A transformation for near strongly singular integrals
A simple transformation using a singularity cancellation technique is presented that enables accurate and efficient computation of near strongly singular integrals involving the gradient of Helmholtz-type potentials for projected observation points that lie external to the source element. The coordinate reference is offset from the projection of the observation point onto the plane containing the source element. In many cases, this permits highly accurate results without the splitting of the source element.
A Simple Transformation for the Numerical Evaluation of Near Strongly Singular Integrals
A simple transformation using a singularity cancellation technique is presented that enables accurate and efficient computation of near strongly singular integrals involving the gradient of Helmholtz-type potentials for projected observation points that lie external to the source element. Unlike previous Duffy-like transformations, the coordinate reference is offset from the projection of the observation point onto the plane containing the source element. In many cases, this permits highly accurate results without the splitting of the source element. When splitting is required, high-aspect-ratio subtriangles are easily avoided.
A Short-Term and High-Resolution Distribution System Load Forecasting Approach Using Support Vector Regression With Hybrid Parameters Optimization
This paper proposes an approach for distribution system load forecasting, which aims to provide highly accurate short-term load forecasting with high resolution utilizing a support vector regression (SVR) based forecaster and a two-step hybrid parameters optimization method. Specifically, because the load profiles in distribution systems contain abrupt deviations, a data normalization is designed as the pretreatment for the collected historical load data. Then an SVR model is trained by the load data to forecast the future load. For better performance of SVR, a two-step hybrid optimization algorithm is proposed to determine the best parameters. In the first step of the hybrid optimization algorithm, a designed grid traverse algorithm (GTA) is used to narrow the parameters searching area from a global to local space. In the second step, based on the result of the GTA, particle swarm optimization is used to determine the best parameters in the local parameter space. After the best parameters are determined, the SVR model is used to forecast the short-term load deviation in the distribution system. The performance of the proposed approach is compared to some classic methods in later sections of this paper.