KR100393847B1 - A Method of Multidisciplinary Design Optimization Using Interdisciplinary Design Variables and Optimal Sensitivity Information - Google Patents

Abstract

The present invention relates to a multi-discipline integrated optimal design method using interdisciplinary variables and optimum sensitivity information to include all the characteristics of the field considered in the product design while maintaining the advantages of the actual design environment. In the superstructure (10), interdisciplinary variables, which are design variables that check the convergence and vibration of the optimal design solution and affect each substructure, Fluctuation of The size of the control unit to be transmitted to the infrastructure optimization control unit, the infrastructure control unit (21, 31, 41) receives the necessary information from the superstructure 10, the infrastructure optimization execution unit (20, 30, 40) And calculate the optimum sensitivity for the design factor from the design optimization solution calculated as the result, and the infrastructure optimization execution unit (20, 30, 40) is calculated by the infrastructure control unit (21, 31, 41) The optimization of the substructure in the superstructure 10 by calculating the search direction in the next iteration step using the optimal design solution and the optimal sensitivity and returning the value to the substructure control part 21, 31, 41. It is designed to optimize the overall design by reflecting the results, and it is possible to use the program used by each expert for the optimization of the infrastructure without modification. It is an invention that can reduce costs and minimize the calculation of infrastructure to reduce the cost and time of calculation.

Description

A Method of Multidisciplinary Design Optimization Using Interdisciplinary Design Variables and Optimal Sensitivity Information}

The present invention relates to a multi-disciplinary optimal design method using interdisciplinary variables and optimal sensitivity information to include all the characteristics of the field considered in the product design while maintaining the advantages of the actual design environment to the maximum. .

In general, in engineering analysis and product design, it is necessary to consider characteristics of various fields in an integrated manner to obtain a robust design that can fully exhibit performance in actual operating environment. The initial multidisciplinary optimal design method was optimized by making one design system with mathematical expressions that define all the design variables and constraints to be considered. There was a difficulty.

In order to improve this, there have been suggested methods to make a design system, which is composed of several fields, into individual sub-structures, to perform independent design, to integrate them, and to obtain a final design. For example, Concurrent System Optimization Subspace Optimization (CSO) and Collaborative Optimization (CO) techniques.

However, in the case of CSSO, many first derivatives are required between each sub-structure, but in most cases the optimization of each sub-structure requires an automated design tool (program) that uses finite element analysis. As a result, the first derivative cannot be obtained through the exact solution, and only an approximate solution using the finite difference method can be obtained. Therefore, additional finite element analysis is required. In addition, in the case of CO, the result of the derivative is not necessarily desired, but since the objective function of each infrastructure is fixed, it is limited to reflect the opinions of the design experts in charge of each infrastructure and the design time is greatly influenced by the design starting point. There are disadvantages.

The multidisciplinary optimization method of the present invention is largely divided into two steps. That is, it is divided into a sub-system that performs an optimization process based on engineering analysis of each field and a system that optimizes the overall design by reflecting the optimization result of each sub-structure. At this time, the design variables (interdisciplinary design variables) affecting all the substructures are selected. In each iteration, the superstructure sets the intersectoral variables to a constant value. Optimization is performed by treating the set interfield variables as fixed design parameters. The result of the substructure optimization and the optimal sensitivity value for the intersectoral variable performed in this way are transferred to the superstructure and used to determine the search direction of the intersectoral variable value to be used in the next iteration step.

The present invention is different from the existing multi-discipline integrated optimal design methodology as follows. First, the tools used to optimize the infrastructure, the objective function and the design optimization can be used by each design expert. This is different from the existing methodology in that the optimization objective function of the infrastructure is limited to a certain form for the optimization of the superstructure. Current engineering designs generally use automated design tools (programs) to achieve optimized results. And each program has its own purpose function format for optimal design. Therefore, when using the methodology with limited objective function, the program itself had to be modified or complex control program added. Therefore, it is possible to use the program used by each design expert without modifying the additional cost savings when the design target is changed.

The second is to use the optimal sensitivity of the sector-specific optimal solution for the intersectoral variables, along with the optimal solution determined at each infrastructure to determine the next direction of search in the superstructure.

The third difference is in the calculation of the optimal sensitivity required for this methodology. This methodology uses the Forward Difference Method which is a kind of finite difference method to calculate the optimum sensitivity. At this time, the perturbation size of the finite difference method coincides with the step size of the intersectoral variable of the superstructure. As a result, it is possible to reuse some of the field-specific optimal solutions calculated in the previous step, which can reduce the amount of computation for the optimization of the infrastructure as a whole. This can lead to a reduction in calculation costs and calculation time.

