Tensegrity form-finding method based on two-stage optimization deep neural network

Abstract

The present invention relates to a tensegrity form-finding method based on a two-stage optimization deep neural network, comprising the following steps: constructing a constraint equation of a tensegrity structure according to the node residual force, the length of the rod of the cable-strut unit and the node distance, and using the constraint equation as the loss function of the deep neural network; using the randomly generated node coordinate vector of the cable-strut unit as the input of the deep neural network, adopting a two-stage optimization method to obtain the output value of the cable-strut unit node coordinate vector that minimizes the value of the loss function, and determining a steady-state configuration based on the output value of the cable-strut unit node coordinate vector; cyclically obtaining multiple steady-state configurations; judging the stability of each steady-state configuration, obtaining a stable configuration that satisfies geometric stability, and completing the tensegrity form-finding. Compared with the prior art, the present invention can perform form-finding of complex tensegrity structures such as multi-stable structures, and the results are reliable. The form-finding process does not involve complex structural finite element calculations, and the form-finding efficiency is high.

Description

Technical Field

[0001] The present invention relates to the technical field of tensegrity structure form-finding, and in particular to a tensegrity form-finding method based on a two-stage optimized deep neural network. Background Art

[0002] Tensegrity is a self-balancing structural system composed of tension units and compression units, and its structural stiffness comes entirely from the internal prestress. Tensegrity has the characteristics of reasonable force, controllable shape and foldability, and is widely used in sculptures, intelligent robots and other fields.

[0003] The form-finding problem of tensegrity structure design has always been one of the research hotspots. The existing technology divides the form-finding methods of tensegrity into two categories: static method and dynamic method. The static method determines the possible equilibrium configuration of the tensegrity structure by given topological relationship. Among them, the classic static method is the force density method, which converts the form-finding problem into finding a set of suitable force density values ​​to obtain feasible node coordinate vectors. The dynamic method is to increase the length of the compression rod to a maximum value while keeping the cable length (or rod length) fixed; or, keep the compression rod length unchanged and reduce the length of the cable to a minimum value.

[0004] With the advancement of computer simulation technology, machine learning has been widely used in various engineering fields, and intelligent optimization algorithms have also been applied to tensegrity structure form-finding, such as genetic algorithms, Monte Carlo simulations, and the like. Intelligent optimization algorithms have strong search capabilities and can solve form-finding problems, but are limited by specific algorithms. The prior art obtains the force density value of the structure by calculation, and then uses deep neural network training data, inputs the force density value, and outputs the node coordinates to solve some complex structural form-finding problems, but the process is cumbersome and inefficient, such as a tensegrity structure form-finding method based on a zeroing neural network disclosed in Chinese patent CN113515822B. Alternatively, an efficient dynamic relaxation-noise-tolerant zeroing neural network form-finding algorithm has been established, which can effectively obtain the structural shape, but the calculation process and algorithm complexity are too high.

[0005] The current form-finding algorithms all have more or less limitations. For example, the dynamic relaxation method may cause the structure to collapse into a two-dimensional structure problem. The optimization algorithm is limited by the efficiency of the algorithm, and has weak form-finding capabilities for complex tensegrity structures, or it is difficult to solve multi-stable form-finding problems. Summary of the invention

[0006] The purpose of the present invention is to provide a tensegrity form-finding method based on a two-stage optimized deep neural network to solve the problems of unreliable form-finding results of complex tensegrity structures and complex and inefficient form-finding process.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A tensegrity form-finding method based on a two-stage optimized deep neural network comprises the following steps:

[0009] 1) Initialize the topological relationship and physical information of the tensegrity structure cable-bar unit;

[0010] 2) randomly generating a set of node coordinate vectors of the cable-strut units, obtaining the initial structure of the tensegrity according to the node coordinate vectors and the topological relationship, and obtaining the second physical information of the cable-strut units in the initial structure of the tensegrity;

[0011] 3) Obtain the node residual force of the cable-strut unit according to physical information 1 and physical information 2;

[0012] 4) Construct the constraint equation of the tensegrity structure according to the node residual force, the length of the cable-strut unit and the node distance, and use the constraint equation as the loss function of the deep neural network;

[0013] 5) using the randomly generated node coordinate vector of the cable-strut unit as the input of the deep neural network, adopting a two-stage optimization method to obtain the output value of the node coordinate vector of the cable-strut unit that minimizes the value of the loss function, and determining a steady-state configuration based on the output value of the node coordinate vector of the cable-strut unit;

[0014] 6) Repeat steps 2) to 5) multiple times to obtain multiple stable configurations;

[0015] 7) Determine the stability of each steady-state configuration, obtain a stable configuration that satisfies geometric stability, and complete tensegrity form-finding.

