Equipment Simulation Design Method and System Based on Adaptive Line Search Grid Fairing

Abstract

The present application relates to a method and system for equipment simulation design based on adaptive line search mesh fairing. The method includes: obtaining an aircraft mesh file; sorting the tetrahedral mesh elements in the aircraft mesh file that are below the quality threshold in ascending order, and performing local topology optimization on the sorting result to obtain an optimized mesh element set; selecting a star-shaped domain including a unique vertex as a local optimization domain in the optimized mesh element set, and constructing a vertex optimization model with the goal of maximizing the worst element quality in the local optimization domain; solving the vertex optimization model to obtain the optimal movement direction and the optimal step size in the optimal movement direction, and updating the vertex position to obtain a fairing mesh, optimizing the aircraft mesh file according to the fairing mesh, and performing simulation design according to the optimized aircraft mesh file. Using this method can shorten the cycle of aircraft simulation design.

Description

Technical Field

[0001] This application relates to the field of simulation technology, and in particular to a method and system for equipment simulation design based on adaptive line search grid smoothing. Background Art

[0002] With the rapid development of computer technology, Computational Fluid Dynamics (CFD) numerical simulation technology has become an important means for performance analysis in the equipment design process such as aircraft aerodynamic shape design, automotive engine thermal management, and ship navigation resistance analysis. Among them, every link of aircraft design is inseparable from the support of CFD technology. After the aircraft shape design is completed, a computational domain is generally constructed according to the designed geometric model, and then a grid file for CFD numerical simulation software calculation is generated. After that, the finite volume method or the finite element method is used to realize the multi-physical field performance evaluation and iterative optimization of the design scheme. Among them, a core preprocessing step of CFD numerical simulation is to further improve the element quality of the initial grid corresponding to the aircraft model through grid vertex smoothing technology. The grid smoothing algorithm can effectively improve the element orthogonality and size gradient characteristics of the initial grid by adjusting the spatial distribution of nodes. This optimization can not only significantly improve the convergence speed of the Navier-Stokes equation solution, but also improve the calculation accuracy of flow field parameters. CFD numerical simulation discretizes and solves the control equations, and completes the numerical calculation of key physical quantities such as velocity field, temperature field, and pressure field in each grid unit, and then derives the core indicators characterizing the performance of the aircraft, including but not limited to the lift-drag ratio characteristics of the aircraft, the heat conduction efficiency of the automotive engine combustion chamber, and the turbulent resistance coefficient of the ship and other performance indicators. Therefore, the grid smoothing technology not only affects the stability of numerical calculations, but also directly relates to the accuracy of aerodynamic and thermodynamic performance predictions of aircraft design schemes.

[0003] Generally, the grid to be optimized is divided into structured grids and unstructured grids according to the topological connection method of grid nodes. Among them, in unstructured grids, due to the random distribution of grid node connection relationships and good local controllability of grid elements, they can better adapt to the boundaries of complex geometries and local grid optimization, and are widely used in various fields of numerical solutions, and are the main research objects of current grid smoothing and optimization technologies.

[0004] The optimization of the flight vehicle simulation-driven design scheme highly depends on the accuracy of CFD calculation results, and generating high-quality meshes in CFD preprocessing is the key prerequisite for quickly obtaining high-precision simulation results. For the complex geometric regions of some flight vehicle models, it is often difficult to directly generate high-quality mesh elements only relying on conventional mesh generation methods (such as Delaunay triangulation, advancing front method, etc.). Therefore, it is particularly crucial to optimize the local vertex positions using a mesh smoothing method after mesh generation.

[0005] In recent years, the Laplacian smoothing algorithm has been widely applied to tetrahedral mesh optimization. This algorithm determines the adjustment direction for each node by defining the Laplacian operator and moves the nodes along this direction at a certain speed to achieve mesh optimization. However, for meshes with complex geometric shapes, the Laplacian smoothing algorithm has a high time complexity, and it may not guarantee the improvement of tetrahedral mesh quality during the optimization process, and may even lead to the deterioration of mesh quality, thus affecting the calculation accuracy and convergence of CFD simulation, and further affecting the simulation results of the flight vehicle design scheme. Another smoothing method is optimization-based mesh smoothing, which improves mesh quality by maximizing the objective function of the mesh quality around vertices. Compared with Laplacian smoothing, this method not only solves the problem of generating illegal elements but also can significantly improve mesh quality. However, the traditional optimization-based smoothing algorithm has a high computational complexity in the process of solving the search direction and is sensitive to the initial step size, easily falling into local optima, resulting in too long optimization time and limited optimization effect. These problems not only affect the computational efficiency and convergence of CFD simulation but also prolong the cycle of flight vehicle simulation-driven design. Summary of the Invention

[0006] Based on this, it is necessary to provide an equipment simulation design method and system based on adaptive line search mesh smoothing for the above technical problems.

