The paper presents a review of the studies that were conducted at Energy Systems Institute (ESI) SB RAS in the field of mathematical modeling of nonlinear input-output dynamic systems with Volterra polynomials. The first part presents an original approach to identification of the Volterra kernels. The approach is based on setting special multi-parameter families of piecewise constant test input signals. It also includes a description of the respective software; presents illustrative calculations on the example of a reference dynamic system as well as results of computer modeling of real heat exchange processes. The second part of the review is devoted to the Volterra polynomial equations of the first kind. Studies of such equations were pioneered and have been carried out in the past decade by the laboratory of ill-posed problems at ESI SB RAS. A special focus in the paper is made on the importance of the Lambert function for the theory of these equations.
The paper addresses the conventional approaches to the short-term forecasting of nonstationary processes in complex power systems using the methodology of artificial neural networks (ANNs). In many practical cases the application of different ANNs can provide a satisfactory forecast. But data preprocessing and analysis can significantly improve the forecast. In this paper the Hilbert-Huang Transform (HHT) is used as one of the most promising tools in this area. Here we focus on HHT since this transform underlies the proposed two-stage intelligent approach to short-term forecasting of nonstationary processes.
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