An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal component analyzers is utilized to establish the model of the underlying nonlinear process with local PPCA models, where a novel composite monitoring statistic is proposed based on the integration of two monitoring statistics in modified PPCA-based fault detection approach. Besides, the weighted mean of the monitoring statistics aforementioned is utilized as a metrics to detect potential abnormalities. The virtues of the proposed algorithm are discussed in comparison with several unsupervised algorithms. Finally, Tennessee Eastman process and an autosuspension model are employed to demonstrate the effectiveness of the proposed scheme further.

Although several data-driven soft sensors are available, online reliable prediction of the Mooney viscosity in industrial rubber mixing processes is still a challenging task. A robust semi-supervised soft sensor, called ensemble deep correntropy kernel regression (EDCKR), is proposed. It integrates the ensemble strategy, deep brief network (DBN), and correntropy kernel regression (CKR) into a unified soft sensing framework. The multilevel DBN-based unsupervised learning stage extracts useful information from all secondary variables. Sequentially, a supervised CKR model is built to explore the relationship between the extracted features and the Mooney viscosity values. Without cumbersome preprocessing steps, the negative effects of outliers are reduced using the CKR-based robust nonlinear estimator. With the help of ensemble strategy, more reliable prediction results are further obtained. An industrial case validates the practicality and reliability of EDCKR.

We present an improved kernel recursive least squares (KRLS) algorithm for the online prediction of nonstationary time series. In order to adaptively sparsify a selected kernel dictionary for the KRLS algorithm, the approximate linear dependency (ALD) criterion based KRLS algorithm is combined with the quantized kernel recursive least squares algorithm to provide an initial framework. In order to sufficiently track the strongly changeable dynamic characteristics due to nonstationarity, a forgetting factor is further inserted into the proposed combined algorithm. It is shown that our proposed algorithm, referred to as the FFIKRLS algorithm, provides a clearly compatible algorithm structure and can be improved by the existing modeling techniques from both mapping and weights updating perspectives. Numerical simulations using benchmark Lorenz time series in comparison with existing methods have demonstrated that the proposed algorithm has superior performance in terms of both predictive accuracy and kernel dictionary size.

Establishing an accurate equivalent model is a critical foundation to describe the energy conversion characteristics of a photovoltaic system, which can support the research of fault analysis, output power prediction, and performance analysis of the photovoltaic system. However, the widely used equivalent models are highly nonlinear and have many unknown parameters, making it difficult to identify these parameters accurately. Our previous work found that the gaining‐sharing knowledge‐based algorithm (GSK) shows promising performance in solving this problem. But its efficacy is not enough to achieve accurate parameters within a relatively limited computing resource. In this context, a dual‐population GSK algorithm (DPGSK), which introduces a dual‐population evolution strategy for more excellent searchability, is proposed to address this issue. In each iteration, the population splits equally and randomly into two subpopulations, one of which performs the junior gaining‐sharing phase while the other performs the senior gaining‐sharing phase. Then two updated subpopulations merge to form a new population. This allows for a grand reconciliation of convergence speed and population diversity, giving DPGSK powerful optimization performance. Afterward, DPGSK is applied to five photovoltaic models and validated for performance against other advanced metaheuristics. Besides, the impact of different components on DPGSK is also investigated. Results and comparisons show that either component is indispensable to DPGSK, and DPGSK strengthens the convergence and achieves accurate and reliable results, demonstrating its superiority over other algorithms in solving this studied problem.

Economic dispatch (ED) of thermal power units is significant for optimal generation operation efficiency of power systems. It is a typical nonconvex and nonlinear optimization problem with many local extrema when considering the valve-point effects, especially for large-scale systems. Considering that differential evolution (DE) is efficient in locating global optimal region, while gain-sharing knowledge-based algorithm (GSK) is effective in refining local solutions, this study presents a new hybrid method, namely GSK-DE, to integrate the advantages of both algorithms for solving large-scale ED problems. We design a dual-population evolution framework in which the population is randomly divided into two equal subpopulations in each iteration. One subpopulation performs GSK, while the other executes DE. Then, the updated individuals of these two subpopulations are combined to generate a new population. In such a manner, the exploration and the exploitation are harmonized well to improve the searching efficiency. The proposed GSK-DE is applied to six ED cases, including 15, 38, 40, 110, 120, and 330 units. Simulation results demonstrate that GSK-DE gives full play to the superiorities of GSK and DE effectively. It possesses a quicker global convergence rate to obtain higher quality dispatch schemes with greater robustness. Moreover, the effect of population size is also examined.

In this paper, distributed model predictive control (DMPC) for island DC micro-grids (MG) with wind/photovoltaic (PV)/battery power is proposed, which coordinates all distributed generations (DG) to stabilize the bus voltage together with the insurance of having computational efficiency under a real-time requirement. Based on the feedback of the bus voltage, the deviation of the current is dispatched to each DG according to cost over the prediction horizon. Moreover, to avoid the excessive fluctuation of the battery power, both the discharge-charge switching times and costs are considered in the model predictive control (MPC) optimization problems. A Lyapunov constraint with a time-varying steady-state is designed in each local MPC to guarantee the stabilization of the entire system. The voltage stabilization of the MG is achieved by this strategy with the cooperation of DGs. The numeric results of applying the proposed method to a MG of the Shanghai Power Supply Company shows the effectiveness of the distributed economic MPC.