Rotating machine fault diagnosis method and related system

Abstract

The invention provides a rotating machine fault diagnosis method and a related system. The rotating machine fault diagnosis method comprises the following steps: S1, constructing a rotor vibration equation according to a vibration behavior of a rotor system under an operation condition; s2, acquiring real-time information of a to-be-diagnosed rotating machine, performing modal analysis based on a rotor vibration equation according to the real-time information of the to-be-diagnosed rotating machine to determine a sensitive frequency band and key features, and forming multi-dimensional feature data; s3, carrying out denoising processing on the multi-dimensional feature data and carrying out signal reconstruction to obtain a reconstructed signal; s4, inputting the reconstruction signal into a pre-trained rotating machine fault model to obtain a fault diagnosis result; and the rotating machine fault model is fused by adopting a neural network ordinary differential equation and a convolutional neural network-gating cycle unit. The method can accurately simulate and predict the continuous dynamic change of the system, improves the diagnosis precision, and enhances the real-time performance and robustness of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of rotating machinery equipment, and particularly relates to a rotating machinery fault diagnosis method and related system. Background Art

[0002] Rotating machinery equipment (such as motors, fans) is widely used in industrial production. Its operating state will directly affect the production efficiency of the equipment and the quality of products. Therefore, during the operation of rotating machinery equipment, it is necessary to monitor the operating state of the equipment in real time to timely detect potential faults, reduce downtime, improve production efficiency, and at the same time reduce maintenance costs.

[0003] For the fault diagnosis of equipment, in the prior art, traditional signal processing methods or machine learning methods are usually used to process the monitoring data of the equipment to achieve the diagnosis of the fault state of the equipment. However, traditional signal processing methods rely on manual feature extraction, which is not only inefficient but also easily restricted by manual experience, and cannot fully utilize the potential information in the signal. For example, methods such as Fourier transform and wavelet transform often cannot capture the complex non-linear dynamic characteristics of rotating machinery faults in time-domain and frequency-domain feature extraction, and have poor processing effects on non-stationary signals. Especially when the signal noise is large, the fault features are often masked, resulting in a decrease in diagnostic accuracy.

[0004] Machine learning methods can achieve automatic diagnosis and prediction of faults by combining machine learning models, improving the intelligence and efficiency of diagnosis. However, when dealing with high-dimensional time-series data, the accuracy of traditional machine learning methods will be affected by the curse of dimensionality. Especially in the case of diverse or rapidly changing fault patterns, the diagnostic accuracy of traditional machine learning methods is often low. For example, although traditional machine learning methods such as support vector machine (SVM) and decision tree can achieve fault classification, these methods rely on manual feature extraction and cannot automatically learn the complex patterns and multi-level features in the signal. Especially when the number of fault types increases, the diagnostic accuracy will further decrease. Although deep neural network (DNN) and convolutional neural network (CNN) can perform end-to-end learning, there are still some problems. For example, some fault diagnosis models only rely on architectures such as convolutional neural network (CNN) to extract features, ignoring the dynamic characteristics in time-series signals. This makes the model perform poorly when dealing with time-series data with long-term dependencies and is prone to losing important time-series information.

[0005] Due to the complex, non-linear, and dynamic characteristics of the rotating machinery system, its faults are often accompanied by complex dynamic processes. However, in the existing technologies, both the above traditional signal processing methods and deep learning methods rely on discrete time series modeling, ignoring the continuity and dynamics of faults, and cannot accurately simulate and predict the continuous changes of the system. Moreover, in the existing technologies, the rotating machinery fault diagnosis methods usually only consider a single signal source (such as vibration signal). Based on a single signal source, it is actually difficult to accurately characterize the rotating machinery faults. It is often necessary to combine multiple signal sources (such as vibration, temperature, sound, etc.) for comprehensive judgment. However, different signal sources belong to different modal data and cannot be directly fused. The fusion methods in the existing technologies are relatively complex, resulting in limited improvement in diagnostic accuracy. Especially when applied to a rotating machinery system with complex, non-linear, and obvious dynamic characteristics, it is difficult to accurately simulate and predict the continuous dynamic changes of the system, and both the diagnostic accuracy and real-time performance may be affected. Therefore, the actual diagnostic real-time performance and robustness are not good.

[0006] In view of this, the inventors of the present application have designed a rotating machinery fault diagnosis method and related system in order to overcome the above technical problems. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a rotating machinery fault diagnosis method and related system to overcome the defect that in the existing technology, the rotating machinery system is complex, non-linear, and has obvious dynamic characteristics, its faults are often accompanied by complex dynamic processes, and both the above traditional signal processing methods and deep learning methods in the existing technology rely on discrete time series modeling, ignoring the continuity and dynamics of faults, and cannot accurately simulate and predict the continuous changes of the system.

[0008] The present invention solves the above technical problems through the following technical solutions:

[0009] The present invention provides a rotating machinery fault diagnosis method, characterized in that the rotating machinery fault diagnosis method includes the following steps: S1. Construct a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions; S2. Obtain the real-time information of the rotating machinery to be diagnosed, and perform modal analysis based on the real-time information of the rotating machinery to be diagnosed according to the rotor vibration equation to determine the sensitive frequency band and key features, and form multi-dimensional feature data; S3. Denoise the multi-dimensional feature data and perform signal reconstruction to obtain a reconstructed signal; S4. Input the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model adopts the fusion of a neural network ordinary differential equation and a convolutional neural network-gated recurrent unit.

[0010] According to one or more embodiments of the present invention, the rotor vibration equation includes time-varying parameters, nonlinear force terms, thermo-mechanical coupling force terms, and fluid-structure coupling force terms; the nonlinear force terms are used to describe the nonlinear behavior of the rotor system; the thermo-mechanical coupling force terms are used to describe the influence of thermal deformation caused by temperature on vibration; the fluid-structure coupling force terms are used to describe the influence of fluid on rotor vibration.

[0011] According to one or more embodiments of the present invention, the expression of the rotor vibration equation is: where M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; is the nonlinear force term; is the thermo-mechanical coupling force term; is the fluid-structure coupling force term; F(t) is the external excitation force.

[0012] According to one or more embodiments of the present invention, the modal analysis in step S2 includes linear modal analysis, and the linear modal analysis method includes the following steps: S 21 、Linearly process the thermo-mechanical coupling force term and the fluid-structure coupling force term through equivalent stiffness, damping, and mass; among them, the expression of the thermo-mechanical coupling force term is: The expression of the fluid-structure coupling force term is: S 22 、Substitute the thermo-mechanical coupling force term and the fluid-structure coupling force term into the vibration equation to form the linearly processed vibration equation where M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force; M fluid is the additional mass of the fluid; C th (t), C fluid (t) are the additional damping of thermo-mechanical coupling and the additional damping of fluid-structure coupling; K th (t), K fluid (t) are the additional stiffness of thermo-mechanical coupling and the additional stiffness of fluid-structure coupling; S 23 、Let the external excitation force F(t)=0, solve the vibration equation to obtain the eigenvalues and eigenvectors of the system: The obtained eigenvalue is: λ=-ζω n ±jω d ; where λ is the eigenvalue; ω n is the natural frequency of the system; ζ is the damping ratio; is the damped vibration frequency; the obtained eigenvector Φ is:

[0013] (K eq -ω 2 M eq )Φ=0; where K eq = K + K th + K fluid , M eq = M + M fluid .

[0014] According to one or more embodiments of the present invention, the modal analysis in step S2 includes nonlinear modal analysis, and the nonlinear modal analysis method includes the following steps: S 21 ', extract the initial mode, ignoring the nonlinear terms f nl , f th , f fiuld , and only consider the modal analysis of the linear equation to form the following formula: where M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force; the modal solution form is: where q n (t) is the modal generalized coordinate; S 22 ', introduce the nonlinear modal equation, project the nonlinear force term of the system onto the modal space, and the nonlinear force term is represented by a function of the modal variable q n (t): where P n is the function form obtained by expanding the nonlinear force term; Substitute the nonlinear force term into the original equation and project it onto the modal coordinate q n to obtain the equation:

[0015] where α nm , β nml are the nonlinear coupling coefficients, calculated by modal projection; ζ n is the modal damping; F n (t) is the modal generalized force; regard the thermal-mechanical coupling force term and the fluid-structure coupling force term as nonlinear correction terms, and expand the thermal-mechanical coupling force term and the fluid-structure coupling force term into function forms of modal variables; the function form of the thermal-mechanical coupling force term is: where α T , γ T are the scaling coefficients of the thermal coupling stiffness and damping; ΔT is the temperature change; the fluid-structure coupling force term The functional form is as follows: where μ, ν, and κ are the scaling coefficients of the fluid added mass, damping, and stiffness, Q is the flow field velocity or pressure field; S 23 ’, solve the nonlinear modal eigenvalue, and solve it by numerical iteration method. Assume the modal solution form is: q n (t) = A n cos(ω n t + φ n ); Substitute it into the nonlinear modal equation, use the averaging method or multi-scale method to separate the nonlinear terms, and obtain the nonlinear frequency correction formula: ω n = ω n.0 + Δω n ; where Δω n represents the nonlinear correction term, and its specific form depends on α nm , β nml coupling coefficient.

[0016] According to one or more embodiments of the present invention, the step S3 uses the complete adaptive noise ensemble empirical mode decomposition method to denoise the multi-dimensional feature data. The step S3 includes the following steps: S 31 、Collect the original signal, select appropriate noise amplitude and number of iterations, set values for each iteration, generate a white noise sequence, and add the white noise to the original signal to obtain a new signal sequence; S 32 、Perform empirical mode decomposition on each signal added with white noise to obtain the intrinsic mode and the residual; Each empirical mode decomposition generates multiple intrinsic mode components, that is, a set of intrinsic modes; Repeat the above empirical mode decomposition process multiple times, and each time a new set of intrinsic modes is generated; S 33 、Number each intrinsic mode, calculate the mean value of the intrinsic modes with the same number corresponding to multiple iterations to obtain the integrated intrinsic mode; Select the required intrinsic modes for retention, and superimpose the retained intrinsic modes to obtain the denoised reconstructed signal.

[0017] According to one or more embodiments of the present invention, the step S3 further uses the method based on the Akaike information criterion and the least absolute shrinkage and selection operator regression to denoise the multi-dimensional feature data, including the following steps: S 34, perform least absolute shrinkage and selection operator (LASSO) regression calculation: Use all the mean-filtered intrinsic mode components as input features, and the original signal as the target variable. Establish the relationship between the signal and the intrinsic mode components through LASSO regression. Based on the length of the original signal in the time domain and the number of mean-filtered intrinsic mode components, form the dimension of the feature matrix and construct the feature matrix. Use the target signal as the response variable. Employ the standard LASSO regression algorithm to estimate the regression coefficients by optimizing the loss function. Calculate the regression coefficients and select the intrinsic mode components with non-zero regression coefficients as the finally retained intrinsic mode components; S 35 , perform Akaike information criterion (AIC) screening for denoising: Based on the residuals obtained from the optimized intrinsic mode functions through LASSO regression, use the AIC to further screen the optimized intrinsic mode components; S 36 , Based on the results of LASSO and AIC screening for denoising, retain the intrinsic mode components with non-zero regression coefficients. For the retained intrinsic mode components after screening, calculate the mean of the corresponding intrinsic mode components in multiple iterations, and obtain the reconstructed signal after weighting.

