A multi-objective optimization design method and system for textured water-lubricated bearings based on two-stage roughness evaluation

Abstract

This invention relates to the field of parameter optimization technology for textured water-lubricated bearings, and discloses a multi-objective optimization design method and system for textured water-lubricated bearings based on two-stage coarse and fine evaluation. The method includes: determining the design variables, optimization objectives, and constraints of the textured water-lubricated bearing; establishing or calling a fast coarse evaluation model, using the design variables as input to obtain the pressure field, shear stress field, and the resulting bearing capacity and friction force; using the output bearing capacity and friction force as the objective function evaluation results to obtain an approximate Pareto solution set; performing a high-precision fine evaluation; and re-determining the Pareto dominance relationship between candidate solutions based on the bearing capacity and friction force corresponding to the candidate solutions calculated by the high-precision fine evaluation, thereby obtaining the texture parameter optimization scheme. This invention can maintain global rapid prediction capabilities while correcting the physical equation constraints of local details in the textured region, reducing the distortion generated by simple surrogate models at texture edges and high-gradient regions.

Description

Technical Field

[0001] This invention belongs to the field of parameter optimization technology for textured water-lubricated bearings, specifically involving a multi-objective optimization design method and system for textured water-lubricated bearings based on two-stage coarse and fine evaluation. It can be used for rapid optimization design of parameters such as texture diameter, texture depth, and texture spacing coefficient of textured water-lubricated radial hydrodynamic bearings. Background Technology

[0002] Water-lubricated sliding bearings offer advantages such as no oil contamination, a wide range of media sources, and good heat dissipation, making them valuable in applications such as marine propulsion systems, hydro-generator sets, high-speed electric spindles, and deep-sea equipment. However, the dynamic viscosity of water is much lower than that of lubricating oil, leading to common problems in water-lubricated bearings, including insufficient load-bearing capacity and weak lubricating film stability. By introducing surface textures such as circular pits and microgrooves onto the bearing's working surface, the pressure distribution of the lubricating film can be altered, enhancing the local micro-dynamic pressure effect, thereby improving load-bearing capacity and reducing friction loss under certain conditions.

[0003] The lubrication performance of textured water-lubricated bearings is closely related to the texture diameter, texture depth, texture spacing, texture distribution area, and operating parameters. Existing optimization design methods typically employ global optimization algorithms to directly search the design space or utilize surrogate models to reduce performance evaluation costs. However, if high-fidelity numerical solutions are called for all candidate design points, the computation time is long; if only fast surrogate models are relied upon for evaluation, evaluation biases may occur in local high-gradient regions, texture edge regions, and strongly coupled parameter combinations, affecting the reliability of the final optimization scheme. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization design method and system for textured water-lubricated bearings based on two-stage coarse and fine evaluation. This method can maintain global rapid prediction capabilities while performing physical equation constraint corrections on local details in the textured region, thereby reducing distortions caused by simple surrogate models at textured edges and high gradient regions.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0006] In a first aspect, this invention proposes a multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation, comprising the following steps:

[0007] The design variables, optimization objectives, and constraints of the textured water-lubricated bearing are determined, and a design space is established. The design variables include texture diameter, texture depth, and texture spacing coefficient. The optimization objectives include maximizing load-bearing capacity and minimizing friction. The constraints include texture distribution area constraints, geometric constraints, and machining accuracy constraints.

[0008] Establish or call the first-stage evaluation model (rapid coarse evaluation model) of the textured water-lubricated bearing. The first-stage evaluation model takes the design variables as input to obtain the pressure field, shear stress field, and bearing capacity and friction force obtained by integrating the obtained pressure field and shear stress field.

[0009] Within the design space, a multi-objective optimization algorithm is used for the first stage search, and the bearing capacity and friction force output by the first stage evaluation model are used as the objective function evaluation results to obtain an approximate Pareto solution set;

[0010] Candidate solutions are selected from the approximate Pareto solution set;

[0011] The candidate solutions are evaluated in a second stage (i.e., high-precision fine evaluation). The second stage evaluation takes the texture parameters in the candidate solutions as input, constructs texture region markers and lubricating film thickness distribution, solves the pressure field and shear stress field, and recalculates the bearing capacity and friction force corresponding to the candidate solutions.

