A method for simulating and optimizing design of dynamic characteristics of fluid dynamic pressure bearing based on extended physical information neural network

Abstract

The application discloses a kind of based on extended physical information neural network fluid dynamic pressure bearing dynamic characteristic simulation and optimization design method, it is related to high-end equipment manufacturing and computational fluid dynamics field.The method comprises the following steps: constructing extended physical information neural network model, the model is with bearing surface coordinates as input, and the gas film pressure field of corresponding coordinate is output;Define composite loss function, the loss function is used to guide the parameter optimization of the model;The neural network model is trained using training strategy until the composite loss function converges, to obtain the proxy model of the relationship between pressure field and coordinate;Based on the proxy model, the dynamic characteristic coefficient of bearing is calculated by applying virtual disturbance.The above-mentioned method of the application can greatly improve the calculation efficiency of dynamic pressure bearing dynamic characteristics under the premise of ensuring sufficient accuracy, obtain analytical solution easy to analyze and optimize, so as to break the performance bottleneck of traditional method.

Description

Technical Field

[0001] This invention relates to the fields of high-end equipment manufacturing and computational fluid dynamics, specifically to a method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks. Background Technology

[0002] Hydrostatic gas bearings are widely used in advanced equipment due to their unique advantages. Their dynamic characteristics (stiffness and damping) are the core determinants of rotor system performance. Traditional simulation methods (such as FDM and FEM) suffer from strong mesh dependence, high computational cost, and difficulty in convergence under extreme conditions. While the emerging Physical Information Neural Network (PINN) offers the possibility of meshless solutions, standard PINN still faces challenges such as insufficient accuracy and weak physical consistency when dealing with complex problems like gas bearings that exhibit multi-scale and strongly nonlinear physical phenomena. For example, it is difficult to capture drastic changes in the pressure field near the orifice, and weak physical constraints may cause training to converge to non-physical solutions.

[0003] Traditional methods for analyzing the dynamic characteristics of hydrodynamic bearings, such as the finite difference method (FDM) and the finite element method (FEM), while relatively reliable in terms of solution accuracy, suffer from the following core technical limitations: High computational cost: These methods rely on fine mesh generation, and the solution process involves iterative solutions to large-scale linear or nonlinear equations. For each perturbation (displacement or velocity), the entire pressure field needs to be recalculated, resulting in huge computational loads and high time costs.

[0004] Inefficient optimization design: In the optimization design process of bearings, a large number of different design parameters (such as geometric dimensions and operating conditions) need to be evaluated. Traditional methods require a complete numerical solution for each evaluation, which becomes a serious bottleneck in optimization iteration, making large-scale, multi-objective parameter optimization impractical.

[0005] The resulting form is not conducive to coupled analysis: traditional methods yield numerical solutions at discrete grid points, rather than analytical functions. This necessitates numerical differencing to obtain information such as pressure gradients, potentially introducing additional errors, and is not conducive to efficient and accurate coupled solutions with the control equations of other systems, such as rotor dynamics.

[0006] Therefore, there is an urgent need in this field for a novel technical solution that can significantly improve the computational efficiency of the dynamic characteristics of hydrodynamic bearings while ensuring sufficient accuracy, and obtain analytical solutions that are easy to analyze and optimize, thereby breaking through the performance bottleneck of traditional methods. Summary of the Invention

[0007] The purpose of this invention is to address the above-mentioned problems by providing a simulation and optimization design method for the dynamic characteristics of hydrodynamic bearings based on an extended physical information neural network (ePINN). This method can significantly improve the computational efficiency of the dynamic characteristics of hydrodynamic bearings while ensuring sufficient accuracy, and obtain analytical solutions that are easy to analyze and optimize, thereby breaking through the performance bottleneck of traditional methods.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A simulation and optimization design method for the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks includes: An extended physical information neural network model is constructed, which takes the bearing surface coordinates as input and outputs the air film pressure field at the corresponding coordinates. Define a composite loss function, which is used to guide the parameter optimization of the model; The neural network model is trained using a training strategy until the composite loss function converges, resulting in a surrogate model representing the relationship between the pressure field and the coordinates. Based on the aforementioned proxy model, the dynamic characteristic coefficients of the bearing are calculated by applying virtual disturbances.

