KR101515397B1 - Robust optimal design method - Google Patents

Abstract

)를 구하는지 여부를 판단하는 단계; (C) 상기 결정론적 최적해(

)를 구하는 판단결과에 따라, 상기 결정론적 최적해(

)를 연산하는 단계; (D) 상기 결정론적 최적해(

) 또는 상기 초기설계정보의 초기값(b⁰)을 기준으로 강건 최적해를 구하기 위한 외부루프(Outer loop) 및 상기 외부루프와 연동하는 내부 루프(Inner loop)를 수행하는 단계; 및 (E) 상기 (D) 단계의 결과가 수렴하는지 판단하여, 상기 (D) 단계의 결과가 비수렴함에 따라 k번째 반복횟수에서의 설계 변수(b^(k))를 갱신하여 상기 (D) 단계로 주입하는 단계;를 포함한다. A robust optimal design method according to an embodiment of the present invention includes: (A) setting initial design information of a target object; (B) Deterministic optimization:

Determining whether or not to obtain the value? (C) the deterministic optimal solution (

), The deterministic optimal solution (

); (D) The deterministic optimal solution (

Performing an outer loop for obtaining a robustness optimal solution based on an initial value b ⁰ of the initial design information or an inner loop for interlocking with the outer loop; And (E) determining whether the result of the step (D) converges, updating the design parameter b ^(k) in the kth iteration count as the result of the step (D) Injecting into the step.

Description

[0001] ROBUST OPTIMAL DESIGN METHOD [0002]

The present invention relates to a robust optimal design method.

Robust Design is a technology that minimizes fluctuation of products and processes in order to improve quality and reliability as part of efforts to improve quality. Through research in the 1950s and early 1960s by Dr. Genichi Taguchi, Robust Design Was developed on the basis of.

The basic principle of the robust design is to design the factors that optimize the product and process design so as to improve the quality of the product by minimizing the influence of the cause without removing the cause of the fluctuation, .

In order to obtain reliable information on the factors involved in engineering decision making, robust design has established a basic principle of statistical design of experiment and analysis method of analysis of variance (ANOVA) S / N ratio (signal to noise) ratio to measure quality, and (2) orthogonal array for studying various design factors at the same time.

The robust design can be applied to all industries such as quality control, experimental design, applied chemical engineering, mechanical engineering, production line design, and product development.

The basic principle of robust design is to optimize product and process design to improve product quality by minimizing the effects of the causes that adversely affect the product, that is, to minimize the impact of performance on various variables. This is called parameter design and quality can compensate for the additional cost by variable factor control for better quality improvement.

This robust design can be applied to all industries such as quality control, experimental design, chemical engineering, mechanical engineering, production line design, and product development.

In particular, as described in Patent Document 1, a robust design method using the Taguchi method is widely used. Since the Taguchi method uses the orthogonal array table, it is difficult to consider a wide design range and design variables are defined only in the discrete space There is a drawback, and it is almost impossible to handle such design constraints in the presence of design constraints.

In addition to the Taguchi method, various robust design methods such as the weighted rms (WRMS) robust design method described in Patent Document 2 are applied. However, the uncertainty range of the parameter and the tolerance range of the design variable are not considered simultaneously No robust design method can not achieve robust optimization in the design process.

Patent Document 1: Registration Patent No. 10-0342272 (registered on June 17, 2002) Patent Document 2: Registered Patent Publication No. 10-1138758 (Registered on April 16, 2012)

It is an object of the present invention to provide a robust optimal design method that achieves robust optimization in the design process by simultaneously considering a range of uncertainty of a parameter and a tolerance range of a design variable.

)를 구하는지 여부를 판단하는 단계; (C) 상기 결정론적 최적해(

)를 구하는 판단결과에 따라, 상기 결정론적 최적해(

)를 연산하는 단계; (D) 상기 결정론적 최적해(

) 또는 상기 초기설계정보의 초기값(b⁰)을 기준으로 강건 최적해를 구하기 위한 외부루프(Outer loop) 및 상기 외부루프와 연동하는 내부 루프(Inner loop)를 수행하는 단계; 및 (E) 상기 (D) 단계의 결과가 수렴하는지 판단하여, 상기 (D) 단계의 결과가 비수렴함에 따라 k번째 반복횟수에서의 설계 변수(b^(k))를 갱신하여 상기 (D) 단계로 주입하는 단계;를 포함한다. A robust optimal design method according to an embodiment of the present invention includes: (A) setting initial design information of a target object; (B) Deterministic optimization:

Determining whether or not to obtain the value? (C) the deterministic optimal solution (

), The deterministic optimal solution (

); (D) The deterministic optimal solution (

Performing an outer loop for obtaining a robustness optimal solution based on an initial value b ⁰ of the initial design information or an inner loop for interlocking with the outer loop; And (E) determining whether the result of the step (D) converges, updating the design parameter b ^(k) in the kth iteration count as the result of the step (D) Injecting into the step.