[0012] Based on the bearing capacity and friction force corresponding to the candidate solutions recalculated in the second stage evaluation, the bearing capacity and friction force obtained in the first stage search are used to re-determine the Pareto dominance relationship between the candidate solutions, forming the final Pareto solution set, and outputting the texture parameter optimization scheme.

[0013] In conjunction with the first aspect, the rapid coarse evaluation model further reconstructs the pressure field and shear stress field of the textured water-lubricated bearing, and calculates the bearing capacity and friction force from the reconstructed pressure field and shear stress field.

[0014] In conjunction with the first aspect, the first evaluation model further includes at least one of the following: a fast reconstruction model based on intrinsic orthogonal decomposition and sparse Gaussian process regression, a reduced-order model, a surrogate model, and a machine learning model.

[0015] In conjunction with the first aspect, the second stage evaluation further includes finite difference solvers based on the Reynolds equations, fast finite difference solvers, local detail correction calculations, high-fidelity numerical solutions, or combinations thereof.

[0016] In conjunction with the first aspect, the fast finite difference solver further uses the texture parameters extracted from the candidate solutions as input, forms texture region markers based on texture diameter, texture depth and texture spacing coefficient, constructs the lubricating film thickness distribution and finite difference discretization scheme, iteratively solves the pressure field and shear stress field, and integrates to calculate the bearing capacity and friction force.

[0017] In conjunction with the first aspect, further, the selection of candidate solutions from the approximate Pareto solution set includes:

[0018] Candidate solutions are selected from the approximate Pareto solution set based on non-dominant relations, objective function sorting, solution set uniformity, bearing capacity level, friction level, or comprehensive balance.

[0019] In conjunction with the first aspect, the fast finite difference solver further improves computational efficiency by employing one or more of the following methods: textured region vectorization labeling, one-time construction of the film thickness matrix and discrete coefficient matrix, red-black projection super-relaxation iteration, and parallel acceleration by a graphics processor.

[0020] In conjunction with the first aspect, the multi-objective optimization algorithm further includes NSGA-II, MOEA / D, MOPSO, genetic algorithm, particle swarm optimization algorithm, or other multi-objective optimization algorithms used to obtain non-dominated solution sets.

[0021] In conjunction with the first aspect, the multi-objective optimization design method of the present invention is further applicable to the parameter optimization of circular pit array textured water-lubricated bearings, and can be extended to the multi-objective optimization design of groove texture, elliptical texture or composite texture lubrication structures.

[0022] Secondly, this invention proposes a multi-objective optimization design system for textured water-lubricated bearings based on two-stage coarse and fine evaluation, used to implement the aforementioned multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation, including:

[0023] The model input determination module is configured to determine the design variables, optimization objectives, and constraints of the textured water-lubricated bearing and establish a design space. The design variables include texture diameter, texture depth, and texture spacing coefficient. The optimization objectives include maximizing load-bearing capacity and minimizing friction. The constraints include texture distribution area constraints, geometric constraints, and machining accuracy constraints.

[0024] The first-stage evaluation module is configured to establish or call the first-stage evaluation model (rapid coarse evaluation model) of the textured water-lubricated bearing. The first-stage evaluation model takes the design variables as input to obtain the pressure field, shear stress field, and bearing capacity and friction force obtained by integrating the obtained pressure field and shear stress field.

[0025] The approximate Pareto solution set acquisition module is configured to perform a first-stage search within the design space using a multi-objective optimization algorithm, and to obtain an approximate Pareto solution set by using the bearing capacity and friction force output by the first evaluation model as the objective function evaluation result.

[0026] The candidate solution selection module is configured to select candidate solutions from the approximate Pareto solution set;

[0027] The second-stage evaluation module is configured to perform a second-stage evaluation (i.e., high-precision fine evaluation) on the candidate solutions. The second-stage evaluation takes the texture parameters in the candidate solutions as input, constructs texture region markers and lubricating film thickness distribution, solves the pressure field and shear stress field, and recalculates the bearing capacity and friction force corresponding to the candidate solutions.

