A Method and Apparatus for Calculating the Performance of Water-Lubricated Bearings Based on Physics Information Neural Networks

Abstract

This invention provides a method and apparatus for calculating the performance of water-lubricated bearings based on a physical information neural network. The method includes: inputting relevant physical parameters of a water-lubricated bearing sample into a multilayer perceptron neural network to obtain a dimensionless pressure field within the water-lubricated bearing sample; the relevant physical parameters include dimensionless circumferential coordinates x and z. Based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample, the Reynolds equation residuals, absolute pressure non-negativity constraints, and boundary condition constraints are determined to obtain a total loss function; the multilayer perceptron neural network is trained based on the total loss function; the dimensionless circumferential coordinates x and z of a target water-lubricated bearing are input into the trained multilayer perceptron neural network to obtain the dimensionless pressure field within the target water-lubricated bearing; and performance indicators are calculated based on the dimensionless pressure field within the target water-lubricated bearing. This invention improves the efficiency and accuracy of bearing performance calculation.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering technology, and in particular to a method and apparatus for calculating the performance of water-lubricated bearings based on physical information neural networks. Background Technology

[0002] Water-lubricated bearings are crucial support components in ships and large machinery, and their performance directly impacts the stable operation of the equipment. With increasing demands for environmental friendliness and energy conservation in shipping and industrial equipment, water-lubricated bearings have gained widespread application due to their pollution-free and low-energy-consumption characteristics. However, under complex operating conditions, water-lubricated bearings are susceptible to factors such as speed fluctuations, load variations, and uneven lubrication, leading to problems like bearing wear and cavitation. Under the influence of these factors, how to quickly and accurately calculate and predict the performance of water-lubricated bearings remains a significant challenge in current technologies.

[0003] Traditional methods for analyzing the performance of water-lubricated bearings largely rely on empirical models or numerical simulations, which are time-consuming, computationally expensive, and have low accuracy. Calculating water-lubricated bearings using the traditional finite element method involves multiple steps, including preprocessing, iterative solving, and post-processing, requiring numerous iterations and complex mesh generation, resulting in long computation times and high computational resource consumption, making it difficult to handle large-scale calculations. Existing deep learning methods are mostly purely data-driven, essentially still fitting data, lacking physical extrapolation capabilities, and failing to consider the physical mechanisms of bearing performance, thus resulting in low prediction accuracy under complex operating conditions.

[0004] Existing methods generally suffer from low computational efficiency and low accuracy, often failing to quickly and accurately predict bearing performance, particularly in the calculation of load capacity, friction force, and friction coefficient, where significant deviations occur. Therefore, there is an urgent need for a prediction method that can consider physical laws while possessing high computational efficiency, in order to improve the speed and accuracy of performance calculations for water-lubricated bearings under complex operating conditions. Summary of the Invention

[0005] This invention provides a method and apparatus for calculating the performance of water-lubricated bearings based on a physical information neural network, which solves the problem of low efficiency and accuracy in the performance calculation of water-lubricated bearings under complex working conditions in the prior art, and improves the efficiency and accuracy of performance calculation of water-lubricated bearings under complex working conditions.

[0006] This invention provides a method for calculating the performance of water-lubricated bearings based on a physical information neural network, comprising:

[0007] The relevant physical parameters of the water-lubricated bearing sample are input into a multilayer perceptron neural network to obtain the dimensionless pressure field within the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z.

[0008] Based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample, determine the Reynolds equation residuals of the water-lubricated bearing sample;

[0009] The water-lubricated bearing sample is subjected to absolute pressure non-negativity constraint based on the dimensionless pressure field, and boundary condition constraint is applied to the water-lubricated bearing sample. The Reynolds equation residual, absolute pressure non-negativity constraint and boundary condition constraint are weighted and summed to determine the total loss function. The multilayer perceptron neural network is trained based on the total loss function.

[0010] The relevant physical parameters of the target water-lubricated bearing are input into the trained multilayer perceptron neural network to obtain the dimensionless pressure field inside the target water-lubricated bearing output by the multilayer perceptron neural network.

[0011] The performance indicators of the target water-lubricated bearing are calculated based on the dimensionless pressure field within the target water-lubricated bearing.

