요인 개수 결정을 위한 평행분석의 정확성 평가

임상돈,장승민 한국심리학회 2017 한국심리학회지 일반 Vol.36 No.4

Parallel analysis is a method of estimating the number of factors by comparing the eigenvalues ​​of sample data with the eigenvalues ​​of random data. This method is considered to be theoretically more valid and empirically more accurate in estimating the number of factors than other methods, such as Kaiser method and scree test, that estimate the number of factors based on the eigenvalues. However, several criticisms have been raised about the validity of the rationale for parallel analysis and various modifications have been proposed. There have also been concerns about the conditions under which parallel analysis shows relatively low accuracy. The current study examined the rationale and limitations of the use of eigenvalues ​​and parallel analysis to estimate the number of factors, and based on this, we specified the conditions under which the accuracy of parallel analysis may be low. We also examined, through a simulation, the effects of various factors that may affect the accuracy of parallel analysis and confirmed the conditions where cautions are needed when applying parallel analysis. The results of the simulation show that the accuracy of estimating the number of factors in the parallel analysis is greatly influenced by the size of factor correlations, the magnitude of factor loadings, the number of factors, and the number of variables per factor. In addition, we confirmed that the accuracy of the parallel analysis is significantly lower when a factor model includes a weak factor with low factor loadings. Overall, the accuracy of the parallel analysis for the reduced correlation matrix (PA-PAF) was higher than the parallel analysis for the correlation matrix (PA-PCA), which in particular, PA-PAF showed high accuracy when factor correlations were high, and PA-PCA showed high accuracy when factor correlations were low. Based on the results of the simulation analyses, we proposed sample sizes required for parallel analysis to provide accuracy of 90% or higher under conditions with different levels of factor correlation, factor loading, and the number of factors. 평행분석은 표본 자료의 고윳값과 무선 자료의 고윳값을 비교하여 요인의 개수를 추정하는 방법이다. 이 방법은 고윳값에 근거하여 요인의 개수를 추정하는 다른 절차들(카이저 방법, 스크리 검사)보다 이론적으로 더 타당한 근거를 갖고 있고 경험적으로도 요인의 개수를 더 정확히 추정하는 것으로 평가 받는다. 그러나 평행분석의 이론적 근거의 타당성에 대해서도 여러 비판이 제기되어 왔고 이에 따른 다양한 수정 절차들도 제안되었다. 또한 평행분석이 상대적으로 낮은 정확성을 나타내는 조건들에 대한 우려도 있어 왔다. 본 연구는 고윳값과 평행분석이 요인의 개수를 추정하는 데 사용될 수 있는 이론적 근거와 한계를 검토하고 이를 바탕으로 평행분석의 정확성이 낮게 나타날 수 있는 조건들을 구체화하였다. 또한 모의실험을 통해 평행분석의 정확성에 영향을 줄 수 있는 다양한 요인들의 효과를 검토하고 평행분석의 사용에 주의를 요하는 조건들을 확인하였다. 모의실험의 결과는 평행분석의 요인수 추정 정확률이 요인상관의 크기, 요인부하량의 크기, 요인의 개수, 요인당 변수의 개수에 따라 크게 영향을 받으며 정확률이 낮은 조건에서 표본크기의 영향이 매우 크다는 것을 보였다. 또한 요인부하량이 낮은 변수들로 구성된 약한 요인이 포함된 경우 요인수 추정의 정확률이 크게 낮아짐을 확인하였다. 전반적으로 상관행렬에 대한 평행분석(PA-PCA)보다 축소상관행렬에 대한 평행분석(PA-PAF)의 정확률이 높았으며 특히 요인상관이 높은 경우에는 PA-PAF가, 요인상관이 낮은 경우에는 PA-PCA가 높은 정확률을 보이는 경향이 확인되었다. 마지막으로 모의실험의 결과를 기초로 요인상관의 크기, 요인부하량의 크기, 요인의 개수의 조합으로 구성되는 다양한 조건에서 평행분석이 90% 이상의 정확률을 제공하기 위해 요구되는 표본크기를 제안하였다.