[0028] The optimization scheme output module is configured to recalculate the bearing capacity and friction force corresponding to the candidate solutions based on the second-stage evaluation, replace the bearing capacity and friction force obtained in the first-stage search in the first-stage evaluation, re-determine the Pareto dominance relationship between the candidate solutions, form the final Pareto solution set, and output the texture parameter optimization scheme.

[0029] Thirdly, the present invention proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-mentioned multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0030] Fourthly, the present invention provides a computer device, characterized in that it comprises:

[0031] Memory, used to store computer programs;

[0032] A processor is used to execute the computer program to implement the steps of the above-described multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0033] Fifthly, the present invention proposes a computer program product, including a computer program, characterized in that: when the computer program is executed by a processor, it implements the steps of the above-mentioned multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0034] This invention obtains an approximate Pareto solution set through a first-stage rapid coarse evaluation, then performs performance correction on the candidate solutions through a second-stage high-precision fine evaluation, and finally outputs the texture parameter combination confirmed by the fine evaluation.

[0035] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0036] (1) In the large-scale design space search stage, the present invention uses a fast evaluation model to improve optimization efficiency, and after the candidate Pareto solution is determined, the key performance parameters are recalculated through high-precision fine evaluation, thus taking into account both optimization efficiency and result reliability. This solves the problems of high-fidelity full-field solution call times, insufficient reliability of simple fast proxy evaluation results, and the need for further correction of candidate optimization schemes in the existing multi-objective optimization design of textured water-lubricated bearings.

[0037] (2) This invention uses a fast coarse evaluation model to perform low-cost search in a wide range of design space, reducing the number of calls to high-precision numerical solutions in the optimization process and improving the efficiency of texture parameter optimization; then, through the second stage of high-precision fine evaluation, the bearing capacity and friction force of candidate Pareto solutions are recalculated, avoiding the performance deviation of candidate schemes caused by relying solely on surrogate model evaluation, and improving the reliability of the final optimization results.

[0038] (3) This invention decouples the multi-objective optimization algorithm from the high-precision fine evaluation process, and can be adapted to different multi-objective optimization algorithms such as NSGA-II, MOEA / D, and MOPSO, and has good compatibility.

[0039] (4) The present invention uses texture diameter, texture depth and texture spacing coefficient as optimization variables, which can directly serve the parameter design of textured water-lubricated bearings with circular pit arrays, and can provide candidate parameter combinations for subsequent experimental verification and engineering applications. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the multi-objective optimization design method for textured water-lubricated bearings in Embodiment 1 of the present invention.

[0041] Figure 2 This is a schematic diagram of the textured water-lubricated bearing and the texture distribution and design variables of the circular pit array in Embodiment 1 of the present invention;

[0042] Figure 3 This is a schematic diagram of the first stage of rapid coarse evaluation multi-objective optimization search in Embodiment 1 of the present invention;

[0043] Figure 4 This is a flowchart illustrating the second stage of high-precision fine evaluation in Embodiment 1 of the present invention;

[0044] Figure 5 This is a schematic diagram showing how the candidate Pareto solutions in Embodiment 1 of the present invention are corrected through a second-stage high-precision fine evaluation to form the final Pareto solution set. Detailed Implementation

[0045] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0046] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0047] Example 1

[0048] like Figure 1 As shown in the figure, the multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation in this embodiment includes the following steps:

[0049] Step S1: Determine the design object, design variables, operating conditions, optimization objectives, and constraints of the textured water-lubricated bearing, and establish the design space. The preferred design object is a textured water-lubricated radial hydrodynamic bearing with a circular pit array; design variables include the texture diameter. Texture depth and texture spacing coefficient The operating conditions include bearing speed, external load, and dynamic viscosity of the lubricating medium, which are used to define the evaluation conditions. In this embodiment, the operating conditions are fixed conditions. In this embodiment, the bearing speed is 5000 rpm, the external load is 200 N, the bearing length and inner diameter are both 40 mm, the radial clearance is 20 μm, the eccentricity is 0.2, the ambient temperature and inlet temperature are both 20℃, the water supply pressure is 0.01 MPa, and the dynamic viscosity of water is 1.002 × 10⁻³ Pa·s. The optimization objectives include maximizing the load-bearing capacity and minimizing the friction force. The constraints include texture distribution area constraints, geometric constraints, and machining accuracy constraints. The constraints are used to screen out candidate parameter combinations that are unmanufacturable or exceed the texture distribution range. For example, the texture is distributed in the circumferential direction of 90° to 180°, with 80% of the effective length in the axial middle, and 10% of the untextured area is retained at each end. The texture diameter, depth, and spacing coefficient meet the value range and machining step length requirements.

