A New Approach to the Gray-Box Identification of Wiener Models With the Application of Gas Turbine Engine Modeling

In this paper, a new approach is presented for the gray-box identification of Wiener models (WM); and to evaluate the performance of the proposed method, it is used to estimate the dynamic behavior of a two-shaft industrial gas turbine (GT). The Wiener models, which have attracted a considerable attention due to their low computational demand and high accuracy, represent modeling techniques based on system identification. These models are composed of a linear dynamic part interconnected with a nonlinear static element, and the unknown parameters of these two parts are generally determined by black-box identification approaches. However, another identification method known as “gray-box identification” can also be employed, which uses the existing information about the static or dynamic behavior of a system to achieve the unknown parameters of the Wiener model. In this study, an innovative approach for improving the Wiener model’s capability of predicting the dynamic behavior of nonlinear systems is presented with the assumption that the static behavior of the examined system is known. In the proposed model called the enhanced Wiener model (EWM), the parameters of the linear dynamic part are allowed to vary with the operating conditions; and thus, this model provides a higher flexibility in estimating the dynamic behavior of the examined system compared to the conventional Wiener models. The EWM consists of a static nonlinear block and a linear dynamic block with varying parameters. Since gas turbine engines are essentially nonlinear in both the steady and transient conditions, the modeling of a gas turbine can be a suitable case for evaluating the effectiveness of the proposed model. In this regard, in order to estimate the parameters of a two-shaft industrial gas turbine, five multi-input single-output (MISO) EWMs with a special structure are employed in which the parameters of the dynamic part of each EWM is determined by an adaptive network-based fuzzy inference system (ANFIS). In order to evaluate the performance of the proposed model, the EWM results are compared with the result obtained by common system identification approaches like Wiener, Hammerstein, Wiener–Hammerstein, nonlinear autoregressive exogenous (NARX), and ANFIS models. The simulation results reveal that the proposed EWM not only is more flexible and effective in predicting the dynamic behavior of the examined gas turbine than the block-structured models, but it also outperforms the NARX and ANFIS models in estimating the static behavior of the gas turbine.