KR101499865B1 - Method and device for optimizing topology of structures based on harmony search method - Google Patents

Abstract

Provided are a method and a device for optimizing topology of a structure by using a harmony search scheme. According to an embodiment of the present invention, there is a method for optimizing topology of a structure by using a harmony search scheme, which includes the steps of: separating design variables applied into a predefined design region into a structural element and a non-structural element; performing finite-element modeling of the structural element and non-structural elements based on the separated design variables; performing a finite-element analysis for the modeled structural element and non-structural elements; randomly searching the entire design region to search for a candidate solution based on the result of the finite-element analysis; amending positions of each element through a probabilistic selection for the candidate solution; storing the candidate solution in a harmony memory according to importance of each element; and determining the candidate solution as an optimal solution when an objective function of the structure corresponding to the candidate solution satisfies a convergence condition.

Description

TECHNICAL FIELD The present invention relates to a method and apparatus for optimizing a topology of a structure using a harmonic search method,

Embodiments of the present invention are directed to a method and apparatus for optimizing the phase of a structure using a harmonic search.

The goal of structural optimization is to find the shape of a structure that can achieve the best performance while satisfying constraints such as structural stress limits or volume constraints.

According to the requirements of the designer, the structural optimization is divided into sizing, shape, and topology optimization. In particular, in the case of topology optimization, boundary conditions and loads It is a method to find the optimal shape considering only the condition.

The phase optimization methods are solid isotropic material with penalization (SIMP) and evolutionary structural optimization (ESO), and it is confirmed that this conventional method is applicable to various phase optimization problems.

The SIMP is filled with a gray element in accordance with the target volume of the entire design area, and then the important part gradually becomes black (the part that is the structure) and the non-important part becomes the white part Quot; portion "). The ESO is a method of filling an entire design area with a black (structure) element and then sequentially removing unnecessary elements to find an optimal phase.

The method of topology-compliant mechanism using SIMP and ESO has several problems.

In the case of SIMP, there is a gray portion in addition to a black portion and a white portion. The reason for the existence of the gray part is that the design area is initially filled with gray elements and then optimized, and the design variables for each element are defined not only by the structure and structure but also by the intermediate area It is because. This phenomenon is problematic in that it is difficult to definitively define the boundary of an optimized phase.

In the case of the ESO, portions that are the structure and portions that are not the structure are clearly distinguished. However, when the methodology is viewed, it takes a considerable amount of time to optimize the target volume because it is required to fill the entire design area with the structure in the initial stage and to adjust the target volume.

Therefore, it is necessary to discretize the design parameters of each element for solving the gray area of the SIMP, and furthermore, in order to solve the problem that it takes a long time to perform the optimization, only the structure element It is necessary to introduce a technique for performing optimization by using the optimization technique.

Related prior art is the registered patent publication No. 10-1134196 entitled " LAP optimum design method and apparatus using ABC algorithm in wireless communication network, registered on March 30, 2012].

A method and an apparatus for optimizing a phase of a structure using a harmonic search method capable of improving a global search ability and a convergence speed by optimizing a phase of a structure by using a harmonic search method that searches the entire design domain in a harmonious manner to provide.

The problems to be solved by the present invention are not limited to the above-mentioned problem (s), and another problem (s) not mentioned can be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided a method of optimizing a phase of a structure using a harmonic search method, the method comprising: discretizing design variables applied to a predefined design domain into a structural element and a non-structural element; Performing finite element modeling on the structural element and the non-structural element based on the discretized design parameter; Performing a finite element analysis on the modeled structural element and the non-structural element; Performing a random search on the entire area of the design area for searching for a candidate solution based on the result of the finite element analysis; Correcting a position of each element through a probability selection for the candidate solution; Storing the candidate solution in a harmony memory (HM) memory according to the importance of each element; And determining the candidate solution as an optimal solution if the objective function of the structure according to the candidate solution satisfies a convergence condition.

If the objective function does not satisfy the convergence condition, the phase optimization method of the structure using the harmonic search method according to an embodiment of the present invention returns to the step of performing the random search and sequentially repeats until the convergence condition is satisfied The method comprising the steps of:

A method for optimizing a phase of a structure using a harmonic search method according to an embodiment of the present invention includes: inputting a boundary condition and a load condition acting on the structure after performing the finite element modeling; And calculating a fitness value of each element based on the input boundary condition and the load condition after the step of performing the finite element analysis.

