SUMMARY
In connection with the global increase in the intensity of use of working equipment related to high-risk facilities and the expiry of the service life limit, the question arises of determining the actual technical condition and forecasting the residual resource. From the analysis of the approaches to determining the technical state and on the analysis of regulatory documents, it becomes clear that the regulated methods of assessing the technical state are obsolete, such that they do not ensure the reliability of the obtained control results.A new technique for determining the actual technical state through monitoring the level of stresses in the body of high-risk objects is proposed. The new technique takes into account additional physical and mechanical parameters that affect the stress-strain state, and have not yet been used. In other words, the technique of multivariable control of stress determination was proposed.Mathematical models of the process of deformation and stress for cylindrical vessels with a spherical and conic dome operating under the action of high pressure are proposed.