• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.481-486
• /
• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.33 no.5
• /
• pp.279-286
• /
• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Asian-Australasian Journal of Animal Sciences
• /
• v.19 no.7
• /
• pp.915-921
• /
• 2006

Various random regression models with different order of Legendre polynomials for permanent environmental and genetic effects were constructed to predict future milk yield of Holstein cows in Korea. A total of 257,908 test-day (TD) milk yield records from a total of 28,135 cows belonging to 1,090 herds were considered for estimating (co)variance of the random covariate coefficients using an expectation-maximization REML algorithm in an animal mixed model. The variances did not change much between the models, having different order of Legendre polynomial, but a decreasing trend was observed with increase in the order of Legendre polynomial in the model. The R-squared value of the model increased and the residual variance reduced with the increase in order of Legendre polynomial in the model. Therefore, a model with $5^{th}$ order of Legendre polynomial was considered for predicting future milk yield. For predicting the future milk yield of cows, 132,771 TD records from 28,135 cows were randomly selected from the above data by way of preceding partial TD record, and then future milk yields were estimated using incomplete records from each cow randomly retained. Results suggested that we could predict the next four months milk yield with an error deviation of 4 kg. The correlation of more than 70% between predicted and observed values was estimated for the next four months milk yield. Even using only 3 TD records of some cows, the average milk yield of Korean Holstein cows would be predicted with high accuracy if compared with observed milk yield. Persistency of each cow was estimated which might be useful for selecting the cows with higher persistency. The results of the present study suggested the use of a $5^{th}$ order Legendre polynomial to predict the future milk yield of each cow.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.8
• /
• pp.664-674
• /
• 2001

In this paper, as a new category of fuzzy-neural networks architecture, we propose Fuzzy Polynomial Neural Networks (FPNN) and discuss a comprehensive design methodology related to its architecture. FPNN dwells on the ideas of fuzzy rule-based computing and neural networks. The FPNN architecture consists of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as Fuzzy Polynomial Neuron(FPN). The conclusion part of the rules, especially the regression polynomial, uses several types of high-order polynomials such as linear, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. It is worth stressing that the number of the layers and the nods in each layer of the FPNN are not predetermined, unlike in the case of the popular multilayer perceptron structure, but these are generated in a dynamic manner. With the aid of two representative time series process data, a detailed design procedure is discussed, and the stability is introduced as a measure of stability of the model for the comparative analysis of various architectures.

• Nuclear Engineering and Technology
• /
• v.28 no.1
• /
• pp.72-78
• /
• 1996

A computer program COVAFIT has been developed and applied to the evaluation of experimental cross sections for MeV energy incident particles. The program utilizes weighted least-square linear regression method with high-order polynomials derived in this study. Meeting the growing demand for the treatment of covariances in nuclear data, it deals with the variance and covariance data provided along with experimental cross sections and yields those for the evaluated ones. The evaluated results on two sets of neutron total cross section of oxygen and three sets of proton cross section for $C^{11}$ production reactions confirm the methodology formulated in and the applicability of the program.

• Proceedings of the KIEE Conference
• /
• 2003.07d
• /
• pp.2519-2521
• /
• 2003

In this paper, we propose Self-Organizing Fuzzy Polynomial Neural Networks(SOFPNN) architecture for optimal model identification and discuss a comprehensive design methodology supporting its development. It is shown that this network exhibits a dynamic structure as the number of its layers as well as the number of nodes in each layer of the SOFPNN are not predetermined (as this is the case in a popular topology of a multilayer perceptron). As the form of the conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership function are studied and the number of the premise input variables used in the rules depends on that of the inputs of its node in each layer. We introduce two kinds of SOFPNN architectures, that is, the basic and modified one with both the generic and the advanced type. The superiority and effectiveness of the proposed SOFPNN architecture is demonstrated through nonlinear function numerical example.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.915-937
• /
• 2021

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Proceedings of the KWS Conference
• /
• 2002.10a
• /
• pp.156-161
• /
• 2002

It depends on the joint configuration, dimensions and constraints on the joint whether the residual stress at the root of single-sided butt weld is tensile or not. Therefore, recommendation is generally made that high R ratio should be used in the fatigue test of this type of joint in order to prevent excessively long life caused by compressive residual stress. in this research, the residual stress profile in butt weld joint was obtained through compliance method, using successive extension of a slot and measurement of the variation of strain during the slot extension. The residual stress profile was firstly assumed to be the linear summation of Legendre polynomials up to 9th order excluding 0th and 1st order. Strain variation on the surface was measured while the slot was being extended by cutting to find out the 8 unknown coefficients of each polynomial tenn. The cut was made by the electric discharge machine. It was concluded that the residual stress near the surface stayed positive, however, it turned into the negative value as soon as it passed through 2 or 3 mm depth. Several fatigue tests were also carried out under zero stress ratio. Test results showed that fatigue life coincides well with the design cuive of butt joint in British Standards, which supports that it is tensile residual stress that exists near the weld root.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.53 no.3
• /
• pp.135-144
• /
• 2004

In this paper, we propose competitive fuzzy polynomial neurons-based advanced Self-Organizing Neural Networks(SONN) architecture for optimal model identification and discuss a comprehensive design methodology supporting its development. The proposed SONN dwells on the ideas of fuzzy rule-based computing and neural networks. And it consists of layers with activation nodes based on fuzzy inference rules and regression polynomial. Each activation node is presented as Fuzzy Polynomial Neuron(FPN) which includes either the simplified or regression polynomial fuzzy inference rules. As the form of the conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership (unction are studied and the number of the premise input variables used in the rules depends on that of the inputs of its node in each layer. We introduce two kinds of SONN architectures, that is, the basic and modified one with both the generic and the advanced type. Here the basic and modified architecture depend on the number of input variables and the order of polynomial in each layer. The number of the layers and the nodes in each layer of the SONN are not predetermined, unlike in the case of the popular multi-layer perceptron structure, but these are generated in a dynamic way. The superiority and effectiveness of the Proposed SONN architecture is demonstrated through two representative numerical examples.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.18 no.5
• /
• pp.1162-1170
• /
• 2014

In this paper, an accurate remote gaze tracking method with two cameras is presented using a modified Starburst algorithm and honography normalization. Starburst algorithm, which was originally developed for head-mounted systems, often fails in detecting accurate pupil centers in remote tracking systems with a larger field of view due to lots of noises. A region of interest area for pupil is found using template matching, and then only within this area Starburst algorithm is applied to yield pupil boundary candidate points. These are used in improved RANSAC ellipse fitting to produce the pupil center. For gaze estimation robust to head movement, an improved homography normalization using four LEDs and calibration based on high order polynomials is proposed. Finally, it is shown that accuracy and robustness of the system is improved using two cameras rather than one camera.