[0018] According to one or more embodiments of the present invention, before inputting the reconstructed signal into a pre-trained rotating machinery fault model in step S4, perform standardized data preprocessing on the reconstructed signal; the standardized data preprocessing analyzes whether the reconstructed time series data approximately conforms to a normal distribution; if it conforms, convert each component of the signal into a form with a mean of 0 and a standard deviation of 1 to eliminate the dimensional and amplitude differences of different components; if the signal deviates from the normal distribution and shows a right-skewed distribution, use logarithmic transformation; if the signal shows a left-skewed distribution, use Box-Cox transformation for processing.

[0019] According to one or more embodiments of the present invention, the steps of standardized data preprocessing in step S4 include: calculating the mean of the reconstructed signal; calculating the standard deviation of the reconstructed signal; performing standardized processing on each data point of the reconstructed signal; and obtaining the preprocessed data of the standardized reconstructed signal.

[0020] According to one or more embodiments of the present invention, in the convolutional neural network-gated recurrent unit of step S4, the convolutional neural network uses a one-dimensional convolutional neural network; the structure of the one-dimensional convolutional neural network includes an input layer, three convolutional layers, and three max-pooling layers, where each convolutional layer includes a one-dimensional convolutional function, a batch normalization layer, and a rectified linear unit.

[0021] According to one or more embodiments of the present invention, the structure of the gated recurrent unit in the convolutional neural network-gated recurrent unit of step S4 includes a reset gate, an update gate, a candidate hidden state, and a final hidden state; the reset gate determines how much past information needs to be retained; the update gate determines how much new information needs to be incorporated into the hidden state; the candidate hidden state is the result of processing the current input and the previous hidden state considering the influence of the reset gate; the final hidden state is calculated through the update gate and the candidate hidden state.

[0022] According to one or more embodiments of the present invention, the neural ordinary differential equation in step S4 is a neural network model that combines deep learning and ordinary differential equations; it simulates a continuous-time dynamic system by parameterizing the solution of the ordinary differential equation, regards the hidden state of the neural network as the solution of the ordinary differential equation, and learns the derivatives of these hidden states through the neural network.

[0023] According to one or more embodiments of the present invention, the steps of data processing by the rotating machinery fault model in step S4 include: S 41 Perform a one-dimensional convolutional neural network process: Use the time series data after normalization processing as the input signal, calculate the feature map for the input signal through one-dimensional convolution; perform batch normalization on each channel to adjust the mean and variance of the output; apply a rectified linear unit function to the output feature map of the batch normalization layer to introduce non-linearity; reduce the time dimension of the feature map through max pooling; stack three convolutional layers to sequentially extract higher-level features; each one-dimensional convolution operation updates the number of channels and the sequence length of the feature map; perform convolution on the sequence length and output the shape of the feature map after several convolutional layers; S 42 Perform a gated recurrent unit process: Transpose the shape of the output feature map of the convolutional layer; the gated recurrent unit receives the data of the above feature map shape and outputs a sequence of final hidden states; in the gated recurrent unit, a new hidden state is generated at each time step, and the final hidden state sequence is the set of the above hidden states; S 43 Perform a neural ordinary differential equation process: The neural ordinary differential equation extracts the information of the complete sequence by selecting the hidden state at the last time step, uses the final hidden state of the gated recurrent unit as the input to the latent space, and models the relationship between the latent variable and the input time series through a probability distribution; sample the initial value of the latent variable from a Gaussian distribution, use the initial value of the latent variable as the initial condition, and predict the value of the latent variable at future time points through an adaptive time-step ordinary differential equation solver.

[0024] According to one or more embodiments of the present invention, the step S 43 The neural ordinary differential equation process in includes the following steps: S 431, Define a function for ordinary differential equations to describe the dynamics of latent space variables; S 432 , Perform time integration to calculate the latent space state at each time point through numerical integration methods; S 433 , Pass the latent variables predicted by the ordinary differential equation to a fully connected layer, which linearly transforms the latent variables through a weight matrix and a bias vector; the fully connected layer outputs a vector representing the raw scores for each class; S 434 , Convert the raw scores into a probability distribution by a softmax function layer; S 435 , The softmax function layer outputs the probability for each class; in fault diagnosis, select the class with the highest probability as the final diagnosis result.

[0025] The present invention also provides a rotating machinery fault diagnosis system, characterized in that the rotating machinery fault diagnosis system adopts the rotating machinery fault diagnosis method as described above, and the rotating machinery fault diagnosis system includes: an equation construction module for constructing a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions; a feature data extraction module for obtaining real-time information of the rotating machinery to be diagnosed, and performing modal analysis based on the real-time information of the rotating machinery to be diagnosed based on the rotor vibration equation to determine the sensitive frequency band and key features, and forming multi-dimensional feature data; a signal reconstruction module for denoising the multi-dimensional feature data and performing signal reconstruction to obtain a reconstructed signal; a diagnosis module for inputting the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model adopts a fusion of neural network ordinary differential equations and convolutional neural network-gated recurrent units.

[0026] The present invention also provides an electronic device, including: a processor and a memory, the memory stores a program or instruction that can run on the processor, and the program or instruction is executed by the processor to implement the rotating machinery fault diagnosis method as described above.

[0027] The present invention also provides a readable storage medium, on which a program or instruction is stored, and when the program or instruction is executed by a processor, the rotating machinery fault diagnosis method as described above is implemented.

[0028] The positive and progressive effects of the present invention are as follows:

[0029] The rotating machinery fault diagnosis method and related system of the present invention at least have the following advantages:

[0030] The present invention constructs a rotor vibration equation considering thermal-mechanical coupling and fluid-structure coupling by combining rotor dynamics, which can more comprehensively and accurately describe the dynamic behavior of complex coupling systems. Then, the extracted fault features are provided to a neural network model based on the fusion of Neural ODEs and one-dimensional CNN-GRU for training and optimization. Neural ODEs are used to simulate continuous-time dynamic systems and capture the dynamic evolution law of fault signals, improving the physical interpretability and computational efficiency of the model. GRU is used to handle long-term and short-term dependencies in time series through a gating mechanism, and combined with one-dimensional CNN to extract multi-scale fault features, which can greatly enhance the adaptability and diagnostic accuracy of the model under complex working conditions, accurately simulate and predict the continuous dynamic changes of the system, improve the diagnostic accuracy, and enhance the real-time performance and robustness of the model, so as to quickly and accurately achieve the early detection and classification of rotating machinery faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The above and other features, properties, and advantages of the present invention will become more apparent through the following description in conjunction with the drawings and embodiments, where the same reference numerals in the drawings always represent the same features, among which:

[0032] Figure 1 is a schematic diagram of the implementation process of an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0033] Figure 2 is a schematic diagram of the effect of the empirical mode decomposition result in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0034] Figure 3 is a schematic diagram of the implementation process of signal denoising and reconstruction based on CEEMDAN-LASSO-AIC in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0035] Figure 4 is a schematic diagram of the structural principle of a neural network model based on the fusion of Neural ODEs and 1D-CNN-GRU in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0036] Figure 5 is a schematic diagram of the structural principle of the 1D-CNN adopted in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0037] Figure 6 is a schematic diagram of the structural principle of the GRU adopted in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0038] Figure 7 is a schematic diagram of the gear state classification confusion matrix obtained in the test results of an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0039] Figure 8 It is a curve graph of the training and verification accuracy and loss of the gear state classification model obtained from the test results of an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0040] Figure 9 It is a schematic diagram of the comparison result of the neural network model performance in the test results of an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0041] Figure 10 It is a fault time domain diagram in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0042] Figure 11 It is a schematic diagram of sample data in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0043] Figure 12 It is a schematic diagram of the reconstructed signal in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0044] Figure 13 It is a schematic diagram of the gear state classification performance evaluation in an embodiment of the rotating machinery fault diagnosis method of the present invention.

[0045] Figure 14 It is a normal time domain schematic diagram in an embodiment of the rotating machinery fault diagnosis method of the present invention. Detailed implementation manners

[0046] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following detailed description of the specific implementation manners of the present invention will be provided in conjunction with the accompanying drawings.

[0047] Now, embodiments of the present invention will be described in detail with reference to the accompanying drawings. Now, preferred embodiments of the present invention will be described in detail, and examples thereof are shown in the drawings. In any possible case, the same reference numerals will be used throughout the drawings to represent the same or similar parts. In addition, although the terms used in the present invention are selected from well-known and commonly used terms, some of the terms mentioned in the specification of the present invention may be selected by the applicant according to his or her judgment, and their detailed meanings are described in the relevant parts of the description herein. In addition, it is required to understand the present invention not only through the actual terms used, but also through the meaning implied by each term. At the same time, for the convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationships.

[0048] See Figure 1 , the present invention provides a rotating machinery fault diagnosis method, and the rotating machinery fault diagnosis method includes the following steps:

[0049] Step S1, construct a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions;

[0050] Step S2: Obtain the real-time information of the rotating machinery to be diagnosed, and perform modal analysis based on the real-time information of the rotating machinery to be diagnosed according to the rotor vibration equation to determine the sensitive frequency band and key features, and form multi-dimensional feature data;

[0051] Step S3: Denoise the multi-dimensional feature data and perform signal reconstruction to obtain a reconstructed signal;

[0052] Step S4: Input the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model adopts the fusion of Neural ODEs (Neural Ordinary Differential Equations) and CNN-GRU (Convolutional Neural Network-Gated Recurrent Unit).

[0053] Preferably, the rotating machinery fault model in step S4 is trained by a neural network model constructed based on Neural ODEs (Neural Ordinary Differential Equations) and one-dimensional CNN-GRU (one-dimensional Convolutional Neural Network-Gated Recurrent Unit). Neural ODEs (Neural Ordinary Differential Equations) are used to capture the dynamic evolution law of the fault signal, the final hidden state of the GRU (Gated Recurrent Unit) is used as the initial condition of Neural ODEs (Neural Ordinary Differential Equations), the GRU (Gated Recurrent Unit) is used to handle the long-term and short-term dependencies in the time series through the gating mechanism, and the CNN (Convolutional Neural Network) is used to extract multi-scale fault features.

[0054] Through the above steps, the rotating machinery fault diagnosis method of the present invention considers the interaction of thermal, mechanical and fluid effects, constructs a rotor vibration equation for complex working conditions of thermal-mechanical coupling and fluid-structure coupling, which can make the vibration equation more comprehensively and accurately describe the dynamic behavior of the complex coupling system, improve the modeling accuracy of faults, and at the same time combine the continuous-time modeling ability of Neural ODEs (Neural Ordinary Differential Equations) with the powerful feature extraction ability of GRU (Gated Recurrent Unit) and 1D-CNN (one-dimensional Convolutional Neural Network), and can accurately capture the evolution law and time series features of the fault signal, thereby greatly improving the accuracy and robustness of fault diagnosis.

[0055] The original data of rotating machinery is usually a time series signal from sensors (such as accelerometers, tachometers, temperature sensors, current sensors, etc.), which is mainly used to capture the dynamic characteristics of the machinery. Using rotor dynamics can help understand the dynamic behavior of the rotating machinery system, and combining rotor dynamics for feature extraction can extract dynamic features closely related to faults.