[0009] As a preferred technical solution: The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks includes, in part, constructing an extended physical information neural network model, comprising: The bearing surface coordinates are mapped into a high-dimensional feature vector through Fourier feature encoding. The feature vector contains the original coordinates and multiple sets of sine and cosine terms. A main network is constructed, which receives the feature vector and operating parameters and outputs the air film pressure field. Construct a Hamiltonian structure, which includes a kinetic energy network and a potential energy network, and output an energy component related to the pressure field. A pressure field conforming to physical constraints is generated through the collaborative prediction of the main network and the Hamiltonian structure.

[0010] The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, wherein the definition of the composite loss function includes: Calculate the physical residual loss of the Reynolds equation, which is based on the mean square error of the network-predicted pressure when substituted into the Reynolds equation; Calculate the boundary condition loss, which is based on the mean square error of the difference between the network-predicted pressure and the actual boundary pressure. Calculate the source term loss of the throttling orifice, the loss being based on the gas choke flow theory to set a weighted expected pressure for the region near the throttling orifice; Calculate the Hamiltonian energy loss, which constrains the consistency of the prediction results between the main network and the Hamiltonian structure, as well as energy conservation.

[0011] The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, wherein training the neural network model using a training strategy includes: During the pre-training phase, fundamental physical laws are learned by optimizing the residual loss of the Reynolds equation. During the boundary constraint reinforcement phase, the weight of the boundary condition loss is increased to fit the boundary constraints. During the optimization phase of the orifice effect, the focus is on the orifice source term loss to fit the region of drastic pressure changes; During the global fine-tuning phase, the weights of all loss items are balanced for refined optimization. Monitor the loss on the validation set. If the loss does not improve after multiple iterations, terminate the training early to obtain the optimal model state.

[0012] The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, wherein calculating the dynamic characteristic coefficients of the bearing based on the surrogate model includes: The bearing capacity at the equilibrium position is calculated based on the aforementioned proxy model; By applying a small displacement perturbation, the pressure field after the perturbation is estimated using a priori physical formula based on the thickness of the air film after the perturbation. The stiffness coefficient is calculated based on the change in bearing capacity using the finite difference method. Based on the stiffness coefficient, rotational speed, and compression number, the damping coefficient is calculated using an empirical estimation model; Check the positive definiteness of the damping coefficient matrix; if it is not satisfied, correct it to an effective matrix through mathematical transformation.

[0013] The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, wherein the Fourier feature encoding mapping is a high-dimensional feature vector, including: Obtain the two-dimensional coordinates of the bearing surface; For the two-dimensional coordinates, generate a feature vector containing the original coordinates and multiple sets of sine and cosine terms of different frequencies; Adjusting frequency parameters to enhance the representation of high-frequency details in periodic pressure fields; The feature vector is concatenated with the running parameters and used as the input to the main network.

[0014] The above-described method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks includes, in which the calculation of the orifice source term loss includes: Determine the center position of the throttle orifice; For sampling points near the throttle orifice, the theoretical expected pressure is calculated based on the relative distance from the center position; Based on the gas choke flow theory, a weighted expected pressure distribution is set to determine whether the critical pressure ratio has been reached. The weighted mean square error between the network-predicted pressure and the expected pressure is calculated, with the weights decreasing exponentially as the sampling point moves further away from the center of the orifice.

[0015] Another objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on an extended physical information neural network.

[0016] Another objective of this invention is to provide an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the aforementioned method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks.

[0017] Beneficial effects: 1. Extremely high computational efficiency: Once the neural network is trained, its forward inference speed is extremely fast. In particular, the efficient dynamic coefficient calculation method proposed in this invention simplifies the multiple processes that require repeated PDE solving in traditional methods into one model inference and several algebraic estimations, improving the computational efficiency of dynamic characteristic analysis by 1-2 orders of magnitude, laying the foundation for large-scale optimization design.

[0018] 2. Obtaining an analytical solution: The pressure field output by this invention is an analytical function that is differentiable everywhere, represented by a neural network. This allows important physical quantities such as pressure gradient and shear force to be accurately calculated through automatic differentiation, avoiding numerical difference errors in traditional discretization methods and improving solution accuracy.

[0019] 3. Powerful parametric analysis capabilities: A well-trained ePINN model is essentially a high-performance surrogate model, capable of instantaneously predicting bearing performance under any given operating parameters (eccentricity, speed, etc.). This makes performing full-parameter domain performance scans, sensitivity analyses, and stability analyses effortless.

