• Title/Summary/Keyword: Shape Function

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Classification of algae in watersheds using elastic shape

  • Tae-Young Heo;Jaehoon Kim;Min Ho Cho
    • Communications for Statistical Applications and Methods
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    • v.31 no.3
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    • pp.309-322
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    • 2024
  • Identifying algae in water is important for managing algal blooms which have great impact on drinking water supply systems. There have been various microscopic approaches developed for algae classification. Many of them are based on the morphological features of algae. However, there have seldom been mathematical frameworks for comparing the shape of algae, represented as a planar continuous curve obtained from an image. In this work, we describe a recent framework for computing shape distance between two different algae based on the elastic metric and a novel functional representation called the square root velocity function (SRVF). We further introduce statistical procedures for multiple shapes of algae including computing the sample mean, the sample covariance, and performing the principal component analysis (PCA). Based on the shape distance, we classify six algal species in watersheds experiencing algal blooms, including three cyanobacteria (Microcystis, Oscillatoria, and Anabaena), two diatoms (Fragilaria and Synedra), and one green algae (Pediastrum). We provide and compare the classification performance of various distance-based and model-based methods. We additionally compare elastic shape distance to non-elastic distance using the nearest neighbor classifiers.

Dynamic analysis of non-symmetric FG cylindrical shell under shock loading by using MLPG method

  • Ferezghi, Yaser Sadeghi;Sohrabi, Mohamad R.;MosaviNezhad, Seyed M.
    • Structural Engineering and Mechanics
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    • v.67 no.6
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    • pp.659-669
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    • 2018
  • The Dynamic equations in the polar coordinates are drawn out using the MLPG method for the non-symmetric FG cylindrical shell. To simulate the mechanical properties of FGM, the nonlinear volume fractions for radial direction are used. The shape function applied in this paper is a form of the radial basis functions, by using this function all the requirements for an effective and suitable shape function are established. Hence in this study, the multiquadrics (MQ) radial basis functions are exploited as the shape function governing the problem. The MLPG method is combined with the the Newmark time approximation scheme to solve dynamic equations in the time domain. The obtained results by the MLPG method to be verified are compared with the analytical solution and the FEM. The obtained results through the MLPG method show a good agreement in comparison to other results and the MLPG method has high accuracy for dynamic analysis of the non-symmetric FG cylindrical shell. To demonstrate the capability of the present method to dynamic analysis of the non-symmetric FG cylindrical shell, it is analyzed dynamically with different volume fraction exponents under harmonic and rectangular shock loading. The present method shows high accuracy, efficiency and capability to dynamic analysis of the non-symmetric FG cylindrical shell with nonlinear grading patterns.

A Study on the Prediction of Fatigue Life by use of Probability Density Function (확률밀도함수를 이용한 피로균열 발생수명 예측에 관한 연구)

  • 김종호
    • Journal of Advanced Marine Engineering and Technology
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    • v.23 no.4
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    • pp.453-461
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    • 1999
  • The estimation of fatigue life at the design stage is very important in order to arrive at feasible and cost effective solutions considering the total lifetime of the structure and machinery compo-nents. In this study the practical procedure of prediction of fatigue life by use of cumulative damage factors based on Miner-Palmgren hypothesis and probability density function is shown with a $135,000m^3$ LNG tank being used as an example. In particular the parameters of Weibull distribution taht determine the stress spectrum are dis-cussed. At the end some of uncertainties associated with fatigue life prediction are discussed. The main results obtained from this study are as follows: 1. The practical procedure of prediction of fatigue life by use of cumulative damage factors expressed in combination of probability density function and S-N data is proposed. 2. The calculated fatigue life is influenced by the shape parameter and stress block. The conser-vative fatigue design can be achieved when using higher value of shape parameter and the stress blocks divded into more stress blocks.

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Mutual interference suppression of the sinusoidal frequency modulated pulse using SHAPE algorithm (SHAPE 알고리즘을 이용한 사인파 주파수 변조 펄스의 상호간섭 억제)

  • Kim, Guenhwan;Lee, Donghwa
    • Journal of Korea Society of Industrial Information Systems
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    • v.27 no.5
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    • pp.49-59
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    • 2022
  • The SHAPE algorithm has the advantage of being able to shape the pulse spectrum as desired and design it not to distort other characteristics, so it was used in the active sonar pulse design. In this paper, we propose a pulse design using the SHAPE algorithm for a multi-static sonar system to reduce the cross-correlation between frequency-adjacent pulses and prevent the performance degradation of the pulses themselves. The boundary function of the SHAPE algorithm is set to be limited to the pulse bandwidth. As a result of applying the proposed design method to the sinusoidal frequency modulated pulse, the peak cross-correlation level (PCCL), which means the degree of cross-correlation, was reduced by 44.23 dB. Although the PCCL decreased by several tens of dB, no significant change in the ambiguity function was observed, and the integrated sidelobe level (ISL), which means the average value of the side lobe, increased by 11.64 dB.

NEW SELECTION APPROACH FOR RESOLUTION AND BASIS FUNCTIONS IN WAVELET REGRESSION

  • Park, Chun Gun
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.289-305
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    • 2014
  • In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.

Crack Analysis of Creep Material Containing Rigid Inclusion with Line Crack Shape (직선 균열 강체 함유물을 내포하는 크?재료의 균열 해석)

  • 이강용;김종성
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.7
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    • pp.91-97
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    • 1998
  • The analysis model is the infinite body consisted of power law creep material containing a rigid inclusion with line crack shape subjected to the arbitrarily directional stress on an infinite boundary. The crack analysis is performed using the complex pseudo-stress function. The strain rate intensity factor is determined in the closed form as new fracture mechanics parmeter which represents the magnitudes of stress and strain rate near the tip in power law creep material.

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Vibration Analysis of Micro Speaker Diaphragm (마이크로 스피커 다이어프램의 진동해석)

  • Hong, D.K.;Woo, B.C.;Ahn, C.W.;Han, G.J.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.551-554
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    • 2005
  • This study uses a characteristic function to explain correlations between the objective function and design variables. Analysis of means and table of orthogonal array were carried out. The change of shape of diaphragm, thickness of diaphragm and voice coil weight based on the table of orthogonal array is made. Therefore this study carried to decide shape of diaphragm, voice coil weight and thickness of diaphragm for minimizing 1st natural frequency and maximizing 2nd natural frequency of diaphragm using design of experiments and characteristic function with constraints. we showed improved design factors that minimized 1st natural frequency and maximized 2nd natural frequency of diaphragm.

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A Study on the Shape Design of Micro Speaker Diaphragm (마이크로 스피커 다이아프램의 형상설계에 관한 연구)

  • Hong, Do-Kwa;Woo, Byung-Chul;Kim, Dong-Young;Ahn, Chan-Woo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.7 s.100
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    • pp.775-780
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    • 2005
  • This study uses a characteristic function to explain correlations between the objective function and design variables. Analysis of means and table of orthogonal array were carried out. The change of shape of diaphragm, thickness of diaphragm and voice coil weight based on the table of orthogonal array Is made. Therefore this study carried to decide design variables for minimizing 1st natural frequency and maximizing 2nd natural frequency of diaphragm using design of experiments and characteristic function with constraints. we showed improved design variables.

AN AVERAGE OF SURFACES AS FUNCTIONS IN THE TWO-PARAMETER WIENER SPACE FOR A PROBABILISTIC 3D SHAPE MODEL

  • Kim, Jeong-Gyoo
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.751-762
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    • 2020
  • We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.