[0056] The rotor system can be regarded as a multi-degree-of-freedom system composed of multiple components (rotors, shafts, bearings, gears, etc.). In this embodiment, by considering the complex working condition rotor vibration equation with time-varying parameters, non-linear force terms, thermal-mechanical coupling force terms, and fluid-structure coupling force terms, the interaction of thermal, mechanical, and fluid effects is considered, which can accurately describe the vibration behavior of the rotor system under complex working conditions, enabling the vibration equation to more comprehensively and accurately describe the dynamic behavior of the complex coupling system and improving the modeling accuracy of faults.

[0057] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the rotor vibration equation includes time-varying parameters, non-linear force terms, thermal-mechanical coupling force terms, and fluid-structure coupling force terms;

[0058] The non-linear force term is used to describe the non-linear behavior of the rotor system; the thermal-mechanical coupling force term is used to describe the influence of thermal deformation caused by temperature on vibration; the fluid-structure coupling force term is used to describe the influence of fluid on rotor vibration.

[0059] Preferably, in the rotor vibration equation in step S1, it includes time-varying parameters, non-linear force terms, thermal-mechanical coupling force terms, and fluid-structure coupling force terms. The non-linear force term is used to describe the non-linear behavior of the rotor system, the thermal-mechanical coupling force term is used to describe the influence of thermal deformation caused by temperature on vibration, and the fluid-structure coupling force term is used to describe the influence of fluid on rotor vibration.

[0060] Aiming at the problems of low diagnostic accuracy and real-time performance of rotating machinery equipment in the prior art, the present invention proposes a rotating machinery fault diagnosis method. By combining rotor dynamics to construct a complex working condition rotor vibration equation considering thermal-mechanical coupling and fluid-structure coupling, and simultaneously integrating Neural ODEs (Neural Ordinary Differential Equations) and CNN-GRU (Convolutional Neural Network-Gated Recurrent Unit) to construct a rotating machinery equipment diagnosis model, it has high accuracy, strong generalization ability, and real-time processing ability.

[0061] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the expression of the rotor vibration equation is:

[0062]

[0063] where M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; is the non-linear force term, used to describe the non-linear behavior of the rotor system; is the thermal-mechanical coupling force term, used to describe the influence of thermal deformation caused by temperature on vibration, such as oil film force;

[0064] is the fluid-structure coupling force term used to describe the influence of the fluid on the rotor vibration; F(t) is the external excitation force.

[0065] It should be noted that by constructing the rotor vibration equation under the above complex working conditions, various physical effects under multiple actual operating conditions can be comprehensively considered. By introducing time-varying parameters, this equation can reflect the dynamic characteristics of the mass, damping, and stiffness matrices changing with time, and describe the real behavior of the rotor system during dynamic operation. At the same time, the nonlinear force term reveals the influence of nonlinear behaviors such as friction and clearance, and the thermal-mechanical coupling force term and the fluid-structure coupling force term comprehensively consider the effect of temperature change on mechanical properties and the influence of fluid-structure interaction. As a result, the vibration equation can accurately characterize the dynamic behavior of the system under complex working conditions, including vibration response, frequency characteristics, and fault characteristics. Furthermore, through the theoretical analysis of the vibration equation, modal characteristics related to faults (such as natural frequencies and vibration modes) and dynamic response characteristics can be extracted. Different fault modes will cause significant changes in the frequency and amplitude of the vibration response. Combining with nonlinear modal analysis can capture high-order nonlinear effects, further reveal fault characteristics, and clarify sensitive frequency bands or key features. By solving the vibration equation, the modal parameters and dynamic response of the system can also be directly obtained, and parameters related to faults (such as frequency, amplitude, phase, etc.) can be extracted. The natural frequencies and vibration modes of the system can be determined through modal analysis. Then, the solution results of the vibration equation are used as input features for the fault diagnosis model. For example, modal parameters (natural frequencies, vibration modes) or time series of dynamic responses are used as inputs to the neural network model, and accurate fault classification and feature learning are achieved through the model to obtain the fault diagnosis results.

[0066] Optionally, the dynamic response of the vibration equation can also be used for fault prediction and equipment health management. For example, by monitoring the change trend of the vibration response, the occurrence and development of faults can be predicted, and the real-time evaluation and warning of the equipment health status can be realized by combining deep learning algorithms, thereby improving the operation reliability and safety of the mechanical system.

[0067] Different fault modes (such as misalignment, imbalance, bearing wear, gear fault, etc.) will affect the vibration response of the rotor system. The vibration caused by imbalance usually shows a low-frequency periodic signal, and its frequency is usually an integer multiple of the rotational speed frequency. The vibration caused by shaft misalignment mainly shows low-frequency periodic fluctuations and often accompanied by multi-band vibrations. Bearing faults usually cause high-frequency pulse signals, and these pulses are closely related to the rotation period of the rotor and the geometric characteristics of the bearing (such as the number of rolling elements). Gear faults may cause vibrations related to the gear meshing frequency and higher-frequency non-stationary pulse signals. The key to feature extraction lies in analyzing the changes in different frequency bands. Modal analysis of the rotor system can extract the natural frequencies and vibration modes of the system. For a time-varying system, at each instant t, M(t), C(t), and K(t) are fixed for time-varying modal extraction. Considering and can be regarded as linear or non-linear characteristics under different conditions, and modal analysis in two cases is proposed.

[0068] The characteristics of the thermo-mechanical coupling force term are linear or non-linear under different working conditions. For example, when the system is under small deformation and small temperature difference conditions, the thermal expansion coefficient and thermal conductivity of the material change little within the working temperature range, and the thermal stress is linearly related to the temperature change, the thermo-mechanical coupling effect can be approximated as linear. In addition, under low-speed or low-load working conditions, the high-order non-linear effects can be ignored and the mechanical behavior also tends to be linear. However, when the system experiences large temperature difference and large deformation, significant thermal expansion and thermal stress changes may occur in the material, resulting in non-linear thermo-mechanical coupling. If physical parameters such as the thermal expansion coefficient and elastic modulus of the material change significantly with temperature, or there is a phase change (such as martensitic phase change), this non-linear characteristic will be more significant. Under high-speed, high-load or dynamic working conditions, the non-linear effects of thermo-mechanical coupling are particularly prominent, such as local high-temperature areas and thermal stress concentration caused by frictional heat generation. Therefore, distinguishing the linear and non-linear characteristics of the thermo-mechanical coupling can further improve the modeling accuracy and the accuracy of system behavior analysis under complex working conditions.

[0069] The linear or non-linear characteristics of the fluid-structure coupling force term depend on the specific working conditions. In the case of small deformation and low-speed flow, the fluid-structure coupling effect can be approximated as linear. Especially when the fluid satisfies the linear Navier-Stokes equation and the solid structure is a linearly elastic material, its mechanical behavior can be simplified to a linear model. In addition, under simple geometric shapes and boundary conditions, the linear assumption is often accurate enough. However, when the system experiences large deformation or the fluid flow is at a high Reynolds number (turbulent flow), the fluid-structure coupling effect shows significant non-linearity, and the complex interaction between the fluid and the structure needs to be considered. Similarly, when the fluid is a non-Newtonian fluid, or the solid structure exhibits non-linear elastic, plastic or viscoelastic characteristics, the fluid-structure coupling characteristics deviate from the linear assumption and a non-linear model needs to be used for description. Therefore, by distinguishing the linear or non-linear of the fluid-structure coupling force term, the modeling accuracy and the accuracy of system behavior analysis under complex working conditions can be further improved.

[0070] Preferably, for the rotating machinery fault diagnosis method of the present invention, linear modal analysis method and non-linear modal analysis method can be respectively adopted for modal analysis according to the linear or non-linear of the thermo-mechanical coupling force term and the fluid-structure coupling force term to adapt to the system behavior analysis under different working conditions.

[0071] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the modal analysis in step S2 includes linear modal analysis, and the linear modal analysis method includes the following steps:

[0072] Step S 21, linearize the thermal-mechanical coupling force term and the fluid-structure coupling force term through equivalent stiffness, damping, and mass;

[0073] Among them, the thermal-mechanical coupling force term can be expressed as:

[0074]

[0075] The fluid-structure coupling force term can be expressed as:

[0076]

[0077] Step S 22 , substitute the thermal-mechanical coupling force term and the fluid-structure coupling force term into the vibration equation to form the linearized vibration equation:

[0078]

[0079] Among them, M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force; M fluid is the added mass of the fluid; C th (t), C fluid (t) are the additional damping of thermal-mechanical coupling and the additional damping of fluid-structure coupling; K th (t), K fluid (t) are the additional stiffness of thermal-mechanical coupling and the additional stiffness of fluid-structure coupling;

[0080] Step S 23 , let the external excitation force F(t) = 0, solve the vibration equation to obtain the eigenvalues and eigenvectors of the system:

[0081]

[0082] The obtained eigenvalues are:

[0083] λ = -ζω n ±jω d (4)

[0084] Among them, λ is the eigenvalue; ω n is the natural frequency of the system; ζ is the damping ratio; is the damped vibration frequency;

[0085] The eigenvector Φ represents the vibration mode of the system in the modal state, and the obtained eigenvector Φ is:

[0086] (K eq -ω2 M eq )Φ = 0 (5)

[0087] Among them, K eq = K + K th + K fluid ,M eq = M + M fluid 。

[0088] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the modal analysis in step S2 includes non-linear modal analysis. The core idea of non-linear modal expansion is to represent the non-linear force terms as functions of modal variables, and simplify them into a finite-dimensional form through expansion and truncation. The non-linear modal analysis method includes the following steps:

[0089] Step S 21 ’, Extract the initial mode. For the rotor vibration equation under complex working conditions, first ignore the non-linear terms f nl 、f th 、f fiuld , and only consider the modal analysis of the linear equation to form the following formula:

[0090]

[0091] Among them, M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force;

[0092] The modal solution form is: Among them, q n (t) is the modal generalized coordinate;

[0093] Step S 22 ’, Introduce the non-linear modal equation, and project the non-linear force terms of the system onto the modal space. The non-linear force terms are represented by functions of the modal variable q n (t):

[0094]

[0095] Among them, P n is the function form obtained through the expansion of the non-linear force terms;

[0096]

[0097] Substitute the non-linear force terms into the original equation and project them onto the modal coordinate q n , and the final equation obtained is:

[0098]

[0099] Among them, α nm , β nml are non - linear coupling coefficients, calculated by modal projection; ζ n is modal damping; F n (t) is the modal generalized force;

[0100] The thermo - mechanical coupling force term and the fluid - structure coupling force term are used as non - linear correction terms, and the thermo - mechanical coupling force term and the fluid - structure coupling force term are expanded into functional forms of modal variables;

[0101] The functional form of the thermo - mechanical coupling force term is:

[0102]

[0103] Among them, α T , γ T are scale coefficients of thermal coupling stiffness and damping; ΔT is the temperature change;

[0104] The functional form of the fluid - structure coupling force term is:

[0105]

[0106] Among them, μ, ν, κ are scale coefficients of fluid added mass, damping and stiffness, and Q is the flow field velocity or pressure field;

[0107] Step S 23 ’, solve the non - linear modal eigenvalue, and solve it by numerical iteration method. Assume the modal solution form is:

[0108] q n (t) = A n cos(ω n t + φ n ) (13)

[0109] Substitute it into the non - linear modal equation, use the averaging method or the multi - scale method to separate the non - linear terms, and obtain the non - linear frequency correction formula:

[0110] ω n = ω n.0 + Δω n (14)

[0111] Among them, Δω n represents the non - linear correction term, and its specific form depends on α nm , β nml coupling coefficients.