[0050] Step S2: Establish or call up a rapid coarse evaluation model for textured water-lubricated bearings. The rapid coarse evaluation model is used to quickly obtain the pressure field, shear stress field, and corresponding load-bearing capacity and friction force evaluation results based on the input design variables (also known as texture parameters). For example... Figure 3As shown, the process involves inputting the design variables and optimization objectives determined in step S1 into the fast coarse evaluation model; initializing the multi-objective optimization algorithm population; generating candidate texture parameter combinations; calling the fast coarse evaluation model to calculate the bearing capacity and friction force; performing non-dominated sorting and solution set update; determining whether the preset termination condition has been met; if the termination condition has been met, outputting an approximate Pareto solution set and selecting candidate solutions to enter the second stage of high-precision fine evaluation; if the termination condition has not been met, returning to the step of initializing the multi-objective optimization algorithm population. The candidate texture parameter combinations include texture diameter, texture depth, and texture spacing coefficient; these combinations can further determine the texture spacing, axial texture quantity, circumferential texture quantity, and texture coverage area.

[0051] In this embodiment, the fast coarse evaluation model preferably adopts a fast reconstruction model based on Proper Orthogonal Decomposition-Sparse Gaussian Process Regression (POD-SGPR). Specifically, the reduced-order basis of the pressure field and shear stress field is first constructed using the Proper Orthogonal Decomposition method, and then the mapping relationship between texture parameters and reduced-order basis function coefficients is established using the Sparse Gaussian Process Regression model. For the texture parameter combination to be evaluated, the corresponding reduced-order basis function coefficients and offset angles are predicted by the Sparse Gaussian Process Regression model, thereby reconstructing the pressure field and shear stress field, and calculating the bearing capacity and friction force by integrating the reconstructed pressure field and shear stress field. In addition to the above-mentioned fast reconstruction model, the fast coarse evaluation model can also adopt other surrogate models, reduced-order models, or machine learning models that can achieve fast performance estimation.

[0052] Step S3: Perform the first-stage multi-objective optimization search within the design space to obtain an approximate Pareto solution set. The multi-objective optimization search uses a fast coarse evaluation model as the objective function evaluation tool, and obtains an approximate Pareto solution set through a multi-objective optimization algorithm. The multi-objective optimization algorithm can be NSGA-II, MOEA / D, MOPSO, or other multi-objective optimization algorithms.

[0053] Step S4: Extract candidate solutions. For example... Figure 4 As shown, candidate solutions are selected from the approximate Pareto solution set obtained in the first stage for high-precision detailed evaluation in the second stage. Candidate solutions can be selected based on non-dominated relations, uniformity of solution set distribution, bearing capacity level, friction level, or comprehensive equilibrium.

[0054] Step S5: Perform the second-stage high-precision detailed evaluation. A second evaluation (high-precision detailed evaluation) is performed on the candidate solutions, recalculating the bearing capacity and frictional force corresponding to the candidate texture parameter combinations. The high-precision detailed evaluation is preferably implemented using a Fast Finite-Difference Solver (FFS) based on the Reynolds equations. Alternatively, high-fidelity numerical solutions, local detail correction calculations, or experimental calibration results can be used for evaluation. Figure 5 As shown, this step specifically involves: inputting the candidate Pareto solutions obtained in the first stage, extracting candidate texture parameter combinations, constructing texture region markers and film thickness distributions, calling FFS to solve for the pressure field and shear stress field corresponding to the candidate texture parameter combinations, and then calculating the bearing capacity and friction force based on the integral of the solved pressure field and shear stress field. It is then determined whether all candidate solutions have completed the second evaluation. If so, proceed to step S6; otherwise, return to the step of extracting candidate texture parameter combinations.

