• Title/Summary/Keyword: sum of squares

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Application Muskingum Flood Routing Model Using Meta-Heuristic Optimization Algorithm : Harmony Search (최적화 알고리즘을 활용한 Muskingum 홍수추적 적용 : 화음탐색법)

  • Kim, Young Nam;Kim, Jin Chul;Lee, Eui Hoon
    • Proceedings of the Korea Water Resources Association Conference
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    • 2019.05a
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    • pp.388-388
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    • 2019
  • 하도 홍수추적의 방법은 크게 수리학적 방법과 수문학적 방법으로 구분할 수 있다. 수리학적 홍수추적 방법은 정확하지만 대량의 자료가 필요하고 시간이 오래 걸린다. 이와 반대로 수문학적 홍수추적 방법은 정확성은 떨어지지만 소량의 자료만 있으면 되고 시간이 적게 걸린다. 여러 수문학적 홍수추적에 관한 연구들이 있으며 대표적으로 Muskingum 방법이 있다. Muskingum 방법 중 Linear Muskingum Model(LMM)은 방정식의 구조적 한계 때문에 정확한 홍수추적이 어려웠고, 이를 개선하기위하여 Nonlinear Muskingum Model(NLMM), Nonlinear Muskingum Model Incorporation Lateral Flow(NLMM-L) 및 Advanced Nonlinear Muskingum Model Incorporating Lateral Flow(ANLMM-L)이 제안되었다. 본 연구는 수문학적 홍수추적 중 Muskingum 방법의 결과 차이가 어떤 요인으로 인해 발생하는지 검토하였다. 최적화 알고리즘으로 화음탐색법(Harmony Search, HS)을 사용하였으며 LMM, NLMM, NLMM-L 및 ANLMM-L의 매개변수를 산정하였다. 각 방법에 적용 시 HS의 매개변수에 변화를 주어 민감도 분석을 실시하였으며, 분석을 위한 홍수자료는 The Willson Flood data (1947)를 선택하였다. 오차비교방법은 Sum of Squares(SSQ), Root Mean Square Errors(RMSE), Nash-Sutcliffe Efficiency(NSE)를 비교하였다. 비교 결과 알고리즘의 성능에 의한 차이보다 홍수추적 방법의 차이가 더 영향이 큰 것으로 나타났다.

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Performance of a Bayesian Design Compared to Some Optimal Designs for Linear Calibration (선형 캘리브레이션에서 베이지안 실험계획과 기존의 최적실험계획과의 효과비교)

  • 김성철
    • The Korean Journal of Applied Statistics
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    • v.10 no.1
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    • pp.69-84
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    • 1997
  • We consider a linear calibration problem, $y_i = $$\alpha + \beta (x_i - x_0) + \epsilon_i$, $i=1, 2, {\cdot}{\cdot},n$ $y_f = \alpha + \beta (x_f - x_0) + \epsilon, $ where we observe $(x_i, y_i)$'s for the controlled calibration experiments and later we make inference about $x_f$ from a new observation $y_f$. The objective of the calibration design problem is to find the optimal design $x = (x_i, \cdots, x_n$ that gives the best estimates for $x_f$. We compare Kim(1989)'s Bayesian design which minimizes the expected value of the posterior variance of $x_f$ and some optimal designs from literature. Kim suggested the Bayesian optimal design based on the analysis of the characteristics of the expected loss function and numerical must be equal to the prior mean and that the sum of squares be as large as possible. The designs to be compared are (1) Buonaccorsi(1986)'s AV optimal design that minimizes the average asymptotic variance of the classical estimators, (2) D-optimal and A-optimal design for the linear regression model that optimize some functions of $M(x) = \sum x_i x_i'$, and (3) Hunter & Lamboy (1981)'s reference design from their paper. In order to compare the designs which are optimal in some sense, we consider two criteria. First, we compare them by the expected posterior variance criterion and secondly, we perform the Monte Carlo simulation to obtain the HPD intervals and compare the lengths of them. If the prior mean of $x_f$ is at the center of the finite design interval, then the Bayesian, AV optimal, D-optimal and A-optimal designs are indentical and they are equally weighted end-point design. However if the prior mean is not at the center, then they are not expected to be identical.In this case, we demonstrate that the almost Bayesian-optimal design was slightly better than the approximate AV optimal design. We also investigate the effects of the prior variance of the parameters and solution for the case when the number of experiments is odd.