[0112] In the above - mentioned embodiments, the rotor vibration under complex working conditions is characterized by time - varying parameters, non - linear force terms, thermal - mechanical coupling terms, and fluid - solid coupling force terms together. The modal variables are used to express the dynamic thermal - mechanical and fluid - solid coupling terms. By using the above non - linear expansion method, the high - order effects of non - linear force terms can be captured, so as to more comprehensively and accurately describe the dynamic behavior of complex coupling systems. Further, through spectrum analysis, time - frequency analysis, and fault frequencies in rotor dynamics, it can be determined which frequency bands or characteristics are more sensitive to a certain type of fault, and modal characteristics, spectrum characteristics, etc. related to the fault type are extracted.

[0113] Through modal analysis, the IMF (intrinsic mode function) components related to fault characteristics can be identified, and the frequency range of noise can be clarified. Thus, in subsequent signal reconstruction, key features can be retained targeted and noise components can be removed, improving the effectiveness and reliability of the signal. The solution results of the vibration equation can further clarify the goal of signal reconstruction, that is, to retain features closely related to fault diagnosis such as modal parameters and dynamic responses, while removing irrelevant components to enhance the interpretability and diagnostic value of key components in the signal. In addition, the above - mentioned vibration equation can also be used as a verification benchmark for the signal reconstruction effect. By comparing the modal parameters of the reconstructed signal with the theoretical results of the vibration equation, it can be evaluated whether the reconstruction retains key fault characteristics. Further, the reconstructed signal is input into the fault diagnosis model to analyze whether its diagnostic performance meets the expectations, so as to ensure the effectiveness and accuracy of signal reconstruction in actual diagnostic applications.

[0114] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, in step S3, CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise) with adaptive noise is used to denoise multi - dimensional feature data. Step S3 includes the following steps:

[0115] Step S 31 Collect the original signal, select appropriate noise amplitudes and the number of iterations, set values for each iteration, generate a white noise sequence, and add the white noise to the original signal to obtain a new signal sequence;

[0116] Step S 32 Perform EMD (empirical mode decomposition) on each signal added with white noise to obtain IMFs (intrinsic modes) and residuals;

[0117] Each empirical mode decomposition generates multiple intrinsic mode components, that is, a set of intrinsic modes;

[0118] Repeat the above empirical mode decomposition process multiple times, and each time a new set of intrinsic modes is generated;

[0119] Step S 33, number each eigenmode, and calculate the average of the eigenmodes with the same number in multiple iterations to obtain the integrated eigenmode;

[0120] Select the required eigenmodes for retention, and superimpose the retained eigenmodes to obtain the denoised reconstructed signal.

[0121] It should be noted that the original data usually has multiple features (such as time domain, frequency domain, time-frequency domain, etc.). Therefore, multi-dimensional data processing is an important link in fault diagnosis, and its main goal is to remove noise from the original data, standardize the signal, and extract useful features. After extracting various feature data through the above steps, it is often affected by environmental noise, sensor errors, etc. Therefore, it is necessary to denoise the signal.

[0122] This embodiment uses CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) to denoise the extracted feature data to solve the non-linearity and non-stationarity problems of complex signals. CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) is an improved empirical mode decomposition method for signal denoising and feature extraction. It reduces the mode mixing phenomenon by adding adaptive noise to the signal, improving the accuracy and stability of signal decomposition.

[0123] Preferably, the detailed process of using CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) for signal denoising is as follows:

[0124] Step S 31 , assume that the collected original signal is x(t), and select appropriate noise amplitude ε and number of iterations N. For each iteration i, generate a white noise sequence ω i (t). Add the white noise to the original signal to obtain a new signal sequence:

[0125] x i (t) = x(t) + εω i (t) (15)

[0126] Step S 32 , perform EMD (Empirical Mode Decomposition) on each signal x i (t) added with noise to obtain a set of IMFs (intrinsic mode functions) and residuals:

[0127]

[0128] Among them, IMF i,k (t) is the k-th IMF (intrinsic mode function) of the i-th iteration; R i (t) is the residual of the i-th iteration.

[0129] Each EMD (Empirical Mode Decomposition) may generate multiple IMF (Intrinsic Mode Function) components, that is, a set of IMFs (Intrinsic Mode Functions). For example, the IMFs (Intrinsic Mode Functions) generated in the first iteration are labeled as:

[0130]

[0131] where M1 is the number of IMFs (Intrinsic Mode Functions) generated in the first iteration.

[0132] Repeat the above process N times, and each time a new set of IMFs (Intrinsic Mode Functions) is generated. In the Nth iteration, the generated IMFs (Intrinsic Mode Functions) are labeled as:

[0133]

[0134] where M N is the number of IMFs (Intrinsic Mode Functions) generated in the Nth iteration.

[0135] An example of the result of performing EMD (Empirical Mode Decomposition) on a signal is as Figure 2 shown.

[0136] Step S 33 , number each IMF (Intrinsic Mode Function), and take the average of the corresponding IMFs (Intrinsic Mode Functions) in N iterations. For example, if the kth IMF (Intrinsic Mode Function) is of concern, the kth IMFs (Intrinsic Mode Functions) in all iterations need to be averaged to obtain the final kth IMF (Intrinsic Mode Function) component. That is, take the average of IMF 1,k (t), IMF 2,k (t), … IMF N,k (t):

[0137]

[0138] During the integration process, a set of IMF (Intrinsic Mode Function) components is generated in each iteration, but the number and characteristics of these components may vary from iteration to iteration. Take the average of the IMFs (Intrinsic Mode Functions) with the same number (if any), and after taking the average of all IMF (Intrinsic Mode Function) components, the integrated IMFs (Intrinsic Mode Functions) are obtained.

[0139] The IMFs (Intrinsic Mode Functions) mainly contain noise, while the low-frequency IMFs (Intrinsic Mode Functions) contain the main features of the signal. Select the IMFs (Intrinsic Mode Functions) to be retained, and superimpose the retained IMFs (Intrinsic Mode Functions) to obtain the denoised signal, that is, the reconstructed signal:

[0140]

[0141] It should be noted that a key issue in the IMF (Intrinsic Mode Function) decomposition process is how to determine the number of each IMF (Intrinsic Mode Function) component obtained by decomposition and which components should be retained for signal reconstruction. In IMF (Intrinsic Mode Function) decomposition, different IMF (Intrinsic Mode Function) components correspond to different frequency band characteristics of the signal. According to the results of rotor dynamics analysis, the frequency bands related to the dynamic response of the rotor system are preferentially screened out.

[0142] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, in step S3, a method based on AIC (Akaike Information Criterion) and LASSO (Least Absolute Shrinkage and Selection Operator) regression is further used to denoise the multi-dimensional feature data, including the following steps:

[0143] Step S 34 Perform least absolute shrinkage and selection operator regression calculation:

[0144] Take all the mean IMF (Intrinsic Mode Function) components as input features, take the original signal as the target variable, and establish the relationship between the signal and the IMF (Intrinsic Mode Function) components through LASSO (Least Absolute Shrinkage and Selection Operator) regression;

[0145] According to the length of the original signal in the time domain and the number of mean IMF (Intrinsic Mode Function) components, form the dimension of the feature matrix and construct the feature matrix;

[0146] Take the target signal as the response variable;

[0147] Use the standard LASSO (Least Absolute Shrinkage and Selection Operator) regression algorithm to estimate the regression coefficients by optimizing the loss function;

[0148] Calculate the regression coefficients, select the IMF (Intrinsic Mode Function) components with non-zero regression coefficients as the finally retained IMF (Intrinsic Mode Function) components;

[0149] Step S 35 Perform AIC (Akaike Information Criterion) screening for denoising:

[0150] According to the residuals obtained from the optimized intrinsic mode function obtained by LASSO (Least Absolute Shrinkage and Selection Operator) regression, further screen the optimized IMF (Intrinsic Mode Function) using AIC (Akaike Information Criterion);

[0151] Step S 36, based on the denoising results screened by LASSO (Least Absolute Shrinkage and Selection Operator) and AIC (Akaike Information Criterion), retain the IMF (Intrinsic Mode Function) components of the regression coefficients. For the retained IMF (Intrinsic Mode Function) components after screening, calculate the mean of the corresponding IMF (Intrinsic Mode Function) components in multiple iterations, and obtain the reconstructed signal after weighting.

[0152] It should be noted that complex vibration signals will be generated during the operation of rotating equipment, and these signals usually contain multiple frequency components and noise. Fault characteristics are often masked by noise, and the characteristic frequencies and amplitude changes corresponding to different fault modes may be relatively subtle. Therefore, accurately extracting fault characteristics is the key to fault diagnosis. In addition, the fault signals of rotating equipment have the characteristics of non-stationarity, multi-modal, high-dimensionality, and redundant information. In the traditional EMD (Empirical Mode Decomposition) method, the number and characteristics of IMF (Intrinsic Mode Function) are affected by noise and data non-stationarity, resulting in the extraction of some irrelevant high-frequency noise components. In this embodiment, further aiming at the characteristics of signal complexity, non-stationarity, and high-dimensionality in the fault diagnosis of rotating equipment, information criterion and sparsity optimization are used to select the retained IMF (Intrinsic Mode Function) components, where the information criterion uses AIC (Akaike Information Criterion), and the sparsity optimization selects LASSO (Least Absolute Shrinkage and Selection Operator) regression, that is, the method based on AIC (Akaike Information Criterion) and LASSO (Least Absolute Shrinkage and Selection Operator) regression is used to select the retained IMF (Intrinsic Mode Function) components.

[0153] The present invention combines the AIC (Akaike Information Criterion) and LASSO (Least Absolute Shrinkage and Selection Operator) regression methods. By retaining the IMF (Intrinsic Mode Function) components related to fault characteristics and removing noise and redundant information at the same time, it can more accurately identify fault modes, improve the adaptability of the model to different working conditions and fault types. At the same time, by reducing the number of retained IMF (Intrinsic Mode Function) components, it can also reduce the computational complexity of the model, improve the real-time performance of fault diagnosis, and the retained IMF (Intrinsic Mode Function) components are closer to fault characteristics, making the result after signal reconstruction more physically meaningful and facilitating fault analysis.

[0154] The basic idea of LASSO (Least Absolute Shrinkage and Selection Operator) regression is to minimize the loss function and add an L1 norm regularization term at the same time, so as to achieve the effect of feature selection. Its optimization objective function is:

[0155]

[0156] where x(t) is the original signal; IMF i (t) is the i-th IMF (Intrinsic Mode Function) component; β iis the regression coefficient of the IMF (Intrinsic Mode Function) component; λ is the regularization parameter; M is the total number of IMF (Intrinsic Mode Function) components, and N is the number of samples of the signal. LASSO (Least Absolute Shrinkage and Selection Operator) regression uses the L1 regularization term to penalize the magnitude of the regression coefficients, forcing some β i to be zero, thus selecting the most important IMF (Intrinsic Mode Function) components.

[0157] Preferably, the step S3 further uses a method based on AIC (Akaike Information Criterion) and LASSO (Least Absolute Shrinkage and Selection Operator) regression to denoise the multi-dimensional feature data, including the following steps:

[0158] Step S 34 : Perform LASSO (Least Absolute Shrinkage and Selection Operator) regression calculation:

[0159] Take all the mean IMF (Intrinsic Mode Function) components as input features, and take the original signal x(t) as the target variable. Establish the relationship between the signal and the IMF (Intrinsic Mode Function) components through LASSO (Least Absolute Shrinkage and Selection Operator) regression.

