This paper presents modeling and parameter identification of the Duhem model to describe the hysteresis in the Piezoelectric actuated nano-stage. First, the parameter identification problem of the Duhem model is modeled into an optimization problem. A modified particle swarm optimization (MPSO) technique, which escapes the problem of local optima in a traditional PSO algorithm, is proposed to identify the parameters of the Duhem model. In particular, a randomness operator is introduced in the optimization process which acts separately on each dimension of the search space, thus improving convergence and model identification properties of PSO. The effectiveness of the proposed MPSO method was demonstrated using different benchmark functions. The proposed MPSO-based identification scheme was used to identify the Duhem model parameters; then, the results were validated using experimental data. The results show that the proposed MPSO method is more effective in optimizing the complex benchmark functions as well as the real-world model identification problems compared to conventional PSO and genetic algorithm (GA).

This paper presents a prediction error-based power forecasting (PEBF) method for a Photovoltaic (PV) system, using Photovoltaics for Utility Scale Applications (PVUSA) model based grey box neural network (GBNN). First, the differential equation based PVUSA model is transformed into a neural network. In the proposed PEBF scheme, the neural network is set to train whenever the difference between predicted and output powers increases from a certain threshold defined based on system dynamics and requirements. The unique design of the PVUSA model based grey box neural network takes far less training time than usual black-box neural network based models. This gives the proposed prediction scheme an advantage of updating the prediction model parameters from frequent training of neural networks with the change in metrological variables. The effectiveness of the proposed prediction scheme is demonstrated by a real case study regarding a 20MW grid-connected PV system located in Dongying city of Shandong province China. To evaluate the efficiency of the developed scheme, different assessment metrics, mean absolute error (MAE), root mean square error (RMSE), weighted mean absolute error (WMAE) and coefficient of determination ( $R^{2}$ ) are applied. The average values of MAE, RMSE, and WMAE were 0.12 %, 0.20% and 0.23% respectively for all cases. The results demonstrate that the proposed scheme predicts the PV power efficiently within the defined error tolerance level, which shows the effectiveness and feasibility of the proposed prediction scheme. The prediction accuracy of the proposed scheme has been compared with the conventional black box neural network models and reveals outperformed performance with respect to prediction accuracy improvement. The proposed prediction scheme will help to balance power production and demands across integrated networks through economic dispatch decisions between the power sources.

A modeling and parameter identification method for rate dependent hysteresis of piezoelectric actuated nano-stage is presented in this work. A system level quasi-static hysteresis model is employed to construct a neural network. To better describe the rate dependent behavior of hysteresis in piezoelectric actuated stage, a Nonlinear AutoRegressive Moving Average with eXogenous input (NARMAX) based dynamic model is incorporated with the quasi-static hysteresis model, where the weights of specifically designed neural network corresponds to the model parameters. To handle the multivalued problem of hysteresis, generalized input gradient is proposed to convert multivalued mapping of hysteresis into one-to-one mapping. The parameters of the nonlinear rate dependent hysteresis in piezoelectric actuated stage is identified by neural network training, taking advantage of their universal function approximation capabilities. The proposed scheme is also compared with conventional black box and particle swarm optimization identification based methods, simulation and experimental results demonstrate significant performance improvement with an error of 20.77nm for proposed method whereas 96.56nm and 31.46nm for black box and particle swarm optimization respectively.

Trajectory Tracking Control for Disturbed Euler-Lagrange Systems: A Fixed-Time Adaptive Approach

The Weibull distribution is widely used in reliability estimation across industries, but accurately identifying its parameters remains a challenging task. This research proposes an efficient method for estimating Weibull distribution parameters by combining the maximum likelihood method with optimization theory. First, the parameter estimation problem is formulated as an optimization problem. A constrained search space partitioning framework is introduced, leveraging parameter-specific minimum and maximum bounds for the shape, location, and scale parameters. By dividing the search space into smaller subspaces for each parameter, the method constrains the search direction, significantly reducing estimation time. To address the local optima problem common in heuristic algorithms, a randomness operator is integrated into the optimization process. The proposed constrained search space partitioning framework is implemented using a conventional g-best version of the particle swarm optimization algorithm with historical fault data. Experimental results demonstrate that the proposed scheme outperforms state-of-the-art methods and conventional optimization-based approaches in terms of estimation accuracy and computational efficiency.