Splashing lubricating oil distribution prediction method based on geometric deep learning

Abstract

The invention relates to the technical field of artificial intelligence, and particularly discloses a splashing lubricating oil distribution prediction method based on geometric deep learning, which comprises the following steps: acquiring multi-working-condition simulation data to generate a training sample, constructing a geometric deep learning model, encoding and inputting to obtain encoding features, operating the encoding features through a processor, fusing the encoding features with condition features, and predicting the distribution of splashing lubricating oil. And inputting into a decoder to predict the stable position of the oil particles. Through the constructed geometric deep learning model, after input characteristics of oil particles to be measured are input, an oil distribution result can be rapidly output through the geometric deep learning model, the stable position of splashing lubricating oil can be predicted, and the stable position of the oil particles in a real physical space of a gear box can be obtained through reverse normalization. And rapid prediction of oil liquid distribution in gear splash lubrication is realized.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, and specifically discloses a method for predicting the distribution of splashed lubricating oil based on geometric deep learning. Background Technology

[0002] Splash lubrication is a lubrication method that relies on rotating components such as gears to carry lubricating oil from an oil sump, delivering oil droplets or mist to key friction surfaces such as gear meshing areas and bearings through splashing. This method is widely used on exposed friction surfaces with relatively low loads, such as engine cylinder walls and piston pins, and is also very common in transmission devices such as gearboxes and reducers.

[0003] In splash lubrication, the distribution of lubricating oil is crucial, as it directly determines whether an effective oil film can be formed between the gear meshing area and key friction points such as bearings. It is a core factor affecting the reliability, efficiency, and lifespan of the transmission system. However, the oil distribution result is difficult to predict directly in the design process.

[0004] In existing technologies, engineers mainly rely on computational fluid dynamics to simulate and analyze oil distribution. The mainstream simulation analysis methods include using fluid volume models combined with complex dynamic mesh technology to simulate the splashing and flow process of lubricating oil, or using meshless particle methods to handle large deformation problems.

[0005] Although the above methods can provide relatively detailed flow field information, they still have the following inherent limitations: the computational cost is extremely high, the modeling process is complex and heavily reliant on the engineer's experience, and they are usually only applicable to specific working conditions, making it difficult to apply them efficiently to multi-working-condition scenarios, which greatly limits their application in the rapid iterative design phase of products.

[0006] This invention provides a method for predicting the distribution of splashed lubricating oil based on geometric deep learning, in order to solve the above-mentioned problems. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting the distribution of splash lubricating oil based on geometric deep learning. By constructing a geometric deep learning model with physical graph modules and local graph modules, the method can quickly predict the distribution of oil in gear splash lubrication.

[0008] To achieve the above objectives, the basic solution of this invention provides a method for predicting the distribution of splashed lubricating oil based on geometric deep learning. The method involves inputting the input features of the oil particles to be measured into a constructed geometric deep learning model, obtaining the predicted stable positions of the oil particles, and then inversely normalizing them to obtain their true physical coordinates. The geometric deep learning model is constructed based on the following steps: Step A1: Simulate and generate simulated particles with particle type labels, oil state labels, and region labels under different working conditions, and obtain the three-dimensional coordinate vector of the simulated particles in the steady state. Step A2: Select simulated particles labeled as oil particles, and use their operating parameters, initial particle state, and label information as input features; Step A3: Input the input features into the geometric deep learning model, and obtain the final encoded features through multi-dimensional feature fusion, dynamic weight encoding, hierarchical feature aggregation and post-processing; Step A4: Construct the physical graph module and the local graph module as processors, and obtain the final graph features by taking the final encoded features as input; Step A5: Perform differential preprocessing on the operating condition parameters and input them into the condition encoder to obtain the basic condition features used to describe the quantitative impact of the operating conditions on the oil distribution. Perform layer normalization on these features and superimpose them with the mapped features to obtain the final condition features. Step A6: Adaptively fuse the final image features and final conditional features and perform layer normalization. Input the result into the decoder to predict the stable position of the oil particles. Based on the error between the result and the corresponding three-dimensional coordinate vector of the simulated particles in the stable state, iteratively train to obtain the final geometric deep learning model. Output the final stable position of the oil particles and map it to the real physical coordinates through inverse normalization.

[0009] Furthermore, in step A1, the area label includes the core area: the gear tooth contact area and the bearing outer ring area. The area label also includes the gap area between the guard and the gear, the oil accumulation area at the bottom of the housing, the inner wall area of ​​the housing, and the remaining area.

[0010] Furthermore, in step A2, the operating parameters include oil volume, gear speed, oil temperature, tooth tip clearance, axial clearance, and radial clearance; the initial state of the particles includes the initial three-dimensional coordinate vector and the initial three-dimensional velocity vector of the oil particles; and the label information includes the region label, particle type label, and oil state label.

[0011] Furthermore, step A3 specifically includes the following sub-steps: Step A301: Decompose the input features into geometric location sub-features, dynamic sub-features, and attribute sub-features; Step A302: Fuse geometric position sub-features, dynamic sub-features and attribute sub-features to obtain initial features, convert the working condition guidance vector constructed from working condition parameters into working condition bias features and add them to the initial features to obtain preprocessed features; Step A303: Perform dynamic weight encoding on the preprocessed features to generate weighted features, and perform hierarchical feature aggregation on the weighted features to generate global encoded features. Add the global encoded features and weighted features element by element to obtain the preliminary encoded features. The post-processing process includes: Step A304: Normalize the regions of the initial encoded features, construct a lightweight denoising network and use the normalized features as input, train the denoising network and the encoder synchronously to obtain the denoised features; Step A305: Add the denoised features to the preprocessed features element by element to obtain the final encoded features.

[0012] Furthermore, in step A301, the geometric position sub-feature is the normalized initial three-dimensional coordinate vector, the dynamic sub-feature is the normalized initial three-dimensional velocity vector, and the attribute sub-feature is a combination of region One-Hot encoding and oil state One-Hot encoding. The region One-Hot encoding is obtained based on region label transformation, and the oil state One-Hot encoding is obtained based on oil state label transformation.

[0013] Furthermore, in step A4, a number of virtual physical nodes are generated using the physical graph module, and global physical constraint features are obtained by dynamically weighting them. These features are then fused with the final encoded features to generate physical graph features. Using a local graph module, the local graph topology is dynamically constructed and updated based on the correlation between oil particle positions and viscous forces, and local graph features are extracted through attention-weighted aggregation. The physical graph features and local graph features are adaptively fused and superimposed to form the final encoded features, which are then normalized by the global layer to generate the final graph features.

