Load forecasting is critical for effective scheduling and operation of power systems, which are becoming increasingly complex and uncertain, especially with the penetration of distributed power. This paper proposes a data-driven deep learning framework to forecast the short-term power load. First, the load data is processed by Box-Cox transformation. The tail-dependence of the power load on electricity price and temperature is then investigated by fitting the parametric Copula models and computing the threshold of peak load. Next, a deep belief network is built to forecast the hourly load of the power system. One-year grid load data collected from urban areas in both Texas and Arkansas, in the United States, is utilized in the case studies on short-term load forecasting (day-ahead and week-ahead) is conducted for four seasons independently. The proposed framework is compared with classical neural networks, support vector regression machine, extreme learning machine, and classical deep belief networks. The load forecasting performance is evaluated using mean absolute percentage error, root mean square error, and hit rate. The proposed framework outperforms the tested state-of-the-art algorithms, with respect to the accuracies of both day-ahead and week-ahead forecasting. Overall, the computational results confirm the effectiveness of the proposed data-driven deep learning framework.

Rule-based models are applicable to model the behavior of complex and nonlinear systems. Due to limited experience and randomness involving constructing information granules, an insufficient credible rules division could reduce the model's accuracy. This paper proposes a new rule-based modeling approach, which utilizes density-based spatial clustering of applications with noise (DBSCAN)-based information granules to construct the rules. First, bear in mind the advantages of density-based clustering, DBSCAN is proposed to generate data structures. Based on these data structures, two rule-based models are constructed: 1) models using DBSCAN clusters to construct granules and rules directly and 2) models generating subgranules in each DBSCAN cluster for rule formation. Experiments involving these two models are completed, and obtained results are compared with those generated with a traditional model involving fuzzy C-means-based granules. Numerical results show that the rule-based model, which builds rules from subgranules of DBSCAN structures, performs the best in analyzing system behaviors.

The study is concerned with a description of large numeric data with the aid of building a limited collection of representative information granules with the objective of capturing the structure of the original data. The proposed development scheme consists of two steps. First, a clustering algorithm characterized by high flexibility of coping with the diverse geometry of data structure and efficient computational overhead is invoked. At the second step, a clustering algorithm applied to the clusters already formed during the first phase, yielding a collection of numeric prototypes is involved and the numeric prototypes produced there are then generalized into their granular prototypes. The quality of granular prototypes is quantified while their build-up is supported by the mechanisms of granular computing such as the principle of justifiable granularity. In this paper, the clustering algorithms of DBSCAN and fuzzy C-means were used in successive phases of the processed approach. The experimental studies concerning synthetic data and publicly available data are covered and the performance of the developed approach is assessed along with a comparative analysis.

The engine knock simulator is useful for the evaluation of the feedback knock controllers and also the calibration of the feedforward control input without experiments in spark-ignition engines. This article proposes a mixture density network (MDN)-based statistical simulator of the engine knock for spark-ignition engines. The simulator can output the simulated knock intensity by the operating condition, which has a consistent probability distribution with the real engine. The statistical analysis is conducted based on the experimental data. According to the analysis results, several important properties about the knock intensity have been revealed. The logarithm of knock intensity is independent and identically distributed under an identical operating condition, whose probability distribution can be approximated by Gaussian mixture model (GMM). The parameter vector of the GMM is a function of the engine’s operation condition. Based on these statistical properties of engine knock, we formulate the problem of establishing a statistical simulator, which includes two subproblems. The first one is how to approximate the function from the operating condition to the parameters of the GMM. The second one is how to output the simulated random data of logarithm of knock intensity that obeys a given distribution. The MDN and the accept–reject algorithm are applied to solve the two subproblem, respectively. Finally, we conducted experimental data-based validations to verify the proposed method.