A method for controlling geometric feature size of topology optimization result based on image processing

Abstract

The application discloses a kind of topological optimization result geometric feature size control method based on image processing, comprising: step one: constructing double-scale topological optimization model;Step two: update double-scale level set function and then drive cross-scale structure configuration update;Step three: the boundary number and the coordinate point of boundary of cross-scale structure are obtained;Step four: based on the coordinate point of boundary of cross-scale structure, macroscopic configuration and microstructure are quantified respectively, and the geometric feature specific value of cross-scale structure is obtained;Step five: regulate the extremely thin component feature of cross-scale structure;Step six: regulate the hole feature of cross-scale structure;Step seven: regulate the special angle feature of cross-scale structure.The application realizes the effective regulation of accurate identification of various geometric features based on image processing technology under the level set framework, promotes design and manufacturing integration, and helps to improve design efficiency and shorten design cycle.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated topological design and additive manufacturing of material structures, and in particular to a method for controlling geometric feature dimensions of topological optimization results based on image processing. Background Art

[0002] Lightweight design is an eternal theme in the structural design of advanced equipment. Topology optimization, as a design method in the conceptual design stage, can improve material utilization and obtain the best force transmission path, making it an effective means of lightweight design. The integration of design and manufacturing, as well as the integration of materials and structures, are important aspects of structural design and are receiving increasing attention. Due to their powerful design and manufacturing capabilities, additive manufacturing and topology optimization technologies have been widely used in aviation, aerospace, automobiles, medical care and other fields. In particular, dual-scale concurrent topology optimization expands the design space and can better meet the multifunctional needs of structural design. In recent years, topology optimization technology has developed rapidly and has been continuously used in structural, fluid, heat transfer and multi-field coupling problems. As a typical boundary-driven method, the level set method has received increasing attention from industry and academia.

[0003] The level set method was originally a key technology in image processing. It was later introduced into topology optimization problems, realizing a new topology optimization method that is different from density-based optimization methods. The advantages of the level set method are that it can maintain a clear configuration of the design results, the absence of grayscale units and checkerboard phenomena, and good numerical stability. The level set method is also continuously applied to the topology optimization design of important aerospace structures. In the topology optimization design of cross-scale structures, it is necessary to introduce two-scale level set functions to characterize the configuration changes of macroscopic structures and microscopic unit cells respectively. This can effectively ensure the clear expression of macroscopic configurations and microscopic unit cells, and also provide a data basis for the subsequent identification of geometric features. The natural advantages of the level set method make geometric feature recognition based on image processing more efficient.

[0004] Although the continuous development and maturity of additive manufacturing technology has improved the ability to form complex configurations in an integrated manner, there are still many geometric constraints in the additive manufacturing process that restrict the process of design and manufacturing integration. In order to achieve the goals of shape and controllability of additive manufacturing and take into account the actual constraints of manufacturing equipment, the design results are often subject to complex geometric constraints such as maximum manufacturing size, minimum manufacturing size, overhang angle, connectivity, etc. The results of topology optimization require multiple rounds of iterative modifications to meet manufacturing requirements. Processing the topology optimization results so that the optimization results meet the design requirements is an important part of achieving design and manufacturing integration. How to give full play to the powerful advantages of the boundary description of the level set method so that the topology optimization results maintain clear configuration boundaries while having good manufacturability is an unavoidable problem in the application of level set topology optimization in actual engineering.

[0005] The current research challenge lies in how to effectively quantify the geometric features of topology optimization results and achieve precise control of geometric features. First, there is little research on the identification of configuration boundaries and the quantification of geometric features. The image processing methods that identify the basis for calculating the geometric size features of components, hole size features, and angle features of configuration boundaries, and accurately identify the coordinate position of the boundaries of the optimization results and calculate the component size, hole size, and angle have not yet been quantified into topology optimization problems. For the distance features and angle features of the topology optimization design results, how to control the distance features and angle features of the boundaries based on the coordinate position of the boundaries without changing the overall configuration, and how to locally adjust the boundary features while maintaining the overall configuration so that the components, holes, or angles meet the constraints, is the main difficulty.

[0006] First, there is currently little research on the identification of configuration boundaries and the quantification of geometric features. Image processing methods that accurately identify the coordinate positions of the boundaries of the optimization results and calculate the component size, hole size, and angle characteristics based on the identification of configuration boundaries have not yet been quantified into topology optimization problems. The main difficulty in solving the distance and angle characteristics of the topology optimization design results is how to manipulate the distance and angle characteristics of the boundaries based on their coordinate positions without changing the overall configuration, and to achieve local adjustment of boundary features to ensure that components, holes, or angles meet the constraints while maintaining the overall configuration. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to effectively quantify the geometric features of the topology optimization results and realize precise control of the geometric features. To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A method for controlling the geometric feature size of topology optimization results based on image processing is used in the topology optimization design and manufacturing of integrated materials and structures. It realizes the integration of topology design and additive manufacturing of cross-scale structures with extremely fine components, extremely small holes, and special angle constraints, which are subject to concentrated and distributed loads and fixed and simply supported boundary constraints. It quantifies the topology optimization design results based on the image binarization method, and uses image processing technology to accurately identify and quantify the macro and micro boundaries of cross-scale structures. Then, by controlling the coordinate points of the boundaries, the distance and angle characteristics of the topology optimization design results are controlled. The implementation steps are as follows:

[0009] Step 1: For cross-scale structures based on additive manufacturing, given the macrostructure design domain, microcell design domain, load and displacement boundary conditions, the design domain and non-design domain at the macro and micro levels are determined, and a dual-scale topology optimization model is constructed. The dual-scale topology optimization model is constructed by taking the volume fraction of the macrostructure as the optimization target, the macro allowable displacement and the micro volume fraction as inequality constraints, the macro-micro finite element equilibrium equations as equality constraints, and the radial basis function coefficients of the dual-scale level set function as design variables.