[0014] Furthermore, the generated virtual physical nodes include viscous nodes, centrifugal force nodes, gravity nodes, surface tension nodes, shield turbulence nodes, and temperature nodes. The characteristics of each virtual physical node are calculated based on physical laws and operating parameters.

[0015] Furthermore, step A5 specifically includes the following sub-steps: Step A501: Classify the working condition parameters to obtain continuous parameters and discrete parameters, then normalize the continuous parameters and encode the discrete parameters, and then concatenate them to obtain the working condition preprocessing vector, and map it to the corresponding subsequent encoding dimension to obtain the mapped features. Step A502: Construct a conditional encoder. Based on the mapped features, learn the correlation between operating conditions and oil distribution through the conditional encoder to obtain basic conditional features. Step A503: Perform layer normalization on the basic conditional features to obtain normalized conditional features, map the mapped features back to 256 dimensions, and add them to the normalized conditional features to obtain the final conditional features.

[0016] The principle and effect of this solution are as follows: 1. Compared with the prior art, the present invention, through the constructed geometric deep learning model, can quickly output the oil distribution results after inputting the input features of the oil particles to be tested, thereby predicting the stable position of splashed lubricating oil. Furthermore, the stable position of the oil particles in the real physical space of the gearbox can be obtained through inverse normalization, thus realizing the rapid prediction of oil distribution in gear splash lubrication.

[0017] 2. Compared with existing technologies, this invention uses a geometric deep learning model to predict the stable position of oil particles under test. The model takes the working parameters, initial state, and label information of the oil particles as input features. Through the configured label information, it accurately filters out oil particles and distinguishes their oil states. It achieves differentiated normalization and dynamic weight encoding of features based on region affiliation, strengthening the feature representation of key lubrication areas such as gear tooth contact areas and bearing outer ring areas. Simultaneously, it provides a basis for the constraint rule adaptation of the physical graph module and the spatial boundary constraints of the decoder, ensuring the targeted nature of feature processing and the physical rationality of the prediction results. Finally, through multi-module collaborative computation, the stable position of the oil particles in real physical space is output. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 The flowchart illustrating the construction process of the geometric deep learning model in the splash lubricating oil distribution prediction method based on geometric deep learning proposed in this application embodiment is shown. Detailed Implementation

[0020] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0021] A method for predicting splash lubricating oil distribution based on geometric deep learning, implementing, for example... Figure 1 As shown, the input features of the oil particles to be tested are input into the constructed geometric deep learning model to obtain the predicted stable position of the oil particles, and the true physical coordinates are obtained by inverse normalization. The geometric deep learning model is constructed based on the following steps: Step A1: Simulate and generate simulated particles with particle type labels, oil state labels, and region labels under different working conditions, and obtain the three-dimensional coordinates of the simulated particles in a steady state.

[0022] In this embodiment, the simulation platform used is the nanoFluidX simulation platform. A gear splash lubrication simulation model is constructed based on this platform. Specifically, a 3D model of the gearbox is established as the gear splash lubrication simulation model. In the 3D model of the gearbox, only key fluid domains such as the housing, gears, shafts, bearings, and guards are retained. The guards are modeled according to the actual tooth tip clearance, axial clearance, radial clearance, and wrap angle. The computational domain is designed as a closed cavity that meets the requirements of particle filling and flow simulation. After the gear splash lubrication simulation model is constructed, the following particles are generated using the pre-processing software SimLab: oil particles representing lubricating oil, air particles representing air inside the housing, wall particles representing the stationary housing / guard, and moving wall particles representing rotating gears / shafts.

[0023] After generating the aforementioned particles, the nanoFluidX core parameters are configured, including the shortest simulation time, lubricating oil density ρ, dynamic viscosity μ, air density, gear rotation direction, and initial angular velocity. During the simulation, the included operating parameters include oil volume, gear speed, oil temperature, and shield clearance. These parameters are combined to generate 50 independent operating conditions. After performing transient simulations on each independent operating condition, the simulated lubricating oil distribution data under steady-state conditions is extracted to obtain the simulated particle position data under steady-state conditions, i.e., three-dimensional coordinate vectors, which are then used as the simulation results.

[0024] The criterion for determining a stable state is the rate of change of the simulated particle position over five consecutive time steps. For values ​​less than 0.5%, the formula for calculating the rate of change of the simulated particle position is as follows: ; In the formula, Indicates the first Simulate the three-dimensional coordinate vector of the particle at each time step. Indicates the first Simulate the three-dimensional coordinate vector of the particle at each time step.

[0025] In this embodiment, each simulated particle is bound to its independent initial position, stable position, all operating parameters covered in the simulation process, and its corresponding particle type label. The initial and stable positions of the simulated particle are both represented by the three-dimensional coordinate vector of the corresponding time step. The particle type labels include 1, 2, 3, and 4, where 1 represents an oil particle, 2 represents an air particle, 3 represents a wall particle, and 4 represents a moving wall particle. Each particle has only one independent particle type label.

[0026] Furthermore, the simulated particles are labeled with state tags according to the rotation speed. Simulated particles generated when the rotation speed is less than 1000 RPM are labeled as continuous oil film, simulated particles generated when the rotation speed is greater than 3000 RPM are labeled as discrete oil droplets, and simulated particles generated when the rotation speed is greater than or equal to 1000 RPM and less than or equal to 3000 RPM are labeled as mixed-state particles.

[0027] Furthermore, in this embodiment, the internal area of ​​the housing is divided into the following six regions: the gear tooth contact area within ±5mm of the gear tooth contact, the bearing outer ring area within ±10mm of the bearing outer ring, the gap area between the protective cover and the gear, the oil accumulation area at the bottom of the housing within ±20mm of the oil surface, the inner wall area within ±5mm of the inner wall of the housing, and the remaining area. Each region is divided into corresponding spatial coordinate ranges. The simulated particles that conform to the corresponding spatial coordinate ranges are labeled with the following region labels according to three-dimensional coordinates: Label 1: Gear tooth contact area, Label 2: Bearing outer ring area, Label 3: Gap area between the protective cover and the gear, Label 4: Oil accumulation area at the bottom of the housing, Label 5: Inner wall area of ​​the housing, Label 6: Remaining area.

