Abstract
The problems arising in the use of finite-difference approximation in a situation when an analytical solution is very difficult or impossible to obtain are investigated. This paper describes the generation of fuzzy inference system based on the CART (classification and regression tree) method. The resulting fuzzy system was used to determine the parameters of the oil reservoir to the well test after tuning parameter. Computational experiments are used to demonstrate the applicability of the fuzzy system for non-linear regression analysis.
Highlights
Mathematical models of the reservoir-reservoir are created by solving the diffusion equation under various boundary conditions
After the structure of the fuzzy system has been determined, its parametric adjustment [6, 9] is required, at which both the rule conclusions and the membership functions of the terms of the input variables are adjusted at the same time
The hybrid optimization method ANFIS [8, 11], in which the linear parameters are tuned for the Kalman filter, and the non-linear parameters by the gradient method of back propagation of the error, proved successful
Summary
Mathematical models of the reservoir-reservoir are created by solving the diffusion equation under various boundary conditions. To obtain analytical solutions of the diffusion Eq (1), the Laplace integral transformation is applied, which leads to a smoothing of the errors of the experimental functions. The application of the Laplace transform is limited to those cases when the solution of the differential equation can be obtained analytically. If an exact solution cannot be obtained, it is possible to replace the differential equation by its finite-difference analogue [4, 5]. The gray box model is convenient for using various methods of system identification
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