[0010] Step 2: Perform macro-micro finite element analysis on the cross-scale structure in the current iteration process, and then calculate the sensitivity of the objective function and constraints in the dual-scale topology optimization model to the time variable of the dual-scale level set function based on the shape derivative principle. Update the dual-scale level set function to drive the update of the cross-scale structure configuration, and then determine whether the updated cross-scale structure meets the convergence conditions of the topology optimization. If so, obtain the topology optimization design result. If not, continue to perform finite element analysis and sensitivity analysis and update the design variables until the convergence conditions are met.

[0011] Step 3: Perform image processing on the dual-scale topology optimization model: Given the resolution factor of the dual-scale level set function, perform bilinear interpolation on the dual-scale level set function. Then, based on the image binarization method, process the dual-scale level set function to obtain a 0-1 distribution of the dual-scale level set function, thereby identifying the macro- and micro-topological features of the cross-scale structure and obtaining the number of boundaries and coordinate points of the cross-scale structure.

[0012] Step 4: Based on the coordinate points of the boundaries of the cross-scale structure, the minimum distance between the coordinates of two points on different boundaries is calculated as a way to detect extremely fine components. The maximum distance between the coordinates of two points on the same boundary or the distance from the coordinates of a point on the same boundary to the center of gravity is calculated as a way to detect extremely small holes. The angle between the coordinates of any three points on the same boundary is calculated as a way to detect special angles. The macroscopic and microscopic configurations are quantified respectively to obtain the specific numerical values ​​of the geometric characteristics of the cross-scale structure.

[0013] Step 5: Controlling the ultra-fine component features of cross-scale structures: For ultra-fine component features, first identify the boundaries with larger radii and keep them unchanged, and scale the boundaries with smaller radii. If the boundaries with smaller radii do not have the problem of ultra-small holes when scaled to meet the component size threshold constraint, the ultra-fine component control is completed. If the boundaries with smaller radii have the problem of ultra-small holes when scaled to meet the component size threshold constraint, the boundaries with smaller radii are deleted.

[0014] Step 6: Controlling Hole Features of Cross-Scale Structures: For extremely small hole features, first identify the radius of the boundary and scale it around its center of gravity until the new boundary satisfies the component size threshold constraint. If the minimum distance between the new boundary and other boundaries satisfies the component size threshold constraint, hole control is complete. If the minimum distance between the new boundary and other boundaries does not satisfy the component size threshold constraint, the boundary is deleted.

[0015] Step 7: Control the special angle features of cross-scale structures: For special angle features, if the angle between the coordinates of any three points on the same boundary does not meet the angle constraint, then determine whether the distance between the two endpoints of the boundary meets the component size threshold constraint. If it is greater than the component size threshold constraint, find and add two points on the two adjacent sides of the boundary that are parallel to the opposite side of the boundary and the distance is equal to the distance constraint, and delete the vertex of the angle; if it is less than the component size threshold constraint, directly delete the vertex without adding a new point.

[0016] The present invention is characterized in that:

[0017] In the step one, a cross-scale topology optimization model is established under the constraints of multiple geometric features including component size, hole size and special angles; in the step two, the rapid convergence of the cross-scale topology optimization is achieved based on the parameterized level set method, and the established convergence indicators include the stability constraint of the objective function and the error values ​​of multiple constraint conditions; in the step three, the topology optimization design results are quantified based on the image binarization method, and the macro-micro boundary features of the cross-scale structure are identified; in the step four, the minimum component size, minimum hole size and boundary angle values ​​of the topology optimization results are calculated based on the coordinate point information on the boundary; in the step five, size control criteria for extremely fine components under different circumstances are constructed; in the step six, size control criteria for extremely small holes under different circumstances are constructed; in the step seven, angle control criteria for special angles under different circumstances are constructed.

[0018] The beneficial effects of the present invention compared with the prior art are:

[0019] The present invention discloses a method for controlling the size of geometric features of topology optimization results based on image processing. Taking into account the manufacturing constraints of extremely fine components, extremely small holes and special angles in the additive manufacturing process, a size control strategy is introduced after obtaining the optimized design results and before processing and manufacturing. This method can achieve accurate identification, quantification and precise quantitative control of multiple geometric features of the topology optimization results.

[0020] The method is aimed at a cross-scale structure, first, a topological optimization model for heat transfer performance and bearing performance of the cross-scale structure is constructed based on a level set method; second, sensitivity analysis results of an objective function and constraint conditions in the optimization model are obtained, and a gradient optimization algorithm is used to solve the topological optimization model to realize topological updating of the cross-scale structure until a final topological optimization design result is obtained; then, the design result is quantified based on an image binarization method, and accurate identification and precise quantification of a macroscopic-microscopic boundary of the cross-scale structure are realized by means of image processing technology; finally, distance and angle of the topological optimization design result are regulated by regulating coordinate points of the boundary. The present application realizes accurate identification and effective regulation of various geometric features based on image processing technology under the level set framework, promotes design and manufacturing integration, and helps to improve design efficiency and shorten design cycle for the geometric features such as extremely thin components, extremely small holes and special angles of the cross-scale topological optimization design result which are difficult to manufacture and process. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a rectification flow chart of a topological optimization result geometric feature size control method based on image processing according to the present application;

[0022] Figure 2 is a geometric model and boundary condition schematic diagram of an embodiment;

[0023] Figure 3 is a configuration result of topological optimization under different design strategies;

[0024] Figure 4 is an iteration process of a macroscopic volume fraction in the topological optimization process;

[0025] Figure 5 is an iteration process of a microscopic volume fraction in the topological optimization process. DETAILED DESCRIPTION

[0026] Exemplary embodiments of the present disclosure will be described more fully hereinafter with reference to the accompanying drawings; however, these embodiments are not intended to limit the present disclosure, but to explain the present disclosure. As those skilled in the art would realize, the described embodiments can be modified in various different ways, all without departing from the scope of the present disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature and explanations intended to conduce the full and enabling disclosure of the present disclosure to those skilled in the art.

