A multi-stable kresling folded superstructure artificial intelligence optimization design method based on physical constraints

Abstract

The application discloses a multi-stable Kresling folded superstructure artificial intelligence optimization design method based on physical constraints, comprising the following steps: constructing a mechanical behavior physical model of a Kresling folded superstructure; and solving the mechanical behavior physical model by using a multi-objective performance optimization algorithm to obtain an optimization result; wherein, firstly, decision variables of the multi-objective performance optimization algorithm and upper and lower limits of the decision variables are determined, iterative calculation is performed based on a target function, and an optimization result of the decision variables is obtained. Under the premise that the structure has multi-stable, variable stiffness and easy folding performance, the application realizes coupled optimization design of the structure folding rate, bearing capacity (or deformation energy) and geometric configuration, and significantly improves the structure customization design efficiency.

Description

Technical Field

[0001] This invention belongs to the field of superstructure optimization design, and specifically relates to an artificial intelligence optimization design method for multistable Kresling folded superstructures based on physical constraints. Background Technology

[0002] Kresling folded superstructures are a typical example of mechanical superstructures. They possess unique mechanical properties such as multi-stability, variable stiffness, and easy folding, which can solve engineering problems that are difficult to overcome by traditional engineering structures. Currently, they show great potential for development and application in fields such as robotics, aerospace equipment, energy harvesting and power generation, buffering and energy absorption, vibration isolation, and lightweight penetration explosion protection.

[0003] Currently, the design methods for Kresling folded superstructures mainly rely on experimentation, analytical computation, numerical simulation, and artificial intelligence optimization. Experimentation is the most intuitive and reliable method for studying structural mechanical properties, but it is costly and time-consuming, thus having significant limitations. Analytical and numerical simulation methods can alleviate the cost and time constraints of experimentation to some extent, but they are still essentially trial-and-error methods; different application scenarios will generate new computational loads, easily leading to wasted computing power. The artificial intelligence methods that have emerged in recent years also have limitations: they require a large amount of numerical simulation or analytical computation results as training samples to obtain a relatively reasonable structural design model, and they also suffer from the "black box" effect, with unclear physical mechanisms. Physically based neural network algorithms (PINN) can overcome the dependence on large amounts of training data to some extent, but they rely on implicit computational models for solving problems, and still have shortcomings in multi-objective optimization and computational efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide an artificial intelligence optimization design method for multi-stable Kresling folded superstructures based on physical constraints. Under the premise that the structure has multi-stable, variable stiffness, and easy folding performance, it realizes the coupled optimization design of structural folding rate, bearing capacity (or deformation energy), and geometric configuration, which significantly improves the efficiency of customized structural design.

[0005] To achieve the above objectives, the solution of the present invention is:

[0006] An AI-based optimization design method for physically constrained multistable Kresling folded superstructures includes,

[0007] Construct a physical model of the mechanical behavior of Kresling folded superstructures;

[0008] The physical model of the mechanical behavior is solved using a multi-objective performance optimization algorithm to obtain the optimization results. First, the decision variables and their upper and lower limits are determined for the multi-objective performance optimization algorithm. Then, iterative calculations are performed based on the objective function to obtain the optimization results of the decision variables.

[0009] The physical model of the mechanical behavior of the Kresling folded superstructure includes the structural bearing capacity. Deformation energy Folding rate Model,

[0010] Bearing capacity ,

[0011] in, Let be the number of sides of the top and bottom polygons of the structure. For the compression modulus of the rod, Let the cross-sectional area of ​​the rod be... For the Poisson's ratio of the rod, This represents the strain of the vertical member at the maximum load-bearing capacity of the structure. , , and These are the included angles of the core layer members;

[0012] deformation energy ,

[0013] in, It is the initial length of the vertical rod;

[0014] Folding rate ,

[0015] in, It is the radius of the circumcircle of the upper and lower polygons of the structure. It is the real-time relative rotation angle of the upper and lower polygons of the structure.

[0016] Among them, the decision variables for determining the multi-objective performance optimization algorithm are: ,

[0017] in, Let be the number of sides of the top and bottom polygons of the structure. It is the radius of the circumcircle of the upper and lower polygons of the structure. It is the initial relative rotation angle of the upper and lower polygons. It is the initial height of the structure. It is the real-time relative rotation angle of the upper and lower polygons of the structure.

[0018] Among them, determining decision variables lower limit and upper limit for,

[0019] ,

[0020] in, Represents infinity; For decision variables, referring to the number of sides of the upper and lower polygons of the structure; The critical relative rotation angle between the upper and lower polygons is the angle at which the deformation mode of the structure changes from compressive-torsional folding to a direct downward compression deformation mode accompanied by tension of the upper polygon under axial compressive load. Greater than 0°.