[0028] Obtain simulated oil distribution data under all operating conditions to construct the input dataset.

[0029] Step A2: Select simulated particles labeled as "oil particles" and use their operating parameters, initial particle state, and label information as input features. In this embodiment, the three-dimensional coordinates of the oil particles in a steady state are used as the output feature.

[0030] Specifically, after obtaining the input dataset, the system filters out oil particles with a particle type label of 1 by using the particle type label of each particle in the input dataset. It then obtains the operating parameters, initial state, and label information for each oil particle. The operating parameters include the oil volume. Gear speed Oil temperature Tooth tip clearance axial clearance radial clearance For each oil particle, construct the following working condition guidance vector. : .

[0031] The initial state of the particles includes the initial three-dimensional coordinate vector of the oil particles. Initial three-dimensional velocity vector An initial state vector is constructed for each oil particle as shown below. : .

[0032] The tag information includes particle type tags, oil state tags, and region tags. In this embodiment, the oil state tags are converted into oil state One-Hot codes, and the region tags are converted into region One-Hot codes.

[0033] A training dataset is constructed using the input and output features of all oil particles. Within this training dataset, the following preprocessing steps are performed on the initial three-dimensional coordinate vectors of the oil particles: Statistics are calculated by grouping by region label to avoid distortion of regional features caused by normalization. All oil particles are traversed and divided into k groups according to their corresponding region label k. Calculate the mean and standard deviation of the initial three-dimensional coordinate vectors of all oil particles in each group. For the initial three-dimensional coordinate vector of each oil particle, retrieve the corresponding mean and standard deviation according to its region label, and perform region difference normalization using the following formula: ; ; ; In the formula, , , They represent the first Initial three-dimensional coordinate vector of each oil particle The value after regional differentiation normalization , , They represent the first All oil particles in the region correspond to axis, axis, The mean of the axis coordinates, , , They represent the first All oil particles in the region correspond to axis, axis, The standard deviation of the axis coordinates.

[0034] After regional difference normalization, input feature encoding and dimensionality integration are performed. Input features include the operating parameters of oil particles, particle initial states, and label information. For each operating condition guidance vector, the operating parameters are normalized using the following formula: ; In the formula, This represents the normalized operating parameters. This represents the original values ​​of the operating parameters after normalization. This represents the minimum value of the normalized operating parameters. This represents the maximum value of the normalized operating parameters.

[0035] The initial state of a particle includes its initial three-dimensional coordinate vector and initial three-dimensional velocity vector. The initial three-dimensional velocity vector of each oil particle is normalized according to the following formula based on the maximum initial velocity under the corresponding operating condition: ; In the formula, This represents the normalized velocity vector. This represents the initial three-dimensional velocity vector of the oil particles, which includes... Initial velocity of shaft , Initial velocity of shaft , Initial velocity of shaft , This represents the maximum initial velocity under the corresponding operating condition, and is a scalar.

[0036] Finally, the input features are obtained by integrating the normalized initial 3D coordinate vectors and initial 3D velocity vectors of the oil particles, as well as the region One-Hot encoding and the oil state One-Hot encoding. The normalized working condition guidance vector is used separately as the working condition guidance signal, collectively constructing the input of the geometric deep learning model. In this embodiment, the stable-state 3D coordinate vectors of the oil particles are used as the output features, and the working condition parameters, initial particle states, and label information of the oil particles are used as the input features to construct the training dataset. The training dataset is divided in a 7:2:1 ratio, with 70% allocated to the training set, 20% to the validation set, and 10% to the test set. Furthermore, the ratio of simulated oil distribution data in the training set, validation set, and test set is 7:3.

[0037] Step A3: Input the input features into the geometric deep learning model, and obtain the final encoded features through multi-dimensional feature fusion, dynamic weight encoding, hierarchical feature aggregation and post-processing.

[0038] Step A3 addresses the issues of weak original oil particle feature representation, lack of prominent information in key areas such as gear tooth contact area and bearing outer ring area, and unexplored dynamic correlations. It provides the processor in step A4 with highly recognizable and physically meaningful deep feature inputs, ensuring the accuracy of subsequent graph calculations.

[0039] Specifically, it includes the following sub-steps: Step A301: Decompose the input features into geometric location sub-features, dynamic sub-features, and attribute sub-features.

[0040] Among them, the geometric position sub-feature is the normalized initial position (initial three-dimensional coordinate vector), the dynamic sub-feature is the normalized initial velocity (initial three-dimensional velocity vector), and the attribute sub-feature is a combination of region One-Hot encoding and oil state One-Hot encoding.

[0041] Step A302: Fuse geometric location sub-features, dynamic sub-features and attribute sub-features to obtain initial features, convert the working condition guidance vector into working condition bias features and add them to the initial features to obtain preprocessed features.

[0042] Specifically, in the process of integrating geometric location sub-features, dynamic sub-features, and attribute sub-features, it is necessary to first map the dimension of the attribute sub-features to the same dimension as the geometric location sub-features and dynamic sub-features, and then add the mapped attribute sub-features and dynamic sub-features element by element to strengthen the association between attributes and dynamics, thereby obtaining enhanced dynamic sub-features.

[0043] The geometric location sub-features are concatenated with the enhanced dynamic sub-features, and then compressed through a single bottleneck linear layer to generate the initial features, as shown in the following expression: ; In the formula, Geometric position sub-features With enhanced dynamic sub-features Vector concatenation, This represents the learnable weight matrix of the bottleneck linear layer. This represents the learnable bias vector of the bottleneck linear layer. Indicates the initial characteristics.

[0044] Then, a linear mapping layer is used to convert the working condition guidance vector into working condition bias features, which are then injected into the initial features as global information to obtain preprocessed features, thereby strengthening the guidance of the working condition on the encoding. The expression is as follows: ; ; In the formula, Indicates the operating condition bias characteristics. This represents the operating condition guidance vector. This represents the learnable weight matrix of the linear mapping layer. This represents the learnable bias vector of the linear mapping layer. This represents the preprocessed features after incorporating the operating condition bias characteristics.

[0045] Step A303: Perform dynamic weight encoding on the preprocessed features to generate weighted features, and perform hierarchical feature aggregation on the weighted features to generate global encoded features. Add the global encoded features and weighted features element by element to obtain the preliminary encoded features.

