CN113515822B - Return-to-zero neural network-based stretching integral structure form finding method - Google Patents

Return-to-zero neural network-based stretching integral structure form finding method Download PDF

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CN113515822B
CN113515822B CN202110754182.1A CN202110754182A CN113515822B CN 113515822 B CN113515822 B CN 113515822B CN 202110754182 A CN202110754182 A CN 202110754182A CN 113515822 B CN113515822 B CN 113515822B
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CN113515822A (en
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孙中波
赵立铭
刘克平
张振国
王刚
刘永柏
李岩
廉宇峰
刘帅师
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Changchun University of Technology
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Abstract

The invention discloses a shape finding method for a whole tensioning structure based on a return-to-zero neural network. Aiming at the shape finding problem of the whole tensioning structure, the shape finding problem of the whole tensioning structure is converted into a nonlinear unconstrained optimization problem by combining a technology for improving a Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and an anti-noise type zero-returning neural network, and an improved anti-noise type zero-returning neural network shape finding algorithm (MBFGS-NTN) is designed. The shape finding algorithm comprises the following steps: a. inputting initial information; b. converting the force density linear equation set into a nonlinear equation set with the node coordinates as variables, converting the nonlinear equation set into a nonlinear unconstrained optimization problem by a least square method, and calculating the gradient of a target function; c. an improved BFGS algorithm is used for calculating an approximate value of a Hessian matrix to replace the Hessian matrix in a return-to-zero neural network model; d. using an improved anti-noise type return-to-zero neural network model to iteratively solve the node coordinates of the tensioning integral structure under the noise condition; e. and obtaining the node coordinates after the 2-norm of the objective function gradient meets a given error condition.

Description

Return-to-zero neural network-based stretching integral structure form finding method
Technical Field
The invention belongs to the technical fields of space structures, integral tensioning structures and the like, and relates to a shape-finding method of an integral tensioning structure based on a return-to-zero neural network.
Background
As a rigid-flexible coupling structure, the integral tensioning structure has the characteristics of adjustable form, controllable stress, tensile strength of a rope, light structure, self-stability and the like, and has great development in the fields of building industry, robot industry, space exploration and the like.
For a tensegrity structure, the emphasis is on maintaining a stable structure in space. However, when designing a tensegrity structure, the stable form of the tensegrity structure cannot be designed in one step. Therefore, the shape-finding process of the integral tensioning structure is developed. The so-called form-finding process of a tensegrity structure is a process of finding a tensegrity structure in a stable state after some initial conditions are given. In this process, many form-finding methods have been devised. Such as force density method, dynamic relaxation method and finite element analysis method. Among these shape-finding methods, the force density shape-finding method has been attracting attention as an accurate and efficient shape-finding method. In recent years, many force density profiling methods have been proposed, such as a method using a combination of eigenvalue decomposition and singular value decomposition, given a set of initial values of force density vectors and a topological matrix C of the tensioned monolithic structure. The force density vector is iterated continuously by Aq =0, D [ X, Y, Z ] =0 until a set of force density vectors q meeting the rank deficiency condition and the stiffness matrix requirement is found. The shape-finding method of the integral tensioning structure has the advantage that the self-balancing state of the integral tensioning structure can be found by means of less initial information. The force density shape-finding method is to find the force density vector of the integral tension structure in a self-balancing state when meeting the rank deficiency condition through a force density linear equation system. However, the force density shape finding method does not involve analysis of physical information of the rope and the rod member, namely, the axial rigidity, the initial length, the cross-sectional area and the like of the rope and the rod member. Therefore, the force density profiling method is not suitable for finding structural configuration details of a tensioned monolithic structure. Therefore, the invention designs an MBFGS-NTN form-finding algorithm by combining a zeroing neural network model and an improved BFGS algorithm based on a force density linear equation set of a tensioning integral structure and by utilizing physical information of rope and rod components. The analysis of the structural configuration details of the rope and rod elements in the shape finding process is realized.
