Browsing by Subject "dimension reduction"

Now showing 1 - 3 of 3
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    Approximation to Multivariate Normal Integral and Its Application in Time-Dependent Reliability Analysis
    (Elsevier, 2021-01) Wei, Xinpeng; Han, Daoru; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    It is common to evaluate high-dimensional normal probabilities in many uncertainty-related applications such as system and time-dependent reliability analysis. An accurate method is proposed to evaluate high-dimensional normal probabilities, especially when they reside in tail areas. The normal probability is at first converted into the cumulative distribution function of the extreme value of the involved normal variables. Then the series expansion method is employed to approximate the extreme value with respect to a smaller number of mutually independent standard normal variables. The moment generating function of the extreme value is obtained using the Gauss-Hermite quadrature method. The saddlepoint approximation method is finally used to estimate the cumulative distribution function of the extreme value, thereby the desired normal probability. The proposed method is then applied to time-dependent reliability analysis where a large number of dependent normal variables are involved with the use of the First Order Reliability Method. Examples show that the proposed method is generally more accurate and robust than the widely used randomized quasi Monte Carlo method and equivalent component method.
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    Force-directed graph embedding with hops distance
    (IEEE, 2023-12) Lotfalizadeh, Hamidreza; Al Hasan, Mohammad; Computer Science, Luddy School of Informatics, Computing, and Engineering
    Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis tasks like node classification, link prediction, and visualization. In this paper, we propose a novel force-directed graph embedding method that utilizes the steady acceleration kinetic formula to embed nodes in a way that preserves graph topology and structural features. Our method simulates a set of customized attractive and repulsive forces between all node pairs with respect to their hop-distance. These forces are then used in Newton’s second law to obtain the acceleration of each node. The method is intuitive, parallelizable, and highly scalable. We evaluate our method on several graph analysis tasks and show that it achieves competitive performance compared to state-of-the-art unsupervised embedding techniques.
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    High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables
    (ASME, 2022-04) Yin, Jianhua; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    Reliability analysis is a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high-dimensional reliability analysis method through a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated after dimension reduction. Dimension reduction is performed with the first iteration of the first-order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.