• Title, Summary, Keyword: Higher order polynomial

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Solution of randomly excited stochastic differential equations with stochastic operator using spectral stochastic finite element method (SSFEM)

  • Hussein, A.;El-Tawil, M.;El-Tahan, W.;Mahmoud, A.A.
    • Structural Engineering and Mechanics
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    • v.28 no.2
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    • pp.129-152
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    • 2008
  • This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

Application of Multi-Attribute Utility Analysis for the Decision Support of Countermeasures in Early Phase of a Nuclear Emergency (원자력 사고시 초기 비상대응 결정지원을 위한 다속성 효용 분석법의 적용)

  • Hwang, Won-Tae;Kim, Eun-Han;Suh, Kyung-Suk;Jeong, Hyo-Joon;Han, Moon-Hee;Lee, Chang-Woo
    • Journal of Radiation Protection and Research
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    • v.29 no.1
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    • pp.65-71
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    • 2004
  • A multi-attribute utility analysis was investigated as a tool for the decision support of countermeasures in early phase of a nuclear accident. The utility function of attributes was assumed to be the second order polynomial expressions, and the weighting constant of attributes was determined using a swing weighting method. Because the main objective of this study focuses on the applicability of a multi-attribute utility analysis as a tool for the decision support of countermeasures in early phase of a nuclear accident, less quantifiable attributes were not included due to lack of information. In postulated accidental scenarios for the application of the designed methodology, the variation of the numerical values of total utility for the considered actions, e.g. sheltering, evacuation and no action, was investigated according to the variation of attributes. As a result, it was shown that the numerical values of total utility for the actions are distinctly different depending on the exposure dose and monetary value of dose. As increasing in both attributes, the rank of the numerical values of total utility increased for evacuation, which is more extreme action than for sheltering, while that of no action decreased. As expected probability of high dose is higher, the break-even values for the monetary value of dose, which are the monetary value of dose when the ranking of actions is changed, were lower. In audition, as aversion psychology for dose is higher, the break-even values for dose were lower.

Models Describing Growth Characteristics of Holstein Dairy Cows Raised in Korea

  • Vijayakumar, Mayakrishnan;Choy, Yun-Ho;Kim, Tae-Il;Lim, Dong-Hyun;Park, Seong-Min;Alam, Mahboob;Choi, Hee-Chul;Ki, Kwang-Seok;Lee, Hyun-Jeong
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.40 no.3
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    • pp.167-176
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    • 2020
  • The objective of the present study was to determine the best model to describe and quantify the changes in live body weight, height at withers, height at rump, body length and chest girth of Holstein cows raised under Korean feeding conditions for 50 months. The five standard growth models namely polynomial linear regression models, regression of growth variables on the first and second-order of ages in days (model 1) and regression of growth variables on age covariates from first to the third-order (model 2) as well as non-linear models were fitted and evaluated for representing growth pattern of Holstein cows raised in Korean feeding circumstances. Nonlinear models fitted were three exponential growth curve models; Brody, Gompertz, and von Bertalanffy functional models. For this purpose, a total of 22 Holstein cows raised in Korea used in the period from April 2016 to May 2020. Each model fitted to monthly growth curve records of dairy cows by using PROC NLIN procedure in SAS program. On the basis of the results, nonlinear models showed the lower root mean square of error (RMSE) for live body weight, height at withers, height at rump, body length and chest girth (12.22, 1.95, 1.55, 4.04, 2.06) with higher correlation coefficiency (R2) values for live body weight, height at withers, height at rump, body length and chest girth (0.99, 0.99, 0.99, 1.00, 1.00). Overall, the evaluation of the different growth models indicated that the Gompertz model used in the study seemed to be the most appropriate one for standard growth of Holstein cows raised under Korean feeding system.

The Improvement of Incompatible Sliding Contact Problem Using Mesh Refinement And Its Application to Railway Skewed Culvert Problem (요소 세분화를 이용한 비적합 미끄러지는 접촉문제의 개선과 철도 사각암거 문제에의 적용)

  • Choi, Chan-Yong;Yeo, In-Ho;Chung, Keun-Young;Lee, Gye-Hee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.30 no.5
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    • pp.435-444
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    • 2017
  • The vehicle-track structure dynamic interaction analysis problem can be treated as sliding contact problem, and it is assumed that vehicle run at a constant speed over a rail modeled as beam elements. Unfortunately, Salome-Meca can not satisfy the compatibility condition for the beam master elements, which are consist of the elements with higher order polynomial shape function, in sliding contact problem. In this study, it is suggested to use more finer beam master element mesh as the remedy for incompatibility in sliding contact problem, and the accuracy of the solution is secured. For this, the effect of beam element mesh refinement consisting runway is analysed through simple examples, and the applicability to the dynamic interaction analysis is evaluated. Finally, the dynamic interaction analysis of railway skewed culvert transition problem is carried out to evaluate the effect of supporting stiffness due to backfill pattern changes and track irregularity due to uneven subgrade settlement.

