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Yayın A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid(Elsevier Science inc, 2005-05-25) Tunga, Mehmet Alper; Demiralp, MetinWhen the values of a multivariate function f(x(1),...,x(N)), having N independent variables like x(1),...,x(N) are given at the nodes of a cartesian, product set in the space of the independent variables and ail interpolation problem is defined to find out the analytical structure of this function some difficulties arise in the standard methods due to the multidimensionality of the problem. Here, the main purpose is to partition this multivariate data into low-variate data and to obtain the analytical structure of the multivariate function by using this partitioned data. High dimensional model representation (HDMR) is used for these types of problems. However, if HDMR requires all components, which means 2(N) number of components, to get a desired accuracy then factorized high dimensional model representation (FHDMR) can be used. This method uses the components of HDMR. This representation is needed when the sought multivariate function has a multiplicative nature. In this work we introduce how to utilize FHDMR for these problems and present illustrative examples.Yayın Hybrid high dimensional model representation (HHDMR) on the partitioned data(Elsevier B.V., 2006-01-01) Tunga, Mehmet Alper; Demiralp, MetinA multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid. One way to construct the solution of this problem is to partition the given multivariate data into low-variate data. High dimensional model representation (HDMR) and generalized high dimensional model representation (GHDMR) methods are used to make this partitioning. Using the components of the HDMR or the GHDMR expansions the multivariate data can be partitioned. When a cartesian product set in the space of the independent variables is given, the HDMR expansion is used. On the other band, if the nodes are the elements of a random discrete data the GHDMR expansion is used instead of HDMR. These two expansions work well for the multivariate data that have the additive nature. If the data have multiplicative nature then factorized high dimensional model representation (FHDMR) is used. But in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature. They have a hybrid nature. So, a new method is developed to obtain better results and it is called hybrid high dimensional model representation (HHDMR). This new expansion includes both the HDMR (or GHDMR) and the FHDMR expansions through a hybridity parameter. In this work, the general structure of this hybrid expansion is given. It has tried to obtain the best value for the hybridity parameter. According to this value the analytical structure of the sought multivariate function can be determined via HHDMR.Yayın Contribution of higher order terms in nonlinear ion-acoustic waves: strongly dispersive case(Physical Soc Japan, 2002-08) Demiray, HilmiContribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed by us [J. Phys. Soc. Jpn. 68 (1999) 1833]. In the analysis it is shown that the lowest order term in the expansion is governed by the nonlinear Schrodinger equation while the second order term is governed by the linear Schrodinger equation. For the small wave number region a set of solution is presented for the evolution equations.Yayın Optimized fractional-order Butterworth filter design in complex F-plane(Springer Nature, 2022-10) Mahata, Shibendu; Herencsar, Norbert; Kubanek, David; Göknar, İzzet CemThis paper introduces a new technique to optimally design the fractional-order Butterworth low-pass filter in the complex F-plane. Design stability is assured by incorporating the critical phase angle as an inequality constraint. The poles of the proposed approximants reside on the unit circle in the stable region of the F-plane. The improved accuracy of the suggested scheme as compared to the recently published literature is demonstrated. A mixed-integer genetic algorithm which considers the parallel combinations of resistors and capacitors for the Valsa network is used to optimize the frequency responses of the fractional-order capacitor emulators as part of the experimental verification using the Sallen–Key filter topology. The total harmonic distortion and spurious-free dynamic range of the practical 1.5th-order Butterwoth filter are measured as 0.13% and 62.18 dBc, respectively; the maximum and mean absolute relative magnitude errors are 0.03929 and 0.02051, respectively.Yayın Genetik algoritma ile kesirli dereceli sistemler için frekans tabanlı yaklaşımların karşılaştırılması(Institute of Electrical and Electronics Engineers Inc., 2025-08-15) Astekin, Dorukhan; Değirmenci, Ali Murat; İstefanopulos, YorgoKesirli dereceli sistemler tam sayı yerine kesirli tümlevsel veya türevsel terimlerin yer aldığı sistemlerdir ve yapısı gereği hesaplama zorluğunu da beraberinde getirmektedir. Bu nedenle birçok çalışmada kesirli dereceli sistemler için bazı yaklaşım yöntemleri araştırmacılar tarafından önerilmektedir. Bu çalışma kapsamında kesirli dereceli sistemler için frekans tabanlı yaklaşım yöntemlerinin karşılaştırılmalı çalışması ve eniyileme yöntemlerinden biri olan genetik algoritma ile tasarlanan kesirli dereceli PID denetleyici ile kesirli dereceli sistemin ve yaklaşımlarının karşılaştırılması sunulmaktadır. Karşılaştırılan yöntemler MATLAB/Simulink ortamında modellenerek benzetim sonuçları verilmektedir.