[0160] Assume that the length of the original signal in the time domain is T, and there are M IMF (Intrinsic Mode Function) components after taking the mean. Therefore, the dimension of the feature matrix X is T×M. Each column represents the values of an IMF (Intrinsic Mode Function) component at all time points, and each row represents the values of all IMF (Intrinsic Mode Function) components at a time point. Construct the feature matrix X:

[0161]

[0162] where IMF i (t) is the value of the i-th IMF (Intrinsic Mode Function) component at time t.

[0163] The target signal x(t) is used as the response variable y, representing the target signal that is expected to be modeled and approximated through LASSO (Least Absolute Shrinkage and Selection Operator) regression:

[0164]

[0165] Use the standard LASSO (Least Absolute Shrinkage and Selection Operator) regression algorithm to estimate the regression coefficient β i :

[0166]

[0167] Among them, X(t)·β represents the predicted value of the regression model, which is calculated as the weighted sum of IMF (Intrinsic Mode Function) components; λ is the regularization parameter that controls the complexity of the model and prevents overfitting.

[0168] Calculate the regression coefficients Select the IMF (Intrinsic Mode Function) components with non-zero regression coefficients as the finally retained IMF (Intrinsic Mode Function) components.

[0169] Step S 35 Perform AIC (Akaike Information Criterion) screening for denoising:

[0170] During EMD (Empirical Mode Decomposition), the residual can be expressed as:

[0171]

[0172] The optimized IMF (Intrinsic Mode Function) obtained through LASSO (Least Absolute Shrinkage and Selection Operator) regression is The obtained residual is Use AIC (Akaike Information Criterion) to further screen the optimized IMF (Intrinsic Mode Function). For the i-th IMF (Intrinsic Mode Function) component, its AIC (Akaike Information Criterion) can be expressed as:

[0173]

[0174] Among them, k i is the number of free parameters of the i-th IMF (Intrinsic Mode Function), which can be regarded as the duration or number of fluctuations of the IMF (Intrinsic Mode Function). After screening by AIC (Akaike Information Criterion), the IMF (Intrinsic Mode Function) components are made more concise, and useful signals are retained.

[0175] Step S 36 Further, based on the results of LASSO (Least Absolute Shrinkage and Selection Operator) regression and AIC (Akaike Information Criterion) screening, retain the IMF (Intrinsic Mode Function) components with regression coefficients For the screened and retained IMF (Intrinsic Mode Function) components, calculate the mean value of the corresponding IMF (Intrinsic Mode Function) components in all N iterations:

[0176]

[0177] Among them, IMF n,i (t) is the value of the i-th retained IMF (Intrinsic Mode Function) component at time t in the n-th iteration.

[0178] After weighting, the reconstructed signal is obtained:

[0179]

[0180] wherein, is the coefficient estimated by LASSO (Least Absolute Shrinkage and Selection Operator) regression.

[0181] It should be noted that in step S 34 and step S 35 of the present invention, by adopting the method based on AIC (Akaike Information Criterion) and LASSO (Least Absolute Shrinkage and Selection Operator) regression to select and retain the IMF (Intrinsic Mode Function) components, the fault features can be effectively extracted, the fault diagnosis accuracy can be improved, the robustness and generalization ability of the model can be enhanced, and at the same time the calculation cost can be reduced, further improving the fault diagnosis accuracy and efficiency of the rotating equipment.

[0182] It should be noted that the reconstructed signal x reconstructed (t) is the same as the original signal x(t), which is a time series data. Compared with the original signal, after IMF (Intrinsic Mode Function) decomposition, LASSO (Least Absolute Shrinkage and Selection Operator) regression, and AIC (Akaike Information Criterion) criterion screening of IMF (Intrinsic Mode Function) components and denoising processing, the main features of the signal can usually be retained while removing noise. The reconstructed signal usually has the same time length and sampling interval as the original signal. Through the denoising process, the waveform of the reconstructed signal may be smoothed, the noise components are significantly reduced, and important trends, periodicities, and other signal features can be retained. The flow of an embodiment of signal denoising and reconstruction based on CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) and LASSO-AIC (Least Absolute Shrinkage and Selection Operator - Akaike Information Criterion) of the present invention is as Figure 3 shown.

[0183] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, before inputting the reconstructed signal into a pre-trained rotating machinery fault model in step S4, data preprocessing of standardizing the reconstructed signal is performed;

[0184] The data preprocessing of standardization analyzes whether the reconstructed time series data approximately conforms to a normal distribution; if it conforms, each component of the signal is converted into a form with a mean of 0 and a standard deviation of 1 to eliminate the dimensional and amplitude differences of different components; if the signal deviates from the normal distribution and shows a right-skewed distribution, logarithmic transformation is adopted; if the signal shows a left-skewed distribution, Box-Cox transformation is used for processing.

[0185] It should be noted that through the rotor dynamics-guided feature extraction, screening, and signal reconstruction, the reconstructed signal can contain a dynamic description of the equipment operating state. For the reconstructed signal, standardized data preprocessing is also required to ensure that each feature of the data is on the same scale, which helps to further improve the performance and convergence speed of the model. Specifically, for the reconstructed time series data x = [x1, x2, … x n , analyze whether the data approximately conforms to the normal distribution. If it conforms, convert each component x i of the signal into a form with a mean of 0 and a standard deviation of 1, thereby eliminating the dimensional and amplitude differences of different components. If the signal deviates from the normal distribution and shows a right-skewed distribution, use logarithmic transformation; if the signal shows a left-skewed distribution, use Box-Cox transformation for processing.

[0186] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the standardized data preprocessing step in step S4 includes:

[0187] Calculate the mean of the reconstructed signal; calculate the standard deviation of the reconstructed signal; perform standardized processing on each data point of the reconstructed signal; obtain the preprocessed data with the reconstructed signal standardized.

[0188] Preferably, the standardized data preprocessing step is specifically:

[0189] (1) Calculate the mean

[0190]

[0191] where n is the number of time series points, and x i is the i-th data point.

[0192] (2) Calculate the standard deviation

[0193]

[0194] (3) Standardized processing

[0195] Perform standardized processing on each data point:

[0196]

[0197] where x s,i is the data point after standardizing the i-th data point.

[0198] Then the reconstructed signal is standardized to:

[0199]

[0200] For multiple time series x (1) (t), x(2) (t), x (3) (t)…, global standardization can be performed.

[0201] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, in the CNN-GRU (Convolutional Neural Network - Gated Recurrent Unit) of step S4, the CNN (Convolutional Neural Network) uses 1D-CNN (One-Dimensional Convolutional Neural Network);

[0202] The one-dimensional convolutional neural network structure includes an input layer, three convolutional layers, and three max pooling layers, where each convolutional layer includes a one-dimensional convolutional function, a batch normalization layer, and a rectified linear unit.

[0203] Preferably, the present invention pre-constructs a neural network model that fuses Neural ODEs (Neural Ordinary Differential Equations) with 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit), forms a training data set from the extracted fault features, and performs training processing on the neural network model to form a rotating machinery equipment fault diagnosis model. The neural network model diagram based on the fusion of Neural ODEs (Neural Ordinary Differential Equations) with 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) is as shown in Figure 4As shown in the figure. Neural ODEs (Neural Ordinary Differential Equations) can provide continuous-time modeling capabilities. For unevenly sampled time series data, they can capture the dynamic evolution law of fault signals, not only reducing the model complexity but also enhancing the physical interpretability of fault evolution, making them particularly suitable for fault analysis of complex rotating machinery systems. 1D-CNN (One-Dimensional Convolutional Neural Network) is good at extracting local features from time series and can quickly identify short-time patterns (such as impact waveforms) in fault signals. Its parameter sharing mechanism and noise robustness give it good feature extraction efficiency and model stability. GRU (Gated Recurrent Unit) captures long-term and short-term dependencies of time series through a gating mechanism and is suitable for modeling non-linear dynamic behaviors. Compared with LSTM (Long Short-Term Memory Network), GRU (Gated Recurrent Unit) has a simpler structure and higher computational efficiency, making it very suitable for dealing with the time correlation of complex mechanical fault signals. In this embodiment, by using 1D-CNN (One-Dimensional Convolutional Neural Network) to extract local spatial features, using GRU (Gated Recurrent Unit) to capture the long-term dependencies of time series, and using Neural ODEs (Neural Ordinary Differential Equations) to simulate the continuous dynamic changes of signals, the model can comprehensively capture the features of fault signals through the complementarity of each part, improving the diagnostic accuracy. At the same time, by fusing Neural ODEs (Neural Ordinary Differential Equations) with 1D-CNN-GRU (One-Dimensional Convolutional Neural Network-Gated Recurrent Unit), multi-scale feature extraction and dynamic modeling of rotating equipment fault signals can be achieved, improving the accuracy and robustness of fault diagnosis for complex dynamic systems.

[0204] Neural ODEs (Neural Ordinary Differential Equations) can simulate continuous-time dynamic systems and are suitable for processing and modeling the dynamic evolution law of fault signals. However, in the fault diagnosis of rotating equipment, the complexity of signals and noise interference pose higher requirements for the robustness and accuracy of the model. To improve the performance of Neural ODEs (Neural Ordinary Differential Equations) in the fault diagnosis of rotating equipment, in this embodiment, first, for the problem that noise interference in vibration signals may mask fault features, a regularization technique (i.e., Lasso regression to process signals) is introduced to reduce the misjudgment rate and significantly improve the diagnostic accuracy in a noisy environment. Second, to cope with the unevenness of the dynamic characteristic change rate of fault signals, an ODE (Ordinary Differential Equation) solver with an adaptive time step is adopted in this embodiment, enabling the model to dynamically adjust the time step according to the signal complexity, thereby more accurately capturing the dynamic changes of the signal and improving the adaptability and accuracy. In addition, by increasing the model depth (such as stacking multiple NeuralODE (Neural Ordinary Differential Equation) layers), the expression ability of the model is significantly improved, enabling it to more effectively simulate complex fault evolution processes.

[0205] The 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) combines the local feature extraction ability of the convolutional neural network and the modeling ability of the GRU (Gated Recurrent Unit) for time series. To further enhance the ability of signal feature extraction and dynamic modeling in the fault diagnosis of rotating equipment, in this embodiment, first, to address the problem that the fault signal contains multiple frequency components, a three-layer convolutional layer and a one-layer GRU (Gated Recurrent Unit) structure are adopted to achieve effective fusion of low-frequency and high-frequency features, enhance the feature extraction ability of the model in complex signals, and thus improve the diagnostic accuracy. Second, to better capture the long-term and short-term dependencies in the fault signal, by increasing the depth of the GRU (Gated Recurrent Unit) layer in this embodiment, the long-term dependence modeling ability in the time series can be optimized, significantly reducing misjudgments caused by insufficient capture of dependencies. In addition, considering the challenge of limited data volume in the fault diagnosis of rotating equipment, this embodiment uses data augmentation technology (i.e., adding noise) to improve the generalization ability of the model, thereby reducing the dependence on a large amount of labeled data and enhancing the applicability of the model under different devices and working conditions, which can not only improve the fault diagnosis accuracy of the model but also greatly enhance the robustness and adaptability in variable working conditions.

