Comparison of Nonlinear Analysis and Equivalent Linear Analysis on 1D Site Response Analysis

( Yonghee Lee ),( Hak-sung Kim ),( Seok-chul Kim ),( Weon-hack Choi ) 대한지질공학회 2019 대한지질공학회 학술발표회논문집 Vol.2019 No.2

Equivalent linear and nonlinear analyses are the most common approaches to perform 1D site response analysis. Since these methods have inherent differences in analysis process (time domain, frequency domain), computed results yield different output. Equivalent linear analysis is a kind of linear analysis considering non-linearity and an approximation of hysteric soil behavior. Nonlinear analysis method is the hysteretic stress-strain response of soil and can represent more actual behavior rather than equivalent linear analysis. In this study 1D nonlinear analysis and equivalent linear analysis are performed with DEEPSOIL version 7.1 for 30 m soil depth. Shear modulus reduction and damping curve was used with Darendeli (2001) that has Ko is 0.5. Curve fitting for modulus reduction and damping function were performed with university of Illinois at Urbana-Champaign (MRDF-UIUC) model. Used soil model is pressure-dependent modified Kondner Zelasko (MKZ) and hysteretic unloading-reloading formulation follows non-masing rule in the nonlinear analyses. The thickness of each layer is 1 m. The used input motion is Northridge earthquake record (scaled from 0.05 g to 1 g). Analyses results show that ground behavior is very similar in the low peak ground acceleration (PGA) level but somewhat different in the high PGA level. In case of strong motion (i.e., PGA > 0.5 g) especially in the initial and decayed part, equivalent linear analyses results show under-prediction tendency but over-prediction tendency in the strong motion part. During strong motion part, soil stiffness decreased in the nonlinear analysis but is same in the equivalent linear analysis.

기업의 부동산 보유정책의 결정요인에 대한 패널자료분석

윤영주,김은주,김정일 한국자료분석학회 2019 Journal of the Korean Data Analysis Society Vol.21 No.3

The objective of this research was to investigate determinants affecting the real estate holding ratio of firms through linear and non-linear panel analysis. For the empirical analysis, a sample of 272 firms were selected based on a suitable balanced panel data analysis for eight years from 2010 to 2017 using a financial statement database provided by Fn-Guide. Linear and non-linear panel analysis were performed using the sample to examine descriptive analysis, correlation analysis for each variable, and association between corporate governance and the real estate holding ratio. The real estate holding ratio was statistically significant only for institutional investor share ratio, size, return on assets, and growth ratio by linear panel analysis. In addition, major stockholder share ratio, foreign investor share ratio, return on assets, research & development ratio, and free cash flow were presented as a reverse U shape, and leverage rate was displayed as a U shape in the non-linear panel analysis. And the relationship between the real estate holding ratio compared to the results using the linear panel analysis could be interpreted differently, since there were significant results for all variables except outside directors ratio and advertisement ratio in the non-linear panel analysis. 본 연구는 기업의 부동산 보유비율에 미치는 결정요인을 선형패널분석과 비선형패널분석을 통하여 규명하는 것을 목적으로 하고 있다. 실증적 분석에서, 표본은 Fn-Guide에서 제공하는 재무제표 데이터베이스를 이용하여 2010년부터 균형패널자료분석에 적합한 272개 기업의 8년간 패널자료를 대상으로 분석하였다. 이들 표본을 대상으로 표본의 기술적 분석, 각 변수의 상관분석, 그리고 기업지배구조와 부동산 보유비율의 상호관련성을 검증하기 위하여 선형패널분석과 비선형패널분석을 실시하였다. 선형패널분석에서는 기관투자자 지분율, 기업규모, 총자산순이익률, 그리고 매출액증가율만이 부동산 보유비율에 유의한 영향을 미치고 있다. 비선형패널분석에서는 대주주 지분율, 외국인투자자 지분율, 총자산순이익률, 연구개발비비율, 그리고 잉여현금흐름비율이 역 U자 형태를 취하고 있으며, 부채비율은 U자 형태를 취하고 있다. 제곱항이 제거된 변수에서는 선형패널분석 결과와 비슷하였으며, 제곱항이 유의한 변수는 더 많은 정보를 제공하여 유의한 해석이 가능하였다. 결과적으로 비선형에서는 사외이사비율과 광고선전비 비율을 제외한 모든 변수들에 대하여 유의한 해석이 가능하여 부동산 보유비율과 관계를 선형패널분석에서의 결과와 다른 해석을 할 수 있다.

