INVERSE CAUCHY PROBLEM FOR BEAMS IN BUILDING STRUCTURES

A quality index of the coefficient grid inverse Cauchy problem for beams in building structures is proposed. The indicator is based on the theory of regularization of inverse problems. An articulated support of a beam on a column is modeled analytically and by a full-scale experiment. Models of measurement and calculation are investigated for a uniform continuous error rate of deflection measurement and calculation of beam identification parameters. Models differ in various combinations of types of external load. A measure of the influence of the error of the measuring instrument and the distribution of approximation grid nodes on the error in determining the coefficients of the beam deflection equation with a fixed first coefficient is proposed. The measure of influence is described by the dimensionless absolute condition number of the problem. The values of the dimensionless absolute condition number and the quality index of the problem are analyzed depending on the distribution of approximation grid nodes, the error of the measuring instrument, and the type of measurement and calculation model. It is proposed to use the obtained analytical dependencies for the analysis of building structures at the stage of experimental and theoretical studies.

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