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Design of 2D MUSIC Algorithm to Reduce Computational Burden (연산량 감소를 위한 2D MUSIC 알고리즘 설계)

  • Choi, Yun Sub;Jin, Mi Hyun;Choi, Heon Ho;Lee, Sang Jeong;Park, Chansik
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.37C no.11
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    • pp.1077-1083
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    • 2012
  • The jamming countermeasures in GNSS includes anti-jamming technique and jammer localization technique. In both techniques, direction of jamming signal is important and generally the MUSIC algorithm is used to find the direction of jamming signal. The MUSIC is super-resolution algorithm for detecting incident direction of signal. But, the search time of MUSIC algorithm is too long because all candidates of incidence angle are searched. This paper proposes the new method that has less computational burdens and therefore faster than the conventional MUSIC algorithm. The proposed method improves performance speed by reducing unnecessary calculations. In the proposed method, the cost function of conventional MUSIC algorithm is decomposed into the sum of squares and if the partial sum of cost function is larger than the minimum cost function so far, then the candidate is rejected and next candidates are searched. If the computed cost function is less than the minimum cost function so far, the minimum cost function so far is replaced with newly computed value. The performance of the proposed method was compared with the conventional MUSIC algorithm using the simulation. The accuracy of the estimaed direction of jamming signal was same as the conventional MUSIC while the search speed of the proposed method was 1.15 times faster than the conventional MUSIC.

Assessment of Autonomic Function in Functional Headache by Heart Rate Variability (심인성(心因性) 두통(頭痛)의 심박변이도(HRV) 분석에 의한 자율신경기능 평가)

  • Kim, Kyung-Ok;Song, Ji-Hyung;Kim, Geun-Woo;Koo, Byung-Soo;Shim, Sang-Min
    • Journal of Oriental Neuropsychiatry
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    • v.13 no.1
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    • pp.19-37
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    • 2002
  • Objectives : This study sought to define autonomic functional difference on heart rate variability between headache patients and normal subjects Methods : We determined, heart rate variability of 52 headache patients and 30 normal subjects by means of three time domain measures: Mean PR(mean pulse rate), SDNN(standard deviation of all normal R-R intervals), RMSSD(the square root of the mean of sum of the squares of differences between adjacent normal R-R intervals), and five frequency domain measures: TP(total power), VLF(very low frequency), LF(low frequency), HF(high frequency). Results : 1) RMSSD, TP, HF, HF Norm of HRV decreased with aging and LF Norm, LF/HF increased with aging in headache patients. 2) There was no significant differences between migraine and tention headache in any standard index of HRV, whereas, HRV of total headache patients were smaller than those of normal subjects. 3) In the gender comparison, SDNN, RMSSD, HF of tention headache patients were the smallest and then migraine patients, normal subjects in order with man, whereas, LF Norm, LF/HF of normal subjects were the smallest with man. RMSSD of migraine patients were the smallest and then tention headache patients, normal subjects in order with women. 4) In the term of history of headache patients, SDNN, RMSSD were getting lower as long term. 5) There was no significant differences of HRV in physical symptom of headache patients. Conclusions : All of these results show that standard index of HRV of headache patients were significantly different with normal subjects.

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Aspects of size effect on discrete element modeling of normal strength concrete

  • Gyurko, Zoltan;Nemes, Rita
    • Computers and Concrete
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    • v.28 no.5
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    • pp.521-532
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    • 2021
  • Present paper focuses on the modeling of size effect on the compressive strength of normal concrete with the application of Discrete Element Method (DEM). Test specimens with different size and shape were cast and uniaxial compressive strength test was performed on each sample. Five different concrete mixes were used, all belonging to a different normal strength concrete class (C20/25, C30/37, C35/45, C45/55, and C50/60). The numerical simulations were carried out by using the PFC 5 software, which applies rigid spheres and contacts between them to model the material. DEM modeling of size effect could be advantageous because the development of micro-cracks in the material can be observed and the failure mode can be visualized. The series of experiments were repeated with the model after calibration. The relationship of the parallel bond strength of the contacts and the laboratory compressive strength test was analyzed by aiming to determine a relation between the compressive strength and the bond strength of different sized models. An equation was derived based on Bazant's size effect law to estimate the parallel bond strength of differently sized specimens. The parameters of the equation were optimized based on measurement data using nonlinear least-squares method with SSE (sum of squared errors) objective function. The laboratory test results showed a good agreement with the literature data (compressive strength is decreasing with the increase of the size of the specimen regardless of the shape). The derived estimation models showed strong correlation with the measurement data. The results indicated that the size effect is stronger on concretes with lower strength class due to the higher level of inhomogeneity of the material. It was observed that size effect is more significant on cube specimens than on cylinder samples, which can be caused by the side ratios of the specimens and the size of the purely compressed zone. A limit value for the minimum size of DE model for cubes and cylinder was determined, above which the size effect on compressive strength can be neglected within the investigated size range. The relationship of model size (particle number) and computational time was analyzed and a method to decrease the computational time (number of iterations) of material genesis is proposed.

