The identification of the multiple model-based Hammerstein parameter varying systems is studied in this paper. The parameters of the considered systems vary as the systems perform on different operating conditions. For each local model, the input nonlinear output-error structure is introduced to describe the dynamical property. Allocating an exponential weighting function to each local model, the nonlinear dynamics of the global system is approximated by combining all local models. The variational Bayesian (VB) approach is adopted to find the solution to the problem of parameter estimation. For the parameter uncertainties, instead of the point estimation, the posterior distribution of each model parameters is obtained under the framework of the VB approach. Two numerical simulation examples and an experiment carried on a multitank system have been employed to demonstrate that the proposed approach can work effectively.

In this study, a multi-direction-based gradient iterative (GI) algorithm for Hammerstein systems with irregular sampling data is proposed. The algorithm updates the parameter estimates using several orthogonal directions at each iteration. The convergence rate is significantly improved with an increasing number of directions. The convergence property and two simulation examples are provided to demonstrate the effectiveness of the proposed algorithm. In addition, the multi-direction-based GI algorithm establishes a relationship between the traditional GI and least squares (LS) algorithms. Thus, our algorithm that combines the LS and GI algorithms constructs an identification framework for a significantly wider class of systems.

Soft sensor, as a significant intelligent inspection technology, has been widely used in modern process industries to achieve effective monitoring and prediction of product quality. However, the redundancy of model inputs and structure in practical industrial process modeling usually results in increased modeling complexity and decreased model performance. In this study, an input variable selection and structure optimization algorithm for long short-term memory (LSTM)-based soft sensor with a dual nonnegative garrote (DNNG) approach was proposed. Firstly, a well-trained initial LSTM model is constructed using the process dataset to capture the temporal dynamic behavior of the industrial process. Secondly, the DNNG algorithm is integrated into the LSTM to reduce the redundancy of input variables and hidden nodes. The strategy efficiently selects the most consequential input variables for the model, and simultaneously simplifies the LSTM structure by eliminating redundant recurrent hidden nodes to reduce model overfitting risk. Moreover, the hyperparameters of the model are determined by combining grid search with blocked cross-validation. Finally, the developed algorithm is compared to other state-of-the-art algorithms using a numerical case and employed to forecast the SO ₂ concentration in the net flue gas emissions of a coal-fired power plant desulphurization system. Comparative results show that the proposed algorithm effectively eliminates redundant variables and streamlines the model structure while presenting better prediction performance than other algorithms.