CN109543232B - Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device - Google Patents
Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device Download PDFInfo
- Publication number
- CN109543232B CN109543232B CN201811252524.4A CN201811252524A CN109543232B CN 109543232 B CN109543232 B CN 109543232B CN 201811252524 A CN201811252524 A CN 201811252524A CN 109543232 B CN109543232 B CN 109543232B
- Authority
- CN
- China
- Prior art keywords
- double
- flat
- cable
- arm holding
- holding pole
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
Abstract
The invention discloses a firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and system, wherein the method comprises the following steps: setting the sectional area of a waist ring inhaul cable as a size variable, the layout height of each layer of inhaul cable as a shape variable and the layout form of each layer of inhaul cable as a topology variable, and determining the preset value range of each variable; the method comprises the following steps of (1) constraining by using preset maximum allowable stress of a double-flat-arm holding rod member and a guy cable, preset maximum allowable displacement of the holding rod member and a preset minimum allowable buckling factor; establishing a synchronous optimization model, and taking the mass of the waist ring inhaul cable as a target function; synchronously optimizing the size, the shape and the topology by adopting an improved firefly algorithm, analyzing and calculating the mechanical property, processing the constraint condition by utilizing a penalty function, and iteratively updating and searching a global optimal solution. The optimization method has clear logic, simple and easy process, less parameters needing to be adjusted, high calculation efficiency and obvious optimization effect.
Description
Technical Field
The invention relates to the technical field of synchronous optimization, in particular to a firefly algorithm-based optimization method and device for a double-flat-arm holding pole waist ring guy cable.
Background
The double-flat-arm holding pole is used as special hoisting equipment, is relatively low in cost and convenient to assemble, has the advantages of being large in hoisting weight, high in efficiency and strong in operability, and is suitable for hoisting construction of large power transmission towers which are high in height, large in root opening and heavy in components. Along with the height crescent of transmission tower, the height of embracing the pole also promotes thereupon, embraces the pole cable and as restraint device, is vital to embracing the safe construction of pole. The pole is embraced to two flat arms uses frequently, and reasonable waist encircles the cable design and not only can improve the intensity and the stability of embracing the pole, can reduce the construction degree of difficulty and cost simultaneously. At the present stage, the design of the waist ring stay cable is based on engineering experience, and the optimum design aiming at the waist ring stay cable is few. Therefore, the synchronous optimization of the size, the shape and the topology of the guy cable is needed to improve the safety and the economy of the holding pole.
The traditional topological optimization algorithm takes the elastic modulus or the sectional area and the like of a structural unit as design variables, the problem dimension is too high, the convergence rate is slow, the optimization efficiency is low, the difficulty in solving the problem of practical engineering is high, and the problem of synchronous optimization of the size, the shape and the topology is difficult to solve.
Although the firefly algorithm has strong optimizing capability, the optimization process still suffers from the problem of premature convergence. The problem of early-maturing convergence of the firefly algorithm needs to be researched, and the algorithm optimization computing capacity and efficiency are improved through improvement of the algorithm.
Disclosure of Invention
The present invention is directed to solving, at least in part, one of the technical problems in the related art.
Therefore, the invention aims to provide a firefly algorithm-based optimization method for the double-flat-arm holding pole waist ring guy cable, which has clear logic, simple and clear flow, easy operation, less parameters needing to be adjusted, high calculation efficiency and obvious optimization effect.
The invention further aims to provide a firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization system.
In order to achieve the purpose, the invention provides a firefly algorithm-based optimization method for the double-flat-arm holding rod waist ring guy cable on the one hand, which comprises the following steps: setting the sectional area of a waist ring stay cable as a size variable, setting the layout height of each layer of stay cable as a shape variable, setting the layout form of each layer of stay cable as a topological variable, and determining the preset value range of each variable; defining constraint conditions, and constraining by using preset maximum allowable stress of a double-flat-arm holding pole rod piece and the inhaul cable, preset maximum allowable displacement of the holding pole rod piece and a preset minimum allowable buckling factor; establishing the size, the shape and the topological synchronous optimization model of the double-flat-arm holding pole waist ring inhaul cable, and taking the mass of the waist ring inhaul cable as an objective function of the synchronous optimization model; and adopting an improved firefly algorithm to carry out synchronous optimization on the size, the shape and the topology of the double-flat-arm holding pole waist ring guy cable, analyzing and calculating the mechanical properties of the double-flat-arm holding pole piece and the waist ring guy cable, processing the constraint condition by utilizing a penalty function, and searching a global optimal solution through iterative update.