[0012] According to the present invention, a method for calculating the performance of water-lubricated bearings based on a physical information neural network is provided, wherein the dimensionless film thickness of the water-lubricated bearing sample is... The calculation formula is:

[0013] .

[0014] Where e is the eccentricity of the water-lubricated bearing sample.

[0015] According to the present invention, a method for calculating the performance of a water-lubricated bearing based on a physical information neural network determines the Reynolds equation residual of the water-lubricated bearing sample using the following formula based on the dimensionless pressure field and dimensionless film thickness of the sample. :

[0016]

[0017] Wherein, N is the number of water-lubricated bearing samples. The dimensionless film thickness of the water-lubricated bearing sample. The dimensionless pressure field of the water-lubricated bearing sample predicted by the multilayer perceptron neural network.

[0018] According to the present invention, a method for calculating the performance of water-lubricated bearings based on a physical information neural network applies an absolute pressure non-negativity constraint to the water-lubricated bearing sample using the following formula based on a first dimensionless pressure field:

[0019]

[0020] in, The absolute pressure is a non-negative constraint, and N is the number of water-lubricated bearing samples. The dimensionless pressure field output by the multilayer perceptron neural network is described. To prevent A preset constant that is zero.

[0021] According to the present invention, a method for calculating the performance of water-lubricated bearings based on a physical information neural network is provided, wherein the boundary conditions of the water-lubricated bearing sample are constrained by the following formula:

[0022]

[0023] in, The boundary condition constraints are defined as follows: N is the number of water-lubricated bearing samples, and P is the number of samples. b The dimensionless pressure on the four sides of the water-lubricated bearing sample. and These are the dimensionless circumferential coordinates and dimensionless axial coordinates on the four boundaries b of the k-th water-lubricated bearing sample, respectively.

[0024] According to the present invention, a method for calculating the performance of water-lubricated bearings based on a physical information neural network, wherein the multilayer perceptron neural network is trained according to the total loss function, further comprising:

[0025] The film thickness of the water-lubricated bearing sample is constrained to ensure that the film thickness of the water-lubricated bearing sample is always positive and physically feasible.

[0026] The dimensionless pressure field output by the multilayer perceptron neural network is constrained using the following formula to achieve absolute pressure non-negativity constraint on the water-lubricated bearing sample:

[0027]

[0028] in, The absolute pressure of the water-lubricated bearing sample. This is a function for converting between dimensionless and absolute pressure. By mapping the dimensionless pressure output by the neural network to the actual physical pressure range, it ensures that the values ​​are within a reasonable engineering range. It is a boundary constraint function that ensures that the pressure on the boundary is forced into environmental pressure, thereby achieving boundary condition correction.

[0029] According to the present invention, a method for calculating the performance of a water-lubricated bearing based on a physical information neural network is provided, wherein the performance indicators of the target water-lubricated bearing include load-bearing capacity, friction force, and friction coefficient.

[0030] The present invention also provides a device for calculating the performance of water-lubricated bearings based on physical information neural networks, comprising:

[0031] The sample prediction module is used to input the relevant physical parameters of the water-lubricated bearing sample into the multilayer perceptron neural network to obtain the dimensionless pressure field in the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z.

[0032] The model training module is used to determine the Reynolds equation residuals of the water-lubricated bearing sample based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample; to apply absolute pressure non-negativity constraints to the water-lubricated bearing sample based on the dimensionless pressure field, and to apply boundary condition constraints to the water-lubricated bearing sample; to determine the total loss function by weighted summation of the Reynolds equation residuals, absolute pressure non-negativity constraints, and boundary condition constraints; and to train the multilayer perceptron neural network based on the total loss function.

[0033] The target prediction module is used to input the relevant physical parameters of the target water-lubricated bearing into the trained multilayer perceptron neural network to obtain the dimensionless pressure field inside the target water-lubricated bearing output by the multilayer perceptron neural network.

[0034] The performance calculation module is used to calculate the performance indicators of the target water-lubricated bearing based on the dimensionless pressure field within the target water-lubricated bearing.