[0016] Furthermore, the calculation formula of the node residual force of the cable-rod unit is:

[0017]

[0018] In the formula, Representation Node i The node residual force, , Representation and Node i Related k The residual force of the compression rod and the residual force of the cable are obtained based on the physical information 1 and the physical information 2. Representation and Node i The number of associated strut elements and cable elements.

[0019] Furthermore, when constructing the constraint equation of the tensegrity structure, the following calculation assumptions are set:

[0020] (1) The materials of the compression rod and the cable are both linear elastic;

[0021] (2) The number and topological relationship of components are given;

[0022] (3) There is no external load.

[0023] Furthermore, the constraint equations include residual force constraints, compression rod length constraints and node distance constraints.

[0024] Furthermore, the loss function includes a loss function: 、Loss function 2 And loss function three ,in,

[0025] The loss function The expression is:

[0026]

[0027] In the formula, Representation Node i The node residual force;

[0028] The loss function 2 The expression is:

[0029]

[0030] In the formula, , is the maximum and minimum value of the unit length, and a is the set length limit value;

[0031] The loss function three The expression is:

[0032]

[0033] In the formula, , are the maximum and minimum values ​​of the node distance, and b is the set distance limit value.

[0034] Furthermore, the process of performing two-stage optimization of the deep neural network includes:

[0035] pass The algorithm performs a one-stage optimization of the hyperparameters of a deep neural network;

[0036] The hyperparameters of deep neural networks are optimized in two stages using the L-BFGS algorithm;

[0037] The two-stage optimization is performed after the first-stage optimization is completed.

[0038] Furthermore, before executing step 7), the multiple steady-state configurations obtained in step 6) are deduplicated and summarized by using a strain potential energy method.

[0039] Furthermore, the determination of the stability of each steady-state configuration specifically includes:

[0040] Obtaining a balance matrix A for a steady-state configuration, performing singular value decomposition on the balance matrix A, and obtaining a displacement modal moment D and a self-stress modal matrix S of the mechanism;

[0041] Determine whether D>0 and S>0 exists. If so, determine the stability of the steady-state configuration by the positivity of the product force formula. If not, directly determine the stability.

[0042] Furthermore, the stability of the steady-state configuration determined by the positivity of the product force formula specifically includes:

[0043] According to the displacement modal moment D of the mechanism and the self-stress modal matrix S, the displacement modal vector of the mechanism and the internal force modal vector of the compression rod are set;

[0044] Constructing a corresponding geometric force matrix G according to the compression rod internal force modal vector and the structural displacement modal vector;

[0045] By judging the product force The positive definiteness of is used to determine whether the steady-state configuration satisfies geometric stability.

[0046] The present invention also provides an electronic device comprising one or more processors, a memory and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the tensegrity form-finding method based on a two-stage optimized deep neural network as described above.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The present invention constructs a total loss function of a deep neural network by comprehensively considering physical information including node residual force, unit length constraint and minimum node distance, and obtains a deep neural network model based on physical information, which can improve the reliability of form-finding of tensegrity structures.

[0049] 2. The present invention adopts a two-stage optimization algorithm to improve the learning ability of the neural network, and obtains the node coordinates of the structural equilibrium state through the optimized deep neural network. In the two-stage optimization, the hyperparameters of the network are firstly trained by the AdamW optimizer to quickly reduce the loss value; after the initial iteration is completed, the L-BFGS optimizer is used for secondary optimization to further approach the optimal solution and finally obtain the node coordinates of the structural equilibrium state.

[0050] 3. The present invention can perform form-finding of complex tensegrity structures such as multi-stable structures, the result is reliable, the form-finding process does not involve complex structural finite element calculations, and the form-finding efficiency is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0052] Figure 1 It is a schematic diagram of the process of the present invention;

[0053] Figure 2 A schematic diagram of a truncated dodecahedron steady-state configuration obtained by a dynamic relaxation method provided in an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of another stable configuration of a truncated dodecahedron obtained by a dynamic relaxation method according to an embodiment of the present invention;

[0055] Figure 4 A schematic diagram of an ideal steady-state configuration of a truncated dodecahedron provided in an embodiment of the present invention;

[0056] Figure 5 A schematic diagram comparing loss values ​​of different optimization algorithm iterations for different steady-state configurations provided by an embodiment of the present invention. In the figure, the horizontal axis is the number of iterations (Number of iterations), the vertical axis is the loss function value (LossValues), the curve pointed by the arrow in the figure is the result curve obtained when using AdamW+L-BFGS of the present invention, and the other is the result curve obtained when using the AdamW optimizer. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] like Figure 1 As shown, the present embodiment provides a method for finding a tensegrity shape by drawing based on a two-stage optimized deep neural network, which mainly includes the following steps:

[0059] S1: Initialize the connection relationship and physical information of the tensegrity structure cable-bar unit.