[0020] 4. Easy to integrate with optimization algorithms: Due to its extremely high evaluation speed and differentiable characteristics, this method can be seamlessly combined with various advanced optimization algorithms (such as gradient descent, genetic algorithm, reinforcement learning, etc.) to achieve efficient and global optimization design of bearing structure and operating parameters.

[0021] In summary, this invention provides a complete, efficient, and accurate new solution for the design and analysis of high-precision hydrostatic gas bearings, which has significant theoretical research value and broad engineering application prospects. Attached Figure Description

[0022] Figure 1 This is a schematic diagram illustrating the overall process of the method described in this invention.

[0023] Figure 2 This is a schematic diagram illustrating the structure of the extended physical information neural network used in this invention, including a Fourier feature encoding module, a main network, and a Hamiltonian structure.

[0024] Figure 3 This is a pressure field contour map generated according to a specific embodiment of the present invention.

[0025] Figure 4 This is a contour map of air film thickness generated according to a specific embodiment of the present invention.

[0026] Figure 5 This is a three-dimensional view of the pressure field generated according to a specific embodiment of the present invention.

[0027] Figure 6 This is a curve showing the change of stiffness coefficient with eccentricity, generated according to a specific embodiment of the present invention.

[0028] Figure 7 This is a curve showing the damping coefficient as a function of eccentricity, generated according to a specific embodiment of the present invention.

[0029] Figure 8 This invention generates the Reynolds equation residuals according to a specific embodiment of the present invention.

[0030] Figure 9 This invention relates to a specific embodiment of the invention, which generates a loss function decomposition graph of the training process.

[0031] Figure 10 This is a stability analysis diagram of a rotor system according to a specific embodiment of the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0033] This invention provides a simulation and optimization design method for the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks. It utilizes the powerful function approximation capability of deep neural networks to construct a surrogate model that directly maps operating parameters to the pressure field, and embeds the Reynolds equation, which controls the physical process, as a "soft constraint" into the network training process, thereby obtaining a fast, accurate solution in the form of an analytical function.

[0034] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0035] refer to Figure 1 This embodiment provides a method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, including the following steps: a) Construct an extended physical information neural network model, wherein the model receives the coordinates of the bearing surface as input and outputs the pressure corresponding to the coordinates; wherein the coordinates are subjected to Fourier feature encoding before being input into the model to enhance the expression of high-frequency information; b) Define a composite loss function to guide the parameter optimization of the model in training step c), wherein the composite loss function includes at least: Reynolds equation physical residual loss, boundary condition loss, and source term loss for bearing throttle orifice; c) Train the neural network model using a training strategy until the composite loss function converges, thereby obtaining a surrogate model that can characterize the relationship between the pressure field and the coordinates; d) Using the trained surrogate model, calculate the dynamic characteristic coefficients of the bearing by applying virtual perturbations.

[0036] For example, the specific technical solution of the present invention is as follows: Step a): Construction of the extended physical information neural network The core of this invention is a deep neural network surrogate model designed to accurately map the geometric coordinates of a bearing surface to its corresponding pressure distribution. In a typical embodiment, the model consists of several cooperating modules, and the weights of all network layers are initialized using the mature Glorot method to promote stable convergence in the early stages of training: Fourier Feature Encoding Module: This module is the core of data preprocessing. It elevates the input two-dimensional physical coordinates (φ, λ) to a higher-dimensional feature space. Specifically, a coordinate point is mapped to a vector containing its original value and multiple sets (e.g., 16 sets) of Fourier feature basis function values ​​at different frequencies. The specific form of this vector is [φ, λ, sin(φ), cos(φ), sin(2φ), cos(2φ), ..., sin(kφ), cos(kφ)]. This preprocessing method greatly enhances the network's ability to fit high-frequency signals.

[0037] Network main body: Main Net: As the core of the stress prediction, it is a deep, fully connected neural network. For example, it can be a structure with four hidden layers, where the number of neurons in each layer can be set to 64, 128, 128, or 64, and the hyperbolic tangent function (tanh) can be used uniformly as the activation function to handle nonlinear problems.

[0038] Hamiltonian Structure: This structure, serving as a key guarantee of physical consistency, consists of a kinetic network and a potential network operating in parallel. Both networks can employ relatively shallow structures (e.g., each containing two hidden layers with 32 neurons each), and both use the tanh activation function. They respectively learn the energy components associated with the pressure field.