The Research of Multiple Regression Analysis in Rural-Urban Income Disparity

Jian Li,Xiangyu Guo 보안공학연구지원센터 2016 International Journal of Smart Home Vol.10 No.11

The multiple linear regression model contains more than one predictor variable and it shows the relationship among multiple variables. In the existing research field of rural-urban income disparity, the method of multiple regression analysis is mainly employed. But the linear relationship among variables is estimated mainly depending on principal component analysis. Principal component analysis is used to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The principal component analysis is widely used for feature extraction to reveal the most main factors from the multiple aspects. A multiply linear regression model integrating principal components analysis is proposed to address on the income gap between the city and country. The influential factors are given and the analysis results are discussed in this paper. The experimental results on income data from 1990 to 2013 show that the proposed method is effective in predicting the income ratio and analyzing the influential factors.

항공기 플랩 제어를 위한 선형 구동기의 구조 안전성 평가

김동협,김상우 항공우주시스템공학회 2019 항공우주시스템공학회지 Vol.13 No.4

The objective of this study was to evaluate the structural safety of the basic design for the linear actuator for the flap control of aircrafts. The kinetic behavior of the linear actuator was determined using the multi-body dynamics (MBD) analysis, and the contact force was calculated to be used as input data for the structural analysis based on the finite element analysis. In the structural analysis, the thermal and static behaviors of the linear actuator satisfying the designed velocity were examined, and the structural safety of the linear actuator evaluated. Moreover, the dynamic behaviors of the key components of the linear actuator were investigated by the modal analysis. The actuation rod linearly moved with about 5 mm/s when the motor operated at 225 rpm and the maximum contact force of 32.83 N occurred between two driving gears. Meanwhile, the structural analysis revealed that the maximum thermal and static stresses were 1.57% and 78% of the yield strength of steel, respectively, and they were in a safe range of the structure. In addition, the linear actuator for the basic design is stable to the resonance by avoiding the natural frequencies of the components. 본 연구에서는 항공기 플랩 제어를 위한 선형 구동기의 기본 설계에 대한 구조 안전성을 평가하였다. 다물체 동역학 분석을 통해 선형 구동기의 기계적 운동을 이해하였고, 접촉 하중을 산출하여 유한요소해석 기반의 구조 분석에 적용하였다. 구조 분석에서는 선형 구동기의 설계 속도 조건에 대한 열, 정적 거동을 검토하였고, 구조적 안전성을 평가하였다. 또한 모드 해석을 수행하여 동적 거동을 분석하였다. 분석 결과, 모터가 225 rpm으로 작동 시 구동 로드는 약 5 mm/s로 병진 운동하였고, 기어 간 최대 32.83 N의 접촉 하중이 발생하였다. 한편, 최대 열 응력과 정 응력은 철의 항복강도의 약 1.57%, 78%로 발생하였고, 각 부품은 서로의 공진 주파수를 회피하였다. 따라서 제안된 선형 구동기의 기본설계는 구조적으로 안전하며, 공진에 대해 안정적임을 밝혔다.