According to the firefly algorithm-based optimization method for the double-flat-arm holding pole waist ring guy cable, the size, the shape and the topology of the guy cable are synchronously optimized by applying the improved firefly algorithm, so that the safety and the economy of the holding pole are improved, the operation is simple and easy, the required adjustment parameters are few, the convergence is fast, and the optimization design of the double-flat-arm holding pole guy cable under multiple design variables and multiple working conditions can be realized.
In addition, the firefly algorithm-based optimization method for the double-flat-arm holding pole waist loop guy cable according to the embodiment of the invention can also have the following additional technical characteristics:
further, in one embodiment of the invention, the double-horizontal-arm holding pole waist ring guy cables are horizontally arranged, one end of each guy cable is connected with the power transmission tower, the other end of each guy cable is connected with the double-horizontal-arm holding pole rod piece, and the length of each guy cable is reduced along with the increase of the height.
Further, in one embodiment of the present invention, the constraint is as follows:
s.t. g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the cable is indicated,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arms holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all For indicating members of double-flat-arm holding polesMinimum allowable buckling factor.
Further, in an embodiment of the present invention, in the improved firefly algorithm, the iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a beta 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most problems, gamma epsilon [0.01,100 ] can be taken]；r ij Is the Cartesian distance of firefly i from firefly j.
Further, in one embodiment of the present invention, the penalty function method is formulated as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
In order to achieve the above object, another aspect of the present invention provides a firefly algorithm based optimization system for a double-flat-arm holding pole waist ring guy cable, comprising: the setting module is used for setting the sectional area of the waist ring stay cable as a size variable, setting the layout height of each layer of stay cable as a shape variable, setting the layout form of each layer of stay cable as a topological variable, and determining the preset value range of each variable; the defining module is used for defining constraint conditions and constraining by the preset maximum allowable stress of the double-flat-arm holding pole rod piece and the inhaul cable, the preset maximum allowable displacement of the holding pole rod piece and a preset minimum allowable buckling factor; the establishing module is used for establishing the size, the shape and the topological synchronous optimization model of the double-flat-arm holding pole waist ring inhaul cable, and taking the mass of the waist ring inhaul cable as an objective function of the synchronous optimization model; and the comprehensive search module is used for performing synchronous optimization on the size, the shape and the topology of the double-flat-arm holding pole waist ring inhaul cable by adopting an improved firefly algorithm, analyzing and calculating the mechanical properties of the double-flat-arm holding pole piece and the waist ring inhaul cable, processing the constraint conditions by utilizing a penalty function, and searching a global optimal solution through iterative update.
According to the firefly algorithm-based optimization system for the double-flat-arm holding pole waist ring guy cable, the size, the shape and the topology of the guy cable are synchronously optimized by applying the improved firefly algorithm, so that the safety and the economy of the holding pole are improved, the operation is simple and easy, the required adjustment parameters are few, the convergence is fast, and the optimization design of the double-flat-arm holding pole guy cable under multiple design variables and multiple working conditions can be realized.
In addition, the firefly algorithm-based double-flat-arm holding pole waist loop inhaul cable optimization system according to the embodiment of the invention can also have the following additional technical characteristics:
further, in one embodiment of the invention, the double-flat-arm holding pole waist ring guy cables are all horizontally arranged, one end of each guy cable is connected with the transmission tower, the other end of each guy cable is connected with the double-flat-arm holding pole rod piece, and the length of each guy cable is reduced along with the increase of the height.
Further, in one embodiment of the present invention, the constraint is as follows:
s.t. g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the cable is indicated,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arm holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all The minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
Further, in an embodiment of the present invention, in the improved firefly algorithm, the iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficientFor most problems, it is desirable to take γ ∈ [0.01,100 ]]；r ij Is the Cartesian distance of firefly i from firefly j.