고성능 수치해석 라이브러리를 적용한 진동해석 프로그램 개발

고도현,부승환 해양환경안전학회 2021 해양환경안전학회지 Vol.27 No.1

선박 및 해양구조물과 같은 대형 유한요소모델의 진동 특성을 평가하기 위해 고유치 해석 및 가진 주파수에 따른 응답 계산을 필수적으로 수행해야 한다. 하지만 이러한 해석들은 과도한 전산 장비와 계산 시간이 요구되어 고성능 해석 프로그램의 개발이 필요하다. 특히 선형연립방정식에서 발생하는 역행렬 계산 및 고유치 해석 시에는 상당한 전산 해석 시간이 발생하기 때문에 최신 고성능 라이브러리를 적용함으로써 이를 개선할 수 있다. 본 연구에서는 병렬식 선형연립방정식 계산 라이브러리인 PARDISO와 고성능 고유치 해석 라이 브러리인 ARPACK을 적용하여 빠르고 정확한 해석이 가능한 진동해석 프로그램을 개발하였다. 끝으로 개발된 해석 프로그램의 정확도와 효율성을 검증하기 위해 여러 선박해양공학 수치 예제를 사용하였고, 상용 유한요소 프로그램인 ABAQUS와의 결과 비교 검토를 통해 개발된 진동해석 프로그램의 신뢰성을 검증, 제시하였다. In order to evaluate the vibrational characteristics of huge finite element models such as ships and offshore structures, it is essential to perform eigenvalue analysis and frequency response analysis. However, these analyzes necessitate excessive equipment and computation time, which require the development of a high-performance analysis program. In particular, a considerable computational analysis time is required when calculating the inverse matrix in a linear system of equations and analyzing the eigenvalue analysis. Therefore, it can be improved by applying the latest high-performance library. In this paper, the vibration analysis program that enables fast and accurate analysis was developed by applying ‘PARDISO’, a parallel linear system of equation calculation library, and ‘ARPACK’, a high-performance eigenvalue analysis library. To verify the accuracy and efficiency of proposed method, we compare ABAQUS with proposed program using numerical examples of marine engineering.

스퀼 저감을 위한 복소 고유치 해석

김성수(Sungsoo Kim),박경환(Kyunghwan Park),박광수(Kwangsoo Park) 한국자동차공학회 2006 한국자동차공학회 춘 추계 학술대회 논문집 Vol.- No.-

In this study, the cause of brake squeal is investigated and the design modification for reducing the squeal is proposed. To estimate the dynamic stability of a disc brake assembly, the complex eigenvalue analysis is performed through the following 3 steps; 1) modal correlation between FE analysis and testing for each component, 2) non-linear static analysis for the braking pressure application, 3) complex eigenvalue analysis for the brake assembly using ABAQUS. The analysis results show good correlation with vehicle testing for the squeal frequency at an unstable mode. To investigate the cause of instability, the mode tracking of the unstable mode is performed with varying friction coefficient up to 0.6. The results reveal that two separated stable modes meet at the friction coefficient of 0.18 and create the complex mode pair. To reduce the instability. the structural modifications are proposed and evaluated by the FE analysis.

웨브에 개구부를 가진 구조부재의 선형좌굴해석

임지선(Lim, Ji-Seon),이상진(Lee, Sang-Jin) 대한건축학회 2021 대한건축학회논문집 Vol.37 No.4

The linear buckling analysis of steel members with web openings is carried out by using a continuum shell finite element having six degrees of freedom. In the analysis, the parameters such as the size, shape and existence of web openings are mainly introduced to see the change of buckling loads and mode shapes of steel members due to the degradation of structural stiffness. The full analysis procedure used in the present study is explicitly described. The subspace iteration is employed in eigenvalue analysis. In particular, for the eigenvalue analysis, the geometric stiffness matrix is formulated by using the stress distributions produced by using linear static analysis with design load. From numerical tests, it is found to be that buckling load and its mode shape of steel members are very sensitive to the existence, size and shape of web opening especially in higher modes. The present numerical results can be used as imperfection data for nonlinear buckling analysis.

고유치해석과 진동계측을 통한 벽식 공동주택의 고유주기 비교

윤성원,정석창,임인식 한국공간구조학회 2006 한국공간구조학회지 Vol.6 No.3

This paper is concerned with the natural periods of ambient vibration and eigenvalue analysis. Ambient vibration tests were conducted to four bearing-wall reinforced concrete buildings ranging from twelve to nineteen stories. The performance of modeling in eigenvalue analysis was investigated using consideration of rigidity out of the plane in the slab and the non-structural bearing wall. Measured natural period was also compared with the value by the KBC2005. Natural period of the short direction in eigenvalue analysis is well fitted with the measured one. In the other hand, Natural period of the long direction in eigenvalue analysis is slightly more overestimated than the measured one. Natural period of the long direction in eigenvalue analysis was found to be enhanced by considering the effect of the stiffness out of the plane of the slab and non-structural wall in the structural modeling.