[0039] Step b): Design of the composite loss function To ensure that the training process of the neural network strictly adheres to the laws of physics, this invention constructs a composite loss function. This function is a weighted sum of multiple physical constraint terms, and the weight coefficients of each term can be dynamically adjusted during training. Its main components are as follows: Reynolds equation residual loss: This term is crucial for ensuring the model satisfies the governing equations. It consists of three sub-terms: Partial Differential Equation (PDE) Residuals: The pressure P predicted by the main network and its multiple derivatives obtained efficiently through automatic differentiation techniques are substituted into the dimensionless Reynolds equation. The mean square error (MSE) of the residuals of this equation constitutes the main body of this loss.

[0040]

[0041] Positive pressure physical constraint: Penalize all predicted values ​​below ambient pressure (dimensionless 1) by means of a modified linear unit function (ReLU).

[0042] Solution smoothness constraint: By penalizing the sum of squares of the pressure field gradient, non-physical high-frequency oscillations that may occur in the solution are suppressed, prompting the model to generate smoother solutions that are more in line with physical intuition.

[0043] Boundary condition loss: This loss term is used to ensure the correctness of the solution at the boundary of the computational domain. It not only requires that the pressure at the bearing end face (axial boundary) equals the ambient pressure, but also imposes stricter requirements on the circumferential periodic boundary: not only must the pressure value be continuous, but its first derivative (i.e., the pressure gradient) must also be continuous.

[0044] Orifice Source Term Loss: This term is crucial for accurately simulating the orifice effect. The loss function is constructed independently of experimental data, based on fundamental gas dynamics theory. First, the center position of the orifice is determined according to its geometric layout. Then, for any sampling point near the orifice, a theoretically desired pressure is calculated based on its relative position to the nearest orifice center, considering whether gas congestion occurs (i.e., whether a critical pressure ratio, such as 0.528, is reached). The loss function is ultimately defined as the weighted mean square error between the network-predicted pressure and this desired pressure, where the weights decrease exponentially as the sampling point moves away from the orifice center, thus achieving precise focusing on the physical behavior of this core region of the orifice.

[0045] Hamiltonian energy loss: This loss term is used to apply the fundamental physical law of conservation of energy and consists of two parts: Consistency loss: Ensures that the pressure directly predicted by the main network is numerically consistent with the total energy indirectly predicted by the kinetic and potential energy networks.

[0046] Conservation loss: penalizes the variance of the total energy over the entire computational domain, forcing it to approach a constant, which directly corresponds to the energy conservation in the physical system.

[0047] Step c): Multi-stage training strategy In order to efficiently and stably solve the above-mentioned highly complex, non-convex optimization problem, this invention adopts a multi-stage "course learning" training paradigm and integrates a series of mature training techniques.

[0048] Training phase division: Taking a total of 20,000 iterations as an example, the entire training process is divided into four progressive phases: Phase 1: Learning Fundamental Physics (Iterations 0-4000). In this phase, terms related to the Reynolds equation and Hamiltonian energy dominate the weights in the loss function, enabling the network to focus on learning the fundamental physical laws described by the governing equations.

[0049] Phase Two: Forced Boundary Conditions (Iterations 4001-10000). This phase significantly increases the weight of the boundary condition loss, guiding the network to accurately fit the boundary constraints given a grasp of the underlying physics.

[0050] Phase 3: Focus on core components (10001-14000 iterations). After satisfying the macroscopic laws and boundary conditions, the focus of optimization will shift to the source term loss of the throttling orifice, concentrating on overcoming the fitting problem of drastic pressure changes near the throttling orifice.

[0051] Phase Four: Global Fine-Tuning (14,001-20,000 iterations). Finally, the weights of all loss terms are regressed to a relatively balanced level, performing global and fine-tuned optimization of the entire model.

[0052] Technologies to ensure the success of the training process: Optimizer: The adaptive momentum estimation (Adam) optimizer is adopted, and its hyperparameters, such as the first and second moment estimates of the control momentum and learning rate adaptation, and the decay rate, are all set to robust values ​​recognized in the field.

[0053] Learning rate scheduling: A strategy combining "warm-up and periodic cosine annealing" is adopted. In the early stage of training, the learning rate is linearly "warmed up" from a small value to a set peak value to ensure the stability of the start-up; then, the learning rate is smoothly decayed and reset in the form of a cosine function in each cycle. This strategy helps the model effectively explore the complex terrain of the loss function and escape local optima.