The robust optimal design method according to an embodiment of the present invention is characterized in that, in the step (A), the initial value (b ⁰ ), design variable (b) and design parameter (p) .

)와 제한조건의 상한함수(

)를 각각 설계변수(b)와 파라미터(p)에 대한 공차범위(△b, △p) 내에서 상한값으로 구성하는 것을 특징으로 한다. In the robust optimum designing method according to an embodiment of the present invention, in the step (D), the outer loop may include an upper limit function of an objective function

) And the upper bound function of the constraint (

) Is made up of an upper limit value within a tolerance range (? B,? P) for the design parameter (b) and the parameter (p), respectively.

), 상기 제한조건의 상한함수(

) 및 최적 민감도를 연산하여 상기 외부루프로 전달하는 것을 특징으로 한다. In the robust optimum designing method according to an embodiment of the present invention, in the step (D), the inner loop calculates an upper limit function

), An upper limit function (

And calculates the optimum sensitivity and transmits the calculated average sensitivity to the outer loop.

In the robust optimal design method according to an embodiment of the present invention, the optimal sensitivity is the sensitivity to the objective function and the constraint condition in the optimal solution of the inner loop, and the optimal sensitivity is used as the sensitivity of the outer loop.

The robust optimal design method according to another embodiment of the present invention is characterized in that, in the step (D), the inner loop uses a linear function for the objective function or a linear function for the constraint.

The robust optimal design method according to another embodiment of the present invention is characterized in that, for the optimal design solution of the inner loop in the step (D), the gradient vector of the design variable or the gradient vector of the parameter in the linear function for the objective function And a determination is made by using the following expression.

In the robust optimal design method according to another embodiment of the present invention, in the step (D), the inner loop generates a slope vector of a design variable in a linear function for the objective function or a linear function for the constraint, The gradient vector of the variable is used as the sensitivity required for the process of calculating the design change amount? B to update the design parameter b ^(k) at the kth iteration count in the step (D).

The features and advantages of the present invention will become more apparent from the following detailed description based on the accompanying drawings.

Prior to this, terms and words used in the present specification and claims should not be construed in a conventional, dictionary sense, and should not be construed as defining the concept of a term appropriately in order to describe the inventor in his or her best way. It should be construed in accordance with the meaning and concept consistent with the technical idea of the present invention.

The robust optimal design method according to the embodiment of the present invention performs a robust design considering the tolerance range of the design parameters or parameters and also uses the optimum sensitivity obtained in the calculation of the inner loop as information for updating the design variables in the outer loop Therefore, it is possible to derive the optimum robustness optimal design without increasing the design cost since no separate sensitivity calculation is required.

1 is a flowchart for explaining a robust optimal design method according to an embodiment of the present invention;
2 is a flowchart illustrating a robust optimal design method according to another embodiment of the present invention.
3 is an illustration of a three-dimensional design structure of an objective function to which the robust optimal design method of the present invention is applied;
Fig. 4 is an exemplary diagram showing a three-dimensional example of the objective function shown in Fig. 3 in two dimensions including a constraint function; Fig.
5 is an exemplary view for explaining a result of applying the robust optimal design method according to another embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The objects, particular advantages and novel features of the present invention will become more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which: FIG. It should be noted that, in the present specification, the reference numerals are added to the constituent elements of the drawings, and the same constituent elements are assigned the same number as much as possible even if they are displayed on different drawings. Also, the terms first, second, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. 1 is a flowchart illustrating a robust optimal design method according to an embodiment of the present invention. Here, the robust optimal design method according to an embodiment of the present invention includes an outer loop for performing an optimal design through a related program in a computer, an inner loop for calculating an upper limit value for an objective function and a constraint condition, ), And a robust optimal design is performed by a double loop method including the above-mentioned method.

