• Analytical Science and Technology
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• v.8 no.1
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• pp.41-45
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• 1995

To analyze mixed rare earth elements quantitatively a nonlinear fitting method was applied to laser induced fluorescence signals. Mixed flourescence signal of two elements, Sm and Eu were resolved independently and determined the concentration of these two elements simultaneously. It was found that detection limit for each element in the mixture was sub-ppb level which was the same as that of the single element sample. Additionally it was found that lifetimes of Sm and Eu extracted from the nonlinear fitting method is the same as in the single element cases.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.768-776
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• 2011

This paper considers a data fitting problem for rational function models using the LM (Levenberg-Marquardt) optimization method. Rational function models have various merits on representing a wide range of shapes and modeling complicated structures by polynomials of low degrees in both the numerator and denominator. However, rational functions are nonlinear in the parameter vector, thereby requiring nonlinear optimization methods to solve the fitting problem. In this paper, we propose a data fitting method for rational function models based on the LM algorithm which is renowned as an effective nonlinear optimization technique. Simulations show that the fitting results are robust against the measurement noises and uncertainties. The effectiveness of the proposed method is further demonstrated by the real application to a 3D depth camera calibration problem.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.2
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• pp.29-38
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• 1982

Nonlinear hydrological model containing the nonlinearity of effective rainfall, lag time and runoff is presented. In the evaluation of rainfall excess, the polynomial fitting method for total rainfall, 5 day antecedant rainfall and direct runoff is developed. In the application to actual watershed, the estimated model parameters of nonlinear lag model reflecting the nonlinearity of lag time are compared with the parameters, by both the fitting method and the correlation, model which are the modified version of the storage function model. The Successive Approximation Method in mathematical solution and Newton-Rhapson method in numerical solution are found to be superior to the conventional numerical graphic method in the analysis of nonlinear processes.

• Journal of Ocean Engineering and Technology
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• v.22 no.3
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• pp.41-46
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• 2008

It is a recent trend for advanced ships and submarines to incorporate composite structures with viscoelastically damping material. Much research has been done on curve-fitting techniquesto identify vibration characteristic parameters such as natural frequencies, modal damping ratios, and mode shapes of the composite structure. In this study, an advanced technique for accurately determining vibration characteristic of a circular cylindrical shell-attached viscoelastically damping material is used, based on a multi-degree of freedom (MDOF) curve-fitting method. First, an initial value is obtained by using a linear least square method. Next, using the initial value, the exact modal parameters of the composite circular cylindrical shell are obtained by using a nonlinear least square method. Results show computation time is greatly decreased and accurate results are obtained by the MDOF curve-fitting method.

• Steel and Composite Structures
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• v.7 no.5
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• pp.355-376
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• 2007

The purpose of this study is to predict and investigate the time-dependent creep behavior of composite materials. For this, firstly the evaluation method for the modulus of elasticity of whole fiber and matrix is presented from the limited information on fiber volume fraction using the singular value decomposition method. Then, the effects of fiber volume fraction on modulus of elasticity of GFRP are verified. Also, as a creep model, the nonlinear curve fitting method based on the Marquardt algorithm is proposed. Using the existing Findley's power creep model and the proposed creep model, the effect of fiber volume fraction on the nonlinear creep behavior of composite materials is verified. Then, for the time-dependent analysis of a composite material subjected to uniaxial tension and simple shear loadings, a user-provided subroutine UMAT is developed to run within ABAQUS. Finally, the creep behavior of center loaded beam structure is investigated using the Hermitian beam elements with shear deformation effect and with time-dependent elastic and shear moduli.

• Journal of the Korea Institute of Military Science and Technology
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• v.9 no.2 s.25
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• pp.20-25
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• 2006

Low frequency towed line array with high array gain and beam resolution is a long range surveillance sensor for anti-submarine warfare. The beam characteristics is however deteriorated due to the distorted line array sensor caused by low towing speed, wind, current, and towing ship maneuvering. An adaptive beamforming method is utilized in this paper to enhance the distorted line array beam performance by estimating and compensating the nonlinear array shape. A polynomial curve fitting in the least square sense is used to estimate the array shape iteratively with the distributed heading sensors data along the array. Real time array shape estimation and nonlinear array beam calculation is applied to a very long towed line array sensor system and the beam performance is evaluated and compared to the linear beamformer for the simulation and sea trial data.

• Current Optics and Photonics
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• v.2 no.1
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• pp.69-78
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• 2018

This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

• Food Science and Biotechnology
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• v.17 no.6
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• pp.1352-1356
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• 2008

Bootstrap method, a computer-intensive statistical technique to estimate the distribution of a statistic was applied to deal with uncertainty and variability of the experimental data in stochastic prediction modeling of microbial growth on a chill-stored food. Three different bootstrapping methods for the curve-fitting to the microbial count data were compared in determining the parameters of Baranyi and Roberts growth model: nonlinear regression to static version function with resampling residuals onto all the experimental microbial count data; static version regression onto mean counts at sampling times; dynamic version fitting of differential equations onto the bootstrapped mean counts. All the methods outputted almost same mean values of the parameters with difference in their distribution. Parameter search according to the dynamic form of differential equations resulted in the largest distribution of the model parameters but produced the confidence interval of the predicted microbial count close to those of nonlinear regression of static equation.

• The Journal of the Acoustical Society of Korea
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• v.14 no.5
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• pp.29-35
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• 1995

Nonlinear distortion arising from the nonlinear movement of the loudspeaker diaphragm degradates the tone quality. The distortion is, in low frequency range, mainly caused by nonlinear characteristics of the suspension stiffness and the force factor. In this paper, the nonlinear suspension stiffness and the nonlinear force factor are modeled to the quadratic functions and a method is proposed to determine their coefficients. An additional mass to the diaphragm moved the quiescent point of the diaphragm and uncoupled the stiffness and the force factor. This made it possible to deter mine the coefficients of the nonlinear suspension stiffness by measuring the resonance frequencies at several quiescent points. The coefficients of the nonlinear force factor are then determined by fitting the curve which is calculated from the waveforms of input voltage and input current, and the displacement of the diaphragm at resonance frequency.

• Journal of Navigation and Port Research
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• v.26 no.3
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• pp.281-288
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• 2002

It might be true that both experimental and analytic techniques have been developed in the vibration analysis end engineering. It could not be said, however, that the experimental method has been also developed as much as analytic method, such as Finite Element Method One of the reason is that computation time becomes longer and that the solution often diverges depending on the choice of initial value in solving nonlinear equation. The equation in experimental modal analysis is usually composed of the nonlinear term of natural frequency and modal damping ratio, and the linear one of equivalent stiffness. In this study, the nonlinear terms were solved first, and then the linear term was obtained. The experimental modal parameters were estimated, applying the developed experimental modal analysis curve-fitting method to the super-structure model. In addition, the number of modes and modal damping ratio could be easily determined by the developed program with the application of graphical techniques and with easy handling button.