[0021] The objective function of the multi-objective performance optimization algorithm is:

[0022] ,

[0023] in, and It is an optimized ratio of folding rate and load-bearing capacity. Represents absolute value. For folding rate, The ratio of the remaining height to the initial height of the representative structure; It is a dimensionless structural bearing capacity, in which For the load-bearing capacity of the structure, For the compression modulus of the rod, The cross-sectional area of ​​the rod; This represents the target value for the optimized design of structural bearing capacity.

[0024] Among them, a multi-objective performance optimization algorithm is used to solve the physical model of mechanical behavior, including,

[0025] Set the particle swarm size, the maximum number of algorithm iterations, and the convergence accuracy;

[0026] Set particles At any moment The speed of the next update and location parameter,

[0027] ,

[0028] in, It is used to balance the weights of local and global searches. and Here, are acceleration coefficients, representing the degree of approach to the individual optimum and the global optimum, respectively. and It is evenly distributed in Random vectors within the region, For particles At any moment Update speed For particles At any moment Location, For particles At any moment The individual's optimal position For example, at time The optimal global position.

[0029] In the solution process, parameters for particle swarm mutation probability and mutation degree are also set to avoid the particle swarm algorithm getting stuck in local optima.

[0030] By adopting the above solution, the present invention has the following beneficial effects compared with the prior art:

[0031] 1. The method provided by this invention can simultaneously achieve precise customized design of structural mechanical properties and geometric configuration, with richer functions and better meeting the needs of practical applications;

[0032] 2. The method provided by this invention is adjustable. By adding restrictions on the number of sides and the height-to-diameter ratio of the polygon, it can meet the application requirements of different specific scenarios.

[0033] 3. Compared with analytical methods and numerical simulation methods, the method provided by this invention has higher structural design efficiency, and a single structural optimization design can be completed on a timescale of seconds;

[0034] 4. Compared with conventional deep learning methods, the method provided by this invention has a clearer physical mechanism and does not require training samples, resulting in higher interpretability and solution efficiency;

[0035] 5. The calculation results of the method provided by this invention have a consistency of over 99% with the numerical simulation results, achieving high solution accuracy while achieving high optimization efficiency. Attached Figure Description

[0036] Figure 1 This is a computational model of a Kresling folded superstructure with 4 polygonal sides according to an embodiment of the present invention;

[0037] Wherein, (a) is a schematic diagram of the structure, and (b) is a top view of the structure;

[0038] Figure 2 This is the optimized design result of the tristable characteristics of the Kresling folded superstructure according to an embodiment of the present invention;

[0039] Figure 3 This is a flowchart of the particle swarm optimization algorithm calculation according to an embodiment of the present invention;

[0040] Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation

[0041] The technical solution and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0042] The terms used in the embodiments of this invention are explained as follows:

[0043] Kresling folding superstructures refer to a novel, high-load-bearing, easily foldable structure comprising upper and lower panels and a core Kresling truss configuration. It exhibits designable multi-stable characteristics. The core truss includes both vertical and diagonal members, with the diagonal members having a tensile modulus of... Much lower than the compressive modulus of the diagonal bar Recommended value The compression modulus of the vertical bar should be similar to that of the diagonal bar, and the tensile modulus of the vertical bar should be similar to that of the vertical bar.

[0044] Physical constraints refer to the physical model of structural mechanical behavior. These are the physical conditions and criteria that the multi-objective performance optimization algorithm proposed in this invention must satisfy. They limit the range of optimization parameters and are beneficial to improving the efficiency and accuracy of the optimization algorithm.

[0045] Structural mechanics behavior physical model refers to the calculation model of mechanical properties such as structural bearing capacity, folding ratio, and deformation energy;

[0046] Multi-objective performance refers to a structure simultaneously meeting multiple objectives such as expected load-bearing capacity, folding ratio, and geometric configuration.

[0047] Structural mechanical properties refer to the load-bearing capacity of a structure. Deformation energy Folding rate Multi-stability and other properties;

[0048] Structural geometry refers to the number of sides of the top and bottom polygons of a structure. circumcircle radius Initial relative rotation angle of the upper and lower polygons Initial height of the structure ;

[0049] Customized design refers to the on-demand design of structural mechanical properties and geometric configurations achieved through the optimization algorithm proposed in this invention;

[0050] The trial-and-error algorithm refers to solving the structural mechanical properties based on a given structural geometry configuration, and then determining whether the requirements are met. If not, the structural geometry configuration is updated and the structural mechanical properties are solved again until the conditions are met.

[0051] Conventional deep learning methods, such as fully connected neural networks (MLP), convolutional neural networks (CNN), recurrent neural networks (RNN), graph neural networks (GNN), generative adversarial networks (GAN), and physical information neural networks (PINN), typically require a certain amount of training data to achieve accurate prediction of targets, resulting in significant initial computational costs.