[0007] An equipment simulation design method based on adaptive line search mesh smoothing, the method includes:

[0008] Obtain a pre-set flight vehicle geometric model, and generate a corresponding flight vehicle mesh file according to the flight vehicle geometric model; the element type of the meshes in the flight vehicle mesh file is tetrahedral mesh;

[0009] Sort the tetrahedral mesh elements in the flight vehicle mesh file that are lower than the quality threshold in ascending order according to the tetrahedral distortion quality evaluation criterion, and perform local topological optimization on the sorting result to obtain an optimized mesh element set;

[0010] Select a star-shaped domain including a unique vertex from the set of optimized grid cells as the local optimization domain, and construct a vertex optimization model with the goal of maximizing the worst cell quality in the local optimization domain;

[0011] Use the preset weighted average method based on the fixed surface distance to calculate the optimal movement direction that satisfies the vertex optimization model. Use the preset quadratic interpolation adaptive line search method to solve the vertex optimization model to obtain the optimal step size in the optimal movement direction. Update the vertex position according to the optimal movement direction and the optimal step size to obtain the smoothed grid. Optimize the aircraft grid file according to the smoothed grid to obtain the optimized aircraft grid file;

[0012] According to the calculation of the optimized aircraft grid file using CFD numerical simulation software, obtain the numerical results of the viscous flow near the boundary layer in the aircraft shape;

[0013] Analyze the physical phenomena existing in the current aircraft shape near the boundary layer region according to the numerical results. When the aircraft shape meets the required aerodynamic performance indicators, output the current aircraft geometry.

[0014] In one of the embodiments, it further includes: obtaining sampling cells according to the cells in the local optimization domain whose cell quality is lower than the sampling threshold, using the finite difference method based on the fixed surface distance to calculate the gradients of the sampling cells in each direction, and performing weighted averaging on the gradients in each direction to obtain the optimal movement direction.

[0015] In one embodiment, it further includes: obtaining the current initially sorted step size sequence and the first sequence optimal step size in the initially sorted step size sequence. If the first sequence optimal step size is less than the maximum step size of the initially sorted step size sequence, perform quadratic difference fitting based on the elements in the initially sorted step size sequence to obtain a fitting function, and find the optimal step size in the optimal moving direction in the fitting function to obtain a first candidate step size; obtaining the current sorted step size sequence and the second sequence optimal step size in the step size sequence. When the grid cells corresponding to adjacent step sizes in the step size sequence are different, use the first-order Taylor expansion to approximate the local behavior of the cell quality evaluation function to solve the intersection point to obtain a second candidate optimal step size; respectively obtain the first interval and the second interval formed by each candidate optimal step size and its adjacent step size, determine the optimal step size according to the magnitude relationship of the endpoint differences between the first interval and the second interval, and perform boundary processing on the interval where the optimal step size is located. Update the step size sequence according to the optimal step size corresponding to each candidate optimal step size; the larger value endpoint of the first interval is the candidate optimal step size, and the smaller value endpoint is the adjacent step size less than the optimal candidate step size; the larger value endpoint of the second interval is the adjacent step size greater than the optimal candidate step size, and the smaller value endpoint is the candidate optimal step size; use the updated step size sequence as the initially sorted step size sequence for the next round of iteration, iteratively update the optimal step size, and stop the iteration until the iteration stop condition is satisfied, and output the current optimal step size.

[0016] In one embodiment, it further includes: calculating the gradients of the sampling unit in each direction by using the finite difference method based on the fixed surface distance as:

[0017] ;

[0018] where is the cell quality evaluation function, is the vertex coordinate, is the perturbation value, , is the vertex distance from the current th cell to the fixed surface, is the perturbation value control coefficient.

[0019] In one embodiment, it further includes: if the first sequence optimal step size is equal to the maximum step size of the initially sorted step size sequence, extrapolate the initially sorted step size sequence.

[0020] In one embodiment, it further includes: obtaining multiple sampling points from the initially sorted step size sequence, using the step sizes corresponding to the sampling points as the abscissa, and using the cell quality corresponding to the step size and the current optimal moving direction as the ordinate to obtain multiple discrete points, and performing quadratic difference fitting based on the multiple discrete points to obtain a fitting function.

[0021] In one embodiment, it further includes: when the quadratic term coefficient in the fitting function is greater than or equal to 0, solving for the extreme point of the fitting function in the step size interval to obtain the first candidate optimal step size; or when the quadratic term coefficient in the fitting function is less than 0, using the bisection method to solve and obtain the first candidate optimal step size.

[0022] In one embodiment, it further includes: when the second sequence optimal step size is equal to the maximum step size of the step size sequence, extrapolating the step size sequence.

[0023] In one embodiment, it further includes: obtaining a first difference based on the endpoint difference of the first interval, and obtaining a second difference based on the endpoint difference of the second interval; if the first difference is greater than the second difference, determining the optimal step size according to the midpoint step size of the first interval; if the second difference is greater than the first difference, determining the optimal step size according to the midpoint step size of the second interval.

[0024] An equipment simulation design system based on adaptive line search grid fairing, the system includes:

[0025] A grid file generation module, configured to obtain a pre-set aircraft geometric model and generate a corresponding aircraft grid file according to the aircraft geometric model; the cell type of the grids in the aircraft grid file is tetrahedral grids;

[0026] A grid preprocessing module, configured to perform ascending sorting on the tetrahedral grid cells below the quality threshold in the aircraft grid file according to the tetrahedral distortion quality evaluation criterion, and perform local topological optimization on the sorting result to obtain an optimized grid cell set;

[0027] A model construction module, configured to select a star-shaped domain including a unique vertex as a local optimization domain in the optimized grid cell set, and construct a vertex optimization model with the goal of maximizing the worst cell quality in the local optimization domain;

[0028] A vertex fairing module, configured to calculate the optimal moving direction that satisfies the vertex optimization model by using a pre-set weighted average method based on the fixed surface distance, solve the vertex optimization model by using a pre-set quadratic interpolation adaptive line search method to obtain the optimal step size in the optimal moving direction, update the vertex position according to the optimal moving direction and the optimal step size to obtain a fairing grid, and optimize the aircraft grid file according to the fairing grid to obtain an optimized aircraft grid file;

[0029] A numerical simulation module, configured to calculate the optimized aircraft grid file by using CFD numerical simulation software to obtain the numerical results of the viscous flow near the boundary layer in the aircraft shape.