Evaluation of responses of semi-rigid frames at target displacements predicted by the nonlinear static analysis

  • Sharma, Vijay;Shrimali, Mahendra K.;Bharti, Shiv D.;Datt, Tushar K.
    • Steel and Composite Structures
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    • v.36 no.4
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    • pp.399-415
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    • 2020
  • Responses of semi-rigid frames having different degrees of semi-rigidity obtained by the nonlinear static analysis (NSA) are evaluated at specific target displacements by comparing them with those obtained by the nonlinear time-history analysis (NTHA) for scaled earthquakes. The peak ground accelerations (PGA) of the earthquakes are scaled such that the obtained peak top story displacements match with the target displacements. Three different types of earthquakes are considered, namely, far-field and near-field earthquakes with directivity and fling-step effects. In order to make the study a comprehensive one, three degrees of semi-rigidity (one fully rigid and the other two semi-rigid), and two frames having different heights are considered. An ensemble of five-time histories of ground motion is included in each type of earthquake. A large number of responses are considered in the study. They include the peak top-story displacement, maximum inter-story drift ratio, peak base shear, total number of plastic hinges, and square root of sum of the squares (SRSS) of the maximum plastic hinge rotations. Results of the study indicate that the nonlinear static analysis provides a fairly good estimate of the peak values of top-story displacements, inter-story drift ratio (for shorter frame), peak base shear and number of plastic hinges; however, the SRSS of maximum plastic hinge rotations in semi-rigid frames are considerably more in the nonlinear static analysis as compared to the nonlinear time history analysis.

Modelling Stem Diameter Variability in Pinus caribaea (Morelet) Plantations in South West Nigeria

  • Adesoye, Peter Oluremi
    • Journal of Forest and Environmental Science
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    • v.32 no.3
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    • pp.280-290
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    • 2016
  • Stem diameter variability is an essential inventory result that provides useful information in forest management decisions. Little has been done to explore the modelling potentials of standard deviation (SDD) and coefficient of variation (CVD) of diameter at breast height (dbh). This study, therefore, was aimed at developing and testing models for predicting SDD and CVD in stands of Pinus caribaea Morelet (pine) in south west Nigeria. Sixty temporary sample plots of size $20m{\times}20m$, ranging between 15 and 37 years were sampled, covering the entire range of pine in south west Nigeria. The dbh (cm), total and merchantable heights (m), number of stems and age of trees were measured within each plot. Basal area ($m^2$), site index (m), relative spacing and percentile positions of dbh at $24^{th}$, $63^{rd}$, $76^{th}$ and $93^{rd}$ (i.e. $P_{24}$, $P_{63}$, $P_{76}$ and $P_{93}$) were computed from measured variables for each plot. Linear mixed model (LMM) was used to test the effects of locations (fixed) and plots (random). Six candidate models (3 for SDD and 3 for CVD), using three categories of explanatory variables (i.e. (i) only stand size measures, (ii) distribution measures, and (iii) combination of i and ii). The best model was chosen based on smaller relative standard error (RSE), prediction residual sum of squares (PRESS), corrected Akaike Information Criterion ($AIC_c$) and larger coefficient of determination ($R^2$). The results of the LMM indicated that location and plot effects were not significant. The CVD and SDD models having only measures of percentiles (i.e. $P_{24}$ and $P_{93}$) as predictors produced better predictions than others. However, CVD model produced the overall best predictions, because of the lower RSE and stability in measuring variability across different stand developments. The results demonstrate the potentials of CVD in modelling stem diameter variability in relationship with percentiles variables.