The method of optimizing a phase of a structure using a harmonic search method according to an embodiment of the present invention may further include the step of calculating a sensitivity number for the design parameter after performing a finite element analysis under the boundary condition and the load condition And calculating the fitness of each element may include calculating a fitness of each element based on the calculated sensitivity number.

The step of correcting the position of each element may include correcting the position of each element through a stochastic selection of a harmonic memory consideration rate (HMCR) and a pitch adjustment (PAR) .

The step of storing the candidate solution in the chord memory space (HM) includes the steps of: determining importance of each element based on the fitness of each element; Performing a finite element analysis for determining the importance; And determining the objective function based on the result of the finite element analysis.

The method of optimizing a topology of a structure using a harmonic search method according to an embodiment of the present invention includes a step of calculating a sensitivity number according to the objective function using the chord memory space HM after determining the objective function As shown in FIG.

It is preferable that the number of the structural elements is constant within the design area such that the initial volume and the target volume of the structure are equal to each other.

The apparatus for optimizing a phase of a structure using a harmonic search method according to an embodiment of the present invention is a system for minimizing a phase of a structure by discretizing design variables applied to a predefined design domain into structure elements and non- A finite element modeling unit for finite element modeling of the element and the non-structural element; And performing a finite element analysis on the modeled structural element and the non-structural element and performing a random search on the entire area of the design area for searching for a candidate solution based on the result of the finite element analysis part; A position of each element is corrected through a probability selection for the candidate solution, and the candidate solution is stored in a harmony memory (HM) according to the importance of each element, And if the function satisfies the convergence condition, determines the candidate solution as an optimal solution.

The details of other embodiments are included in the detailed description and the accompanying drawings.

According to an embodiment of the present invention, the global search ability and the convergence speed can be improved by optimizing the phase of the structure using the harmonic search method that searches the entire design domain in a harmonic manner.

According to the embodiment of the present invention, when the design area is large, a very efficient convergence speed can be obtained.

According to an embodiment of the present invention, it is possible to shorten the phase optimization time by improving the global search ability and the convergence speed.

According to an embodiment of the present invention, it is possible to surely define the boundary of the optimized phase by discretizing the design parameters of each element. By optimizing using a predetermined number of structure elements corresponding to the target volume from the beginning, Can be further reduced.

FIG. 1 is a block diagram illustrating a structure topology optimizing apparatus using a harmonic search method according to an embodiment of the present invention. Referring to FIG.
FIGS. 2A to 2C are views illustrating a cantilever beam problem using HS according to an embodiment of the present invention.
3A to 3C are views showing an embodiment of an MBB beam problem using HS according to an embodiment of the present invention.
FIGS. 4 to 6 are flowcharts illustrating a phase optimization method of a structure using a harmonic search method according to an embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and / or features of the present invention, and how to accomplish them, will become apparent with reference to the embodiments described in detail below with reference to the accompanying drawings. It should be understood, however, that the invention is not limited to the disclosed embodiments, but is capable of many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a structure topology optimizing apparatus using a harmonic search method according to an embodiment of the present invention. Referring to FIG.

1, a structure topology optimizing apparatus 100 using a harmonic search method according to an embodiment of the present invention includes a finite element modeling unit 110, a candidate solution search unit 120, an optimal solution determining unit 130 And a control unit 140. The control unit 140 may be a microcomputer.

The finite element modeling unit 110 discretizes design variables applied to the design domain into structural elements and non-structural elements. Here, the design area may be defined in advance or may be defined when the design parameter is discretized.

As described above, in the embodiment of the present invention, by discretizing the design variables into the structural element and the non-structural element, it is possible to reliably define the optimized phase boundary by solving the gray area generated in SIMP, .

The finite element modeling unit 110 performs finite element modeling on the structure element and the non-structure element based on the discretized design parameter. Here, the finite element modeling is a method of creating a three-dimensional shape of a finite element in a virtual space inside a computer. In general, a finite element analysis program provides various modeling methods.

In one embodiment of the present invention, the number of structural elements is preferably constant within the design area such that the initial volume and target volume of the structure are equal. That is, the number of the structural elements can be set to a predetermined number in accordance with the target volume from the beginning in the design area.

Thus, according to an embodiment of the present invention, by optimizing the number of structural elements in the design area to be constant from the beginning to the target volume, the initial volume and target volume of the structure are optimized to be the same Can be reduced.

Therefore, according to the embodiment of the present invention, it is possible to relatively quickly find an element that should ultimately become a structure, thereby effectively improving the phase optimization problems of the structure.