Further, in one embodiment of the present invention, the penalty function method is formulated as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flowchart of a firefly algorithm based optimization method for a double-flat-arm holding pole waist loop guy cable according to an embodiment of the invention;
FIG. 2 is a specific flow chart of a firefly algorithm-based optimization method for a double-flat-arm holding pole waist loop guy cable according to an embodiment of the invention;
fig. 3 is a schematic structural view of a double flat arm pole and a transmission tower according to an embodiment of the present invention, wherein, (a) the double flat arm pole and the transmission tower, (b) a standard knot, and (c) a pole;
fig. 4 is a double flat arm pole bustle cable routing style according to an embodiment of the present invention, wherein (a) τ =1, (b) τ =2, (c) τ =3, (d) τ =4, (e) τ =5;
fig. 5 is a schematic structural diagram of a firefly algorithm-based double-flat-arm holding pole waistring cable optimization system according to the embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative and intended to explain the present invention and should not be construed as limiting the present invention.
The following describes a firefly algorithm-based double-flat-arm holding pole waist loop guy cable optimization method and system provided by the embodiment of the invention with reference to the accompanying drawings, and first, the firefly algorithm-based double-flat-arm holding pole waist loop guy cable optimization method provided by the embodiment of the invention will be described with reference to the accompanying drawings.
Fig. 1 is a flowchart of a firefly algorithm-based optimization method for a double-flat-arm holding pole waist loop guy cable according to an embodiment of the present invention.
As shown in fig. 1, the firefly algorithm-based double-flat-arm holding rod waist ring guy cable optimization method comprises the following steps:
in step S101, the sectional area of the waist ring stay is set as a size variable, the layout height of each layer of stay is set as a shape variable, the layout form of each layer of stay is set as a topology variable, and a preset value range of each variable is determined.
Further, in one embodiment of the invention, the double-flat-arm holding pole waist ring guy cables are horizontally arranged, one end of each guy cable is connected with the power transmission tower, the other end of each guy cable is connected with the double-flat-arm holding pole rod piece, and the length of each guy cable is reduced along with the increase of the height.
For example, setting the optimized variable x = [ A, z, tau ] of the pole-holding waist ring guy cable]. Considering that the guy cables are all of the same type in engineering, the size variable is the cross section area of the guy cable and is represented by A. Thus, the shape variable is the cable height, i.e. z = [ z ] 1 ,…,z k ,…,z n ]Wherein z is k And represents the cable laying height of the k-th layer. The topological variable is in a cable layout form, namely tau = [ tau = 1 ,…,τ k ,…,τ n ]In which τ is k The k-th layer cable layout form is shown, and different tau values represent different cable layout forms.
In step S102, constraint conditions are defined, and the constraint conditions are constrained by the preset maximum allowable stress of the double-flat-arm holding pole rod and the inhaul cable, the preset maximum allowable displacement of the holding pole rod, and the preset minimum allowable buckling factor.
Further, in one embodiment of the present invention, the constraints are as follows:
s.t. g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the pulling cable is shown,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arm holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all The minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
In step S103, a synchronous optimization model of the size, shape and topology of the double-flat-arm derrick waist-ring guy cable is established, and the mass of the waist-ring guy cable is used as an objective function of the synchronous optimization model.
Specifically, ANSYS software is used for establishing an optimization model, the waist ring inhaul cable quality is taken as a target function, and the formula is as follows:
min f(x)
wherein f is an objective function, namely the mass of the waist ring stay cable.
In step S104, an improved firefly algorithm is used to perform synchronous optimization of size, shape and topology on the double-flat-arm holding pole waist ring guy cable, the mechanical properties of the double-flat-arm holding pole member and the waist ring guy cable are analyzed and calculated, constraint conditions are processed by using penalty functions, and a global optimal solution is searched through iterative update.
That is to say, the improved firefly algorithm is adopted to carry out optimization design on the double-flat-arm holding rod waist ring guy cable, the mechanical properties of the holding rod under different working conditions are analyzed, the constraint conditions are processed by using a penalty function method, the scheme which does not meet the design requirements is punished, the design scheme is rejected by an elite strategy in the algorithm, and the optimal solution which meets the constraint conditions is searched through multiple iterations.
Further, in one embodiment of the present invention, in the improved firefly algorithm, the iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most of problems, gamma belongs to [0.01,100 ]]；r ij Is the Cartesian distance of firefly i from firefly j.
