A bearing residual service life prediction method and system based on a digital twin model

Abstract

The application discloses a bearing residual service life prediction method and system based on a digital twin model, and comprises the following steps: constructing a five-degree-of-freedom bearing digital twin model; updating and correcting the defect parameters in the five-degree-of-freedom bearing digital twin model by using the measured bearing vibration signals, and generating a full-life-cycle defect size evolution curve; constructing and training a residual neural network, establishing a nonlinear mapping relationship between the real bearing vibration signal features and the defect size of the five-degree-of-freedom bearing digital twin model through the full-life-cycle defect size evolution curve; obtaining the topological structure of the defect information based on the nonlinear mapping relationship, and constructing a graph convolution distillation network comprising a teacher model and a student model based on the topological structure; collecting new bearing vibration signals, and predicting the residual service life of the bearing through the graph convolution distillation network. The application significantly improves the accuracy and robustness of the bearing residual service life prediction result.

Description

Technical Field

[0001] This invention belongs to the field of bearing remaining service prediction technology, specifically relating to a method and system for predicting bearing remaining service based on a digital twin model. Background Technology

[0002] Modern industrial machinery typically withstands high loads and complex operating conditions. Bearings, as a crucial component of these machines, play a vital role in supporting and transmitting loads, significantly impacting equipment performance and reliability. Therefore, bearings are widely used in various industrial sectors, including machinery manufacturing, aerospace, energy generation and transmission, and rail transportation. Accurately assessing bearing health and predicting their remaining life is essential for predictive maintenance and minimizing equipment failure risks to maximize reliability. Thus, predicting the remaining life of bearings is of significant research importance.

[0003] Existing methods for predicting the remaining service life of bearings based on digital twins include simplified models that only simulate a single displacement response, ignoring the combined effects of internal and external components. This reduces the authenticity of the expression of complex degradation information inside the bearing. Furthermore, neglecting the interaction between geometric continuity and physical consistency makes it difficult to obtain high-fidelity data, limiting the physical interpretability of generating defect size evolution curves throughout the entire life cycle. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a novel digital twin model construction process based on the physical updating and correction of bearing defects to predict remaining service life, which significantly improves the accuracy and robustness of bearing remaining service life prediction results.

[0005] To achieve the above objectives, the present invention provides the following solution: A method for predicting the remaining service life of bearings based on a digital twin model includes: Based on Hertzian contact theory and Newton's second law, a five-degree-of-freedom digital twin model of a bearing is constructed to simulate the composite motion of various components inside the bearing and the excitation of defects. A dual-feature real-time iteration and geometric model calibration method is adopted to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model using measured bearing vibration signals, thereby generating a full-life-cycle defect size evolution curve. A residual neural network is constructed and trained, and a nonlinear mapping relationship is established between the characteristics of the real bearing vibration signal and the defect size of the five-degree-of-freedom bearing digital twin model through the full life cycle defect size evolution curve. The topology for obtaining defect information is based on the nonlinear mapping relationship, and a graph convolutional distillation network containing teacher and student models is constructed based on the topology. New bearing vibration signals are collected and, through the graph convolutional distillation network, the remaining service life of the bearing is predicted.

[0006] Preferably, the method for constructing the five-degree-of-freedom bearing digital twin model includes: Establish dynamic differential equations that include two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling element; When the rolling element passes through the local defect area of ​​the bearing, the instantaneous displacement change is calculated in segments based on the contact position between the rolling element and the edge of the defect and the depth of the defect, and a time-varying displacement excitation function is constructed. The time-varying displacement excitation function is introduced into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during the defect evolution process, thus completing the construction of the five-degree-of-freedom bearing digital twin model.

[0007] Preferably, the method for updating and correcting the defect parameters in the five-degree-of-freedom bearing digital twin model includes: By using measured and simulated bearing vibration signals, a weighted objective function including peak error and root mean square error is constructed. The peak density and signal-to-noise ratio of the signal are introduced as adaptive weight adjustment factors. The variable step size rule iterative search is used to make the statistical characteristics of the simulated bearing vibration signal approximate the optimal defect size parameters of the measured bearing vibration signal, and the data-driven optimal defect size estimate is obtained. Based on the healthy stage, transition stage and accelerated degradation stage of the bearing degradation process, physical prior models of Gaussian distribution, linear or step function and exponential function are established respectively. The data-driven optimal defect size estimate is weighted and fused with the physical prior model through Bayesian update process to obtain the corrected defect size. Based on the double-pulse phenomenon generated when the rolling element passes through the defect in the measured bearing vibration signal, the defect center angle solution equation is established in combination with the bearing geometric parameters. The defect width is calculated and the corrected defect size is geometrically calibrated to obtain the defect size evolution curve throughout the entire life cycle.

[0008] Preferably, the method for establishing the nonlinear mapping relationship includes: The root mean square value of the measured bearing vibration signal is extracted as the network input, and the defect size evolution curve throughout the entire life cycle is used as the label data. Based on the network input and the label data, a fully connected neural network with residual connections is constructed, and the fully connected neural network is trained to learn the nonlinear mapping relationship from the statistical characteristics of vibration signals to the size of physical defects.

