VMD-PIML bearing fault prediction method based on physical information constraint

Abstract

The invention discloses a VMD-PIML bearing fault prediction method based on physical information constraint, and the method comprises the steps: firstly improving an FNGO algorithm, initializing eagle group distribution through introducing chaotic mapping, and introducing a sine function and a refraction reverse learning strategy, thereby improving the calculation precision and search capability of the algorithm; iterating VMD important parameter composition [K, alpha] by using an improved FNGO algorithm, and extracting signal features; and finally, using an improved FNGO algorithm to optimize hyper-parameters in the PIML prediction model. By using the PIML prediction model, physical constraint and a machine learning model can be combined, bearing signal features can be synthesized, and the accuracy and robustness of model prediction can be improved. Compared with the prior art, the method has the advantages that the PIML prediction model is constrained through physical knowledge, the improved NGO algorithm is used for optimizing the VMD denoising model and the PIML prediction model, and generalization and robustness of bearing fault prediction are improved.

Description

Technical Field

[0001] The invention belongs to the field of fault prediction and relates to a VMD-PIML bearing fault prediction method constrained by physical information. Background Art

[0002] The reducer is an indispensable and important component in the production industry. It converts the high-speed rotating power source into a low-speed high-torque output by reducing the rotation, providing reliable power support for the operation of mechanical equipment. As the core component of the reducer, the operating status of the bearing is directly related to the performance and reliability of the entire mechanical system. The bearing failure is defined according to the national standard GB / T. However, the bearing is inside the machine and the operating status cannot be monitored in real time and accurately. Bearing fault detection based on vibration signals can perform non-contact detection and has real-time monitoring capabilities, which can better solve the above problems. The collection process of bearing vibration signals will be affected by non-human factors such as the equipment operating environment, which seriously affects the accuracy of bearing fault detection.

[0003] Early bearing fault prediction went through the stages of manual experience analysis and diagnosis, vibration analysis, and signal processing technology analysis. Due to the high cost of manual analysis and diagnosis in complex scenarios, although there are technologies such as spectral kurtosis and Gini index based on time-frequency analysis for fault prediction, with the continuous development of deep learning technology, deep learning models have powerful computing and processing capabilities for data, but single deep learning models still have the problem of gradient disappearance and the problem of ignoring the solution results that do not conform to physical principles and empirical verification laws.

[0004] Common signal preprocessing methods include: wavelet threshold denoising, empirical mode decomposition (EMD), singular value decomposition (SVD), etc. VMD denoising technology can adaptively separate the various modal components of the signal, and can effectively maintain the integrity of the signal for non-stationary signals and complex background noise, but there are still problems such as difficulty in selecting the modal number, limited nonlinear signal processing capabilities, and incomplete denoising. Summary of the invention

[0005] Purpose of the invention: In response to the problems pointed out in the background technology, the present invention discloses a VMD-PIML bearing fault prediction method based on physical data constraints, uses an intelligent optimization algorithm to optimize the VMD denoising technology, reduces the degree of fault signal pollution, uses VMD to extract fault-related characteristic frequencies, combines physical knowledge constraints with machine learning models, constructs an improved PIML model, and improves the accuracy and robustness of bearing fault prediction.

[0006] Technical solution: The present invention proposes a VMD-PIML bearing fault prediction method based on physical information constraints, comprising the following steps:

[0007] Step 1: Obtain the vibration signals of the bearing parts in the reducer in the manufacturing industry and store them as a data set;

[0008] Step 2: Optimize the Northern Goshawk Algorithm NGO by using chaotic mapping, introducing fused sine function and refraction reverse learning strategy learning factor to obtain the improved Northern Goshawk Algorithm FNGO, so that the algorithm can jump out of the local optimal solution within the search range, and increase the algorithm's exploration ability, global search ability and calculation accuracy;

[0009] Step 3: Normalize the collected data set, use the improved Northern Goshawk algorithm FNGO to iterate the quadratic penalty factor ɑ and the number of intrinsic mode functions K of the VMD model, perform VMD denoising technology on the vibration signal data, decompose it into several IMFs, and extract key features;

[0010] Step 4: Build a PIML prediction model, use the improved Northern Goshawk algorithm FNGO to optimize the learning rate, batch size, and network structure of the constructed PIML model, and use the key features extracted in step 3 to train the optimized PIML prediction model with physical constraints added;

[0011] Step 5: Use softmax to perform fault classification processing and complete the bearing fault prediction based on vibration signals.