Further, in one embodiment of the present invention, the penalty function method is formulated as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v A penalty factor representing the v-th inequality constraint.
The following describes in detail specific implementation steps and implementation examples of a firefly algorithm-based double-flat-arm holding pole waist ring guy cable optimization method:
(1) Setting the sectional area of a waist ring stay cable as a size variable, setting the layout height of each layer of stay cable as a shape variable, setting the layout form of each layer of stay cable as a topological variable, and determining the value range of each design variable;
(2) Defining constraint conditions, and using the maximum allowable stress of the holding pole rod piece and the inhaul cable, the maximum allowable displacement of the holding pole and the minimum allowable buckling factor as constraints;
(3) Establishing a synchronous optimization model of the size, the shape and the topology of the double-flat-arm holding rod waist ring guy cable, wherein the model takes the mass of the waist ring guy cable as a target function;
(4) The firefly algorithm is adopted to synchronously optimize the size, shape and topology of the double-flat-arm holding pole waist ring guy cable, the mechanical properties of the double-flat-arm holding pole and the guy cable are analyzed and calculated, constraint conditions are processed by a penalty function method, and a global optimal solution is searched through iterative updating.
In the step (1), setting an optimized variable x = [ A, z, tau ] of the holding pole waist ring inhaul cable]. Considering that the stay cables in the engineering all use the same type, the size variable is the cross section area of the stay cable, and is represented by A. The double-flat-arm holding pole waist ring inhaul cables are horizontally arranged, one end of each double-flat-arm holding pole waist ring inhaul cable is connected with the power transmission tower, the other end of each double-flat-arm holding pole waist ring inhaul cable is connected with the holding pole, and the length of each inhaul cable is reduced along with the increase of the height of each inhaul cable. Thus, the shape variable is the cable height, i.e. z = [ z ] 1 ,…,z k ,…,z n ]Wherein z is k And represents the cable laying height of the k-th layer. The topological variable is in a guy cable layout form, namely tau = [ tau = 1 ,…,τ k ,…,τ n ]In which τ is k The k-th layer cable layout form is shown, and different tau values represent different cable layout forms.
In step (2), the constraints are as follows:
s.t. g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the pulling cable is shown,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arm holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all The minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
In the step (3), an optimization model is established by using ANSYS software, the mass of the waist ring stay cable is taken as a target function, and the formula is as follows:
min f(x)
wherein f is an objective function, namely the mass of the waist ring stay cable.
In step (4), in the improved firefly algorithm, the parameter and independent variable iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a beta 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most of problems, gamma belongs to [0.01,100 ]]；r ij Is the Cartesian distance of firefly i from firefly j.
In step (4), the formula of the penalty function is as follows:
wherein F (x) represents a penalized objective function value, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
As shown in fig. 2, a description is given below to a firefly algorithm-based optimization process of a double-flat-arm holding pole waist loop guy cable with reference to specific data.
(1) Carrying out finite element parametric modeling on the double-flat-arm holding pole inhaul cable by using ANSYS;
(2) Initializing parameters, a firefly position and brightness of a firefly algorithm by using MATLAB, and setting a value range and a constraint condition of a design variable;
(3) Updating the parameters of the algorithm, the firefly position and the brightness;
(4) Calling a finite element model of the double-flat-arm holding pole cable, performing finite element analysis by using ANSYS, and extracting a target function value and a constraint variable value of the holding pole cable;
(5) Judging whether the constraint condition is satisfied, and processing the solution which does not satisfy the constraint condition by using a penalty function method;
(6) Updating the fitness value and sequencing the fitness value;
(7) Judging whether a termination condition is met, if so, outputting an optimization result, and terminating the algorithm; otherwise, returning to the step (3) to continue the iteration until the termination condition is met.
As shown in FIG. 3, the working height of the double-flat-arm derrick is 78m, the double-flat-arm derrick comprises 4 layers of guys, the hoisting amplitude is 17m, and the hoisting weight is 7.6t. The standard knot size is 1.5m × 1.5m × 3.0m. Maximum allowable stress sigma of rod all Is 310MPa; maximum allowable stress of stay cable
Maximum allowable displacement d of holding pole all Is 700mm; minimum permissible buckling factor lambda all Is 3.