[0009] Preferably, the method for constructing the graph convolutional distillation network includes: Sliding window sampling and linear transformation are performed on the defect size feature data. The similarity matrix between features is calculated and an initial dynamic adjacency matrix that integrates time dependence and spatial weight is generated through a gating mechanism. A signal similarity graph and a defect topology graph are constructed. A mutation reconnection strategy is introduced to enhance the connection strength of defect mutation points and their neighborhoods. Combined with the initial dynamic adjacency matrix, the final dynamic adjacency matrix is ​​generated. The teacher model extracts the spatiotemporal features of defect evolution using the final dynamic adjacency matrix and a multi-layer graph convolutional network. The student model learns the feature extraction capabilities of the teacher model under the constraint of the total loss function through a lightweight structural design and the introduction of a knowledge distillation strategy, thus completing the construction of the graph convolutional distillation network.

[0010] Preferably, the total loss function is composed of a weighted sum of prediction error loss, structural consistency loss, adjacency matrix sparsity loss, and local structure loss, which ultimately guides the student model training and outputs the prediction result of the remaining service life of the bearing.

[0011] The present invention also provides a bearing remaining service life prediction system based on a digital twin model, for implementing the method, comprising: The twin model construction module is used to construct a five-degree-of-freedom digital twin model of a bearing based on Hertzian contact theory and Newton's second law to simulate the composite motion of various components inside the bearing and the excitation of defects. The evolution curve generation module is used to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model by using the measured bearing vibration signal with the dual-feature real-time iteration and geometric model calibration method, and generate the full life cycle defect size evolution curve. The nonlinear mapping module is used to construct and train a residual neural network to establish a nonlinear mapping relationship between the characteristics of the real bearing vibration signal and the defect size of the five-degree-of-freedom bearing digital twin model through the full life cycle defect size evolution curve. A network model construction module is used to obtain the topology of defect information based on the nonlinear mapping relationship, and to construct a graph convolutional distillation network containing teacher and student models based on the topology. The life prediction module is used to collect new bearing vibration signals and predict the remaining service life of the bearing through the graph convolutional distillation network.

[0012] Preferably, the twin model construction module includes: Differential equation building unit, used to establish dynamic differential equations containing two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling body; The excitation function construction unit is used to construct a time-varying displacement excitation function by calculating the instantaneous displacement change in segments based on the contact position between the rolling element and the edge of the defect and the depth of the defect when the rolling element passes through the local defect area of ​​the bearing. The digital twin model construction unit is used to introduce the time-varying displacement excitation function into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during the defect evolution process, and complete the construction of the five-degree-of-freedom bearing digital twin model.