First, the robust optimal design method according to an embodiment of the present invention sets initial design information of a target object (S110).

Specifically, an initial value ( b ⁰ ) of a design parameter of a target object to be designed is set using a computer program in a design stage of a large structure and a mechanical system that can be applied to an optimum design such as an aircraft, an automobile, a robot, , And defines the tolerances (? B,? P) of the design variables (b) and (p), respectively.

)를 구하는지 여부를 판단한다(S120). After setting the initial design information, the objective function given in the initial value ( b ⁰ ) is minimized according to the user's selection, and a deterministic optimization solution satisfying the constraint condition is performed.

(S120). ≪ / RTI >

의 목적함수를 최소화하고 동시에

의 제한조건을 만족하는 설계변수(b)의 결정론적 최적해(

)를 사용자의 선택에 의해 구하는지 여부를 판단할 수 있다. That is, for a given initial value b ⁰ ,

Minimizing the objective function of

The deterministic optimal solution of the design variable (b) satisfying the constraint of

) Can be determined by the user's choice.

)를 구하는 것으로 판단되면, 아래의 [수학식 1]에 기재된 바와 같이 설계변수(b)의 결정론적 최적해(

)를 구하는 연산과정을 수행한다(S130). Thus, the user can determine the deterministic optimal solution (b) of the design variable b for the initial value & lt ; RTI ID = ^{0.0 &} gt;

), The deterministic optimal solution of the design parameter (b) as shown in the following formula (1)

(S130). ≪ / RTI >

(b: the design variables, f (b): the objective function, g _i (b): _i th constraint, n: number of design parameters, m: the number of constraints, b _L: lower limit value of the design variable, b _U: Upper limit of design variable)

)를 구하는 연산과정에 따라 초기값(b ⁰ )에서 이동한 결정론적 최적해(

; K=Z)의 위치지점이 획득되고, 이동한 최적해(

)의 위치지점을 시작으로 강건 최적화를 위한 외부루프(outer loop) 과정을 수행한다(S140). This deterministic optimal solution (

), The deterministic optimal solution shifted from the initial value ( b ⁰ )

; K = Z) is obtained, and the shifted optimal solution (

(S140), the outer loop process for robust optimization is performed starting from the position point of the outer loop.

)를 구하지 않는 것으로 판단되면, 컴퓨터는 [수학식 1]에 기재된 설계변수(b)의 결정론적 최적해(

)를 구하는 연산과정을 생략하고 초기값(b ⁰ )을 시작으로 강건 최적해를 위한 외부루프(outer loop) 과정을 수행할 수 있다. On the other hand, if the user determines the deterministic optimal solution (b) of the design variable b for the initial value b ⁰

), The computer calculates the deterministic optimal solution of the design parameter (b) in Equation (1)

) Can be omitted and an outer loop process for the robustness optimal solution can be performed starting from the initial value b ⁰ .

)와 제한조건의 상한함수(

)를 각각 설계변수(b)와 파라미터(p)에 대한 공차범위(△b, △p) 내에서 상한값으로 구성하는 점에서 특징이 있다. Here, the outer loop process for the robustness optimal solution can be expressed by the upper limit function of the objective function (

) And the upper bound function of the constraint (

) Is constituted by an upper limit value within the tolerance range (? B,? P) for the design parameter (b) and the parameter (p), respectively.

The outer loop process for the robust optimization solution is performed in conjunction with the inner loop process. In particular, the upper limit value and the sensitivity value of the objective function and the constraint condition, which are required for the outer loop process, Can be obtained from the optimum design result.

Accordingly, an inner loop process is performed in conjunction with step S140 of performing the outer loop process (S150).

), 민감도 값 등이 필요한데, 이는 내부루프 과정을 수행하는 단계(S150)에서 최적설계 결과로부터 얻을 수 있다. The step S140 of performing the outer loop process and the step S150 of performing the inner loop process are a double loop process and an inner loop process S150. The optimum design is performed to calculate the upper limit value and the sensitivity of the objective function and the constraint condition required for the process of calculating the design change amount (δb) for updating the design variable in the step of performing the outer loop process (S140). That is, in the step of performing the outer loop process (S140), the upper limit function of the objective function for the design variable (b)

), And sensitivity value, which can be obtained from the optimum design result in the step of performing the inner loop process (S150).