Calculates of GPS Satellite Coordinates Using Rapid and Ultra-Rapid Precise Ephemerides (신속정밀제도력과 초신속정밀궤도력을 이용한 GPS 위성좌표 계산)

  • Park Joung Hyun;Lee Young Wook;Lee Eun Soo
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.22 no.4
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    • pp.383-390
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    • 2004
  • IGS provides so accute a final precise ephmerides which is offered in the 13rd, and it also offers a rapid precise ephmerides for more prompt application and an ultra-rapid precise ephmerides for real-time application. The purpose of this study is to analyze the accuracy of a rapid precise ephemerides and an ultra-rapid precise ephemerides based on a final precise ephmerides and determine the degree of the Lagrange Interpolation which needs to decide the location of a satellite. As the result of this study, the root mean square error of x,y,z coordinates of a rapid precise ephemerides was $\pm$0.0l6m or so, and the root mean square error of an observed ultra-rapid precise ephemerides was approximately $\pm$0.024m. The root mean square error of an ultra-rapid precise ephemerides predicted for 24 hours was $\pm$0.07m or so and the one of an ultra-rapid precise ephemerides predicted for 6 hours was $\pm$0.04m or so. Therefore, I could figure out that it had higher accuracy than a broadcast ephemerides. Also, in case that the location of a satellite was calculated with the method of the Lagrange Interpolation, it was confirmed that using the 9th order polynomial was efficient.

Efficient Mining of Frequent Subgraph with Connectivity Constraint

  • Moon, Hyun-S.;Lee, Kwang-H.;Lee, Do-Heon
    • Proceedings of the Korean Society for Bioinformatics Conference
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    • pp.267-271
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    • 2005
  • The goal of data mining is to extract new and useful knowledge from large scale datasets. As the amount of available data grows explosively, it became vitally important to develop faster data mining algorithms for various types of data. Recently, an interest in developing data mining algorithms that operate on graphs has been increased. Especially, mining frequent patterns from structured data such as graphs has been concerned by many research groups. A graph is a highly adaptable representation scheme that used in many domains including chemistry, bioinformatics and physics. For example, the chemical structure of a given substance can be modelled by an undirected labelled graph in which each node corresponds to an atom and each edge corresponds to a chemical bond between atoms. Internet can also be modelled as a directed graph in which each node corresponds to an web site and each edge corresponds to a hypertext link between web sites. Notably in bioinformatics area, various kinds of newly discovered data such as gene regulation networks or protein interaction networks could be modelled as graphs. There have been a number of attempts to find useful knowledge from these graph structured data. One of the most powerful analysis tool for graph structured data is frequent subgraph analysis. Recurring patterns in graph data can provide incomparable insights into that graph data. However, to find recurring subgraphs is extremely expensive in computational side. At the core of the problem, there are two computationally challenging problems. 1) Subgraph isomorphism and 2) Enumeration of subgraphs. Problems related to the former are subgraph isomorphism problem (Is graph A contains graph B?) and graph isomorphism problem(Are two graphs A and B the same or not?). Even these simplified versions of the subgraph mining problem are known to be NP-complete or Polymorphism-complete and no polynomial time algorithm has been existed so far. The later is also a difficult problem. We should generate all of 2$^n$ subgraphs if there is no constraint where n is the number of vertices of the input graph. In order to find frequent subgraphs from larger graph database, it is essential to give appropriate constraint to the subgraphs to find. Most of the current approaches are focus on the frequencies of a subgraph: the higher the frequency of a graph is, the more attentions should be given to that graph. Recently, several algorithms which use level by level approaches to find frequent subgraphs have been developed. Some of the recently emerging applications suggest that other constraints such as connectivity also could be useful in mining subgraphs : more strongly connected parts of a graph are more informative. If we restrict the set of subgraphs to mine to more strongly connected parts, its computational complexity could be decreased significantly. In this paper, we present an efficient algorithm to mine frequent subgraphs that are more strongly connected. Experimental study shows that the algorithm is scaling to larger graphs which have more than ten thousand vertices.

