A Modified Discrete Karhunen-Loeve Random Field Estimator
Based upon the modified Karhunen-Loeve model of the gravity disturbance vector proposed by us recently, a corresponding Karhunen-Loeve random field estimator is developed in this paper for a two-dimensional grid of gravity data in a local finite region.The new eigenvectors obey the "required" orthogonality relations on the chosen grid provided the KL expansion is now separated into odd and even integers. The closed-form solution of the estimator isthen obtained under the "diagonal" assumption for the gain coefficients. It is shown that this assumption, without which nosolution is possible, enables the estimator to reproduce the data atgrid points when the noise in the data is absent and the number of terms in the Karhunen-Loeve expansion are equal to the number of grid points.
A Modified Karhunen-Loeve Model of Gravity Disturbance Vector
A modified anisotropic Karhunen-Loeve (KL) model for the gravity disturbing potential is proposed. This model, unlike the previous KL model of Bose, does not vanish on the boundaries of a local region. Laplace's equation for the gravity disturbing potential and flatearth Vening-Meinesz relationships of the gravity disturbance vectorcomponents (¿,¿,¿g) when the model is isotropic, are exploited to determine the unknown parameters of the model. The resulting model, in addition to having random boundary values, has three more parameters than those found in Bose's KL model. This should provide extra flexibility in fitting the model to the noisy data available in a local finite region.
Physical Principles of Wind Energy Conversion
The primary component of a wind turbine is the energy converter which transforms the kinetic energy contained in the moving air, into mechanical energy. For the initial discussions of principles, the exact nature of the energy converter is irrelevant. The extraction of mechanical energy from a stream of moving air with the help of a diskshaped, rotating wind energy converter follows its own basic rules.