[0035] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the water-lubricated bearing performance calculation method based on physical information neural networks as described above.

[0036] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the water-lubricated bearing performance calculation method based on physical information neural networks as described above.

[0037] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the water-lubricated bearing performance calculation method based on physical information neural networks as described above.

[0038] The present invention provides a method and apparatus for calculating the performance of water-lubricated bearings based on physical information neural networks. By introducing physical prior formulas as physical constraints, it combines physical laws with deep learning, thereby improving the stability and accuracy of the calculation model and enabling efficient and accurate calculation of the performance of water-lubricated bearings under complex working conditions. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating the method for calculating the performance of water-lubricated bearings based on physical information neural networks provided by this invention.

[0041] Figure 2 This is a schematic diagram of the physical information-based neural network structure in the physical information-based neural network performance calculation method for water-lubricated bearings provided by the present invention;

[0042] Figure 3 This is a schematic diagram showing the change of sampling point distribution with training rounds in the water-lubricated bearing performance calculation method based on physical information neural network provided by the present invention;

[0043] Figure 4 This is a schematic diagram illustrating the change of Reynolds residual with the number of iterations in the water-lubricated bearing performance calculation method based on physical information neural network provided by this invention;

[0044] Figure 5 This is a schematic diagram of the residual distribution of the Reynolds equation in the water-lubricated bearing performance calculation method based on physical information neural network provided by the present invention;

[0045] Figure 6 This is a schematic diagram of the dimensionless pressure distribution of a water-lubricated bearing in the performance calculation method of a water-lubricated bearing based on a physical information neural network provided by the present invention.

[0046] Figure 7 This is a schematic diagram of the structure of the water-lubricated bearing performance calculation device based on physical information neural network provided by the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0048] The following is combined Figure 1The present invention describes a method for calculating the performance of water-lubricated bearings based on a physical information neural network, comprising:

[0049] Step 101: Input the relevant physical parameters of the water-lubricated bearing sample into the multilayer perceptron neural network to obtain the dimensionless pressure field in the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z.

[0050] Step 102: Determine the Reynolds equation residual of the water-lubricated bearing sample based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample; apply absolute pressure non-negativity constraints to the water-lubricated bearing sample based on the first dimensionless pressure field, and apply boundary condition constraints to the water-lubricated bearing sample; calculate the total loss function by weighted summation of the Reynolds equation residual, absolute pressure non-negativity constraints, and boundary condition constraints; and train the multilayer perceptron neural network based on the total loss function.

[0051] Step 103: Input the relevant physical parameters of the target water-lubricated bearing into the trained multilayer perceptron neural network to obtain the dimensionless pressure field inside the target water-lubricated bearing output by the multilayer perceptron neural network.

[0052] Step 104: Calculate the performance indicators of the target water-lubricated bearing based on the dimensionless pressure field within the target water-lubricated bearing.

[0053] In recent years, with the rapid iteration and upgrading of artificial intelligence, AI-based fluid dynamics simulation has also flourished. AI-driven scientific research has become the fifth paradigm driving technological innovation, but its application in fluid dynamics calculations for water-lubricated bearings is still in its early stages. Currently, data-driven neural networks heavily rely on data for training when dealing with water-lubricated bearing calculation problems, neglecting physical laws. This often leads to a certain deviation between the predicted and actual results and weak generalization ability.

[0054] The method based on physical information neural networks proposed in this embodiment combines the function approximation capability of traditional neural networks and directly integrates known physical laws into the training of the neural network. During the training process, physical constraints are constructed by introducing the control equations, boundary conditions, and initial conditions of physical laws. Error calculation can also be performed using observation data, enabling rapid solutions in the absence of mesh, limited data, or no data.

[0055] First, define the physical characteristics of the water-lubricated bearing, including its geometric parameters: journal radius. Bearing length L and radial clearance C, shaft surface linear velocity Lubricating medium properties: density ρ and viscosity And other related physical parameters.

[0056] By introducing dimensionless variables to address the characteristics of fluids in lubricated bearings, the units of physical quantities such as pressure, film thickness, and velocity in water-lubricated bearings are converted into dimensionless quantities using an appropriate scale. This reduces the range of variables that need to be processed and unifies different physical systems under a standard framework.