[0027] As Figure 1As shown, the present invention discloses a method for controlling the size of geometric features of topology optimization results based on image processing. This method targets cross-scale structures. First, a topology optimization model for the heat transfer performance and load-bearing performance of cross-scale structures is constructed based on the level set method; secondly, the sensitivity analysis results of the objective function and constraints in the optimization model are obtained, and the topology optimization model is solved based on the gradient optimization algorithm to realize the topology update of the cross-scale structure until the final topology optimization design result is obtained; then, the design results are quantified based on the image binarization method, and the image processing technology is used to realize the accurate identification and precise quantification of the macro-micro boundaries of the cross-scale structure; finally, the distance and angle of the topology optimization design results are controlled by regulating the coordinate points of the boundaries. The present invention targets geometric features that are difficult to manufacture and process, such as extremely fine components, extremely small holes and special angles in the cross-scale topology optimization design results. Based on the image processing technology under the level set framework, the present invention realizes the effective control of the precise identification of multiple geometric features, promotes the integration of design and manufacturing, and helps to improve design efficiency and shorten the design cycle. The following is combined with Figure 1 Describe the method in detail, such as Figure 1 As shown, the method includes the following steps:

[0028] Step 1: For cross-scale structures based on additive manufacturing, given the macrostructure design domain, the microcell design domain, and the load and displacement boundary conditions, the design and non-design domains at the macro and micro levels are determined, and a dual-scale topology optimization model is constructed. This involves using the volume fraction of the macrostructure as the optimization target, the macroallowable displacement and the microvolume fraction as inequality constraints, the macro- and micro-finite element equilibrium equations as equality constraints, and the radial basis function coefficients of the dual-scale level set function as design variables. This dual-scale topology optimization model, also known as the dual-scale macro- and micro-topology optimization model, is constructed. Among them, volume fraction, macro-allowable displacement, micro-volume fraction, macro-micro finite element equilibrium equation, dual-scale level set function, and radial basis function coefficient are well-known contents of the optimization model in this field. The dual-scale topology optimization model refers to a topology optimization model in which the design variables are the parameters of the macrostructure and the microscopic unit cell, the macro-allowable displacement refers to the allowable displacement of the macrostructure, the micro-volume fraction refers to the volume fraction of the microscopic unit cell, the macro-micro finite element equilibrium equation refers to the equilibrium equation of the macrostructure and the microscopic unit cell, the dual-scale level set function refers to the level set function at the macro and micro levels, and the radial basis function coefficient refers to the coefficient of the radial basis function polynomial.

[0029] Step 2: Perform macro-micro finite element analysis on the cross-scale structure in the current iteration. Then, based on the shape derivative principle, calculate the sensitivity of the objective function and constraints in the dual-scale topology optimization model to the time variable of the dual-scale level set function. Update the dual-scale level set function to drive the cross-scale structural configuration update. Then determine whether the current cross-scale structure meets the convergence conditions of the topology optimization. If so, obtain the topology optimization design result. If not, continue to perform finite element analysis and sensitivity analysis and update the design variables until the convergence conditions are met. Among them, the shape derivative principle refers to the shape derivative principle in the calculus of multivariate functions, and the configuration update refers to the change in the structural topology optimization. The convergence conditions include the change in the objective function being less than the allowable value of its change and the deviation between the constraint and the allowable value of the constraint being less than the allowable value of the deviation. Finite element analysis refers to the calculation of the structural response based on the finite element method after discretizing the macrostructure and micro-unit cells. Sensitivity analysis refers to the calculation of the sensitivity of the objective function and constraints in the optimization model to the level set function. The design variables include the coefficients of the dual-scale radial basis function.

[0030] Step 3: Perform image processing on the topology optimization design results. Given the resolution factor of the two-scale level set function, perform bilinear interpolation on the two-scale level set function. Then, based on the image binarization method, process the two-scale level set function to obtain a 0-1 distributed two-scale level set function, thereby identifying the macro- and micro-topological features of the cross-scale structure and obtaining the number of boundaries and coordinate points of the cross-scale structure. The method of identifying the macro- and micro-topological features of the cross-scale structure through the 0-1 distributed two-scale level set function is to equal the level set function value to 1 inside the structure and equal the level set function value to 0 outside the structure. The 0-1 change is the structural boundary. The macro- and micro-topological features include the boundaries of the macrostructure and the boundaries of the microscopic unit cell.

[0031] Step 4: Based on the coordinate points of the cross-scale structure's boundaries, the minimum distance between two points on different boundaries is calculated as a method for detecting extremely fine components. The maximum distance between two points on the same boundary, or the distance from a point on the same boundary to the center of gravity, is calculated as a method for detecting extremely small holes. The angle between any three points on the same boundary is calculated as a method for detecting special angles. The macroscopic and microscopic configurations are quantified to obtain specific numerical values ​​for the geometric characteristics of the cross-scale structure. The macroscopic configuration is the topological configuration of the cross-scale structure at the macroscopic level, and the microscopic configuration is the topological configuration of the microscopic unit cell of the cross-scale structure.