[0030] A result output module, which is used to analyze the physical phenomena existing in the current aircraft shape near the boundary layer region according to the numerical result, and output the current aircraft geometry when the aircraft shape meets the required aerodynamic performance index.

[0031] The above-mentioned equipment simulation design method and system based on adaptive line search grid fairing can provide a basis for subsequent optimization by obtaining the aircraft geometric model to generate a tetrahedral mesh file. Sort the low-quality mesh elements in ascending order according to the tetrahedral distortion quality evaluation criterion and perform local topology optimization, which can improve the mesh structure quality. Select a star-shaped domain to construct a vertex optimization model with the goal of maximizing the worst element quality, which can specifically improve the local mesh quality. Use the weighted average method based on the fixed surface distance to calculate the optimal movement direction, and solve the optimal step size based on the quadratic interpolation adaptive line search method, which can reduce the computational complexity, avoid being sensitive to the initial step size and falling into the local optimum problem, improve the solution accuracy and robustness. Update the vertex position to fair the mesh according to the optimal direction and step size, optimize the aircraft mesh file, which can accelerate the CFD simulation convergence, improve the calculation accuracy, use the CFD numerical simulation software to calculate and analyze the results, and output the aircraft geometry according to the index, which can form a full-process simulation-driven design scheme, and improve the design efficiency and reliability. The embodiments of the present invention can improve the mesh optimization speed and accuracy, thereby shortening the cycle of aircraft simulation design. Brief Description of the Drawings

[0032] Figure 1 It is an application scenario diagram of the equipment simulation design method based on adaptive line search grid fairing in an embodiment;

[0033] Figure 2 It is a schematic diagram of the mesh optimization process in an embodiment;

[0034] Figure 3 It is a schematic diagram of the process of the grid fairing algorithm based on adaptive line search in an embodiment;

[0035] Figure 4 It is to calculate the final direction by sampling the gradient components of the unit in an embodiment Schematic diagram;

[0036] Figure 5 It is a structural block diagram of the equipment simulation design system based on adaptive line search grid fairing in an embodiment. Detailed Description of the Embodiments

[0037] In order to make the purpose, technical solutions and advantages of the present application clearer, the following further describes the present application in detail with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0038] In one embodiment, as Figure 1 shown, a method for equipment simulation design based on adaptive line search grid fairing is provided, including the following steps:

[0039] Step 102, obtain a pre-set aircraft geometric model, and generate a corresponding aircraft grid file according to the aircraft geometric model.

[0040] The aircraft geometric model is designed using CAD software and imported into grid generation software to generate a corresponding aircraft grid file. The cell type of the grid in the aircraft grid file is a tetrahedral grid. As Figure 2 shown in the schematic diagram of the grid optimization process, it starts from the input of the initial grid, and sequentially performs grid preprocessing, topology optimization, and processing based on the optimization-based adaptive line search fairing algorithm. Subsequently, it is judged whether the current worst cell quality is greater than or equal to the worst quality threshold q , if satisfied, output the optimized grid and end the process; if not satisfied, further judge whether the number of algorithm iteration rounds reaches the upper limit n , if reached, output the optimized grid and end the process, if not reached, return and continue. In the early stage, the foundation is laid through preprocessing and topology optimization to improve the grid quality. The adaptive line search fairing algorithm performs targeted fairing, improves the quality and avoids illegal cells. The iterative judgment mechanism avoids ineffective loops and controls the calculation cost. Overall, it can effectively improve the worst cell quality, reduce the computational complexity, accelerate convergence, and has both high precision and strong robustness, accelerating the CFD simulation convergence and improving the calculation accuracy.

[0041] Step 104, sort the tetrahedral grid cells in the aircraft grid file that are below the quality threshold according to the tetrahedral distortion quality evaluation criterion in ascending order, and perform local topology optimization on the sorting result to obtain an optimized grid cell set.

[0042] According to the tetrahedral distortion quality evaluation criterion sort the tetrahedral grid cells in the initial grid that are below the threshold in ascending order, and give priority to optimizing the cells with poor quality to ensure that subsequent optimization can efficiently focus on the cells that have the greatest impact on the overall grid quality. The sorted optimized cell set is , where the formula of the tetrahedral distortion quality evaluation criterion is defined as follows:

[0043] ;

[0044] Among them, represents the sum of the volumes of the current tetrahedral cell and is the radius of the circumscribed sphere of the current cell, the value range of is between 0 and 1. When is 1, it indicates an ideal tetrahedral cell.

[0045] Using local topology optimization to optimize the tetrahedral mesh The optimization was performed by using edge swapping, including traditional 2-3, 3-2 and 4-4 flipping and edge collapse, and performing combined recursive optimization. The optimized grid is recorded as Local topology optimization reconstructs the mesh topology connectivity through edge exchange and edge collapse operations, providing a better initial mesh structure configuration for smoothing optimization.