The present invention has been invented in view of the above-described circumstances, and it is possible to process and optimize the inter-variable variables so that the design can include the characteristics of all fields considered in the product design while maintaining the advantages of the actual design environment to the maximum. An object of the present invention is to provide a multi-discipline integrated optimal design method using sensitivity information.

1 is an overall configuration diagram for implementing the present invention,

2A to 2C are flowcharts illustrating an optimal solution calculation process using a multi-disciplinary integrated optimal design method using inter-field variables and optimal sensitivity information according to the present invention.

* Description of the symbols for the main parts of the drawings *

10-superstructure, 20,30,40-infrastructure optimization executive,

21,31,41-Infrastructure controls.

Hereinafter, the configuration and operation of the preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings.

Figure 1 shows the overall configuration for implementing the present invention, showing the separation of the entire multi-discipline integrated design problem to configure the superstructure and substructure.

Reference numerals 20, 30, and 40 refer to an infrastructure optimization execution unit which separates the entire multidisciplinary optimal design problem according to the design field and uses the separated design problem. At this time, each infrastructure optimization execution unit 20, 30, 40 is any design optimization means set to minimize the objective function. One of the characteristics of the present invention is that the design optimization means used at this time can be used as it is if the optimum design solution for the set design parameters (design parameter) is calculated. In addition, the infrastructure control unit 21, 31, 41 receives the necessary information from the superstructure 10 to drive the infrastructure optimization execution unit 20, 30, 40 and design factors from the design optimization solution calculated as a result Calculate the optimal sensitivity for. In other words, the infrastructure optimization execution unit 20, 30, 40 receives the design data from the infrastructure control unit 21, 31, 41, calculates the optimal solution, and calculates the value of the infrastructure control unit ( 21, 31, 41).

Next, intersectoral variables, which are design variables that affect each infrastructure Select. In general, multidisciplinary optimal design problems are related to several engineering disciplines by common design variables. The present invention selects design variables that affect all fields in this way and determines them as intersectoral variables, and each substructure treats the intersectoral design variables as a fixed design parameter. Construct an optimization design problem. The intersectoral variables configured in this way have a constant value at each iteration in the superstructure 10. ( In the first iteration It is set to the value of, and is transferred to the infrastructure, and the infrastructure treats the set value as a fixed factor to perform the optimization process for each field.

21, 31, and 41 are infrastructure controls Perform the infrastructure optimization process and calculate the optimal sensitivity. In the present invention, to calculate the optimum sensitivity Results of the infrastructure optimization performed on To Increased by The optimum sensitivity is calculated by using the forward difference method as shown in Equation 1 below using the result of the optimization of the substructure. here Means iteration Is the perturbation size used for the finite difference.

Reference numeral 10 denotes the superstructure that constructs the objective function using the optimal solution calculated from the substructure and the optimal sensitivity of the intersectoral variables treated as fixed factors. At this time, the objective function of the superstructure 10 is to find an intersectoral variable that exists near the optimum solution of each substructure to the current intersectoral variable setting value and is optimized for the entire design problem. In more detail, interdisciplinary variables (j = 1, NN is the optimal solution of the i th infrastructure for In this case, the objective function of the superstructure is expressed by Equation 2 below.

(NSUB is the number of infrastructure)

This type of objective function is a commonly used method of optimizing multi-objective functions.

At this time Set the value of the inter-variable variable in the first iteration Is the optimal sensitivity of the i infrastructure The optimal solution function of the substructure used in the superstructure Is expressed by Equation 3 below.

By substituting Equation 3 into Equation 2, the superstructure objective function shown in Equation 4 can be obtained.

Equation 3 represents the objective function of Equation 1 Linearized function in the vicinity. therefore To reduce If the slope of is positive If the slope is negative, You can increase it. Therefore, if a factor that determines the search direction in the next iteration step is DIR, the value is calculated as in Equation 5 below.

In addition, according to the value of DIR, which determines the search direction in the repetition stage, Is selected as shown in each equation below.

, then

, then

, then stop iteration

In the superstructure Amount of change Is used to calculate the sensitivity of the infrastructure. By matching with, we can reduce additional computation for optimization when using forward difference method. In the superstructure of on If necessary, the amount needed for infrastructure optimization and sensitivity calculation Wow Between Is the previous iteration step ( First iteration) Is equal to the value of. Therefore, in order to obtain optimum sensitivity You only need to calculate. In a similar way from the superstructure of on , Then we need to calculate the infrastructure and calculate the sensitivity Wow Between Is the previous iteration step ( First iteration) Is equal to the value of. The above-mentioned contents are summarized as in Equations 9 and 10 below.

(In both cases Only holds if)

By using Equations 9 and 10, the amount of calculations for optimization of infrastructure and sensitivity calculation can be reduced.