[0012] Furthermore, the improved northern goshawk algorithm FNGO is obtained by optimizing the northern goshawk algorithm NGO by using chaotic mapping, introducing fused sine function and refraction reverse learning strategy learning factor. The improvement steps are as follows:

[0013] Initialize the goshawk population, the dimension of the problem space, the initial position of the goshawk, and the objective function, introduce chaotic mapping, and adjust the initial position of the goshawk to prevent uneven distribution and fall into the local optimal problem;

[0014] The i-th goshawk updates its search position in the N-dimensional search space, and the position of the i-th goshawk in the j-dimensional search space is updated as follows:

[0015] X i，j new，p1 =(X i，1 new，p1 ,X i，2 new，p1 ,...,X i，N new,p1 )

[0016] Where N represents the dimension of the problem space, i represents the i-th goshawk, j represents the dimension, j = 1, 2, ..., N;

[0017] In the first stage of the algorithm, i.e. the prey hunting stage, the goshawk updates the formula for identifying the prey hunting position as follows:

[0018]

[0019] Where, X i,j new,p1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the current position of the jth dimension of the i-th goshawk individual, l is a random number in [0, 1], I is 1 or 2, P i，j is the prey position, F pi represents the fitness of the hunting position, F i represents the fitness of the current position of the i-th goshawk;

[0020] The update position is determined based on whether the fitness meets the requirements, as shown below:

[0021]

[0022] Where, X i,j new,p1 represents the new position of the i-th goshawk in the j-th dimension, F i new,p1 represents the target fitness of the i-th goshawk after update;

[0023] The introduction of sine function and refraction reverse learning strategy enhances the global search capability and local search accuracy of the algorithm and prevents it from falling into the local optimal problem. The position formula is updated as follows:

[0024]

[0025] Where, X i,j new,p1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the position of the jth variable of the i-th goshawk individual, l is a random number, I is 1 or 2, F pi represents the fitness of the hunting position, F i represents the fitness of the current position of the i-th goshawk, R is the decay factor that decreases with the number of iterations, K is the constant that controls the strength of the refraction direction learning strategy, and X i,j opposite is the reverse position of the current position, θ represents the angle introduced into the sine function calculation, and n is a random number;

[0026] In the second stage of the algorithm, i.e. the pursuit and escape stage, after the introduction of the sine function and the refraction reverse learning strategy, the update formula is as follows:

[0027]

[0028] Where φ is the calculated refraction angle after the second stage update, X best,j is the optimal position, K is a constant that controls the intensity of reflection, and X i,j opposite is the reverse position of the current position, and M is the attenuation factor by which the number of iterations decreases;

[0029] The final optimization of the position of the i-th goshawk in the second stage is as follows:

[0030]

[0031] Where, X i represents the updated position in the second stage, F i new,p2 Represents the fitness of the i-th goshawk after updating its position.

[0032] Furthermore, the PIML prediction model based on physical constraints is as follows:

[0033] The physical behavior of the vibration signal is described by the partial differential equation PDED, which is obtained by separating the variables and solving the characteristic equation to obtain the natural frequencies and solutions of the system. The equation form is as follows:

[0034]

[0035] In the formula, u is the displacement generated when the bearing is in operation, m is the bearing mass, c is the damping coefficient, k is the stiffness coefficient, and t is the operating time;

[0036] Use the training set for training, use the optimization strategy, take the loss function as the target, introduce relevant physical constraints as part of the loss function, iterate the training, save the best training model parameters, and use the Huber loss function as the loss function. The formula is as follows:

[0037]

[0038] In the formula, a represents the residual between the predicted value and the true value, and δ is an integer parameter, which controls the inflection point of the loss function from MSE to MAE. δ is used to enhance the sensitivity to outliers.