[0052] like Figure 4 As shown, this invention provides an artificial intelligence optimization design method for multistable Kresling folded superstructures based on physical constraints, which specifically includes the following steps;

[0053] The first step is to establish a physical model of the structural mechanical behavior, including the structural bearing capacity. Deformation energy Folding rate Model.

[0054] in, , For the compression modulus of the rod, Let the cross-sectional area of ​​the rod be... For the Poisson's ratio of the rod, This represents the strain of the vertical member at the maximum load-bearing capacity of the structure. , and These are the included angles of the core layer members; , It is the initial length of the vertical rod; ; , It is the radius of the circumcircle of the upper and lower polygons of the structure. It is the real-time relative rotation angle of the upper and lower polygons of the structure.

[0055] The second step involves determining the decision variables for the multi-objective performance optimization algorithm based on the physical model. From the first step, the fundamental parameters determining the physical model and geometric configuration of the structure's mechanical behavior are: , , , , Therefore, the decision variables of the optimization algorithm .

[0056] The third step is to construct the objective function for the multi-objective performance optimization algorithm: .in, Represents absolute value; This represents the ratio of the remaining height of the structure to its initial height. It is a given value, and the target folding ratio of the structure is... ; and It is the optimized ratio of folding rate and load-bearing capacity, which is determined according to the order of magnitude of folding rate and load-bearing capacity and their relative importance; It is a dimensionless structural bearing capacity, equal to The purpose of making it dimensionless is to make it roughly on the same order of magnitude as the folding rate. This represents the dimensionless objective value for structural bearing capacity optimization design. This objective function allows for customized design of structural folding ratio and bearing capacity. The dimensionless bearing capacity of the structure in the objective function is then expressed as... Replace with dimensionless deformation energy The dimensionless structural bearing capacity in the objective function Replace with dimensionless target deformation energy It allows for customized design of structural folding ratio and deformation energy, among which, equal At this point, the objective function is: .

[0057] Assuming the target folding ratio of the Kresling folded superstructure is 90% and the target load-bearing capacity is 5000N, and both are equally important, then the objective function is adjusted as follows: .

[0058] The fourth step is to determine the upper and lower limits of the decision variables for the structural multi-objective performance optimization algorithm. To ensure that the decision variables have realistic physical meaning, the structural geometric configuration parameters ( , , , , Constraints on the range, establishing lower limits for decision variables. and upper limit : .in Represents infinity. In practical applications, this is used to determine the number of sides of the polygons above and below the structure. For integers, it is usually necessary to specify them directly. The specific values ​​are chosen to avoid the limitations of the particle swarm algorithm due to the lack of integer variable constraints, and to achieve a customized design of the number of polygon sides. The upper and lower limits determine the multi-stable characteristics of the structure. When the upper limit is greater than zero, the structure will exhibit tristable or bistable characteristics; when When the upper limit is less than zero, the structure will exhibit bistable or monostable characteristics; the positive and negative signs here only represent the positional relationship, see the specific implementation details.

[0059] For prefabricated structures, fewer sides make transportation and installation easier, and also make it easier to avoid problems with difficult boundary closure. Therefore, this section focuses on... Optimization will be performed using a structure with a height-to-diameter ratio of 4 as an example. Furthermore, to avoid redundant calculations during the optimization process, the height-to-diameter ratio of the structure can be adjusted. Achieve simultaneous parameter and Optimization. Additionally, to achieve tristable structural properties, The value should be greater than zero. In summary, for polygons with 4 sides and an aspect ratio of 0.5 to 1.0... Range of values Structure (such as) Figure 1 As shown), the upper and lower limits of its decision variables are: .

[0060] Step 5: Set the basic parameters of the particle swarm optimization algorithm. Based on the number of decision variables and the complexity of the objective function, specify the number of particles, the maximum number of iterations, and the convergence accuracy. Set the particle update rate. and location parameter: ,in, This is used to balance the weights of local and global searches, and is typically set to 0.5 to 1.0; in this embodiment, the value is 0.9. and The acceleration coefficients represent the degree of approach to the individual optimum and the global optimum, respectively; in this embodiment, the value is 1.49. and It is evenly distributed in Random vectors within the region. Furthermore, to prevent the particle swarm algorithm from getting trapped in local optima, a mutation process was added to the particle swarm during the iteration process, referencing the genetic algorithm. The mutation probability and mutation severity parameters were further set to 0.2 and 0.1, respectively.

