Open Access
ARTICLE
Pugazhenthi Sivasankar1,*, Austin B. Probe2, Tarek A. Elgohary1
Digital Engineering and Digital Twin, DOI:10.32604/dedt.2024.052805
（This article belongs to the Special Issue: Advances in Methods of Computational Modeling in Engineering Sciences, a Special Issue in Memory of Professor Satya Atluri)
Abstract In Space Situational Awareness (SSA), accurate and efficient uncertainty quantification and propagation are essential for various applications, such as conjunction analysis, track correlation, and orbit prediction. The propagation of the probability density function (PDF) in nonlinear systems results in non-Gaussian distributions, which are difficult to approximate. Furthermore, the computational cost of approximating the PDF increases exponentially with the number of random variables, a phenomenon known as the curse of dimensionality. To address these challenges, the Orthogonal Probability Approximation (OPA) method is presented for high-fidelity uncertainty propagation and PDF approximation in nonlinear dynamical systems. The method… More >
Open Access
ARTICLE
Yao Jin1,2,*, Jie Zhao1,2, Xiaozhe Tan1,2, Linghou Miao1,2, Wenxing Yu1,2
Digital Engineering and Digital Twin, DOI:10.32604/dedt.2024.048142
Abstract Substation siting is an important foundation and a key task in power system planning. The article is based on a three-dimensional GIS platform combined with an improved BP neural network algorithm and proposes a substation siting method that is more efficient, accurate and provides a better user experience. Firstly, the BP algorithm is enhanced to improve its convergence speed and computational efficiency for a more accurate and reasonable calculation of optimal site selection. Then, a 24-item selection index system with 7 categories is proposed, which provides quantifiable data support and an evaluation basis for substation… More >
Open Access
ARTICLE
Chein-Shan Liu, Chung-Lun Kuo*
Digital Engineering and Digital Twin, DOI:10.32604/dedt.2024.042804
（This article belongs to the Special Issue: Advances in Methods of Computational Modeling in Engineering Sciences, a Special Issue in Memory of Professor Satya Atluri)
Abstract A new concept of projective solution is introduced for the second-order linear partial differential equations (PDEs) endowed with constant coefficients. In terms of a projective variable the PDE is transformed to a second-order ordinary differential equation (ODE) with constant coefficients at the first time. The characteristic form appears as the coefficient preceding the second-order derivative term. Depending on the characteristic form and coefficients we can derive various parameters-dependent particular solutions, which can be adopted as the bases to expand the solution. The Helmholtz and wave equations are solved by the projection method. We project the… More >
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