[0032] Step 5: Control the extremely fine component features of cross-scale structures: For extremely fine component features, first identify the boundary with a larger radius and keep it unchanged, and scale the boundary with a smaller radius. If the boundary with a smaller radius does not have an extremely small hole problem when scaled to meet the component size threshold constraint, then the extremely fine component control is completed. If the boundary with a smaller radius has an extremely small hole problem when scaled to meet the component size threshold constraint, then the boundary with a smaller radius is deleted. The larger radius and smaller radius above refer to the larger or smaller one when compared with the other. The above-mentioned component size threshold constraint can include the length and width of the component. The extremely small hole problem is that the radius of the hole is less than the threshold. The identification method is to calculate the distance from the point on the hole boundary to the center of gravity of the boundary and compare it with the threshold. If the distance is less than the threshold, it is judged as an extremely small hole problem. The scaling ratio can be the proportional coefficient of the threshold and the radius.

[0033] Step 6: Controlling Hole Features of Cross-Scale Structures: For extremely small hole features, first identify the radius of the boundary and scale it around its center of gravity until the new boundary satisfies the component size threshold constraint. If the minimum distance between the new boundary and other boundaries satisfies the component size threshold constraint, hole control is complete. If the minimum distance between the new boundary and other boundaries does not satisfy the component size threshold constraint, the boundary is deleted. The component size threshold constraint can include the length and width of the component, and the scaling ratio can be the ratio of the threshold to the actual length or the ratio of the threshold to the actual width.

[0034] Step 7: Regulate the special angular features of cross-scale structures: For special angular features, if the angle between any three points on the same boundary does not satisfy the angle constraint, determine whether the distance between the two endpoints of the boundary satisfies the component size threshold constraint. If it does, find and add two points on the two adjacent sides of the boundary that are parallel to the opposite side of the boundary and at a distance equal to the distance constraint, and delete the vertex of the angle. If it does, delete the vertex directly without adding a new point. Angle constraints can include angles that must be less than a maximum value or greater than a minimum value. Component size threshold constraints can include maximum and minimum angle constraints.

[0035] Specifically, the step 1 of "using the radial basis function coefficients of the dual-scale level set function as design variables to construct a dual-scale topology optimization model" means establishing a mathematical model for dual-scale topology optimization based on the level set method, which specifically includes the following formula calculation process:

[0036] ,

[0037] In the formula, find represents the design variable, min represents the minimization of the objective function, st represents the constraint condition, all variables with superscript "Ma" represent macro variables, superscript "Mi" represent micro variables, and subscript "targ" represents the constraint value (threshold). represents the level set function, represents the spatial variable of the level set function, The coefficients of the radial basis function representing the level set function are only related to the time variable of the level set function. Related variables, represents the volume fraction, Represents the structure boundary, Indicates the same boundary The minimum value from any coordinate point on the represents the number of boundaries, Represents two boundaries and The minimum distance between Represents the component size threshold constraint, and Indicates the boundary number, Representing boundaries On the The coordinates of the points, Indicates is the vertex, and the angle formed by two adjacent points as endpoints, represents the entire design domain, represents the global stiffness matrix, represents the overall displacement column vector, represents the overall load column vector, Represents the flexibility of the cross-scale structure and is the objective function in the optimization model. represents the level set function The projection function, The function expression is:

[0038] .

[0039] Specifically, the second step of "performing a macro-micro finite element analysis on the cross-scale structure in the current state, and then calculating the sensitivity of the objective function and constraints in the dual-scale topology optimization model to the time variable of the dual-scale level set function based on the shape derivative principle, updating the dual-scale level set function to drive the update of the cross-scale structure configuration, and then judging whether the updated cross-scale structure meets the convergence conditions of the topology optimization. If so, a topology optimization design result is obtained. If not, finite element analysis and sensitivity analysis are continued and the design variables are updated until the convergence conditions are met" includes:

[0040] The macro-micro finite element analysis of the current cross-scale structure includes: first, calculating the equivalent elastic tensor of the unit cell by the homogenization method:

[0041] ,

[0042] Where, represents the equivalent elastic tensor, represents the actual elastic tensor of the homogeneous structure, represents the 3rd-order identity matrix, represents the finite element strain matrix, represents a vector constructed by periodic boundary conditions, and the superscript T represents matrix transpose.

[0043] Substituting the equivalent elastic tensor of the unit cell into the finite element equation of the macrostructure, the displacement field of the macrostructure can be calculated:

[0044] .

[0045] The results of finite element analysis serve as the data source for sensitivity analysis. Sensitivity analysis is a typical method for constructing the velocity field of the level set function. The velocity field of the level set function is essential for solving the level set equation and updating the level set function. After updating the level set function, convergence is performed to determine whether the current results meet design requirements. Based on the principle of shape derivatives, the sensitivity of the objective function and constraints in the two-scale topology optimization model with respect to the time variable of the two-scale level set function (sensitivities with respect to the macroscopic level set function and sensitivity with respect to the microscopic level set function) is calculated. This is then used to construct the velocity field for the updated level set function. This allows for continuous modification of the level set function distribution, thereby achieving cross-scale structural boundary changes. The sensitivity calculation can be performed using known methods in the art and will not be elaborated here. After calculating the sensitivity, the velocity field is constructed by aligning the velocity field with the inverse of the sensitivity. The level set function is modified by solving the level set equation to update the coefficients of the radial basis functions, thereby modifying the distribution of the level set function to achieve cross-scale structural configurations. The level set equation and radial basis functions are well known in the art and are typical ordinary differential equations and polynomial functions.

[0046] Determine whether the updated cross-scale structure meets the convergence conditions:

[0047] ,

[0048] Where, is the objective function, is the objective function of the kth iteration, is the objective function of the qth iteration, Indicates the The macroscopic volume fraction of the iteration, represents the mesoscopic volume fraction of the kth iteration, represents the allowable value of the macroscopic volume fraction, the subscript q represents the number of iterations, and the subscript represents the number of iterations, 、 and represent the error thresholds of the objective function, macroscopic volume fraction, and microscopic volume fraction, respectively.