At this time, the optimal condition for performing the inner loop process (S150) can be mathematically expressed by a formula such as Equation (3). Here, since the calculation methods for the objective function and the constraint condition are the same, the process will be described by taking the case of the objective function as an example as described in the following [Equation 3].

(c) design parameters in step (S150) of performing an inner loop process, (q) design parameters in step (S150) of performing an inner loop process, Variable, p: design parameter in step S140 of performing the outer loop process)

Of course, the optimal condition for the constraint of g _i (b) can be mathematically expressed as a formulation as described in Equation (4) below.

Karush-Kuhn-Tucker (KKT) should be satisfied as a necessary condition for harm in the optimization problem having the restriction condition as in the above-mentioned Equation (3). The Lagrange function for Equation (3) can be expressed as shown in Equation (5) below.

Where u and v are the Lagrange multiplier vectors for the constraints of the design variable (c) in the inner loop, and x and y are the constraints of the design parameter (p) in the inner loop, respectively. Lagrange multiplier vector. Also, s ₁ , s ₂ , s ₃ , s ₄ are relaxation variable vectors.

The Karushi-Kuhn-Tucker condition means that the design point for making the gradient vector of the Lagrangian function expressed by Equation (5) be 0 can be the local minimum point, and Lagrange multiplier ( u, v, x, y ) must always be zero. That is, the local minimum point of the optimization problem with the constraint is a root satisfying the simultaneous equations expressed by [Equation 6].

Accordingly, the Karushi-Kuhn-Tucker condition for Equation (3) can be expressed by Equation (5) and Equation (6) below.

The condition satisfying the condition of Equation (6) may occur in various cases depending on a combination of the constraints activated in the inner loop, and the optimal solution of the inner loop for each case may be expressed by Equation (7) Can be expressed.

Therefore, the optimal solution and the Lagrangian multiplier satisfying each condition in Equation (7) with respect to the optimal solution of the inner loop are expressed by Equation (8) below.

In this way, the design parameter b of the outer loop is treated as a parameter in the inner loop, and a constant b is considered as a constant at the optimal point (c ^* ) of the inner loop (lower loop) - When Δb or b + Δb is changed, the rate of change of the optimal value with respect to the rate of change of parameter is defined as optimal sensitivity. In this case, the general form of the optimal sensitivity for the objective function in the step of performing the inner loop process (S150) is expressed by Equation (9) below.

In addition, the vector and the Lagrangian multiplier for the constraint conditions in the above-described Equation (3) can be expressed as Equation (10) below.

( h (c, q) : vector for constraints of the inner loop, w: Lagrange multiplier vector)

When the vector and the Lagrangian multiplier for the constraints of Equation (10) are applied to Equation (9), the optimal sensitivity for design parameters and design parameters can be expressed as Equation (11) below.

이고

이므로, 아래의 [수학식 12]와 같은 조건관계를 확인할 수 있다. In Equation (11)

ego

, It is possible to confirm the conditional relationship as shown in the following equation (12).

Equation (12) can be expressed by the following equation (2), where the optimal solution of the inner loop is converged to the lower limit value and the upper limit value for the tolerance range? B and? P of the design parameter b or parameter p, The following equations (13) and (14) can be obtained.

)은 외부루프(outer loop)에서 최적설계를 수행하기 위해 필요한 설계변수에 대한 상한함수의 목적함수에 대한 민감도(

)와 동일하다는 결론을 얻을 수 있다. The results of Equations (13) and (14) are obtained as the result of the step of performing the inner loop process (S150). The optimal values of the objective function and the constraint function at the optimal point (c ^* ) of the inner loop Sensitivity value (

) Is the sensitivity of the upper bound function to the objective function for the design variables needed to perform the optimal design in the outer loop (

) Is the same.

Then, the upper limit value and the optimal sensitivity value for the objective function and the constraint obtained through the inner loop are injected into the outer loop process (S140), so that it is necessary to update the design variable (b) And is used in the process of obtaining the design change amount? B.

It is determined whether the result of the interlocking process of the dual loop converges with respect to the tolerance range? B and? P of the design parameter b or the parameter p at step S160.

If the determination step S160 is not satisfied, an arbitrary design parameter b ^k is updated using the upper limit value and the optimal sensitivity obtained through the double loop process, and the repetition number is defined as k = k + 1, Loop process in which the step of performing the outer loop process (S140) and the step of performing the inner loop process (S150) are interlocked can be performed again.