Disclosure of Invention
The invention discloses a method for finding the shape of a tensioned integral structure based on a return-to-zero neural network, which aims at the tensioned integral structure without external support or external force and meets the requirement of a modified rigidity matrix of the tensioned integral structure, namely an approximate Hessian matrix
Figure 278900DEST_PATH_IMAGE002
Under the positive definite condition, finding the self-balancing state of the integral tensioning structure, and combining the attached figure 1 of the specification, the technical scheme of the invention is as follows:
s1: inputting initial information including a topological matrix C of the integral tensioning structure, randomly given X, Y and Z values of initial node coordinates, young modulus, cross section area, initial length and the like of the integral tensioning structure rope and rod member;
s2: converting the force density linear equation set into a nonlinear equation set, converting the force density linear equation set into a nonlinear unconstrained optimization problem by a least square method, and further converting the shape finding problem into a nonlinear unconstrained optimization problem; the force density vector is represented as follows:
Figure 855375DEST_PATH_IMAGE003
in the process of forming a stretching integral structure without external support, namely external force, the external force is 0, and the force density vector and the current length of the rope and the rod are calculated
Figure 578480DEST_PATH_IMAGE004
Substituted in formula Aq =0, let
Figure 658431DEST_PATH_IMAGE005
Thus, a nonlinear system of equations can be obtained:
Figure 12052DEST_PATH_IMAGE006
the method is characterized in that the form finding problem of the integral tensioning structure is converted into a nonlinear unconstrained optimization problem by a least square method, and the specific form is as follows:
Figure 606982DEST_PATH_IMAGE007
s3: calculating the gradient of the objective function;
s4: calculating an improved BFGS matrix approximating a Hessian matrix according to an improved BFGS algorithm
Figure 71461DEST_PATH_IMAGE008
；
S5: the approximate Hessian matrix obtained in the step S4
Figure DEST_PATH_IMAGE010
Substituting into the anti-noise return-to-zero neural network model to calculate the node coordinates
Figure 554656DEST_PATH_IMAGE012
In the calculation process, the problem of stretching the whole structure to find the shape under the noise condition is considered, and an MBFGS-NTN model polluted by the noise is as follows:
Figure 141495DEST_PATH_IMAGE013
in the shape finding process, noise comes from errors brought by the fact that the BFGS matrix is improved to serve as an approximate Hessian matrix, and rounding errors generated in the process of computing the self-balancing state of the integral tensioning structure, and the MBFGS-NTN shape finding algorithm can still obtain the self-balancing state of the integral tensioning structure after being interfered by the noise formed by the computing errors and the external environment through verification;
s6: judging whether the 2-norm of the gradient of the target function is smaller than a given error, if so, ending the iteration process, otherwise, returning to the step S3, and enabling the iteration time variable
Figure 161403DEST_PATH_IMAGE015
。
The specific process of the step S1 is as follows:
based on the integral structure to be shaped, a topological information matrix C is solved, and initial information is input, wherein the initial information comprises given initial coordinates of nodes, cross sectional areas of ropes and rod members, young modulus, initial length and other information.
The specific process of the step S2 is as follows:
s201: according to the force density shape finding method, the specific representation method of the force density vector is as follows:
Figure 429574DEST_PATH_IMAGE003
wherein q represents the force density vector, f represents the structural internal force, l represents the existing rope and rod length,
Figure 280855DEST_PATH_IMAGE017
represents the initial length of the rope or rod, E represents the Young's modulusS represents the cross-sectional area of the rope and the rod, and alpha, beta represents the initial and end elements at the two ends of the rope and the rod respectively;
s202: the rope and rod member now has a length expressed as
Figure 976279DEST_PATH_IMAGE004
；
S203: the force density linear equation is specifically formed as follows:
Figure 483483DEST_PATH_IMAGE018
wherein x, y and z respectively represent coordinate values in the directions of x, y and z of the node coordinates,
Figure 555345DEST_PATH_IMAGE020
，
Figure 261132DEST_PATH_IMAGE022
and
Figure 393036DEST_PATH_IMAGE023
respectively representing external forces in the x, y and z directions;
s204: in addition, let
Figure 121958DEST_PATH_IMAGE024
;
S205: the concrete representation method of the current length and the force density of the rope and the rod member is substituted into a force density linear equation system, and the following formula can be obtained:
Figure 997510DEST_PATH_IMAGE025
s206: in the form-finding process of the integral tensioning structure, the integral tensioning stable structure which is in a self-balancing state and is not interfered by external force is found. Therefore, the external force is 0 during the forming process, so the above formula is actually expressed as follows during the forming process of the tensile integral structure:
Figure 26646DEST_PATH_IMAGE006
s207: in order to convert the shape finding problem into a nonlinear unconstrained optimization problem, the following nonlinear unconstrained optimization problem is obtained by using a least square method:
Figure 860610DEST_PATH_IMAGE026
wherein n represents the number of nodes in the integral tensioning structure;
s208: obtaining an objective function to be solved, namely:
Figure 607986DEST_PATH_IMAGE007
s209: therefore, the shape finding problem of the integral tensioning structure is converted into a nonlinear unconstrained optimization problem.