[0039] Physical constraints include Newton's second law, Hooke's law, simple harmonic motion, damping ratio, and free vibration equations, natural frequencies, mode shapes, and modal analysis combined with dynamics and vibration theory;

[0040] The natural frequency equation is shown below:

[0041]

[0042] In the formula, ω n is the natural angular frequency, f is the natural frequency, k is the system stiffness, and m is the system mass;

[0043] The formula for simple harmonic motion is as follows:

[0044] X(t)=A.cos(ωt+φ)

[0045] Where A is the amplitude of the bearing under operation, φ is the initial phase, ω is the angular frequency of the restraining force when the bearing is running, and ω is the condition that the object satisfies the periodic motion under the interaction of the restoring force and the inertial force;

[0046] The bearing running system is subject to simple harmonic excitation and the partial differential equation update is as follows:

[0047]

[0048] Where F0 is the amplitude of the bearing under running condition, and ω is the angular frequency of the restraining force when the bearing is running.

[0049] Furthermore, in step 4, the PIML prediction model based on physical constraints reconciles the physical constraints and the loss function, and the reconciliation formula is as follows:

[0050] μ(x,λ)=l(x)+λg(x)

[0051] Where g(x) is the physical constraint of the bearing, μ(x, λ) is the Lagrangian function, l(x) is the original loss function of the model, and λ is the Lagrangian multiplication;

[0052] Find (x * ,λ * ) so that μ(x * ,λ)≤μ(x * ,λ * )≤μ(x,λ * ), (x * ,λ * ) is the product of the bearing signal input and the Lagrange number that meets the calculation conditions, and x * Whether the physical constraints of the bearing are met. If not, λ needs to be adjusted.

[0053] Furthermore, when training the PIML prediction model, the physical laws and prior knowledge of bearing operation are integrated into the machine learning model, and the friction, wear, and heat conduction of the bearing are described by a mathematical model. When training the PIML prediction model, physical constraints are added to solve the problem of ignoring the solution results that do not conform to physical principles and empirical verification laws.

[0054] Furthermore, the improved FNGO algorithm is used to iteratively optimize the learning rate, batch size, and network structure in the constructed PIML prediction model, wherein the network structure includes the number of layers and the number of neurons.

[0055] Furthermore, after using the PIML prediction model to predict the bearing fault, the attention mechanism is introduced to fuse the IMF signal features decomposed by the VMD model and the features output by the PIML prediction model.

[0056] Beneficial effects:

[0057] The present invention uses a VMD-PIML bearing fault prediction method constrained by physical information, which integrates the operating physical laws and prior knowledge into the machine learning model to solve the problem that the model ignores that the solution results do not conform to physical principles and empirical verification laws. At the same time, the attention mechanism is introduced to enhance the prediction accuracy of the model and the convergence of the model, thereby improving the robustness and generalization of the model.

[0058] The present invention is based on data normalization and FNGO algorithm improvement, and uses VMD to perform denoising preprocessing on the original bearing vibration signal data to obtain a series of modal components, thereby better screening the useful vibration signals in the original data source, reducing the degree of experimental data contamination and improving the accuracy of bearing fault detection.

[0059] The present invention improves the northern goshawk algorithm, introduces chaotic mapping to initialize the hawk group to prevent the individuals of the population from falling into the local optimal problem, introduces the factors that integrate the sine-cosine strategy and the refraction reverse learning strategy, improves the exploration ability and global search ability of the algorithm, and improves the linear decreasing trend of the algorithm step search factor, optimizes the calculation performance of the algorithm, and enhances the adaptability, stability and convergence speed of the calculation ability of the algorithm when solving complex optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The overall flow chart of the VMD-PIML bearing fault prediction method based on physical information constraints in the present invention;

[0061] Figure 2 Iterative optimization diagram of the improved Northern Goshawk algorithm and other algorithms according to the example of the present invention;

[0062] Figure 3 This is a bearing vibration signal diagram after VMD denoising in an example of the present invention;

[0063] Figure 4 The structural diagram of the PIML model constructed for the example of the present invention. DETAILED DESCRIPTION

[0064] In order to further illustrate the technical method used in the present invention and the effect achieved, the following will be combined with the attached embodiment of the present invention. Figure 1 The technical solution of the present invention in the example of the VMD-PIML bearing fault prediction method constrained by physical information is described in detail, and the specific implementation method includes the following steps:

[0065] Step 1: Obtain the vibration signal of the bearing parts in the reducer in the manufacturing industry. The sampling frequency of the vibration signal is 12kH, and each segment of the signal is 10s. Store it as a data set. Set the signal reception model as:

[0066] F(t)=m(t)+n

[0067] Where F(t) is the vibration signal and n is the noise signal.