[0057] A dimensionless pressure coefficient is introduced when calculating the loss in the Reynolds equation: Introducing a dimensionless coefficient for film thickness: Dimensionless pressure It is used to represent the pressure distribution within the bearing, where x and z are dimensionless circumferential and axial coordinates, respectively.

[0058] To predict the performance of water-lubricated bearings, particularly pressure distribution, this embodiment employs a multilayer perceptron (MLP) neural network architecture and guides the network training with physical information. Figure 2 As shown, the network structure is as follows:

[0059] Input layer: The input to the neural network is the dimensionless coordinates x and z of the bearing, that is, the input features are (x, z), which represent the spatial location of the pressure distribution inside the bearing.

[0060] Hidden layers: The network contains multiple hidden layers, each using the Tanh activation function to ensure that the network can learn complex nonlinear relationships.

[0061] Output layer: The network output is a dimensionless pressure field, representing the pressure distribution within the bearing. The pressure field predicted by the model will be used for subsequent performance calculations.

[0062] To ensure the neural network's output conforms to physical laws and accurately predicts bearing performance, this embodiment designs a physical information-driven loss function. The loss function comprises three main parts: the Reynolds equation residuals (…). Absolute pressure nonnegativity constraint and boundary condition constraints The total loss function is a weighted sum of the Reynolds equation residuals, the absolute pressure nonnegativity constraint, and the boundary condition constraint.

[0063] The Adam optimization algorithm can be used for network training. The training process includes the following steps:

[0064] Data sampling: Uniform sampling is performed within a unit grid to generate dimensionless coordinates. and A sample dataset was created to ensure that the data covered the entire computational domain of the bearing. These sample points were used to train the neural network, enabling it to make accurate predictions under different operating conditions.

[0065] Training: The neural network was trained for 9000 iterations using the Adam optimization algorithm, with a learning rate set to [value missing]. Minimize the total loss function during training. The network parameters are optimized. The total loss function includes a weighted sum of the residuals of the Reynolds equation, the absolute pressure non-negativity constraint, and the boundary condition constraints, ensuring that the pressure field output by the network conforms to physical laws. The distribution of sampling points changes with the training epochs as follows: Figure 3 As shown, the Reynolds residual changes with the number of iterations as follows: Figure 4 As shown, the distribution of Reynolds residuals in different regions of the water film is as follows: Figure 5 As shown.

[0066] Hard constraint application: The network output corrects the film thickness and pressure through physical constraints to ensure that the output pressure distribution conforms to physical laws.

[0067] This embodiment's physics-based neural network method combines the advantages of both physics-driven and data-driven approaches. However, most existing purely data-driven methods use neural networks as their model architecture, and neural networks themselves suffer from weak model generalization ability and high uncertainty in prediction results. This uncertainty may be introduced into the computational model, leading to a decrease in the accuracy of the prediction results.

[0068] The beneficial effects of this embodiment are as follows: For the problem of solving water-lubricated bearings, this embodiment introduces physical prior formulas as physical constraints, combines physical laws with deep learning, improves the stability and accuracy of the calculation model, and can efficiently and accurately calculate the performance of water-lubricated bearings under complex working conditions.

[0069] Based on the above embodiments, the dimensionless film thickness of the water-lubricated bearing sample in this embodiment... The calculation formula is:

[0070] .

[0071] Where e is the eccentricity of the water-lubricated bearing sample.

[0072] Based on the above embodiments, this embodiment determines the Reynolds equation residual of the water-lubricated bearing sample using the following formula, based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample. :

[0073]

[0074] Wherein, N is the number of water-lubricated bearing samples. The dimensionless film thickness of the water-lubricated bearing sample. The dimensionless pressure field of the water-lubricated bearing sample predicted by the multilayer perceptron neural network.

[0075] The Reynolds equation describes the change in pressure distribution within a water-lubricated bearing, and its form is:

[0076]

[0077] The loss function constrains the pressure field output by the network by calculating the residuals of the Reynolds equations, ensuring that it conforms to the laws of fluid dynamics.