The specific process of the step S3 is as follows:
s301, calculating a Jacobian matrix of R (X), namely:
Figure 21650DEST_PATH_IMAGE027
s302: computing
Figure 639713DEST_PATH_IMAGE028
，
Figure 644578DEST_PATH_IMAGE029
；
Wherein the content of the first and second substances,
Figure 613671DEST_PATH_IMAGE031
expressing the gradient of the objective function, let
Figure 565447DEST_PATH_IMAGE033
，
Figure 303595DEST_PATH_IMAGE034
Representing objectsAn approximation of the Hessian matrix of the function.
The specific process of the step S4 is as follows:
s401: the stiffness matrix plays an important role in the form-finding process of the tensioning integral structure, and if negative characteristic values or zero characteristic values appear in the stiffness matrix in the form-finding process, the singularity of the stiffness matrix can be caused, so that the form-finding process of the tensioning integral structure is unstable, and even the form-finding failure can be caused;
s402: the stiffness matrix is represented as follows:
Figure 744941DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 201330DEST_PATH_IMAGE038
which represents the stiffness of the material, is,
Figure 956797DEST_PATH_IMAGE040
represents the geometric stiffness;
s403: taking a three-dimensional tension monolithic structure as an example, the concrete representation modes of two rigidity matrixes are as follows:
Figure 549452DEST_PATH_IMAGE041
Figure 364961DEST_PATH_IMAGE043
wherein the content of the first and second substances,
Figure 845664DEST_PATH_IMAGE044
，
Figure 404822DEST_PATH_IMAGE046
，
Figure 851983DEST_PATH_IMAGE048
a force density matrix representing the tensioning system,
Figure 838394DEST_PATH_IMAGE049
representing a tensor product;
s404: in the shape finding process, the rigidity matrix needs to be kept positive and definite, and in the shape finding process, the rigidity matrix has negative or zero characteristic value conditions, so that the integral structure is stretched unstably in the shape finding process, and an improved BFGS algorithm is introduced to overcome the singular condition of the rigidity matrix;
s405: the gradient J (X) of R (X) is equal to the rigidity matrix in value, so the approximate Hessian matrix of the singular condition in the shape finding process is overcome by adopting the improved BFGS algorithm, namely the gradient J (X) of R (X) is equal to the rigidity matrix in value
Figure 66113DEST_PATH_IMAGE050
Instead, a strictly positive definite matrix;
s406: wherein the content of the first and second substances,
Figure 163382DEST_PATH_IMAGE052
；
s407: improved BFGS algorithm
Figure 465050DEST_PATH_IMAGE054
Is replaced by the shape as
Figure 622362DEST_PATH_IMAGE055
A modified stiffness matrix of form, wherein
Figure 71798DEST_PATH_IMAGE056
Is a positive number greater than zero, I is an identity matrix;
s408: replacing the Hessian matrix with a modified stiffness matrix by
Figure 972758DEST_PATH_IMAGE057
The method comprises the following steps:
Figure 394512DEST_PATH_IMAGE058
wherein the content of the first and second substances,
Figure 722725DEST_PATH_IMAGE060
，
Figure 659457DEST_PATH_IMAGE061
，
Figure 98529DEST_PATH_IMAGE062
，
Figure 374789DEST_PATH_IMAGE063
;
s409: by improving the BFGS algorithm, the approximate Hessian matrix, namely the modified rigidity matrix, can be ensured in the process of stretching the whole structure to find the shape
Figure 873904DEST_PATH_IMAGE065
Is strictly positive.