[0060] In this embodiment, physical information 1 includes the length and stiffness of the compression rod and the cable in the cable-rod unit. Since the cable-rod stiffness of the actual cable-rod tension structure varies greatly, the stiffness used in this embodiment is 10 for the rod unit stiffness and 1 for the cable unit stiffness; the initial length of the compression rod is set to 1000, and the initial length of the cable is set to 100.

[0061] S2: randomly generate a set of node coordinate vectors of the cable-strut unit, and obtain the initial structure of the tensegrity according to the node coordinate vectors and the unit topological relationship; calculate the physical information 2 of the cable-strut unit in the initial structure.

[0062] In this embodiment, the second physical information includes the length and angle vector of the cable-rod unit.

[0063] S3: According to physical information 1 and physical information 2, the node residual force of the cable-strut unit is obtained.

[0064] The calculation process of the node residual force is as follows:

[0065] Calculation of the residual forces in the strut element and the residual force of the cable generated by the cable unit :

[0066]

[0067]

[0068] In the formula, , are the stiffness of the compression rod element and the cable element, , Respectively represent the current length and original length of the component (compression bar element or cable element), i Representation Node i ;

[0069] The calculation formula for the node residual force of the cable-strut element is:

[0070]

[0071] In the formula, Representation Node i The node residual force, , Representation and Node i The k associated residual forces in the compression rods and cables, Representation and Node i The number of associated strut elements and cable elements.

[0072] S4: The constraint equation of the tensegrity structure is constructed according to the node residual force, the member length of the cable-strut unit and the node distance. The constraint equation is used as the loss function of the deep neural network to obtain a deep neural network based on physical information.

[0073] For a tensegrity structure consisting of n units and having b degrees of freedom, the constraint equations are calculated with the following assumptions:

[0074] (1) The materials of the compression rods and cables are linear elastic; (2) The number and topological relationship of the components are given; (3) There is no external load, and in order to ensure that the structure can be formed, length constraints and node distance constraints are added to the structure.

[0075] The constraint equations of the tensegrity structure include residual force constraint, strut length constraint and node distance constraint. The loss function calculation formula obtained from the constraint equations is as follows:

[0076] The loss function obtained by the residual force physical constraint is :

[0077]

[0078] Simply ensuring that the residual force of the structure is minimized cannot maintain the configuration of the structure, and the length of the structural rod must be limited. The length limit value used in this embodiment is 80%, that is, the difference between the longest rod and the shortest rod cannot be greater than 80% of the length of the longest rod. The loss function obtained by the compression rod length constraint condition is :

[0079]

[0080] In the formula, , is the maximum and minimum value of the unit length;

[0081] If the distance between nodes is too close, the structure is very likely to become unstable. It is necessary to ensure that the nodes of the structure are not too close. The set distance limit value used in this embodiment is 20%, that is, the distance between the two closest nodes should be more than 20% of the distance between the farthest nodes. The loss function obtained by the node distance constraint is :

[0082]

[0083] in, , is the maximum and minimum value of the node distance.

[0084] S5: Set the randomly generated cable-strut unit node coordinate vector as the input quantity, through Algorithms and The algorithm performs two-stage self-service optimization on the hyperparameters of the neural network, and obtains a two-stage optimized deep neural network model based on physical information. The two-stage optimization process includes: The algorithm performs a first-stage optimization on the hyperparameters of the deep neural network, and uses the L-BFGS algorithm to perform a second-stage optimization on the hyperparameters of the deep neural network, including the optimization of hyperparameters such as learning rate, weight, and bias.

[0085] pass The algorithm performs one-stage optimization of the hyperparameters of a deep neural network as follows:

[0086] S51: Calculate learning rate Gradient , and its calculation formula is as follows:

[0087]

[0088] in, It is expressed as the gradient calculation for the hyperparameters. is the gradient operator, expressed as , Indicated in the parameter The loss function below.

