Photovoltaic (PV) power forecasting can provide strong support for the safe operation of the power system. Existing forecasting methods are ineffective for grid scheduling decisions or risk analysis. The novel multicluster interval prediction method is proposed to consider the volatility and randomness of PV power output. First, this method utilizes the sparse autoencoder (SAE) and Bayesian regularized NARX network (BRNARX) for point forecasting of PV power. Second, density peak clustering improved by kernel Mahalanobis distance (KMDDPC) is applied to classify the dataset into multiple clusters, including forecasting error and meteorological factors. Finally, the joint probability density is established by multivariate kernel density estimation (MKDE) to accomplish the PV power interval prediction. The proposed hybrid method is applied for the interval prediction of PV power at Yulara, Australia. Comparative research of point forecasting is implemented to evaluate the machine learning and deep learning methods, with the proposed SAE‐BRNARX under four different periods. Results shows that the average values of nRMSE, MRE, nMAE, and R² for the four periods are 4.45%, 0.90%, −0.15%, 3.39%, and 95.93%, respectively. Moreover, the results of interval prediction obtained by the other interval prediction approaches are compared with the proposed KMDDPC‐MKDE. It shows that the average values of PICP, PINAW, ACE, and nMPICD for four periods are 93.93%, 9.50%, 3.93%, and 7.10% at 90% confidence level, respectively. Outcomes demonstrate that the proposed method can obtain more accuracy, a higher coverage rate, narrower average bandwidth, and a closer distance between the middle of interval and actual value than other methods.

Entropy measures the randomness or uncertainty of a stochastic process, and the entropy rate refers to the limit of the time average of entropy. The generalized entropy rate in the form of delayed averages can overcome the redundancy of initial information while ensuring stationarity. Therefore, it has better practical value. A Hidden Markov Model (HMM) contains two stochastic processes, a stochastic process in which all states can be observed and a Markov chain in which all states cannot be observed. The entropy rate is an important characteristic of HMMs. The transition matrix of a homogeneous HMM is unique, while a Nonhomogeneous Hidden Markov Model (NHMM) requires the transition matrices to be dependent on time variables. From the perspective of model structure, NHMMs are novel extensions of homogeneous HMMs. In this paper, the concepts of the generalized entropy rate and NHMMs are defined and fully explained, a strong limit theorem and limit properties of a norm are presented, and then generalized entropy ergodic theorems with an almost surely convergence for NHMMs are obtained. These results provide concise formulas for the computation and estimation of the generalized entropy rate for NHMMs.

Health state assessment is a key technology for system Prognostic and Health Management (PHM) and an important basis for remaining useful life prediction and maintenance decision-making. Rolling bearings are key components of rotating machinery equipment and also one of the most vulnerable components. It has important theoretical and practical significance to evaluate the health state of rolling bearings. In this paper, the empirical mode decomposition (EMD) method is used to extract the vibration signal characteristics of rolling bearings, the dimension of the features is reduced by Mahalanobis-Taguchi system (MTS), and a Hidden Markov Model (HMM) is combined with Mahalanobis distance (MD) to complete health state assessment of rolling bearings. The experimental bearing life cycle data set provided by the Intelligent Maintenance Center of the University of Cincinnati is selected to verify the effectiveness of the proposed method. The experimental results show that the method can detect an early failure and has good sensitivity.

This paper presents a general strong limit theorem for delayed sum of functions of random variables for a hidden time inhomogeneous Markov chain (HTIMC), and as corollaries, some strong laws of large numbers for HTIMC are established thereby.