[0013] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention constructs a five-degree-of-freedom bearing digital twin model to finely simulate the coupled motion of the bearing's inner ring, outer ring, and rolling elements. This enables the model to realistically reproduce the independent motion trajectories and composite degradation information of multiple components within the bearing, significantly improving the fidelity of the digital twin's mapping to the physical entity. The introduction of a dual-feature real-time iteration and geometric model calibration method ensures that the defect evolution curve maintains physical geometric continuity and consistency during the update process, enhancing the model's ability to track the actual defect expansion process throughout the entire lifespan and effectively avoiding the limitations of traditional interactive methods that lack physical interpretability in parameter updates. By leveraging the real-time mapping relationship established by the residual neural network and the graph convolutional distillation network, high-fidelity physical degradation prior knowledge is efficiently integrated into the lightweight student model. This significantly reduces computational complexity while addressing the problem of insufficient degradation data, meeting the dual requirements of real-time monitoring and deployment efficiency in industrial scenarios. Finally, by utilizing the deep fusion of physical mechanisms and data-driven approaches, the problem of unrealistic faults in a single model is solved, significantly improving the accuracy and robustness of the bearing's remaining service life prediction results. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart of the method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the five-degree-of-freedom dynamic twin model of the bearing provided by the present invention; Figure 3 This is a schematic diagram of the defect expansion process provided by the present invention; wherein, (a) represents the defect generation stage and (b) represents the defect expansion stage; Figure 4 This is a schematic diagram of the physical phenomenon of double pulse provided by the present invention; wherein, (a) represents the vibration curve of the bearing part, and (b) represents the motion process of the rolling element in the defect; Figure 5 This is a schematic diagram of the defective adjacency topology strategy provided by the present invention; Figure 6 This is a schematic diagram of the frequency domain envelope spectrum of the simulation signal of the five-degree-of-freedom dynamic twin model of the bearing, which is provided by the present invention; Figure 7 The XJTU-SY bearing dataset in this embodiment of the invention shows partial bearing defect curve results; where (a) represents the defect curve result of bearing 1-1, and (b) represents the defect curve result of bearing 1-3. Figure 8 The XJTU-SY bearing dataset in this embodiment of the invention shows the results of calibration of some bearing defect curves; where (a) represents the result of calibration of bearing 1-1 defect curve, and (b) represents the result of calibration of bearing 1-3 defect curve. Figure 9 These are partial defect size curve prediction results of the XJTU-SY bearing dataset in this embodiment of the invention; wherein, (a) represents the defect size curve prediction result of bearing 1-2, (b) represents the defect size curve prediction result of bearing 1-5, (c) represents the defect size curve prediction result of bearing 2-2, (d) represents the defect size curve prediction result of bearing 2-4, (e) represents the defect size curve prediction result of bearing 3-3, and (f) represents the defect size curve prediction result of bearing 3-5. Figure 10 This is a comparison of the defect size prediction effect of the present invention with the defect size curve prediction effect of other methods; wherein, (a) represents the comparison of the defect size prediction effect of the present invention with other methods in bearing 1-1, and (b) represents the comparison of the defect size prediction effect of the present invention with other methods in bearing 1-3. Figure 11 This is a comparison chart of the RUL prediction performance of the XJTU-SY dataset with other methods in this embodiment of the invention; Figure 12 These are RUL visualization diagrams of each model in the ablation experiment in the embodiments of the present invention; (a) represents the RUL visualization diagram of the ablation experiment of bearings 1-3, (b) represents the RUL visualization diagram of the ablation experiment of bearings 1-4, (c) represents the RUL visualization diagram of the ablation experiment of bearings 2-3, (d) represents the RUL visualization diagram of the ablation experiment of bearings 2-5, (e) represents the RUL visualization diagram of the ablation experiment of bearings 3-3, and (f) represents the RUL visualization diagram of the ablation experiment of bearings 3-4. Figure 13This is a visualization diagram of the adjacency matrix performance of each model in the ablation experiment of the present invention; (a) represents the adjacency matrix diagram of the defective adjacency topology of bearings 1-5, (b) represents the adjacency matrix diagram of the defect-free adjacency topology of bearings 1-5, (c) represents the adjacency matrix diagram of the defective adjacency topology of bearings 2-4, and (d) represents the adjacency matrix diagram of the defect-free adjacency topology of bearings 2-4. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Example 1: like Figure 1 As shown, a method for predicting the remaining service life of bearings based on a digital twin model includes: S1: Based on Hertzian contact theory and Newton's second law, a five-degree-of-freedom digital twin model of a bearing is constructed to simulate the combined motion of various components inside the bearing and defect excitation. Specifically, the digital twin model generates simulation data reflecting the dynamic behavior of the bearing throughout its entire life cycle by simulating the coupled motion of the inner ring, outer ring, and rolling elements. Figure 2 As shown. A further implementation method for constructing a five-degree-of-freedom bearing digital twin model includes: A dynamic differential equation is established, comprising two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling element. When the rolling element passes through a local defect region of the bearing, the instantaneous displacement change is calculated piecewise based on the contact position between the rolling element and the defect edge and the defect depth, thus constructing a time-varying displacement excitation function. This time-varying displacement excitation function is then incorporated into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during defect evolution, completing the construction of a five-degree-of-freedom bearing digital twin model. Figure 3 As shown.

[0019] Specifically, based on the derivation of Newton's second law, let the general differential equation be expressed as follows: ; in, It is a generalized displacement vector; This represents the mass matrix, which includes the inner ring, outer ring, and resonator. and Let these represent the damping matrix and stiffness matrix of the system, respectively. This represents the nonlinear excitation load vector generated by the Hertzian contact.

[0020] The equation of motion for the inner circle is expressed as follows: ; in, It's the quality of the inner ring. Indicates the damping coefficient. It's stiffness. This represents a nonlinear contact force, where g represents gravitational acceleration. This represents the horizontal displacement of the bearing's inner ring. This represents the vertical displacement of the bearing's inner ring.

[0021] The equation of motion for the outer ring is expressed as follows: ; in, It's the quality of the outer ring. Indicates the damping coefficient. It's stiffness. Indicates rolling element damping, This represents the horizontal displacement of the bearing's outer ring. This represents the vertical displacement of the bearing's outer ring. This represents the vertical displacement of the rolling element.

[0022] The equation of motion for a rolling element is expressed as follows: ; in, It is the mass of the rolling element.

[0023] The expression for nonlinear contact force is: ; ; in, It is the first The overall deflection of the rolling element It is the contact stiffness between the rolling element and the raceway. It is the number of rolling elements. It is the first The angular position of each rolling element.

[0024] The expression is: ; ; ; ; in, Indicates time, Indicates angular velocity, Represents the outer diameter. Indicates the diameter of the pitch circle. Indicates the angular velocity of the inner ring rotation. Indicates the diameter of the rolling element. Indicates the bearing contact angle. This indicates the rotational speed of the shaft.

[0025] The expression is: ; in, and This indicates the vibration displacement of the bearing inner ring in the horizontal and vertical directions. Indicates the radial clearance of the bearing. This represents a displacement excitation that varies over time.

[0026] The expression is: ; L represents the length of the bearing defect.

[0027] The maximum displacement excitation is always less than the defect depth, and the displacement excitation is time-varying (time-varying displacement excitation function). The expression is: ; This represents displacement excitation.