[0049] When the error between the objective function variation and the macro-micro volume fraction and the allowable value (the allowable value is 0.005) in the dual-scale topology optimization model for five consecutive times meets the threshold (the threshold can be set to 0.005), the topology optimization ends and the topology optimization design result is obtained; if the constraints are not met, finite element analysis, sensitivity analysis, and level set function update are performed until the constraints are met.

[0050] Specifically, the step three of "performing image processing on the topology optimization design results. Given a resolution factor of the two-scale level set function, performing bilinear interpolation on the two-scale level set function, and then processing the two-scale level set function based on an image binarization method to obtain a two-scale level set function with a 0-1 distribution, thereby identifying the macroscopic and microscopic topological features of the cross-scale structure and obtaining the number of boundaries and coordinate points of the cross-scale structure" includes:

[0051] Based on the geometric feature constraints of the dual-scale macro-micro topology optimization model in step 1 (the geometric feature constraints refer to the component size, hole size, and angle constraints of the dual-scale macro-micro topology optimization model in step 1), data source acquisition (data source acquisition refers to obtaining the level set function in step 1). Given the resolution factor of the dual-scale level set function, bilinear interpolation is performed on the level set function to refine the level set function. Then, based on the image binarization method, the dual-scale level set function is processed to obtain a 0-1 distribution dual-scale level set function, that is, the refined level set function is grayscale transformed. The specific transformation formula is:

[0052] ,

[0053] Where, Yes The gray value after transformation, is the threshold value of grayscale transformation, is the grayscale value before transformation:

[0054] ,

[0055] Where, 、 and are the pixel values ​​of red, green and blue respectively. The threshold for grayscale conversion can be a constant or an adaptive value.

[0056] Next, execute "then identify the macro-micro topological features of the cross-scale structure and obtain the number of boundaries and coordinate points of the boundaries of the cross-scale structure": Boundary identification can be achieved using the Moore neighborhood tracking algorithm. This algorithm determines the initial detection point based on the binary data and extracts the pixel data around the detection point. Using the eight-neighborhood edge detection method, the pixel data within the eight neighborhoods is judged in a counterclockwise direction until the first non-zero pixel data is obtained. If there is a non-zero pixel, the neighborhood where the first non-zero pixel appears becomes the next detection point; if there is no non-zero pixel in all eight neighborhoods, the first non-zero pixel found among all the pixels becomes the detection point until all non-zero pixels are detected, thereby obtaining all the boundary features of the topology optimization result. All non-zero pixels are combined to form the boundary features of the topology optimization result.

[0057] Specifically, the fourth step "based on the coordinate points of the boundary of the cross-scale structure, the minimum distance between the coordinates of two points on different boundaries is calculated as a way to detect extremely fine components, the maximum distance between the coordinates of two points on the same boundary or the distance from the coordinates of the point on the same boundary to the center of gravity is calculated as a way to detect extremely small holes, and the angle between the coordinates of any three points on the same boundary is calculated as a way to detect special angles, and the macroscopic configuration and the microscopic configuration are quantified respectively to obtain the specific numerical values ​​of the geometric characteristics of the cross-scale structure" includes: for the identification of the characteristics of extremely fine components, the calculation of the coordinates of different boundaries and The distance between the coordinate points on :

[0058] ,

[0059] Where, It's a boundary The coordinate points on It's a boundary The coordinate points on the . For all the coordinate points, the total distances are formed. Minimum value It is the minimum distance between two components, which allows the identification of extremely fine components.

[0060] For the recognition of extremely small hole features, first calculate the boundary Center of Gravity :

[0061] ,

[0062] Where, is the number of coordinate points on the boundary. Then calculate the distance from any point on the boundary to the center of gravity :

[0063] ,

[0064] The distances obtained for all coordinate points are composed of Minimum value It is the minimum radius of the hole in the boundary, thereby identifying the hole.

[0065] For the identification of special angle features, the angle formed by three adjacent coordinate points is calculated using the cosine theorem The cosine of :

[0066] ,

[0067] Where, and On the same boundary The points on both sides are used to calculate the included angle based on the cosine result. If the included angle satisfies the angle constraint, it is a special angle feature.

[0068] Specifically, step 5, "regulating the ultra-fine component features of cross-scale structures: for ultra-fine component features, first identify the boundary with a larger radius and keep it unchanged, and scale the boundary with a smaller radius. If the boundary with a smaller radius does not have an ultra-small hole problem when scaled to meet the component size constraint, the ultra-fine component regulation is completed. If the boundary with a smaller radius has an ultra-small hole problem when scaled to meet the component size constraint, the boundary with a smaller radius is deleted," includes:

[0069] The control of extremely fine component features is achieved through boundary scaling. Minimum value It is the minimum distance between the components of the two boundaries, thereby identifying the extremely fine components. For the identified extremely fine components, calculate the distance between the two boundaries. and Minimum radius and Identification and The larger radius of the boundary and keep it unchanged, and Scaling is done by taking the smaller radius of the boundary. Let's assume ,and Representing a smaller radius, the scaling factor is:

[0070] ,

[0071] Where, is the size threshold, It's a boundary All points to the boundary Center of Gravity The minimum distance, if scaled to meet the component size threshold When constraining, there is no problem of extremely small holes in the boundary with a smaller radius, so the extremely fine component control is completed, and the scaled boundary The coordinates of the point on are:

[0072] ,

[0073] If scaled to meet the component size threshold When constraining, if there are extremely small holes in the boundaries with smaller radius, the boundaries with smaller radius will be deleted.

