A 3D model of optimal contours phased development of oval-shaped open pit mines is proposed in the article. It is assumed that with enough accuracy the volumetric contour of the open pit mine is interpolated by an elongated elliptic hyperboloid. The calculation formulas for mineral resources are derived and optimal volumes of overburden are determined depending on the mining phase. In this case, the total number of mining phases is set in advance. The stripping ratio is used as a quality criterion of the optimization task. The problem of optimal control is solved using the Bellman function in dynamic programming. All the necessary calculation formulas are obtained in the final form by solving the optimization problem. Their simplicity and substantiation of each conclusion ensure that the results of this study can be successfully applied in practical calculations of the design and planning of mining operations in open pit mining.
Abstract:The paper discusses the coefficient inverse problem for one-dimensional heat equation with inaccurate initial data. A conjugate difference problem is developed on difference level. The problem is solved by method of interval analysis. Condition of applicability of Thomas method and its computational convergence are obtained. Estimates of the interval width of solutions of difference problems and functions of Thomas method are also gained.
The current paper presents results of the inverse theory approach utilized for the analytical estimation of thermo-physical properties for a multi-layered medium terrain with homogenized experimental measurements. We demonstrate the derivation steps of the exact solution for the heat transfer problem with third-kind boundary conditions due to natural convection on the outlets posed for the considered experimental domain. There are received analytical expressions. Initially, we illustrate the homogenization of the boundary conditions. We then discuss the process of derivation for the analytical solution of the posed problem with the help of key elements of the Fourier method. We provide an algorithm for applying the contact condition to extend received expressions for multiple layers. After that we demonstrate the major steps for the construction of nonlinear systems of equations to be solved in order to obtain exact values of key thermo-physical and geometrical parameters of the investigated medium with the help of received exact analytical expressions. Along with analytical procedures, we present a posed experimental design and discuss an algorithm of numerical exploitation for a suggested method, outlining its advantages and possible limitations in terms of initial approximations.
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