[0028] As the defect size increases, the maximum displacement excitation gradually increases until it equals the defect depth. Time-varying displacement excitation The expression is: ; in, Indicates the starting angle position of the local defect. Indicates the angle of the local defect range. This indicates the angle at which the rolling element contacts the bottom edge of the local defect.

[0029] S2: A dual-feature real-time iteration and geometric model calibration method is adopted to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model using measured bearing vibration signals, generating a full-life-cycle defect size evolution curve; a further implementation method for updating and correcting the defect parameters in the five-degree-of-freedom bearing digital twin model includes: Using measured and simulated bearing vibration signals, a weighted objective function incorporating peak error and root mean square error is constructed. The peak density and signal-to-noise ratio of the signals are introduced as adaptive weight adjustment factors. A variable step-size rule iterative search is employed to approximate the optimal defect size parameters of the measured bearing vibration signal with the statistical characteristics of the simulated bearing vibration signal, thus obtaining a data-driven optimal defect size estimate. Specifically, let the measured signal be... Based on the current defects The simulation output is To overcome local noise interference, the signal is randomly divided into... There are three non-uniform segments. The objective function is defined as follows: ; ; ; in, Characterizing differences in impact features The mean values ​​of global RMS and local RMS were used to enhance the sensitivity to local energy fluctuations and characterize energy differences.

[0030] To adapt to signal characteristics under different operating conditions, the weighting coefficients... and Dynamically generated based on the statistical characteristics of the measured signal. Introducing the signal's peak density. With signal-to-noise ratio As a regulating factor, the expression is as follows: ; ; in, Represents the basic weight. Representing a small random perturbation, this adaptive adjustment amount avoids getting trapped in local optima and satisfies... . This represents the critical value used to determine whether a signal characteristic belongs to a state of peak density.

[0031] Subsequently, in order to improve the convergence speed and prevent oscillations, defects The update follows an improved variable step size rule. In the first... In each iteration, the step size is adjusted based on the error gradient direction and the improvement rate. The update expression is as follows: ; Defects obtained in the above stages It only represents the optimal solution for fitting the data at the current moment, and may be subject to physically unreasonable abrupt changes due to transient noise.

[0032] Based on the healthy stage, transition stage, and accelerated degradation stage of the bearing degradation process, physical prior models with Gaussian distribution, linear or step function, and exponential function are established respectively. The data-driven optimal defect size estimate is weighted and fused with the physical prior model through a Bayesian update process to obtain the corrected defect size. Based on the double pulse phenomenon generated when the rolling element passes through the defect in the measured bearing vibration signal, the defect center angle solution equation is established in combination with the bearing geometric parameters. The defect width is calculated and the corrected defect size is geometrically calibrated to obtain the defect size evolution curve throughout the entire life cycle.

[0033] Specifically, the second stage introduces a multi-stage physical model of bearing degradation as a regularization constraint. Make corrections. Based on the type of bearing signal change, establish a time-varying mechanism. Physical prior functions of evolution The bearing signal changes were divided into three stages: healthy, transitional, and accelerated degradation. Judgment and prior modeling were then performed based on these stages. During the healthy stage, the bearing signal changes were relatively stable, and the bearing defect size remained at an initial, small level. Nearby, at this point we need to assume It follows a Gaussian distribution, and its expression is as follows: ; in, This refers to the inherent variance of the bearing's random uncertainty under healthy conditions, caused by system noise, changes in lubricating oil film thickness, thermal expansion, or measurement errors.

[0034] Bearing transition phase signals are mainly divided into gradual and abrupt types. Gradual signals use a linear growth function model, while abrupt signals use... Function simulation of step: ; ; in, The linear degradation rate representing the gradual change period. This represents the start time of the transition phase. This represents the step rate of the Sigmoid function.

[0035] The signal changes drastically when the bearing is in the accelerated degradation phase. Assuming the signal grows exponentially or linearly at a high speed, the previous moment's estimate is taken as the baseline: ; This represents the relative growth rate during the accelerated degradation phase.

[0036] At this point, the final output defect This is the first phase of data-driven results. With physical priors The weighted fusion constitutes a simple Bayesian update process: ; in, Combining the current moment With physical prior constraints. Represents historical prior weights.

[0037] Based on the geometric relationship of the rolling element's trajectory within the defect, the defect center angle can be solved using the following expression. : ; in, To maintain the frame angular velocity, Where is the radius of the rolling element. The center reference distance. OQ represents the length of the pitch circle radius plus the rolling element radius. represent Figure 4 The time from midpoint B to point C.

[0038] Determine the defect width by using the defect center angle. and update The expression is as follows: .

[0039] S3: Construct and train a residual neural network to establish a nonlinear mapping relationship between the characteristics of real bearing vibration signals and the defect size of a five-degree-of-freedom bearing digital twin model through the life-cycle defect size evolution curve; a further implementation method is that the method for establishing the nonlinear mapping relationship includes: The root mean square value of the measured bearing vibration signal is extracted as the network input, and the defect size evolution curve throughout the entire life cycle is used as the label data. Based on the network input and the label data, a fully connected neural network with residual connections is constructed and trained to learn the nonlinear mapping relationship from the statistical characteristics of vibration signals to the physical defect size.

