• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• 한국군사과학기술학회지
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• 제17권2호
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• pp.182-188
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• 2014

Source localization is an important problem in the field of sonar and radar, etc. For the purpose of source localization, two or more spatially separated sensors are often used to measure the time difference of arrivals of a radiating source whose transmitted signal waveform is unknown. The NLS(Nonlinear Least Square) cost function with curve fitting method was proposed recently, which provide robust source localization performance by reducing estimation ambiguity. However, even this algorithm shows degraded performance in a multipath environment. To estimates source localization correctly, source localization algorithm that eliminate the effect of multipath signals is required. In this paper, PMP(Power Matching Procedure) is added to the algorithm, which provides improved source localization performance by properly cutting out the effect of multipath signals. Through simulation the performance of the proposed source localization algorithm is verified.

• 드라이브 ㆍ 컨트롤
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• 제14권4호
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• pp.45-50
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• 2017

The gas spring is a hydropneumatic adjusting element, consisting of a pressure tube, a piston rod, a piston and a connection fitting. The gas spring is filled with compressed nitrogen within the cylinder. The filling pressure acts on both sides of the piston and because of area difference it produces an extension force. Therefore, a gas spring is similar in function compare to mechanical coil spring. Conversely, optimization is a process of finding the best set of parameters to reach a goal while not violating certain constraints. The AMESim software provides NLPQL (Nonlinear Programming by Quadratic Lagrangian) and GA (genetic algorithm) for optimization. The NLPQL method builds a quadratic approximation to the Lagrange function and linear approximations to all output constraints at each iteration, starting with the identity matrix for the Hessian of the Lagrangian, and gradually updating it using the BFGS method. On each iteration, a quadratic programming problem is solved to find an improved design until the final convergence to the optimum design. In this study, we conducted optimization design of the gas spring reaction force with NLPQL.

• International Journal of Naval Architecture and Ocean Engineering
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• 제12권1호
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• pp.657-666
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• 2020

A reliable and cost-effective technique for the development of corrosion damage model is introduced to predict nonlinear time-dependent corrosion wastage of steel structures. A detailed explanation on how to propose a generalised mathematical formulation of the corrosion model is investigated in this paper (Part I), and verification and application of the developed method are covered in the following paper (Part II) by adopting corrosion data of a ship's ballast tank structure. In this study, probabilistic approaches including statistical analysis were applied to select the best fit probability density function (PDF) for the measured corrosion data. The sub-parameters of selected PDF, e.g., the largest extreme value distribution consisting of scale, and shape parameters, can be formulated as a function of time using curve fitting method. The proposed technique to formulate the refined time-dependent corrosion wastage model (TDCWM) will be useful for engineers as it provides an easy and accurate prediction of the 1) starting time of corrosion, 2) remaining life of the structure, and 3) nonlinear corrosion damage amount over time. In addition, the obtained outcome can be utilised for the development of simplified engineering software shown in Appendix B.

• ETRI Journal
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• 제27권2호
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• pp.188-194
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• 2005

We report on the improvement of critical dimension (CD) linearity on a photomask by applying the concept of process proximity correction to a laser lithographic process used for the fabrication of photomasks. Rule-based laser process proximity correction (LPC) was performed using an automated optical proximity correction tool and we obtained dramatic improvement of CD linearity on a photomask. A study on model-based LPC was executed using a two-Gaussian kernel function and we extracted model parameters for the laser lithographic process by fitting the model-predicted CD linearity data with measured ones. Model-predicted bias values of isolated space (I/S), arrayed contact (A/C) and isolated contact (I/C) were in good agreement with those obtained by the nonlinear curve-fitting method used for the rule-based LPC.

• 로봇학회논문지
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• 제11권4호
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• pp.300-309
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• 2016

This paper proposes a method for motion estimation of consecutive cameras using 3-D straight lines. The motion estimation algorithm uses two non-parallel 3-D line correspondences to quickly establish an initial guess for the relative pose of adjacent frames, which requires less correspondences than that of current approaches requiring three correspondences when using 3-D points or 3-D planes. The estimated motion is further refined by a nonlinear optimization technique with inlier correspondences for higher accuracy. Since there is no dominant line representation in 3-D space, we simulate two line representations, which can be thought as mainly adopted methods in the field, and verify one as the best choice from the simulation results. We also propose a simple but effective 3-D line fitting algorithm considering the fact that the variance arises in the projective directions thus can be reduced to 2-D fitting problem. We provide experimental results of the proposed motion estimation system comparing with state-of-the-art algorithms using an open benchmark dataset.