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Studies on the Time Distribution of Heavy Storms (暴雨의 時間的 分布에 關한 硏究)

  • Lee, Keun-Hoo
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.26 no.2
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    • pp.69-84
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    • 1984
  • This study was carried out to investigate the time distribution of single storms and to establish the model of storm patterns in korea. Rainfall recording charts collected from 42 metheorological stations covering the Korean peninsula were analyzed. A single storm was defined as a rain period seperated from preceding and succeeding rainfall by 6 hours and more. Among the defined single storms, 1199 storms exceeding total rainfall of 80 mm were qualified for the study. Storm patterns were cklassified by quartile classification method and the relationship between cummulative percent of rainfalls and cummulative storm time was established for each quartile storm group. Time distribution models for each stations were prepared through the various analytical and inferential procedures. Obtained results are summarized as follows: 1. The percentile frequency of quartile storms for the first to the fourth quartile were 22.0%, 26.5%, 28.9% and 22.6%, respectively. The large variation of percentile frequency was show between the same quartile storms. The advanced type storm pattern was predominant in the west coastal type storm patterns predominantly when compared to the single storms with small total rainfalls. 3. The single storms with long storm durations tended to show delayed type storm patterns predominantly when compared to the single storms with short storm durations. 4. The percentile time distribution of quartile storms for 42 rin gaging stations was estimated. Large variations were observed between the percentiles of time distributions of different stations. 5. No significant differences were generally found between the time distribution of rainfalls with greater total rainfall and with less total rainfall. This fact suggests that the size of the total rainfall of single storms was not the main factor affecting the time distribution of heavy storms. 6. Also, no significant difference were found between the time distribution of rainfalls with long duration and with short duration. The fact indicates that the storm duration was no the main factor affecting the time distribution of heavy storms. 7. In Korea, among all single storms, 39.0% show 80 to 100mm of total rainfall which stands for the mode of the frequency distribution of total rainfalls. The median value of rainfalls for all single storms from the 42 stations was 108mm. The shape of the frequency distribution of total rainfalls showed right skewed features. No significant differences were shown in the shape of distribution histograms for total rainfall of quartile storms. The mode of rainfalls for the advanced type quartile storms was 80~100mm and their frequencies were 39~43% for respective quartiles. For the delayed type quartile storms, the mode was 80~100mm and their frequencies were 36!38%. 8. In Korea, 29% of all single storms show 720 to 1080 minutes of storm durations which was the highest frequency in the frequency distribution of storm durations. The median of the storm duration for all single storms form 42 stations was 1026 minutes. The shape of the frequency distribution was right skewed feature. For the advanced type storms, the higher frequency of occurrence was shown by the single storms with short durations, whereas for the delayed type quartile storms, the higher frequency was shown gy the long duration single storms. 9. The total rainfall of single storms was positively correlated to storm durations in all the stations throughout the nation. This fact was also true for most of the quartile storms. 10. The third order polynomial regression models were established for estimating the time distribution of quartile storms at different stations. The model test by relative error method resulted good agreements between estimated and observed values with the relative error of less than 0.10 in average.

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Effects of the Dietary Protein and Energy Levels on Growth in Fat Cod (Hexagrammos otakii Jordan et Starks) (사료의 단백질 및 에너지 함량이 쥐노래미 성장에 미치는 영향)

  • LEE Jong Kwan;LEE Sang-Min
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.29 no.4
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    • pp.464-473
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    • 1996
  • Two-month feeding experiment was conducted to investigate the optimum dietary protein level and energy to protein ratio in fat cod (Hexagrammos otakii Jordan et STARKS). The fish averaging 29 g were fed with one of the isocaloric diets containing 30, 40, 50 or $60\%$ of protein, or with one of the isoproteic diets containing 9, 10, 11 or 12 of available energy/protein (E/P) ratio. Weight gain and feed efficiency increased significantly with dietary protein level up to $50\%$, then decreased with $60\%$ protein diet (P<0.05). Daily protein intake increased significantly with dietary protein level, whereas protein efficiency ratio decreased with dietary protein level (P<0.05). Second order polynomial regression analyses of percent weight gain and daily protein intake may indicate that the adequate dietary protein level is $45\%$ and daily protein requirement per 100g fish is 1.5g for maximal growth. Weight gain, feed efficiency and protein efficiency from fish led the diet containing 12 of E/P ratio were significantly higher than those from fish fed the other diets (P<0.05). Daily feed or protein intake from fish fed the diet containing 12 of E/P ratio was significantly lower than those from fish fed the other diets (P<0.05). Daily lipid intake increased significantly with dietary E/P ratio (P<0.05).

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