[0206] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the structure of the GRU (Gated Recurrent Unit) in the CNN-GRU (Convolutional Neural Network - Gated Recurrent Unit) of step S4 includes a reset gate, an update gate, a candidate hidden state, and a final hidden state;

[0207] The reset gate determines how much past information needs to be retained;

[0208] The update gate determines how much new information needs to be incorporated into the hidden;

[0209] The candidate hidden state is the result of processing the current input and the previous hidden state considering the influence of the reset gate;

[0210] The final hidden state is calculated through the update gate and the candidate hidden state.

[0211] Preferably, referring to Figure 5 , an embodiment of the 1D-CNN (One-Dimensional Convolutional Neural Network) structure includes an input layer, three convolutional layers, and three max-pooling layers, where each convolutional layer includes a one-dimensional convolutional function, a batch normalization layer, and a rectified linear unit function. The role of the pooling layer is to reduce the size of the model, improve the calculation speed, and at the same time improve the robustness of the extracted features. The max-pooling layer in the network is mainly used to effectively reduce the size of the network while retaining the main features, accelerate the calculation speed of the network, reduce the training time of the network, prevent overfitting during the network training process, and improve the generalization ability of the model.

[0212] The GRU (Gated Recurrent Unit) is a variant of the RNN (Recurrent Neural Network), which solves the problem of vanishing gradients or exploding gradients of traditional RNNs (Recurrent Neural Networks) when processing long sequences by introducing a gating mechanism. As Figure 6 shown, the structure of the GRU (Gated Recurrent Unit) includes four parts: a reset gate, an update gate, a candidate hidden state, and a final hidden state. The reset gate determines how much past information needs to be retained, and the update gate determines how much new information needs to be incorporated into the hidden state. The candidate hidden state is the result of processing the current input and the previous hidden state considering the influence of the reset gate. The final hidden state is calculated through the update gate and the candidate hidden state.

[0213] Preferably, the reset gate can be expressed as:

[0214] r t =σ(W r ·[h t-1 ,x t ) (29)

[0215] where σ is the sigmoid activation function; W r is the weight matrix of the reset gate; h t-1 is the hidden state at the previous moment; x t is the input at the current moment.

[0216] Preferably, the update gate can be expressed as:

[0217] z t =σ(W z ·[h t-1 ,x t ) (30)

[0218] where W z is the weight matrix of the update gate.

[0219] Preferably, the candidate hidden state can be expressed as:

[0220]

[0221] where * represents element-wise multiplication; W h is the weight matrix of the candidate hidden state.

[0222] Preferably, the final hidden state can be expressed as:

[0223]

[0224] Preferably, the GRU (Gated Recurrent Unit) can specifically adopt the following calculation process: the input x t at the current moment and the hidden state h t-1It is fed into a GRU (Gated Recurrent Unit). Using the input and the previous hidden state, the reset gate r is calculated through their respective weight matrices and the sigmoid activation function. t and the update gate z t . The previous hidden state is adjusted by the reset gate, combined with the current input, and passed through a weight matrix and the tanh activation function to obtain a candidate hidden state According to the value of the update gate, the previous hidden state and the candidate hidden state are weighted and averaged to obtain the final hidden state h at the current moment. t The final hidden state h t is used as the output at the current moment.

[0225] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the NEURALODES (Neural Ordinary Differential Equations) in step S4 is a neural network model that combines deep learning and ODEs (Ordinary Differential Equations); it simulates a continuous-time dynamic system by parameterizing the solution of an ODE (Ordinary Differential Equation), regards the hidden state of the neural network as the solution of the ordinary differential equation, and learns the derivatives of these hidden states through the neural network.

[0226] It should be noted that Neural ODEs (Neural Ordinary Differential Equations) is a new type of neural network model that combines deep learning and ODEs (Ordinary Differential Equations). It simulates a continuous-time dynamic system by parameterizing the solution of an ODE (Ordinary Differential Equation), and is particularly suitable for processing and modeling continuous-time sequence data. The hidden state of the neural network is regarded as the solution of the ODE (Ordinary Differential Equation), and the derivatives of these hidden states are learned through the neural network. In practical applications, NeuralODEs (Neural Ordinary Differential Equations) usually combines an ODE (Ordinary Differential Equation) solver with an adaptive time step to achieve efficient adaptive computing. In the fault diagnosis of rotating equipment, in order to more efficiently and accurately simulate and analyze the dynamic changes of fault signals, an ODE (Ordinary Differential Equation) solver with an adaptive time step is used to improve the robustness of the model. In regions where the signal changes rapidly, the solver automatically reduces the time step to improve accuracy; while in regions where the signal changes slowly, the time step is increased to reduce the amount of calculation.

[0227] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the steps of data processing in the rotating machinery fault model in step S4 include:

[0228] Step S 41 、perform a 1D-CNN (One-Dimensional Convolutional Neural Network) process:

[0229] Taking the time series data after normalization processing as the input signal, calculating the feature map for the input signal through one-dimensional convolution;

[0230] Perform batch normalization on each channel to adjust the mean and variance of the output;

[0231] Apply the rectified linear unit function to the output feature map of the batch normalization layer to introduce non-linearity;

[0232] Reduce the time dimension of the feature map through max pooling;

[0233] Stack three convolutional layers to sequentially extract higher-level features;

[0234] Each one-dimensional convolutional operation updates the number of channels and the sequence length of the feature map;

[0235] Convolve the sequence length to output the shape of the feature map after several convolutional layers;

[0236] Step S 42 、Perform the GRU (Gated Recurrent Unit) process:

[0237] Transpose the shape of the output feature map of the convolutional layer;

[0238] The GRU (Gated Recurrent Unit) receives the data of the above feature map shape and outputs a sequence of final hidden states;

[0239] In the GRU (Gated Recurrent Unit), a new hidden state is generated at each time step, and the final hidden state sequence is the set of the above hidden states;

[0240] Step S 43 、Perform the neural ordinary differential equation process:

[0241] The neural ordinary differential equation extracts the information of the complete sequence by selecting the hidden state at the last time step, takes the final hidden state of the gated recurrent unit as the input of the latent space, and models the relationship between the latent variable and the input time series through probability distribution;

[0242] Sample the initial value of the latent variable from the Gaussian distribution, use the initial value of the latent variable as the initial condition, and predict the value of the latent variable at future time points through the ordinary differential equation solver with adaptive time steps.

[0243] Preferably, in an embodiment of the rotating machinery fault diagnosis method of the present invention, the data processing flow of the neural network model based on the fusion of Neural ODEs (neural ordinary differential equations) and 1D-CNN-GRU (one-dimensional convolutional neural network - gated recurrent unit) is specifically as follows:

[0244] Step S 41 、Perform the 1D-CNN (one-dimensional convolutional neural network) process:

[0245] Input signal x s is the time series data after normalization, with the shape of (N, L). Where N is the feature dimension of the signal and L is the length of the signal time series.

[0246] For signal x s calculate the feature map through one-dimensional convolution:

[0247]

[0248] Among them, ω ij (k) is the weight of the convolution kernel, and the size of the convolution kernel is K; b i is the bias of the i-th convolution kernel; y i (t) is the eigenvalue of output channel i, and t is the time step.

[0249] Perform batch normalization on each channel to adjust the mean and variance of the output:

[0250]

[0251] Among them, μ i 、 are the mean and variance of channel i in the current mini-batch; ò is a small constant to prevent division by zero; γ i 、β i are learnable scaling and translation parameters.

[0252] Apply the rectified linear unit function to the output feature map of the batch normalization layer to introduce non-linearity:

[0253]

[0254] Among them, α is a small integer, usually set to 0.01.

[0255] Reduce the time dimension of the feature map through max pooling:

[0256]

[0257] Stack three layers of convolutions to extract higher-level features in turn. The standard shape of the input signal in the 1D-CNN (one-dimensional convolutional neural network) is:

[0258]

[0259] Among them, B is the batch size; C in = N is the feature dimension, corresponding to the number of channels; L in is the length of the input time series.

[0260] Each one-dimensional convolution operation updates the number of channels and the sequence length of the feature map. The number of convolutional kernels determines the number of output channels. Assume that the number of convolutional kernels in the convolutional layer is k, then:

[0261] C out = k (38)

[0262] After convolution, the sequence length is:

[0263]

[0264] where P is the padding size and S is the stride.

[0265] The output shape of the feature map after several convolutional layers (including convolution, batch normalization, rectified linear unit, and pooling) is:

[0266]

[0267] Step S 42 , perform the GRU (Gated Recurrent Unit) process:

[0268] To adapt to the input format of the GRU (Gated Recurrent Unit), the output of the convolutional layer needs to be transposed:

[0269]

[0270] The GRU (Gated Recurrent Unit) accepts data of the above shape and outputs the final hidden state h t sequence:

[0271]

[0272] where H is the number of units in the hidden layer, that is, the number of features output at each time step.

[0273] In the GRU (Gated Recurrent Unit), a new hidden state h i is generated at each time step, and the final hidden state sequence is the set of these hidden states, denoted as [h1, h2... h N .

[0274] Step S 43 , perform the neural ordinary differential equation process:

[0275] In the rotating machinery fault model, Neural ODEs (neural ordinary differential equations) extract the information extraction result of the complete sequence by selecting the hidden state h N at the last time step, and use the final hidden state h N of the GRU (Gated Recurrent Unit) as the input to the latent space. Through the probability distribution q(z t0 |xt0 ...x tN )Model the relationship between the latent variable and the input time series, expressed as:

[0276] q(z t0 |x t0 ...x tN ) = N(μ, σ 2 ) (43)

[0277] where μ and σ are calculated by h N through an additional neural network layer.

[0278] Sample the latent variable z from the Gaussian distribution t0 : z t0 ~N(μ(h N ), σ 2 (h N )) and use z t0 as the initial condition to predict the value of z at future time points through an ODE (ordinary differential equation) solver with an adaptive time step.

[0279] As a preferred embodiment of the rotating machinery fault diagnosis method of the present invention, the NeuralODEs (neural network ordinary differential equation) process in the step S 43 includes the following steps:

[0280] Step S 431 : Define the function of the ODE (ordinary differential equation) to describe the dynamics of the latent space variables using an ordinary differential equation;

[0281] Step S 432 : Perform time integration to calculate the latent space state at each time point through a numerical integration method;

[0282] Step S 433 : Pass the latent variable predicted by the ODE (ordinary differential equation) to the fully connected layer, and the fully connected layer performs a linear transformation on the latent variable through a weight matrix and a bias vector; the fully connected layer outputs a vector representing the raw scores for each class;

[0283] Step S 434 : Convert the raw scores into a probability distribution by the softmax function layer;

[0284] Step S 435 : The softmax function layer outputs the probability for each class; in fault diagnosis, select the class with the highest probability as the final diagnosis result.

[0285] Preferably, in an embodiment of the present invention, the execution steps of Neural ODEs (neural network ordinary differential equation) in the rotating machinery fault model include:

[0286] Step S 431 , Define the function of ODE (ordinary differential equation): Describe the dynamics of the latent space variable z t using the following differential equation:

[0287]

[0288] where f is a function parameterized by a neural network; θ is the network parameter.

[0289] Step S 432 , Perform time integration: Calculate the latent space states at time points t N+1 , …, t M using a numerical integration method:

[0290]

[0291] Step S 433 , Pass the latent variables predicted by the ODE (ordinary differential equation) to the fully connected layer, and the fully connected layer performs a linear transformation on the latent variables through the weight matrix W y and the bias vector b y :

[0292]

[0293] The output z′ of the fully connected layer is a vector representing the raw scores for each class:

[0294] z′ = [z′1, z′2, …, z′ C T (47)

[0295] where C is the number of classes.

