Bearing life prediction method based on kinetic model and cross-domain graph network

Abstract

The invention discloses a rolling bearing life prediction method based on a dynamical model and a cross-domain graph network, and the method comprises the steps: building a simulation model based on a five-degree-of-freedom dynamical model of a rolling bearing, and combining a multi-target particle swarm optimization algorithm with a bearing actual measurement signal to dynamically update the parameters of the dynamical simulation model. And the defect evolution process of the simulation model in different degradation stages is explored, and the full-life-cycle simulation data of the rolling bearing are generated, so that the defect that the full-life-cycle data of the bearing are difficult to collect in actual engineering is overcome. Designing a multi-layer cross-domain graph neural network model, performing nonlinear transformation on graph node features to extract space information of neighbor nodes, and extracting time dependence of the neighbor nodes by combining a hidden layer state at a previous moment; and taking the complete labeled simulation data as source domain data, taking the incomplete label-free actual measurement data as target domain data, reducing the distribution difference between the source domain data and the target domain data through a multi-layer domain adaptation mechanism, and finally realizing cross-domain prediction of the service life of the bearing.

Description

Technical Field

[0001] The present invention belongs to the technical field of deep learning, fault prediction and health management, and relates to a bearing life prediction method based on a dynamic model and a cross-domain graph network. Background Art

[0002] As a widely used rotating component in mechanical equipment, bearings play a huge role in supporting and transmitting loads. Due to heavy loads, long operating time, and harsh working conditions, bearings are prone to wear, corrosion, and surface peeling, resulting in a high failure rate. Bearing failures can easily cause equipment damage and even major safety accidents, resulting in economic losses and casualties. Under the background of "Made in China 2025", industrial production is becoming more and more automated and intelligent. Relying on the development of advanced sensing and testing technology and artificial intelligence, the prediction of the remaining service life of bearings can help formulate effective mechanical equipment maintenance plans to avoid unexpected failures and equipment downtime. Therefore, bearing health status monitoring and life prediction are crucial to ensure the reliability and safety of mechanical equipment.

[0003] Data-driven methods are currently widely used in bearing life prediction. However, in practical scenarios, the limited availability of source domain data poses a challenge to training high-precision bearing remaining life prediction models. The reason for data scarcity is that the collection of bearing life cycle data requires strict environmental requirements and requires a lot of time and operating costs. In addition, due to changes in operating conditions, it is still difficult to generate data with high similarity to the target domain data through physical simulation. Therefore, the scarcity of available high-similarity life cycle data remains the main problem limiting the application of cross-domain remaining service life prediction methods. Summary of the invention

[0004] The purpose of the present invention is to provide a bearing life prediction method based on a dynamic model and a cross-domain graph network to solve the problems existing in the rolling bearing life prediction.

[0005] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is a bearing life prediction method based on a dynamic model and a cross-domain graph network. The method constructs a simulation model based on the five-degree-of-freedom dynamic model of the rolling bearing, and uses a multi-objective particle swarm optimization algorithm combined with the measured signal of the bearing to dynamically update the parameters of the dynamic simulation model. The defect evolution process of the simulation model at different degradation stages is explored, and the simulation data of the entire life cycle of the rolling bearing is generated to make up for the defect that the full life cycle data of the bearing is difficult to collect in actual engineering. A multi-layer cross-domain graph neural network model is designed, and the graph node features are nonlinearly transformed to extract the spatial information of the neighboring nodes, and the time dependency of the adjacent nodes is extracted by combining the hidden layer state at the previous moment. The complete and labeled simulation data is used as the source domain data, and the incomplete and unlabeled measured data is used as the target domain data. The distribution difference between the source domain and the target domain data is reduced through a multi-layer domain adaptation mechanism, and finally the cross-domain prediction of the bearing life is realized.

[0006] Construction of S1 bearing simulation model;

[0007] S1.1 Construction of five-degree-of-freedom dynamic model;

[0008] This section builds a bearing degradation dynamics simulation model based on the actual bearing parameters and operating conditions. It can interact with the bearing entity in real time on parameters such as load and speed, and update its own parameters based on the actual bearing signal. The inner and outer rings of the bearing each have two degrees of freedom, representing the horizontal displacement (x i ,x o ) and vertical displacement (y i ,y o ), while the unit resonator has only one degree of freedom, representing the vertical displacement (y r ).

[0009] The dynamic differential equation of the bearing is as follows:

[0010]

[0011] Where m is the mass, c is the damping coefficient, k is the stiffness, and F i is the external radial load, f x 、f y are the nonlinear contact forces in the horizontal and vertical directions, respectively.