Efficient Correlation Method for Satellite Thermal Analysis Model Using Multiple Linear Regression and Optimization Algorithms

Jaewon Kang,김건웅,Somin Shin,김정호 한국항공우주학회 2023 International Journal of Aeronautical and Space Sc Vol.24 No.5

As the thermal analysis model of satellites is used as an important indicator for thermal design, it must accurately simulate the thermal behaviour of actual satellites for precise thermal design. To increase the accuracy of the thermal analysis model, it must be correlated using the thermal balance test data for actual satellite models. To achieve this, we herein propose an efficient correlation method for satellite thermal analysis models using multiple linear regression techniques with quadratic terms and optimization algorithms. The proposed method reduces the amount of computation by choosing dominant parameters through sensitivity analysis and creating a multiple linear regression model that can replace the thermal analysis model in the subsequent optimization process. Subsequently, optimization algorithms are applied to the multiple linear regression model to perform the correlation of the thermal analysis model. In this study, the numerical validation of the proposed method was performed using numerical data from a reference thermal analysis model to verify the reliability and accuracy of the proposed method before it was applied to the correlation of the thermal analysis model using experimental data. The thermal analysis result of the reference thermal analysis model was set as the target value to correlate, and quantitative performance evaluation was performed for various combinations of optimization algorithms and design of experiments methods by comparing the estimated analysis parameters. The results of this study demonstrate that the proposed method can efficiently produce an accurate correlation model for thermal analysis.

