The use of photovoltaic systems has increased in recent years due to their decreasing costs and improved performance. However, these systems can be susceptible to faults that can reduce efficiency and energy yield. To prevent and reduce these problems, preventive or predictive maintenance and effective monitoring are necessary. PV health monitoring systems and automatic fault detection and diagnosis methods are critical for ensuring PV plants’ reliability, high-efficiency operation, and safety. This paper presents a new framework for developing fault detection in photovoltaic (PV) systems. The proposed approach uses machine learning algorithms to predict energy power production and detect anomalies in PV plants by comparing the predicted power from a model and the measured power from sensors. The framework utilizes historical data to train the prediction model, and live data is compared with predicted values to analyze residuals and detect abnormal scenarios. The proposed approach has been shown to accurately distinguish anomalies using constructed thresholding, either static or dynamic thresholds. The paper also reports experimental results using the Matthews correlation coefficient, a more reliable statistical rate for an imbalanced dataset. The proposed approach leads to a reasonable anomaly detection rate, with an MCC of 0.736 and a balanced ACC of 0.863.

In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [1,2] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.

In this paper, we introduce and study a Halpern inertial method for solving the general perturbed Krasnoselskii-Mann type algorithm in Hilbert space settings, where the underlying mapping is quasi-nonexpansive. We discuss convergence analysis of the method under some mild assumptions on the control sequences. We additionally present a numerical example to demonstrate the effectiveness of the method. Finally, we apply the method in solving image restoration problems. We evaluate the quality of the improvement in the Signal-to-Noise Ratio (ISNR) and the restored images using the Structural Similarity Index Measure (SSIM) metrics. The results of this work generalize and expand upon numerous results found in the literature.

In this paper, we investigate an uncertain multiobjective optimization problem involving nonsmooth and nonconvex functions. The notion of a (local/global) robust weak sharp efficient solution is introduced. Then, we establish necessary and sufficient optimality conditions for local and/or the robust weak sharp efficient solutions of the considered problem. These optimality conditions are presented in terms of multipliers and Mordukhovich/limiting subdifferentials of the related functions.