The optimization design is carried out by adopting the firefly algorithm-based optimization method for the double-flat-arm holding rod waist ring guy cable.
1) ANSYS is used for establishing a finite element model of double-flat-arm holding rod waist ring stay cable
The double-flat-arm holding rod finite element model is built by a rod unit and a Beam unit, wherein the main rod is simulated by the Beam unit Beam188, and the cross rod and the web members are simulated by the rod unit Link 8. The inhaul cable adopts a Link10 unit, and simulates the characteristic that the inhaul cable is only pulled and is not pressed. The optimization design variables are the section area, height coordinate and layout form of the inhaul cable. In combination with the actual engineering, all the inhaul cables are of the same sectional area, the lower limit of the inhaul cable arrangement height is 0m, the upper limit of the inhaul cable arrangement height is 78m, the inhaul cable arrangement forms are 5, the available inhaul cable sectional areas are shown in table 1 (inhaul cable models), and the arrangement forms are shown in fig. 4.
TABLE 1
2) Load condition
The load conditions to be considered in the design of the double-flat-arm holding pole are shown in the table 2.
TABLE 2
3) By adopting the method provided by the invention, the ANSYS and MATLAB software are utilized to complete the optimized design of the double-flat-arm holding rod waist ring inhaul cable. The initial design and the optimal design result of the double-flat-arm holding pole waist ring guy cable are shown in the following table 3 for comparison of design variables and quality, table 4 for comparison of maximum holding pole displacement (unit: mm), table 5 for comparison of maximum pole stress (unit: MPa), table 6 for comparison of maximum guy cable stress (unit: MPa) and table 7 for comparison of buckling factors:
TABLE 3
TABLE 4
TABLE 5
TABLE 6
TABLE 7
The data in tables 3 to 7 are analyzed to show that:
(1) The mass of the double-flat-arm holding pole waist ring inhaul cable optimized by the improved firefly algorithm is reduced from 1370.95kg to 780.71kg, and is reduced by 43.05%.
(2) Compared with the initial scheme, the maximum displacement under each working condition after the double-flat-arm holding pole inhaul cable is optimized is obviously reduced.
(3) Compared with the initial scheme, the maximum rod stress under each working condition after the double-flat-arm holding rod inhaul cable is optimized is obviously reduced.
(4) Compared with the initial scheme, the maximum cable stress under each working condition after the double-flat-arm holding pole cable is optimized is less in change and is smaller than the allowable stress.
(5) Compared with the initial scheme, the bending factor under each working condition is obviously increased after the double-flat-arm holding pole inhaul cable is optimized, and the stability is obviously enhanced.
According to the optimization design method of the double-flat-arm holding pole inhaul cable based on the improved firefly algorithm, the actual engineering is optimally designed, the holding pole displacement and the rod piece stress are obviously reduced after optimization, the buckling factor is obviously increased, and the stability is improved. The stress change of the stay cable is small, the design specification requirement is met, the mass of the stay cable is reduced by 43.05%, and the optimization effect is obvious.
According to the firefly algorithm-based optimization method for the double-flat-arm holding pole waist ring guy cable, the improved firefly algorithm is applied to synchronously optimize the size, the shape and the topology of the guy cable, so that the safety and the economy of the holding pole are improved, the operation is simple and easy, the required adjustment parameters are few, the convergence is fast, and the optimization design of the double-flat-arm holding pole guy cable under multiple design variables and multiple working conditions can be solved.
Next, a firefly algorithm-based double-flat-arm holding pole waist loop inhaul cable optimization system provided according to an embodiment of the present invention is described with reference to the drawings.
Fig. 5 is a schematic structural diagram of a firefly algorithm-based double-flat-arm holding pole waist loop inhaul cable optimization system according to an embodiment of the present invention.
As shown in fig. 5, the firefly algorithm based double flat arm holding pole waist loop guy cable optimization system 10 includes: a setting module 100, a definition module 200, a building module 300 and an integrated search module 400.