[0012] The nonlinear contact force calculation formula is:

[0013]

[0014] Where K j is the contact stiffness between the ball and the raceway, n b represents the number of balls, represents the relative deformation at the jth ball position, θ jis the angular displacement. The model also introduces the phase deviation of ball sliding to enhance the fidelity of the bearing signal, which can be expressed as:

[0015]

[0016] Where t is time, ω c is the angular velocity, d is the diameter, θ slip is the phase deviation degree, D m is the pitch diameter. α is the bearing contact angle, ω s is the angular velocity of the inner ring, and n is the shaft speed.

[0017] The relative deformation of the bearing can be expressed as:

[0018] δ j =(x i -x o )cosθ j +(y i -y o )sinθ j +η+β j Δd

[0019] Where η is the radial clearance of the bearing and Δd is the displacement excitation caused by the ball passing through the defect. j Model the circumferential cross-angle peeling and simulate the defect angle position θ d This defines the spalling region as a step function, where β j is defined as follows:

[0020]

[0021] The outer ring peeling position is θ d and The speed of the inner ring defect is the same as the rotor speed, that is, θ d =ω s t+θ do (where θ do is the initial position of the ball).

[0022] The displacement excitation generated when the ball passes over a defect varies depending on the size of the defect. When the defect width is small, the ball cannot completely descend to the bottom of the defect. Therefore, the maximum displacement excitation experienced by the ball remains below the depth of the defect. As the defect size increases, the ball can eventually descend to the bottom of the defect. In this case, the maximum displacement excitation of the rolling element is the same as the depth of the defect, which is usually observed in the late stages of bearing degradation.

[0023] In scenario 1, the displacement excitation of the rolling element can be calculated as:

[0024]

[0025] where θ d is the angular position of the defect, is the circumferential span angle of the defect, b 1 is the circumferential width of the defect. cd is the maximum displacement of the rolling element.

[0026] The displacement excitation of the rolling element in scenario 2 can be expressed as:

[0027]

[0028] where θ n =θ d +2n j π, H is the defect depth, and It is the angle corresponding to the rolling element entering and leaving the defect.

[0029] S1.2 parameter optimization mechanism;

[0030] In order to minimize the difference between the simulated signal and the measured signal, a multi-objective optimization algorithm is used to update the dynamic model parameters based on the real-time signal. The cosine similarity and peak value of the two signals are used as the optimization objectives of the algorithm, aiming to reduce the difference between the simulated signal and the actual signal.

[0031] In the present invention, a multi-objective particle swarm optimization algorithm is integrated into the dynamic model, and the parameters are adjusted according to the actual measurement signal. The basic principle is that particles find the optimal parameters through their own and collective information. In the process of finding the optimal solution, each particle can adjust the search direction according to its own memory of the optimal solution location and the collective knowledge shared by the group. After iteration, the particle swarm can find the global optimal solution. The updated particle speed is as follows:

[0032]

[0033] in represents the velocity of particle i at the nth iteration, represents the position of particle i, is the historical optimal solution of particle i, Represents the historical optimal solution of the group. 1 and r 2 is a random number between 0 and 1, l 1 and l 2 is the learning factor.

[0034] S2 multi-layer cross-domain graph neural network;

[0035] The proposed multi-layer cross-domain graph neural network consists of three modules: graph attention layer, long short-term memory unit and regressor. The graph convolution layer uses the relationship between nodes in the graph to extract the spatial features of the bearing through nonlinear transformation, and reduces the distribution difference between graph data in different domains through the maximum mean difference loss. Subsequently, these extracted features are input into the gated recurrent unit to further extract the temporal features by combining the information of the hidden layer at the previous moment. Then, the feature distribution difference is reduced by the maximum mean difference loss. Finally, the regressor is used to predict the remaining service life.

[0036] There are connections between the various components of the rolling bearing, and these connections are expressed through the relationship between nodes and edges in the non-Euclidean space graph data. The bearing vibration signal is converted into graph data and transmitted to the graph network model. The converted source domain graph data is recorded as f(G s )=G[A s ,X s ], the target domain graph data is recorded as f(G t )=G[A t ,X t ] (where X represents the node feature matrix and A represents the adjacency matrix), after input, the spatial degradation features are extracted through a three-layer graph attention network, which is expressed as:

[0037]

[0038] Where f(A,X) is the output of the network layer, b i is the bias vector of the i-th layer, W i is the trainable parameter matrix of the i-th layer, σ is the activation function, is the attention coefficient between the graph node and its neighbors, expressed as:

[0039]

[0040] Where δ is the activation function, is the feature representation of the i-th node in the n-1 layer, is the set of neighbor nodes of the ith node.