[0046] Step 106 , selecting a star-shaped structure domain including a unique vertex in the set of optimized mesh cells as a local optimization domain, and constructing a vertex optimization model with the goal of maximizing the worst cell quality in the local optimization domain.

[0047] Building a vertex optimization model includes:

[0048] Assuming that Euclidean space Define the local optimization domain grid in ,in Each tetrahedral mesh element in the grid has an element quality evaluation function , obtained through the distortion quality evaluation function , local optimization domain grid (star structure domain grid) There is a unique vertex in ,and Quality It is defined as the minimum value of the quality of all units connected to the vertex, that is, the worst unit quality. Representation and Vertex For a set of adjacent tetrahedral units, the vertex quality analytical function formula is as follows:

[0049] ;

[0050] By moving the vertices Location Maximize Vertex Quality , that is, by maximizing the vertex quality analytical function , the local optimization domain grid can be calculated Midpoint The best location , the formula is as follows:

[0051] ;

[0052] in is a continuously differentiable function, and the composite function There will be discontinuous partial derivatives, so this problem can be regarded as a nonsmooth optimization problem, and the solution model is as follows:

[0053] ;

[0054] where, is the central vertex coordinate in the optimization domain, is the vertex at each iteration where it is located is the moving direction, is the moving step size.

[0055] Step 108: Calculate the optimal moving direction that satisfies the vertex optimization model by using the pre-set weighted average method based on the fixed surface distance, solve the optimal step size in the optimal moving direction of the vertex optimization model by using the pre-set quadratic interpolation adaptive line search method, update the vertex position according to the optimal moving direction and the optimal step size to obtain the smoothed mesh, and optimize the aircraft mesh file according to the smoothed mesh to obtain the optimized aircraft mesh file.

[0056] Steps 106 and 108 are the mesh smoothing algorithm based on adaptive line search proposed in this application. The algorithm flow is as Figure 3 shown, and the vertices of the mesh in are smoothed. The smoothed mesh is denoted as . The algorithm includes establishing a vertex optimization model, calculating the search direction by using the weighted average method based on the fixed surface distance, fitting the step size interval by using quadratic interpolation, optimizing the step size by using adaptive line search. When the iteration stop condition is met, the calculation of the step size is ended and the vertex position is updated according to the existing search direction and step size.

[0057] This method uses the weighted average of the fixed surface distance to calculate the search direction. In terms of solving the step size, it has advantages such as low computational complexity and fast convergence speed. The proposed quadratic interpolation adaptive line search algorithm reduces the sensitivity of the initial step size, reduces the possibility of falling into local optima, improves the accuracy and robustness of step size solution, and realizes strong global optimization ability after combining local topology optimization techniques such as edge swapping and edge collapse.

[0058] Step 110: Calculate the numerical results of the viscous flow near the boundary layer in the aircraft shape by using the CFD numerical simulation software for the optimized aircraft mesh file.

[0059] Save the optimized mesh as a mesh file in the cgns format or other formats. Read the aircraft mesh file obtained in the previous step by using the CFD software.

[0060] Step 112: Analyze the physical phenomena existing in the current aircraft shape near the boundary layer region according to the numerical results. When the aircraft shape meets the required aerodynamic performance indicators, output the current aircraft geometry.

[0061] Set the initial conditions and boundary conditions according to the requirements, and obtain the performance indicators of the aircraft design scheme through the corresponding processing functions. Evaluate the numerical simulation results of the aircraft design scheme. If the numerical simulation indicators meet the design requirements, output the design scheme. When the aircraft shape does not meet the required aerodynamic performance indicators, redesign the geometry of the aircraft.

[0062] In the above equipment simulation design method based on adaptive line search grid smoothing, by obtaining the aircraft geometric model to generate a tetrahedral mesh file, it can provide a basis for subsequent optimization. Sort the low-quality mesh elements in ascending order according to the tetrahedral distortion quality evaluation criterion and perform local topology optimization, which can improve the mesh structure quality. Select the star-shaped domain to construct a vertex optimization model, aiming to maximize the worst element quality, which can specifically improve the local mesh quality. Use the weighted average method based on the fixed surface distance to calculate the optimal movement direction, and solve the optimal step size based on the quadratic interpolation adaptive line search method, which can reduce the computational complexity, avoid being sensitive to the initial step size and falling into the local optimum problem, improve the solution accuracy and robustness. Update the vertex position to smooth the mesh according to the optimal direction and step size, optimize the aircraft mesh file, which can accelerate the CFD simulation convergence, improve the calculation accuracy, use the CFD numerical simulation software to calculate and analyze the results, and output the aircraft geometry according to the indicators, which can form a full-process simulation-driven design scheme, improving the design efficiency and reliability. In the embodiment of the present invention, it can improve the mesh optimization speed and accuracy, thereby shortening the cycle of aircraft simulation design.

[0063] In one embodiment, calculating the optimal movement direction that meets the vertex optimization model by using the pre-set weighted average method based on the fixed surface distance includes: obtaining the sampling cells according to the cells with element quality lower than the sampling threshold in the local optimization domain, calculating the gradients of the sampling cells in each direction by using the finite difference method based on the fixed surface distance, and performing weighted average on the gradients in each direction to obtain the optimal movement direction.