[0078] Based on the above embodiments, this embodiment applies an absolute pressure non-negativity constraint to the water-lubricated bearing sample according to the first dimensionless pressure field using the following formula:

[0079]

[0080] in, The absolute pressure is a non-negative constraint, and N is the number of water-lubricated bearing samples. The dimensionless pressure field output by the multilayer perceptron neural network is described. To prevent A preset constant that is zero.

[0081] To ensure that the absolute pressure within the bearing is always positive, this embodiment adds a non-negative absolute pressure constraint to the loss function. This constraint forces the neural network to ensure that its output absolute pressure is always positive, conforming to physical constraints.

[0082] Based on the above embodiments, this embodiment applies boundary condition constraints to the water-lubricated bearing sample using the following formula:

[0083]

[0084] in, The boundary condition constraints are defined as follows: N is the number of water-lubricated bearing samples, and P is the number of samples. b The dimensionless pressure is located on the four sides of the water-lubricated bearing sample.

[0085] In the physical model of a water-lubricated bearing, the boundary conditions require that the pressure on the bearing's four boundaries must be the ambient pressure. To ensure this physical requirement, boundary condition constraint terms are added to the loss function. .

[0086] The total loss function is a weighted sum of the Reynolds equation residuals, the absolute pressure nonnegativity constraint, and the boundary condition constraints:

[0087]

[0088] in, , , and To balance the hyperparameters of various losses, the training process of the network is optimized by adjusting these parameters so that the pressure field output by the network not only conforms to the Reynolds equation, but also satisfies the physical requirement of nonnegativity of pressure, and strictly adheres to the boundary conditions. For measurement data, if the total loss function Less than the set threshold If the training is successful, the trained multilayer perceptron neural network is obtained; otherwise, the training of the multilayer perceptron neural network continues.

[0089] Based on the above embodiments, this embodiment further includes training the multilayer perceptron neural network according to the total loss function, and also includes:

[0090] Film thickness of water-lubricated bearings It is determined by the eccentricity and dimensionless circumferential coordinates Decision-making is defined as:

[0091]

[0092] Since film thickness is a key factor affecting bearing performance, it is closely related to the distribution of the pressure field. To ensure that the film thickness is reasonable and physically realistic throughout the entire computational domain, the neural network output needs to be corrected using physical equations to ensure that the film thickness is always positive and physically feasible.

[0093] For absolute pressure in lubricated bearings Physically, it is required that it is always greater than or equal to zero, i.e., absolute pressure. To ensure this, this embodiment enforces the absolute pressure non-negativity constraint as a hard constraint. Specifically, the pressure predicted by the network... The following hard constraints are applied in each training step:

[0094]

[0095] in, The absolute pressure of the water-lubricated bearing sample. This is a function for converting between dimensionless pressure and absolute pressure. This is a boundary constraint function that ensures the pressure on the boundary is forced to conform to ambient pressure, thus achieving boundary condition correction. Applying this constraint to the pressure field output by the network ensures that the bearing pressure distribution not only conforms to the fluid dynamics model but also guarantees the accuracy of the boundary conditions.

[0096] For the boundary conditions around the bearing, physics requires that the pressure at the circumferential and axial boundaries must be ambient pressure. To achieve this, the network multiplies the output pressure field by the boundary constraint function. This is used for calibration. This hard constraint, through physical guidance, ensures that the pressure at the bearing boundary is always ambient pressure, conforming to actual physical conditions.

[0097] During training, by enforcing these physical constraints, the pressure field output by the neural network not only satisfies the dynamic characteristics of the Reynolds equations but also conforms to actual physical boundary conditions, preventing the network from generating unrealistic negative pressure values ​​or excessive pressure fluctuations. By embedding physical constraints into the loss function and training process, this embodiment significantly improves the network's prediction accuracy and ensures the physical consistency of the results.

[0098] Through these hard constraints, this embodiment ensures that the neural network always adheres to physical laws when solving the performance calculation problem of water-lubricated bearings, outputting a physically feasible and accurate pressure distribution. This process enhances the model's credibility and application value, especially in providing reliable physical evidence for real-time performance prediction under complex operating conditions.