[0041] The distribution difference between the simulated signal and the actual signal will have a strong impact on the accuracy of the prediction results. After spatial feature extraction, the source domain and target domain data are represented as P(G s ) and Q(G t ), map it to Hilbert space, and use Gaussian kernel to calculate the kernel matrix of the two domains. The distribution difference measure between graph data is achieved by comparing the mean operator difference of the regularized feature representation in Hilbert space, which can be defined as:

[0042]

[0043] in represents the K-MMD loss between the source domain and the target domain, H represents the Hilbert space with kernel k, and f(K i s ) and f(K i t ) represent the feature representations of the source domain and target domain data after spatial feature extraction operations.

[0044] The state of the bearing system changes over time, and the vibration response includes a time series feature. The time series feature can capture the dynamic changes and trends in the data, including information about how different parameters evolve over time, such as vibration modes. The proposed model can effectively capture the time series feature by analyzing the time series properties of the data, which can be expressed as:

[0045] y t =δ(Φ y .[h t-1 ,x t ]+b y )

[0046] q t =δ(Φ q .[h t-1 ,x t ]+b q )

[0047]

[0048] r t =δ(Φ r .[h t-1 ,x t ]+b r )

[0049] h t =r t .tanh(C t )

[0050] Among them, Φ y ,Φ q ,Φ c ,Φ r is the weighting matrix, b y ,b q ,b c ,b r Represents the bias of the network layer. The long short-term memory layer combines spatial and temporal features to create a fusion result, which is then fed into the regression head to predict the remaining useful life of the bearing.

[0051] In order to further adapt the prediction knowledge of the simulated signal to the actual signal, after the time series feature extraction, the maximum mean difference loss is used again to reduce the distribution difference, which can be expressed as:

[0052]

[0053] Where P(l s ) and Q(l t ) are the temporal features of the source domain and the target domain respectively, is the T-MMD loss, and k is the feature kernel of the Hilbert space.

[0054] The output of the long short-term memory module combines spatial and temporal features and is fed into the regressor to predict the remaining life of the bearing. The regressor consists of a fully connected layer and a sigmoid function, and the output can be expressed as:

[0055]

[0056] where w a and b a are weights and biases respectively. h is the input of the regression head. The output of the regression head represents the predicted remaining life of the bearing.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The present invention designs a method based on a dynamic model and a cross-domain graph network to predict bearing life. In order to overcome the problem that it is difficult to collect actual data, resulting in insufficient training of data-driven prediction models, a rolling bearing simulation model is constructed based on the five-degree-of-freedom dynamic model of the bearing. This method generates vibration responses under different displacement excitations by simulating the defect evolution process of the bearing at different degradation stages. The multi-objective particle swarm optimization algorithm is used to dynamically update the parameters of the dynamic simulation model in combination with the measured signal of the bearing, so as to realize the real-time state interaction between the simulation model and the actual bearing. A multi-layer cross-domain graph neural network model is designed, and the graph node features are nonlinearly transformed to extract the spatial information of neighbor nodes, and the time dependency of adjacent nodes is extracted by combining the hidden layer state at the previous moment. The complete and labeled simulation data is used as the source domain data, and the incomplete and unlabeled measured data is used as the target domain data. The distribution difference between the source domain and target domain data is reduced through a multi-layer domain adaptation mechanism, and finally the cross-domain prediction of bearing life is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a principle flow chart of the rolling bearing life prediction method based on dynamic model and cross-domain graph network.

[0060] Figure 2 This is the overall flow chart of the proposed method.

[0061] Figure 3 It is a schematic diagram of the five-degree-of-freedom dynamic model of the bearing.

[0062] Figure 4 It is a schematic diagram of the proposed multi-layer cross-domain graph neural network model.

[0063] Figure 5 The prediction results of the proposed method on different bearing data are as follows. (a) The prediction result of bearing 1_2, (b) The prediction result of bearing 1_3, (c) The prediction result of bearing 1_4, (d) The prediction result of bearing 2_2, (e) The prediction result of bearing 2_3, (f) The prediction result of bearing 2_4, (g) The prediction result of bearing 3_2, (h) The prediction result of bearing 3_3, (i) The prediction result of bearing 3_4.