The specific process of the step S5 is as follows:
design an anti-noise return-to-zero neural network model pair node coordinate combined with an improved BFGS algorithm
Figure 297932DEST_PATH_IMAGE067
And (5) performing iteration to solve the node coordinates meeting the error requirement.
S501: the noise contaminated MBFGS-NTN model is as follows:
Figure 275115DEST_PATH_IMAGE068
wherein e represents noise, such as rounding error generated due to MATLAB calculation precision in the process of stretching integral structure form finding algorithm, and the corrected stiffness matrix calculated by BFGS algorithm is improved
Figure 937041DEST_PATH_IMAGE070
Instead of errors of the Hessian matrix, etc., experiments have shown that it is necessary to consider noise and anti-noise terms.
The specific process of the step S6 is as follows:
and if the calculated 2-norm of the gradient of the target function meets the error requirement, terminating the iteration, otherwise, adding 1 to the iteration variable k, and returning to the step S2.
Compared with the prior art, the invention has the advantages that:
the invention provides a technology for improving an anti-noise type zeroing neural network shape-finding algorithm (MBFGS-NTN) by combining an improved BFGS algorithm and a zeroing neural network model. The method is characterized in that a Hessian matrix in a traditional zero-returning neural network model is assumed to be positive, so that the zero-returning neural network model is effective in the calculation process, but the Hessian matrix in the zero-returning neural network model is difficult to keep positive in the actual shape-finding process, so that the MBFGS-NTN shape-finding algorithm adopts an improved BFGS algorithm, and replaces the Hessian matrix with an approximate Hessian matrix
Figure 934953DEST_PATH_IMAGE070
Approximate Hessian matrix
Figure DEST_PATH_IMAGE074
And the shape finding process is strictly positive, so that the effectiveness of the MBFGS-NTN algorithm is ensured, and the positive determination of the rigidity matrix of the integral tensioning structure in a self-balancing state is ensured, thereby ensuring the stability of the integral tensioning structure. Compared with the traditional form-finding algorithm, the improved anti-noise type zero-returning neural network form-finding algorithm with anti-noise capability is designed, and the form-finding problem of a tensioning integral structure under the noise condition is considered. Finally, compared with the traditional force density form-finding algorithm, by introducing the information such as the cross sectional areas of the rope and the rod member, the Young modulus, the initial length and the like, the invention realizes the analysis of the structural configuration details of the tension integral structure in a self-balancing state.
Drawings
FIG. 1 is a flow chart of a method for shaping a tensioned monolithic structure based on a return-to-zero neural network;
FIG. 2 is a three-dimensional structure diagram of a hexagonal prism tensioning integral structure before form finding;
FIG. 3 is a three-dimensional structure diagram of a hexagonal prism tensioning integral structure after shape finding;
fig. 4 is a diagram of the neuron structure of the MBFGS-NTN algorithm.
Detailed Description
The invention will be further illustrated with reference to the following examples and drawings in the description:
fig. 1 is a flow chart of a method for finding the shape of a tensioned overall structure based on a return-to-zero neural network, as shown in fig. 1, the method comprises the following specific steps:
: inputting initial conditions and topology information, and enabling an iteration variable k =0;
programming an MBFGS-NTN form-finding algorithm based on an MATLAB platform, and performing form-finding analysis on the hexagonal prism tensioning integral structure shown in the figure 2 based on the algorithm;
s101: the structure has 12 nodes, 24 ropes and rod members, wherein 18 ropes and 6 rods;
s102: solving the structural topological matrix according to the description
Figure DEST_PATH_IMAGE076
Inputting known information including initially given node coordinates, young modulus, cross-sectional areas of ropes and rods, initial length, topological matrix and the like;
s103: let the initial iteration number variable k =0.
