모수 복원 상황에서 MIRT 척도연계 방법의 기능 진단

김성훈(Seong hoon Kim),민경석(Kyung Seok Min),강동희(Dong hee Kang) 한국교육평가학회 2016 교육평가연구 Vol.29 No.4

다차원 문항반응이론(MIRT) 척도연계 방법은, 공통 문항 혹은 공통 피험자에 기초하여, 두 다차원 능력척도를 연계하는 함수의 회전행렬과 위치벡터를 추정한다. MIRT 연구에서 척도연계의 필요성은 임의의 “0-I” 능력척도 상에서 추정된 문항모수와 기저 능력분포를 목표하는 모집단 능력척도 상에서 복원하고자 할 때 전형적으로 발생한다. 본 연구는 공통-문항 기반 MIRT 척도연계를 위해 제안된 세 가지 방법, Direct 방법, TCF 방법 및 LLM방법의 특성과 기능을 모수 복원 상황을 전제로 하여 비교 분석하고자 하였다. 세 척도연계 방법의 특성과 기능이 뚜렷이 드러나도록 모집단 능력분포의 평균, 분산 및 공분산을 특정한 값으로 설정하여 모의실험을 실시하였다. 주요 결과는 다음과 같았다. 첫째, Direct, TCF 및 LLM 방법은 모두 비대칭적으로 척도연계를 수행하였다. 둘째, Direct 및 TCF 방법은 사각(oblique) 회전행렬을 추정함으로써 목표 능력척도 상에서 문항모수 및 모집단 능력분포를 적절히 추정한 반면, LLM 방법은 준-직교(pseudo-orthogonal) 회전행렬을 추정함으로써 모집단 능력 변수들 간의 상관이 0에 가까운 경우를 제외하고 문항모수와 능력분포를 편향 추정하였다. 셋째, 세 척도연계 방법 모두는 연계하고자 하는 두 능력척도 간 능력차원의 연결 문제를 완전히 수리적으로 해결하며 따라서 한 능력척도 상에서의 능력차원의 순서가 다른 능력척도 상에서 바뀔 수 있었다. 이러한 주요 결과와 관련하여, 세 척도연계 방법의 실제 사용상의 유의점과 개선 방향에 대해 논의하였다. In multidimensional item response theory (MIRT), scale linking methods, developed under the anchor-item or common-examinee design, attempt to estimate the rotation matrix and location vector of the linking function that connects two multidimensional ability scales (i.e., coordinate systems). In MIRT applications, the need for scale linking typically occurs when the recovery of parameters is being investigated and the parameters that are expressed on an arbitrary “0-I” scale should be placed onto the true simulation scale. Assuming such a parameter-recovery situation, the present study investigated the characteristics and performances of the three “common-item” based MIRT linking methods, Direct, TCF, and LLM. A critical study factor was the population two-dimensional ability distribution, whose means, variances and covariance were varied so that the characteristics and performances of the three methods might be clearly revealed. The major results were as follows. First, all three methods performed “non-symmetric” scale linking. Second, in the recovery of item parameters and ability distributions on the simulation scale, the Direct and TCF methods performed well because they estimated “oblique” rotation matrices. On the other hand, the LLM method recovered poorly the parameters except when the population covariance was zero, because it estimated “pseudo-orthogonal” rotation matrices. Third, it was observed for all the linking methods that the dimension-matching between two multidimensional scales was determined entirely by mathematics and thus the order of dimensions in the ability scale prior to scale linking could be changed after scale linking.

Analysis of Scaling Parameters of the Batch Unscented Transformation for Precision Orbit Determination using Satellite Laser Ranging Data

김재혁,박상영,김영록,박은서,조중현,임형철,박장현,박종욱 한국우주과학회 2011 Journal of Astronomy and Space Sciences Vol.28 No.3

The current study analyzes the effects of the scaling parameters of the batch unscented transformation on precision satellite orbit determination. Satellite laser ranging (SLR) data are used in the orbit determination algorithm, which consists of dynamics model, observation model and filtering algorithm mposed of the batch unscented transformation. TOPEX/Poseidon SLR data are used by utilizing the normal point (NP) data observed from ground station. The filtering algorithm includes a repeated series of processes to determine the appropriate scaling parameters for the batch unscented transformation. To determine appropriate scaling parameters, general ranges of the scaling parameters of α, β, κ, λ are established. Depending on the range settings, each parameter was assigned to the filtering algorithm at regular intervals. Appropriate scaling parameters are determined for observation data obtained from several observatories, by analyzing the relationship between tuning properties of the scaling parameters and estimated orbit precision. The orbit determination of satellite using the batch unscented transformation can achieve levels of accuracy within several tens of cm with the appropriate scaling parameters. The analyses in the present study give insights into the roles of scaling parameters in the batch unscented transformation method.