[0046] In this embodiment, the preprocessed features are concatenated with the region One-Hot encoding to form an attention input vector, which is then input into a two-layer fully connected network to calculate the attention weight for each oil particle, as shown in the following expression: ; In the formula, Indicates the first Attention weights for each oil particle This represents the activation function. This represents the learnable weight matrix of layer two in a fully connected network. This represents the learnable weight matrix of layer one in a fully connected network. Represents the attention input vector, , This represents the bias vector of layer 1 in a fully connected network. This represents the bias vector of layer 2 in a fully connected network.

[0047] Then, the preprocessed features and attention weights are multiplied element-wise according to the following formula to generate weighted features. To enhance the characteristic representation of oil particles in key areas: .

[0048] Next, the average attention weight of oil particles in each region is calculated to ensure that the average weight of key regions is greater than or equal to 0.7 and that of non-key regions is less than or equal to 0.6, thereby verifying the validity of the weights. If the condition is not met, the learning rate is adjusted and the attention layer is retrained until the weight pattern is met.

[0049] The obtained weighted features are sequentially subjected to local encoding, global aggregation, and hierarchical fusion processes to achieve hierarchical feature aggregation and obtain preliminary encoded features that take into account both local correlations and the weights of key regions. Specifically, the process includes the following steps: The oil particles corresponding to the weighted features are divided into 6 local subsets based on region labels. The Euclidean distance between oil particles is calculated in millimeters based on the normalized initial positions, and a neighborhood threshold is set for each region. In this embodiment, the neighborhood threshold is set as follows when operating at different speeds: When the speed is low, that is, when the gear speed is less than 1000 RPM, the neighborhood threshold of the gear tooth contact area is 3 mm, the neighborhood threshold of the bearing outer ring area is 4 mm, and the neighborhood threshold of the remaining area is 5 mm.

[0050] When the gear is at a medium speed, that is, the gear speed is greater than or equal to 1000 RPM but less than or equal to 3000 RPM, the neighborhood threshold of the gear tooth contact area is 4 mm, the neighborhood threshold of the bearing outer ring area is 5 mm, and the neighborhood threshold of the remaining areas is 7 mm.

[0051] When operating at high speeds, i.e., gear speeds greater than 3000 RPM, the neighborhood threshold for the gear tooth contact area is 5 mm, the neighborhood threshold for the bearing outer ring area is 6 mm, and the neighborhood threshold for the remaining areas is 9 mm.

[0052] Based on the neighborhood threshold set above, nearest-neighbor oil particles are selected to construct a local graph. Then, a local graph convolution module is used to extract the local correlation features of oil particles within the region, such as the relative position correlation of oil particles in the gear tooth contact area, as expressed below: ; In the formula, Indicates the first Local graph adjacency matrix of each region Indicates the first A subset of the weighted features of each region Indicates the first Local correlation characteristics of each region.

[0053] And calculate the mean vector of the local correlation features of the six regions according to the following formula. : ; In the formula, Indicates the first The total number of oil particles in each region Indicates the first The first region Local correlation characteristics of individual oil particles.

[0054] The mean vectors of the local correlation features of the six regions are then input into the global attention layer to learn the contribution weights of each region to the global oil distribution. The expression is as follows: ; In the formula, Represents the normalization function. This represents the learnable weight matrix of the global attention layer. This represents the bias vector of the global attention layer.

[0055] Based on the contribution weight, all local correlation features of the six regions are aggregated to obtain the global encoding features. The expression is as follows: .

[0056] The global encoding features and weighted features are added element-wise to obtain preliminary encoding features that take into account both local correlations and the weights of key regions. : .

[0057] In step A3, the post-processing steps include: Step A304: Normalize the regions of the initial encoded features, construct a lightweight denoising network and use the normalized features as input, train the denoising network and the encoder synchronously to obtain the denoised features.

[0058] Specifically, based on local correlation features, the following coding feature statistics for each region are calculated: The mean of the coding features of each region, the first The standard deviation of the coding features of each region, the preliminary coding features of each oil particle, according to its region label. The corresponding mean and standard deviation of the encoded features are used to perform layer normalization according to the following formula to obtain the normalized features. : ; In the formula, Indicates the first The mean of the encoded features of each region Indicates the first Standard deviation of coding features for each region.

[0059] Next, a lightweight CNN denoising network with two 1×1 convolutional kernels, LeakyReLU activation function, and negative slope of 0.1 is constructed. The normalized features are input into the CNN denoising network to smooth high-frequency noise in the features, thereby achieving feature denoising, and the denoised features are output. .

[0060] In this embodiment, the denoising network and encoder are trained synchronously. During training, a feature similarity constraint before and after denoising is added to the loss function, i.e., the denoising loss function is constructed using the MSE loss, to avoid losing effective features during denoising. The expression is as follows: ; In the formula, Indicates the number of oil particles. It is the L2 norm. Indicates the first Normalized characteristics of individual oil particles Indicates the first Features of individual oil particles after noise reduction.

[0061] Training constraints This ensures a balance between noise reduction and feature integrity.

[0062] Step A305: Add the denoised features to the preprocessed features element by element to obtain the final encoded features.

[0063] In this embodiment, the denoised features are added to the preprocessed features using the following formula to generate the final encoded features. : .

[0064] Step A4: Construct a physical graph module, generate several virtual physical nodes, and obtain global physical constraint features by dynamically weighting them. Then, fuse these features with the final encoded features to generate physical graph features. A local graph module is constructed, which dynamically builds and updates the local graph topology based on the correlation between oil particle positions and viscous forces, and extracts local graph features through attention-weighted aggregation. By predicting fusion weights through a fully connected network, physical graph features and local graph features are adaptively fused and superimposed with the final encoded features, which are then normalized by a global layer to generate the final graph features.

[0065] Step A4 addresses the problem of predictions deviating from reality caused by traditional graph models focusing only on local correlations and neglecting physical laws (such as centrifugal force and shield turbulence). It also compensates for the shortcomings of single graph structures in depicting global constraints or local details, providing a high-quality feature foundation for subsequent conditional fusion and decoding prediction.

[0066] Specifically, it includes the following sub-steps: Step A401: Construct a physical graph module to generate the following virtual physical nodes: viscosity node, centrifugal force node, gravity node, surface tension node, shield turbulence node, and temperature node. Normalize the virtual physical node features. Using the operating condition guidance vector and the region One-Hot encoding as input, predict the weight of each virtual node. Weight the virtual physical node features according to the weights to obtain global physical constraint features. Calculate the attention similarity between the encoded features and the global constraint features. Broadcast the global constraint features to each oil particle and fuse them with the encoded features to generate physical graph features.