[0099] Based on the above embodiments, the performance indicators of the target water-lubricated bearing in this embodiment include load-bearing capacity, friction force, and coefficient of friction.

[0100] After training, this invention evaluates bearing performance by assessing the pressure distribution on a regular grid and calculating bearing performance indicators, including load-bearing capacity, through numerical integration. ), friction ( ) and coefficient of friction ( ).like Figure 6 As shown, the contour plot illustrates the dimensional pressure distribution and the residuals of the Reynolds equation, evaluating the model's performance under different operating conditions.

[0101] The following bearing performance parameters are calculated by integrating the pressure field value:

[0102] Bearing capacity represents the total load borne by a bearing; it is the resultant force of all compressive forces acting on the bearing. Its calculation formula is:

[0103]

[0104] in, For the pressure distribution within the bearing, and These are the length of the bearing and the circumferential arc length, respectively.

[0105] Friction force represents the force generated by friction in the bearing's load-bearing capacity. It is assumed that the shear force within the bearing follows the Couette shear model. Its calculation formula is:

[0106]

[0107] in, For shear stress, its form is: .

[0108] The coefficient of friction is the ratio of frictional force to bearing capacity, used to evaluate the frictional performance of a bearing. Its calculation formula is:

[0109]

[0110] in, For friction, For load-bearing capacity.

[0111] By comparing with traditional finite element methods and other data-driven methods, the significant advantages of this method in terms of computational efficiency, prediction accuracy, and physical interpretability are verified. Experimental results show that this invention can accurately predict the load-bearing capacity, friction force, and friction coefficient of water-lubricated bearings, while significantly improving computational efficiency.

[0112] The following describes the water-lubricated bearing performance calculation device based on physical information neural network provided by the present invention. The water-lubricated bearing performance calculation device based on physical information neural network described below and the water-lubricated bearing performance calculation method based on physical information neural network described above can be referred to in correspondence.

[0113] like Figure 7 As shown, the device includes a sample prediction module 701, a model training module 702, a target prediction module 703, and a performance calculation module 704, wherein:

[0114] The sample prediction module 701 is used to input the relevant physical parameters of the water-lubricated bearing sample into the multilayer perceptron neural network to obtain the dimensionless pressure field in the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z.

[0115] The model training module 702 is used to determine the Reynolds equation residual of the water-lubricated bearing sample based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample; to apply absolute pressure non-negativity constraints to the water-lubricated bearing sample based on the dimensionless pressure field, and to apply boundary condition constraints to the water-lubricated bearing sample; to determine the total loss function by weighted summation of the Reynolds equation residual, absolute pressure non-negativity constraints, and boundary condition constraints; and to train the multilayer perceptron neural network based on the total loss function.

[0116] The target prediction module 703 is used to input the relevant physical parameters of the target water-lubricated bearing into the trained multilayer perceptron neural network to obtain the dimensionless pressure field in the target water-lubricated bearing output by the multilayer perceptron neural network.

[0117] The performance calculation module 704 is used to calculate the performance index of the target water-lubricated bearing based on the dimensionless pressure field inside the target water-lubricated bearing.