Determination of thermo-elastic parameters for dynamical modeling of 2.5D C/SiC braided composites

Sufang Chen,Qingguo Fei,Dong Jiang,Zhifu Cao 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.1

An approach on determining elastic parameters and Coefficient of thermal expansion (CTE) of a 2.5-dimensional (2.5D) braided composites is proposed in this paper, by adopting mesoscopic mechanics integrated Finite element (FE) modeling. According to the geometric features of meso-structure, Representative volume cell (RVC) models of composite for predicting thermo-elastic parameters are established. On the basis of the models, homogenized parameter prediction is carried out in three steps: Firstly, equivalent elastic properties is predicted subject to periodic displacement boundary conditions; secondly, the equivalent thermal modulus is determined by using the periodic non-adiabatic temperature boundary conditions; thirdly, using the obtained elastic parameters and thermal modulus to calculate the equivalent coefficient of thermal expansion. A multiscale finite element analysis is conducted: The thermo-elastic parameters of yarn is calculated using the RVC model; subsequently, the equivalent parameters of the yarn are substituted into the RVC of 2.5D braided C/SiC composites, to predict the thermo-elastic parameters. Results indicate that the CTE determined by homogenized parameter prediction of 2.5D C/SiC composites shows good agreements with the experimental results. At last, the refined FE model and the equivalent homogeneous model are employed to verify the effectiveness of the predicted parameters in terms of effective modeling. After the comparative analysis on thermal modal data between refined model and equivalent model, the acquired results demonstrate the effectiveness of the proposed method in determining thermo-elastic parameters.

Evaluation of Thermal-hydraulic and Scaling Characteristics for Storage Vault

Seung-hwan Yu,Kyung-sik Bang,Donghee Kim,Kwan-Soo Lee 한국방사성폐기물학회 2015 방사성폐기물학회지 Vol.13 No.2

본 연구에서는 저장볼트(storage vault)의 실험을 위하여 1/4 축소모델 내 튜브의 적정 발열량을 선정하고자 상사해석을 수행하였다. 저장볼트에 대한 열 및 유동 해석을 우선적으로 수행하였고, 크기를 1/4로 축소한 저장볼트에 대하여 동일한 전산해석을 수행하였다. 전산해석 결과를 바탕으로, 제안된 무차원수를 비교하 여 원형모델과 온도분포와 유동분포가 유사하게 되는 발열량을 선정하였다. 1/4 축소 저장볼트 내 튜브의 열유속이 1.3배일 때, 원형 저장볼트와 1/4 축소 저장볼트의 온도장 및 유동장이 상사되었다. 이 때, 1/4 축 소 저장볼트 내 발열량은 약 190 W이다. This research studied a scaling analysis for the selection of proper heat generation at tube for 1/4-scale storage vaults. First of all, the temperature field and velocity distribution of an original scale storage vault were analyzed and then numerical analysis of a 1/4-scale storage vault was performed to compare each model. The proper heat generation for a 1/4-scale storage vault, at which the temperature and velocity field of a 1/4-scale storage vault showed the best agreement with that of the original storage vault, was evaluated with proposed dimensionless parameters. The behavior of temperature and velocity of fluid in the 1/4-scale case were most similar to those of the original scale, using a heat flux 1.3 times higher than that seen in the original scale, which was approximately 190 W.