[0055] Step S6: Re-determine the Pareto dominance relationship and output the final Pareto solution set and optimized scheme. Based on the bearing capacity and friction force results obtained from the high-precision detailed evaluation in the second stage, re-determine the Pareto dominance relationship between candidate solutions to form the final Pareto solution set, and select the recommended optimized design scheme from it.

[0056] In this invention, a fast finite difference (FD) solver is used as a high-precision fine-grained evaluation tool in the second stage. Specifically, the FD solver takes candidate texture parameter combinations as input, determines the spatial distribution of the circular pit texture based on the texture diameter, texture depth, and texture spacing coefficient, and forms texture region markers within the bearing unfolded lubricating film computational domain. Subsequently, it constructs the lubricating film thickness distribution based on the bearing geometry, eccentricity, and texture depth, and establishes a finite difference discretization scheme based on the steady-state Reynolds equation. Then, it iteratively solves the pressure field and shear stress field under the candidate scheme, and finally integrates to calculate the bearing capacity and friction force. The FD solver can improve computational efficiency by employing one or more of the following methods: texture region vectorization marking, one-time construction of the film thickness matrix and discrete coefficient matrix, red-black projection super-relaxation iteration, and parallel computing acceleration using a graphics processor. The bearing geometric parameters include the bearing radius or bearing diameter, bearing axial length, radial clearance, circumferential calculation range, axial effective length, and texture distribution area boundary. The texture distribution area boundary includes the circumferential texture coverage range and the axial texture coverage range. The circumferential texture coverage range is 90° to 180° within the bearing convergence zone, and the axial texture coverage range is 80% of the effective length area in the middle of the bearing. 10% of the untextured area is reserved at each of the two ends of the axial direction.

[0057] The texture diameter, texture depth, and texture spacing coefficient are used as optimization design variables in this invention; the texture spacing, circumferential texture quantity, axial texture quantity, circumferential coverage length, and axial coverage length can be further determined from the texture diameter and texture spacing coefficient.

[0058] It should be noted that in this invention, the fast finite difference solver serves as a high-precision fine evaluation tool in the second stage, used to perform performance correction on the candidate Pareto solutions obtained from the fast coarse evaluation in the first stage.

[0059] Example 2

[0060] This embodiment includes a two-stage process: a first stage of rapid coarse evaluation search and a second stage of high-precision fine evaluation correction. Combined with specific experimental data, the multi-objective optimization design method of the present invention is further explained.

[0061] This embodiment takes a water-lubricated radial hydrodynamic bearing with a textured surface of equally spaced circular recesses as the research object. For example... Figure 2 As shown, the texture is distributed in the convergence zone of the hydrodynamic bearing, with a circumferential coverage range of 90° to 180°; axially, it is distributed over 80% of the effective length of the bearing's center, with 10% of the area at each end of the axial direction remaining untextured; the texture is symmetrically distributed about the bearing's axial centerline. The texture diameter is selected... Texture depth and texture spacing coefficient These three texture parameters are used as optimization design variables, with the optimization objectives being to maximize load-bearing capacity and minimize friction.

[0062] Figure 2 middle, Indicates the texture diameter; Indicates the texture spacing coefficient; Indicates the texture spacing; Indicates the center angle of the texture distribution area; Indicates the length of the circumferential texture distribution; Indicates the length of the axial texture distribution; Indicates the number of circumferential single-sided texture arrays; Indicates the number of axial single-sided texture arrays.

[0063] In this embodiment, considering processing accuracy and manufacturability, a minimum step size constraint is set during the search process, wherein the minimum changes in texture diameter, texture depth and texture spacing coefficient are 1 μm, 0.1 μm and 0.01, respectively.