[0064] In this embodiment, calculating the search direction by using the weighted average method based on the fixed surface distance includes:

[0065] To balance the optimization mesh quality and optimization efficiency, a method with lower time overhead is used to solve the search direction , considering that while optimizing the worst element quality, it may deteriorate the quality of other elements adjacent to the vertex Therefore, only sample and calculate the gradients of the cells that meet the quality lower than the sampling threshold, that is , thus focusing on the direction with the fastest quality improvement while considering other poorer units.

[0066] For the search direction solution, first use the finite difference method based on the fixed surface distance to calculate the gradient of the tetrahedral elements adjacent to the point that satisfy the threshold condition, where the perturbation value is defined as follows:

[0067] .

[0068] As Figure 4 shown in the schematic diagram of calculating the final direction by sampling the gradient components of the unit, for the point the distance to the fixed surface of the current th unit , is the perturbation value control coefficient, and the gradient calculation formula is defined as follows:

[0069] ;

[0070] The final movement direction is obtained by weighted averaging the gradient components , and the formula is as follows:

[0071] ;

[0072] where is the weight factor of the gradient component, used to adjust the contribution of each gradient component to the final movement direction , N is the total number of sampled gradients.

[0073] In one embodiment, solving for the optimal step size in the optimal movement direction by using a preset quadratic interpolation adaptive line search method for the vertex optimization model includes: obtaining the current initially sorted step size sequence and the first sequence optimal step size in the initially sorted step size sequence. If the first sequence optimal step size is less than the maximum value of the step sizes in the initially sorted step size sequence, then perform quadratic difference fitting based on the elements in the initially sorted step size sequence to obtain a fitting function, and search for the optimal step size in the optimal movement direction in the fitting function to obtain a first candidate step size; obtaining the current sorted step size sequence and the second sequence optimal step size in the step size sequence. When the grid cells corresponding to adjacent step sizes in the step size sequence are different, use the first-order Taylor expansion to approximately solve for the intersection point of the local behavior of the cell quality evaluation function to obtain a second candidate optimal step size; respectively obtain the first interval and the second interval formed by each candidate optimal step size and its adjacent step size, determine the optimal step size according to the magnitude relationship of the endpoint differences between the first interval and the second interval, and perform boundary processing on the interval where the optimal step size is located. Update the step size sequence according to the optimal step sizes corresponding to each candidate optimal step size; the larger value endpoint of the first interval is the candidate optimal step size, and the smaller value endpoint is the adjacent step size less than the optimal candidate step size; the larger value endpoint of the second interval is the adjacent step size greater than the optimal candidate step size, and the smaller value endpoint is the candidate optimal step size; use the updated step size sequence as the initially sorted step size sequence for the next round of iteration, iteratively update the optimal step size, and stop the iteration until the iteration stop condition is satisfied, and output the current optimal step size.

[0074] In this embodiment, the quadratic interpolation adaptive line search method includes: using quadratic interpolation to fit the step size interval; using adaptive line search to optimize the step size; when the iteration stop condition is satisfied, end the calculation of the step size and update the vertex position according to the existing search direction and step size.

[0075] Using quadratic interpolation to fit the step size interval includes:

[0076] First, sort the initial step sizes in ascending order, and calculate the size of the current step size sequence and the maximum value of the optimal step size ; determine whether it is equal to , if "yes", extrapolate the current step size interval, if "no", then determine whether it belongs to the interval. When this condition is satisfied, set the objective function as , representing the grid quality evaluation function along the search direction , and it is necessary to maximize to locate the optimal step size. Approximate the local behavior through the quadratic interpolation function , and the formula is as follows:

[0077] ;

[0078] Among them, the coefficients , , are determined by three sampling points , where , and represent the initial sampling step size, represents the value of the grid quality evaluation function along the search direction . When , let By solving at the extreme point of the step size interval , the maximum value of can be quickly approximated. When , by using the bisection method to solve , the advantage of this method is that it constructs an interpolation function through multiple sampling points, reduces the dependence on the initial value of a single step size, the analysis of the extreme point of the quadratic function avoids multiple iterations of the initial step size, accelerates the convergence process of the solution, and extrapolates or contracts the search interval according to the position of the extreme point to approach the global optimal solution.

[0079] Adopting an adaptive line search to optimize the step size includes:

[0080] First, optimize the step size interval. Sort the step size sequence in ascending order, and screen out the current optimal step size corresponding to each . If the optimal step size is located at the boundary of the step size interval, extrapolate the search range of the step size interval to avoid missing potential extreme value regions. When the worst quality cells corresponding to adjacent step sizes and are different, it indicates that there is an extreme point in this interval of the objective function. At this time, use the first-order Taylor expansion to approximate and the local behavior of to solve the intersection point , and the solution formula is as follows:

[0081] ;

[0082] Through this approximation, the candidate position of the extreme point can be quickly located, and the search interval can be narrowed.

[0083] Screen the step size sequence. Fixing the step size or adjusting the step size in equal proportion is likely to cause the algorithm to converge prematurely to a local solution. Through multi-step size screening, fine adjustment can be made with a smaller step size when approaching the optimal solution, improving the accuracy of the solution. To screen the optimal step sizes obtained from the maximum value of the quadratic interpolation and the first-order Taylor approximation in the local solution domain , first calculate adjacent step difference and , which is defined as follows:

[0084] ;

[0085] ;

[0086] If it indicates that the objective function changes significantly in the interval , and it is necessary to further refine the search in this interval, adjust the step size based on the trend, and take the midpoint step size of as , otherwise, similarly take the midpoint step size of

[0087] . Finally, perform boundary processing on the step size interval, and introduce a convergence control parameter ε to avoid too large a step size.