다양한 규모매개변수를 이용한 비정상성 Gumbel 모형의 비교 연구

장한진,김수영,허준행 한국수자원학회 2015 한국수자원학회논문집 Vol.48 No.5

비정상성 빈도해석을 위해 개발된 비정상성 확률분포 모형들은 대부분 매개변수에 시간항을 포함하는 형태로 정의된다. 이 중에서도 우리나라에 널리 사용되고 있는 Gumbel 모형에 대해 살펴보면, 비정상성 Gumbel 모형의 위치 및 규모매개변수 는 시간에 대해 선형(linear) 및 지수(exponential) 함수의 관계를 보이는 형태로 가정한다. 규모매개변수의 지수함수의 형태는 음(-)의 값이 추정되는 것을 방지하기 위해 제안되어 널리 사용되고 있으나 이로 인해 확률수문량이 과다산정되는 문제가 발생하기도 한다. 본 연구에서는 이러한 문제를 해결하기 위해 비정상성 Gumbel 모형의 규모매개변수의 다양한 형태를 비교하고자 한다. 이를 위해 비정상성 Gumbel 모형의 규모매개변수를 지수함수, 선형, 로그 형태로 가정하여 비교하 였다. 각 모형의 매개변수의 추정은 최우도법을 적용하였고 규모매개변수의 형태별 정확도 비교를 위해 모의실험을 수행하 였으며, 실제 자료에 대한 적용으로 자료기간 30년 이상을 보유하면서 경향성을 가지는 강우량 자료들을 대상으로 비정상성 빈도해석을 수행하였다. 그 결과, 지수함수 형태를 가정한 규모매개변수를 가지는 비정상성 Gumbel 모형이 가장 작은 오차를 가지는 것으로 분석되었다. Most nonstationary frequency models are defined as the probability models containing the time-dependent parameters. For frequency analysis of annual maximum rainfall data, the Gumbel distribution is generally recommended in Korea. For the nonstationary Gumbel models, the time-dependent location and scale parameters are defined as linear and exponential relationship, respectively. The exponentially time-varying scale parameter of nonstationary Gumbel model is generally used because the scale parameter should be positive. However, the exponential form of scale parameter occasionally provides overestimated quantiles. In this study, various forms of time-varying scale parameters such as exponential, linear, and logarithmic forms were proposed and compared. The parameters were estimated based on the method of maximum likelihood. To compare the accuracy of each scale parameter, Monte Carlo simulation was performed for various conditions. Additionally, nonstationary frequency analysis was conducted for the sites which have more than 30 years data with a trend in rainfall data. As a result, nonstationary Gumbel model with exponentially time-varying scale parameter generally has the smallest root mean square error comparing with another forms.

Storage Vault의 열유동 및 상사특성 평가

유승환,방경식,김동희,이관수 한국방사성폐기물학회 2015 방사성폐기물학회지 Vol.13 No.2

본 연구에서는 저장볼트(storage vault)의 실험을 위하여 1/4 축소모델 내 튜브의 적정 발열량을 선정하고자 상사해석을 수 행하였다. 저장볼트에 대한 열 및 유동 해석을 우선적으로 수행하였고, 크기를 1/4로 축소한 저장볼트에 대하여 동일한 전 산해석을 수행하였다. 전산해석 결과를 바탕으로, 제안된 무차원수를 비교하여 원형모델과 온도분포와 유동분포가 유사하 게 되는 발열량을 선정하였다. 1/4 축소 저장볼트 내 튜브의 열유속이 1.3배일 때, 원형 저장볼트와 1/4 축소 저장볼트의 온 도장 및 유동장이 상사되었다. 이 때, 1/4 축소 저장볼트 내 발열량은 약 190 W이다. This research studied a scaling analysis for the selection of proper heat generation at tube for 1/4-scale storage vaults. First of all, the temperature field and velocity distribution of an original scale storage vault were analyzed and then numerical analysis of a 1/4-scale storage vault was performed to compare each model. The proper heat generation for a 1/4-scale storage vault, at which the temperature and velocity field of a 1/4-scale storage vault showed the best agreement with that of the original storage vault, was evaluated with proposed dimensionless parameters. The behavior of temperature and velocity of fluid in the 1/4-scale case were most similar to those of the original scale, using a heat flux 1.3 times higher than that seen in the original scale, which was approximately 190 W.