[0067] Each virtual physical node's characteristics are calculated based on physical laws and operating parameters, specifically: sticky nodes The formula used to describe the pulling effect of viscous forces on oil particles is as follows: ; In the formula, Indicates the first The initial velocity of each oil particle Indicates the first The Euclidean distance between each oil particle and the center of the gear is used to calculate the radial distance within the gear's rotation plane. , Indicates the dynamic viscosity of the oil. This indicates the base viscosity at 25°C. , Indicates the viscosity temperature coefficient. , Indicates the actual temperature of the oil. Indicates the reference temperature. .

[0068] ; In the formula, Indicates the first individual oil particles Axis coordinates Indicates the first individual oil particles Axis coordinates Indicates the center of the gear Axis coordinates Indicates the center of the gear Axis coordinates.

[0069] Centrifugal force node The formula used to describe the driving effect of centrifugal force on the splashing of oil particles is as follows: ; In the formula, Indicates the density of the oil. .

[0070] Gravity node The formula used to describe the effect of gravity on the falling oil particles is as follows: ; In the formula, Represents gravitational acceleration. Indicates the first individual oil particles Axis coordinates.

[0071] Surface tension nodes The formula used to describe the effect of surface tension on oil droplet polymerization is as follows: ; In the formula, Indicates the surface tension of lubricating oil. .

[0072] Shield spoiler nodes The formula used to describe the obstruction effect of the shield on the flow of oil particles is as follows: ; In the formula, Indicates the turbulence coefficient. , Indicates the first The distance from each oil particle to the gap in the shield.

[0073] Temperature node Used to describe the regulatory effect of temperature on the physical properties of oils. .

[0074] Min-max normalization is performed on the features of the 6 virtual nodes, as shown in the following expression: ; In the formula, Indicates the first Normalized features of virtual nodes Indicates the first Original characteristics of virtual nodes Indicates the first The maximum value of a virtual node. Indicates the first The minimum value of virtual nodes.

[0075] In this embodiment, a single-layer fully connected network is used as the dynamic weights for physical constraints. The inputs are the working condition guidance vector and the region One-Hot encoding, and the outputs are the predicted weights of six virtual nodes. The sum of the predicted weights is constrained to 1 by Softmax activation, as shown in the following expression: ; In the formula, This represents the learnable weight matrix of a fully connected network layer. This represents the operating condition guidance vector. Indicates the region One-Hot encoding, This represents the learnable bias vector of a fully connected network layer.

[0076] The global physical constraint features are obtained by weighting the features of the six normalized virtual nodes according to the prediction weights. The expression is as follows: ; In the formula, Indicates the first The predicted weights of each virtual node.

[0077] Next, the attention similarity between the encoded features of each oil particle and the global physical constraint features is calculated to measure the correlation between the oil particles and the global physical constraints. The expression is as follows: ; In the formula, Indicates the first Attention similarity between individual oil particle encoding features and global physical constraint features. Indicates the first The coding features of individual oil particles This represents the transpose of the global physical constraint features, with the denominator being the square root of the feature dimension.

[0078] The global physical constraint features are broadcast to each oil particle through attention similarity, and then fused with the encoded features to generate the physical map features of each oil particle, as shown in the following expression: ; In the formula, Indicates the first Physical characteristics of individual oil particles.

[0079] Step A402: Construct a local graph module. Based on the initial position of the oil particles after inverse normalization, dynamically set the neighborhood threshold according to the rotation speed to filter the top 20 nearest neighbor oil particles that meet the conditions of distance and viscosity force correlation to construct a local graph adjacency matrix. Calculate the feature importance score of the oil particles and their neighbors and obtain the attention weight by Softmax normalization. Weighted aggregate the nearest neighbor encoded features to generate local graph features.

[0080] In this embodiment, based on the neighborhood threshold r of the current oil particle, for each oil particle... to satisfy oil particles As oil particles Among the candidate neighbors, Indicates oil particles The initial position coordinate vector after inverse normalization, Indicates oil particles The initial position coordinate vector after inverse normalization is then used to calculate the oil particles using the following formula. With oil particles Viscous force correlation : ; In the formula, Indicates oil particles The initial velocity after denormalization Indicates oil particles The initial velocities after denormalization are all represented in vector form.

[0081] Sort the oils in descending order of viscosity correlation, retain the first 20 nearest neighbors, and construct the oil as shown in the following formula. Local graph adjacency matrix : .

[0082] In this embodiment, by calculating particles Its neighboring oil particles initial velocity change rate To dynamically update the local graph topology, the calculation formula is as follows: ; In the formula, Indicates oil particles exist The speed of time, Indicates oil particles exist The speed of time, Indicates time interval, .

[0083] when At that time, a local graph update is triggered, and... Excessive levels of adjacent oil particles Recalculate its relationship with oil particles The correlation between the Euclidean distance and the viscous force; if the correlation between the viscous force and the viscous force is less than 0.01 N / m 2 Then oil particles And new candidates satisfying a viscosity force correlation degree greater than or equal to 0.01 N / m are added from the candidate pool. 2 Oil particles, to maintain oil particles The nearest neighbor count is 20, where the candidate pool consists of other unselected particles within a range of r+2mm. Furthermore, with an update frequency of two time steps, oil particles are checked once during each update. Its neighboring oil particles The initial velocity change rate ensures that the topology follows the dynamic changes of oil particles.

[0084] Then, by calculating the oil particles in the local diagram With oil particles Feature Importance Score To extract local graph features and perform graph attention enhancement, the calculation formula is as follows: ; In the formula, and Both represent multidimensional learnable weight matrices. Indicates oil particles The coding features, Indicates oil particles The coding features.

[0085] Attention weights are obtained through Softmax normalization. , Highlighting the important neighboring effect on oil particles The impact.

[0086] Finally, local map features for each oil particle are generated by weighted aggregation of nearest neighbor features, as shown in the following expression: ; In the formula, express Activation function Indicates oil particles The nearest neighbor set, Indicates oil particles Local map features.

[0087] Step A403: Using the working condition vector and the region One-Hot encoding as input, predict the fusion weights of the physical map features and the local map features, dynamically fuse the physical map features and the local map features according to the fusion weights to obtain the initial fused features, add the initial fused features to the final encoded features, and obtain the final map features after performing global layer normalization.

