• Structural Engineering and Mechanics
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• 제6권6호
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• pp.659-671
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• 1998

Exercise of complete control on all aspects of any manufacturing / fabrication process is very difficult, leading to uncertainties in the material properties and geometric dimensions of structural components. This is especially true for laminated composites because of the large number of parameters associated with its fabrication. When the basic parameters like elastic modulus, density and Poisson's ratio are random, the derived response characteristics such as deflections, natural frequencies, buckling loads, stresses and strains are also random, being functions of the basic random system parameters. In this study the basic elastic properties of a composite lamina are assumed to be independent random variables. Perturbation formulation is used to model the random parameters assuming the dispersions small compared to the mean values. The system equations are analyzed to obtain the mean and the variance of the plate natural frequencies. Several application problems of free vibration analysis of composite plates, employing the proposed method are discussed. The analysis indicates that, at times it may be important to include the effect of randomness in material properties of composite laminates.

• 응용통계연구
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• 제19권3호
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• pp.545-554
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• 2006

로그선형모형에 기반을 둔 다차원 임의 분할표를 생성하는 방법을 제안하였다. 이를 위해 Lee(1997)가 제안한 선형 결합에 의한 결합분포 생성 방법을 적용하였으며, Pearson 통계량을 연관성 측도로 사용하는 것을 제안하였다. 세 변수가 서로 완전한 연관을 갖는 삼차원 결합분포를 생성할 수 있으므로 본 연구에서 제안한 방법은 사차원 이상 다차원 임의 분할표를 생성하는 문제로 확장될 수 있다.

• 대한수학회보
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• 제40권4호
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• pp.715-722
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• 2003

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}=\;{\Sigma_{j=0}}^{\infty}a_{j}{\epsilon}_{t-j}, where {${\in}_{t}$｝is a strictly stationary associated sequence of random variables with $E_{{\in}_t}{\;}={\;}0.{\;}E({\in}_t^2){\;}<{\;}{\infty}{\;}and{\;}{a_j}$ is a sequence of real numbers with (equation omitted). A central limit theorem for a stationary linear process generated by stationary associated processes is also discussed.

• 한국해안해양공학회지
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• 제15권4호
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• pp.214-223
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• 2003

신뢰성 기법을 도입하여 경사식 해안 구조물에 발생하는 월파현상을 해석하였다. 월파와 관련된 많은 변수를 고려할 수 있을 뿐만 아니라 예측능력이 우수하다고 판단되는 경험식을 이용하여 신뢰함수가 유도되었다. 일반적으로 인정되는 범위내에서 설정된 확률변수의 통계적 특성과 분포함수를 이용하여 허용 월파량을 초과하는 파괴확률이 무차원 천단고의 함수로 산정되었다. 피복재의 종류와 구조물 전면의 경사에 따른 파괴확률의 차이도 해석되었다 또한 상치 콘크리트 전면에 거치된 피복재의 천단폭 변화에 대하여도 해석하였다. 마지막으로 각 확률변수의 불확실성에 따른 민감도 분석이 수행되었다. 월파와 관련된 제반 특성들이 잘 묘사되었을 뿐만 아니라 결정론적 설계법에서는 규명할 수 없는 허용 월파량을 초과하는 파괴확률들이 정량적으로 산정 되었다. 따라서 천단고를 결정할 때 확률적인 개념을 가미함으로서 설계의 효율성을 높일 수 있다.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.229-235
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• 2001

Let {X$\_$n/, n$\geq$1] be a stationary sequence of negatively associated random variables with distribution function F(x)=P(X$_1$$\leq$x). The empirical distribution function F$\_$n/(x) based on X$_1$, X$_2$,....., X$\_$n/ is proposed as an estimator for F$\_$n/(x). Strong consistency and asymptotic normality of F$\_$n/(x) are studied. We also apply these ideas to estimation of the survival function.