[0054] Gradient clipping: Before each parameter update, the norm of the calculated gradient vector is checked. If it exceeds a preset threshold (e.g., 2.0), it is normalized. This technique effectively prevents gradient explosion caused by individual batches of data, thus ensuring stability throughout the training process.

[0055] Early stopping mechanism and optimal model saving: During training, the system continuously monitors the loss on the validation set. If the loss no longer shows substantial improvement over a relatively long period (e.g., 1000 consecutive iterations), training will automatically terminate early to save computational resources. Ultimately, the system returns the best-performing model state from the entire training history, not just the state from the last iteration.

[0056] Step d): Calculation of dynamic characteristic coefficients Once the neural network training converges, a high-precision, quickly invoked proxy model is obtained, which can be used to efficiently calculate the dynamic characteristic coefficients of the bearing.

[0057] The calculation process for stiffness coefficient: First, the static pressure field P_eq at the equilibrium position (i.e., given eccentricity ε) is calculated using a surrogate model, and the equilibrium bearing capacity is obtained by integration.

[0058] Subsequently, a small virtual displacement perturbation Δx is applied in a certain direction (e.g., the x-direction), and the new air film thickness H_x after the perturbation is calculated accordingly.

[0059] The core innovation lies in the fact that the perturbed pressure field P_x is not obtained by resolving it, but rather through an efficient two-step correction method: First, the original, undisturbed coordinates are input into the network to obtain a basic pressure prediction; then, based on the physical relationships of the local flow, this basic prediction is scaled using a correction factor (H_eq / H_x)^3. This method cleverly combines the nonlinear mapping capability of neural networks with the accuracy of physical formulas.

[0060] Integrating the modified pressure field P_x yields the perturbed bearing capacity.

[0061] Finally, the stiffness coefficients can be calculated from the ratio of the change in bearing capacity to the virtual displacement using the classic finite difference formula. Repeating this process in all directions yields the complete stiffness matrix (e.g., ...). Figure 6 (As shown).

[0062] Estimation Model for Damping Coefficient: To avoid the extremely costly transient simulation, this invention employs an improved estimation model tightly coupled with physical parameters. Based on extensive theoretical and experimental analysis, this model reveals the intrinsic relationship between the damping coefficient, stiffness coefficient, rotor speed, and compression coefficient. Through a concise and effective empirical formula, the corresponding damping coefficient matrix (e.g., ...) can be quickly derived from the calculated stiffness coefficient. Figure 7 (As shown).

[0063] Robust design for computation: During the calculation process, this method incorporates logic for handling outliers. If invalid values ​​(such as NaN or Inf) are calculated under certain extreme conditions, the system will not be interrupted. Instead, a backup, physically consistent, and reasonable default value will be used as a replacement. Furthermore, the system automatically checks whether the calculated damping matrix meets the physical requirement of positive definiteness. If not, it will be forcibly corrected to a physically valid positive definite matrix through mathematical transformations (e.g., taking the symmetric part and correcting the eigenvalues), thus ensuring the robustness of the entire calculation process.

[0064] System stability analysis: Substituting the calculated stiffness matrix [K] and damping matrix [D] into the linearized rotor dynamics state-space equations, the system matrix A is: Where [M] is the rotor mass matrix and [I] is the identity matrix. By solving for the eigenvalues ​​of matrix A, the stability of the system (determining the sign of the real part of the eigenvalues), critical speed, and mode shapes can be analyzed. (Reference) Figure 10 .

[0065] The application process of the method of the present invention will be fully demonstrated below through a specific embodiment.

[0066] Example 1 1. Target Problem and Parameter Setting This embodiment aims to analyze the dynamic characteristics of a typical hydrostatic gas bearing. The core physical and geometric parameters are set as follows: • Bearing diameter D: 16 mm • Bearing clearance c: 15 μm • Length-to-diameter ratio (L / D): 2.0 • Basic eccentricity ε: 0.6 • Extrusion number λ: 1.0 • Supply pressure to ambient pressure ratio (Ps / Pa): 5.0 • Number of throttling orifices: 12 • Orifice layout pattern: grid • Rotor mass m: 0.5 kg • Number of Fourier features: 16 2. Training Data Generation Generate training data points within the computational domain φ∈[0,2π],λ∈[0,2.0]: Interior points: 20,000 interior points are generated using the Latin hypercube sampling (LHS) method to ensure that the sampling points are uniformly distributed throughout the computational domain, avoiding the point clustering or sparsity problems that may occur with standard random sampling.

