• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.3_4
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• pp.34-47
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• 1995

It is experienced fact as a regular annual event that the structure to he designed on unreasonable flood for the agricultural structures including reservoirs have been brought not only loss of lives, but also enormous property damage. For the solution of this problem at issue, this study was conducted to develop an optimal runoff hydrograph model by comparison of the peak flows and time to peak between observed and simulated flows derived by linear time-invariant and linear time-variant models under the condition of having a short duration of heavy rainfall with uniform rainfall intensity at nine small watersheds which are within the range of 55.9 to 140.7 square kilometers in area in Han, Geum, Nagdong and Yeongsan Rivers. The results obtained through this study can be summarized as follows. 1. Storage constants and Gamma function arguments were calculated within the range of 1.2 to 6.42 and of 1.28 to 8.05 respectively by the moment method as the parameters for the analysis of runoff hydrograph based on linear time-invariant model. 2. Parameters for both linear time-invariant and linear time-variant models were calibrated with nine gaged watershed data, using a trial and error method. The resulting parameters including Gamma function argument, N and storage constant, K for linear time-invariant model were related statistically to watershed characteristic variables such as area, slope, length of main stream and the centroid length of the basin. 3. Average relative errors of the simulated peak discharge of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 0.75 and 5.42 percent respectively to the peak of observed runoff hydrographs. Correlation coefficients for the statistical analysis in the same condition were shown to be 0.999 and 0.978 with a high significance respectively. Therefore, it can be concluded that the accuracy of a linear time-variant model is approaching more closely to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 4. Average relative errors of the time to peak of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 16.44 and 19.89 percent respectively to the time to peak of observed runoff hydrographs. Correlation coefficients in the same condition were also shown to be 0.999 and 0.886 with a high significance respectively. 5. It can be seen that the shape of simulated hydrograph based on a linear time- variant model is getting closer to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 6. Two different models were verified with different rainfall-runoff events from data for the calibration by relative error and correlation analysis. Consequently, it can be generally concluded that verification results for the peak discharge and time to peak of simulated runoff hydrographs were in good agreement with those of calibrated runoff hydrographs.

• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.3
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• pp.112-126
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• 1996

This study was conducted to develop an optimal runoff bydrograph model by comparison of the peak discharge and time to peak between observed and simulated flows derived by four different models, that is, linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models under the conditions of heavy rainfalls with regionally uniform rainfall intensity in short durations at nine small watersheds. The results obtained through this study can be summarized as follows. 1. Parameters for four models including linear time-invariant, linear time-variant, nonlinear time-invariant and nonlinear time-variant models were calibrated using a trial and error method with rainfall and runoff data for the applied watersheds. Regression analysis among parameters, rainfall and watershed characteristics were established for both linear time-invariant and nonlinear time-invariant models. 2. Correlation coefficients of the simulated peak discharge of calibrated runoff hydrographs by using four models were shown to be a high significant to the peak of observed runoff graphs. Especially, it can be concluded that the simulated peak discharge of a linear time-variant model is approaching more closely to the observed runoff hydrograph in comparison with those of three models in the applied watersheds. 3. Correlation coefficients of the simulated time to peak of calibrated runoff hydrographs by using a linear time-variant model were shown to be a high significant to the time to peak of observed runoff hydrographs than those of the other models. 4. The peak discharge and time to peak of simulated runoff hydrogaphs by using linear time-variant model are verified to be approached more closely to those of observed runoff hydrographs than those of three models in the applied watersheds. 5. It can be generally concluded that the shape of simulated hydrograph based on a linear time-variant model is getting closer to the observed runoff hydrograph than those of three models in the applied watersheds. 6. Simulated hydrographs using the nonlinear time-variant model which is based on more closely to the theoritical background of the natural runoff process are not closer to the observed runoff hydrographs in comparison with those of three models in the applied watersheds. Consequently, it is to be desired that futher study for the nonlinear time-variant model should be continued with verification using rainfall-runoff data of the other watersheds in addition to the review of analyical techniques.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.4
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• pp.87-100
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• 1995

In order to control systems which contain nonlinearities of uncertainties, control strategies must deal with the effects of them. Since most of control methods based on system mathematical models have been mainly developed focused on stability robustness against nonlinearities or uncertainties under the assumption that controlled systems are linear time invariant, they have certain amount of limitations to smartly improve the transient responses of systems disturbed by nonlinearities or uncertainties. In this paper, a nonlinear fuzzy PID control method is suggested which can stably improve the transient responses of systems disturbed by nonlinearities, as well as systems whose mathematical characteristics are not perfectly known. Although the derivation process is based on the design process similar to general fuzzy logic controller, resultant control law has analytical forms with time varying PID gains rather than linguistic forms, so that implementation using common-used versatile microprocessors cna be achieved easily and effectively in real-time control aspect.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.153-159
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• 2008

For $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$, all the derivations of the evaluation algebra $\mathbb{F}[e^{{\pm}x}]_{\{{\partial}\}}$ is found in the paper (see [16]). For $M=\{{\partial}_1,\;{\partial}_1^2\},\;Der_{non}(\mathbb{F}[e^{{\pm}x}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ is found in the paper (see [2]). For $M=({\partial}_1^2,\;{\partial}_2^2)$, we find $Der_{non}(\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M))$ of the evaluation algebra $\mathbb{F}[e^{{\pm}x},\;e^{{\pm}y}]_M$ in this paper.

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.4
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• pp.583-592
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• 1999

In order to control systems which contain nonlinearities control strategies must deal with the effects of them. Since most of control methods based on system mathematical models have been mainly developed focused on stability robustness against nonlinearities or uncertainties under the assumption that controlled systems are linear time invariant they have certain amount of limita-tions to smartly improve control perfomances of systems disturbed by nonlinearities or uncertainties. In this paper the fuzzy PID control law is suggested which can improve control performances of the nonlinear heavy load hydraulic systems disturbed by nonlinearities and uncertainties. Although the derivation process is based on the design process similar to general fuzzy logic con-troller resultant control law has analytical forms with time varying PID gains rather than linguis-tic forms so that implementation using commn-used versatile microprocessors can be achieved easily and effectively in real-time control aspect.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2611-2613
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• 2000

This paper deals with a novel approach to unknown inputs observer(UIO) design for linear time-invariant dynamical systems using a fast Walsh transform and Walsh function's differential operation. Generally, UIO has a derivation of system outputs which is not available from the measurement directly. And it is an obstacle to estimate the unknown inputs properly when unexpected measurement noises are presented. Therefore, this paper propose an algebraic approach to eliminate such problems by using a Walsh function's differential operation.

• Journal of Advanced Navigation Technology
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• v.20 no.5
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• pp.475-481
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• 2016

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

• Korean Journal of Remote Sensing
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• v.22 no.1
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• pp.1-10
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• 2006

During the northern burning season, biomass burning is found north of the equator, while satellite estimates from the residual-type method such as the CCD method show higher ozone south of the equator. This discrepancy is called the tropical Atlantic paradox (Thompson et ai., 2000). We use satellite and ground-based measurements to investigate the paradox. When the background tropospheric ozone over the Pacific Ocean from TOMS measurements is subtracted from the latitudinal total ozone distribution (e.g. TOMS-Pacific method), the results show remarkable agreement with the latitudinal stratospheric ozone distribution using the CCD method. The latitudinal tropospheric ozone distribution using the CCD method, with a persistent maximum over the southern tropical Atlantic, is also seen in the latitudinal tropospheric ozone distribution using the TOMS-Pacific method. It suggests that the complicated CCD method can be replaced by the simple TOMS-Pacific method. However, the tropical Atlantic paradox exists in the results of both the CCD and TOMS-Pacific methods during the northern buming season. In order to investigate this paradox, we compare the latitudinal ozone distributions using the CCD and TOMS-Pacific methods by using the SAGE measurements (e.g. TOMS-SAGE method) and the SHADOZ ozonesoundings (e.g. TOMS-Sonde method) assuming zonally invariant stratospheric ozone, which is the same assumption as of the CCD method. During the northern burning season, the latitudinal distributions in the tropospheric ozone derived from the TOMS-SAGE and TOMS-Sonde methods show higher tropospheric ozone over the northern tropical Atlantic than the southern Atlantic due to a stronger gradient in stratospheric ozone relative to that from the CCD and TOMS-Pacific methods. This indicates that the latitudinal tropospheric ozone distribution can be changed depending on the data that is used to determine the latitudinal stratospheric ozone distribution. Therefore, there is a possibility that the north-south gradient in stratospheric ozone over the Atlantic can be a solution of the paradox.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.1 no.1
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• pp.21-32
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• 1981

Recent trends in design standards development in some European countries and U.S.A. have encouraged the use of probabilistic limit sate design concepts. Reliability based design criteria such as LSD, LRFD, PBLSD, adopted in those advanced countries have the potentials that they afford for symplifying the design process and placing it on a consistent reliability bases for various construction materials. A reliability based design criteria for RC flexural members are proposed in this study. Lind-Hasofer's invariant second-moment reliability theory is used in the derivation of an algorithmic reliability analysis method as well as an iterative determination of load and resistance factors. In addition, Cornell's Mean First-Order Second Moment Method is employed as a practical tool for the approximate reliability analysis and the derivation of design criteria. Uncertainty measures for flexural resistance and load effects are based on the Ellingwood's approach for the evaluation of uncertainties of loads and resistances. The implied relative safety levels of RC flexural members designed by the strength design provisions of the current standard code were evaluated using the second moment reliability analysis method proposed in this study. And then, resistance and load factors corresponding to the target reliability index(${\beta}=4$) which is considered to be appropriate level of reliability considering our practices are calculated by using the proposed methods. These reliability based factors were compared to those specified by our current ultimate strength design provisions. It was found that the reliability levels of flexural members designed by current code are not appropriate, and the code specified resistance and load factors were considerably different from the reliability based resistance and load factors proposed in this study.