[0068] Step 2: Normalize the data set and use FNOG-VMD to decompose the vibration signal source.

[0069] Step 2.1 uses normalization processing on the obtained f(t), and the formula is as follows:

[0070]

[0071] In the formula, X is the original signal value, X min and X max are the minimum and maximum values ​​of the signal, respectively, and the normalized signal value X nor In the interval [0, 1].

[0072] Step 2.2 Obtain K IMFs for the FNGO-VMD decomposition model and set the optimal decomposition parameters [K, ɑ]. The VMD algorithm process can be viewed as the following steps:

[0073] Step 2.3 uses Hilbert transform to solve the K value and then transforms it into solving the constrained variational problem. The formula is as follows:

[0074]

[0075] Where U k (t) is the kth modal component signal after VMD decomposition, ω k is the center frequency of the kth modal component signal, t represents time, δ(t) is the Dirac function, j is the imaginary number sign, f is the same as the original signal, and k is an integer greater than or equal to 1.

[0076] Step 2.5 solves the above formula for the optimal solution, introducing the Lagrange multiplier and the quadratic penalty coefficient ɑ. The solution to the variational formula is as follows:

[0077]

[0078] In the formula, ɑ is the quadratic penalty factor, λ is the Lagrange multiplier, Derivative the expression in brackets with respect to t.

[0079] Step 2.6 Decompose the original signal into K modal component signals through Parseval / Plancherel Fourier isometric transform and update the component frequency U K and center frequency, which is expressed as follows:

[0080]

[0081]

[0082] Where U k are the frequencies of k modal component signals, X(ω) is the original input signal, and n is the current number of iterations.

[0083] Lagrange update coefficient, its update formula is as follows:

[0084]

[0085] Where ι is the update parameter of the Lagrange multiplier, ι is taken as 10 -3 .

[0086] Step 2.7 sets the judgment threshold ε, and the iteration ends when the equation is satisfied. The formula is as follows:

[0087]

[0088] Where ω is the convergence criterion tolerance value, and ε is taken as 10- 6 .

[0089] The improved Northern Goshawk algorithm FNGO is used in two places in this invention: one is to participate in VMD denoising for the key parameters modal component K and quadratic penalty factor ɑ. The other is to optimize the hyperparameters in the PIML model, and iteratively optimize the learning rate, batch size, network structure (such as the number of layers and neurons), regularization coefficient, etc.

[0090] The improved northern goshawk algorithm FNGO introduces chaotic mapping when initializing the goshawk population number N, the dimension of the problem space, the initial position of the goshawk, and the objective function. It adjusts the initial position of the goshawk to prevent uneven distribution and fall into the local optimal problem. The eagle group is marked as U, and the goshawk population is represented by a matrix as follows:

[0091]

[0092] Let the position of the i-th goshawk be X i, identify the prey hunting position in the jth dimension, then the position of the i-th goshawk is updated as:

[0093] X i，j new，p1 =(X i，1 new，p1 ,X i，2 new,p1 ,...,X i，N new,p1 )

[0094] In the first stage of the algorithm (prey hunting stage), the goshawk updates the formula for identifying the prey hunting position as follows:

[0095]

[0096] Where, X i,j newp1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the current position of the jth dimension of the i-th goshawk individual, L is a random number in [0, 1], I can be 1 or 2, P i，j is the prey position, F pi represents the fitness of the hunting position, F i Represents the fitness of the current position of the i-th goshawk.

[0097] The update position is determined based on whether the fitness meets the requirements, as shown below:

[0098]

[0099] Where, X i new,p1 represents the new position of the i-th goshawk in the j-th dimension, F i new,p1 Represents the updated target fitness.