[0089] S52: Get the mean of the first-order moment estimate for dynamically adjusting the learning rate , and its calculation formula is as follows:

[0090]

[0091] In the formula, is the momentum parameter in the AdamW algorithm;

[0092] S53: Get the mean square error of the second-order moment estimate for dynamic adjustment of the learning rate , and its calculation formula is as follows:

[0093]

[0094] In the formula, is the momentum parameter in the AdamW algorithm;

[0095] S54: Mean and mean square error To perform error correction, the calculation formula is as follows:

[0096]

[0097]

[0098] S55: Update learning rate , the update formula is as follows:

[0099]

[0100] In the formula, is the weight decay coefficient of the deep neural network, , is a random adjustment parameter.

[0101] Adam is a first-order optimization algorithm based on gradient. It combines the ideas of momentum and RMSProp. It dynamically adjusts the learning rate by exponentially weighted average of first-order momentum and second-order momentum, thereby accelerating the process of gradient descent. The AdamW algorithm used in this embodiment improves the shortcomings of the Adam algorithm in dealing with weight decay, making it more suitable for training deep neural networks.

[0102] The steps for two-stage optimization of the hyperparameters of a deep neural network using the L-BFGS algorithm are as follows:

[0103] S56: Set the initial Hessian inverse approximation matrix to a scalar matrix (where E is the identity matrix), where the step factor The calculation formula is as follows:

[0104]

[0105] In the formula, represents a pair of hyperparameter vectors stored by L-BFGS, s k-1 is the difference between the current position and the previous position, y k−1 is the difference in gradients, and the subscript k indicates the kth step;

[0106] S57: For two scalar sequences q and The calculation formula for the cycle is as follows:

[0107] set up , parameter update formula:

[0108]

[0109] In the formula, represents the momentum parameter in the L-BFGS algorithm, m represents the number of hyperparameter vectors stored in L-BFGS, Represented as the independent variable of the kth step;

[0110] S58: Search direction vector r Perform loop calculations ， The calculation formula is as follows:

[0111] set up , parameter update formula:

[0112]

[0113] In the formula, represents the momentum parameter in the L-BFGS algorithm, and m represents the number of hyperparameter vectors stored by L-BFGS;

[0114] S59: After two cycles, the final search direction is obtained ,in ; Use line search method to determine the step , determine the update formula:

[0115]

[0116] renew and , and store the most recent m for the hyperparameter vector.

[0117] The L-BFGS algorithm used in this embodiment accelerates convergence by approximating the second-order derivative of the objective function, but unlike the traditional BFGS algorithm, the L-BFGS algorithm does not explicitly store the complete Hessian matrix, but only uses a small amount of historical information, which is suitable for high-dimensional problems. The L-BFGS algorithm reduces the amount of storage and calculation for high-dimensional problems. BFGS needs to store the complete Hessian matrix, with a time and space complexity of . However, L-BFGS only retains the sum pairs of the most recent m iterations and uses them to construct an approximation of the Hessian matrix. The L-BFGS algorithm significantly reduces storage and calculation costs by storing only the most recent m pairs of vectors. The two-loop update method avoids explicitly calculating and storing the inverse of the Hessian matrix. The time complexity of the L-BFGS algorithm is about O(mn), and the space complexity is about O(mn), where n is the dimension of the variable, and m is the number of iterations retained, usually m is between 3 and 20. The L-BFGS algorithm has high efficiency and good convergence performance in large-scale optimization problems.

[0118] S6: Record the loss function value and the node coordinate vector of the corresponding cable-strut unit during the M-th iteration of the model, and output the node coordinate vector of the cable-strut unit with the smallest loss function value.

[0119] In this embodiment, the first-stage optimization is iterated 100 times and the second-stage optimization is iterated 50 times.

[0120] S7: Set the iteration cycle of S2-S6 N times, and use the strain potential energy method to deduce the steady-state configuration of each iteration result, and summarize all the steady-state configurations of the tensegrity structure.

[0121] S8: Determine the stability of all steady-state configurations through the positivity of the product force formula and output the stable configuration.

[0122] The method for judging the stability of all steady-state configurations by the positivity of the product force formula is as follows:

[0123] S81: The equilibrium matrix A of the steady-state configuration is subjected to singular value decomposition to obtain the displacement modal moment D and the self-stress modal matrix S of the mechanism;

[0124] The expressions of the mechanism displacement modal moment D and self-stress modal matrix S are as follows:

[0125]

[0126]

[0127] S82: When D>0, S>0, it is necessary to further judge the stability of the steady-state configuration through the positivity of the product force formula; otherwise, the stability can be judged directly.