: the shape finding problem of the hexagonal prism tensioning integral structure is converted into a nonlinear unconstrained optimization problem with the node coordinates as variables;
the specific form is as follows:
Figure DEST_PATH_IMAGE077
: calculating the gradient of the target function corresponding to the hexagonal prism tensioning integral structure
Figure DEST_PATH_IMAGE078
And the like;
calculating a nonlinear system of equations R (X) transformed from a linear system of equations of force density and a Jacobian matrix thereof
Figure DEST_PATH_IMAGE079
And the target function f (X) of the unconstrained optimization problem obtained by the nonlinear equation system through the least square method and the gradient thereof
Figure DEST_PATH_IMAGE080
Namely:
Figure DEST_PATH_IMAGE082
。
: calculating an approximate Hessian matrix by adopting an improved BFGS algorithm
Figure 745477DEST_PATH_IMAGE070
；
S401：
Figure 526351DEST_PATH_IMAGE060
；
S402：
Figure 42783DEST_PATH_IMAGE061
；
S403：
Figure 680438DEST_PATH_IMAGE062
；
S404：
Figure 16742DEST_PATH_IMAGE063
；
S405：
Figure 335727DEST_PATH_IMAGE058
。
Calculating node coordinates by MBFGS-NTN shape finding algorithm
Figure DEST_PATH_IMAGE083
；
S501: using an approximate Hessian matrix
Figure 34562DEST_PATH_IMAGE070
Replacing a Hessian matrix in the return-to-zero neural network model, and calculating a formula through an MBFGS-NTN shape finding algorithm:
Figure DEST_PATH_IMAGE084
calculating node coordinates
Figure DEST_PATH_IMAGE086
；
S502: when the hexagonal prism tensioning integral structure is subjected to the shape finding process by using the MBFGS-NTN shape finding algorithm, the noise in the shape finding algorithm is selected to be linear random noise, and the mathematical model of the noise is
Figure DEST_PATH_IMAGE087
；
Wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE089
in order to be a noise figure, the noise figure,
Figure DEST_PATH_IMAGE091
for the sampling interval and k for the number of iterations, when
Figure DEST_PATH_IMAGE093
Linear random noise is converted into constant noise;
s503: the linear random noise represents an error existing in a system in the integral tensioning structure, and if the noise is not considered in the shape finding algorithm model, the error is increased along with the increase of the iteration times, so that the shape finding algorithm cannot accurately find the self-balancing state of the integral tensioning structure.
Judging whether the 2-norm of the gradient of the target function meets the error requirement, if so, finishing the iteration process, and if not, returning to S2 to continue the iteration process;
after 7 iterations, the 2-norm value of the objective function gradient satisfies less than a given error
Figure DEST_PATH_IMAGE094
After iteration is finished, the deviation angle of the hexagonal prism tensioning integral structure in the self-balancing state is calculated to be 60.329 degrees, and after comparison with the form-finding algorithm result of the tensioning integral structure in the same way as other papers, the result is combinedThe results are basically consistent, and the deviation is within 1 degree. At the same time, the stiffness matrix is corrected
Figure DEST_PATH_IMAGE095
The minimum characteristic value of (2) is 0.1193 which is greater than 0, and meets the positive definite condition of the rigidity matrix, so the tensioning overall structure is a stable structure, and the self-balancing structure of the hexagonal prism tensioning overall structure after shape finding is shown in figure 3;
fig. 4 is a structural diagram of the MBFGS-NTN shaping algorithm, and the expression of the MBFGS-NTN shaping algorithm is as follows:
Figure DEST_PATH_IMAGE097
Figure DEST_PATH_IMAGE098
m and n are input quantities respectively
Figure DEST_PATH_IMAGE099
And gradient
Figure DEST_PATH_IMAGE100
The dimension (c) of (a) is,
Figure DEST_PATH_IMAGE102
representing an approximate Hessian matrix
Figure 550775DEST_PATH_IMAGE095
Component value of (a).