[0088] The iteration stop conditions include: (1) The difference between the intervals where the optimal step size is located is less than the interval threshold ; (2) The number of step size iteration rounds is greater than the set number of iteration rounds ; (3) The change value of the worst grid quality between two iteration rounds is less than the convergence threshold

[0089] . When one of the above three conditions is met, end the calculation of the step size and update the vertex position according to the existing search direction and step size.

[0090] In one embodiment, calculating the gradients of the sampling unit in each direction by using the finite difference method based on the fixed surface distance includes: calculating the gradients of the sampling unit in each direction by using the finite difference method based on the fixed surface distance as:

[0091] ;

[0092] where is the unit quality evaluation function, is the vertex coordinate, is the perturbation value, , is the vertex distance from the fixed surface of the current th unit , is the perturbation value control coefficient.

[0093] In one embodiment, the method further includes: if the optimal step size of the first sequence is equal to the maximum step size of the initial step size sequence, extrapolate the initial step size sequence.

[0094] In one embodiment, quadratic difference fitting is performed according to the elements in the initial step size sequence, and the obtained fitting function includes: obtaining a plurality of sampling points from the initial step size sequence, using the step sizes corresponding to the sampling points as the abscissa, and using the cell quality corresponding to the step size and the current optimal moving direction as the ordinate to obtain a plurality of discrete points, and performing quadratic difference fitting according to the plurality of discrete points to obtain the fitting function.

[0095] In one embodiment, finding the optimal step size in the optimal moving direction in the fitting function to obtain the first candidate step size includes: when the quadratic term coefficient in the fitting function is greater than or equal to 0, solving the extreme point of the fitting function in the step size interval to obtain the first candidate optimal step size.

[0096] In one embodiment, finding the optimal step size in the optimal moving direction in the fitting function to obtain the first candidate step size includes: when the quadratic term coefficient in the fitting function is less than 0, using the bisection method to solve to obtain the first candidate optimal step size.

[0097] In one embodiment, the method further includes: when the second sequence optimal step size is equal to the maximum step size of the step size sequence, extrapolating the step size sequence.

[0098] In one embodiment, determining the optimal step size according to the magnitude relationship of the endpoint differences between the first interval and the second interval includes: obtaining a first difference according to the endpoint difference of the first interval and obtaining a second difference according to the endpoint difference of the second interval; if the first difference is greater than the second difference, determining the optimal step size according to the midpoint step size of the first interval; if the second difference is greater than the first difference, determining the optimal step size according to the midpoint step size of the second interval.

[0099] It should be understood that although Figure 1 the steps in the flowchart are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, the execution of these steps has no strict order restriction, and these steps can be executed in other orders. Moreover, Figure 1 at least a part of the steps in

[0100] In one embodiment, as Figure 5 shown, an equipment simulation design system based on adaptive line search grid smoothing is provided, including:

[0101] The mesh file generation module 502 is configured to obtain a pre-set aircraft geometric model and generate a corresponding aircraft mesh file according to the aircraft geometric model; the element type of the meshes in the aircraft mesh file is tetrahedral meshes;

[0102] The mesh preprocessing module 504 is configured to sort the tetrahedral mesh elements in the aircraft mesh file that are below the quality threshold in ascending order according to the tetrahedral distortion quality assessment criterion, and perform local topological optimization on the sorting result to obtain an optimized mesh element set;

[0103] The model construction module 506 is configured to select a star-shaped domain including a unique vertex as a local optimization domain from the optimized mesh element set, and construct a vertex optimization model with the goal of maximizing the worst element quality in the local optimization domain;

[0104] The vertex smoothing module 508 is configured to calculate the optimal movement direction that satisfies the vertex optimization model by using a pre-set weighted average method based on the fixed surface distance, solve the vertex optimization model by using a pre-set quadratic interpolation adaptive line search method to obtain the optimal step size in the optimal movement direction, update the vertex positions according to the optimal movement direction and the optimal step size to obtain a smoothed mesh, and optimize the aircraft mesh file according to the smoothed mesh to obtain an optimized aircraft mesh file;

[0105] The numerical simulation module 510 is configured to calculate the optimized aircraft mesh file by using CFD numerical simulation software to obtain the numerical results of the viscous flow near the boundary layer in the aircraft shape;

[0106] The result output module 512 is configured to analyze the physical phenomena existing in the current aircraft shape near the boundary layer region according to the numerical results, and output the current aircraft geometric shape when the aircraft shape meets the required aerodynamic performance indicators.

[0107] In one embodiment, it is further configured to obtain sampling elements according to the elements in the local optimization domain whose element quality is lower than the sampling threshold, calculate the gradients of the sampling elements in each direction by using the finite difference method based on the fixed surface distance, and perform weighted average on the gradients in each direction to obtain the optimal movement direction.