[0100] The introduction of sine function and refraction reverse learning strategy learning factors enhances the global search capability and local search accuracy of the algorithm, prevents falling into the local optimal problem, and speeds up the calculation efficiency. The above position formula is updated as follows:

[0101]

[0102] Where, X i,j new,p1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the position of the jth variable of the i-th goshawk individual, l is a random number, I is 1 or 2, F pi represents the fitness of the hunting position, F irepresents the fitness of the current position of the i-th goshawk, R is the decay factor that decreases with the number of iterations, K is the constant that controls the strength of the refraction direction learning strategy, and X i,j opposite is the reverse position of the current position, θ represents the angle introduced into the sine function calculation, and n is a random number.

[0103] The calculation formula for the current reverse position is as follows:

[0104]

[0105] Where a and b are the boundaries of the current search space, X i,j is the current location.

[0106] The second stage of the algorithm (the pursuit and escape stage), the goshawk position X i new,p2 As shown below:

[0107]

[0108] X i,j new,p2 represents the updated position of the goshawk, M is the decay factor of the number of iterations, and r is a random number.

[0109] After introducing the sine function and refraction reverse learning strategy, the update formula is as follows:

[0110]

[0111] Where φ is the calculated refraction angle after the second stage update, X best,j is the optimal position, K is a constant that controls the intensity of reflection, and X i,j opposite is the reverse position of the current position, and M is the attenuation factor by which the number of iterations decreases.

[0112] The final optimization of the position of the i-th goshawk in the second stage is as follows:

[0113]

[0114] Where, X i represents the updated position in the second phase, F i new,p2 Indicates the fitness after updating the position.

[0115] The above improvements adjust the search direction through the sine function and use the refraction reverse learning strategy to jump out of the local optimal solution, thereby increasing the algorithm's exploration ability, global search ability, and calculation accuracy.

[0116] Step 3: After VMD denoising, local feature extraction information is performed to train the PIML prediction model. There are a total of ten types of bearing conditions in the data set: Normal, inner race fault (0.007 inch) (InnerRaceFault0.007inch), inner race fault (0.014 inch) (InnerRaceFault0.014inch), inner race fault (0.021 inch) (InnerRaceFault0.021inch), outer race fault (0.007 inch) (OuterRaceFault0.007inch), outer race fault (0.014 inch) (OuterRaceFault0.014inch), outer race fault (0.021 inch) (OuterRaceFault0.021inch), ball fault (0.007 inch) (BallFault0.007inch), ball fault (0.014 inch) (BallFault0.014inch), ball fault (0.021 inch) (BallFault0.021inch).

[0117] Step 3.1 initializes the model weights, uses a deep residual shrinkage network to build a PIML model, uses the improved Northern Goshawk algorithm FNGO to iteratively optimize the hyperparameters in the PIML model built using the residual shrinkage network, adjusts the hyperparameters in the model, such as learning rate, batch size, and number of iterations, and uses stratified sampling to split the data set into 80% training set and 20% test data set.

[0118] Step 3.2: The physical behavior of the vibration signal is described by a partial differential equation (PDED) by separating the variables and solving the characteristic equation to the natural frequencies and solutions of the system. The equation form is as follows:

[0119]

[0120] Where u is the displacement of the bearing under operation, m is the bearing mass, c is the damping coefficient, k is the stiffness coefficient, and t is the bearing operation time.

[0121] Step 3.3 uses the above training set for training, uses the optimization strategy, takes the loss function as the target, and introduces relevant physical constraints as part of the loss function. Iterates the training and saves the best training model parameters. The loss function uses the Huber loss function, which can better improve the prediction performance of the experimental results and prevent overfitting. The formula is as follows:

[0122]

[0123] Where a represents the residual between the predicted value and the true value, and δ is an integer parameter that controls the inflection point of the loss function from MSE to MAE. δ is used to enhance the sensitivity to outliers.

[0124] The physical constraints mentioned above in this solution include Newton's second law, Hooke's law, simple harmonic motion, damping ratio, free vibration equations combining dynamics and vibration theory, natural frequency, vibration mode and modal analysis, etc. This solution only points out some relevant formulas, including other physical principles used. The natural frequency equation is as follows:

[0125]

[0126] In the formula, ω n is the natural angular frequency of the bearing, f is the natural frequency, k is the bearing running stiffness, and m is the bearing mass.