Claims (2)

1. A method for shaping a tensioned overall structure based on a return-to-zero neural network is characterized by comprising the following steps:
s1: inputting initial information including a topological matrix C of the integral tensioning structure, randomly given X, Y and Z values of initial node coordinates, young modulus, cross section area, initial length and the like of the integral tensioning structure rope and rod member;
s2: converting the force density linear equation set into a nonlinear equation set, converting the force density linear equation set into a nonlinear unconstrained optimization problem by a least square method, and further converting the shape finding problem into a nonlinear unconstrained optimization problem; the force density vector is represented as follows:
Figure 150533DEST_PATH_IMAGE001
wherein q represents the force density vector, f represents the structural internal force, l represents the length of the existing rope or rod,
Figure 179669DEST_PATH_IMAGE002
represents the initial length of the cord, stem, E represents the Young' S modulus, S represents the cross-sectional area of the cord, stem and
Figure 685737DEST_PATH_IMAGE003
respectively representing the initial and end elements at the two ends of the rope and the rod; in the process of stretching and forming the whole structure without external support, namely external force, the external force is 0, and the force density vector and the current lengths of the rope and the rod are adjusted
Figure 433113DEST_PATH_IMAGE004
Substituted formula
Figure 50039DEST_PATH_IMAGE005
In the middle, let
Figure 199260DEST_PATH_IMAGE006
Thus, a nonlinear system of equations can be obtained:
Figure 876229DEST_PATH_IMAGE007
wherein R (X) represents the residual of the external force minus the internal force of the node,
Figure 110902DEST_PATH_IMAGE008
representing the coordinate vector of the node, and stretching by the least square methodThe overall structure shape finding problem is converted into a nonlinear unconstrained optimization problem, and the specific form is as follows:
Figure 265939DEST_PATH_IMAGE009
s3: calculating the gradient of the objective function;
s4: calculating an improved BFGS matrix approximating a Hessian matrix according to an improved BFGS algorithm
Figure 535247DEST_PATH_IMAGE010
；
S5: the approximate Hessian matrix obtained in the step S4 is used
Figure 179855DEST_PATH_IMAGE011
Substituting into the anti-noise return-to-zero neural network model to calculate the node coordinates
Figure 839506DEST_PATH_IMAGE012
In the calculation process, the problem of stretching the whole structure to find the shape under the noise condition is considered, and the MBFGS-NTN model polluted by the noise is as follows:
Figure 860552DEST_PATH_IMAGE013
in the above formula, the first and second carbon atoms are,
Figure 656470DEST_PATH_IMAGE014
，
Figure 471979DEST_PATH_IMAGE015
，
Figure 681243DEST_PATH_IMAGE016
in order to be the sampling interval of the sample,
Figure 240401DEST_PATH_IMAGE017
to converge onThe number e represents a noise item, in the shape finding process, noise comes from errors brought by the fact that the BFGS matrix is used as an approximate Hessian matrix, and rounding errors generated in the process of computing the self-balancing state of the integral stretching structure, and the MBFGS-NTN shape finding algorithm can still obtain the self-balancing state of the integral stretching structure after being interfered by noise formed by computing errors and an external environment through an experience test;
s6: judging whether the 2-norm of the gradient of the target function is smaller than a given error, if so, ending the iteration process, otherwise, returning to the step S3, and enabling the iteration time variable
Figure 156404DEST_PATH_IMAGE018
。
2. The method for form-finding a tensioned overall structure based on a return-to-zero neural network as claimed in claim 1, wherein in step S4, an improved BFGS-type anti-noise return-to-zero neural network is designed, which is different from a conventional anti-noise return-to-zero neural network (noise-complete zeroing neural network), and unlike the return-to-zero neural network, a Hessian matrix in a normal zeroing neural network is assumed to be positive, but in an actual form-finding process of a tensioned overall structure, the Hessian matrix is difficult to keep positive, if the Hessian matrix is not positive in a calculation process of the return-to-zero neural network model, the fgs algorithm fails, and therefore, an improved BFGS algorithm is adopted, so that an approximate Hessian matrix is strictly positive in a form-finding process, the effectiveness and accuracy of the fgs-NTN form-finding algorithm are ensured, and the stability of the tensioned overall structure in an iteration process is ensured, and the mbn-NTN model is as follows:
Figure 142815DEST_PATH_IMAGE019
simulation experiment results show that the MBFGS-NTN form finding algorithm can be used for finding a tensioning integral structure meeting design requirements.