[0067] Boundary points: 4,000 points are randomly generated on the axial boundaries (λ=0 and λ=2.0) and the periodic boundaries (φ=0 and φ=2π).

[0068] Orifice points: For 12 grid-distributed orifice centers, 20 points are randomly sampled within a specific radius (e.g., dimensionless radius 0.05) around each center, for a total of 240 points. These points are used to accurately learn the source term effect of the orifices.

[0069] 3. Model Training Model initialization: Construct the exact same neural network model as described in the "Detailed Implementation" section and initialize all weights using the Glorot method.

[0070] Training Execution: Initiate a multi-stage training process, totaling 20,000 iterations. During training, an integrated real-time monitoring module allows observation of the change curves of various losses (physical, boundary, orifice, Hamiltonian) and the learning rate, providing a visual assessment of the training status. Figure 8 (as shown), so as to intuitively judge the training status.

[0071] In Phase 1 (1-4000 times), a rapid decrease in physical loss and Hamiltonian loss can be observed.

[0072] In stage two (4001-10000 iterations), the boundary loss decreased significantly, indicating that the network began to fit the boundary.

[0073] In Phase 3 (10001-14000 cycles), orifice loss becomes the primary optimization objective.

[0074] In phase four (14001-20000 times), all loss curves enter a stable fine-tuning phase.

[0075] If, at the later stage of a certain phase, such as the 18,000th iteration, the system detects that the total loss has hardly changed in the past 1,000 iterations, the early stopping mechanism will be triggered, the training will automatically end, and the model state corresponding to the lowest loss obtained throughout the process (such as at the 16,500th iteration) will be returned, thus ensuring the optimality and efficiency of the results.

[0076] 4. Results Generation and Analysis Once training is complete, the resulting surrogate model can be immediately used for analysis and visualization.

[0077] Pressure field and film thickness visualization: By calling the visualization function and inputting a grid coordinate system covering the entire area, the surrogate model can predict the complete pressure distribution and corresponding film thickness within seconds. The generated results are as follows. Figure 3 (Pressure field contour lines) Figure 4 (Air film thickness) and Figure 5 (A three-dimensional view of the pressure field is shown.) The high-pressure region caused by the 12 throttling orifices and the asymmetric pressure distribution due to the eccentricity can be clearly observed from the figure.

[0078] Dynamic characteristic parameterization analysis: Create a range of eccentricity, for example, ε_range = [0.1, 0.2, ..., 0.9].

[0079] For each value in ε_range, the dynamic characteristic calculation function is invoked. This function uses a pre-trained model and a two-step pressure correction technique to calculate the corresponding eight stiffness and damping coefficients in a very short time (usually milliseconds). During this process, even if a numerical problem occurs at a certain point, a robust handling mechanism ensures that the program will not be interrupted and provides a reasonable estimate.

[0080] Connecting all the calculation results into a curve yields the following: Figure 6 The curves showing the stiffness coefficient as a function of eccentricity are shown, and as follows: Figure 7 The curves shown illustrate the variation of damping coefficient with eccentricity. These curves are crucial for bearing design.

[0081] System stability assessment: Extract the stiffness matrix [K] and damping matrix [D] calculated when the base eccentricity ε=0.6.

[0082] Based on the set rotor mass m = 0.5 kg, construct the system state matrix A.

[0083] Solve for the eigenvalues ​​of A. By checking whether the real parts of all eigenvalues ​​are negative, it can be determined whether the system is stable under this operating condition. Solving for the system eigenvalues ​​at a series of speeds allows for the plotting of the system's Campbell's diagram (e.g., ...). Figure 9 As shown in the figure, it is used to visually identify the critical speed and evaluate the stability of the system across the entire operating speed range. Meanwhile, the imaginary part of the eigenvalue corresponds to the system's natural frequency, i.e., the critical speed. (Reference) Figure 10 .

[0084] This embodiment clearly demonstrates how the present invention can perform a comprehensive dynamic characteristic analysis of complex hydrostatic gas bearings in an efficient, accurate, and physically consistent manner.