[0127] In simple harmonic motion, the object performs periodic motion under the interaction of restoring force and inertial force to meet the conditions. The formula is as follows:

[0128] X(t)=A.cos(ωt+φ)

[0129] Where A is the amplitude of the bearing under operating conditions, φ is the initial phase, and ω is the angular frequency of the constraint force.

[0130] The formula for obtaining ω is as follows:

[0131] ω=2πf

[0132] The bearing running system is subject to simple harmonic excitation and the partial differential equation update is as follows:

[0133]

[0134] Where F0 is the amplitude of the bearing under running condition, and ω is the angular frequency of the restraining force when the bearing is running.

[0135] The relevant physical constraints and loss functions are reconciled, and the reconciliation formula is as follows:

[0136] μ(x,λ)=l(x)+λg(x)

[0137] Where g(x) is the physical constraint, μ(x, λ) is the Lagrangian function, L(x) is the original loss function, and λ is the Lagrangian multiplication. Find (x*, λ*) such that μ(x*, λ)≤μ(x*, λ*)≤μ(x, λ*), and check whether x* satisfies the physical constraint. If not, adjust λ.

[0138] Step 3.4: The constructed PIML model consists of multiple residual blocks, each of which contains the following calculations. The signal test set is input into the convolutional layer calculation as follows:

[0139] y conv =W*x+b

[0140] Where W is the convolution kernel, * represents the convolution operation, x is the input data, and b is the bias term.

[0141] Step 3.5 performs batch normalization on the convolutional layer output, and the calculation formula is as follows:

[0142]

[0143] Where γ, β are the learned scaling factors and offsets, and E[yconv] and Var[yconv] are the mean and variance of the convolutional layer output.

[0144] Step 3.6 performs residual connection, and its calculation formula is as follows:

[0145] y res =max(0,y bn )+x

[0146] Wherein, x represents the input related signal data, and ybn represents the standardized calculation result of the above convolution.

[0147] Step 3.7: Perform soft thresholding layer calculation to remove data-related interference. The calculation is as follows:

[0148] y soft =sign(y res ).max(0,|y res |-T)

[0149] Where T is the threshold parameter and sign(yres) is the sign function of the output signal.

[0150] In step 3.8, the test set is used as input to the constructed PIML model, and the key features are extracted from the IMFs after VMD decomposition. In this scheme, the attention mechanism is selected to fuse the VMD extracted features and the output features in the PIML model. The calculation formula is as follows:

[0151] In the self-attention mechanism, one feature sequence is used as a query, and another feature sequence is used as a key-value pair. The calculation process formula is as follows:

[0152] Q=XW Q ,K=XW K , V = XWV

[0153] In the formula, X is the input feature, W Q , W K , W v represents the dimension of the self-attention head, .

[0154] Through attention score calculation and attention weight normalization calculation, the calculation formula is as follows:

[0155]

[0156] Where, d k is the scaling factor, Q is the query matrix, K is the key matrix, and Q i K j T is the result of matrix multiplication, α ij is the attention score.

[0157] Finally, feature fusion is performed, and the attention weight is used to fuse the value V to obtain the fused feature representation as shown below:

[0158]

[0159] Multi-head attention is an extension of the self-attention mechanism, and its calculation formula is as follows:

[0160] headi=Attrntion(QW i Q , KW i K , VW i V )

[0161] MultiHead(Q,K,V)=Concat(head1,head2....headn)W 0

[0162] Where W 0 is the output projection matrix and h is the number of multiheads.

[0163] Step 3.9: Use softmax to complete fault prediction based on vibration signals.

[0164] The patent of this invention can be combined with relevant enterprise systems to perform relevant reducer bearing fault detection.

[0165] Reference Figure 2, the improved FNGO algorithm is iteratively compared with DBO, GEO, RIME, BWO, and NGO. The CEC2005 function set is used for testing. The CEC2005 function set is a set of standardized test functions proposed in 2005, which includes various types of functions, such as unimodal, multimodal, mixed and composite functions. The algorithm is iterated 1000 times, and the number of particles of each algorithm is set to 100. The optimization ability and convergence speed of the intelligent optimization algorithm are compared.

