### 1. Introduction

### 2. Structural Analysis of the Initial Design

### 2.1 Calculation of Design Load Conditions

### 2.2 FEM-based Structural Analysis

### 3. DOE-based Structural Design Improvement and Sensitivity Evaluation

### 3.1 DOE Theory

*m*is an integer of 2 or more, 3

*is the experiment size, and (3*

^{m}*− 1)/2 is the number of rows in the OAT.*

^{m}*k*, BBD can easily generate orthogonal blocks with a small number of experimental points, through which a quadratic regression equation can be obtained.

*factor experiments and detects the curved change in the amount of responses caused by changes in the level of variables (Park, 2012). In CCD, the number of center points becomes at least one, and the number of axial points becomes 2*

^{k}*k*. If the number of center points is

*n*, then the number of CCD experiments

_{o}*n*can be defined by the following equation.

*k*> 2, the DOE method can be performed with significantly fewer experiments than factorial design, and it is highly advantageous if the experimental cost is high. Moreover, rather than performing DOE again when the regression model estimation must be changed, CCD can perform sequential experiments that add new data points to the center and axis.

### 3.2 Comparison of Best Design Cases and Structural Design Sensitivity According to DOE Characteristics

### 3.3 Review of DOE Suitability Through Approximate Modeling

*n*experimental points calculated using the DOE techniques (OAD, BBD, and CCD), if matrix

*Z*expressed by

*k*basic variables and the real response vector

*g*is given, then the relationship between

*g*and

*Z*can be expressed as follows.

*e*and estimate the unknown RSM approximation coefficient vector

*A*, a least squares function is applied as follows.

_{R}*R*

^{2}as shown in Eq. (7). where

*t*is the actual value,

_{i}*y*is the predicted value estimated from the approximate model, and

_{i}*t̄*is the average of the actual values. When

_{i}*R*

^{2}is 1.0, the predicted value estimated from the approximate model exactly matches the actual value in the entire design space. Table 11 shows the accuracy analysis results of the RSM generated by the response function using each DOE technique.

### 4. Conclusions

The structural analysis results of the initial design stage demonstrated that design improvements are required to secure the strength and safety of the AOSC’s structural design. For this purpose, the influence of the major design members on strength performance was analyzed using DOE, and design improvement cases that satisfy the allowable stress while minimizing weight increase were explored.

Among the three DOE methods considered in this study (OAD, BBD, and CCD), the best design case in all DOE methods satisfied the allowable yield stress at a level in which the maximum stress was similar for all design load cases compared to the initial design, although there was a variation in weight. The weight increase rate of CCD was lower than that of OAD and BBD, and that of BBD was the highest. Considering the weight increase rate and the number of experiments of DOE, which represents the numerical calculation cost, CCD was shown to be the most efficient method for deriving improvement cases for the AOSC’s structural design.

Given that the design problem investigated in this study in relation to CCD involves the nonlinear response characteristics of stress and five design factors, it was found that the most suitable method to evaluate the main effect and generate a high-accuracy approximate model is to conduct 43 runs of three-level experiments.

As demonstrated in the structural design sensitivity analysis, in all DOE methods, the effect of the main frame (DF-#1) was greatest on the maximum stress of the weight and design load cases, and the strength of the collector frame (DF-#4) showed the lowest significant effect. The main effect on weight was nearly identical in all DOE methods, while that on the strength of DF-#1 in BBD was higher than the other DOE methods.

To verify the suitability of the sensitivity analysis results of major structural members and the exploration of DOE-based AOSC improvement cases applied in this study, approximate modeling using RSM was conducted for each DOE technique. The design space exploration accuracy of RSM generated from each DOE method was examined. According to the results, the accuracy of the approximate model did not differ from the actual value in all DOE methods, and in terms of the accuracy of the approximate model for the response function under each design load case, an error of less than 3% of the actual value was observed, and the difference between DOE methods was found to be very small.

This study found that the overall DOE implementation method used to analyze the sensitivity of major structural members and explore enhanced design cases of the AOSC’s structure was reasonable; this includes the number of experiments, level of design variables, and DOE method selection. The DOE method-based design exploration approach proposed in this study is considered to be useful for enhancing the design performance of ocean and fisheries equipment that rely on empirical design techniques or must apply new designs.