• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1367-1376
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• 2018

In practice, the density function of a random variable X is always unknown. Even its smoothness parameter is unknown to us. In this paper, we will consider a density smoothness parameter estimation problem via wavelet theory. The smoothness parameter is defined in the sense of equivalent Besov norms. It is well-known that it is almost impossible to estimate this kind of parameter in general case. But it becomes possible when we add some conditions (to our proof, we can not remove them) to the density function. Besides, the density function contains impurities. It is covered by some additive noises, which is the key point we want to show in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.399-401
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• 1989

Utilizing an interconnected set of neuron-like elements, the present study is to provide a method of parameter estimation for a second order linear time invariant system of self-tuning controller. The result from the proposed method is evaluated by comparing with those obtained by the recursive least square (RLS) identification algorithm and extended recursive least square (ERLS) algorithm, and it shows that, although the smoothness of system performance is still to be improved, the effectiveness of shorter computing time is demonstrated which may be of considerable value to real time computing.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1194-1200
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• 2006

In this paper, we propose an adaptive MAP (Maximum A Posteriori) high-resolution image reconstruction algorithm using local statistics. In order to preserve the edge information of an original high-resolution image, a visibility function defined by local statistics of the low-resolution image is incorporated into MAP estimation process, so that the local smoothness is adaptively controlled. The weighted non-quadratic convex functional is defined to obtain the optimal solution that is as close as possible to the original high-resolution image. An iterative algorithm is utilized for obtaining the solution, and the smoothing parameter is updated at each iteration step from the partially reconstructed high-resolution image is required. Experimental results demonstrate the capability of the proposed algorithm.

• Korean Journal of Computational Design and Engineering
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• v.9 no.3
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• pp.183-191
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• 2004

This paper deals with smooth curve fitting of data corrupt by noise. Most research efforts have been concentrated on employing the smoothness penalty function with the estimation of its optimal parameter in order to avoid the 'overfilling and underfitting' dilemma in noisy data fitting problems. Our approach, called DBSF(Differentiation-Based Smooth Fitting), is different from the above-mentioned method. The main idea is that optimal functions approximately estimating the derivative of noisy curve data are generated first using genetic programming, and then their integral values are evaluated and used to recover the original curve form. To show the effectiveness of this approach, DBSP is demonstrated by presenting two illustrative examples and the application of estimating the principal dimensions of bulk cargo ships in the conceptual design stage.

• Geomechanics and Engineering
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• v.30 no.2
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• pp.187-199
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• 2022

Kriging metamodel, as a flexible machine learning method for approximating deterministic analysis models of an engineering system, has been widely used for efficiently estimating slope reliability in recent years. However, the autocorrelation function (ACF), a key input to Kriging that affects the accuracy of reliability estimation, is usually selected based on empiricism. This paper proposes an adaption of the Kriging method, named as Genetic Algorithm optimized Whittle-Matérn Kriging (GAWMK), for addressing this issue. The non-classical two-parameter Whittle-Matérn (WM) function, which can represent different ACFs in the Matérn family by controlling a smoothness parameter, is adopted in GAWMK to avoid subjectively selecting ACFs. The genetic algorithm is used to optimize the WM model to adaptively select the optimal autocorrelation structure of the GAWMK model. Monte Carlo simulation is then performed based on GAWMK for a subsequent slope reliability analysis. Applications to one explicit analytical example and two slope examples are presented to illustrate and validate the proposed method. It is found that reliability results estimated by the Kriging models using randomly chosen ACFs might be biased. The proposed method performs reasonably well in slope reliability estimation.

• Geophysics and Geophysical Exploration
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• v.9 no.1
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• pp.86-92
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• 2006

The full-waveform inversion algorithm using normalised seismic wavefields can avoid potential inversion errors due to source estimation required in conventional full-waveform inversion methods. In this paper, we have modified the inversion scheme to install a weighted smoothness constraint for better resolution, and to implement a staged approach using normalised wavefields in order of increasing frequency instead of inverting all frequency components simultaneously. The newly developed scheme is verified by using a simple two-dimensional fault model. One of the most significant improvements is based on introducing weights in model parameters, which can be derived from integrated sensitivities. The model-parameter weighting matrix is effective in selectively relaxing the smoothness constraint and in reducing artefacts in the reconstructed image. Simultaneous multiple-frequency inversion can almost be replicated by multiple single-frequency inversions. In particular, consecutively ordered single-frequency inversion, in which lower frequencies are used first, is useful for computation efficiency.

• Smart Structures and Systems
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• v.25 no.5
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• pp.569-580
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• 2020

The identification of delays and delay compensation are critical problems in real-time hybrid simulations (RTHS). Conventional delay compensation methods are mostly based on the assumption of a constant delay. However, the system delay may vary during tests owing to the nonlinearity of the loading system and/or the behavioral variations of the specimen. To address this issue, this study presents an adaptive delay compensation method based on a discrete model of the loading system. In particular, the parameters of this discrete model are identified and updated online with the least-squares method to represent a servo hydraulic loading system. Furthermore, based on this model, the system delays are compensated for by generating system commands using the desired displacements, achieved displacements, and previous displacement commands. This method is more general than the existing compensation methods because it can predict commands based on multiple displacement categories. Moreover, this method is straightforward and suitable for implementation on digital signal processing boards because it relies solely on the displacements rather than on velocity and/or acceleration data. The virtual and real RTHS results show that the studied method exhibits satisfactory estimation smoothness and compensation accuracy. Furthermore, considering the measurement noise, the low-order parameter models of this method are more favorable than that the high-order parameter models.

• Geophysics and Geophysical Exploration
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• v.6 no.4
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• pp.199-206
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• 2003

Characteristics of the static shift are discussed by comparing the three-dimensional MT inversion with/without static shift parameterization. The galvanic distortion by small-scale shallow feature often leads severe distortion in inverted resistivity structures. The new inversion algorithm is applied to four numerical data sets contaminated by different amount of static shift. In real field data interpretations, we generally do not have any a-priori information about how much the data contains the static shift. In this study, we developed an algorithm for finding both Lagrangian multiplier for smoothness and the trade-off parameter for static shift, simultaneously in 3-D MT inversion. Applications of this inversion routine for the numerical data sets showed quite reasonable estimation of static shift parameters without any a-priori information. The inversion scheme is successfully applied to all the four data sets, even when the static shift does not obey the Gaussian distribution. Allowing the static shift parameters have non-zero degree of freedom to the inversion, we could get more accurate block resistivities as well as static shifts in the data. When inversion does not consider the static shift as inversion parameters (conventional MT inversion), the block resistivities on the surface are modified considerably to match possible static shift. The inhomogeneous blocks on the surface can generate the static shift at low frequencies. By those mechanisms, the conventional 3-D MT inversion can reconstruct the resistivity structures to some extent in the deeper parts even when moderate static shifts are in the data. As frequency increased, however, the galvanic distortion is not frequency independent any more, and thus the conventional inversion failed to fit the apparent resistivity and phase, especially when strong static shift is added. Even in such case, however, reasonable estimation of block resistivity as well as static shift parameters were obtained by 3-D MT inversion with static shift parameterization.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.677-692
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• 2018

The total fertility rate of Korea was 1.05 in 2017, showing a return to the 1.08 level in the year 2005. 1.05 is a very low fertility level that is far from replacement level fertility or safety zone 1.5. The number may indicate a low fertility trap. It is therefore important to predict fertility than at any other time. In the meantime, we have predicted the age-specific fertility rate and total fertility rate by various statistical methods. When the data trend is disconnected or fluctuating, it applied a nonparametric method applying the smoothness and weight. In addition, the Bayesian method of using the pre-distribution of fertility rates in advanced countries with reference to the three-stage transition phenomenon have been applied. This paper examines which method is reasonable in terms of precision and feasibility by applying estimation, forecasting, and comparing the results of the recent variability of the Korean fertility rate with parametric, non-parametric and Bayesian methods. The results of the analysis showed that the total fertility rate was in the order of KOSTAT's total fertility rate, Bayesian, parametric and non-parametric method outcomes. Given the level of TFR 1.05 in 2017, the predicted total fertility rate derived from the parametric and nonparametric models is most reasonable. In addition, if a fertility rate data is highly complete and a quality is good, the parametric model approach is superior to other methods in terms of parameter estimation, calculation efficiency and goodness-of-fit.