Effect of Acupuncture at the Field of the Auricular Branch of the Vagus Nerve on Autonomic Nervous System Change (미주신경 감각분지 분포영역의 자침이 자율신경 변화에 미치는 영향)

  • An, Sunjoo;Keum, Dongho
    • Journal of Korean Medicine Rehabilitation
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    • v.31 no.2
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    • pp.81-97
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    • 2021
  • Objectives This study was designed to identify the changes of autonomic nervous system (ANS) which was induced by acupuncture at the field of the auricular branch of the vagus nerve. Methods 30 healthy adults were selected and classified into two groups; experimental group, control group. After providing mental stress, acupuncture was applied at external ear in experimental group and no treatment executed in control group. The evaluation of ANS function was measured by heart rate variability (HRV). We statically analyzed the difference of HRV parameters which include mean heart rate (MHRT), standard deviation of all N-N intervals (SDNN), square root of the mean of the sum of the squares of differences between adjacent N-N intervals (RMSSD), total power (TP), low frequency power (LF), high frequency power (HF), LF/HF ratio. Results All subjects showed significant increase in SDNN, LF after stress stimulation (p<0.05). Immediately after intervention, MHRT was significantly decreased (p<0.001) and RMSSD, HF were significantly increased in experimental group (p<0.05). After the end of intervention, SDNN, HF, RMSSD, TP, LF were significantly increased in experimental group (p<0.01, p<0.05). And when comparing baseline HRV, SDNN, LF were significantly increased in control group (p<0.01) and SDNN, RMSSD, TP, LF were significantly increased in experimental group (p<0.05). In the subgroup analysis, normal balance of ANS group showed significant increase in TP, LF, SDNN, HF (p<0.01, p<0.05). Conclusions We suggested that acupuncture at external ear, region of the vagus nerve distribution could increase parasympathetic activity and cause changes and reregulation of the ANS.

Statistical Methods for Multivariate Missing Data in Health Survey Research (보건조사연구에서 다변량결측치가 내포된 자료를 효율적으로 분석하기 위한 통계학적 방법)

  • Kim, Dong-Kee;Park, Eun-Cheol;Sohn, Myong-Sei;Kim, Han-Joong;Park, Hyung-Uk;Ahn, Chae-Hyung;Lim, Jong-Gun;Song, Ki-Jun
    • Journal of Preventive Medicine and Public Health
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    • v.31 no.4 s.63
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    • pp.875-884
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    • 1998
  • Missing observations are common in medical research and health survey research. Several statistical methods to handle the missing data problem have been proposed. The EM algorithm (Expectation-Maximization algorithm) is one of the ways of efficiently handling the missing data problem based on sufficient statistics. In this paper, we developed statistical models and methods for survey data with multivariate missing observations. Especially, we adopted the EM algorithm to handle the multivariate missing observations. We assume that the multivariate observations follow a multivariate normal distribution, where the mean vector and the covariance matrix are primarily of interest. We applied the proposed statistical method to analyze data from a health survey. The data set we used came from a physician survey on Resource-Based Relative Value Scale(RBRVS). In addition to the EM algorithm, we applied the complete case analysis, which uses only completely observed cases, and the available case analysis, which utilizes all available information. The residual and normal probability plots were evaluated to access the assumption of normality. We found that the residual sum of squares from the EM algorithm was smaller than those of the complete-case and the available-case analyses.

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Investigating the Effect of Planting Density on Parameter Estimation of Stand Growth Models (식재(植栽) 밀도(密度)가 임분생장(林分生長)모델 모수(母數) 추정(推定)에 미치는 효과(效果)에 관(關)한 연구(硏究))

  • Li, Fengri;Kwon, Soonduk;Chung, Joosang
    • Journal of Korean Society of Forest Science
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    • v.88 no.4
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    • pp.446-453
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    • 1999
  • In this study, the effects of stand planting density on parameters of stand height and basal area growth models were investigated. We used the Korf equation as the base model in estimating the parameters of the growth models for cryptomeria plantation forest stands. Then, in order to investigate the effects of the change in plantation density on the parameter estimates, the "extra sums of square" principle, which provided a reasonable statistical procedure for a performance test, was used. The results of the test coincide with the understandings that stand height growth is not affected significantly by the planting density and the growth curves of stand basal area approaches a common asymptote regardless of the stand density for a given site. However, the shapes of the basal area growth curves were affected significantly by the planting density. Based on the results of the test, we developed a basal area growth model to account for the effects of initial planting density in cryptomeria plantation forest stands.

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