The robustness optimum design method according to an embodiment of the present invention configured as described above is characterized in that in step S140 of performing the outer loop process as it is, It does not perform the sensitivity calculation separately for performing the optimum design in the outer loop.

Accordingly, the robust optimal design method according to an embodiment of the present invention can perform a robust optimization design that simultaneously considers the tolerances of design parameters and parameters in a dual-loop manner.

Hereinafter, a robust optimum design method according to another embodiment of the present invention will be described with reference to FIGS. 2 to 5. FIG. FIG. 2 is a flowchart for explaining a robust optimal design method according to another embodiment of the present invention, FIG. 3 is an illustration of a three-dimensional design structure of an objective function to which the robust optimum design method of the present invention is applied, FIG. 5 is a diagram illustrating an example of a three-dimensional example of the objective function shown in FIG. 3, including a constraint function. FIG. 5 is a view for explaining a result of applying the robust optimal design method according to another embodiment of the present invention Fig.

The robust optimum design method according to another embodiment of the present invention includes a double loop including an outer loop for performing a robust optimal design and an inner loop for calculating an upper limit value of an objective function and a constraint, loop method, and the inner loop uses a linearized function expression of the objective function or the constraint function.

First, the robust optimal design method according to another embodiment of the present invention sets initial design information of an object to be designed (S210).

Specifically, the initial value ( b ⁰ ) of the design variables of the object to be designed by using the computer program in the design stage of the large structure and the mechanical system which can be applied to the optimum design such as aircraft, automobile, , And the tolerances (? B,? P) of the design variables (b) and (p) are defined.

)를 구하는지 여부를 판단한다(S220). After setting the initial design information, the objective function given in the initial value ( b ⁰ ) is minimized according to the user's selection, and a deterministic optimization solution satisfying the constraint condition is performed.

(S220).

의 목적함수를 최소화하고 동시에

의 제한조건을 만족하는 설계변수(b)의 결정론적 최적해(

)를 구하는지 여부를 판단한다. That is, for a given initial value b ⁰ ,

Minimizing the objective function of

The deterministic optimal solution of the design variable (b) satisfying the constraint of

) Is determined.

)를 구하는 것으로 판단되면, 아래의 [수학식 15]에 기재된 바와 같이 설계변수(b)의 결정론적 최적해(

)를 구하는 연산과정을 수행한다(S230). In this way, the user and the deterministic optimal solution for the initial value (b ⁰⁾ (

), The deterministic optimal solution of the design parameter (b) as described in the following equation (15)

(S230). ≪ / RTI >

(b: the design variables, f (b): the objective function, g _i (b): _i th constraint, n: number of design parameters, m: the number of constraints, b _L: lower limit value of the design variable, b _U: Upper limit of design variable)

)를 구하는 연산과정에 따라 도 5에 도시된 초기값(b ⁰ )에서 결정론적 최적해(

; k = z)의 위치지점이 획득되고, 이동한 최적해(

)의 위치지점을 시작으로 강건 최적화를 위한 외부루프(outer loop) 과정을 수행한다(S240). Then the deterministic optimal solution (

( B ⁰ ) shown in FIG. 5 according to an operation procedure for obtaining a deterministic optimal solution (

; k = z) is obtained, and the shifted optimal solution (

The outer loop process for robust optimization is performed starting from the position point of the target node (S240).

)를 구하지 않는 것으로 판단되면, [수학식 15]에 기재된 설계변수(b)의 결정론적 최적해(

)를 구하는 연산과정을 생략하고, 초기값(b ⁰ )을 시작으로 강건 최적해를 위한 외부루프(outer loop) 과정을 수행할 수 있다. On the other hand, if the user determines the deterministic optimal solution (b) of the design variable b for the initial value b ⁰

) Is not obtained, the deterministic optimal solution (a) of the design parameter (b) described in the expression (15)

) Can be omitted, and an outer loop process for the robustness optimal solution can be performed starting from the initial value ( b ⁰ ).

)와 제한조건의 상한함수(

)는 각각 설계변수(b)와 파라미터(p)에 대한 공차범위(△b, △p) 내에서 상한값으로 구성된다. Here, the outer loop process for the robustness optimal solution may be expressed by the upper limit function of the objective function (

) And the upper bound function of the constraint (

) Consists of the upper limits within the tolerance range (? B,? P) for the design parameters (b) and (p), respectively.