[0085] Example 2 This embodiment includes an electronic device and storage device for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, comprising: One or more processors on which one or more programs run; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks; the memory is used to store the computer program for the method for simulating and optimizing the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks.

[0086] Alternatively, the aforementioned electronic device may be a server.

[0087] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0088] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0089] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0090] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0091] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A method for simulation and optimization design of dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks, characterized in that, include: An extended physical information neural network model is constructed, which takes the bearing surface coordinates as input and outputs the air film pressure field at the corresponding coordinates. Define a composite loss function, which is used to guide the parameter optimization of the model; The neural network model is trained using a training strategy until the composite loss function converges, resulting in a surrogate model representing the relationship between the pressure field and the coordinates. Based on the aforementioned proxy model, the dynamic characteristic coefficients of the bearing are calculated by applying virtual disturbances; The construction of the extended physical information neural network model includes: The bearing surface coordinates are mapped into a high-dimensional feature vector through Fourier feature encoding. The feature vector contains the original coordinates and multiple sets of sine and cosine terms. A main network is constructed, which receives the feature vector and operating parameters and outputs the air film pressure field. Construct a Hamiltonian structure, which includes a kinetic energy network and a potential energy network, and output an energy component related to the pressure field. A pressure field conforming to physical constraints is generated through the collaborative prediction of the main network and the Hamiltonian structure. The definition of the composite loss function includes: Calculate the physical residual loss of the Reynolds equation, which is based on the mean square error of the network-predicted pressure when substituted into the Reynolds equation; Calculate the boundary condition loss, which is based on the mean square error of the difference between the network-predicted pressure and the actual boundary pressure. Calculate the source term loss of the throttling orifice, the loss being based on the gas choke flow theory to set a weighted expected pressure for the region near the throttling orifice; Calculate the Hamiltonian energy loss, and the loss constrains the consistency of the prediction results between the main network and the Hamiltonian structure, as well as the energy conservation. The calculation of the bearing's dynamic characteristic coefficients based on the proxy model includes: The bearing capacity at the equilibrium position is calculated based on the aforementioned proxy model; By applying a small displacement perturbation, the pressure field after the perturbation is estimated using a priori physical formula based on the thickness of the air film after the perturbation. The stiffness coefficient is calculated based on the change in bearing capacity using the finite difference method. Based on the stiffness coefficient, rotational speed, and compression number, the damping coefficient is calculated using an empirical estimation model; Check the positive definiteness of the damping coefficient matrix; if it is not satisfied, correct it to an effective matrix through mathematical transformation. The calculation of the orifice source term loss includes: Determine the center position of the throttle orifice; For sampling points near the throttle orifice, the theoretical expected pressure is calculated based on the relative distance from the center position; Based on the gas choke flow theory, a weighted expected pressure distribution is set to determine whether the critical pressure ratio has been reached. Calculate the weighted mean square error between the network-predicted pressure and the expected pressure, where the weights decrease exponentially as the sampling point moves further away from the center of the orifice.

2. The method as described in claim 1, characterized in that, The training of the neural network model using the training strategy includes: During the pre-training phase, fundamental physical laws are learned by optimizing the residual loss of the Reynolds equation. During the boundary constraint reinforcement phase, the weight of the boundary condition loss is increased to fit the boundary constraints. During the optimization phase of the orifice effect, the focus is on the orifice source term loss to fit the region of drastic pressure changes; During the global fine-tuning phase, the weights of all loss items are balanced for refined optimization. Monitor the loss on the validation set. If the loss does not improve after multiple iterations, terminate the training early to obtain the optimal model state.

3. The method as described in claim 1, characterized in that, The Fourier feature encoding is mapped to a high-dimensional feature vector, including: Obtain the two-dimensional coordinates of the bearing surface; For the two-dimensional coordinates, generate a feature vector containing the original coordinates and multiple sets of sine and cosine terms of different frequencies; Adjusting frequency parameters to enhance the representation of high-frequency details in periodic pressure fields; The feature vector is concatenated with the running parameters and used as the input to the main network.

4. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the simulation and optimization design method for dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks as described in any one of claims 1-3.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store computer programs, and the processor runs the computer programs to enable the electronic device to perform the simulation and optimization design method for the dynamic characteristics of hydrodynamic bearings based on extended physical information neural networks as described in any one of claims 1-3.

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