[0064] The first stage employs a fast reconstruction model based on intrinsic orthogonal decomposition-sparse Gaussian process regression as the initial evaluation tool (also known as the fast coarse evaluation model) for the first evaluation (i.e., fast coarse evaluation). For any candidate texture parameter combination, the reduced-order basis function coefficients and offset angles of the pressure field and shear stress field are first predicted using this initial evaluation tool, and then the pressure field and shear stress field are reconstructed. The bearing capacity and friction force are obtained by integrating the reconstructed pressure field and shear stress field. Subsequently, the bearing capacity and friction force are used as objective function values ​​and input into a multi-objective optimization algorithm.

[0065] To compare the applicability of different multi-objective optimization algorithms in the multi-objective optimization problem of maximizing the bearing capacity and minimizing the friction of textured water-lubricated bearings, this embodiment uses NSGA-II, MOEA / D, and MOPSO for optimization search, respectively. The three algorithms use the same design variable space, the same objective function definition, and the same two-stage evaluation process. The algorithm settings are shown in Table 1.

[0066] Table 1. Settings for the three algorithms

[0067]

[0068] The second stage selects candidate solutions from the approximate Pareto optimal solution set obtained in the first stage and performs a second evaluation (i.e., high-precision fine evaluation) using a fast finite difference solver. For each set of candidate texture parameters, the fast finite difference solver constructs texture region markers and lubricating film thickness distributions based on texture geometry parameters, establishes a finite difference discretization scheme based on the steady-state Reynolds equation, iteratively solves the pressure field and shear stress field, and re-integrates to calculate the bearing capacity and friction force. Subsequently, based on the results of the second evaluation, the non-dominated relationships between candidate solutions are re-determined to obtain the final Pareto solution set.

[0069] Under the parameter settings of this embodiment (i.e., the algorithm parameter settings in Table 1), taking the NSGA-II results as an example, the load-bearing capacity ranges from 267.950 N to 294.538 N in the final Pareto solution set, and the frictional force ranges from 2.466 N to 2.491 N. The load-bearing capacity of the unwoven bearing is approximately 213.21 N, and the frictional force is approximately 2.659 N. Compared with the unwoven bearing, the optimized woven bearing achieves a maximum increase in load-bearing capacity of approximately 38.15% and a maximum reduction in frictional force of approximately 7.24%.

[0070] Three recommended optimal design schemes were obtained from the final Pareto solution set, as shown in Table 2.

[0071] Table 2. Three recommended optimization design schemes obtained from the final Pareto solution set.

[0072]

[0073] As shown in Table 2, the present invention improves the reliability of candidate texture parameter evaluation results while maintaining optimization efficiency through a two-stage process of "rapid coarse evaluation search + high-precision fine evaluation correction", and can obtain a combination of texture parameters that takes into account both high load-bearing capacity and low friction.

[0074] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, without departing from the technical concept of the present invention, the optimization algorithm, candidate solution screening method, and high-precision fine evaluation method can be adjusted according to the specific bearing structure, texture shape, lubrication medium, and operating conditions; the texture shape may include groove texture, elliptical texture, or composite texture, all of which should be included within the protection scope of the present invention.

[0075] The two-stage evaluation approach of this invention primarily overcomes the contradiction between "high computational cost of high-precision evaluation" and "the potential misjudgment of Pareto dominance relationships due to rapid surrogate evaluation results" in multi-objective optimization of textured water-lubricated bearings. Specifically, after the texture parameters are changed, the pressure field and shear stress field will change significantly at the texture edge and in local high-gradient regions, and the bearing capacity and friction force are relatively sensitive to local field variables. If high-precision numerical solutions are called for each candidate texture parameter combination throughout the entire design space, the computational cost is too high and it is not suitable for large-scale multi-objective search. If only rapid surrogate models or reduced-order models are relied upon for evaluation, the prediction bias of the surrogate model in local high-gradient regions may cause the evaluation values ​​of bearing capacity and friction force to deviate from the true results, thereby changing the Pareto dominance relationships between candidate solutions and causing the final Pareto solution set to have sorting bias or misselection.

