• KIPS Transactions on Software and Data Engineering
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• v.11 no.1
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• pp.1-10
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• 2022

Deep neural networks are widely used to solve various problems. In a fully connected neural network, the nonlinear activation function is a function that nonlinearly transforms the input value and outputs it. The nonlinear activation function plays an important role in solving the nonlinear problem, and various nonlinear activation functions have been studied. In this study, we propose a combined parametric activation function that can improve the performance of a fully connected neural network. Combined parametric activation functions can be created by simply adding parametric activation functions. The parametric activation function is a function that can be optimized in the direction of minimizing the loss function by applying a parameter that converts the scale and location of the activation function according to the input data. By combining the parametric activation functions, more diverse nonlinear intervals can be created, and the parameters of the parametric activation functions can be optimized in the direction of minimizing the loss function. The performance of the combined parametric activation function was tested through the MNIST classification problem and the Fashion MNIST classification problem, and as a result, it was confirmed that it has better performance than the existing nonlinear activation function and parametric activation function.

• KIPS Transactions on Software and Data Engineering
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• v.11 no.9
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• pp.371-380
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• 2022

Convolutional neural networks are widely used to manipulate data arranged in a grid, such as images. A general convolutional neural network consists of a convolutional layers and a fully connected layers, and each layer contains a nonlinear activation functions. This paper proposes a combined parametric activation function to improve the performance of convolutional neural networks. The combined parametric activation function is created by adding the parametric activation functions to which parameters that convert the scale and location of the activation function are applied. Various nonlinear intervals can be created according to parameters that convert multiple scales and locations, and parameters can be learned in the direction of minimizing the loss function calculated by the given input data. As a result of testing the performance of the convolutional neural network using the combined parametric activation function on the MNIST, Fashion MNIST, CIFAR10 and CIFAR100 classification problems, it was confirmed that it had better performance than other activation functions.

• KIPS Transactions on Software and Data Engineering
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• v.10 no.10
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• pp.407-420
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• 2021

Deep neural networks are widely used to solve various problems. However, the deep neural network with a deep hidden layer frequently has a vanishing gradient or exploding gradient problem, which is a major obstacle to learning the deep neural network. In this paper, we propose a parametric activation function to alleviate the vanishing gradient problem that can be caused by nonlinear activation function. The proposed parametric activation function can be obtained by applying a parameter that can convert the scale and location of the activation function according to the characteristics of the input data, and the loss function can be minimized without limiting the derivative of the activation function through the backpropagation process. Through the XOR problem with 10 hidden layers and the MNIST classification problem with 8 hidden layers, the performance of the original nonlinear and parametric activation functions was compared, and it was confirmed that the proposed parametric activation function has superior performance in alleviating the vanishing gradient.

• The Journal of the Korea Contents Association
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• v.21 no.3
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• pp.616-625
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• 2021

Deep neural networks are an approximation method that approximates an arbitrary function to a linear model and then repeats additional approximation using a nonlinear active function. In this process, the method of evaluating the performance of approximation uses the loss function. Existing in-depth learning methods implement approximation that takes into account loss functions in the linear approximation process, but non-linear approximation phases that use active functions use non-linear transformation that is not related to reduction of loss functions of loss. This study proposes parametric activation functions that introduce scale parameters that can change the scale of activation functions and location parameters that can change the location of activation functions. By introducing parametric activation functions based on scale and location parameters, the performance of nonlinear approximation using activation functions can be improved. The scale and location parameters in each hidden layer can improve the performance of the deep neural network by determining parameters that minimize the loss function value through the learning process using the primary differential coefficient of the loss function for the parameters in the backpropagation. Through MNIST classification problems and XOR problems, parametric activation functions have been found to have superior performance over existing activation functions.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.6
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• pp.590-600
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• 2008

This paper concerns the development of a designer friendly hull form parameterization and its coupling with advanced global optimization algorithms. As optimization algorithms, we choose the Partial Swarm Optimization(PSO) recently introduced to solve global optimization problems. Most general-purpose optimization softwares used in industrial applications use gradient-based algorithms, mainly due to their convergence properties and computational efficiency when a relatively few number of variables are considered. However, local optimizers have difficulties with local minima and non-connected feasible regions. Because of the increase of computer power and of the development of efficient Global Optimization (GO) methods, in recent years nongradient-based algorithms have attracted much attention. Furthermore, GO methods provide several advantages over local approaches. In the paper, the derivative-based SQP and the GO approach PSO are compared with their relative performances in solving some typical ship design optimization problem focusing on their effectiveness and efficiency.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.5
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• pp.542-550
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• 2007

A geometry modification is one of main keys in achieving a successful optimization. The optimized hull form generated from the geometry modification should be a realistic, faired form from the ship manufacturing point of view. This paper presents a practical hull optimization procedure using a parametric modification function. In the parametric modification function method, the initial ship geometry was easily deformed according to the variations of design parameters. For example, bulbous bow can be modified with several parameters such as bulb area, bulb length, bulb height etc. Design parameters are considered as design variables to modify hull form, which can reduce the number of design variables in optimization process and hence reduce its time cost. To verify the use of the parametric modification function, optimization for KCS was performed at its design speed (FN=0.26) and the wave making resistance is calculated using a well proven potential code with fully nonlinear free surface conditions. The design variables used are key design parameters such as Cp curve, section shape and bulb shape. This study shows that the hull form optimized by the parametric modification function brings 7.6% reduction in wave making resistance. In addition, for verification and comparison purpose, a direct geometry variation method using a bell-shape modification function is used. It is shown that the optimal hull form generated by the bell-shaped modification function is very similar to that produced by the parametric modification function. However, the total running time of the parametric optimization is six times shorter than that of the bell shape modification method, showing the effectiveness and practicalness from a designer point of view in ship yards.

• Journal of the Society of Naval Architects of Korea
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• v.59 no.2
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• pp.96-108
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• 2022

In this paper, we propose a systematic hull form variation technique which automatically satisfies the displacement constraint and guarantees a high level of fairness. This method is possible through multiple parameter correction curves. The present method is to improve the hull form variation method based on parametric modification function and consists of two sub-categories: SAC variation and section lines modification. For SAC variation, the utilization of two B-Spline curves satisfying GC¹ condition led to the satisfaction of displacement constraint and high level of fairness at the same time. Section lines modification methods involves in using two fuctions: the first is the waterplane modification function combining two cubic splines. the other function is the sectional area modification function consisting of 2nd order polynomial over the DLWL(Design Load Waterline) and 3rd order polynomial below the DLWL, This function enables not only the fundamental U-V section shape variation but also systematically modified section lines. The present method is expected to be more useful in the hull form optimization process using CFD compared to the existing method.