Verification of the RRA-Algorithm Regularization for the Analysis of Stochastic Structures in Bioinformatic Intelligent Systems

摘要

This article deals with methods for the analysis of experimental data in intelligent systems for medical monitoring, the control of diagnostic and therapy processes and biomedical facilities. These methods are relevant for creating mathematical models for dynamic systems with stochastic properties as well as for managing complex subsystems of bio information systems (BIS).The nonlinear dynamic properties of such structures and their evolution in terms of random processes and values manifest themselves as complex (non-Gaussian, polymodal) distributions to be subject to correct identification.The distribution law for stochastic characteristics is necessary to form a mathematical probabilistic model of a local object for the BIS control. Based thereon it is possible to present an experimental-mathematical model of the human respiratory or digestive system functioning, to create systems for monitoring of critical parameters in the course of therapy, to predict and synthesize medicines. When identifying the distribution laws for stochastic structures, it is necessary to solve systems of ill-conditioned equations.BIS models in the form of differential or integral equations also require to solve high-order approximating algebraic systems. Algorithms for solving ill-conditioned systems are based on regularization methods. For these purposes the article suggests the RRA-algorithm procedure. The RRA-algorithm is a variation of the Tikhonov method and it is suggested as a regularization method for first kind Fredholm integral equation. To verify the RRA-algorithm for solving systems of algebraic equations with conditioning numbers of level 1012and higher, solutions of test first kind Fredholm integral equation are presented.