We demonstrate that noises form in the beginning of the latent period of objects’ transition into an emergency state, causing continuous changes in the statistical characteristics of the technological parameters. The theoretical foundations of analysis of noise as a carrier of diagnostic information have been proposed, and the algorithms for forming the correlation matrices of technological parameters equivalent to the matrices of their useful signals have been developed. We also propose the theoretical foundations of solving the problems of monitoring and identification of the latent period of changes in the technical condition of industrial facilities. Various intelligent robust systems of noise monitoring of the beginning of accidents at the facilities and objects of industries and fields, such as oil and gas extraction, construction, energy development, transport, seismology, aviation, medicine, etc. have been designed, built and put into operation. The proposed technologies can also become widely used for solving numerous problems of recognition, identification, modeling and control in various areas of science, technology and engineering.