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.
Preparation and performance evaluation of swine manure bio-oil modified rubber asphalt binder
Abstract In order to study the effect of the preparation process of swine manure bio-oil modified rubber asphalt binder on the rheological properties of the binder, the matrix asphalt and asphalt rubber were used as the control group, and swine manure bio-oil modified rubber asphalt binders were obtained by three preparation processes. Then the rheological properties of five binders were evaluated by rotational viscosity, DSR, MSCR and BBR tests. The results show that the addition of swine manure bio-oil to asphalt rubber is beneficial to the workability, but cause negative effect on its high temperature performance, fatigue performance and low temperature crack resistance. The preparation method of premixing bio-oil and rubber powder can reduce the degradation of high-temperature performance of asphalt rubber caused by addition of swine manure bio-oil to a certain extent. The fatigue properties of the three bio-binders are close, and the critical temperature is less than 25 °C. The process of premixing bio-oil and rubber powder will increase the creep stiffness and reduce the low-temperature performance. However, the low-temperature performance of the binder obtained by this process is still better than that of the matrix asphalt and can meet the requirements of use. Therefore, it is recommended to use the preparation process of premixing bio-oil and rubber powder to prepare swine manure bio-oil modified asphalt rubber.