Abstract <p>In this monograph, numerous results of theoretical and experimental research that are obtained by the authors in the fields of distributed measurement media and solving inverse operator problems in mathematical physics, methods for processing fractal (self-similar) signals and fractal geometry, and fluctuation-noise methods for monitoring and diagnosing complex systems using hydrogen fuel cells as an example have been presented. Algorithmic and software implementations of the proposed methods have been discussed. The paper devotes considerable attention to solving applied problems of measurement, signal processing, monitoring, and diagnostics.</p>