The article presents an algorithm for managing the fluidized bed boiler during solid fuel combustion at the enterprises of the fuel and energy complex. The review of technological features of fuel combustion in low-power boilers of high-temperature fluidized bed is performed. The calculated parameters of the furnace processes in transient operating modes are modeled. A program for managing calculated parameters in dynamic modes from the operator’s graphical panel has been developed, which is used as a training model in the educational process of training thermal-power and sanitary engineers.

The article proposes a developed expert information system for assessing environmental risks for complexly structured and uncertain source data. The result of using the program is the desubjectivization of the decision-making process in the presence of a large amount of heterogeneous information. It is supposed to use the system as a technical means of monitoring and assessing the harmful effects of military installations on the environment. The program should serve to increase the effectiveness of environmental protection measures at special facilities of the Ministry of Defense of the Russian Federation. The mathematical algorithm of the developed software application is based on the theory of fuzzy sets (Mamdani’s logical inference diagram). The solution involves finding the degree of truth and bringing to clarity the initially fuzzy input data by the centroid method and, as a result, a score assessment of the quality of environmental characteristics.

The article presents the scheme and principle of operation of a combined fluidized bed unit with re-utilization of heat from exhaust gases of a diesel generator and indicates the requirements for the functioning and operation of these types of installations. It presents theoretical and experimental graphs of the required volumes of air replacement with diesel exhaust gases in nominal and fractional modes, fuel economy, transients of changes in the fluidized bed temperature from time to time when various disturbing effects are applied.

The paper considers Hermite polynomials that act as a self-similar basis for the decomposition of functions in phase space. It is shown that the equations of behavior of nonlinear dynamical systems are simplified. It is also noted that the wavelet decomposition over Hermite polynomials reduces the number of approximation coefficients and improves the quality of approximation.

The article discusses methods of factor analysis to identify heterogeneity in the conditions of spatial distribution and flow formation in aquatic ecosystems. Various factor analysis algorithms were studied to take into account the conjugate action of many factors. Examples of ranking the established dependencies by the value of their own significance criteria are shown. Deficiencies of factor analysis methods in certain software applications were identified because of a possible incorrect interpretation of the results due to the complexity of the technology. The possibility of using factor analysis tools to describe the spatial structures of hydrological data and identify risk zones associated with the instability of the hydrological regime was identified.