[0076] This invention overcomes the aforementioned problems through a "two-stage coarse and fine evaluation" approach. The first stage employs a fast coarse evaluation model to perform a low-cost search across a large design space, quickly obtaining an approximate Pareto solution set, thus avoiding high-precision solutions for all candidate points. The second stage performs a high-precision fine evaluation only on candidate solutions within the approximate Pareto solution set, recalculating the bearing capacity and friction of the candidate solutions, and replacing the first-stage coarse evaluation results with the fine evaluation results. This re-determines the Pareto dominance relationships between candidate solutions, forming the final Pareto solution set. Therefore, this invention does not simply superimpose two conventional models; instead, it utilizes coarse evaluation to complete the global search and uses fine evaluation to correct objective function deviations and misjudgments of dominance relationships near the Pareto front, reducing the number of high-precision solution calls while improving the reliability of the final optimization scheme.

[0077] Example 3

[0078] Based on the same inventive concept as Embodiment 1, this embodiment introduces a multi-objective optimization design system for textured water-lubricated bearings based on two-stage coarse and fine evaluation, used to implement the above-mentioned multi-objective optimization design method for textured water-lubricated bearings. The system includes:

[0079] The model input determination module is configured to determine the design variables, optimization objectives, and constraints of the textured water-lubricated bearing and establish a design space. The design variables include texture diameter, texture depth, and texture spacing coefficient. The optimization objectives include maximizing load-bearing capacity and minimizing friction. The constraints include texture distribution area constraints, geometric constraints, and machining accuracy constraints.

[0080] The first-stage evaluation module is configured to establish or call the first-stage evaluation model (rapid coarse evaluation model) of the textured water-lubricated bearing. The first-stage evaluation model takes the design variables as input to obtain the pressure field, shear stress field, and bearing capacity and friction force obtained by integrating the obtained pressure field and shear stress field.

[0081] The approximate Pareto solution set acquisition module is configured to perform a first-stage search within the design space using a multi-objective optimization algorithm, and to obtain an approximate Pareto solution set by using the bearing capacity and friction force output by the first evaluation model as the objective function evaluation result.

[0082] The candidate solution selection module is configured to select candidate solutions from the approximate Pareto solution set;

[0083] The second-stage evaluation module is configured to perform a second-stage evaluation (i.e., high-precision fine evaluation) on the candidate solutions. The second-stage evaluation takes the texture parameters in the candidate solutions as input, constructs texture region markers and lubricating film thickness distribution, solves the pressure field and shear stress field, and recalculates the bearing capacity and friction force corresponding to the candidate solutions.

[0084] The optimization scheme output module is configured to recalculate the bearing capacity and friction force corresponding to the candidate solutions based on the second-stage evaluation, replace the bearing capacity and friction force obtained in the first-stage search in the first-stage evaluation, re-determine the Pareto dominance relationship between the candidate solutions, form the final Pareto solution set, and output the texture parameter optimization scheme.

[0085] Example 4

[0086] Based on the same inventive concept as other embodiments, this embodiment introduces a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0087] Example 5

[0088] Based on the same inventive concept as other embodiments, this embodiment introduces a computer device, including: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the above-described multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0089] Example 6

[0090] Based on the same inventive concept as other embodiments, this embodiment introduces a computer program product, including a computer program that, when executed by a processor, implements the above-described steps of multi-objective optimization design of textured water-lubricated bearings based on two-stage coarse and fine evaluation.

[0091] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can 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.

[0092] 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.

[0093] 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.

[0094] 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.

[0095] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other modifications under the guidance of the present invention, and these modifications are all within the protection scope of the present invention.