[0166] Reference Figure 3 This scheme uses the public data set Case Western Reserve University (CWRU) bearing data set for verification. The Case Western Reserve University (CWRU) bearing data set is a public data set, which is organized into 10 types of bearing operation status signal data. The experimental platform is obtained through an experimental device including a 2hp motor, a torque sensor, a decoder and a power tester. The core components of the bearing test device include a 1.5KW motor. The faulty bearing is located at the drive end of the motor, and the bearing model is SKF6205. The bearing fault types included in the data set include inner ring fault, rolling element fault and outer ring fault. The outer ring fault is divided into three different damage locations: 3 o'clock, 6 o'clock and 12 o'clock. The improved FNGO algorithm is used to iteratively optimize the important parameters in VMD, the number of intrinsic mode functions K and the quadratic penalty coefficient ɑ, and the optimal VMD parameters [K, ɑ] are formed. Several IMFs are obtained, and several decomposition signals of the reducer bearing under the same state are obtained. Each signal corresponds to a feature vector.

[0167] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A VMD-PIML bearing fault prediction method based on physical information constraints, characterized in that: The following steps are involved: Step 1: Obtain the vibration signals of the bearing parts in the reducer in the manufacturing industry and store them as a data set; Step 2: Optimize the Northern Goshawk Algorithm NGO by using chaotic mapping, introducing fused sine function and refraction reverse learning strategy learning factor to obtain the improved Northern Goshawk Algorithm FNGO, so that the algorithm can jump out of the local optimal solution within the search range, and increase the algorithm's exploration ability, global search ability and calculation accuracy; Step 3: Normalize the collected data set, use the improved Northern Goshawk algorithm FNGO to iterate the quadratic penalty factor ɑ and the number of intrinsic mode functions K of the VMD model, perform VMD denoising technology on the vibration signal data, decompose it into several IMFs, and extract key features; Step 4: Build a PIML prediction model, use the improved Northern Goshawk algorithm FNGO to optimize the learning rate, batch size, and network structure of the constructed PIML model, and use the key features extracted in step 3 to train the optimized PIML prediction model with physical constraints added; Step 5: Use softmax to perform fault classification processing and complete the bearing fault prediction based on vibration signals.

2. According to claim 1, a VMD-PIML bearing fault prediction method based on physical information constraints is characterized in that: The improved Northern Goshawk algorithm FNGO is obtained by optimizing the Northern Goshawk algorithm NGO by using chaotic mapping, introducing fused sine function and refraction reverse learning strategy learning factor. The improvement steps are as follows: Initialize the goshawk population, the dimension of the problem space, the initial position of the goshawk, and the objective function, introduce chaotic mapping, and adjust the initial position of the goshawk to prevent uneven distribution and fall into the local optimal problem; The i-th goshawk updates its search position in the N-dimensional search space, and the position of the i-th goshawk in the j-dimensional search space is updated as follows: x ij new,p1 =(X i，1 new，p1 ,X i，2 new,p1 ,...,X i，N new,p1 ) Where N represents the dimension of the problem space, i represents the i-th goshawk, j represents the dimension, j = 1, 2, ..., N; In the first stage of the algorithm, i.e. the prey hunting stage, the goshawk updates the formula for identifying the prey hunting position as follows: Where, X i,j new,p1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the current position of the jth dimension of the i-th goshawk individual, l is a random number in [0, 1], I is 1 or 2, P i，j is the prey position, F pi represents the fitness of the hunting position, F i represents the fitness of the current position of the i-th goshawk; The update position is determined based on whether the fitness meets the requirements, as shown below: Where, X i,j new,p1 represents the new position of the i-th goshawk in the j-th dimension, F i new,p1 represents the target fitness of the i-th goshawk after update; The introduction of sine function and refraction reverse learning strategy enhances the global search capability and local search accuracy of the algorithm and prevents it from falling into the local optimal problem. The position formula is updated as follows: Where, X i,j new,p1 represents the position of the i-th goshawk in the j-th dimension, X i,j is the position of the jth variable of the i-th goshawk individual, l is a random number, I is 1 or 2, F pi represents the fitness of the hunting position, F i represents the fitness of the current position of the i-th goshawk, R is the decay factor that decreases with the number of iterations, K is the constant that controls the strength of the refraction direction learning strategy, and X i,j opposite is the reverse position of the current position, θ represents the angle introduced into the sine function calculation, and n is a random number; In the second stage of the algorithm, i.e. the pursuit and escape stage, after the introduction of the sine function and the refraction reverse learning strategy, the update formula is as follows: Where φ is the calculated refraction angle after the second stage update, X best,j is the optimal position, K is a constant that controls the intensity of reflection, and X i,j opposite is the reverse position of the current position, and M is the attenuation factor by which the number of iterations decreases; The final optimization of the position of the i-th goshawk in the second stage is as follows: Where, X i represents the updated position in the second stage, F i new,p2 Represents the fitness of the i-th goshawk after updating its position.