[0064] Figure 6 is the prediction accuracy of various methods in different experimental data. DETAILED DESCRIPTION

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0066] Figure 1 This is a flow chart of the rolling bearing life prediction method based on a dynamic model and a cross-domain graph network of the present invention. Figure 2 The following is a detailed description of the principle of the bearing life prediction method based on the dynamic model and the cross-domain graph network in conjunction with the flow chart.

[0067] (1) Use the acceleration sensor to obtain the bearing vibration acceleration signal of the entire life cycle as the signal to be analyzed. Take the XJTU-SY bearing data set of Xi'an Jiaotong University as an example. This data set is collected from the accelerated bearing degradation experiment on the experimental platform. The test bearing model is LDK UER-204, and the vibration signal is collected using the DT9837 portable dynamic signal acquisition device. The sampling interval is 1 minute, the duration of each sampling is 1.28 seconds, and the sampling frequency is set to 25.6kHz.

[0068] (2) Figure 3 The following is a schematic diagram of the constructed five-degree-of-freedom dynamic model of the bearing. The parameters of the dynamic simulation model are set according to the actual parameters of the bearing, with the inner ring diameter of 29.3mm, the outer ring diameter of 39.8mm, and the ball diameter of 7.92mm. In addition, the number of rolling elements is 8, the radial force is 12kN, and the speed is set to 2100r / min. In order to match the characteristics of the actual signal, the simulation signal is sampled at a frequency of 25.6kHz, and the single sampling time is 1.28 seconds.

[0069] (3) The complete labeled simulation data is used as the source domain, and the incomplete unlabeled actual data is used as the target domain to predict the remaining service life of the entire actual bearing. This is to verify the effectiveness of the proposed bearing remaining service life prediction method when complete actual data cannot be obtained.

[0070] (4) Build a multi-layer cross-domain graph neural network, use the constructed graph data as the network input, and the life curve as the network output, extract the bearing degradation information at different times from the time domain and space domain, and establish a mapping relationship between monitoring data and degradation trend. Figure 4 This is the schematic diagram of the constructed multi-layer cross-domain graph neural network.

[0071] (5) The effectiveness of the proposed method is verified by comparative experiments with other advanced methods. The experiments show that the proposed method has better prediction performance than the existing advanced methods in terms of the performance of remaining service life prediction. The prediction results and errors of the proposed method for different bearing data are shown in Figure 2. Figure 5 The prediction accuracy of various methods in different experiments is shown in Figure 6 shown.

