In this paper, the theory of the Lagrange polynomial approximation of a directly non-measurable characteristic of an element of a mechanical structure by means of an information-measuring system of numerical differentiation is refined. It is shown how to obtain the maximal accuracy of approximation on the basis of the theory of inverse problems and the method of reduction of measurements. For a cantilever beam loaded with concentrated force at its free end, a method has been developed for the experimental and calculated determination of the bending moment at the fixed end of the beam. The basis of the method is the procedure for the optimal placement of sensors and transformation of sensor output signals, if the length of the beam and the initial parameters of the elastic line (lateral displacement and the angle of rotation on the support) are not accurate.
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