틸팅차량용 휠 제동장치의 스퀼 소음 해석

차정권(Cha, Jung-Kwon),박영일(Park, Yeong-Il) 한국소음진동공학회 2010 한국소음진동공학회 논문집 Vol.20 No.1

Squeal, a kind of self-excited vibration, is generated by the friction between the disc and the friction materials. It occurs at the ending stage of the braking process, and radiates and audible frequency range of 1 kHz to 10 kHz. Squeal is generated from unstability because of the coupling between the translation and rotation of the system. This instability is caused by the follower force and follower force is normal component of the friction force. In this paper modal analysis of wheel brake system was performed in order to predict the squeal phenomenon. It was shown that the prediction of system instability is possible by FEM. A finite element model of that brake system was made. Some parts of a real brake was selected and modeled. Modal analysis method performs analyses of each brake system component. Experimental modal analysis was performed for each brake components and experimental results were compared with analytical results from FEM. To predict the dynamic unstability of a whole system, the complex eigenvalue analysis for assembly modeling of components confirmed by modal analysis is performed. The finite element models of the disk brake assembly have been constructed, and the squeal noise problems have been solved by complex eigenvalue analysis. The complex eigenvalue analysis results compared with real train test.

A Study on Optimization of Resistive SFCL for Multi-Machine Power System Using Eigenvalue Analysis

Sung, Byung Chul,Park, Jung-Wook The Korean Institute of Electrical Engineers 2014 The Journal of International Council on Electrical Vol.4 No.2

This paper describes the optimization of a resistive superconducting fault current limiter (SFCL) applied to a multi-machine power system. Since the resistive SFCL is useful to provide a quick protection and reduce the fault current with its unique characteristics during a fault, it can be easily known that the transient stability of the entire system is improved effectively. However, when the SFCL is applied to a complex electric power system, especially a multi-machine power system, its direct optimization is difficult only considering fault conditions of the power system. Therefore, the resistive SFCL is optimized systematically by the eigenvalue analysis because it is effective to verify the transient stability and to evaluate the relationship between the parameters of a controller and the stability of the power system. Also, the dynamic effects of the SFCL on all generators of the multi-machine system can be considered synthetically with the eigenvalue analysis. Finally, the performance of the optimized SFCL is evaluated by time-domain simulation, and it is shown that that the optimized SFCL improves aggregately the damping performance of low-frequency oscillations in the entire multi-machine power system.

Analysis of Low-Frequency Squeal in Automotive Disc Brake by Optimizing Groove and Caliper Shapes

Kim, Cheol,Kwon, Yonghwan,Kim, Dongwon Korean Society for Precision Engineering 2018 International Journal of Precision Engineering and Vol.19 No.4

A low-frequency squeal that occurs due to the coupling phenomena of various vibrational modes in a disc brake system may cause annoyance to passengers. In an effort to remove the irritating low-frequency squeal of the disc brake, we carried out complex eigenvalue analysis and investigated the contribution ratio of each part to the occurrence of squealing. To this end, we developed a reliable and accurate finite element (FE) model of each brake part and compared it to the model test results. Throughout the complex eigenvalue analysis for the FE models, all unstable modes and corresponding frequencies in the brake system were calculated. The dominant parts that contributed largely to the squealing of the brake system were also elicited by the component contribution factor (CCF) analysis. Parts such as the disc, carrier, pad, and knuckle, were determined as large contributors to squealing. To reduce squealing, the tie-bar shape and the groove shape around the disc hub were optimized by FE-based shape optimization. A new disc with an optimal groove and a new tie-bar were manufactured, and dynamo squeal tests were conducted for a comparison to the numerical prediction. A fairly good correlation was observed between the experimental and numerical analysis results.

Derivation of formulas for perturbation analysis with modes of close eigenvalues

Liu, X.L. Techno-Press 2000 Structural Engineering and Mechanics, An Int'l Jou Vol.10 No.5

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

Coupled motion analysis of a tension leg platform with a tender semi-submersible system

Choi, Young-Myung,Nam, Bo Woo,Hong, Sa Young,Jung, Dong Woo,Kim, Hyun Joe Elsevier 2018 Ocean engineering Vol.156 No.-

<P><B>Abstract</B></P> <P>In this study, an experimental and numerical analysis have been carried out to investigate the coupled behavior of a Tension Leg Platform (TLP) combined with tender semi-submersible platform with focus on the multi-modal behaviors. Free decay tests were conducted for the TLP and semi-submersible, which showed that the TLP and semi-submersible system had complex coupled behaviors with multiple natural mode frequency components. To investigate this behavior rigorously, an eigenvalue analysis was applied. The natural modes and periods of the multi-body system were identified from the eigenvalue analysis. A selected set of model experiments was compared with corresponding numerical simulations which showed a good agreement.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The TLP with a tender semi-submersible are investigated by the nonlinear time domain simulation and a series of model tests. </LI> <LI> The eigenvalue analysis and the results of experiments show the TLP with the tender semi-submersible has several modes. </LI> <LI> Parametric sensitivity of the hawser stiffness on the multi-body system is investigated. </LI> <LI> Horizontal motions of multi-bodies in waves have several frequency components : incident waves, out-of-phase motion and in-phase motion. </LI> <LI> The frequency domain analysisis useful to calculate the hawser loads and to predict the resonances in the low frequency region. </LI> </UL> </P>