[0040] S4: Obtain the topological structure of defect information based on nonlinear mapping relationships, and construct a graph convolutional distillation network containing teacher and student models based on the topological structure; a further implementation method is that the method for constructing the graph convolutional distillation network includes: The defect size feature data is sampled using a sliding window and subjected to a linear transformation. The similarity matrix between features is calculated, and an initial dynamic adjacency matrix fusing time dependencies and spatial weights is generated through a gating mechanism. Specifically, a linear transformation projects the input features onto a new feature space, as shown in the following expression: ; in, It is the input feature matrix. and These are learnable weights and biases.

[0041] To capture the temporal dependencies between nodes, a similarity matrix is ​​calculated between the transformed features and then applied to the similarity matrix. The function is normalized to obtain the time dependency matrix, as shown in the following expression: ; in, yes Activation function These are learnable weights. It is a learnable bias. This represents the unnormalized similarity score between the i-th time node and the j-th time node. represents the similarity score between the i-th time node and any k-th time node in the sequence, and N represents the total number of time steps in the input sequence.

[0042] To apply it to the adjacency matrix, it needs to be extended to matrix form through a broadcast mechanism to modulate the time-dependent matrix, as shown in the following expression: ; in, This indicates element-wise multiplication. This represents the adaptive gating weight matrix after being expanded by the broadcast mechanism.

[0043] Then, message passing is performed using a dynamic adjacency matrix, as shown in the following expression: ; in, It is another learnable weight matrix used to transform features to capture more complex dependencies.

[0044] Knowledge extraction is achieved through internal constraints, resulting in structural consistency loss and matrix sparsity loss. The weighted combination of these two losses yields the local structural loss, expressed as follows: ; Among them, hyperparameters Control the strength of the constraints.

[0045] Then, an adaptive fusion weight was defined. The expression is as follows: ; in, and They represent Signal characteristics at any given moment and defect characteristics throughout the entire lifecycle; and These are the local standard deviation operators for the features, used to measure the volatility and quality of the data; These are dynamically calculated weights used for subsequent weighted fusion of the adjacency matrix.

[0046] A signal similarity graph and a defect topology graph are constructed. A mutation reconnection strategy is introduced to enhance the connection strength of defect mutation points and their neighborhoods. Combined with the initial dynamic adjacency matrix, the final dynamic adjacency matrix is ​​generated.

[0047] Specifically, constructing a signal similarity map With defect topology diagram For two parallel spatial graph structures, the initial similarity is calculated based on the Euclidean distance of defect features, as shown in the following expression: ; in, This is the scaling factor.

[0048] The model closely focuses on... and The principle is determined The point at time t is a point of change. Connection enhancement is performed on this point and its neighborhood, as shown in the following expression: ; in, Represents the set of mutation point indices; Indicates the strength of mutation reconnection, used to force and enhance topological dependencies before and after the mutation occurs; This is the size of the reconnection time window.

[0049] By fusion weights Obtain the dynamic adjacency matrix : ; use Spatial-dimensional message aggregation is performed on the fused features, expressed as follows: ; in, For the first Hidden layer representation; initial input The fused feature vector; The state transition matrix is ​​a learnable matrix. and These represent layer normalization and nonlinear activation functions, respectively.

[0050] The teacher model extracts the spatiotemporal features of defect evolution using the final dynamic adjacency matrix and a multi-layer graph convolutional network. The student model, through lightweight structural design and the introduction of a knowledge distillation strategy, learns the feature extraction capabilities of the teacher model under the constraint of the total loss function, thus completing the construction of the graph convolutional distillation network. With the merged dynamic adjacency matrix Given the network topology, the time-series and physical defect features of nodes are aggregated through multiple layers of GCN. The feature propagation formula corresponding to the l-th layer is: ; in, This is the current hidden layer feature matrix; These are the learnable linear transformation weights for this layer; It is the ReLU nonlinear activation function.

[0051] During the network construction and training phases, an overall loss function incorporating the mean squared error of RUL predictions and the differences in teacher and student distributions is introduced for optimization: ; in, and These are the predicted values ​​and actual lifespan labels of the student model, respectively. Used to measure the feature representation of the student model and Divergence between the feature representations of the teacher model; This is the balancing coefficient. Through backpropagation of the gradient of this loss function, the lightweight student network is driven to accurately inherit the high-dimensional spatiotemporal feature extraction capability of the teacher model.

[0052] A further implementation method is that the total loss function is composed of a weighted sum of prediction error loss, structural consistency loss, adjacency matrix sparsity loss, and local structure loss, which ultimately guides the training of the student model and outputs the prediction result of the remaining service life of the bearing.

[0053] S5: Collect new bearing vibration signals and predict the remaining service life of the bearing through a graph convolutional distillation network.

