Abstract. The determination of periodic stationarity conditions for periodic autoregressive moving average (PARMA) processes is a prerequisite to their analysis. Means of obtaining these conditions in analytically simple forms are sought. It is shown that periodic stationarity conditions for univariate and multivariate PARMA processes can always be reduced to eigenvalue problems, which are computationally and analytically easier to deal with. Two different lumpings of the periodic process are considered along this line. The first is the common w-span lumping over all w periods. The second lumping considered is the p-span lumping of the p th order periodic autoregressive process over p periods, which is based on a recently introduced lumping technique. It is shown that p-span lumping may yield the periodic stationarity conditions in an analytically simpler form as compared to w-span lumping when p < w.

The integration of improved control techniques with advanced information technologies enables the rapid development of smart grids. The necessity of having an efficient, reliable, and flexible communication infrastructure is achieved by enabling real-time data exchange between numerous intelligent and traditional electrical grid elements. The performance and efficiency of the power grid are enhanced with the incorporation of communication networks, intelligent automation, advanced sensors, and information technologies. Although smart grid technologies bring about valuable economic, social, and environmental benefits, testing the combination of heterogeneous and co-existing Cyber-Physical-Smart Grids (CP-SGs) with conventional technologies presents many challenges. The examination for both hardware and software components of the Smart Grid (SG) system is essential prior to the deployment in real-time systems. This can take place by developing a prototype to mimic the real operational circumstances with adequate configurations and precision. Therefore, it is essential to summarize state-of-the-art technologies of industrial control system testbeds and evaluate new technologies and vulnerabilities with the motivation of stimulating discoveries and designs. In this paper, a comprehensive review of the advancement of CP-SGs with their corresponding testbeds including diverse testing paradigms has been performed. In particular, we broadly discuss CP-SG testbed architectures along with the associated functions and main vulnerabilities. The testbed requirements, constraints, and applications are also discussed. Finally, the trends and future research directions are highlighted and specified.

This paper surveys the deep learning (DL) approaches for intrusion-detection systems (IDSs) in Internet of Things (IoT) and the associated datasets toward identifying gaps, weaknesses, and a neutral reference architecture. A comparative study of IDSs is provided, with a review of anomaly-based IDSs on DL approaches, which include supervised, unsupervised, and hybrid methods. All techniques in these three categories have essentially been used in IoT environments. To date, only a few have been used in the anomaly-based IDS for IoT. For each of these anomaly-based IDSs, the implementation of the four categories of feature(s) extraction, classification, prediction, and regression were evaluated. We studied important performance metrics and benchmark detection rates, including the requisite efficiency of the various methods. Four machine learning algorithms were evaluated for classification purposes: Logistic Regression (LR), Support Vector Machine (SVM), Decision Tree (DT), and an Artificial Neural Network (ANN). Therefore, we compared each via the Receiver Operating Characteristic (ROC) curve. The study model exhibits promising outcomes for all classes of attacks. The scope of our analysis examines attacks targeting the IoT ecosystem using empirically based, simulation-generated datasets (namely the Bot-IoT and the IoTID20 datasets).

The heterogeneous and interoperable nature of the cyber-physical system (CPS) has enabled the smart grid (SG) to operate near the stability limits with an inconsiderable accuracy margin. This has imposed the need for more intelligent, predictive, fast, and accurate algorithms that are able to operate the grid autonomously to avoid cascading failures and/or blackouts. In this paper, a new comprehensive identification system is proposed that employs various machine learning architectures for classifying stability records in smart grid networks. Specifically, seven machine learning architectures are investigated, including optimizable support vector machine (SVM), decision trees classifier (DTC), logistic regression classifier (LRC), naïve Bayes classifier (NBC), linear discriminant classifier (LDC), k-nearest neighbor (kNN), and ensemble boosted classifier (EBC). The developed models are evaluated and contrasted in terms of various performance evaluation metrics such as accuracy, precision, recall, harmonic mean, prediction overhead, and others. Moreover, the system performance was evaluated on a recent and significant dataset for smart grid network stability (SGN_Stab2018), scoring a high identification accuracy (99.90%) with low identification overhead (4.17 μSec) for the optimizable SVM architecture. We also provide an in-depth description of our implementation in conjunction with an extensive experimental evaluation as well as a comparison with state-of-the-art models. The comparison outcomes obtained indicate that the optimized model provides a compact and efficient model that can successfully and accurately predict the voltage stability margin (VSM) considering different operating conditions, employing the fewest possible input features. Eventually, the results revealed the competency and superiority of the proposed optimized model over the other available models. The technique also speeds up the training process by reducing the number of simulations on a detailed power system model around operating points where correct predictions are made.

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