[0108] In one embodiment, it is further used to obtain the current initially sorted step size sequence and the first sequence optimal step size in the initially sorted step size sequence. If the first sequence optimal step size is less than the maximum step size of the initially sorted step size sequence, quadratic difference fitting is performed based on the elements in the initially sorted step size sequence to obtain a fitting function, and the optimal step size in the optimal moving direction is searched in the fitting function to obtain the first candidate step size; obtain the current sorted step size sequence and the second sequence optimal step size in the step size sequence. When the grid cells corresponding to adjacent step sizes in the step size sequence are different, the intersection point is solved by using the first-order Taylor expansion to approximate the local behavior of the cell quality evaluation function to obtain the second candidate optimal step size; respectively obtain the first interval and the second interval formed by each candidate optimal step size and its adjacent step size, determine the optimal step size according to the magnitude relationship of the endpoint differences between the first interval and the second interval, perform boundary processing on the interval where the optimal step size is located, and update the step size sequence according to the optimal step size corresponding to each candidate optimal step size; the larger value endpoint of the first interval is the candidate optimal step size, and the smaller value endpoint is the adjacent step size less than the optimal candidate step size; the larger value endpoint of the second interval is the adjacent step size greater than the optimal candidate step size, and the smaller value endpoint is the candidate optimal step size; use the updated step size sequence as the initially sorted step size sequence for the next round of iteration, iteratively update the optimal step size, and stop the iteration until the iteration stop condition is met, and output the current optimal step size.

[0109] In one embodiment, it is further used to calculate the gradient of the sampling unit in each direction by using the finite difference method based on the fixed surface distance as:

[0110] ;

[0111] Wherein, is the cell quality evaluation function, is the vertex coordinate, is the perturbation value, , is the vertex distance from the current th cell to the fixed surface, is the perturbation value control coefficient.

[0112] In one embodiment, it is further used to extrapolate the initially sorted step size sequence if the first sequence optimal step size is equal to the maximum step size of the initially sorted step size sequence.

[0113] In one embodiment, it is further used to obtain multiple sampling points from the initially sorted step size sequence, use the step sizes corresponding to the sampling points as the abscissa, and use the cell quality corresponding to the step size and the current optimal moving direction as the ordinate to obtain multiple discrete points, and perform quadratic difference fitting based on the multiple discrete points to obtain a fitting function.

[0114] In one embodiment, it is further configured to, when the quadratic term coefficient in the fitting function is greater than or equal to 0, solve for the extreme point of the fitting function in the step size interval to obtain a first candidate optimal step size; or, when the quadratic term coefficient in the fitting function is less than 0, use the bisection method to solve and obtain a first candidate optimal step size.

[0115] In one embodiment, it is further configured to extrapolate the step size sequence when the second sequence optimal step size is equal to the maximum step size of the step size sequence.

[0116] In one embodiment, it is further configured to obtain a first difference based on the endpoint difference of the first interval and a second difference based on the endpoint difference of the second interval; if the first difference is greater than the second difference, determine the optimal step size according to the midpoint step size of the first interval; if the second difference is greater than the first difference, determine the optimal step size according to the midpoint step size of the second interval.

[0117] For the specific limitations of the equipment simulation design system based on adaptive line search grid smoothing, reference can be made to the limitations of the equipment simulation design method based on adaptive line search grid smoothing in the foregoing text, which will not be elaborated here. Each module in the above-mentioned equipment simulation design system based on adaptive line search grid smoothing can be implemented in whole or in part by software, hardware, and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or stored in the memory of the computer device in the form of software, so as to facilitate the processor to call and execute the operations corresponding to the above-mentioned modules.

[0118] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0119] The above-described embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. An equipment simulation design method based on adaptive line search grid smoothing, characterized in that: The method comprises: Acquire a preset aircraft geometry model, and generate a corresponding aircraft mesh file according to the aircraft geometry model; the unit type of the mesh in the aircraft mesh file is a tetrahedral mesh; According to the tetrahedron distortion quality evaluation criterion, the tetrahedron mesh units in the aircraft mesh file that are below the quality threshold are sorted in ascending order, and local topology optimization is performed on the sorted results to obtain an optimized mesh unit set; Selecting a star-shaped structure domain including a unique vertex in the set of optimized grid cells as a local optimization domain, and constructing a vertex optimization model with the goal of maximizing the worst cell quality in the local optimization domain; The optimal moving direction satisfying the vertex optimization model is calculated by using a preset weighted average method based on fixed surface distance, the vertex optimization model is solved by using a preset adaptive line search method based on quadratic interpolation to obtain an optimal step length in the optimal moving direction, the vertex position is updated according to the optimal moving direction and the optimal step length to obtain a smoothed mesh, and the aircraft mesh file is optimized according to the smoothed mesh to obtain an optimized aircraft mesh file; By calculating the optimized aircraft grid file using CFD numerical simulation software, a numerical result of viscous flow near the boundary layer in the aircraft shape is obtained; The physical phenomena existing in the current aircraft shape near the boundary layer region are analyzed according to the numerical results, and when the aircraft shape reaches the required aerodynamic performance index, the current aircraft geometry is output.

2. The method according to claim 1, characterized in that The optimal moving direction that satisfies the vertex optimization model is calculated by using a preset weighted average method based on fixed surface distance, including: The sampling unit is obtained according to the units whose unit quality is lower than the sampling threshold in the local optimization domain. The gradient of the sampling unit in each direction is calculated by the finite difference method based on the fixed surface distance. The optimal moving direction is obtained by weighted average of the gradients in each direction.