[0054] Example 2 The present invention also provides a bearing remaining service life prediction system based on a digital twin model, for implementing the method of Embodiment 1, comprising: The twin model construction module is used to construct a five-degree-of-freedom digital twin model of a bearing based on Hertzian contact theory and Newton's second law to simulate the composite motion of various components inside the bearing and the excitation of defects. The evolution curve generation module is used to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model by using the measured bearing vibration signal and employing a dual-feature real-time iteration and geometric model calibration method to generate a full life cycle defect size evolution curve. The nonlinear mapping module is used to construct and train a residual neural network, and establish a nonlinear mapping relationship between the characteristics of real bearing vibration signals and the defect size of a five-degree-of-freedom bearing digital twin model through the life cycle defect size evolution curve; The network model building module is used to obtain the topology of defect information based on nonlinear mapping relationships, and to build a graph convolutional distillation network containing teacher and student models based on the topology. The life prediction module is used to collect new bearing vibration signals and predict the remaining service life of the bearing through a graph convolutional distillation network.

[0055] A further implementation method is that the twin model construction module includes: Differential equation building unit, used to establish dynamic differential equations containing two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling body; The excitation function construction unit is used to construct a time-varying displacement excitation function by calculating the instantaneous displacement change in segments based on the contact position between the rolling element and the edge of the defect and the depth of the defect when the rolling element passes through the local defect area of ​​the bearing. The digital twin model building unit is used to introduce the time-varying displacement excitation function into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during the defect evolution process, and complete the construction of a five-degree-of-freedom bearing digital twin model.

[0056] Example 3 The following annotations provide details for the corresponding English abbreviations and terms, to facilitate subsequent descriptions and explanations: RUL: Remaining service life; RMS: Root Mean Square; RMSE: Root Mean Square Error; XJTU-SY: Dataset name.

[0057] The following is a further explanation with reference to specific embodiments: Taking the XJTU-SY dataset as an example, 15 bearings were selected under two operating conditions: Condition 1 (2100 rpm / 12000 N), bearings 1-1 to 1-5; Condition 2 (2250 rpm / 11000 N), bearings 2-1 to 2-5; and Condition 3 (2400 rpm / 10000 N), bearings 3-1 to 3-5. In this example, 13 features in the time-frequency domain include kurtosis, entropy, fractal dimension, peak factor, impulse factor, crest factor, energy ratio, spectral flatness, mean, variance, skewness, peak vibration, and root mean square vibration. These features have been proven effective in predicting the bearing's RUL (Relative Limiting Rank). Then, two types of graph data with different adjacency matrices were constructed.

[0058] Figure 4 This is a schematic diagram of the physical phenomenon of the double pulse provided by the present invention. When the rolling element passes through the outer ring defect, the vibration signal exhibits a repeatable response pattern. As the rolling element contacts the edge of the defect, the vibration signal begins to decrease slowly due to the reduced load, reaching the entry point at this time. A The rolling element completely loses contact with the inner and outer rings, and the displacement is fully restored, corresponding to the peak value of the main pulse in the signal. At this point, the main peak value is reached. B The rolling element collides with the defect exit edge, triggering a high-frequency impact response, at which point the exit point is reached. C By extracting the time from reaching the peak and the time from the peak to the collision, a basis for defect estimation can be established.

[0059] Figure 5 This is a schematic diagram of the defect adjacency topology strategy provided by the present invention. The defect topology construction process introduces a mutation reconnection strategy to accurately capture the instantaneous state transitions of bearing failure. When the dynamic adjacency matrix detects anomalies in the statistical distribution of defect features, it enhances the connection strength of the mutation point and its neighborhood. Furthermore, a structured regularization mechanism with fused weights constrains background noise interference, forming an adaptive graph convolutional evolution mechanism capable of deeply mining the nonlinear degradation patterns throughout the entire lifecycle.

[0060] Figure 6This is a schematic diagram of the frequency domain envelope spectrum of the simulated signal from the five-degree-of-freedom dynamic twin model of the bearing, as presented in this invention. It can be seen that the spectral analysis results of the twin signal fully confirm the effectiveness of the constructed digital twin model in simulating bearing fault characteristics. Within the frequency range of 0 to 500 Hz, the signal clearly reconstructs the characteristic frequency of the outer race fault and its higher harmonic components. The fundamental frequency is accurately located at 107.8 Hz, and the second to fourth harmonic peaks at 215.6 Hz, 323.4 Hz, and 432.0 Hz are significant and clearly distinguishable. Not only is the frequency positioning highly consistent with the theoretical calculation values, but the amplitude distribution also exhibits attenuation characteristics that conform to physical laws. This indicates that the digital twin model presented in this paper possesses extremely high signal fidelity and can accurately capture the periodic impact response induced by bearing defects, verifying its reliability.

[0061] Figure 7 The XJTU-SY bearing dataset in this embodiment of the invention shows partial bearing defect curve results. Overall, it can be seen that the dynamic response characteristics of bearing 1-1 undergo a significant abrupt change at the 78th sample point. This evolution indicates that the defect geometry has crossed a critical threshold, satisfying the physical conditions for triggering a double-pulse dynamic response.