The outer loop process for the robust optimization solution is performed in conjunction with the inner loop process. In particular, the upper limit value of the objective function, the upper limit value of the constraint condition, and the sensitivity value for the design parameters required for the outer loop process, It can be obtained from the optimal design result of the loop (Inner loop).

Accordingly, an inner loop process is performed in conjunction with the outer loop process (S240) (S250).

), 민감도 값 등이 필요한데, 이는 내부루프 과정을 수행하는 단계(S250)에서 최적설계 결과로부터 얻을 수 있다. A step S240 of performing the outer loop process and a step S250 of performing an inner loop process are a double loop process interlocked with each other and include an inner loop process (S250), an optimal design is performed to calculate the upper limit value and the sensitivity of the objective function and the constraint condition, which are necessary for calculating the design change amount (δb) required for the update of the design variable in the step of performing the outer loop process (S240) do. That is, in the step of performing the outer loop process (S240), the upper limit function of the objective function for the design variable (b)

), And sensitivity value, which can be obtained from the optimum design result in step S250 of performing the inner loop process.

In this case, the process of performing the inner loop process (S250) may be expressed as Equation (17) below to calculate the linear function for the objective function and the constraint function.

(c) a design parameter in step (S250) of performing an inner loop process, (q) a design parameter in step (S250) of performing an inner loop process, and (b) Variable p, design parameter in step S240 of performing the outer loop process)

Here, the linearized function f _L (c, q) of the objective function f (c, q) within the tolerance range Δb, Δp for the design variable b ^(k ) ) Can be expressed by the following equation (18).

Expression (S250) of performing the inner loop process using the linearized function f _L (c, q) of the equation (18) can be expressed by the following equation (19).

로 표현되는 설계변수의 경사도 벡터 또는

로 표현되는 설계파라미터의 경사도 벡터 각각에 대한 부호를 이용하여 최적설계 해를 쉽게 판단할 수 있다. In the step S250 of performing the inner loop process which can be represented by the following equation (19), the optimum design solution is the upper bound or the lower limit of the design parameter b ^(k) bound. Accordingly, in the equation (18) of the linearized function f _L (c, q)

The slope vector of the design variable expressed as

The optimum design solution can be easily determined by using the sign for each of the gradient vector of the design parameter expressed as < EMI ID = 1.0 >

That is, the optimal solution of the inner loop according to the sign of the gradient vector is expressed by Equation (20).

Accordingly, the result of Equation (20) is injected into the step of performing the outer loop process (S240) as a result of performing the inner loop process (S250).

Whether or not the result of the interlocking process of the double loop satisfies the tolerance range (? B,? P) between the design parameters (b) and (p) is determined (S260).

If the determination step S260 is not satisfied, the design parameter b ^(k) is updated using the upper limit value and the optimal sensitivity value obtained through the double loop process, and the repetition number is defined as k = k + 1 Loop process in which the outer loop process is performed (S240) and the inner loop process is performed (S250) are interlocked with each other.

The robust optimum design method according to another embodiment of the present invention configured as described above is characterized in that it is not necessary to optimize a separate linear planning problem to obtain an optimal value of an inner loop, It is possible to easily calculate the solution of the inner loop from the coefficient sign of the gradient vector with respect to the constraint function.

의 경사도 벡터 등을 외부루프 과정을 수행하는 단계(S240)에서 설계변수 갱신을 위한 민감도로 사용하기 때문에, 외부루프에서 최적설계를 수행하는데 필요한 민감도 계산을 별도로 수행하지 않는다. In addition, the robust optimal design method according to another embodiment of the present invention may be performed in a linearization process of an objective function and a constraint function during an inner loop process (S250)

The sensitivity vector for updating the design variables is used in the step of performing the outer loop process in step S240. Therefore, the sensitivity calculation for performing the optimum design in the outer loop is not performed separately.

Another embodiment of the present invention can use the following expression (21) as an example.

)와 g₁(b), g₂(b), g₃(b)의 제한조건함수는 도 4의 2차원 예시도와 같이 도시될 수 있고, (3.0, 3.5)의 좌표에 초기값(b ⁰ )을 설정할 수 있다. The objective function described in Equation (21)

) And g ₁ (b), g ₂ (b), g Initial values to the coordinates of the ₃ (b) the constraint functions are two-dimensional and may be shown as an example to help, (3.0, 3.5) in Fig. 4 (b ⁰ ) Can be set.