The candidate solution search unit 120 performs a finite element analysis on the modeled structural element and the non-structural element. In order to perform the finite element analysis, a finite element model for the structure element and the non-structure element can be formulated.

Here, the above formula means that a differential equation for finite element analysis is obtained. We can obtain the eigenvalue, displacement, acceleration, velocity, mass, stiffness, damping matrix, and natural frequency of each node of the model using the formulated differential equation. The principle of analyzing the finite element of the model in the finite element analysis program is already known, and a detailed description will be omitted.

The candidate solution search unit 120 may calculate a sensitivity number for each element of the design variable. The candidate solution search unit 120 may calculate a fitness value of each element based on the calculated sensitivity number under the input boundary condition and the load condition.

The candidate solution search unit 120 performs a random search on the entire region of the design region for searching for a candidate solution based on the result of the finite element analysis. That is, the candidate solution search unit 120 may randomly generate a solution vector to obtain the solution (candidate solution), and store the candidate solution in a harmony memory (HM) memory space. In other words, a randomly configured candidate solution can be stored in the above-mentioned chord memory space HM.

As described above, the candidate solution stored in the chord memory space HM is determined by whether or not the resultant value of the objective function calculated by substituting the harmonic vector into the objective function remains in the chord memory space HM depending on whether the result value of the objective function is good or bad, It can be determined whether or not to be erased in the memory space HM.

That is, the candidate solution stored in the chord memory space HM remains in the chord memory space HM if the result value of the objective function is good, and is erased in the chord memory space HM if it is not good.

To this end, the optimal solution determining unit 130 may correct the position of each element by selecting a probability for the candidate solution. At this time, the optimal solution determining unit 130 may correct the position of each element through a stochastic selection of a HMCR (Harmony Memory Considering Rate) and a Pitch Adjustment (PAR).

More specifically, the memory recall (HMCR) refers to a probability selection method for selecting a candidate solution based on a probability (HMCR) to be adopted in an existing chord storage space (HM). And, the pitch adjustment (PAR) refers to a process of adjusting to some degree the candidate solution selected in the memory recall (HMCR).

That is, the pitch adjustment (PAR) searches the objective function values in the surrounding area in the forward direction of the executable area on the basis of the candidate solution selected in the memory recall (HMCR), and if there is a direction in which the solution can be updated Direction to adjust the pitch.

The memory recall (HMCR) and the pitch adjustment (PAR) can be expressed as Equation (1) below. That is, the optimal solution determining unit 130 may correct the position of each element by performing stochastic selection of the memory recall (HMCR) and the pitch adjustment (PAR) using the following equation (1).

[Equation 1]

The optimum solution determining unit 130 may store the candidate solution in the chord memory space HM according to the importance of each element whose position is corrected.

For this, the optimal solution determining unit 130 may determine the importance of each element based on the fitness of each element, and perform a finite element analysis for determining the importance. The optimal solution determining unit 130 may determine the objective function of the structure based on the result of the finite element analysis.

In this case, the importance of each element may be in inverse proportion to the fitness of each element. That is, the importance of each of the above elements becomes higher as the fitness of each element becomes lower, and becomes lower as the fitness of each element becomes higher.

The optimum solution determining unit 130 may store (maintain) the candidate solution in the chord memory space HM with a higher value of the relative importance of each element.

On the other hand, the optimal solution determining unit 130 can delete the candidate solution in the chord memory space HM with a lower value of the relative importance of each element.

The optimum solution determining unit 130 may calculate an objective function for the chord storage space HM using the result of the finite element analysis. The optimal solution determining unit 130 may calculate the sensitivity number according to the objective function using the chord memory space HM.

When the objective function of the structure according to the candidate solution satisfies the convergence condition, the optimal solution determining unit 130 determines the candidate solution as the optimal solution. On the other hand, if the objective function of the structure according to the candidate solution does not satisfy the convergence condition, the optimization solution determining unit 130 returns to the step of performing the random search, The following steps can be repeated in sequence (see FIG. 4).

The control unit 140 may be configured to optimize the phase of the structure using the harmonic search method according to an embodiment of the present invention, that is, the finite element modeling unit 110, the candidate solution search unit 120, The operation of the determination unit 130 and the like can be controlled as a whole.