[0062] Figure 8 The calibration results of some bearing defect curves in the XJTU-SY bearing dataset in this embodiment of the invention. It can be seen that in the final stage of bearing failure, there is a certain deviation between the original curves obtained based on the first two stages and the calibrated trajectory. This phenomenon is because, under severe damage, as the defect size increases, the bearing's dynamic response exhibits significant non-stationarity and instability, leading to a decrease in the sensitivity of analytical parameters during time-domain feature matching, thus introducing computational errors. By introducing a calibration mechanism and using a defect size geometric model to correct the trajectories of the first two stages, a high-fidelity bearing life-cycle defect evolution curve is finally obtained. It can be seen that the difference between the calibrated and updated mapping curve and the predicted defect size curve is very small. The effectiveness of the mapping model is verified; this model can map the actual bearing's dynamic response well to the defect size of the twin bearing, revealing the relationship between bearing vibration signals and operational defect sizes.

[0063] Figure 9This is a partial defect size curve prediction result from the XJTU-SY bearing dataset in this embodiment of the invention. It can be seen that after dynamic parameter updates and defect calibration, the bearing defect size curve generated by the model exhibits extremely high consistency with the actual bearing vibration signal curve, and all evaluation indicators verify the superiority of the mapping model. Experimental results show that by comparing the predicted defect size evolution trajectory with the dynamic changes of the bearing vibration signal in six test cases, a high degree of temporal synchronization and trend consistency between the two can be clearly observed throughout the entire life cycle. Whether in the early healthy and stable stage of the bearing or in the accelerated degradation stage after the fault occurs, the defect size value predicted by the model can keenly capture every significant abrupt change and fluctuation in the vibration signal.

[0064] Figure 10 This paper compares the bearing defect size prediction results of this invention with those of other methods. It can be seen that although there are slight differences in specific numerical values ​​among the different methods, the full-life-cycle defect curve generated by this method maintains a high degree of consistency with other models in terms of overall degradation trend. It clearly presents the typical nonlinear evolution characteristics of bearing defects, from initial gradual growth to rapid expansion in the final stage, thus verifying the effectiveness of the method proposed in this paper.

[0065] Figure 11 This is a comparison chart of the RUL prediction performance of the XJTU-SY dataset with other methods in this embodiment of the invention. It can be seen that in most cases, from an overall average performance perspective, the proposed method has an average RMSE of only 0.07966, which is significantly lower than DC-DGCN's 0.1108 and the classic C-LSTM model's 0.1378, representing a reduction in prediction error of approximately 28.1% and 42.2% respectively, demonstrating a clear accuracy advantage. Particularly in the Bearing 3-5 load conditions, the proposed method achieves an RMSE as low as 0.041269, while the errors of other comparative methods all exceed 0.140. This indicates that the model maintains extremely high fitting ability even when facing complex nonlinear degradation features, validating its effectiveness and generalization potential in the RUL prediction task.

[0066] Figure 12This is a visualization of the RUL (Relative Limiting Rank) of each model in the ablation experiment of this invention. As can be seen from the figure, the model incorporating "defective adjacency topology" exhibits significant superiority and robustness compared to the baseline model without "defective adjacency topology." Specifically, although both types of models can reflect the degradation trend of the device, the model with defective adjacency topology shows a higher degree of fit to the actual RUL throughout the entire lifecycle, and its corresponding error shadow area is significantly narrower than the baseline model without considering defects over most time steps. Especially in the drastic fluctuation stage of the later stages of degradation, the model with defective adjacency topology demonstrates stronger anti-interference ability and smoothness. This strongly proves that retaining or simulating specific topological defects in the graph structure not only does not hinder feature aggregation, but may also enhance the model's ability to generalize and capture nonlinear degradation features by reducing the risk of oversmoothing or introducing structural regularization, thereby effectively improving the final prediction accuracy.

[0067] Figure 13 This is a visualization of the adjacency matrix performance of each model in the ablation experiment of this invention. It can be seen that the defective adjacency topology actually acts as a structural regularization mechanism, effectively reducing redundant connections and potential background noise interference, while forcing the model to focus more on capturing the inter-node dependencies based on bearing degradation information during the bearing degradation process. This not only maintains the integrity of the information but also potentially improves the efficiency of the graph neural network in extracting key degradation features by mitigating the oversmoothing effect.

[0068] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the remaining service life of bearings based on a digital twin model, characterized in that, include: Based on Hertzian contact theory and Newton's second law, a five-degree-of-freedom digital twin model of a bearing is constructed to simulate the composite motion of various components inside the bearing and the excitation of defects. A dual-feature real-time iteration and geometric model calibration method is adopted to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model using measured bearing vibration signals, thereby generating a full-life-cycle defect size evolution curve. A residual neural network is constructed and trained, and a nonlinear mapping relationship is established between the characteristics of the real bearing vibration signal and the defect size of the five-degree-of-freedom bearing digital twin model through the full life cycle defect size evolution curve. The topology for obtaining defect information is based on the nonlinear mapping relationship, and a graph convolutional distillation network containing teacher and student models is constructed based on the topology. New bearing vibration signals are collected and, through the graph convolutional distillation network, the remaining service life of the bearing is predicted.