[0088] Specifically, a two-layer fully connected network is constructed, using the working condition vector and the region One-Hot encoding as input, to predict the fusion weight α, as shown in the following expression: ; In the formula, This represents a 64×12 dimensional learnable weight matrix. This represents a 1×64-dimensional learnable weight matrix. This represents a 64×1 dimensional learnable bias vector. This represents a 1×1 dimensional learnable bias vector.

[0089] The following initial fusion features were ultimately obtained: ; In the formula, Representing the characteristics of a physical graph, This represents the features of a local graph.

[0090] The initial fused features are then added to the encoded features to obtain the final features, as shown in the following expression: .

[0091] The final mean and standard deviation are calculated based on the final features of all oil particles in the current batch. Global layer normalization is then performed to obtain the final map features, as shown in the following expression: ; In the formula, Indicates the features of the final graph. This represents the final mean. This represents the final standard deviation.

[0092] Step A5: Perform differential preprocessing on the operating condition parameters and input them into the condition encoder to obtain the basic condition features used to describe the quantitative impact of the operating conditions on the oil distribution. Normalize the execution layer and superimpose it with the mapped features to obtain the final condition features.

[0093] Step A5 can solve the problems of incompatibility between working condition parameters and graph feature dimensions and the failure to effectively inject physical priors, providing working condition guidance signals for subsequent "graph feature-condition feature fusion" and ensuring that the fused features take into account both spatial details and working condition adaptability.

[0094] Specifically, it includes the following sub-steps: Step A501: Classify the operating condition parameters to obtain continuous parameters and discrete parameters, then normalize the continuous parameters and encode the discrete parameters, and then concatenate them to obtain the operating condition preprocessing vector, and map it to the corresponding subsequent encoding dimension to obtain the mapped features.

[0095] Specifically, operating parameters are classified into continuous parameters and discrete parameters according to parameter type. Continuous parameters include oil volume, gear speed, and oil temperature, while discrete parameters include tooth tip clearance, axial clearance, and radial clearance.

[0096] The continuous parameters are normalized using the min-max method as follows: ; In the formula, This represents the normalized operating condition parameter values. This represents the original operating condition parameter values. This represents the maximum value of the parameter for this operating condition in the training set. This represents the minimum value of the parameter for this operating condition in the training set.

[0097] The discrete combined parameters are mapped to discrete indices according to each gap value, and a 3D index vector is constructed together. Then, one-hot encoding is performed on the index vector of each gap, and the vectors are concatenated to form a discrete feature vector.

[0098] The normalized continuous parameters are concatenated with the discrete parameters to form the working condition preprocessing vector. The preprocessed vector of the working condition is input into a single linear mapping layer to obtain the mapped features. .

[0099] Step A502: Construct a conditional encoder. Based on the mapped features, the conditional encoder learns the correlation between operating conditions and oil distribution to obtain basic conditional features.

[0100] Specifically, a two-layer fully connected network combined with a conditional attention layer is used as the conditional encoder architecture. The mapped features are taken as input, and the output is the basic conditional features. .

[0101] In the first fully connected layer, the mapped features are used as input, and a LeakyReLU activation function with a negative slope of 0.1 is applied to learn the nonlinear correlation features of the operating parameters.

[0102] In the operating condition attention layer, the influence weights of different operating condition parameters are dynamically adjusted based on the following formula: ; In the formula, Indicates the first Attention weights for each operating condition parameter This represents the learnable weight matrix of the first fully connected layer. Represents the features after mapping No. Features corresponding to each operating condition parameter This represents the learnable bias vector of the first fully connected layer. Indicates the first The physical prior initial weights of each operating parameter are determined. In this embodiment, the initial weight of rotational speed is 0.4, the initial weight of shield clearance is 0.3, the initial weight of oil volume is 0.2, and the initial weight of temperature is 0.1.

[0103] The second fully connected layer takes the output of the first fully connected layer after attention weighting as input and uses the Tanh activation function to output the basic conditional features.

[0104] In this embodiment, the conditional encoder needs to be jointly trained with the encoder of step A3, the physical graph module of step A4, and the local graph module. The physical graph module and the local graph module are mounted in the processor. During the training process, the following three loss functions are used: ; In the formula, This indicates the loss associated with the operating condition and oil distribution. This represents the Pearson correlation coefficient. , Indicates the final conditional feature, This represents the stable position label of the oil, and the final conditional features are adapted to the dimension of the stable position label of the oil through an explicit broadcasting mechanism.

[0105] ; In the formula, Indicates feature smoothing loss, This represents the final condition characteristic of operating condition a. This represents the final condition characteristic of operating condition b.

[0106] ; In the formula, This represents the dimension matching loss.

[0107] Step A503: Perform layer normalization on the basic conditional features to obtain normalized conditional features, map the mapped features back to 256 dimensions, and add them to the normalized conditional features to obtain the final conditional features.

[0108] Specifically, perform layer normalization on the basic conditional features according to the following formula to generate normalized conditional features. , The numerical range is controlled within [-1.5, 1.5]: .

[0109] In the formula, It represents the standard deviation of the conditional characteristics after normalization.

[0110] The mapped features are then mapped back to 256 dimensions and added to the normalized conditional features to obtain the final conditional features. The expression is as follows: .

[0111] Step A6: Adaptively fuse the final image features and final conditional features and perform layer normalization. Input the result into the decoder to predict the stable position of the oil particles. Based on the error between the result and the corresponding three-dimensional coordinate vector of the simulated particles in the stable state, iteratively train to obtain the final geometric deep learning model. Output the final stable position of the oil particles and map it to the real physical coordinates through inverse normalization.

[0112] Specifically, it includes the following sub-steps: Step A601: Align the final image features with the final condition features, predict the fusion weights through a fully connected network based on the region labels and operating parameters, adaptively fuse the final image features and the final condition features according to the fusion weights and perform layer normalization to obtain the normalized fused features.

[0113] Based on region labels and operating parameters, a dynamic fusion weight, including the final graph feature weight ω1 and the final conditional feature weight ω2, is predicted through a single fully connected fusion weight sub-network, as shown in the following expression: ; In the formula, Represents the learnable weight matrix. This represents the learnable bias vector.

[0114] Based on the obtained dynamic fusion weights, feature fusion is performed according to the following formula to obtain the fused feature vector. : ; In the formula, Indicates the features of the final graph. This indicates the final condition feature.