The setting module 100 is configured to set a cross-sectional area of a waist-ring cable as a size variable, set a layout height of each layer of cables as a shape variable, set a layout form of each layer of cables as a topology variable, and determine a preset value range of each variable. The defining module 200 is configured to define constraint conditions, and constrain the pole members of the double-flat-arm pole and the inhaul cables with a preset maximum allowable stress, a preset maximum allowable displacement, and a preset minimum allowable buckling factor. The establishing module 300 is used for establishing a synchronous optimization model of the size, the shape and the topology of the double-flat-arm holding pole waist ring guy cable, and taking the mass of the waist ring guy cable as an objective function of the synchronous optimization model. The comprehensive search module 400 is configured to perform synchronous optimization of size, shape and topology on the double-flat-arm holding pole waist ring guy cable by using an improved firefly algorithm, analyze and calculate mechanical properties of the double-flat-arm holding pole member and the waist ring guy cable, process a constraint condition by using a penalty function, and search for a global optimal solution through iterative update. The optimization system 10 of the embodiment of the invention has the advantages of clear logic, concise flow, easy operation, less parameters to be adjusted, high calculation efficiency and remarkable optimization effect.
Further, in one embodiment of the invention, the double-flat-arm holding pole waist ring guy cables are horizontally arranged, one end of each guy cable is connected with the power transmission tower, the other end of each guy cable is connected with the double-flat-arm holding pole rod piece, and the length of each guy cable is reduced along with the increase of the height.
Further, in one embodiment of the present invention, the constraints are as follows:
s.t. g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all Show two flat arm and embrace poleThe maximum allowable stress of the rod member is,
the maximum stress of the cable is indicated,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arm holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all And the minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
Further, in one embodiment of the present invention, in the improved firefly algorithm, the iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most of problems, gamma belongs to [0.01,100 ]]；r ij Is the Cartesian distance of firefly i from firefly j.
Further, in one embodiment of the present invention, the penalty function method is formulated as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
It should be noted that the foregoing explanation of the method embodiment is also applicable to the firefly algorithm-based double-flat-arm holding rod waist loop guy cable optimization system, and details are not repeated here.
According to the firefly algorithm-based double-flat-arm holding pole waist ring inhaul cable optimization system provided by the embodiment of the invention, the size, the shape and the topology of the inhaul cable are synchronously optimized by applying the improved firefly algorithm, so that the safety and the economy of the holding pole are improved, the operation is simple and easy, the required adjustment parameters are few, the convergence is fast, and the optimization design of the double-flat-arm holding pole inhaul cable under multiple design variables and multiple working conditions can be solved.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood according to specific situations by those of ordinary skill in the art.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "above," and "over" a second feature may be directly on or obliquely above the second feature, or simply mean that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example" or "some examples" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (10)
1. A firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method is characterized by comprising the following steps:
setting the sectional area of a waist ring stay cable as a size variable, setting the layout height of each layer of stay cable as a shape variable, setting the layout form of each layer of stay cable as a topological variable, and determining the preset value range of each variable;
defining constraint conditions, and constraining by using the preset maximum allowable stress of a double-flat-arm holding pole rod piece and the inhaul cable, the preset maximum allowable displacement of the holding pole rod piece and a preset minimum allowable buckling factor;
establishing the size, the shape and the topological synchronous optimization model of the double-flat-arm holding pole waist ring inhaul cable, and taking the mass of the waist ring inhaul cable as an objective function of the synchronous optimization model; and
and carrying out synchronous optimization on the size, the shape and the topology of the double-flat-arm holding pole waist ring inhaul cable by adopting an improved firefly algorithm, analyzing and calculating the mechanical properties of the double-flat-arm holding pole piece and the waist ring inhaul cable, processing the constraint condition by utilizing a penalty function, and searching for a global optimal solution through iterative update.
2. The firefly algorithm-based optimization method for the double-horizontal-arm holding pole lumbar ring guy cable according to claim 1, wherein the double-horizontal-arm holding pole lumbar ring guy cable is horizontally arranged, one end of the double-horizontal-arm holding pole lumbar ring guy cable is connected with a power transmission tower, the other end of the double-horizontal-arm holding pole lumbar ring guy cable is connected with the double-horizontal-arm holding pole rod piece, and the length of the guy cable is reduced along with the increase of the height of the guy cable.