Next, the overall operation of the present invention will be described in detail with reference to a flowchart illustrating the overall multi-discipline integrated optimal design method of FIG. 2. In this case, there is one inter-variable ( ) Will be described.

First, FIG. 2 may be divided into three parts. First, the first part consisting of steps 1001, 1002, 1003, 1004, 1005, 1006, 1010, 1011, 1012, 1080, 1081, 1082, 1083, 1084, 1060, 1061, 1062 and 1101, 1102, 1103, 1104, 1105 , The second part consisting of steps 1106, 1107, and 1108, and finally the third part consisting of steps 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, and 1027 Part.

The first part examines the convergence and vibration of the optimal design solution Fluctuation of Adjust the size of the. It also commands the infrastructure controls according to the search direction. In the second part, the substructure optimization execution unit is driven according to the command of the superstructure determined according to the search direction, and the optimal solution and the optimum sensitivity for each field are calculated. The third part is to calculate the search direction in the next iteration step using the optimal design solution and the optimum sensitivity calculated in the infrastructure.

Looking at the overall methodology flow, we first set the default values of the variables used throughout the methodology in the first part, and when the infrastructure or the design oscillates Reduce the variance of the equation to find the design solution. Next, in the second part, we obtain the actual design optimal solution for each field and based on this, in the third part, And set it like this Using the iterative process, the first part is executed and the optimized design solution is obtained.

This will be described in detail below.

First, as shown in FIG. 1, a design problem is divided into fields to form a substructure. At this time, the infrastructure optimization execution unit of each sector of the infrastructure uses an optimization program selected by the relevant design experts.

Next time on the superstructure Set the range of (1001) and change And variable to store the setting value of the intersectoral variable in each iteration step An initial value of is set (1002).

Temporary variable stored to check whether the repetition step vibrates Variables for Storing and Interim Storage To initialize , (1003).

In 1004, a variable to set the optimization method of the infrastructure selected to reduce the number of calculations of the infrastructure. To initialize ). Is set to 1 In the case of infrastructure optimization control If only the optimization process for is performed, the process of ④ can be obtained to obtain the optimum sensitivity. In the case of infrastructure optimization If only the optimization process for is performed, the process of ③ can be obtained.

Number of iterations And indexes to use at junctions 1080 and 1081 To initialize (1005).

Step 1006 serves to count the repetition steps.

In step 1010, if it is the first iteration step ( Into the infrastructure control department Wow And then perform the infrastructure optimization process corresponding to ②. After the second iteration ( ) Subdivide again Is the first iteration that is modified and returns ) (1080) Is modified to 2 (1083), and the infrastructure controls Wow And then perform the infrastructure optimization process corresponding to process ②. if Is modified and is the second return iteration ( ) In the case (1081) Is set to 0 (1084) and at the branch point 1012, the infrastructure control unit Wow Carry out process 3 or process 4. And finally Is not modified ( ) Has a total iteration of 2 at bifurcation 1082 ( ) At the junction 1012 According to the setting of Wow To carry out process ③ or process ④, and if the total repetition step is 3 or more, check whether the vibration of the repetition step is at step 1011 and at step 1012 According to the setting of Wow Transfer to and select process ③ or process ④ accordingly. The value of Is 1 (1062) if unmodified, 0 (1084) if unmodified (1005) or more than one iteration was performed after it was modified, and 2 (1083) if one iteration was performed after it was modified. Has Table 1 , , This is a summary of the execution order according to the setting value of.

Action flow One 0 0 1010 → ② or less 2 0 1 (or 2) 1010 → 1080 → 1081 → 1082 → 1012 and below One 1 (or 2) 1080 → 1083 → ② or less 3 0 1 (or 2) 1010 → 1080 → 1081 → 1082 → 1011 and below One 1 (or 2) 1010 → 1080 → 1083 → ② or less 2 1 (or 2) 1010 → 1080 → 1081 → 1084 → 1012 and below

In the case of the second and subsequent iterations, check whether or not oscillation of the optimization process of the superstructure is performed (1011). The optimization process is performed by reducing the size of the (1060, 1061, 1062). In step 1060, Is the margin of error ( ) Is the process of checking whether or not. If within the margin of error, repeat the iteration step, otherwise Decreases by a percentage (1061), To let you know that was modified Store 1 in 1062. After that, repeat the process below 1006.

Junction 1012 The corresponding infrastructure optimization process should be performed according to the set value of. As explained earlier When is set to 1 In the case of the infrastructure control department If only the optimization process for is performed, the process of ④ can be obtained to obtain the optimum sensitivity. In case of infrastructure control Perform the process of ③ that can obtain the optimum sensitivity by performing only the optimization process for.

