This book explores a novel approach and the methods of mathematical modeling for technical objects that fall under the category of systems with discretely distributed parameters, whether in time or space. The primary aim of the proposed mathematical methods and approach is to enhance distributed automated systems for monitoring, forecasting, and control, thereby supporting the resolution of challenges related to the efficiency and safety of operations. At the core of this approach are the principles of structural and temporal decomposition of multidimensional processes in mathematical modeling. Key techniques include the use of a customizable orthogonal basis derived from Schur component decomposition or singular value decomposition of covariance matrices based on sampled realizations of the process, as well as the application of preliminary clustering of process realizations and the decomposition of the process into universal quasi-orthogonal basis functions—such as envelope functions, among others. This book is intended for researchers and professionals interested in the challenges of modeling, recognition, and forecasting within energy and other technological processes.