[0074] Specifically, step 6, "regulating the extremely small hole features of the cross-scale structure: for the extremely small hole features, first identify the radius of the boundary, and scale the boundary with the center of gravity of the boundary as the center until the new boundary meets the component size threshold constraint: if the minimum distance between the boundary and other boundaries at this time meets the component size threshold constraint, the hole regulation is completed; if the minimum distance between the boundary and other boundaries at this time does not meet the component size threshold constraint, the boundary is deleted," includes:

[0075] For extremely small hole features, first identify the boundary Radius , with the center of gravity of the boundary Scale the border to the center until the new border Meet the size threshold Constraints, the scaling factor is:

[0076] ,

[0077] Scaled boundaries The coordinates of the point on are:

[0078] ,

[0079] If the minimum distance between the Meeting component size thresholds Constraint, the hole control is completed; if the minimum distance between the other boundaries does not meet the component size threshold constraint, the boundary is deleted.

[0080] Specifically, the step seven "regulating the special angle features of cross-scale structures: for special angle features, if the angle between the three points of any three coordinates on the same boundary does not satisfy the angle constraint, then determine whether the distance between the two endpoints of the boundary satisfies the component size threshold constraint. If it is greater than the component size threshold constraint, then find and add two points on the two adjacent sides of the boundary that are parallel to the opposite side of the boundary and have a distance equal to the component size threshold constraint, and delete the vertex of the angle; if it is less than the component size threshold constraint, directly delete the vertex without adding a new point" includes: for special angle features, if the angle between the three points does not satisfy the angle constraint , then determine whether the distance between the two endpoints meets the size threshold Constraint, if greater than the size threshold Constraint, then find and add parallel edges on two adjacent edges that are parallel to the opposite edge and have a distance equal to the size threshold. Constrain the two points and move the vertex Delete, and the newly added points satisfy:

[0081] ,

[0082] Where, and They are line segments and line segments The point on.

[0083] If the angle between the three points does not satisfy the angle constraint , then determine whether the distance between the two endpoints meets the size threshold Constraint, if less than the size threshold Constraint, directly move the vertex Delete and do not add new points. Here, the angle constraint Can be 150°, size threshold It can be 1.5 mm.

[0084] Example:

[0085] The method for controlling geometric feature size of topology optimization results based on image processing disclosed in the present invention is applicable to cross-scale topology optimization design of any structure, such as Figure 2 The cross-scale topology optimization problem for an L-shaped flat plate structure is shown in the figure. The macroscopic design domain is a square with a length and width of 600 mm, resulting from removing the 300 mm square in the upper right corner. The microscopic design domain has a length and width of 1 mm. The proposed method for controlling the geometric features of topology optimization results based on image processing demonstrates the effectiveness of dimensional control. Figure 3is the configuration result of topology optimization under different design strategies. The material elastic modulus is 2×105 MPa, and the Poisson's ratio is 0.3. The upper side boundary of the design area is applied with a rigid support constraint, and the right side middle position is subjected to a concentrated load with an amplitude equal to kN, the direction is 45° with the vertical direction. The size constraint parameters of each working condition are compared in Table 1, wherein the percentage refers to the ratio of the size constraint value to the design domain, and the angle constraint is , Figure 3 The middle is the equivalent elastic tensor, Figure 3 The design results of macro and micro configurations and local details are also given. Figure 3 The left upper graph of Fig. 1 is the design result of working condition 1 shown in Table 1, the right upper graph is the design result of working condition 2, the left lower graph is the design result of working condition 3, and the right lower graph is the design result of working condition 4. The iteration history curves of macroscopic volume fraction and microscopic volume fraction in the topology optimization process are shown in Figure 4 and Figure 5 The macroscopic and microscopic volume fractions, actual displacements and total calculation times of the topology optimization under different design strategies are shown in Table 2.

[0086] Table 1 Comparison of parameters of each working condition

[0087]

[0088] Table 2 Final results of the examples

[0089]

[0090] The results show that:

[0091] The geometry feature size control method based on image processing can effectively realize accurate control of geometric features under different size constraint conditions, and can quickly converge. The size constraint has a significant effect on the design result, and excessive size constraint can even cause significant changes in the result (working condition 2). The higher the size constraint level, the more material is needed to maintain manufacturability (0.2392→0.3342). The size control method can maintain effectiveness under different constraint levels, and realize accurate quantitative control of multiple geometric features of macro and micro configurations. There are two reasons for the emergence of relatively thick rods in the macro configuration of case 2: high level of size constraint, which requires strict size limitation to ensure manufacturability requirements; in addition, due to the uneven distribution of geometric features on the boundary and the uneven distribution of points, the boundary scaling does not match the ideal situation.

[0092] From the final configuration result, the image processing-based topology optimization result geometric feature size control method can control various geometric features, all cases not meeting the angle constraint are good, smooth transition can be realized, stress concentration phenomenon caused by residual stress can be effectively avoided, and the safety and service life of the structure are improved. The method proposed in the application can be quickly completed, and the total time including topology optimization is about 1 minute, and the time for only image processing to realize geometric feature control is not more than 1 minute.

[0093] The above is only the specific steps of the application, and does not constitute any limitation on the protection scope of the application; it can be extended to the field of topology optimization design of different mechanics and thermodynamics problems, and any technical solution formed by equivalent transformation or equivalent replacement falls within the protection scope of the application.

[0094] In the specification provided herein, a large number of specific details are described. However, it can be understood that the embodiments of the application can be practiced without these specific details. In some examples, well-known methods, structures and techniques are not shown in detail in order not to obscure the understanding of the present specification. In addition, it should be noted that the language used in the present specification is mainly selected for readability and teaching purposes, rather than for explaining or limiting the subject matter of the present application.

