The use of a fractal-cluster theory apparatus is proposed to describe random information signals in the information space when technological parameters of a power plant unit deviate from standard specifications. It is found that when random information signals with warning signs are transmitted, the degree of filling of the three-dimensional phase information space changes, which is characterized by the informational fractal dimension as a decimal value. This demonstrates a clear connection between the degree of space filling and the changing quality of information in the information space. Analytical expressions are derived, allowing the establishment of a relationship between the increase in the amount of accidental information due to deviations from standard technological parameters and changes in the informational dimension of random fractal signals in space coordinates and real-time. This approach provides a robust tool for detecting potential failures by analyzing the behavior of the fractal dimension of the signals. Furthermore, it is determined that changes in the informational dimension of signals act as a sensitive indicator of the emergence of unstable system operating modes. This enables not only the identification of critical parameter deviations but also the assessment of potential accident risks at early stages.