This paper presents a hybrid model based on the displacement back analysis to estimate the earth stress magnitude and direction from the obtained borehole displacements. An artificial neural network (ANN) is used to map the non-linear relationship between the maximum horizontal earth stress, σH, the minimum horizontal earth stress, σh, the direction of the largest horizontal earth stress, θ and the borehole displacements. The genetic algorithm (GA) is used to search the set of unknown earth stresses and direction according to the objective function. Results of the numerical experiments show that the displacement back analysis method can effectively identify the earth stress based on the wellbore motions during drilling. and Obsahuje seznam literatury
We study singular boundary value problems with mixed boundary conditions of the form (p(t)u ' ) ' + p(t)f(t, u, p(t)u ' ) = 0, lim t→0+ p(t)u ' (t) = 0, u(T) = 0, where [0, T] ⊂ . We assume that D ⊂ R 2 , f satisfies the Carathéodory conditions on (0, T) × D, p ∈ C[0, T] and 1/p need not be integrable on [0, T]. Here f can have time singularities at t = 0 and/or t = T and a space singularity at x = 0. Moreover, f can change its sign. Provided f is nonnegative it can have even a space singularity at y = 0. We present conditions for the existence of solutions positive on [0, T).