Semi-supervised learning acts as an effective way to leverage massive unlabeled data. In this paper, we propose a novel training strategy, termed as Semi-supervised Contrastive Learning (SsCL), which combines the well-known contrastive loss in self-supervised learning with the cross entropy loss in semi-supervised learning, and jointly optimizes the two objectives in an end-to-end way. The highlight is that different from self-training based semi-supervised learning that conducts prediction and retraining over the same model weights, SsCL interchanges the predictions over the unlabeled data between the two branches, and thus formulates a co-calibration procedure, which we find is beneficial for better prediction and avoid being trapped in local minimum. Towards this goal, the contrastive loss branch models pairwise similarities among samples, using the pseudo labels generated from the cross entropy branch, and in turn calibrates the prediction distribution of the cross entropy branch with the contrastive similarity. We show that SsCL produces more discriminative representation and is beneficial to semi-supervised learning. Notably, on ImageNet with ResNet50 as the backbone, SsCL achieves 60.2% and 72.1% top-1 accuracy with 1% and 10% labeled samples, respectively, which significantly outperforms the baseline, and is better than previous semi-supervised and self-supervised methods.

Rapid growth of diversity, uncertainty, and coupling effect of units in modern energy systems jointly challenges the traditional model-based situation awareness (SA) in Energy Internet of Things (EIoT). This work explores the digital twin of EIoT (EIoT-DT) and then provides a novel data-driven SA paradigm, named DT-SA, as a promising alternative. Based on the combination of the latest data technologies and machine learning algorithms, DT-SA transfers those stubborn SA challenges to digital space, and then addresses them by building a domain-specific and data-friendly digital twin (DT) model upon massive data. The established model can be quantitatively tested via iterative virtual–real interaction and, thus, be evaluated and updated through closed-loop feedback to improve its performance in the physical world. To this end, some engineering and scientific problems are raised: 1) virtual–real interaction mechanism relevant to resource flow and data flow; 2) unified modeling and analysis of heterogeneous spatial–temporal data; 3) DT configuration and evolution; and 4) domain-specific DT-SA characterization. To solve these problems, cloud-edge-terminal configuration, big data analytics (BDA), DT, and SA indicator systems are studied, respectively. Then, the random matrix theory (RMT) and overarching DT-SA framework are designed as a roadmap. Besides, some potential applications and undergoing projects on the terminal, edge, or cloud are discussed, e.g., condition assessment of equipment, digital monitoring and diagnosis of the power grid network, and EIoT construction in the smart city. Finally, some perspectives and recommendations are proposed in conclusion for future research. This research can be regarded as an efficient handbook for both energy engineering and data science, which may benefit enterprise digitization, smart city, etc.

The online monitoring data in distribution networks contain rich information on the running states of the networks. By leveraging the data, this paper proposes a spatio-temporal correlation analysis approach for anomaly detection and location in distribution networks. First, spatio-temporal matrix for each feeder line in a distribution network is formulated and the spectrum of its covariance matrix is analyzed. The spectrum is complex and exhibits two aspects: 1) bulk, which arises from random noise or fluctuations and 2) spikes, which represents factors caused by anomaly signals or fault disturbances. Then, by connecting the estimation of the number of factors to the limiting empirical spectral density of covariance matrices of residuals, the spatio-temporal parameters are accurately estimated, during which free random variable techniques are used. Based on the estimators, anomaly indicators are designed to detect and locate the anomalies by exploring the variations of spatio-temporal correlations in the data. The proposed approach is sensitive to the anomalies and robust to random fluctuations, which makes it possible for detecting early anomalies and reducing false alarming rate. Case studies on both synthetic data and real-world online monitoring data verify the effectiveness and advantages of the proposed approach.

Recently, the robustification of principal component analysis (PCA) has attracted much research attention in numerous areas of science and engineering. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. With this model, the nuclear norm and l1-norm penalties are usually used for low-rank and sparsity promotion. Although the nuclear norm and l1-norm are favorable due to their convexity, they have a bias problem. In comparison, nonconvex penalties can be expected to yield better recovery performance. In this work, we consider a formulation for robust PCA using generalized nonconvex penalties for low-rank and sparsity inducing. This nonconvex formulation is efficiently solved by a multi-block alternative direction method of multipliers (ADMM) algorithm. A sufficient condition for the convergence of this new ADMM algorithm has been derived. Furthermore, to address the important issue of nonconvex penalty selection, we have evaluated the new algorithm via numerical experiments in various low-rank and sparsity conditions. The results indicate that“, exact” recovery of the low-rank principle component can be achieved only by nonconvex regularization. Matlab code is available at https://github.com/FWen/RPCA.git.

Data-driven approaches, when tasked with situation awareness, are suitable for complex grids with massive datasets. It is a challenge, however, to efficiently turn these massive datasets into useful big data analytics. To address such a challenge, this paper, based on random matrix theory (RMT), proposes a data-driven approach. The approach models massive datasets as large random matrices; it is model-free and requiring no knowledge about physical model parameters. In particular, the large data dimension N and the large time span T, from the spatial aspect and the temporal aspect respectively, lead to favorable results. The beautiful thing lies in that these linear eigenvalue statistics (LESs) built from data matrices follow Gaussian distributions for very general conditions, due to the latest breakthroughs in probability on the central limit theorems of those LESs. Numerous case studies, with both simulated data and field data, are given to validate the proposed new algorithms.

Together with the rapid development of the Internet of Things, human activity recognition (HAR) using wearable inertial measurement units (IMUs) becomes a promising technology for many research areas. Recently, deep-learning-based methods pave a new way of understanding and performing analysis of the complex data in the HAR system. However, the performance of these methods is mostly based on the quality and quantity of the collected data. In this article, we innovatively propose to build a large data set based on virtual IMUs and then address technical issues by introducing a multiple-domain deep learning framework consisting of three technical parts. In the first part, we propose to learn the single-frame human activity from the noisy IMU data with hybrid convolutional neural networks in the semisupervised form. For the second part, the extracted data features are fused according to the principle of uncertainty-aware consistency, which reduces the uncertainty by weighting the importance of the features. The transfer learning is performed in the last part based on the newly released archive of motion capture as surface shapes data set, containing abundant synthetic human poses, which enhances the variety and diversity of the training data set and is beneficial for the process of training and feature transfer in the proposed method. The efficiency and effectiveness of the proposed method have been demonstrated in the real deep inertial poser data set. The experimental results show that the proposed methods can surprisingly converge within a few iterations and outperform all competing methods.