이상근의 가곡에 나타난 가사 그리기와 음악적 매개변수들의 관계 연구: 연가곡집 《가을 저녁의 시》를 중심으로

정희영 ( Hee-young Jeong ) 이상근기념사업회 2015 이상근 연구 Vol.1 No.-

This study aims to analyze the parameters Sang-geun Lee used to shape the lyrics of his song cycles and to discuss his compositional characteristics and its musical implications. Composer Sang-geun Lee, composed numerous works in various genres, such aschoral music, opera, piano music, chamber music, and orchestral music. He is considered one of the important figures in the 20th century Western music in Korea. He was also active as a conductor, critic, and educator. His songs are acclaimed as masterworks for its remarkable creativity and artistry, and the song genre clearly reveals his musical world. Sang-geun Lee’s writing, ‘A study of Korean songs’ (1955) shows his keen interest in song genre. In his writing, he strongly stressed the importance of choosing a poem when it comes to composing a song, by saying, “There is no need to imitate Schubert who added a beautiful music for such a poor (worthless) poem (In other words, the music is too good for the poem).” After composing his early songs based on lyrics from Koryo Gayo and Minyosi, Sang-geun Lee chose poets who shared the time and space with him, to name a few, poet Chun-Su Kim (1922-2004), Jang-Hyun Ahn (1928-2003), and Chi-Hwan Yoo (1908-1967). Using their poems as lyrics, Sang-geun Lee tried to communicate with experiences during turbulent times in Korea, from emancipation (or liberation), war to dictatorship. His songs include four short compositions “Haegok”, “If you”, “Dongdong”, and “Badaya”, and four song cycles, Songs dedicated to Thee, The Poem of an Autumn Evening, Aga I, and Aga II. For his song cycle Poems of an Autumn Evening, he used a modern compositional technique that he did not use for his earlier works. Because of this modern compositional technique, this cycle holds a prominent place in his song writing development. Since he did not see the lyrics as a simple tool delivering the meaning of melody, but as a companion that leads and creates the overall musical atmosphere, he concentrated on bringing out the characteristics of the lyricsmusically. In other words, he applied the technique of text painting to achieve the musical shape of the lyrics (poems) using musical parameters, such as structure, scale, harmony and so on. His song cycle The Poem of an Autumn Evening consists of eight songs. He used Chun-Su Kim’s early collections of poems written during 1950s, four poems from Cloud and Rose (29 poems) and Swamp (21 poems). After a thorough analysis of The Poem of an Autumn Evening, I categorized musical parameters and its characteristics that I discovered in Sang-geun Lee’s song cycle, Poems on an Autumn Evening into three parts. First, Sang-geun Lee used various musical parameters as musical tools in each section of the work to match the structure of poem to the musical form, which results in the overall unity and diversity at the same time. In other words, he used scales in various ways in each section of the work including a major and minor scale, a pentatonic scale and a scale that he created. He consistently used a specific intro, bridge, and a group of chords at the beginning and the end of each section of the work. To express the musical climax of the work, he always used the highest range of pitches with articulations and dynamics such as an accent, tenuto, crescendo, forte, fortis-simo, and so forth. When he tried to emphasize a specific poetic text, he repeated the text smoothly by using a rhythmic extension or repetition without distracting the unity between the overall structure of music and the poem. Second, he used a technique that either contrasts or match the lyrics and its musical atmosphere in order to express the implications of the lyrics. For this, he first considered the direction of the melody, whether it is moving downward or in contrary motion of the two parts, song and accompaniment. Then he used a unique scale that creates the right musical color to describe the atmosphere or mixed two scales. He also applied a technique of changing a central tone or tempo. He used these techniques to represent the contrasting psychological state of the poetic self. Lastly, he succeeded in describing a specific poetic text vividly by using musical ornamentation in song part, a homophonic texture in which song and piano part move in rhythmic unison, and so on. Poems on an Autumn Evening is one of the representative modern song cycles in Korea, because the composer, Sang-geun Lee, achieved a musical shape of poems using traditional techniques such as a three-part-structure, scale of major and minor, functional harmonic cadence as well as modern compositional techniques such as a church mode, pentatonic scale, frequent change of tempo, chromatic melody, and dissonant chord. This helps us to understand why Sang-geun Lee holds a prominent position as a representative Korean composer as well as his contribution to the development of modern art song in Korea.

Modelling of graded rectangular micro-plates with variable length scale parameters

Reza Aghazadeh,Serkan Dag,Ender Cigeroglu 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.5

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

Modelling of graded rectangular micro-plates with variable length scale parameters

Aghazadeh, Reza,Dag, Serkan,Cigeroglu, Ender Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.5

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

Analysis of Center Frequency Effect on Damping Parameters Estimation Using Continuous Wavelet Transform

이석민 대한토목학회 2021 KSCE JOURNAL OF CIVIL ENGINEERING Vol.25 No.4

This paper aims to improve the use of continuous wavelet transform (CWT) to identify the damping parameters from the free decay responses of structures. Numerical response functions (impulse response functions) were simulated with lower frequencies and higher damping parameters using the Hilbert Transform, and the damping parameters were estimated by extracting wavelet coefficients that corresponded to the frequency components of these numerical response functions. Numerical simulations were also performed on single-, separated- and closed-mode systems to analyze the effect of the center frequency of the mother wavelet on the estimation of system damping parameters. Experiments were performed on a two-span H-Beam. This study focuses on the damping parameter estimation errors for the center frequency setting of the mother wavelet function. The reliability of the estimated damping parameters can be improved by selecting the center frequencies of the mother wavelet function so that each corresponding scale is localized at half of the total scale.