The paper describes a novel online identification algorithm for a two-mass drive system. The multi-layer extended Kalman Filter (MKF) is proposed in the paper. The proposed estimator has two layers. In the first one, three single extended Kalman filters (EKF) are placed. In the second layer, based on the incoming signals from the first layer, the final states and parameters of the two-mass system are calculated. In the considered drive system, the stiffness coefficient of the elastic shaft and the time constant of the load machine is estimated. To improve the quality of estimated states, an additional system based on II types of fuzzy sets is proposed. The application of fuzzy MKF allows for a shorter identification time, as well as improves the accuracy of estimated parameters. The identified parameters of the two-mass system are used to calculate the coefficients of the implemented control structure. Theoretical considerations are supported by simulations and experimental tests.

This paper proposes the usage of the fuzzy rule-based Bayesian algorithm to determine which residential appliances can be considered for the Demand Response program. In contrast with other related studies, this research recognizes both randomness and fuzziness in appliance usage. Moreover, the input data for usage prediction consists of nodal price values (which represent the actual power system conditions), appliance operation time, and time of day. The case study of residential power consumer behavior modeling was implemented to show the functionality of the proposed methodology. The results of applying the suggested algorithm are presented as colored 3D control surfaces. In addition, the performance of the model was verified using R squared coefficient and root mean square error. The conducted studies show that the proposed approach can be used to predict when the selected appliances can be used under specific circumstances. Research of this type may be useful for evaluation of the demand response programs and support residential load forecasting.