FIGS. 2A through 2C and FIGS. 3A through 3C are views illustrating embodiments of a phase optimization problem using a coarse search method according to an embodiment of the present invention. 2A to 2C are views showing an embodiment of a cantilever beam problem using HS (Harmony Search) according to an embodiment of the present invention. FIG. 5 is a view showing an embodiment of the MBB beam problem using the method of FIG.

First, the problem defined in relation to the Cantilever beam is as shown in FIG. 2A. The initial optimization mode for the phase optimization of the Cantilever beam is as shown in FIG. 2B. As shown in FIG. 2B, in the initial optimization mode, a discretization process of design variables divided into a structural element and a non-structural element is applied. At this time, the number of structural elements in the design region is set to be constant Can be applied. The result of performing the phase optimization based on the initial optimization mode as shown in FIG. 2B is as shown in FIG. 2C. That is, if the phase of design optimization is performed by using the HS based on the discretization process of the design variables and the same design process of the initial volume and the target volume, an optimized phase is derived as shown in FIG.

Next, the problem defined with respect to the MBB beam (Messerschmitt-Bolkow-Blohm beam) is as shown in FIG. 3A. The initial optimization mode for phase optimization of the MBB beam is as shown in FIG. 3B. As shown in FIG. 3B, in the initial optimization mode, a discretization process of a design variable divided into a structural element and a non-structural element is applied. At this time, the number of structural elements in the design region is set to be constant Can be applied. The result of performing the phase optimization based on the initial optimization mode as shown in FIG. 3B is as shown in FIG. 3C. In other words, if a design phase is optimized and a series of phase optimization steps using HS are performed based on the same design process of the initial volume and the target volume, optimized phase is derived as shown in FIG. 3c.

FIGS. 4 to 6 are flowcharts illustrating a phase optimization method of a structure using a harmonic search method according to an embodiment of the present invention. 5 is a detailed flowchart of a process of correcting the position of each element through probability selection in the phase optimization method of FIG. 4. FIG. 6 is a flowchart illustrating the phase optimization of FIG. A detailed flowchart of a process of storing the candidate solution in the chord memory space HM is shown. For reference, the phase optimization method may be performed by the phase optimization apparatus 100 of FIG.

Referring first to FIG. 4, in step 410, the phase optimizer discretizes design variables applied to a design domain into structural elements and non-structural elements, and based on the discretized design variables, We perform finite element modeling for the element.

Next, in step 420, the phase optimizer inputs boundary conditions and loading conditions acting on the structure.

Next, in step 430, the phase optimizer performs a finite element analysis on the modeled structural element and the non-structural element, and calculates a sensitivity number for the design variable.

Next, in step 440, the phase optimizer calculates the fitness of each element. At this time, the phase optimizer may calculate the fitness of each element based on the calculated sensitivity number under the input boundary condition and the load condition.

Next, in step 450, the phase optimizer performs a random search on the entire area of the design area for searching for a candidate solution based on the result of the finite element analysis.

Next, at step 460, the phase optimizer corrects the position of each element through a probability selection for the candidate solution. At this time, the phase optimizer can correct the position of each element through a stochastic selection of a memory recall (HMCR) and a pitch adjustment (PAR).

That is, as shown in FIG. 5, at step 510, the phase optimizer performs a stochastic selection of the memory recall (HMCR). At this time, if the value of the HMCR is less than a preset reference value (e.g., 0.85) (in the "YES" direction of 510), the phase optimizer performs step 520.

That is, in step 520, the phase optimizer performs a stochastic selection of the pitch adjustment (PAR). If the value of the PAR is greater than or equal to a preset reference value (e.g., 0.45) (the "NO" direction of 520), the phase optimizer returns to step 450 of FIG. 4 to perform a random search for the entire area again do.

On the other hand, if the value of the PAR is less than a preset reference value (direction of "YES " in 520), the phase optimizer performs step 470 of FIG. If the value of the HMCR is equal to or greater than a preset reference value ("NO" direction of 510), the phase optimizer performs step 470 of FIG.

Referring again to FIG. 1, in step 470, the phase optimization apparatus stores the candidate solution in the chord memory space HM according to the importance of each element.

Specifically, referring to FIG. 6, in step 610, the phase optimizer determines importance of each element based on the fitness of each element. Thereafter, in step 620, the phase optimizer performs a finite element analysis for determining the importance. Thereafter, in step 630, the phase optimization apparatus stores the candidate solution in the chord memory space HM based on the result of the finite element analysis.

Referring again to FIG. 1, in step 480, the phase optimizer calculates an objective function for the chord storage space HM using the result of the finite element analysis, and uses the chord storage space HM And calculates the sensitivity number according to the objective function.