3. The firefly algorithm-based double-flat-arm holding pole waist loop guy cable optimization method according to claim 1, wherein the constraint conditions are as follows:
s.t.g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the cable is indicated,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arms holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents all The minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
4. The firefly algorithm-based double flat arm holding pole waist loop guy cable optimization method according to claim 1, wherein in the improved firefly algorithm, an iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]Random number vectors within the interval; beta is a 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most problems, gamma epsilon [0.01,100 ] can be taken]；r ij Is the Cartesian distance of firefly i from firefly j.
5. The firefly algorithm-based double flat arm derrick lumbar loop cable optimization method of claim 1, wherein the penalty function formula is as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
6. The utility model provides a two flat arms embrace pole waist ring cable optimizing system based on firefly algorithm which characterized in that includes:
the setting module is used for setting the sectional area of the waist ring stay cable as a size variable, setting the layout height of each layer of stay cable as a shape variable, setting the layout form of each layer of stay cable as a topological variable, and determining the preset value range of each variable;
the defining module is used for defining constraint conditions and constraining by the preset maximum allowable stress of the double-flat-arm holding pole rod piece and the inhaul cable, the preset maximum allowable displacement of the holding pole rod piece and a preset minimum allowable buckling factor;
the establishing module is used for establishing the size, the shape and the topological synchronous optimization model of the double-flat-arm holding pole waist ring inhaul cable, and taking the mass of the waist ring inhaul cable as an objective function of the synchronous optimization model; and
and the comprehensive search module is used for adopting an improved firefly algorithm to carry out synchronous optimization on the size, the shape and the topology of the double-flat-arm holding pole waist ring guy cable, analyzing and calculating the mechanical properties of the double-flat-arm holding pole piece and the waist ring guy cable, processing the constraint condition by utilizing a penalty function, and searching a global optimal solution through iterative update.
7. The firefly algorithm-based double-horizontal-arm holding pole lumbar ring inhaul cable optimization system according to claim 6, wherein the double-horizontal-arm holding pole lumbar ring inhaul cables are all horizontally arranged, one end of each double-horizontal-arm holding pole lumbar ring inhaul cable is connected with a power transmission tower, the other end of each double-horizontal-arm holding pole lumbar ring inhaul cable is connected with the double-horizontal-arm holding pole rod piece, and the lengths of the inhaul cables decrease with the increase of the height.
8. The firefly algorithm-based double flat arm derrick girdle cable optimization system of claim 6, wherein the constraint conditions are as follows:
s.t.g 1 ＝σ max -σ all ≤0
g 3 ＝d max -d all ≤0
g 4 ＝λ all -λ≤0
wherein, g v (v =1,2,3,4) represents a constraint function, σ max Expressing the maximum stress, sigma, of the double-flat-arm holding pole member all The maximum allowable stress of the double-flat-arm holding pole rod piece is shown,
the maximum stress of the cable is indicated,
represents the maximum allowable stress of the cable, d max Represents the maximum displacement of the double flat arm holding pole rod piece, d all The maximum allowable displacement of the double-flat-arm holding pole rod piece is represented, lambda represents the buckling factor of the double-flat-arm holding pole rod piece, and lambda represents the maximum allowable displacement of the double-flat-arm holding pole rod piece all The minimum allowable buckling factor of the double-flat-arm holding pole rod piece is shown.
9. The firefly algorithm-based dual flat arm holding pole lumbar ring guy cable optimization system of claim 6, wherein in the improved firefly algorithm, the iterative formula is as follows:
x i (t+1)＝x i (t)+β(x j (t)-x i (t))+α(t)ε i
r ij ＝||x i -x j ||
wherein x is i And x j The spatial positions of the fireflies i and j; beta is the attraction of the firefly; alpha is a step size factor and is adaptively changed along with the iteration times t; epsilon i Is uniformly distributed in [ -0.5,0.5]A random number vector within the interval; beta is a beta 0 And beta min Upper and lower limits of beta, respectively; gamma is the light absorption coefficient, and for most of problems, gamma belongs to [0.01,100 ]]；r ij Is the Cartesian distance of firefly i from firefly j.