)이며 (4.8318, 3.6428)의 좌표로 표시할 수 있다. Accordingly, the result of the robust optimum design method according to another embodiment of the present invention is a deterministic optimal solution that does not take into account the tolerance range of the design parameters or design parameters, such as "I"

(4.8318, 3.6428), respectively.

)를 구하는지 여부를 판단하는 단계(S220)를 수행하지 않고, 설계변수의 초기값(b ⁰ )에서 이중루프 과정으로 강건최적설계를 수행하는 단계(S240, S250)을 수행한 결과이다. Further, the coordinate points indicated by "II" (4.1748, 3.7739) in FIG. 5 can be represented by the robust optimal point according to another embodiment of the present invention. Here, the robust optimal point denoted by "II" is the deterministic optimal solution (

) Without performing a step (S220) of determining whether the areas, the result of performing step (S240, S250) for performing the optimum design robustness to double-loop process from the initial value (b ⁰⁾ of the design variables.

On the other hand, conventionally, the result of applying the optimization method using the Taylor series can be expressed by the coordinates (4.3755, 37574) indicated by "III" in FIG.

As shown in the following Table 1, the robust optimal design method according to another embodiment of the present invention calls the objective function 30 times and the constraint function 90 times, whereas the conventional optimization method using the Taylor series The method invokes the objective function 60 times and the constraint function 144 times.

Therefore, the robust optimum design method according to another embodiment of the present invention reduces the calculation process more than the conventional robust optimization method, and in particular, it does not require a separate optimal design process for performing the inner loop process, have.

Although the technical idea of the present invention has been specifically described according to the above preferred embodiments, it is to be noted that the above-described embodiments are intended to be illustrative and not restrictive.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention.

: 결정론적 최적해 p: 설계파라미터
b^(k): k번째 반복횟수에서의 설계 변수
△b: 설계변수의 공차 △p: 설계파라미터의 공차
δb: 설계변화량

: 목적함수의 상한함수

: 제한조건의 상한함수 b ⁰ : initial value for the design variable b: design variable
f (b): objective function g _i (b): i th constraint

: Deterministic optimal solution p: design parameter
b ^(k) : design variable at kth iteration
Δ b: Tolerance of the design variable Δ p: Tolerance of the design parameter
δb: design variation

: Upper bound function of objective function

: Upper limit function of constraint

Claims (8)

(A) setting initial design information of an object to be designed;
(B) Deterministic optimization:

Determining whether or not to obtain the value?
(C) In the step (B), the deterministic optimal solution

), The deterministic optimal solution (

);
(D) The deterministic optimal solution (

Performing an outer loop for obtaining a robustness optimal solution based on an initial value b ⁰ of the initial design information or an inner loop for interlocking with the outer loop; And
Determining whether the result of step (D) converges, updating the design parameter b ^(k) at the kth iteration count as the result of step (D) ;
The method comprising the steps of:
The method according to claim 1,
Wherein, in the step (A), the initial design information includes an initial value (b ⁰ ), a design parameter (b), and a design parameter (p) of the object.
3. The method of claim 2,
In the step (D), the outer loop calculates an upper limit function of the objective function

) And the upper bound function of the constraint (

) Is configured as an upper limit value within a tolerance range (? B,? P) for the design parameter (b) and the parameter (p), respectively.
The method of claim 3,
In step (D), the inner loop calculates an upper limit function of the objective function

), An upper limit function (

And the optimal sensitivity is calculated and transmitted to the outer loop.
5. The method of claim 4,
The optimal sensitivity is the sensitivity to the objective function and the constraint at the optimal solution of the inner loop,
Wherein the optimal sensitivity is used as the sensitivity of the outer loop.
The method of claim 3,
Wherein the inner loop uses a linear function for the objective function or a linear function for the constraint in the step (D).
The method according to claim 6,
Wherein in the step (D), the optimal design solution of the inner loop is determined by using a sign for each of the slope vector of the design variable or the gradient vector of the parameter in the linear function for the objective function.
The method according to claim 6,
In the step (D), the inner loop generates a slope vector of a design variable in a linear function for the objective function or a linear function for the constraint,
The inclination vector of the design variable is used as the sensitivity required for the process of calculating the design change amount? B to update the design parameter b ^(k) at the kth iteration count in the step (D) Robust Optimal Design Method.

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