3. The VMD-PIML bearing fault prediction method based on physical information constraints according to claim 1 is characterized in that: The PIML prediction model based on physical constraints is as follows: The physical behavior of the vibration signal is described by the partial differential equation PDED, which is obtained by separating the variables and solving the characteristic equation to obtain the natural frequencies and solutions of the system. The equation form is as follows: In the formula, u is the displacement generated when the bearing is in operation, m is the bearing mass, c is the damping coefficient, k is the stiffness coefficient, and t is the operating time; Use the training set for training, use the optimization strategy, take the loss function as the target, introduce relevant physical constraints as part of the loss function, iterate the training, save the best training model parameters, and use the Huber loss function as the loss function. The formula is as follows: In the formula, a represents the residual between the predicted value and the true value, and δ is an integer parameter, which controls the inflection point of the loss function from MSE to MAE. δ is used to enhance the sensitivity to outliers. Physical constraints include Newton's second law, Hooke's law, simple harmonic motion, damping ratio, and free vibration equations, natural frequencies, mode shapes, and modal analysis combined with dynamics and vibration theory; The natural frequency equation is shown below: In the formula, ω n is the natural angular frequency, f is the natural frequency, k is the system stiffness, and m is the system mass; The formula for simple harmonic motion is as follows: X(t)=A.cos(ωt+φ) Where A is the amplitude of the bearing under operation, φ is the initial phase, ω is the angular frequency of the restraining force when the bearing is running, and ω is the condition that the object satisfies the periodic motion under the interaction of the restoring force and the inertial force; The bearing running system is subject to simple harmonic excitation and the partial differential equation update is as follows: Where F0 is the amplitude of the bearing under running condition, and ω is the angular frequency of the restraining force when the bearing is running.

4. The VMD-PIML bearing fault prediction method based on physical information constraints according to claim 3 is characterized in that: In step 4, the PIML prediction model based on physical constraints reconciles the physical constraints and the loss function. The reconciliation formula is as follows: Where g(x) is the physical constraint of the bearing, μ(x, λ) is the Lagrangian function, l(x) is the original loss function of the model, and λ is the Lagrangian multiplication; Find (x * ,λ * ) so that μ(x * ,λ)≤μ(x * ,λ * )≤μ(x,λ * ), (x * ,λ * ) is the product of the bearing signal input and the Lagrange number that meets the calculation conditions, and x * Whether the physical constraints of the bearing are met. If not, λ needs to be adjusted.

5. A VMD-PIML bearing fault prediction method based on physical information constraints according to claim 3 or 4, characterized in that: When training the PIML prediction model, the physical laws and prior knowledge of bearing operation are integrated into the machine learning model, and the friction, wear, and heat conduction of the bearing are described by a mathematical model. When training the PIML prediction model, physical constraints are added to solve the problem of ignoring the solution results that do not conform to physical principles and empirical verification laws.

6. The VMD-PIML bearing fault prediction method based on physical information constraints according to claim 1 is characterized in that: The improved FNGO algorithm is used to iteratively optimize the learning rate, batch size, and network structure in the constructed PIML prediction model, wherein the network structure includes the number of layers and the number of neurons.

7. The VMD-PIML bearing fault prediction method based on physical information constraints according to claim 1 is characterized in that: After using the PIML prediction model to predict the bearing fault, the attention mechanism is introduced to fuse the IMF signal features decomposed by the VMD model and the features output by the PIML prediction model.

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