Method for gradual deformation of a boolean simulation model of a heterogeneous medium constrained by dynamic data

摘要

At each iteration a combined version is obtained by combining an initial version of N1(t) objects corresponding to a first mean value and a second independent version of the same model of N2(t) objects corresponding to a second means value. This combination is such that the number N(t) of objects has a value equal to the sum of the first and second mean values N1(t) and N2(t) : An iterative optimization process is carried out from versions each including the objects of which the number is pulled from a random Poisson variable by defined means, and an objective function measuring the space between the real and simulated dynamic data from a simulator is minimized by adjusting the combination coefficients. The iterative adjustment process is followed until an optimal version is obtained for the stochastic model. At each iteration, for a same mean value of the combination, the first and second mean values are varied in a concomitant way to vary the number of objects from each combined version gradually. The size of the objects is associated with the process for generation of the number of objects in such a way as to make an object appear or disappear progressively. The number N(t) of objects in the combination of mean lambda is related to the number of respective objects Ni(i=1.n) of the combined versions by the formula N(t){lambda } = S(i=1)n (Ni{ai(t)lambda }) with S(i=1)n (ai=1) and alpha i(t)lambda is the mean of the variable Ni at the moment of the combination. For a combination implying only two versions, trigonometric functions are chosen for the coefficients a1, a2 such as alpha 1 = cos 2(t) and alpha 2 = sin 2(t).