Claims

1. A multi-objective optimization design method and system for textured water-lubricated bearings based on two-stage coarse and fine evaluation, characterized in that, include: Determine the design variables, optimization objectives, and constraints for textured water-lubricated bearings, and establish the design space; The design variables include texture diameter, texture depth, and texture spacing coefficient, and the optimization objectives include maximizing load-bearing capacity and minimizing friction. Establish or call the first-stage evaluation model of the textured water-lubricated bearing. The first-stage evaluation model takes the design variables as input to obtain the pressure field, shear stress field, and bearing capacity and friction force obtained by integrating the obtained pressure field and shear stress field. Within the design space, a multi-objective optimization algorithm is used for the first stage search, and the bearing capacity and friction force output by the first stage evaluation model are used as the objective function evaluation results to obtain an approximate Pareto solution set; Candidate solutions are selected from the approximate Pareto solution set; The candidate solutions are evaluated in a second stage. The second stage evaluation takes the texture parameters in the candidate solutions as input, constructs texture region markers and lubricating film thickness distribution, solves the pressure field and shear stress field, and recalculates the bearing capacity and friction force corresponding to the candidate solutions. Based on the bearing capacity and friction force corresponding to the candidate solutions recalculated in the second stage evaluation, the bearing capacity and friction force obtained in the first stage search are used to re-determine the Pareto dominance relationship between the candidate solutions, forming the final Pareto solution set, and outputting the texture parameter optimization scheme.

2. The multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in claim 1, characterized in that: The first evaluation model includes at least one of the following: a fast reconstruction model based on intrinsic orthogonal decomposition and sparse Gaussian process regression, a reduced-order model, a surrogate model, and a machine learning model.

3. The multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in claim 1, characterized in that: The second-stage evaluation includes finite difference solvers based on the Reynolds equation, fast finite difference solvers, local correction calculations, high-fidelity numerical solutions, or combinations thereof.

4. The multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation according to claim 3, characterized in that: The fast finite difference solver takes the texture parameters extracted from the candidate solutions as input, forms texture region markers based on texture diameter, texture depth and texture spacing coefficient, constructs the lubricating film thickness distribution and finite difference discretization scheme, iteratively solves the pressure field and shear stress field, and integrates to calculate the bearing capacity and friction force.

5. The multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation according to claim 1, characterized in that: The selection of candidate solutions from the approximate Pareto solution set includes: Candidate solutions are selected from the approximate Pareto solution set based on non-dominant relations, objective function sorting, solution set uniformity, bearing capacity level, friction level, or comprehensive balance.

6. The multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation according to claim 3, characterized in that: The fast finite difference solver improves computational efficiency by employing one or more of the following methods: textured region vectorization labeling, one-time construction of the film thickness matrix and discrete coefficient matrix, red-black projection super-relaxation iteration, and parallel acceleration by graphics processor.

7. A multi-objective optimization design system for textured water-lubricated bearings based on two-stage coarse and fine evaluation, characterized in that, The method for implementing the multi-objective optimization design of textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in any of claims 1 to 6 includes: The model input determination module is configured to determine the design variables, optimization objectives, and constraints of the textured water-lubricated bearing and establish the design space. The design variables include texture diameter, texture depth, and texture spacing coefficient, and the optimization objectives include maximizing load capacity and minimizing friction. The first-stage evaluation module is configured to establish or call the first-stage evaluation model of the textured water-lubricated bearing. The first-stage evaluation model takes the design variables as input to obtain the pressure field, shear stress field, and bearing capacity and friction force obtained by integrating the obtained pressure field and shear stress field. The approximate Pareto solution set acquisition module is configured to perform a first-stage search within the design space using a multi-objective optimization algorithm, and to obtain an approximate Pareto solution set by using the bearing capacity and friction force output by the first evaluation model as the objective function evaluation result. The candidate solution selection module is configured to select candidate solutions from the approximate Pareto solution set; The second-stage evaluation module is configured to perform a second-stage evaluation on the candidate solutions. The second-stage evaluation takes the texture parameters in the candidate solutions as input, constructs texture region markers and lubricating film thickness distribution, solves the pressure field and shear stress field, and recalculates the bearing capacity and friction force corresponding to the candidate solutions. The optimization scheme output module is configured to recalculate the bearing capacity and friction force corresponding to the candidate solutions based on the second-stage evaluation, replace the bearing capacity and friction force obtained in the first-stage search in the first-stage evaluation, re-determine the Pareto dominance relationship between the candidate solutions, form the final Pareto solution set, and output the texture parameter optimization scheme.

8. A 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 steps of the multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in any one of claims 1 to 6.

9. A computer device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the steps of the multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the steps of the multi-objective optimization design method for textured water-lubricated bearings based on two-stage coarse and fine evaluation as described in any one of claims 1 to 6.

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