고정 효과 회귀분석 vs. 무선 효과 위계적 선형모델(HLM): 가족 구성 및 정보 프라이버시 염려가 비판적 정보 추구 행위에 미치는 영향

류성진 한국언론학회 2024 커뮤니케이션 이론 Vol.20 No.1

In the case of regression analysis, it is necessary to diagnose whether the assumptions such as linearity, normality, homoscedasticity, and independence of residuals, multicollinearity are satisfied before full-scale analysis. If some assumptions are not met, appropriate measures, such as data transformation, must be applied to the data to achieve valid and reliable analysis results only after full-scale analysis is performed after the assumptions are met. Textbooks or papers dealing with the diagnosis of residual linearity, normality, homoscedasticity, and multicollinearity among the various assumptions introduced earlier are not difficult to find in communication academia. However, papers and discussions on the assumption of independence are hard to find in those area. In this repect, the study aims to introduce the assumption of residual independence, diagnosis, and statistical analysis technique that can overcome violation of residual independence, that is, hierarchical linear model(hereinafter, HLM). If clustering occurs due to interactions among members within the group, residual independence may be violated, which leads to an increase in standard error, resulting in a problem of testing inappropriate statistical significance. HLM has the advantage of being able to test appropriate statistical significance in consideration of such residual non-independence. In this study, in order to clearly explain the characteristics of HLM, we tried to conduct a comparative analysis with the results of fixed effect regression analysis. Using 2023 media panel survey data, the two statistical analysis techniques presented above were applied to test the differences in the impact of information privacy concerns on media literacy according to family composition. As a result of the analysis, the effect on media literacy according to family composition was statistically significant in the fixed effect regression analysis, and the interaction between family composition and information privacy concerns on media literacy was significant. However, in the case of this regression analysis, Durbin Watson d statistics confirmed that the assumption of independence was violated, confirming that there is a possibility of committing a Type I error. To the contrary, HLM revealed that the average difference in random effects of influence on media literacy according to family composition and the difference in the slope of random effects of information privacy concerns on media literacy according to family composition were not statistically significant, either. This study confirmed that in the case of data that can violate the assumption of residual independence, that is, if group clustering is likely to occur, using HLM is an effect way to reduce Type I errors. 회귀분석의 경우 본격적인 분석에 앞서 잔차의 선형성, 정규성, 등분산성, 독립성, 다중공선성 등의 가정 충족 여부를 진단해야 한다. 만일 일부 가정이 충족되지 않을 경우, 데이터에 적절한 조치, 예를 들어, 데이터 변환 등을 통해 가정을 충족한이후분석을 실행할 때 타당하고 신뢰할 수 있는 분석 결과를 얻을 수 있다. 커뮤니케이션 학계에서는 앞서 소개한 잔차의 선형성, 정규성, 등분산성, 다중공선성에 대한 가정 진단을 다룬 교재나 논문을 어렵지 않게 접할 수 있다. 그러나 독립성 가정을 다룬 논문이나 논의는 의외로 찾기가 쉽지 않다. 이 점에 착안하여, 이 연구는 잔차의 독립성 가정 및 진단 방법을 소개하고자 한다. 더불어, 잔차의 독립성 위배를 극복할 수 있는 통계분석기법, 즉 위계적 선형모델(hierarchical linear model: HLM)도 함께 소개하고자 한다. 집단 내 구성원 간 상호작용으로 인한 군집화가 발생할 때 잔차 독립성은 위배될 가능성이 있으며, 이는 곧 표준오차의 증가로 이어져부적절한통계적유의성을검증하는문제가 발생한다. HLM은 이 같은 잔차의 비독립성을 고려하여 타당한 방식으로 통계적 유의성을 검증할 수 있다는 장점이 있다. 이번 연구에서는 HLM의 특징을 명확하게 설명할 목적으로 기존 연구에서 일반적으로실행하는고정 효과 OLS 회귀분석의 결과와 비교분석을 진행했다. 2022년 미디어패널조사데이터를활용하여 가족 구성에따라정보 프라이버시 염려가 비판적 정보 추구 행위에 미치는 영향의 차이를 검정하기 위해 앞서 제시한 두 가지 통계분석기법을 적용하여 비교분석했다. 분석 결과, 고정 효과 OLS 회귀분석에서는 가족 구성에 따라 비판적 정보 추구 행위에 미치는 영향이 통계적으로 유의미했으며, 비판적 정보 추구 행위에 미치는 가족 구성과 정보 프라이버시 염려 간 상호작용은 유의미한 것으로 드러났다. 그러나 잔차 간 독립성 가정을 진단한 결과, 이 가정은 위배되었음이 밝혀졌고, 따라서 유의성 검증에 대한 제1종 오류를 범할 위험이 있음을 확인할 수 있었다. 이를 극복하기 위해 HLM을 실행한 결과, 가족 구성에 따라 비판적 정보 추구 행위에 미치는 영향의 무선 효과 평균 차이 그리고 가족 구성에 따라 정보 프라이버시 염려가 비판적 정보 추구 행위에 미치는 영향, 즉 무선 효과 기울기 차이는 통계적으로 유의미하지 않은 것으로 드러났다. 이번 연구 결과를 통해 잔차의 독립성 가정을 위배할 수 있는 데이터의 경우, 즉 집단의 군집화가 발생할 가능성이 있는 경우, 향후 연구자들은 HLM 사용을 신중하게 고려해 보길 이번 연구는 제안하고자 한다.

A study on the fatigue analysis for a vertical caisson on FPSO subjected to the nonlinear wave loading

Gam, MinJu,Jang, Beom-Seon,Park, JungHo Elsevier 2017 Ocean engineering Vol.137 No.-