Claims

1. A method for controlling geometric feature dimensions of topology optimization results based on image processing, characterized in that: include: Step 1: For cross-scale structures based on additive manufacturing, given the macroscopic structural design domain, microscopic unit cell design domain, load and displacement boundary conditions, determine the design domain and non-design domain at the macro and micro levels, and construct a dual-scale topology optimization model; The dual-scale topology optimization model is constructed by taking the volume fraction of the macrostructure as the optimization target, the macroscopic allowable displacement and the microscopic volume fraction as inequality constraints, the macroscopic and microscopic finite element equilibrium equations as equality constraints, and the radial basis function coefficients of the dual-scale level set function as design variables. Step 2: Perform macro-micro finite element analysis on the cross-scale structure in the current iteration process, and then calculate the sensitivity of the objective function and constraints in the dual-scale topology optimization model to the time variable of the dual-scale level set function based on the shape derivative principle. Update the dual-scale level set function to drive the update of the cross-scale structure configuration, and then determine whether the updated cross-scale structure meets the convergence conditions of the topology optimization. If so, obtain the topology optimization design result. If not, continue to perform finite element analysis and sensitivity analysis and update the design variables until the convergence conditions are met. Step 3: Perform image processing on the dual-scale topology optimization model: Given the resolution factor of the dual-scale level set function, perform bilinear interpolation on the dual-scale level set function. Then, based on the image binarization method, process the dual-scale level set function to obtain a 0-1 distribution of the dual-scale level set function, thereby identifying the macro- and micro-topological features of the cross-scale structure and obtaining the number of boundaries and coordinate points of the cross-scale structure. Step 4: Based on the coordinate points of the boundaries of the cross-scale structure, the minimum distance between the coordinates of two points on different boundaries is calculated as a way to detect extremely fine components. The maximum distance between the coordinates of two points on the same boundary or the distance from the coordinates of a point on the same boundary to the center of gravity is calculated as a way to detect extremely small holes. The angle between the coordinates of any three points on the same boundary is calculated as a way to detect special angles. The macroscopic and microscopic configurations are quantified respectively to obtain the specific numerical values ​​of the geometric characteristics of the cross-scale structure. Step 5: Controlling the ultra-fine component features of cross-scale structures: For ultra-fine component features, first identify the boundaries with larger radii and keep them unchanged, and scale the boundaries with smaller radii. If the boundaries with smaller radii do not have the problem of ultra-small holes when scaled to meet the component size threshold constraint, the ultra-fine component control is completed. If the boundaries with smaller radii have the problem of ultra-small holes when scaled to meet the component size threshold constraint, the boundaries with smaller radii are deleted. Step 6: Controlling Hole Features of Cross-Scale Structures: For extremely small hole features, first identify the radius of the boundary and scale it around its center of gravity until the new boundary satisfies the component size threshold constraint. If the minimum distance between the new boundary and other boundaries satisfies the component size threshold constraint, hole control is complete. If the minimum distance between the new boundary and other boundaries does not satisfy the component size threshold constraint, the boundary is deleted. Step 7: Control the special angle features of cross-scale structures: For special angle features, if the angle between the coordinates of any three points on the same boundary does not meet the angle constraint, then determine whether the distance between the two endpoints of the boundary meets the component size threshold constraint. If it is greater than the component size threshold constraint, find and add two points on the two adjacent sides of the boundary that are parallel to the opposite side of the boundary and the distance is equal to the distance constraint, and delete the vertex of the angle; if it is less than the component size threshold constraint, directly delete the vertex without adding a new point.

2. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: In step 1, the radial basis function coefficients of the dual-scale level set function are used as design variables to construct a dual-scale topology optimization model, which includes the following formula calculation process: ， In the formula, find represents the design variable, min represents the minimization of the objective function, st represents the constraint condition, all variables with superscript "Ma" represent macro variables, superscript "Mi" represent micro variables, and subscript "targ" represents the constraint value (threshold). represents the level set function, represents the spatial variable of the level set function, The coefficients of the radial basis function representing the level set function are only related to the time variable of the level set function. Related variables, represents the volume fraction, Represents the structure boundary, Indicates the same boundary The minimum value from any coordinate point on the represents the number of boundaries, Represents two boundaries and The minimum distance between Represents the component size threshold constraint, and Indicates the boundary number, Representing boundaries On the The coordinates of the points, Indicates is the vertex, and the angle formed by two adjacent points as endpoints, represents the entire design domain, represents the global stiffness matrix, represents the overall displacement column vector, represents the overall load column vector, Represents the flexibility of the cross-scale structure and is the objective function in the optimization model. represents the level set function The projection function, The function expression is: 。 3. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: In step 2, a macro-micro finite element analysis is performed on the current cross-scale structure. Then, based on the shape derivative principle, the sensitivity of the objective function and constraints in the dual-scale topology optimization model to the time variable of the dual-scale level set function is calculated. The dual-scale level set function is updated to drive the update of the cross-scale structure configuration. Then, it is determined whether the updated cross-scale structure meets the convergence conditions of the topology optimization. If so, the topology optimization design result is obtained. If not, the finite element analysis and sensitivity analysis are continued and the design variables are updated until the convergence conditions are met, including: For the dual-scale topology optimization model in step 1, for the finite element analysis under a given structural state: first, the equivalent elastic tensor of the unit cell is calculated using the homogenization method: ， Where, represents the equivalent elastic tensor, represents the actual elastic tensor of the homogeneous structure, represents the 3rd-order identity matrix, represents the finite element strain matrix, represents the vector constructed by periodic boundary conditions, and the superscript T represents the matrix transpose; Substitute the equivalent elastic tensor of the unit cell into the finite element equation of the macrostructure to calculate the displacement field of the macrostructure: ； Judging whether the current cross-scale structure meets the convergence conditions of topology optimization includes: ， Where, is the objective function, is the objective function of the kth iteration, is the objective function of the qth iteration, Indicates the The macroscopic volume fraction of the iteration, represents the allowable value of the macroscopic volume fraction, the subscript q represents the number of iterations, and the subscript represents the number of iterations, 、 and represent the error thresholds of the objective function, macroscopic volume fraction, and microscopic volume fraction, respectively; When the error between the objective function variation and the macro-micro volume fraction and the allowable value in the dual-scale topology optimization model for five consecutive times meets the threshold, the topology optimization ends and the topology optimization design result is obtained. If the constraints are not met, finite element analysis, sensitivity analysis, and level set function update are performed until the constraints are met.

4. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: Step 3: "Performing image processing on the dual-scale topology optimization model, giving the resolution factor of the dual-scale level set function, performing bilinear interpolation on the dual-scale level set function, and then processing the dual-scale level set function based on the image binarization method to obtain a 0-1 distribution of the dual-scale level set function, thereby identifying the macro- and micro-topological features of the cross-scale structure and obtaining the number of boundaries and coordinate points of the cross-scale structure" includes: According to the geometric feature constraints of the two-scale topology optimization model in step one, the level set function of step one is obtained. Given the resolution multiple of the two-scale level set function, the level set function is bilinearly interpolated to refine the level set function. Then, the two-scale level set function is processed based on the image binarization method to obtain a 0-1 distribution two-scale level set function, that is, the refined level set function is grayscale transformed. The transformation formula is: ， Where, Yes The gray value after transformation, is the threshold value of grayscale transformation, is the grayscale value before transformation; The initial detection point is determined based on the binary data, and the pixel data around the detection point is extracted. The eight-neighborhood edge detection method is used to judge the pixel data in the eight neighborhoods in a counterclockwise direction until the first non-zero pixel data is obtained; if there is a non-zero pixel, the neighborhood where the first non-zero pixel appears becomes the next detection point; if there is no non-zero pixel in all eight neighborhoods, the first non-zero pixel found among all the pixels becomes the detection point, until all non-zero pixels are detected, thereby obtaining all the boundary features of the topology optimization result.

5. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: Step 4: "Based on the coordinate points of the boundaries of the cross-scale structure, the minimum distance between the coordinates of two points on different boundaries is calculated as a way to detect extremely fine components, the maximum distance between the coordinates of two points on the same boundary or the distance from the coordinates of a point on the same boundary to the center of gravity is calculated as a way to detect extremely small holes, and the angle between the coordinates of any three points on the same boundary is calculated as a way to detect special angles. The macroscopic configuration and the microscopic configuration are quantified respectively to obtain the specific numerical values ​​of the geometric characteristics of the cross-scale structure" includes: for the identification of the characteristics of extremely fine components, the calculation of the coordinates of different boundaries and The distance between the coordinate points on : ， Where, It's a boundary The coordinate points on It's a boundary The coordinate points on the Minimum value It is the minimum distance of components between two boundaries, thus identifying extremely fine components; For the recognition of extremely small hole features, first calculate the boundary Center of Gravity : ， Where, is the number of coordinate points on the boundary, and then calculate the distance from any point on the boundary to the center of gravity : ， The distances obtained for all coordinate points are Minimum value It is the minimum radius of the hole in the boundary, thus identifying the hole; For the identification of special angle features, the angle formed by three adjacent coordinate points is calculated using the cosine theorem The cosine of : ， Where, and On the same boundary The included angle of the points on both sides is calculated based on the cosine result. If the included angle meets the angle constraint condition, it is a special angle feature.

6. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: In step 5, the ultra-fine component features of the cross-scale structure are regulated: for the ultra-fine component features, the boundary with a larger radius is first identified and kept unchanged, and the boundary with a smaller radius is scaled. If the boundary with a smaller radius does not have the problem of ultra-small holes when scaled to meet the component size constraint, the ultra-fine component regulation is completed. If the boundary with a smaller radius has the problem of ultra-small holes when scaled to meet the component size constraint, the boundary with a smaller radius is deleted, including: For the identified very fine components, two boundaries are calculated and Minimum radius and , identification and The larger radius of the boundary and keep it unchanged, for the two boundaries and Smaller medium radius border Zoom in or out; If there are no extremely small holes in the boundary with a smaller radius when scaling to meet the component size threshold constraint, then the extremely fine component control is completed; If a border with a smaller radius has a very small hole when scaling to meet the component size threshold constraint, the border with a smaller radius is removed.

7. The method for controlling geometric feature dimensions of topology optimization results based on image processing according to claim 1, characterized in that: In step 7, the special angle feature of the cross-scale structure is regulated: for the special angle feature, if the angle between the coordinates of any three points on the same boundary does not satisfy the angle constraint, then determine whether the distance between the two endpoints of the boundary satisfies the component size threshold constraint. If it is greater than the component size threshold constraint, find and add two points on the two adjacent sides of the boundary that are parallel to the opposite side of the boundary and have a distance equal to the component size threshold constraint, and delete the vertex of the angle; If the size is smaller than the component size threshold constraint, the vertex is deleted directly without adding a new point, including: For special angle features, if the angle between the three points does not satisfy the angle constraint , then determine whether the distance between the two endpoints meets the size threshold Constraint, if greater than the size threshold Constraint, then find and add parallel edges on two adjacent edges that are parallel to the opposite edge and have a distance equal to the size threshold. Constrain the two points and move the vertex Delete, and the newly added points satisfy: ， Where, and They are line segments and line segments The point on.

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