• Journal of the Korean Statistical Society
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• 제13권2호
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• pp.87-106
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• 1984

It ${X_t}$ is a sequence of independent identically distributed normal random variables, then the conditional probability density of $X_1, X_2, \cdots, X_n$ given the first p+1 sample autocovariances converges to the maximum entropy probability density satisfying the corresponding covariance constraints as the length of the sample sequence tends to infinity. This establishes that the maximum entropy probability density and the associated Gaussian autoregressive process arise naturally as the answers of conditional limit problems.

• 한국재난정보학회 논문집
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• 제19권4호
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• pp.924-935
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• 2023

Purpose: The central aim of this study is to leverage machine learning techniques for the classification of Intrusion Detection System (IDS) data, with a specific focus on identifying the variables responsible for enhancing overall performance. Method: First, we classified 'R2L(Remote to Local)' and 'U2R (User to Root)' attacks in the NSL-KDD dataset, which are difficult to detect due to class imbalance, using seven machine learning models, including Logistic Regression (LR) and K-Nearest Neighbor (KNN). Next, we use the SHapley Additive exPlanation (SHAP) for two classification models that showed high performance, Random Forest (RF) and Light Gradient-Boosting Machine (LGBM), to check the importance of variables that affect classification for each model. Result: In the case of RF, the 'service' variable and in the case of LGBM, the 'dst_host_srv_count' variable were confirmed to be the most important variables. These pivotal variables serve as key factors capable of enhancing performance in the context of classification for each respective model. Conclusion: In conclusion, this paper successfully identifies the optimal models, RF and LGBM, for classifying 'R2L' and 'U2R' attacks, while elucidating the crucial variables associated with each selected model.

• Earthquakes and Structures
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• 제3권1호
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• pp.17-35
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• 2012

Simplified equations for fundamental period of vibration of skeletal structures provided by most seismic design provisions suffer from the absence of any associated confidence levels and of any reference to their empirical basis. Therefore, such equations may typically give a sector of designers the false impression of yielding a fairly accurate value of the period of vibration. This paper, although not addressing simplified codes equations, introduces a set of mathematical equations utilizing the theory of error propagation and First-Order Second-Moment (FOSM) techniques to determine bounds on the relative error in theoretically calculated fundamental period of vibration of skeletal structures. In a complementary step, and for verification purposes, Monte Carlo simulation technique has been also applied. The latter, despite involving larger computational effort, is expected to provide more precise estimates than FOSM methods. Studies of parametric uncertainties applied to reinforced concrete frame bents - potentially idealized as SDOF systems - are conducted demonstrating the effect of randomness and uncertainty of various relevant properties, shaping both mass and stiffness, on the variance (i.e. relative error) in the estimated period of vibration. Correlation between mass and stiffness parameters - regarded as random variables - is also thoroughly discussed. According to achieved results, a relative error in the period of vibration in the order of 19% for new designs/constructions and of about 25% for existing structures for assessment purposes - and even climbing up to about 36% in some special applications and/or circumstances - is acknowledged when adopting estimates gathered from the literature for relative errors in the relevant random input variables.

• 대한수학회지
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• 제47권2호
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• pp.263-275
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• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1991년도 가을 학술발표회 논문집
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• pp.57-62
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• 1991

For the purpose of developing the method for efficiently calculating the design sensitivity and the reliability for the complicated structure such as ship structure, the probabilistic finite element method is introduced to formulate the deterministic design sensitivity analysis method and incorporated with the second moment reliability methods such as MVFOSM, AFOSM and SORM. Also, the probabilistic design sensitivity analysis needed in the reliability-based design is performed. The reliability analysis is carried out for the initial yielding failure, in which the derivative derived in the deterministic desin sensitivity is used. The present PFEM-based reliability method shows good agreement with Monte Carlo method in terms with the variance of response and the associated probability of failure even at the first or first few iteration steps. The probabilistic design sensitivity analysis evaluates explicitly the contribution of each random variable to probability of failure. Further, the reliability index variation can be easily predicted by the variation of the mean and the variance of the random variables.