolutional layers, and the whole is a fully convolutional neural network structure; The loss function during FBC-GAN training is: in, , , is the weight value; A forward generator representing the forward mapping from input sample X to generated sample Y, An inverse generator that represents the inverse mapping from input sample Y to generated sample X; , They represent the discriminator of forward mapping and the discriminator of reverse mapping respectively; represents the spectrum constraint loss, and its calculation formula is: in, and Respectively represent the real and imaginary parts of the measured spectrum; and Respectively represent the real and imaginary parts of the generated data; Denotes the adversarial loss, and the calculation formula is: represents the cycle consistency loss, and the calculation formula is: represents the identity mapping loss, which is calculated as: in, , They respectively represent the expected values ​​of the results after the data in the two domains participate in the calculation; S5: Input the noise frequency domain simulation data into the trained FBC-GAN to generate signal samples of bearing faults; S6: Obtain the corresponding time domain bearing fault samples through IFFT.

2. The method for generating rolling bearing fault samples based on a digital twin model according to claim 1, characterized in that: In step S2, the multi-degree-of-freedom fault bearing dynamics model used is a dynamics model that considers the five degrees of freedom of the inner ring of the angular contact ball bearing, the three degrees of freedom of the rolling element, and the three degrees of freedom of the cage, and considers the interaction between the various components and the high-speed effect; The three-degree-of-freedom dynamic model assumes that the outer ring of the rolling bearing is fixed and the inner ring rotates around the z-axis at a speed Rotation, record the rolling element under the external load along y b Direction and y z The displacement in the direction is y b , z b ; The inner ring of the bearing is in the coordinate system The displacement below is y ib , z ib , the contact angle between the rolling element and the inner and outer rings is obtained as: in, is the contact angle, , are the contact angles of the rolling element and the inner and outer rings, h j is an additional half-sine displacement excitation; , They are the distances from the center of curvature of the inner and outer raceways to the center of the rolling element; The inner ring of the bearing is in the coordinate system Displacement under y ib , z ib for: in, and Representing coordinate system Middle j Rolling element along , Directional displacement; is the mass of the rolling element; and Represent the contact forces with the inner and outer rings respectively; and Respectively j The centrifugal force and gyroscopic torque on each rolling element; and are the inner and outer raceway distribution coefficients, D is the rolling element diameter, c is the equivalent damping; Similarly, the dynamic equations of the cage and inner ring are as follows: in, and Respectively represent the mass and moment of inertia of the cage; and For the cage in the coordinate system Displacement along the Y and Z directions; Indicates the median diameter of the rolling bearing. Indicates the rotation speed of the cage, Indicates the tangential friction between the rolling element and the cage pocket, Indicates the number of rolling elements; x , y , z is the displacement of the inner ring along the X, Y, and Z directions; m Indicates the quality of the inner ring; is the damping coefficient of the inner ring; , , is the contact force along the X, Y, and Z directions; , , are the loading forces in three directions; is the inner ring speed; and are the moments of inertia about the x-axis and y-axis respectively; and are the angular displacements of the inner ring around the x-axis and y-axis respectively; and They represent the torque of the inner ring around the x-axis and y-axis respectively.

3. The method for generating rolling bearing fault samples based on a digital twin model according to claim 1, characterized in that: In step S2, when adding noise, the Gaussian white noise added in each training is just the same in noise level, and the noise added each time is random.

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