[0115] Then, perform layer normalization on the fused feature vector according to the following formula to obtain the normalized fused features. : ; In the formula, This represents the mean of the fused features of the training set. The standard deviation represents the fused features of the training set.

[0116] Step A602: Construct a physical constraint decoder to predict the stable positions of oil particles and inversely normalize them to the real physical space.

[0117] In this embodiment, a 3-layer fully connected network with a region attention layer and a physical constraint layer is used as the decoder. The input is the normalized fused features, and the output is the predicted stable position of oil particles, adapted to geometric position attributes. The functions and parameters of each layer are as follows: The first fully connected layer: After input normalization, the fused features are fed into the hidden layer. The LeakyReLU activation function is configured to learn the non-linear correlation of the fused normalized features, thus obtaining the output features of the first fully connected layer. The expression is as follows: ; In the formula, and Both indicate that the parameters can be learned during the training process. This represents the fused feature vector after normalization.

[0118] Region Attention Layer: Based on region labels of oil particles, a dynamic weight generation function is used. Calculate the feature weights for each region, and perform weighted enhancement on the output features of the first fully connected layer to highlight the feature representation of the core lubrication areas: the gear tooth contact area and the bearing outer ring area, thus obtaining the features after incorporating region attention. The expression is as follows: ; In the formula, This represents the output features of the first fully connected layer. Region labels representing oil particles.

[0119] The second fully connected layer: Input the features after adding region attention to the hidden layer, configure the LeakyReLU activation function to further compress the feature dimension and remove redundant information, and output the features of the second fully connected layer, as shown in the following expression: ; In the formula, and All of these represent parameters that can be learned during the training process.

[0120] Physical constraint layer: Based on the region labels of oil particles, and according to the spatial coordinate range of each region, the activation value range of oil particles in each region is limited to the spatial coordinate range of their respective region. If it does not conform, it is pulled back to the region range through linear correction, thus obtaining a three-dimensional feature vector that conforms to the physical boundary constraints. The expression is as follows: ; In the formula, This represents the corrected effective predicted coordinate vector.

[0121] ; ; ; In the formula, This represents the temporary predicted coordinate vector after linear mapping of the output features from the second fully connected layer. Indicates the first The maximum value of the coordinate vector range for each region Indicates the first Minimum value of the range of coordinate vectors for each region.

[0122] Third fully connected layer: Input 3D feature vector Configure the Tanh activation function to output the predicted three-dimensional normalized coordinate vector of the stable position of the oil particles. The expression is as follows: ; In the formula, and All of these represent parameters that can be learned during the training process.

[0123] Furthermore, in iterations A3 to A6, the decoder is jointly trained with each module in the geometric deep learning model from steps A3 to A5. During training, the loss function is a weighted sum of the working condition-oil distribution correlation loss, feature smoothing loss, dimension matching loss, position error loss, cross-entropy loss, and physical constraint loss, expressed as follows: ; In the formula, Indicates position error loss, Represents cross-entropy loss, Represents physical constraint loss. ,in, , , , , , .

[0124] ; In the formula, Indicates the number of oil particles. Indicates the first The predicted value of the three-dimensional normalized coordinate vector of the stable position of the nth oil particle, that is, the nth The predicted location of each oil particle, ( , , Indicates the first The three-dimensional coordinate vector of the steady state of the nth oil particle, that is, the nth... The actual location of each oil particle.

[0125] ; In the formula, This indicates the total number of oil particles. This represents the number of nearest neighbors for each oil particle. Indicates a true local association label, when the first... The oil particle and the first If each oil particle is a nearest neighbor, then ,otherwise , This represents the predicted local association probability, i.e., the predicted first-order probability. The oil particle and the first The probability that an oil particle is a nearest neighbor. .

[0126] ; In the formula, This represents the penalty function, which applies when oil particles in the oil pool area... When the oil level is greater than the oil surface height, the penalty value is 0.1. When the oil particles in the gap area of ​​the shield are less than 2mm away from the shield, the penalty value is 0.2. When there is no violation, the penalty value is 0. Indicates the first The region label for each oil particle.

[0127] After the iterative training stops when the stopping condition is met, the iterative training ends, yielding the final geometric deep learning model and the predicted stable positions of oil particles. In this example, iterative training stops after any of the following conditions are met: The maximum number of iterations is reached; in this embodiment, the maximum number of iterations is 100.

[0128] If the total loss decreases by less than 1e-5 during 10 consecutive rounds of iterative training, and the decrease in a single round is less than or equal to 5%, then the iterative training is stopped.

[0129] The iterative training stops when the position error loss and physical constraint loss are less than their respective preset thresholds and the engineering accuracy indicators meet the standards.

[0130] The preset threshold for position error loss is 0.005, the preset threshold for physical constraint loss is 0.001, and the engineering accuracy indicators include: root mean square error of predicted stable position of oil particles ≤ 0.3 mm, average relative error ≤ 3%, and average relative error of gear tooth surface contact area and bearing outer ring area ≤ 2%.

[0131] Furthermore, for each oil particle, the corresponding statistic is called according to its region label k, mapping the predicted stable position of the oil particle output by the decoder after training to the real physical coordinates. To perform denormalization, the expression is as follows: ; In the formula, This corresponds to the predicted three-dimensional normalized coordinate vector of the stable position of the oil particles output by the decoder after training, including the predicted values ​​of the X-axis, Y-axis, and Z-axis coordinates. , , , Indicates the first The maximum value of the dimension corresponding to each region. Indicates the first The minimum value of the dimension corresponding to each region.

[0132] The final obtained three-dimensional coordinate vector That is, the stable position of the oil particle in the actual physical space of the gearbox.

[0133] This invention utilizes a constructed geometric deep learning model. After inputting the input features of the oil particles to be tested, the model can quickly output the oil distribution results, thereby predicting the stable position of splashed lubricating oil. Furthermore, by inverse normalization, the stable position of the oil particles in the actual physical space of the gearbox can be obtained, thus completing the prediction of the splashed lubricating oil distribution.

[0134] The geometric deep learning model constructed in this invention is equipped with a processor that combines physical graphs and local graphs. The physical graph module injects global physical constraints such as viscosity and centrifugal force, while the local graph module captures spatial details and dynamic relationships, thus avoiding the prediction results from deviating from the actual physical laws. At the same time, it strengthens the feature representation of key areas such as the contact area of ​​gear teeth and the outer ring area of ​​bearings.