Claims

1. A bearing life prediction method based on a dynamic model and a cross-domain graph network, characterized in that: The implementation steps of this method are as follows: Construction of S1 bearing simulation model; S1.1 Construction of five-degree-of-freedom dynamic model; The bearing degradation dynamics simulation model is built according to the actual bearing parameters and operating conditions. It interacts with the bearing entity in real time on load and speed parameters, and updates its own parameters according to the actual bearing signals. The inner and outer rings of the bearing each have two degrees of freedom, representing the horizontal displacement (x i ,x o ) and vertical displacement (y i ,y o ), while the unit resonator has only one degree of freedom, representing the vertical displacement (y r ); The dynamic differential equation of the bearing is as follows: Where m is the mass, c is the damping coefficient, k is the stiffness, and F i is the external radial load, f x 、f y are the nonlinear contact forces in the horizontal and vertical directions respectively; The nonlinear contact force calculation formula is: Where K j is the contact stiffness between the ball and the raceway, n b represents the number of balls, represents the relative deformation at the jth ball position, θ j is the angular displacement; the bearing degradation dynamics simulation model introduces the phase deviation of ball sliding to enhance the fidelity of the bearing signal, which is expressed as: Where t is time, ω c is the angular velocity, d is the diameter, θ slip is the phase deviation degree, D m is the pitch diameter; α is the bearing contact angle, ω s is the angular velocity of the inner circle, n is the shaft speed; The relative deformation of the bearing is expressed as: d j =(x i -x o )cosθ j +(y i -y o )sinθ j +n+b j Δd Where η is the radial clearance of the bearing, Δd is the displacement excitation caused by the ball passing through the defect; the failure switch β j Model the circumferential cross-angle peeling and simulate the defect angle position θ d The contact loss at the point where the peeling area is defined as a step function, where β j is defined as follows: The outer ring peeling position is θ d and The speed of the inner ring defect is the same as the rotor speed, that is, θ d =ω s t+θ do , where θ do is the initial position of the ball; In scenario 1, the displacement excitation of the rolling element is calculated as: where θ d is the angular position of the defect, is the circumferential span angle of the defect, b1 is the circumferential width of the defect; cd is the maximum displacement of the rolling element; The displacement excitation of the rolling element in scenario 2 is expressed as: where θ n =θ d +2n j π, H is the defect depth, and It is the angle corresponding to the rolling element entering and leaving the defect; S1.2 parameter optimization mechanism; In order to minimize the difference between the simulated signal and the measured signal, a multi-objective optimization algorithm is used to update the dynamic model parameters based on the real-time signal. The cosine similarity and peak value of the two signals are used as the optimization targets of the algorithm, aiming to reduce the difference between the simulated signal and the actual signal. The multi-objective particle swarm optimization algorithm is integrated into the dynamic model. The parameters are adjusted according to the actual measurement signal. The particles search for the optimal parameters through their own and collective information. In the process of searching for the optimal solution, each particle adjusts the search direction according to its own memory of the optimal solution location and the collective knowledge shared by the group. After iteration, the particle swarm finds the global optimal solution. The updated particle speed is as follows: in represents the velocity of particle i at the nth iteration, represents the position of particle i, is the historical optimal solution of particle i, represents the historical optimal solution of the group; r1 and r2 are random numbers between 0 and 1, l1 and l2 are learning factors; S2 multi-layer cross-domain graph neural network; The proposed multi-layer cross-domain graph neural network consists of three modules: graph attention layer, long short-term memory unit and regressor. The graph convolution layer uses the relationship between nodes in the graph to extract the spatial features of the bearing through nonlinear transformation, and reduces the distribution difference between graph data in different domains through the maximum mean difference loss. Subsequently, these extracted features are input into the gated recurrent unit to further extract the temporal features by combining the information of the hidden layer at the previous moment. Then, the feature distribution difference is reduced through the maximum mean difference loss. Finally, the regressor is used to predict the remaining service life. There are connections between the various components of the rolling bearing, and these connections are expressed through the relationship between nodes and edges in the non-Euclidean space graph data. The bearing vibration signal is converted into graph data and transmitted to the graph network model. The converted source domain graph data is recorded as f(G s )=G[A s ,X s ], the target domain graph data is recorded as f(G t )=G[A t ,X t ], where X represents the node feature matrix and A represents the adjacency matrix. After input, the spatial degradation features are extracted through a three-layer graph attention network, which is expressed as: Where f(A,X) is the output of the network layer, b i is the bias vector of the i-th layer, W i is the trainable parameter matrix of the i-th layer, σ is the activation function, is the attention coefficient between the graph node and its neighbors, expressed as: Where δ is the activation function, Y i (n-1) is the feature representation of the i-th node in the graph at the n-1th layer, Y k (n-1) is the set of neighbor nodes of the i-th node; After spatial feature extraction, the source domain and target domain data are represented as P(G s ) and Q(G t ), map it to Hilbert space, and use Gaussian kernel to calculate the kernel matrix of the two domains; the distribution difference measure between graph data is achieved by comparing the mean operator difference of the regularized feature representation in Hilbert space, which is defined as: in represents the K-MMD loss between the source domain and the target domain, H represents the Hilbert space with kernel k, and f(K i s ) and f(K i t ) represent the feature representation of source domain and target domain data after spatial feature extraction operation respectively; The state of the bearing system changes over time, and the vibration response includes a time series feature. The time series feature captures the dynamic changes and trends in the data, including information about how different parameters evolve over time. The graph network model effectively captures the time series feature by analyzing the time series nature of the data, which can be expressed as: y t =δ(Φ y .[h t-1 ,x t ]+b y ) q t =δ(Φ q .[h t-1 ,x t ]+b q ) r t =δ(Φ r .[h t-1 ,x t ]+b r ) h t =r t .tanh(C t ) Among them, Φ y ,Φ q ,Φ c ,Φ r is the weighting matrix, b y ,b q ,b c ,b r Represents the bias of the network layer; the long short-term memory layer combines spatial and temporal features to create a fusion result, which is then fed into the regression head to predict the remaining service life of the bearing; In order to adapt the prediction knowledge of the simulated signal to the actual signal, after the time series feature extraction, the maximum mean difference loss is used again to reduce the distribution difference, which is expressed as: Where P(l s ) and Q(l t ) are the temporal features of the source domain and the target domain respectively, is T-MMD loss, k is the characteristic kernel of Hilbert space; The output of the long short-term memory module combines spatial and temporal features and is sent to the regressor to predict the remaining life of the bearing; the regressor consists of a fully connected layer and a sigmoid function, and the output result is expressed as: where w a and b a are weight and bias respectively; h is the input of the regression head; the output of the regression head represents the predicted remaining life of the bearing.

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