3. The method according to claim 1, characterized in that: The method of using a preset quadratic interpolation-based adaptive line search method to solve the vertex optimization model to obtain an optimal step length in an optimal moving direction includes: Obtain the current initial step length sequence sorted in ascending order and the optimal step length of the first sequence in the initial step length sequence; if the optimal step length of the first sequence is less than the maximum step length of the initial step length sequence, perform quadratic difference fitting according to the elements in the initial step length sequence to obtain a fitting function; search the optimal step length in the optimal moving direction in the fitting function to obtain a first candidate step length; Obtaining the current step length sequence sorted in ascending order and the second sequence optimal step length in the step length sequence, and when the grid units corresponding to adjacent step lengths in the step length sequence are different, solving the intersection point by using the first-order Taylor expansion to approximate the local behavior of the unit quality evaluation function to obtain the second candidate optimal step length; The first interval and the second interval formed by each candidate optimal step length and the adjacent step length are respectively obtained, the optimal step length is determined according to the size relationship of the endpoint difference between the first interval and the second interval, and the boundary processing is performed on the interval where the optimal step length is located, and the step length sequence is updated according to the optimal step length corresponding to each candidate optimal step length; the larger value endpoint of the first interval is the candidate optimal step length, and the smaller value endpoint is the adjacent step length smaller than the optimal candidate step length; the larger value endpoint of the second interval is the adjacent step length larger than the optimal candidate step length, and the smaller value endpoint is the candidate optimal step length; The updated step length sequence is used as the initial step length sequence for the next round of iteration, and the optimal step length is iteratively updated until the iteration stop condition is met, then the iteration is stopped and the current optimal step length is output.

4. The method according to claim 2, characterized in that: The gradients of the sampling unit in various directions calculated using the finite difference method based on fixed surface distance include: The finite difference method based on fixed surface distance is used to calculate the gradient of the sampling unit in each direction: ； in, is the unit quality assessment function, are vertex coordinates, is the disturbance value, , Vertex Distance from current Units The distance of the fixed surface, is the disturbance value control coefficient.

5. The method according to claim 3, characterized in that: The method further comprises: If the optimal step length of the first sequence is equal to the maximum step length of the initial step length sequence, the initial step length sequence is extrapolated.

6. The method according to claim 3, characterized in that According to the elements in the initial step sequence, a quadratic difference fitting is performed to obtain the fitting function including: A plurality of sampling points are obtained from the initial step sequence, the step corresponding to the sampling point is used as the horizontal coordinate, and the unit mass corresponding to the step and the current optimal moving direction is used as the vertical coordinate to obtain a plurality of discrete points, and a quadratic difference fitting is performed according to the plurality of discrete points to obtain a fitting function.

7. The method according to claim 3, characterized in that Searching for the optimal step length in the optimal moving direction in the fitting function to obtain the first candidate step length includes: When the coefficient of the quadratic term in the fitting function is greater than or equal to 0, the extreme point of the fitting function in the step length interval is solved to obtain the first candidate optimal step length, or, when the coefficient of the quadratic term in the fitting function is less than 0, the dichotomy method is used to solve to obtain the first candidate optimal step length.

8. The method according to claim 3, characterized in that The method further comprises: When the optimal step length of the second sequence is equal to the maximum step length of the step length sequence, the step length sequence is extrapolated.

9. The method according to claim 3, characterized in that: Determining the optimal step length according to the magnitude relationship between the endpoints of the first interval and the second interval comprises: A first difference is obtained according to the endpoint difference of the first interval, and a second difference is obtained according to the endpoint difference of the second interval; If the first difference is greater than the second difference, determining the optimal step length according to the midpoint step length of the first interval; If the second difference is greater than the first difference, the optimal step length is determined according to the midpoint step length of the second interval.

10. An equipment simulation design system based on adaptive line search grid smoothing, characterized in that: The system comprises: A mesh file generation module, used to obtain a preset aircraft geometry model, and generate a corresponding aircraft mesh file according to the aircraft geometry model; the unit type of the mesh in the aircraft mesh file is a tetrahedral mesh; A mesh preprocessing module, used for sorting tetrahedral mesh units in the aircraft mesh file that are below a quality threshold in ascending order according to a tetrahedral distortion quality evaluation criterion, and performing local topological optimization on the sorting results to obtain an optimized mesh unit set; A model building module, used for selecting a star-shaped structure domain including a unique vertex in the set of optimized grid cells as a local optimization domain, and building a vertex optimization model with the goal of maximizing the worst cell quality in the local optimization domain; A vertex smoothing module, used for calculating an optimal moving direction satisfying a vertex optimization model by using a preset weighted average method based on fixed surface distance, solving the vertex optimization model by using a preset adaptive line search method based on quadratic interpolation to obtain an optimal step length in the optimal moving direction, updating the vertex position according to the optimal moving direction and the optimal step length to obtain a smoothed mesh, optimizing an aircraft mesh file according to the smoothed mesh, and obtaining an optimized aircraft mesh file; A numerical simulation module, used to calculate the optimized aircraft grid file by using CFD numerical simulation software to obtain numerical results of viscous flow near the boundary layer in the aircraft shape; The result output module is used to analyze the physical phenomena existing in the current aircraft shape near the boundary layer area according to the numerical results, and output the current aircraft geometry when the aircraft shape reaches the required aerodynamic performance index.

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