<P><B>Abstract</B></P> <P>A cylindrical type hull appurtenance attached to the side hull like a seawater caisson or a riser tube is subject to the drag force and inertia force defined by the Morison equation, as well as global hull girder loads. When performing fatigue analysis for a structure subject to Morison load, the nonlinearity of drag term in the Morison equation should be taken into account for an exact structural safety assessment in an appropriate way. This research proposes a time domain approach (Level II method) in order to take into account the nonlinearity, as well as a proper combination of local hotspot stress induced by the Morison load and global hull girder stress. It is based on a representation of irregular wave as a combination of a large number of regular waves. It enables for reflecting phase angle differences of particle velocities along the vertical tube. The phase difference with global stress is also taken into account. The method also includes the vertical motion of the caisson and the wave elevation above the mean water line. The nonlinearity of drag term can be treated by linearizing the drag term in the frequency domain analysis. For the frequency domain approach, Level I method using a linearization coefficient is proposed to yield a fatigue damage equivalent to the time domain analysis. It incorporates the different contributions of horizontal velocities along the vertical tube on the hotspot stress at a connecting bracket on the side hull. The proposed methods are verified through a caisson in FPSO example and various comparative studies. Various comparative studies are performed for a verification of spectral code, an evaluation of rain flow counting effect and the combination of motion and stretching effect, a verification of rain flow counting(RFC) code and linearization coefficient. Through these case studies, it is found that the proposed spectral fatigue analysis with linearized Morison’s force results in a good agreement with time domain analysis with a drastic reduction of computational time. In this paper, a FPSO model with a seawater caisson is used as a verification example. The proposed methods are expected to be applied to many similar tubular structures on the side of floating offshore structure, such as, riser guide tube, protection frame for riser guide tube, collision protector and so on. In addition, jacket or jack-up rig consisting of tubular members could be good applications.</P> <P><B>Highlights</B></P> <P> <UL> <LI> This paper proposes fatigue analysis procedures for a vertical caisson. </LI> <LI> The nonlinearity of Morison equation is considered in the time domain approach. </LI> <LI> A use of linearization coefficient in the frequency domain analysis is proposed. </LI> </UL> </P>

On the Relationship between ??-sensitivity Analysis and Sensitivity Analysis using an Optimal Basis

Park, Chan-Kyoo,Kim, Woo-Je,Park, Soondal 한국경영과학회 2004 Management Science and Financial Engineering Vol.10 No.2

e-sensitivity analysis is a kind of methods for performing sensitivity analysis for linear programming. Its main advantage is that it can be directly applied for interior-point methods with a little computation. Although e-sensitivity analysis was proposed several years ago, there have been no studies on its relationship with other sensitivity analysis methods. In this paper, we discuss the relationship between e-sensitivity analysis and sensitivity analysis using an optimal basis. First, we present a property of e-sensitivity analysis, from which we derive a simplified formula for finding the characteristic region of e-sensitivity analysis. Next, using the simplified formula, we examine the relationship between e-sensitivity analysis and sensitivity analysis using optimal basis when an e-optimal solution is sufficiently close to an optimal extreme solution. We show that under primal nondegeneracy or dual nondegeneracy of an optimal extreme solution, the characteristic region of e-sensitivity analysis converges to that of sensitivity analysis using an optimal basis. However, for the case of both primal and dual degeneracy, we present an example in which the characteristic region of e-sensitivity analysis is different from that of sensitivity analysis using an optimal basis.

임상의를 위한 다변량 분석의 실제

오주한(Joo Han Oh),정석원(Seok Won Chung) 대한견주관절의학회 2013 대한견주관절의학회지 Vol.16 No.1

임상 의학의 연구에 사용되는 대표적 다변량 분석 방법은 다중 회귀 분석 방법인데, 이는 인과 관계를 토대로 여러 개의 변수에 의한 한꺼번에의 영향력을 분석하기 위한 방법이다. 다중 회귀 분석은 기본적으로 회귀분석의 기본 가정을 만족해야 함은 물론, 여러 개의 독립 변수들이 포함되기 때문에 변수들을 모형에 포함시키는 방법 및 다중 공선성 문제에 대한 고려가 필요하다. 다중 회귀 분석 모형의 설명력은 결정 계수 R2으로 표현되어 1에 가까울수록 설명력이 크며, 각 독립 변수들의 결과에의 영향력은 회귀 계수인 β값으로 표현된다. 다중 회귀 분석은 종속 변수의 형태에 따라 다중 선형 회귀 분석, 다중 로지스틱 회귀 분석, 콕스 회귀 분석으로 나눌 수 있다. 종속 변수가 연속 변수인 경우 다중 선형 회귀 분석, 범주형 변수인 경우 다중 로지스틱 회귀 분석, 시간의 영향을 고려한 상태 변수인 경우는 콕스 회귀 분석을 시행해야 하며, 각각 결과에의 영향력은 회귀 계수 β, 교차비, 위험비로 평가한다. 이러한 다변량 분석에 대한 이해는 연구를 계획하고 결과를 분석하고자 하는 임상 의사에게 있어 보다 효율적인 연구를 위해 필수적인 소양이라고 할 수 있다. In medical research, multivariate analysis, especially multiple regression analysis, is used to analyze the influence of multiple variables on the result. Multiple regression analysis should include variables in the model and the problem of multi-collinearity as there are many variables as well as the basic assumption of regression analysis. The multiple regression model is expressed as the coefficient of determination, R2 and the influence of independent variables on result as a regression coefficient, β. Multiple regression analysis can be divided into multiple linear regression analysis, multiple logistic regression analysis, and Cox regression analysis according to the type of dependent variables (continuous variable, categorical variable (binary logit), and state variable, respectively), and the influence of variables on the result is evaluated by regression coefficient β, odds ratio, and hazard ratio, respectively. The knowledge of multivariate analysis enables clinicians to analyze the result accurately and to design the further research efficiently.