[0128] In this embodiment, the structural stability judgment rule based on the displacement modal moment D of the mechanism and the self-stress modal matrix S is as follows:

[0129] If the mechanism displacement mode D = 0 and the self-stress mode s = 0, there is no internal mechanism displacement in the system, the structure is statically determinate, and is geometrically stable;

[0130] If D>0, S=0, it means that the structure has mechanical displacement, but due to the lack of self-stress, it cannot withstand external loads and is geometrically unstable;

[0131] When S>0 and D=0, the structure is a statically indeterminate and dynamically determinate system. For any load, it has a finite set of internal force solutions, a unique displacement solution, and a self-stress mode. This type of structure is a hyperstatic structure and is geometrically stable.

[0132] If D>0, S>0, it means that the structure has both self-stress and mechanism displacement. For this type of situation, it is necessary to further use the positive definiteness of the product force matrix Q to make a judgment.

[0133] S83: according to the displacement modal moment D of the mechanism and the self-stress modal matrix S, setting the displacement modal vector of the mechanism and the internal force modal vector of the compression rod;

[0134] The expressions of the mechanism displacement modal vector d and the compression rod internal force modal vector t are as follows:

[0135]

[0136]

[0137] in, and represent the combination coefficients of displacement mode and internal force mode respectively.

[0138] S84: Set the geometric force vector G corresponding to the i-th compression rod internal force modal vector and the j-th structural displacement modal vector ij , to ensure that the internal force of the compression rod is negative;

[0139] Geometric force vector G ij The expression is as follows:

[0140]

[0141] S85: By judging the product force The positive definiteness of is used to determine whether the steady-state configuration belongs to a stable first-order infinitesimal mechanism, where is the geometric force matrix.

[0142] For any non-zero vector If yes:

[0143]

[0144] In the formula, , that is, when the product force F is positive, the structure can be stiffened under the self-stress mode, and the structure satisfies geometric stability.

[0145] The tensegrity form-finding method based on a two-stage optimized deep neural network provided in this embodiment constructs a total loss function of the neural network by comprehensively considering physical information including node residual forces, unit length constraints, and minimum node distances; at the same time, in order to improve the learning ability of the neural network, a two-stage optimization model is adopted. First, the hyperparameters of the network are preliminarily trained through the AdamW optimizer to quickly reduce the loss value; after the initial iteration is completed, the L-BFGS optimizer is used for secondary optimization to further approximate the optimal solution and finally obtain the node coordinates of the structural equilibrium state. The dual optimizer two-stage optimized deep neural network analysis method based on physical information of the present invention can perform form-finding of complex tensegrity structures such as multi-stable states, and the results are reliable. The form-finding process does not involve complex structural finite element calculations, and the form-finding efficiency is high.

[0146] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0147] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0148] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0149] Case Study:

[0150] Combine the following Figure 2-Figure 5 A case study describing the tensegrity form-finding method provided by the present invention.

[0151] This case constructs five structures of different dimensions and different stable configurations to verify the advantages of this method in tensegrity structure form-finding. The plane octagon is a monostable plane structure system, the icosahedron structure is a monostable spatial structure system; the truncated semi-octahedron, truncated dodecahedron and truncated icosahedron are all multistable spatial structure systems.

[0152] When using the dynamic relaxation method for comparative analysis, a collapse to two dimensions occurred and all steady states could not be obtained. Figure 2-Figure 3As shown in the figure, when the truncated dodecahedron is analyzed by the dynamic relaxation method, only two stable configurations are obtained after 50 large cycle iterations; Figure 4 The structure shown. The steady-state structure that can be obtained by the dynamic relaxation method can also be obtained by the PIDNN neural network without collapse. In addition, the mechanism of calculating the residual force by the form-finding method in this case is derived from dynamic relaxation, so it inherits the strong structural symmetry of the dynamic relaxation method, which can effectively overcome the disadvantage of poor symmetry of the form-finding method of the force density method.

