• Structural Engineering and Mechanics
• /
• v.39 no.5
• /
• pp.703-716
• /
• 2011

The accurate dynamic analysis of structures is usually performed by a fine finite element discretization with very large number of degrees of freedom. Apart from modal analysis, one can reduce the number of final equations by assuming the deformed shape of the structure as a linear combination of independent Ritz vectors. The efficiency of this method relies heavily on the vectors selected. In this paper, a new set of Ritz vectors is proposed. It is primarily proved that these vectors are linearly independent. Subsequently, various two and three-dimensional examples are analyzed based on the proposed method. In each case, the results are compared with the ones obtained based on usual Ritz and modal analysis methods. It is finally concluded that the proposed method is very effective and efficient method for dynamic analysis of structures in frequency domain.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.9-26
• /
• 2001

In some previous papers the author extended two algorithms proposed by Z. Kovarik for approximate orthogonalization of a finite set of linearly independent vectors from a Hibert space, to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular matrix. In this paper we describe combinations between these two methods and the classical Kaczmarz’s iteration. We prove that, in the case of a consistent least-squares problem, the new algorithms so obtained converge ti any of its solutions (depending on the initial approximation). The numerical experiments described in the last section of the paper on a problem obtained after the discretization of a first kind integral equation ilustrate the fast convergence of the new algorithms. AMS Mathematics Subject Classification : 65F10, 65F20.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.16 no.3
• /
• pp.303-308
• /
• 2006

To solve the rule explosion problem in multi input fuzzy logic system, a method of converting a given fuzzy system to 2 layered hierarchical fuzzy system is presented where the collection of the THEN-parts of the fuzzy rules of given fuzzy system is considered as vectors of fuzzy rule. At the 1 st layer, linearly independent fuzzy rule vectors generated from the given fuzzy logic system are used and, at the 2nd layer, linear combinations of these independent fuzzy rule vectors are used for fuzzy logic units at each layer. The resultant 2 layered hierarchical fuzzy system has not only equivalent approximation capability, but less number of fuzzy rules compared with the conventional fuzzy logic system.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.5
• /
• pp.598-603
• /
• 2007

To solve the rule explosion problem in multi-input fuzzy system, a method of converting a given fuzzy system to 2 layered hierarchical fuzzy system has been reported, where at the 1st layer, linearly independent fuzzy rule vectors generated from the given fuzzy system are used and, at the 2nd layer, linear combinations of these independent fuzzy rule vectors are used. In this paper, the steapest descent algorithm is presented to learn the fuzzy rule vectors and related coefficients for the equivalent 2 layered hierarchical structure. By simulation of learning of ball and beam control system, the feasibility of proposed learning scheme is shown.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1221-1228
• /
• 2009

In this paper we formulated the volume of parallel 2n-hedron spanned by timelike linearly independent vectors in the Lorentz vector space.

• Journal of Korean Institute of Industrial Engineers
• /
• v.26 no.3
• /
• pp.220-226
• /
• 2000

The problem (P) of optimizing a linear function $d^Tx$ over the set of efficient points for a multiple objective linear program (M) is difficult because the efficient set is nonconvex. There are some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve (P) with a linear program. In this paper we investigate a system of the linear equations $C^T{\alpha}$ = d and construct two linearly independent positive vectors u, v such that ${\alpha}$ = u - v. From those vectors u, v, solving an weighted sum linear program for finding an efficient extreme point for the (M) is a way of getting an optimal solution of the problem (P). Therefore the theorems presented in this paper provided us an easy way of solving nonconvex program (P) with a weighted sum linear program.

• The Korean Journal of Applied Statistics
• /
• v.27 no.4
• /
• pp.553-560
• /
• 2014

This paper deals with estimable functions of parameters of less than full rank linear model. In general, the parameters of an overspecified model are not uniquely determined by least squares solutions. It discusses how to formulate linear estimable functions as functions of parameters in the model and shows how to use projection matrices to check out whether a parameter or function of the pamameters is estimable. It also presents a method to form a basis set of estimable functions using linearly independent characteristic vectors generating the row space of the model matrix.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2000.04a
• /
• pp.53-56
• /
• 2000

The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector ｄ and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.

• The Journal of the Acoustical Society of Korea
• /
• v.22 no.4
• /
• pp.299-307
• /
• 2003

There have been many studies on speaker normalization which aims to minimize the effects of speaker's vocal tract length on the recognition performance of the speaker independent speech recognition system. In this paper, we propose a simple vector quantizer based linear warping speaker normalization method based on the observation that the vector quantizer can be successfully used for speaker verification. For this purpose, we firstly generate an optimal codebook which will be used as the basis of the speaker normalization, and then the warping factor of the unknown speaker will be extracted by comparing the feature vectors and the codebook. Finally, the extracted warping factor is used to linearly warp the Mel scale filter bank adopted in the course of MFCC calculation. To test the performance of the proposed method, a series of recognition experiments are conducted on discrete HMM with thirteen mono-syllabic Korean number utterances. The results showed that about 29% of word error rate can be reduced, and that the proposed warping factor extraction method is useful due to its simplicity compared to other line search warping methods.

• Geomechanics and Engineering
• /
• v.27 no.6
• /
• pp.551-560
• /
• 2021

Due to the low strength and high compressibility characteristics, the loess deposits tunnels are prone to large deformations and collapse. An accurate stability evaluation for loess deposits is of considerable significance in deformation control and safety work during tunnel construction. 37 groups of representative data based on real loess deposits cases were adopted to establish the stability evaluation model for the tunnel project in Yan'an, China. Physical and mechanical indices, including water content, cohesion, internal friction angle, elastic modulus, and poisson ratio are selected as index system on the stability level of loess. The data set is randomly divided into 80% as the training set and 20% as the test set. Firstly, principal component analysis (PCA) is used to convert the five index system to three linearly independent principal components X1, X2 and X3. Then, the principal components were used as input vectors for probabilistic neural network (PNN) to map the nonlinear relationship between the index system and stability level of loess. Furthermore, Leave-One-Out cross validation was applied for the training set to find the suitable smoothing factor. At last, the established model with the target smoothing factor 0.04 was applied for the test set, and a 100% prediction accuracy rate was obtained. This intelligent classification method for loess deposits can be easily conducted, which has wide potential applications in evaluating loess deposits.