수정된 등가선형해석기법의 정확성 평가

정창균(Jeong Chang-Gyun),곽동엽(Kwak Dong-Yeop),박두희(Park Duhee),김광균(Kim Kwangkyun) 한국지반환경공학회 2010 한국지반환경공학회논문집 Vol.11 No.6

1차원 등가선형 지반응답해석은 지반에 의한 지진동의 증폭현상을 모사하는데 널리 사용되고 있다. 등가선형해석은 적은 수의 입력변수를 필요로하므로 사용하기 편리하며 해석 소요시간이 짧다는 장점을 가지고 있는 반면, 시간에 따라서 변화하는 지반의 비선형 거동을 모사할 수 없으며 일정한 전단탄성계수와 감쇠비를 해석 내내 적용하는 선형해석이라는 단점을 가지고 있다. 이와 같은 등가선형해석의 단점을 보완하기 위하여 진동 주파수와 변형률과의 관계를 모사하는 다양한 형태의 수정된 등가선형해석기법들이 개발되었다. 수정된 기법들은 전단변형률 푸리에 스펙트럼을 사용한다는 점에서는 동일하지만, 이로부터 변형률의 주파수 의존도를 정의하는 과정에서는 차이를 보이고 있다. 본 연구에서는 두 가지 수정된 등가선형해석기법들의 정확성을 평가하기 위하여 국내에서 조사된 두 개의 토층에서 일련의 비선형, 등가선형, 수정된 등가선형 지반응답해석을 수행하였다. 해석 결과, 수정된 등가선형해석기법들은 고주파수 요소를 과대 예측할 수 있으며, 특히 고주파수 요소가 풍부한 인공지진파를 입력 지진파로 사용하였을 경우 비현실적인 응답이 계산될 수 있는 것으로 나타났다. One-dimensional equivalent linear site response analysis is widely used in practice due to its simplicity, requiring only few input parameters, and low computational cost. The main limitation of the procedure is that it is essentially a linear method, in which the time dependent change in the soil properties cannot be modeled and constant values of shear modulus and damping is used throughout the duration of the analysis. Various forms of modified equivalent linear analyses have been developed to enhance the accuracy of the equivalent linear method by incorporating the dependence of the shear strain with the loading frequency. The methods are identical in that it uses the shear strain Fourier spectrum as the backbone of the analysis, but differ in the method in which the strain Fourier spectrum is smoothed. This study used two domestically measured soil profiles to perform a series of nonlinear, equivalent linear, and modified equivalent linear site response analyses to verify the accuracy of two modified procedures. The results of the analyses indicate that the modified equivalent linear analysis can highly overestimate the amplification of the high frequency components of the ground motion. The degree of overestimation is dependent on the characteristics of the input ground motion. Use of a motion rich in high frequency contents can result in unrealistic response.