Infrastructure optimization process ② first In the Infrastructure Optimization Executive Compute (1101). next time To Increase by the infrastructure optimization executive Compute (1102).

Infrastructure optimization process ③ Has a value equal to the previous iteration ( In the first iteration) Matches the value of on Stores the value of (1105), To Increase by the infrastructure optimization executive Compute (1106).

Infrastructure optimization process ④ In the Infrastructure Optimization Execution Unit for Is calculated (1107), Has a value equal to the previous iteration ( In the first iteration) Matches the value of on Store the value of (1108).

The infrastructure control unit calculates the Wow The optimal sensitivity is calculated by using the forward difference method from the value of (11) (1103).

The infrastructure control department has the next iteration step ( Temporary variables for use in the first iteration) on of, on Save it as superstructure Wow After that, the superstructure performs the process ⑥ or less.

NSUB infrastructure optimal solutions and optimal sensitivity from all infrastructure controls , (Where i = 1, NSUB), then in ⑥, Compute the direction search factor DIR to calculate (1014).

Temporary Variables for Use in Junction 1011 on Save (1015).

If the value of DIR is 0 (1016) Current It is not possible to reduce the objective function of the superstructure by changing it to the size of. Adjust That is, in step 1060 Is the margin of error ( ), If it is within the error range, end the repetition step. Decreases by a percentage (1061), To let you know that was modified Store 1 in 1062. After that, the process is repeated 1006 steps or less.

Temporary variable if the value of DIR is positive at divergence point 1017 on Save (1018), To Reduced by (1019) Check whether is smaller than the lower limit that was initially set (1020). If it is larger than the lower limit, the variable tells you how to optimize the infrastructure. Set 1 to and perform the process ① or less, but less than the lower limit. Is restored to the original value (1021) and the process ⑤ is performed below.

Temporary variable if the value of DIR is negative in step 1017 on Save (1022), To By (1023) (1024) Check whether is greater than the upper limit set initially. If less than the upper limit, the variable tells how to optimize the infrastructure. Set 2 to and perform the process ① or less but if it is larger than the upper limit Restore to the original value (1025) and perform the following process ⑤.

As described above, the present invention can be used without modifying the program used by each expert for the optimization of the infrastructure, so that the additional cost required when the design target is changed, and the calculation of the infrastructure is minimized by minimizing the calculation of the infrastructure. And there is an advantage to save time.

Claims (5)

In the superstructure (10), interdisciplinary variables, which are design variables that check the convergence and vibration of the optimal design solution and affect all of them, Fluctuation of To be sized and passed to the infrastructure optimization control, The infrastructure control unit 21, 31, 41 receives the necessary information from the superstructure 10 to drive the infrastructure optimization execution units 20, 30, 40 and the design factors from the design optimization solution calculated as a result. Calculate the optimal sensitivity to the The infrastructure optimization execution unit (20, 30, 40) calculates the search direction in the next iteration step using the optimal design solution and the optimum sensitivity calculated by the infrastructure control unit (21, 31, 41), and then calculates the value. By returning the control to the substructure control unit (21, 31, 41) by reflecting the optimization result of the substructure in the superstructure 10, the multidisciplinary process using the inter-sectoral variables and optimal sensitivity information to optimize the overall design Integrated Optimal Design Method. 2. The process and optimal sensitivity of intersectoral variables according to claim 1, wherein the objective function of the superstructure constructed by using the optimal solution of each substructure and the optimal sensitivity of the substructure optimal solution to the interdisciplinary variables is expressed by the following equation. Multidisciplinary optimal design method using information. (From here Is the number of infrastructure, Is Optimal of the second infrastructure, Is Optimal sensitivity of the first infrastructure, Is an intersectoral variable, Is the set value of the intersectoral variable) The method according to claim 1, wherein the direction search factors composed of each substructure optimal solution and optimal sensitivity are calculated by the following equation to calculate the intersectoral variables to be used in the next iteration step. Multi-discipline integrated optimal design method. (here Is Optimal of the second infrastructure, Is an iterative step, Is an intersectoral variable, Is Optimal sensitivity of the first infrastructure) The method according to claim 1, wherein the inter-sectoral variable processing and optimal sensitivity information are used to reduce the amount of change in the intersectoral variable to confirm the convergence of the setting values of the intersectoral variable to be used in the next iteration step using the direction search factor. Sector-integrated optimal design method. The method of claim 1, wherein the infrastructure optimization control unit (21, 31, 41) in order to calculate the optimum sensitivity of each substructure by the finite difference method finite difference between the inter-sectoral variable change in the superstructure 10 Multidisciplinary optimal design method using inter-sectoral variable processing and optimal sensitivity information characterized by matching the variation of variables used in the difference and using the optimal solution calculated in the previous iteration.