[0153] To verify the superiority of the dual optimizer, we selected the truncated icosahedron with the highest complexity for optimizer comparison analysis. We selected AdamW+L-BFGS and AdamW optimizers respectively, with the number of iterations being 150. When AdamW+L-BFGS was selected, AdamW was used for the first 100 iterations, and L-BFGS was used for 101 to 150 iterations. The results are shown in the figure below. Figure 5 As shown. Figure 5 It can be seen that the AdamW optimization algorithm can play an optimization role and has the best optimization effect, but when it reaches a relatively low value, its optimization almost stops. When it iterates to a relatively low loss function, L-BFGS is introduced for local optimization. It can be seen that under the action of the L-BFGS optimizer, the loss functions of the four steady-state configurations are very well optimized. The two-stage optimization of AdamW+L-BFGS has extremely significant advantages over other optimizers and has a strong node coordinate search capability.

[0154] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0155] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0156] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A tensegrity form-finding method based on a two-stage optimized deep neural network, characterized in that: The following steps are involved: 1) Initialize the topological relationship and physical information of the tensegrity structure cable-bar unit; 2) randomly generating a set of node coordinate vectors of the cable-strut units, obtaining the initial structure of the tensegrity according to the node coordinate vectors and the topological relationship, and obtaining the second physical information of the cable-strut units in the initial structure of the tensegrity; 3) Obtain the node residual force of the cable-strut unit according to physical information 1 and physical information 2; 4) Construct the constraint equation of the tensegrity structure according to the node residual force, the length of the cable-strut unit and the node distance, and use the constraint equation as the loss function of the deep neural network; 5) using the randomly generated node coordinate vector of the cable-strut unit as the input of the deep neural network, adopting a two-stage optimization method to obtain the output value of the node coordinate vector of the cable-strut unit that minimizes the value of the loss function, and determining a steady-state configuration based on the output value of the node coordinate vector of the cable-strut unit; 6) Repeat steps 2) to 5) multiple times to obtain multiple stable configurations; 7) Determine the stability of each steady-state configuration, obtain a stable configuration that satisfies geometric stability, and complete tensegrity form-finding; The constraint equations include residual force constraint, compression rod length constraint and node distance constraint; The loss function includes a loss function: 、Loss function 2 And loss function three ,in, The loss function The expression is: ， In the formula, Representation Node i The node residual force; The loss function 2 The expression is: ， In the formula, , is the maximum and minimum value of the unit length, and a is the set length limit value; The loss function three The expression is: ， In the formula, , are the maximum and minimum values ​​of the node distance, and b is the set distance limit value.

2. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 1, characterized in that: The calculation formula of the node residual force of the cable-strut unit is: ， In the formula, Representation Node i The node residual force, , Representation and Node i Related k The residual force of the compression rod and the residual force of the cable are obtained based on the physical information 1 and the physical information 2. Representation and Node i The number of associated strut elements and cable elements.

3. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 1, characterized in that: When constructing the constraint equations of the tensegrity structure, the following calculation assumptions are set: (1) The materials of the compression rod and the cable are both linear elastic; (2) The number and topological relationship of components are given; (3) There is no external load.

4. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 1, characterized in that: The two-stage optimization process of the deep neural network includes: pass The algorithm performs a one-stage optimization of the hyperparameters of a deep neural network; The hyperparameters of deep neural networks are optimized in two stages using the L-BFGS algorithm; The two-stage optimization is performed after the first-stage optimization is completed.

5. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 1, characterized in that: Before executing step 7), the plurality of steady-state configurations obtained in step 6) are deduplicated and summarized by using a strain potential energy method.

6. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 1, characterized in that: The determination of the stability of each steady-state configuration specifically includes: Obtaining a balance matrix A for a steady-state configuration, performing singular value decomposition on the balance matrix A, and obtaining a displacement modal moment D and a self-stress modal matrix S of the mechanism; Determine whether D>0 and S>0 exists. If so, determine the stability of the steady-state configuration by the positivity of the product force formula. If not, directly determine the stability.

7. The tensegrity form-finding method based on two-stage optimized deep neural network according to claim 6, characterized in that: The stability of the steady-state configuration determined by the positivity of the product force formula specifically includes: According to the displacement modal moment D of the mechanism and the self-stress modal matrix S, the displacement modal vector of the mechanism and the internal force modal vector of the compression rod are set; Constructing a corresponding geometric force matrix G according to the compression rod internal force modal vector and the structural displacement modal vector; By judging the product force The positive definiteness of is used to determine whether the steady-state configuration satisfies geometric stability.

8. An electronic device, characterized in that: The method comprises one or more processors, a memory and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the tensegrity form-finding method based on a two-stage optimized deep neural network as described in any one of claims 1 to 7.

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