2. The method according to claim 1, characterized in that, The method for constructing the five-degree-of-freedom bearing digital twin model includes: Establish dynamic differential equations that include two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling element; When the rolling element passes through the local defect area of ​​the bearing, the instantaneous displacement change is calculated in segments based on the contact position between the rolling element and the edge of the defect and the depth of the defect, and a time-varying displacement excitation function is constructed. The time-varying displacement excitation function is introduced into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during the defect evolution process, thus completing the construction of the five-degree-of-freedom bearing digital twin model.

3. The method according to claim 1, characterized in that, The method for updating and correcting the defect parameters in the five-degree-of-freedom bearing digital twin model includes: By using measured and simulated bearing vibration signals, a weighted objective function including peak error and root mean square error is constructed. The peak density and signal-to-noise ratio of the signal are introduced as adaptive weight adjustment factors. The variable step size rule iterative search is used to make the statistical characteristics of the simulated bearing vibration signal approximate the optimal defect size parameters of the measured bearing vibration signal, and the data-driven optimal defect size estimate is obtained. Based on the healthy stage, transition stage and accelerated degradation stage of the bearing degradation process, physical prior models of Gaussian distribution, linear or step function and exponential function are established respectively. The data-driven optimal defect size estimate is weighted and fused with the physical prior model through Bayesian update process to obtain the corrected defect size. Based on the double-pulse phenomenon generated when the rolling element passes through the defect in the measured bearing vibration signal, the defect center angle solution equation is established in combination with the bearing geometric parameters. The defect width is calculated and the corrected defect size is geometrically calibrated to obtain the defect size evolution curve throughout the entire life cycle.

4. The method according to claim 1, characterized in that, The methods for establishing the nonlinear mapping relationship include: The root mean square value of the measured bearing vibration signal is extracted as the network input, and the defect size evolution curve throughout the entire life cycle is used as the label data. Based on the network input and the label data, a fully connected neural network with residual connections is constructed, and the fully connected neural network is trained to learn the nonlinear mapping relationship from the statistical characteristics of vibration signals to the size of physical defects.

5. The method according to claim 1, characterized in that, The method for constructing the graph convolutional distillation network includes: Sliding window sampling and linear transformation are performed on the defect size feature data. The similarity matrix between features is calculated and an initial dynamic adjacency matrix that integrates time dependence and spatial weight is generated through a gating mechanism. A signal similarity graph and a defect topology graph are constructed. A mutation reconnection strategy is introduced to enhance the connection strength of defect mutation points and their neighborhoods. Combined with the initial dynamic adjacency matrix, the final dynamic adjacency matrix is ​​generated. The teacher model extracts the spatiotemporal features of defect evolution using the final dynamic adjacency matrix and a multi-layer graph convolutional network. The student model learns the feature extraction capabilities of the teacher model under the constraint of the total loss function through a lightweight structural design and the introduction of a knowledge distillation strategy, thus completing the construction of the graph convolutional distillation network.

6. The method according to claim 5, characterized in that, The total loss function is composed of a weighted average of prediction error loss, structural consistency loss, adjacency matrix sparsity loss, and local structure loss, which ultimately guides student model training and outputs the prediction results of the remaining service life of the bearing.

7. A bearing remaining service life prediction system based on a digital twin model, used to implement the method described in any one of claims 1-6, characterized in that, include: The twin model construction module is used to construct a five-degree-of-freedom digital twin model of a bearing based on Hertzian contact theory and Newton's second law to simulate the composite motion of various components inside the bearing and the excitation of defects. The evolution curve generation module is used to update and correct the defect parameters in the five-degree-of-freedom bearing digital twin model by using the measured bearing vibration signal with the dual-feature real-time iteration and geometric model calibration method, and generate the full life cycle defect size evolution curve. The nonlinear mapping module is used to construct and train a residual neural network to establish a nonlinear mapping relationship between the characteristics of the real bearing vibration signal and the defect size of the five-degree-of-freedom bearing digital twin model through the full life cycle defect size evolution curve. A network model construction module is used to obtain the topology of defect information based on the nonlinear mapping relationship, and to construct a graph convolutional distillation network containing teacher and student models based on the topology. The life prediction module is used to collect new bearing vibration signals and predict the remaining service life of the bearing through the graph convolutional distillation network.

8. The system according to claim 7, characterized in that, The twin model construction module includes: Differential equation building unit, used to establish dynamic differential equations containing two degrees of freedom for the inner ring, two degrees of freedom for the outer ring, and one degree of freedom for the rolling body; The excitation function construction unit is used to construct a time-varying displacement excitation function by calculating the instantaneous displacement change in segments based on the contact position between the rolling element and the edge of the defect and the depth of the defect when the rolling element passes through the local defect area of ​​the bearing. The digital twin model construction unit is used to introduce the time-varying displacement excitation function into the elastic deformation calculation of the dynamic differential equation to simulate the real-time dynamic response of the bearing during the defect evolution process, and complete the construction of the five-degree-of-freedom bearing digital twin model.

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