10. The firefly algorithm based dual flat arm derrick lumbar loop cable optimization system of claim 6, wherein the penalty function formula is as follows:
wherein F (x) represents a penalized objective function value, F (x) represents an objective function, g v Represents the v-th inequality constraint, phi v And a penalty coefficient representing the v-th inequality constraint.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811252524.4A CN109543232B (en) | 2018-10-25 | 2018-10-25 | Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811252524.4A CN109543232B (en) | 2018-10-25 | 2018-10-25 | Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109543232A CN109543232A (en) | 2019-03-29 |
| CN109543232B true CN109543232B (en) | 2022-12-09 |
Family
ID=65845523
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811252524.4A Active CN109543232B (en) | 2018-10-25 | 2018-10-25 | Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109543232B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107016196A (en) * | 2017-04-10 | 2017-08-04 | 合肥工业大学 | A kind of narrow base angle steel Transmission Tower Optimization Design based on glowworm swarm algorithm |
| WO2018001147A1 (en) * | 2016-06-29 | 2018-01-04 | 深圳市智能机器人研究院 | Optimized tensioned cord model-based method and system for monitoring bridge cable |
-
2018
- 2018-10-25 CN CN201811252524.4A patent/CN109543232B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2018001147A1 (en) * | 2016-06-29 | 2018-01-04 | 深圳市智能机器人研究院 | Optimized tensioned cord model-based method and system for monitoring bridge cable |
| CN107016196A (en) * | 2017-04-10 | 2017-08-04 | 合肥工业大学 | A kind of narrow base angle steel Transmission Tower Optimization Design based on glowworm swarm algorithm |
Non-Patent Citations (1)
| Title |
|---|
| 具有混沌搜索策略的萤火虫优化算法;刘长平等;《系统管理学报》;20130715(第04期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109543232A (en) | 2019-03-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107563010B (en) | Shape feature-based multi-scale structural material integrated design method | |
| CN102622485B (en) | Morphological analysis inverse iteration method for determining space structural lofting states of cable-strut-beam system | |
| KR102462922B1 (en) | Offshore wind turbine basic structure and lightweight design method | |
| CN105243185B (en) | A kind of tension integral structure based on Monte Carlo method looks for shape method | |
| CN108875286A (en) | A kind of parameter optimization method of suspension bridge analysis of Integral Structure | |
| CN110210130B (en) | Shape optimization method for I-beam two-dimensional model | |
| CN111651907B (en) | Modeling analysis method of complex cable net system | |
| CN102750408A (en) | Pull rod installing layout method of airplane auxiliary power device | |
| CN110569519A (en) | Topological optimization design method for dynamic and static mechanical properties of three-dimensional continuum structure considering non-design domain | |
| CN108197417A (en) | A kind of curve stiffened panel finite element method | |
| US20200065447A1 (en) | Method for fixture shape optimization design of space membrane structure for inhibiting wrinkling | |
| CN109543232B (en) | Firefly algorithm-based double-flat-arm holding rod waist ring inhaul cable optimization method and device | |
| CN108170947B (en) | Method for acquiring novel lattice structure based on firefly algorithm | |
| CN116432331A (en) | Non-hinge multi-input multi-output flexible mechanism buckling-restrained topological optimization design method | |
| CN111985018A (en) | Calculation method for designing wind load of ultrahigh large-span tower and line based on inertia force method and tower line separation method and considering tower line coupling influence | |
| CN103065015B (en) | A kind of bearing structure low-carbon (LC) material-saving method for designing based on internal force path geometry form | |
| CN105760549B (en) | Nearest Neighbor based on attribute graph model | |
| CN108563904A (en) | A kind of anchoring system anchor chain short form test method based on static state and dynamic equivalent | |
| CN107016179B (en) | Shape finding method for string structure | |
| Zhao et al. | Intelligent design algorithm for branching structures based on updated force density method | |
| CN108021758B (en) | Finite element-based cable net antenna equal tension shape finding method | |
| Qiao et al. | Automatic optimal design of passive vibration control devices for buildings using two-level evolutionary algorithm | |
| CN112287424B (en) | Calculation method for designing wind load of ultrahigh large-span tower and line based on effective load method and tower line separation method and considering tower line coupling influence | |
| CN106156443A (en) | A kind of laying stiffening ring and method and device of meridian rib on cooling tower | |
| CN109145323A (en) | Design method, device and the antenna of antenna |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |