• Honam Mathematical Journal
• /
• v.45 no.4
• /
• pp.619-628
• /
• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.26 no.2B
• /
• pp.131-137
• /
• 2006

We have investigated the properties of the Singular Spectrum Analysis (SSA) coupled with the Linear Recurrent Formula which made it possible to complement the parametric time series model. The SSA has been applied to extract the underlying properties of the principal component of hydrologic time series, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. Generally, the prediction by the SSA method can be applied to hydrologic time series governed (may be approximately) by the linear recurrent formulae. This study has examined the forecasting ability of the SSA-LRF model. These methods were applied to monthly discharge and water surface level data. These models indicated that two of the time series have good abilities of forecasting, particularly showing promising results during the period of one year. Thus, the method presented in this study suggests a competitive methodology for the forecast of hydrologic time series.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.215-220
• /
• 1992

Using a matrix method, pp. Antosik and C. Swartz have obtained a series of nice properties of bounded multiplier convergent (BMC) series on metric linear spaces ([1],[8],[9]). In this paper, we establish a basic property of BMC series on topological vector spaces which is a generalization of a result due to J. Batt([2], Th.2). From this, we have obtained a kind of inclusion theorem of operator spaces. This theorem yields a nice result on infinite systems of linear equations.

• International Journal of Contents
• /
• v.10 no.1
• /
• pp.47-53
• /
• 2014

The paper considers the challenges involved in measuring the similarities between time series, such as time shifts and the mixture of frequencies. To improve recognition accuracy, we investigate an improved linear dynamical system for discovering prominent features by exploiting the evolving dynamics and correlations in a time series, as the quality of unsupervised pattern recognition relies strongly on the extracted features. The proposed approach yields a set of compact extracted features that boosts the accuracy and reliability of clustering for time series data. Experimental evaluations are carried out on time series applications from the scientific, socio-economic, and business domains. The results show that our method exhibits improved clustering performance compared to conventional methods. In addition, the computation time of the proposed approach increases linearly with the length of the time series.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.2
• /
• pp.265-274
• /
• 2003

Time series data are influenced by the external events such as holiday, strike, oil shock, and political change, so the external events cause a sudden change to the time series data. We regard the observation as outlier that occurred as a result of external events. In general, it is called intervention if we know the period and the reason of external events, and it makes an analyst difficult to establish a time series model. Therefore, it is important that we analyze the styles and effects of intervention. In this paper, we considered the linear time series model with invention and compared with nonlinear time series models such as ARCH, GARCH model and also we compared with the combination prediction method that Tong(1990) introduced. In the practical case study, we compared prediction power with RMSE among linear, nonlinear time series model with intervention and combination prediction method.

• The Transactions of the Korean Institute of Electrical Engineers P
• /
• v.53 no.4
• /
• pp.175-182
• /
• 2004

This paper presents a new method for finding the Block Pulse series coefficients, deriving the Block Pulse integration operational matrices and generalizing the integration operational matrices which are necessary for the control fields using the Block Pulse functions. In order to apply the Block Pulse function technique to the problems of state estimation or parameter identification more efficiently, it is necessary to find the more exact value of the Block Pulse series coefficients and integral operational matrices. This paper presents the method for improving the accuracy of the Block Pulse series coefficients and derives generalized integration operational matrix and applied the matrix to the analysis of linear time-invariant system.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.37 no.6
• /
• pp.376-382
• /
• 1988

A small-signal low-frequency disturbance of the input line affects the regulated-output voltage of the series resonant converter. To mitigate the detrimental effect, the output feedback PI-controller is employed. Small-signal linear models are represented to characterize the closed loop series resonant converter system. Design equations for the PI-controller which satisfy stability and percent ripple conditions are derived from the closed-loop linear model. Experimental results are presented which show excellent correlation with theory.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.1
• /
• pp.73-80
• /
• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.2
• /
• pp.168-175
• /
• 1999

In this paper, a modified RBF(Radial Basis Function) network structure is suggested for the prediction of a time-series with non-linear, non-stationary characteristics. Coventional RBF network predicting time series by using past outputs sense the trajectory of the time series and react when there exists strong relation between input and hidden activation function's RBF center. But this response is highly sensitive to level and trend of time serieses. In order to overcome such dependencies, hidden activation functions are modified to react to the increments of input variable and multiplied by increment(or dectement) for prediction. When the suggested structure is applied to prediction of Macyey-Glass chaotic time series, Lorenz equation, and Rossler equation, improved performances are obtained.

• Structural Engineering and Mechanics
• /
• v.27 no.3
• /
• pp.333-345
• /
• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.