[0118] This embodiment introduces a priori physical formulas as physical constraints, combining physical laws with deep learning to improve the stability and accuracy of the computational model, enabling efficient and precise calculation of the performance of water-lubricated bearings under complex working conditions.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the performance of water-lubricated bearings based on physical information neural networks, characterized in that, include: The relevant physical parameters of the water-lubricated bearing sample are input into a multilayer perceptron neural network to obtain the dimensionless pressure field within the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z. Based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample, determine the Reynolds equation residuals of the water-lubricated bearing sample; The water-lubricated bearing sample is subjected to absolute pressure non-negativity constraint based on the dimensionless pressure field, and boundary condition constraint is applied to the water-lubricated bearing sample. The Reynolds equation residual, absolute pressure non-negativity constraint and boundary condition constraint are weighted and summed to determine the total loss function. The multilayer perceptron neural network is trained based on the total loss function. The relevant physical parameters of the target water-lubricated bearing are input into the trained multilayer perceptron neural network to obtain the dimensionless pressure field inside the target water-lubricated bearing output by the multilayer perceptron neural network. Calculate the performance indicators of the target water-lubricated bearing based on the dimensionless pressure field within the target water-lubricated bearing; The dimensionless film thickness of the water-lubricated bearing sample The calculation formula is: ； Where e is the eccentricity of the water-lubricated bearing sample; The Reynolds equation residuals for the water-lubricated bearing sample are determined using the following formula based on the dimensionless pressure field and dimensionless film thickness of the sample. : ； Wherein, N is the number of water-lubricated bearing samples. The dimensionless film thickness of the water-lubricated bearing sample. The dimensionless pressure field of the water-lubricated bearing sample predicted by the multilayer perceptron neural network. The water-lubricated bearing sample is subjected to an absolute pressure non-negativity constraint based on the dimensionless pressure field using the following formula: ； in, The absolute pressure is a non-negative constraint, and N is the number of water-lubricated bearing samples. The dimensionless pressure field output by the multilayer perceptron neural network is described. To prevent A preset constant that is zero; The boundary conditions for the water-lubricated bearing sample are constrained using the following formula: ； in, The boundary condition constraints are defined as follows: N is the number of water-lubricated bearing samples, and P is the number of samples. b Let P be the dimensionless pressure on the four edges of the water-lubricated bearing sample, and let P be the absolute pressure of the water-lubricated bearing sample. and These are the dimensionless circumferential coordinates and dimensionless axial coordinates on the four boundaries b of the k-th water-lubricated bearing sample, respectively.

2. The method for calculating the performance of water-lubricated bearings based on physical information neural networks according to claim 1, characterized in that, Training the multilayer perceptron neural network according to the total loss function further includes: The film thickness of the water-lubricated bearing sample is constrained to ensure that the film thickness of the water-lubricated bearing sample is always positive and physically feasible. The dimensionless pressure field output by the multilayer perceptron neural network is constrained using the following formula to achieve absolute pressure non-negativity constraint on the water-lubricated bearing sample: ； in, This refers to the absolute pressure after the water-lubricated bearing is constrained. This is a function for converting between dimensionless pressure and absolute pressure. It is a boundary constraint function that ensures that the pressure on the boundary is forced into environmental pressure, thereby achieving boundary condition correction.

3. The method for calculating the performance of water-lubricated bearings based on physical information neural networks according to claim 1, characterized in that, The performance indicators of the target water-lubricated bearing include load capacity, friction force, and coefficient of friction.

4. A device for calculating the performance of water-lubricated bearings based on a physical information neural network, characterized in that, The method for calculating the performance of water-lubricated bearings based on physical information neural networks, as described in any one of claims 1-3, includes: The sample prediction module is used to input the relevant physical parameters of the water-lubricated bearing sample into the multilayer perceptron neural network to obtain the dimensionless pressure field in the water-lubricated bearing sample output by the multilayer perceptron neural network. The relevant physical parameters include dimensionless circumferential coordinate x and dimensionless axial coordinate z. The model training module is used to determine the Reynolds equation residuals of the water-lubricated bearing sample based on the dimensionless pressure field and dimensionless film thickness of the water-lubricated bearing sample; to apply absolute pressure non-negativity constraints to the water-lubricated bearing sample based on the dimensionless pressure field, and to apply boundary condition constraints to the water-lubricated bearing sample; to determine the total loss function by weighted summation of the Reynolds equation residuals, absolute pressure non-negativity constraints, and boundary condition constraints; and to train the multilayer perceptron neural network based on the total loss function. The target prediction module is used to input the relevant physical parameters of the target water-lubricated bearing into the trained multilayer perceptron neural network to obtain the dimensionless pressure field inside the target water-lubricated bearing output by the multilayer perceptron neural network. The performance calculation module is used to calculate the performance indicators of the target water-lubricated bearing based on the dimensionless pressure field inside the target water-lubricated bearing. The dimensionless film thickness of the water-lubricated bearing sample The calculation formula is: ； Where e is the eccentricity of the water-lubricated bearing sample.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the water-lubricated bearing performance calculation method based on physical information neural network as described in any one of claims 1 to 3.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the performance of water-lubricated bearings based on a physical information neural network as described in any one of claims 1 to 3.

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