[0296] Step S 434 , Convert the raw scores z′ to a probability distribution p by the Softmax (normalized exponential function) layer:

[0297]

[0298] where z i ′ is the raw score for the i-th class by the fully connected layer; p i is the predicted probability for the i-th class.

[0299] Step S 435 , The Softmax (normalized exponential function) layer outputs the probability for each class, representing the prediction confidence of the model for each fault class. In fault diagnosis, the class with the highest probability can be selected as the final diagnosis result.

[0300] ​It should be noted that in the present invention, by using the final hidden state of the GRU (Gated Recurrent Unit) as the initial condition of the Neural ODEs (Neural Ordinary Differential Equations), effective capture of dynamic features and dynamic modeling of fault signals are achieved; introducing Gaussian distribution to model latent variables and quantifying signal uncertainty can improve the robustness of the model; at the same time, multi-scale feature fusion and Softmax (Normalized Exponential Function) output are adopted, which can improve the accuracy and interpretability of fault diagnosis. Moreover, with an adaptive time-step solver, it can also flexibly handle irregularly sampled data, significantly improving the performance and practicality of the model in the fault diagnosis of rotating equipment.

[0301] As described above, in an embodiment of the rotating machinery fault diagnosis method of the present invention, by combining rotor dynamics to construct a complex-condition rotor vibration equation considering thermal-mechanical coupling and fluid-structure coupling and nonlinear modal analysis, the dynamic behavior of the complex coupling system can be described more comprehensively and accurately. The CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) with adaptive noise is used for signal denoising processing, and the retained IMF (Intrinsic Mode Function) components are selected based on information criteria and sparsity optimization. Compared with traditional methods, it can more effectively reduce the mode mixing phenomenon, improve the accuracy and stability of signal decomposition, and thus better extract fault features. Finally, the extracted fault features are given to a neural network model based on the fusion of Neural ODEs (Neural Ordinary Differential Equations) and 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) for training and optimization. The Neural ODEs can simulate continuous-time dynamic systems, capture the dynamic evolution law of fault signals, reduce the model complexity, and at the same time enhance the physical interpretability of fault evolution. The GRU (Gated Recurrent Unit) can capture the long-term and short-term dependencies of time series through the gating mechanism. Combined with the local spatial features extracted by the 1D-CNN (One-Dimensional Convolutional Neural Network), it can extract fault features at multiple scales and enhance the adaptability to complex conditions, thereby improving the diagnostic accuracy.

[0302] To verify the effectiveness of the present invention, it is tested and verified in a specific application embodiment. The fault diagnosis analysis of a gearbox is selected as the specific application embodiment of the present invention. Based on the vibration equation of the rotating machinery, the vibration equation of the gearbox is constructed, and nonlinear modal analysis is performed on the vibration equation of the gearbox to accurately reflect the dynamic characteristics of the system, and further identify the intrinsic mode function components related to the gearbox fault. A time-domain example when a fault occurs is Figure 10 as shown.

[0303] In this embodiment, the gear failure is taken as an example, and the real data of the gear is collected. The time span of the real data set is 3 years, among which the number of normal samples, gear wear abnormal samples and gear tooth breakage abnormal samples are 4820, 1193 and 98 respectively. The specific sample data features include vibration speed, kurtosis index and minimum value. Here, a small segment (0-5000) of a time domain waveform sample data is used as a display. The above-mentioned similar time domain waveform sample data contains more than 100,000 parameters. The sample data is displayed as follows: Figure 11 shown.

[0304] All sample data are processed by CEEMDAN-LASSO-AIC (Completely Adaptive Noise Ensemble Empirical Mode Decomposition-Minimum Absolute Value Shrinkage and Selection Operator-Akaike Information Criterion) to extract IMF (Intrinsic Mode) components and denoise, and reconstruct the signal. Figure 12 The figure shows the reconstructed signal based on the sample data already shown.

[0305] All reconstructed signals are divided into training set, validation set and test set in a ratio of 8:1:1. The data is input into the model for training, and the performance of the model in different categories is shown in the performance indicator table. The gear state classification performance evaluation results are as follows: Figure 13 As shown, Figure 13 The Precision, Recall, F1-Measure, and Support for each category are listed.

[0306] After evaluating the different gear faults, relevant measures can be taken to speed up the work progress. For the above fault time domain diagram, the normal time domain diagram after taking measures is as follows Figure 14 shown.

[0307] In order to further visualize the classification performance of the model, a confusion matrix is used to show the relationship between the true label and the predicted label. Each row of the confusion matrix represents the true label, and each column represents the predicted label. Through the confusion matrix, we can intuitively see which categories the model performs well on and which categories may be misclassified. The specific confusion matrix for gear state classification is as follows: Figure 7 shown.

[0308] Finally, the model accuracy and loss charts are used to show the performance of the model during the training process. Figure 8 The accuracy of the training data and validation data and the change of the loss with the number of training epochs are shown in the figure, which can be used to evaluate whether the model is overfitting or underfitting, and adjust the model parameters to optimize the performance. Compared with other neural networks, the performance is compared from three dimensions. Figure 9As shown. From the results, it can be seen that CNN-LSTM (Convolutional Neural Network - Long Short-Term Memory Network) and CNN-GRU (Convolutional Neural Network - Gated Recurrent Unit) integrate the advantages of the high speed of convolutional neural networks and the high accuracy of recurrent neural networks, reducing the model training time while improving the model's recognition rate. Compared with 1D-CNN-LSTM (One-Dimensional Convolutional Neural Network - Long Short-Term Memory Network), 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) has a shorter training time, higher model accuracy, and lower loss.

[0309] According to the data distribution characteristics of different fault types, adjust the learning rate decay strategy. Also, according to the real-time requirements of the fault diagnosis task, optimize the structural parameters of the model. In fault diagnosis scenarios that require rapid response, appropriately reduce the number of neural network layers and the number of neurons in each layer to reduce the computational complexity of the model and improve the diagnosis speed; while in occasions with extremely high requirements for diagnosis accuracy, increase the network depth and width, introduce more feature extraction layers and classification layers, so that the model can more finely depict fault characteristics, thereby improving the diagnosis accuracy. Through the above comprehensive optimization measures, the neural network model of the present invention can also exhibit more excellent performance under different fault types and diagnosis requirements.

[0310] The present invention also provides a rotating machinery fault diagnosis system. The rotating machinery fault diagnosis system adopts the above-mentioned rotating machinery fault diagnosis method. The rotating machinery fault diagnosis system includes:

[0311] An equation construction module for constructing a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions;

[0312] A feature data extraction module for obtaining real-time information of the rotating machinery to be diagnosed, and performing modal analysis based on the real-time information of the rotating machinery to be diagnosed based on the rotor vibration equation to determine the sensitive frequency band and key features, and forming multi-dimensional feature data;

[0313] A signal reconstruction module for denoising the multi-dimensional feature data and performing signal reconstruction to obtain a reconstructed signal;

[0314] A diagnosis module for inputting the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model adopts the fusion of Neural ODEs (Neural Ordinary Differential Equations) and CNN-GRU (Convolutional Neural Network - Gated Recurrent Unit).

[0315] The present invention also provides an electronic device, including: a processor and a memory. The memory stores a program or instruction that can run on the processor, and the program or instruction is executed by the processor to implement the above-mentioned rotating machinery fault diagnosis method.

[0316] The present invention also provides a readable storage medium, on which a program or instructions are stored, and when the program or instructions are executed by a processor, the above-mentioned rotating machinery fault diagnosis method is implemented.

[0317] It should be noted that Neural ODEs (Neural Ordinary Differential Equations) can simulate continuous-time dynamic systems, are suitable for processing and modeling continuous-time series data, can capture the dynamic evolution law of fault signals, reduce the model complexity, and at the same time enhance the physical interpretability of fault evolution, and are particularly suitable for fault analysis of complex mechanical systems. GRU (Gated Recurrent Unit) captures the long-term and short-term dependencies of time series through a gating mechanism and has advantages in modeling non-linear dynamic behaviors. Combined with 1D-CNN (One-Dimensional Convolutional Neural Network) to extract local spatial features, it can extract fault features at multiple scales, enhance the adaptability to complex working conditions, and thus improve the diagnosis accuracy.

[0318] In summary, the rotating machinery fault diagnosis method and related system of the present invention that integrates Neural ODEs (Neural Ordinary Differential Equations) and CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) realizes rotating machinery fault diagnosis by integrating Neural ODEs (Neural Ordinary Differential Equations) and 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit). First, a complex working condition rotor vibration equation considering thermal-mechanical coupling and fluid-structure coupling is constructed in combination with rotor dynamics, which can more comprehensively and accurately describe the dynamic behavior of the complex coupling system. Then, the extracted fault features are provided to a rotating machinery equipment diagnosis model constructed by a neural network model based on the integration of Neural ODEs (Neural Ordinary Differential Equations) and 1D-CNN-GRU (One-Dimensional Convolutional Neural Network - Gated Recurrent Unit) for training and optimization. Neural ODEs (Neural Ordinary Differential Equations) are used to simulate continuous-time dynamic systems, capture the dynamic evolution law of fault signals, improve the physical interpretability and computational efficiency of the model. GRU (Gated Recurrent Unit) is used to process the long-term and short-term dependencies in time series through a gating mechanism, combined with 1D-CNN (One-Dimensional Convolutional Neural Network) to extract multi-scale fault features, greatly enhancing the adaptability and diagnosis accuracy of the model under complex working conditions, being able to overcome the deficiencies of traditional methods in signal processing, feature extraction, fault modeling, data fusion, etc., accurately simulate and predict the continuous dynamic changes of the system, improve the diagnosis accuracy while enhancing the real-time performance and robustness of the model, so as to quickly and accurately achieve early detection and classification of rotating machinery faults, and ensure the safety and reliability of industrial equipment operation.

[0319] Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that these are only examples, and the protection scope of the present invention is defined by the appended claims. Without departing from the principles and essence of the present invention, those skilled in the art can make various changes or modifications to these embodiments, but these changes and modifications all fall within the protection scope of the present invention.

Claims

1. A method for diagnosing faults in rotating machinery, characterized in that, The rotating machinery fault diagnosis method includes the following steps: S1. Construct a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions; S2. Obtain the real-time information of the rotating machinery to be diagnosed, and perform modal analysis based on the real-time information of the rotating machinery to be diagnosed based on the rotor vibration equation to determine the sensitive frequency band and key features, and form multi-dimensional feature data; S3. Denoise the multi-dimensional feature data and perform signal reconstruction to obtain a reconstructed signal; S4. Input the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model uses the fusion of neural network ordinary differential equations and convolutional neural network-gated recurrent units.

2. The rotating machinery fault diagnosis method according to claim 1, wherein, The rotor vibration equation includes time-varying parameters, non-linear force terms, thermal-mechanical coupling force terms, and fluid-structure coupling force terms; The non-linear force term is used to describe the non-linear behavior of the rotor system; The thermal-mechanical coupling force term is used to describe the influence of thermal deformation caused by temperature on vibration; The fluid-structure coupling force term is used to describe the influence of fluid on rotor vibration.

3. The rotating machinery fault diagnosis method according to claim 2, wherein, The expression of the rotor vibration equation is: where, M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; is the non-linear force term; is the thermal-mechanical coupling force term; is the fluid-structure coupling force term; F(t) is the external excitation force.

