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Identification of piecewise constant filtration parameters and boundaries of their constancy domains. (English. Russian original) Zbl 1377.93059
Autom. Remote Control 78, No. 8, 1404-1416 (2017); translation from Avtom. Telemekh. 2017, No. 8, 60-75 (2017).
Summary: Consideration is given to the numerical solution of the problem of parametric identification of the processes obeying the parabolic equations using an example of the processes of underground oil filtration. The identified parameters belong to the given functional classes such as the piecewise constant and piecewise linear functions. In the problem, not only to determine the values of the coefficients is needed, but also to identify the constancy boundaries of the coefficients. For numerical solution of the problem, an approach is suggested based on reduction of the initial problem to that of finite-dimensional optimization with a special structure of constraints. Formulas are obtained for the gradient of the objective functional in the discretized problem allowing one to apply the efficient methods of first-order optimization. The results of numerical experiments on the model problems are presented.
MSC:
93B30 System identification
35K20 Initial-boundary value problems for second-order parabolic equations
49K45 Optimality conditions for problems involving randomness
49M25 Discrete approximations in optimal control
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