[0061] The sixth step is to submit the completed multi-objective performance optimization algorithm for the structure to be calculated iteratively by the computer, such as... Figure 3 As shown, the optimized calculation output is as follows: the optimized geometry of the Kresling folded superstructure is... equal The structure has a 90% folding ratio and a load-bearing capacity of 5000N. On a laptop equipped with an 11th-generation Intel® Core™ i7-11800H CPU @ 2.30 GHz, the above-mentioned structural optimization design takes less than 2 seconds, demonstrating the efficiency of the optimization method provided by this invention. This was achieved through theoretical calculations. equal The structure has a folding rate of 90% and a structural bearing capacity of 5000N, as shown in Table 1.

[0062] Table 1

[0063]

[0064] Numerical simulation calculation equal The structure exhibits tristable characteristics, such as Figure 2 As shown, the reliability and accuracy of the proposed optimization algorithm are verified.

[0065] In summary, the present invention has achieved multi-objective performance optimization design of structural mechanical properties and geometric configuration.

[0066] This invention establishes a nonlinear coupled optimization algorithm for structural mechanical performance and geometric configuration based on the physical model of structural mechanical behavior. It can realize the customized design of structural mechanical performance and geometric configuration, significantly avoiding the time consumption of trial and error algorithms and the limitations of conventional deep learning models that depend on the amount of training data. It is accurate, reliable, requires no training data, and is more efficient.

[0067] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0068] In this invention, "and / or" means either the existence of each individually or the existence of both simultaneously.

[0069] Based on the above-described preferred embodiments of the present invention, and through the above description, those skilled in the art can make various changes and modifications without departing from the technical concept of the present invention. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. An artificial intelligence optimization design method for multistable Kresling folded superstructures based on physical constraints, characterized in that: include, Construct a physical model of the mechanical behavior of Kresling folded superstructures; The physical model of the mechanical behavior is solved using a multi-objective performance optimization algorithm to obtain the optimization results. First, the decision variables and their upper and lower limits are determined for the multi-objective performance optimization algorithm. Then, iterative calculations are performed based on the objective function to obtain the optimization results of the decision variables.

2. The method as described in claim 1, characterized in that: The physical model of the mechanical behavior of the Kresling folded superstructure includes the structure's load-bearing capacity. Deformation energy Folding rate Model, Bearing capacity , in, Let be the number of sides of the top and bottom polygons of the structure. For the compression modulus of the rod, Let the cross-sectional area of ​​the rod be _____. For the Poisson's ratio of the rod, This represents the strain of the vertical member at the maximum load-bearing capacity of the structure. , , and These are the included angles of the core layer members; deformation energy , in, It is the initial length of the vertical rod; Folding rate , in, It is the radius of the circumcircle of the upper and lower polygons of the structure. It is the real-time relative rotation angle of the upper and lower polygons of the structure.

3. The method as described in claim 1, characterized in that: The decision variables for the multi-objective performance optimization algorithm are determined as follows: , in, Let be the number of sides of the top and bottom polygons of the structure. It is the radius of the circumcircle of the upper and lower polygons of the structure. It is the initial relative rotation angle of the upper and lower polygons. It is the initial height of the structure. It is the real-time relative rotation angle of the upper and lower polygons of the structure.

4. The method as described in claim 3, characterized in that: Determine decision variables lower limit and upper limit for, ， in, Represents infinity; For decision variables, referring to the number of sides of the upper and lower polygons of the structure; The critical relative rotation angle between the upper and lower polygons is the angle at which the deformation mode of the structure changes from compressive-torsional folding to a direct downward compression deformation mode accompanied by tension of the upper polygon under axial compressive load. Greater than 0°.

5. The method as described in claim 1, characterized in that: The objective function of the multi-objective performance optimization algorithm is: ， in, and It is an optimized ratio of folding rate and load-bearing capacity. Represents absolute value. For folding rate, The ratio of the remaining height to the initial height of the representative structure; It is a dimensionless structural bearing capacity, in which For the load-bearing capacity of the structure, For the compression modulus of the rod, The cross-sectional area of ​​the rod; This represents the target value for the optimized design of structural bearing capacity.

6. The method as described in claim 1, characterized in that: A multi-objective performance optimization algorithm is used to solve the physical model of mechanical behavior, including: Set the particle swarm size, the maximum number of algorithm iterations, and the convergence accuracy; Set particles At any moment The speed of the next update and location parameter, ， in, It is used to balance the weights of local and global searches. and Here, are acceleration coefficients, representing the degree of approach to the individual optimum and the global optimum, respectively. and It is evenly distributed in Random vectors within the region, For particles At any moment Update speed For particles At any moment Location, For particles At any moment The individual's optimal position For example, at time The optimal global position.

7. The method as described in claim 6, characterized in that: During the solution process, parameters for particle swarm mutation probability and mutation degree are also set to avoid the particle swarm algorithm getting trapped in local optima.

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