4. The rotating machinery fault diagnosis method according to claim 3, wherein The modal analysis in step S2 includes linear modal analysis, and the linear modal analysis method includes the following steps: S 21 、Linearize the thermal-mechanical coupling force term and the fluid-structure coupling force term through equivalent stiffness, damping, and mass; Among them, the thermo-mechanical coupling force term has the following expression: Fluid-structure coupling force term The expression is as follows: S 22 2. Substitute the thermal-mechanical coupling force term and the fluid-structure coupling force term into the vibration equation to form the vibration equation after linearization: Among them, M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force; M fluid is the added fluid mass; C th (t), C fluid (t) are the thermo-mechanical coupling added damping and the fluid-structure coupling added damping; K th (t), K fluid (t) are the thermo-mechanical coupling added stiffness and the fluid-structure coupling added stiffness; S 23 、Set the external excitation force F(t) = 0, solve the vibration equation to obtain the eigenvalues and eigenvectors of the system: The obtained eigenvalues are: λ = -ζω n ±jω d where λ is the eigenvalue; ω n is the natural frequency of the system; ζ is the damping ratio; is the damped vibration frequency; The obtained eigenvector Φ is: (K eq -ω 2 M eq )Φ = 0 Among them, K eq = K + K th + K fluid , M eq = M + M fluid .

5. The rotating machinery fault diagnosis method according to claim 3, characterized in that, The modal analysis in step S2 includes non-linear modal analysis, and the non-linear modal analysis method includes the following steps: S 21 ’, extract the initial mode and ignore the non - linear terms f nl , f th , f fiuld , only consider the modal analysis of the linear equation to form the following formula: Where, M(t) is the time-varying mass matrix; C(t) is the time-varying damping matrix; K(t) is the time-varying stiffness matrix; F(t) is the external excitation force; The modal solution form is as follows: where q n (t) is the modal generalized coordinate; S 22 ', introducing the nonlinear modal equation, and projecting the nonlinear force term of the system into the modal space. The nonlinear force term is represented by a function of the modal variable q n (t): where, P n is a functional form obtained by expanding a non-linear force term; Substitute the non - linear force term into the original equation and project it onto the modal coordinate q n , and the equation is obtained: Among them, α nm , β nml are non-linear coupling coefficients, calculated by modal projection; ζ n is modal damping; F n (t) is the modal generalized force; Take the thermal-mechanical coupling force term and the fluid-structure coupling force term as non-linear correction terms, and expand the thermal-mechanical coupling force term and the fluid-structure coupling force term into the functional form of modal variables; Thermal-mechanical coupling force term The functional form of which is: where α T , γ T are scale factors for thermally coupled stiffness and damping; ΔT is the temperature change; Fluid-structure coupling force term The functional form is as follows: Where, μ, ν, κ are the scaling coefficients of the fluid added mass, damping and stiffness, and Q is the flow field velocity or pressure field; S 23 ’, solving the nonlinear modal eigenvalue by numerical iteration method. Assume the form of the modal solution is: q n q(t) = A n cos(ω n t + φ n ) Substitute into the non-linear modal equation, and use the averaging method or multi-scale method to separate the non-linear terms to obtain a non-linear frequency correction formula: ω n = ω n.0 + Δω n Among them, Δω n represents the non-linear correction term, and its specific form depends on α nm , β nml coupling coefficient.

6. The method for diagnosing faults of a rotating machine according to claim 1, wherein Step S3 uses the complete adaptive noise ensemble empirical mode decomposition method to denoise the multi-dimensional feature data, and step S3 includes the following steps: S 31 , collect the original signal, select appropriate noise amplitude and number of iterations, set the value for each iteration, generate a white noise sequence, and add the white noise to the original signal to obtain a new signal sequence; S 32 Perform empirical mode decomposition on each signal with added white noise to obtain the intrinsic mode and the residual; Each empirical mode decomposition generates multiple intrinsic mode components, that is, a set of intrinsic modes; Repeat the above empirical mode decomposition process multiple times, and each time a new set of intrinsic modes is generated; S 33 , number each eigenmode, and average the eigenmodes with the same number in multiple iterations to obtain the integrated eigenmode; Select the required intrinsic modes for retention, and superimpose the retained intrinsic modes to obtain a denoised reconstructed signal.

7. The rotating machinery fault diagnosis method according to claim 6, wherein Step S3 further uses the method of regression based on the Akaike information criterion and the least absolute shrinkage and selection operator to denoise the multi-dimensional feature data, including the following steps: S 34 , perform least absolute shrinkage and selection operator regression calculation: Take all the averaged intrinsic mode components as input features, take the original signal as the target variable, and establish the relationship between the signal and the intrinsic mode components through the least absolute shrinkage and selection operator regression; According to the length of the original signal in the time domain and the number of averaged intrinsic mode components, form the dimension of the feature matrix, and construct the feature matrix; Take the target signal as the response variable; Use the standard least absolute shrinkage and selection operator regression algorithm to estimate the regression coefficients by optimizing the loss function; Calculate the regression coefficients, and select the intrinsic mode components with non-zero regression coefficients as the finally retained intrinsic mode components; S 35 , perform Akaike information criterion screening for denoising: According to the residual obtained from the optimized intrinsic mode function obtained by least absolute shrinkage and selection operator regression, the optimized intrinsic mode is further screened using the Akaike information criterion; S 36 Based on the results of denoising screened by the least absolute shrinkage and selection operator and the Akaike information criterion, the intrinsic mode components of the regression coefficients are retained. For the retained intrinsic mode components after screening, the corresponding intrinsic mode components in multiple iterations are averaged and weighted to obtain the reconstructed signal.

8. The rotating machinery fault diagnosis method according to claim 7, wherein Before inputting the reconstructed signal into the pre-trained rotating machinery fault model in step S4, perform standardized data preprocessing on the reconstructed signal; The standardized data preprocessing analyzes whether the reconstructed time series data approximately conforms to a normal distribution; if it does, convert each component of the signal into a form with a mean of 0 and a standard deviation of 1 to eliminate the dimensional and amplitude differences of different components; if the signal deviates from the normal distribution and shows a right-skewed distribution, use logarithmic transformation; if the signal shows a left-skewed distribution, use Box-Cox transformation for processing.

9. The rotating machinery fault diagnosis method according to claim 8, wherein The standardized data preprocessing steps in step S4 include: Calculate the mean of the reconstructed signal; calculate the standard deviation of the reconstructed signal; perform standardized processing on each data point of the reconstructed signal; obtain the preprocessed data of the standardized reconstructed signal.

10. The rotating machinery fault diagnosis method according to claim 1, wherein In the convolutional neural network-gated recurrent unit of step S4, the convolutional neural network uses a one-dimensional convolutional neural network; The one-dimensional convolutional neural network structure includes an input layer, three convolutional layers, and three max-pooling layers, where each convolutional layer includes a one-dimensional convolutional function, a batch normalization layer, and a rectified linear unit function.

11. The rotating machinery fault diagnosis method according to claim 10, characterized in that, In the convolutional neural network-gated recurrent unit of step S4, the structure of the gated recurrent unit includes a reset gate, an update gate, a candidate hidden state, and a final hidden state; The reset gate determines how much past information needs to be retained; The update gate determines how much new information needs to be incorporated into the hidden state; The candidate hidden state is the result of processing the current input and the previous hidden state considering the influence of the reset gate; The final hidden state is calculated through the update gate and the candidate hidden state.

12. The rotating machinery fault diagnosis method according to claim 11, wherein, The neural ordinary differential equation in step S4 is a neural network model that combines deep learning and ordinary differential equations; it simulates a continuous-time dynamic system by parameterizing the solution of the ordinary differential equation, treats the hidden state of the neural network as the solution of the ordinary differential equation, and learns the derivatives of these hidden states through the neural network.

13. The rotating machinery fault diagnosis method according to claim 12, wherein The steps for the rotating machinery fault model to process data in step S4 include: S 41 , perform a one-dimensional convolutional neural network process: Take the time series data after standardized processing as the input signal, and calculate the feature map for the input signal through one-dimensional convolution; Perform batch normalization on each channel to adjust the mean and variance of the output; Apply a rectified linear unit function to the output feature map of the batch normalization layer to introduce non-linearity; Reduce the time dimension of the feature map through max-pooling; Stack three convolutional layers to sequentially extract higher-level features; Each one-dimensional convolutional operation updates the number of channels and the sequence length of the feature map; Convolve the sequence length and output the shape of the feature map after several convolutional layers; S 42 , perform the gated recurrent unit process: Transpose the output shape of the convolutional layer feature map; The gated recurrent unit receives the data of the above feature map shape and outputs a sequence of the final hidden state; In the gated recurrent unit, a new hidden state is generated at each time step, and the final hidden state sequence is the set of the above hidden states; S 43 , perform the neural network ordinary differential equation process: The neural ordinary differential equation represents the information extraction result of the complete sequence by selecting the hidden state at the last time step, uses the final hidden state of the gated recurrent unit as the input to the latent space, and models the relationship between the latent variable and the input time series through probability distribution; Samples the initial value of the latent variable from the Gaussian distribution, uses the initial value of the latent variable as the initial condition, and predicts the value of the latent variable at future time points through an ordinary differential equation solver with an adaptive time step.

14. The rotating machinery fault diagnosis method according to claim 13, wherein The said step S 43 The neural network ordinary differential equation process in it includes the following steps: S 431 , define a function of ordinary differential equations to describe the dynamics of latent space variables using ordinary differential equations; S 432 , perform time integration and calculate the potential space state at each time point through numerical integration methods; S 433 , passing the latent variables predicted by the ordinary differential equation to a fully connected layer, which linearly transforms the latent variables through a weight matrix and a bias vector; the fully connected layer outputs a vector representing the raw scores for each class; S 434 , the normalization exponential function layer converts the original scores into a probability distribution; S 435 The softmax function layer outputs the probability of each category; in fault diagnosis, the category with the highest probability is selected as the final diagnosis result.

15. A rotating machinery fault diagnosis system, characterized in that The rotating machinery fault diagnosis system adopts the rotating machinery fault diagnosis method according to any one of claims 1-14, and the rotating machinery fault diagnosis system includes: An equation construction module for constructing a rotor vibration equation according to the vibration behavior of the rotor system under operating conditions; A feature data extraction module for obtaining real-time information of the rotating machinery to be diagnosed, and performing modal analysis based on the real-time information of the rotating machinery to be diagnosed based on the rotor vibration equation to determine the sensitive frequency band and key features, and forming multi-dimensional feature data; A signal reconstruction module for denoising the multi-dimensional feature data and performing signal reconstruction to obtain a reconstructed signal; A diagnosis module for inputting the reconstructed signal into a pre-trained rotating machinery fault model to obtain a fault diagnosis result; the rotating machinery fault model adopts the fusion of a neural ordinary differential equation and a convolutional neural network-gated recurrent unit.

16. An electronic device, characterized in that, Including: A processor and a memory, the memory stores programs or instructions that can run on the processor, and the programs or instructions are executed by the processor to implement the rotating machinery fault diagnosis method according to any one of claims 1-14.

17. A readable storage medium, characterized in that, The program or instruction is stored on the readable storage medium, and when the program or instruction is executed by the processor, the rotating machinery fault diagnosis method according to any one of claims 1-14 is implemented.

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