[0135] During the training of the geometric deep learning model, based on the input dataset obtained through simulation, covering multiple working conditions, and by dividing the inside of the gearbox into 6 regions and the state of each particle, a multi-dimensional label is bound to each particle, and the region to which each particle belongs is marked, a clear mapping between particle and spatial position is established, the spatial belonging of the particle is clarified, feature distortion caused by the normalization of particle coordinates in different regions is avoided, and the predicted stable position of oil particles is ensured to conform to the spatial constraints of each region.

[0136] In summary, this invention uses a constructed geometric deep learning model to predict the stable position of oil particles under test. The model takes the working parameters, initial state, and label information of the oil particles as input features. Through the configured label information, it accurately filters out oil particles and distinguishes their oil states (continuous oil film, discrete oil droplets, and mixed-state particles). It achieves differentiated normalization and dynamic weight encoding of features based on region affiliation, strengthening the feature representation of key lubrication areas such as gear tooth contact areas and bearing outer ring areas. Simultaneously, it provides a basis for the constraint rule adaptation of the physical graph module and the spatial boundary constraints of the decoder, ensuring the targeted nature of feature processing and the physical rationality of the prediction results. Finally, through multi-module collaborative computation, the stable position of the oil particles in real physical space is output.

[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any indirect modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A geometric deep learning-based splash lubricant distribution prediction method, characterized in that, input features of the to-be-tested oil particles are input into the constructed geometric deep learning model to obtain predicted oil particle stable positions and real physical coordinates through inverse normalization, and the geometric deep learning model is constructed based on the following steps: Step A1: simulate to generate simulation particles with particle type labels, oil state labels and region labels under different working conditions, and obtain three-dimensional coordinate vectors of the simulation particles in the stable state; Step A2: select simulation particles with particle type labels as oil particles, and use their working condition parameters, initial particle state and label information as input features; Step A3: input the input features into the geometric deep learning model, and obtain the final encoding features through multi-dimensional feature fusion, dynamic weight coding, hierarchical feature aggregation and post-processing; Step A4: construct a physical graph module and a local graph module as processors, input the final encoding features to obtain the final graph features; Step A5: differentially preprocess the working condition parameters and input them into the condition encoder to obtain the basic condition features for describing the quantitative influence of the working conditions on the oil distribution, perform layer normalization on the basic condition features, and superimpose them with the mapped features to obtain the final condition features; Step A6: adaptively fuse the final graph features and the final condition features, perform layer normalization, input into the decoder to predict the stable position of the oil particle, and based on the error iteration training of the corresponding three-dimensional coordinate vectors of the simulation particles in the stable state, obtain the final geometric deep learning model, output the final stable position of the oil particle, and map it to the real physical coordinates through inverse normalization.

2. The method according to claim 1, wherein, In step A1, the region label includes the core region: gear tooth surface contact region, bearing outer ring region, and the region label also includes the gap region between the shroud and the gear, the oil accumulation region at the bottom of the box, the inner wall region of the box, and the remaining region.

3. The method for predicting splash lubricating oil distribution based on geometric deep learning according to claim 1, characterized in that, In step A2, the working condition parameters include oil volume, gear speed, oil temperature, addendum gap, axial gap and radial gap, the initial particle state includes initial three-dimensional coordinate vector and initial three-dimensional velocity vector, and the label information includes region label, particle type label and oil state label.

4. The method of claim 3, wherein the method is based on a geometric deep learning. 3 The step A3 specifically includes the following substeps: Step A301: split the input features into geometric position sub-features, dynamic sub-features and attribute sub-features; Step A302: fuse the geometric position sub-features, dynamic sub-features and attribute sub-features to obtain initial features, convert the working condition guide vector constructed by the working condition parameters into a working condition bias feature, and add it to the initial features to obtain preprocessed features; Step A303: perform dynamic weight coding on the preprocessed features to generate weighted features, and perform hierarchical feature aggregation on the weighted features to generate global encoding features, and add the global encoding features and the weighted features element by element to obtain preliminary encoding features; The post-processing process includes: Step A304: region normalization is performed on the preliminary encoding features, a lightweight denoising network is constructed, and the normalized features are input into the denoising network, and the denoising network is trained synchronously with the encoder to obtain denoised features; Step A305: add the denoised features and the preprocessed features element by element to obtain the final encoding features.

5. The method of claim 4, wherein the method is based on a geometric deep learning. In step A301, the geometric position sub-feature is the normalized initial three-dimensional coordinate vector, the dynamic sub-feature is the normalized initial three-dimensional velocity vector, and the attribute sub-feature is the combination of the region One-Hot encoding and the oil state One-Hot encoding, wherein the region One-Hot encoding is obtained based on the region label conversion, and the oil state One-Hot encoding is obtained based on the oil state label conversion. ​ 6. The method for predicting splash lubricating oil distribution based on geometric deep learning according to claim 1, characterized in that, In step A4, a physical graph module is used to generate a plurality of virtual physical nodes, obtain global physical constraint features by weighting with dynamic weights, and fuse the global physical constraint features with final encoding features to generate physical graph features. A local graph module is used to dynamically construct and update a local graph topology based on the correlation between the oil particle position and the viscous force, and to extract local graph features by attention weighting aggregation. The physical graph features and the local graph features are adaptively fused and superimposed on the final encoding features, and then normalized by a global layer to generate final graph features.

7. The method of claim 6, wherein the method is based on a geometric deep learning. The generated virtual physical nodes include viscous nodes, centrifugal force nodes, gravity nodes, surface tension nodes, shroud disturbance nodes, and temperature nodes, and the features of each virtual physical node are calculated based on physical laws and working condition parameters. ​ 8. The method of claim 1, wherein the method is based on a geometric deep learning. 8 The step A5 specifically includes the following sub-steps: Step A501: classifying working condition parameters to obtain continuous parameters and discrete parameters, normalizing the continuous parameters, encoding the discrete parameters, and then splicing them to obtain a working condition preprocessing vector, and mapping the working condition preprocessing vector to adapt to the subsequent encoding dimension to obtain a mapped feature; Step A502: constructing a conditional encoder, learning the correlation between the working condition and the oil distribution based on the mapped feature through the conditional encoder to obtain a basic conditional feature; Step A503: performing layer normalization on the basic conditional feature to obtain a normalized conditional feature, mapping the mapped feature to 256 dimensions again, and adding the mapped feature to the normalized conditional feature to obtain a final conditional feature.

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