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Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101279483A (en) * 2008-05-29 2008-10-08 山东省公路建设（集团）有限公司 Integral tension, relaxation system and technique for pre-tensioned prestressing tension technique
CN104504284A (en) * 2015-01-04 2015-04-08 西安电子科技大学 Loose cable net form-finding method based on catenary element
CN106021930A (en) * 2016-05-23 2016-10-12 哈尔滨工业大学 Minimum mass tensegrity design method under effect of torsional moment
CN109584321A (en) * 2017-09-29 2019-04-05 通用电气公司 System and method for the image reconstruction based on deep learning
CN110413756A (en) * 2019-07-29 2019-11-05 北京小米智能科技有限公司 The method, device and equipment of natural language processing
CN110792173A (en) * 2019-10-28 2020-02-14 中冶建筑研究总院有限公司 Tensioning integral triangular prism structure and shape finding method
CN110990913A (en) * 2019-11-13 2020-04-10 中铁大桥勘测设计院集团有限公司 Side span shape finding method adopting horizontal plane internal force control
CN111666615A (en) * 2020-05-14 2020-09-15 大连理工大学 Suspension bridge space cable form finding method based on finite elements
CN112800515A (en) * 2021-01-18 2021-05-14 辽宁工程技术大学 Combined iterative algorithm based tree structure shape finding optimization design method

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7933847B2 (en) * 2007-10-17 2011-04-26 Microsoft Corporation Limited-memory quasi-newton optimization algorithm for L1-regularized objectives
US8937399B2 (en) * 2007-12-10 2015-01-20 V Squared Wind, Inc. Efficient systems and methods for construction and operation of mobile wind power platforms
WO2010068780A1 (en) * 2008-12-10 2010-06-17 V Squared Wind, Inc. Efficient systems and methods for construction and operation of accelerating machines
CN109816107A (en) * 2017-11-20 2019-05-28 天津大学 A kind of quasi- newton neural network BP training algorithm of the BFGS based on heterogeneous computing platforms
US11308075B2 (en) * 2017-12-28 2022-04-19 Cilag Gmbh International Surgical network, instrument, and cloud responses based on validation of received dataset and authentication of its source and integrity

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101279483A (en) * 2008-05-29 2008-10-08 山东省公路建设（集团）有限公司 Integral tension, relaxation system and technique for pre-tensioned prestressing tension technique
CN104504284A (en) * 2015-01-04 2015-04-08 西安电子科技大学 Loose cable net form-finding method based on catenary element
CN106021930A (en) * 2016-05-23 2016-10-12 哈尔滨工业大学 Minimum mass tensegrity design method under effect of torsional moment
CN109584321A (en) * 2017-09-29 2019-04-05 通用电气公司 System and method for the image reconstruction based on deep learning
CN110413756A (en) * 2019-07-29 2019-11-05 北京小米智能科技有限公司 The method, device and equipment of natural language processing
CN110792173A (en) * 2019-10-28 2020-02-14 中冶建筑研究总院有限公司 Tensioning integral triangular prism structure and shape finding method
CN110990913A (en) * 2019-11-13 2020-04-10 中铁大桥勘测设计院集团有限公司 Side span shape finding method adopting horizontal plane internal force control
CN111666615A (en) * 2020-05-14 2020-09-15 大连理工大学 Suspension bridge space cable form finding method based on finite elements
CN112800515A (en) * 2021-01-18 2021-05-14 辽宁工程技术大学 Combined iterative algorithm based tree structure shape finding optimization design method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
BFGS人工神经网络求解无约束优化问题;周小建 等;《南通大学学报（自然科学版）》;20060531;15-17 *
Noise-suppressing zeroing neural network for online solving time-varying nonlinear optimization problem: a control-based approach;Zhongbo Sun等;《Neural Computing and Applications》;20191206;11505–11520 *
Tensegrity Structures: Form-finding, Modelling, Structural Analysis, Design and Control;BEng;《MUSA ABDULKAREEM》;20130331;1-333 *

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