• 대기
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• 제24권3호
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• pp.379-390
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• 2014

This study explores the long-term trends of surface air temperatures in 11 KMA stations over the period of 1960~2012. Both linear and nonlinear trends are examined for the $95^{th}$, $50^{th}$, and $5^{th}$ percentiles of daily maximum ($T_{max}$) and minimum temperatures ($T_{min}$) by using quantile regression method. It is found that in most stations linear trends of $T_{max}$ and $T_{min}$ are generally stronger in winter than in summer, and warming trend of the $5^{th}$ percentile temperature (cold extreme) is stronger than that of the $95^{th}$ percentile temperature (warm extreme) in both seasons. The nonlinear trends, which are evaluated by the second order polynomial fitting, show a strong nonlinearity in winter. Specifically, winter temperatures have increased until 2000s but slightly decreased afterward in all percentiles. This contrasts with the $95^{th}$ and $50^{th}$ percentiles of summer $T_{min}$ that show a decreasing trend until 1980s then an increasing trend. While this result is consistent with a seasonal dependence of the recent global warming hiatus, most of the nonlinear trends are statistically insignificant, making a quantitative attribution of nonlinear temperature trends challenging.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2009년도 춘계학술대회 논문집 에너지변화시스템부문
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• pp.55-57
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• 2009

This paper deals with an improved core loss calculation under the load conditions, namely, no-load, AC-load and DC-load of multi-pole PM generator from curve fitting method using modified Steinmetz equation considered anomalous loss. For an accurate calculation, magnetic field analyses in stator core considering the time harmonics are performed. And using the nonlinear finite element analysis (FEA), we applied separated rotating and alternating magnetic field to core loss calculation. In order to verify the core loss results by proposed method, the experimental system for no-load core loss measurement has been implemented with DC motor, power analyzer and manufactured PM generator. And, the analysis results with rotational speed agree extremely well with those obtained by measurement.

• 한국음향학회지
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• 제27권5호
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• pp.221-228
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• 2008

소나 시스템에서 참조 신호를 이용하여 어레이 형상을 추정하는 경우, 참조 신호는 어레이와 충분히 떨어져 있지 않기 때문에 근거리 신호 모델링이 필요하다. 근거리 신호 모델링을 기반으로 하는 어레이 형상 추정 기법은 일반적으로 수신된 참조 신호의 공간 공분산 행렬을 이용한다. 이러한 기법 중 1개의 참조 신호만을 이용하여 공간 공분산 행렬의 고유치 분해 후 최대 고유치에 해당하는 고유 벡터를 참조 신호의 조향 벡터로 구성하여 어레이 형상을 추정하는 근거리 고유벡터 기법이 있다. 본 논문에서는 1개 이상의 참조 신호를 이용하여 공간 공분산 행렬로부터 구한 잡음 부공간과 신호 부공간이 서로 직교한다는 특성을 이용하여 Newton-type 반복 기법으로 센서 위치를 추정해 나가는 간략화된 부공간 근사 기법을 제안한다. 또한 근거리 고유 벡터 기법과 간략화된 부공간 근사 기법의 성능을 다양한 환경에서 분석해 본다. 모의 실험 결과 한 개의 참조 신호를 이용하는 경우에 근거리 고유 벡터 기법과 간략화된 부공간 근사 기법이 거의 동일한 성능을 보임을 확인할 수 있었다. 또한 근거리 고유 벡터 기법이 참조 신호를 2개 이상 사용할 수 없는데 반해 간략화된 부공간 근사 기법은 두 개의 참조 신호를 이용함으로써 참조 신호의 입사 방향에 관계없이 안정적인 형상 추정 결과를 얻을 수 있음을 확인하였다.

• 터널과지하공간
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• 제6권3호
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• pp.209-222
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• 1996

Shut-in pressure, reopenting pressure and fracture orientation are very important parameters to be evaluated precisely in in-situ stress measurement by hydraulic fracturing. Graphical methods on pressure-time curves have been conventionally used, even though these are seriously dependent on subjectivity of interpreters. So there have been many demands on new method to objectivity in determining parameters. We have developed integrated hydrofracturing data processing program (HYDFRAC), based on nonlinear regression analysis and can be invoked under the Window graphical user interface. HYDFRAC consiste of three routines, that is shut-in pressure routine, reopening pressure routine, and fracture delineation routine. Each of routines include independent modules according to parameter determination methods. Its application to field tests ensured both objectivity and facility in determining of hydraulic fracturing parameters. Determining shut-in pressures at each pressurization cycles, we adopted the exponential pressure-decay method(EPD method), the bilinear pressure-decay-rate method (PDR method), and the tangent intersection method in order to find the pressurization-cyclic tendency of shut-in pressures. The estimated pressure by PDR method exists in the range of the upper and lower values by EPD method, and lies near to the upper value more than the lower. Being the pressurization cycle increased, the range of upper and lower limits come to be stabilized gradually. By graphical superposition method and bilinear pressure-accumulated volume method, reopening pressures were determined. Vertical and inclined fracture attitudes were determined by applying the directional statistics and sinusoidal curve fitting, respectively. The results of evaluation of hydrofracturing parameters showed that statistical methods could enhance the objectivity better than graphical methods.