Next, in step 490, the phase optimizer determines whether the objective function of the structure according to the candidate solution satisfies the convergence condition.

As a result of the determination, if the convergence condition is satisfied (in the "YES" direction of 490), then in step 495, the phase optimization apparatus determines the candidate solution as the optimal solution.

On the other hand, if it is determined that the echo convergence condition is not satisfied (No in step 490), the phase optimizer returns to step 440 and repeats the steps sequentially until the convergence condition is satisfied.

Embodiments of the present invention include computer readable media including program instructions for performing various computer implemented operations. The computer-readable medium may include program instructions, local data files, local data structures, etc., alone or in combination. The media may be those specially designed and constructed for the present invention or may be those known to those skilled in the computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floppy disks, and ROMs, And hardware devices specifically configured to store and execute the same program instructions. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined by the scope of the appended claims and equivalents thereof.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, Modification is possible. Accordingly, the spirit of the present invention should be understood only in accordance with the following claims, and all equivalents or equivalent variations thereof are included in the scope of the present invention.

110: finite element modeling unit
120: candidate search unit
130: optimal solution determining unit
140:

Claims (9)

Discretizing a design parameter applied to a predefined design domain into a structural element and a non-structural element in a finite element modeling unit of the phase optimization apparatus;
Performing finite element modeling on the structural element and the non-structural element based on the discretized design parameter in the finite element modeling unit;
Performing a finite element analysis on the modeled structural element and the non-structural element in a candidate solution search unit of the phase optimization apparatus;
Performing a random search on the entire region of the design region for a candidate solution search based on a result of the finite element analysis;
Correcting a position of each element through a probability selection for the candidate solution in an optimal solution determining unit of the phase optimizing apparatus;
Storing the candidate solution in a harmony memory (HM) according to the importance of each element in the optimal solution determination unit; And
If the objective function of the structure according to the candidate solution satisfies the convergence condition in the optimal solution determining unit, determining the candidate solution as the optimal solution
And a phase optimization method of a structure using a harmonic search method.
The method according to claim 1,
If the objective function does not satisfy the convergence condition, returning to the step of performing the random search, and repeatedly performing the convergence until the convergence condition is satisfied
The method of claim 1, further comprising:
The method according to claim 1,
Inputting a boundary condition and a load condition acting on the structure in the candidate solution search unit after performing the finite element modeling; And
Calculating a fitness value of each element based on the input boundary condition and the load condition after performing the finite element analysis in the candidate solution search step
The method of claim 1, further comprising:
The method of claim 3,
Calculating a sensitivity number for the design parameter in the candidate solution search unit after performing the finite element analysis;
Further comprising:
The step of calculating the fitness of each element
Calculating a fitness of each element based on the calculated sensitivity number
And a phase optimization method of a structure using a harmonic search method.
The method according to claim 1,
The step of correcting the position of each element
A step of correcting the position of each element through a stochastic selection of a HMCR (Harmony Memory Considering Rate) and a Pitch Adjustment (PAR: Pitch Adjusting Rate)
And a phase optimization method of a structure using a harmonic search method.
The method of claim 3,
The step of storing the candidate solution in the chord memory space (HM)
Determining importance of each element based on the fitness of each element;
Performing a finite element analysis for determining the importance; And
Determining an objective function of the structure based on a result of the finite element analysis
And a phase optimization method of a structure using a harmonic search method.
The method according to claim 6,
Calculating a sensitivity number according to the objective function using the chord storage space (HM) in the optimum solution determining unit after the step of determining the objective function;
The method of claim 1, further comprising:
The method according to claim 1,
The number of structural elements
Wherein the initial volume and the target volume of the structure are constant in the design region so that the initial volume and the target volume of the structure are equal to each other.
A finite element modeling unit for finely element modeling the structural element and the non-structural element based on the discretized design variables, discretizing design variables applied to a predefined design area into structural elements and non-structural elements;
And performing a finite element analysis on the modeled structural element and the non-structural element and performing a random search on the entire area of the design area for searching for a candidate solution based on the result of the finite element analysis part;
A position of each element is corrected through a probability selection for the candidate solution, and the candidate solution is stored in a harmony memory (HM) according to the importance of each element, When the function satisfies the convergence condition, the optimal solution determining unit determines the candidate solution as the optimal solution,
And a phase optimization unit for optimizing the phase of the structure using the harmonic search method.

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