Lamine Mili

Junbo Zhao, Lamine Mili

This paper is the second of a two-part series that discusses the implementation issues and test results of a robust Unscented Kalman Filter (UKF) for power system dynamic state estimation with non-Gaussian synchrophasor measurement noise. The tuning of the parameters of our Generalized Maximum-Likelihood-type robust UKF (GM-UKF) is presented and discussed in a systematic way. Using simulations carried out on the IEEE 39-bus system, its performance is evaluated under different scenarios, including i) the occurrence of two different types of noises following thick-tailed distributions, namely the Laplace or Cauchy probability distributions for real and reactive power measurements; ii) the occurrence of observation and innovation outliers; iii) the occurrence of PMU measurement losses due to communication failures; iv) cyber attacks; and v) strong system nonlinearities. It is also compared to the UKF and the Generalized Maximum-Likelihood-type robust iterated EKF (GM-IEKF). Simulation results reveal that the GM-UKF outperforms the GM-IEKF and the UKF in all scenarios considered. In particular, when the system is operating under stressed conditions, inducing system nonlinearities, the GM-IEKF and the UKF diverge while our GM-UKF does converge. In addition, when the power measurement noises obey a Cauchy distribution, our GM-UKF converges to a state estimate vector that exhibits a much higher statistical efficiency than that of the GM-IEKF; by contrast, the UKF fails to converge. Finally, potential applications and future work of the proposed GM-UKF are discussed in concluding remarks section.

Yashodhan D. Hakke, Almuatazbellah M. Boker, Lamine Mili et al.

During disasters, cascading failures across power grids, communication networks, and social behavior amplify community fear and undermine cooperation. Existing cyber-physical-social (CPS) models simulate these coupled dynamics but lack mechanisms for active intervention. We extend the CPS resilience model of Valinejad and Mili (2023) with control channels for three agencies, communication, power, and emergency management, and formulate the resulting system as a three-player non-zero-sum differential game solved via online actor-critic reinforcement learning. Simulations based on Hurricane Harvey data show 70% mean fear reduction with improved infrastructure recovery; cross-validation in the case of Hurricane Irma (without refitting) achieves 50% fear reduction, confirming generalizability.

Padmaksha Roy, Lamine Mili, Almuatazbellah Boker

In this paper, we address the problem of class-generalizable anomaly detection, where the objective is to develop a unified model by focusing our learning on the available normal data and a small amount of anomaly data in order to detect the completely unseen anomalies, also referred to as the out-of-distribution (OOD) classes. Adding to this challenge is the fact that the anomaly data is rare and costly to label. To achieve this, we propose a multidirectional meta-learning algorithm -- at the inner level, the model aims to learn the manifold of the normal data (representation); at the outer level, the model is meta-tuned with a few anomaly samples to maximize the softmax confidence margin between the normal and anomaly samples (decision surface calibration), treating normals as in-distribution (ID) and anomalies as out-of-distribution (OOD). By iteratively repeating this process over multiple episodes of predominantly normal and a small number of anomaly samples, we realize a multidirectional meta-learning framework. This two-level optimization, enhanced by multidirectional training, enables stronger generalization to unseen anomaly classes.

Padmaksha Roy, Almuatazbellah Boker, Lamine Mili

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be indicated by the simultaneous deviation of interrelated time series from their expected collective behavior, even when no individual time series exhibits a clearly abnormal pattern on its own. In many existing approaches, time series variables are assumed to be (conditionally) independent, which oversimplifies real-world interactions. Our approach addresses this by modeling joint dependencies in the latent space and decoupling the modeling of \textit{marginal distributions, temporal dynamics, and inter-variable dependencies}. We use a transformer encoder to capture temporal patterns, and to model spatial (inter-variable) dependencies, we fit a multi-variate likelihood and a copula. The temporal and the spatial components are trained jointly in a latent space using a self-supervised contrastive learning objective to learn meaningful feature representations to separate normal and anomaly samples.

Marcos Netto, Yoshihiko Susuki, Lamine Mili

This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique generalizes the original definition of the linear mode-in-state participation factors. Two numerical examples are provided to demonstrate the performance of our approach: one relying on a canonical nonlinear dynamical system, and the other based on the two-area four-machine power system. The Koopman mode decomposition is capable of coping with a large class of nonlinearity, thereby making our technique able to deal with oscillations arising in practice due to nonlinearities while being fast to compute and compatible with real-time applications.

Kiran Karra, Lamine Mili

This paper introduces a new property of estimators of the strength of statistical association, which helps characterize how well an estimator will perform in scenarios where dependencies between continuous and discrete random variables need to be rank ordered. The new property, termed the estimator response curve, is easily computable and provides a marginal distribution agnostic way to assess an estimator's performance. It overcomes notable drawbacks of current metrics of assessment, including statistical power, bias, and consistency. We utilize the estimator response curve to test various measures of the strength of association that satisfy the data processing inequality (DPI), and show that the CIM estimator's performance compares favorably to kNN, vME, AP, and H_{MI} estimators of mutual information. The estimators which were identified to be suboptimal, according to the estimator response curve, perform worse than the more optimal estimators when tested with real-world data from four different areas of science, all with varying dimensionalities and sizes.

Kiran Karra, Lamine Mili

This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula Index for Detecting Dependence and Monotonicity (CIM), satisfies several desirable properties of measures of association, including Renyi's properties, the data processing inequality (DPI), and consequently self-equitability. Synthetic data simulations reveal that the statistical power of CIM compares favorably to other state-of-the-art measures of association that are proven to satisfy the DPI. Simulation results with real-world data reveal the CIM's unique ability to detect the monotonicity structure among stochastic signals to find interesting dependencies in large datasets. Additionally, simulations show that the CIM shows favorable performance to estimators of mutual information when discovering Markov network structure.

Reza Arghandeh, Alexandra von Meier, Laura Mehrmanesh et al.

In recent years, advanced sensors, intelligent automation, communication networks, and information technologies have been integrated into the electric grid to enhance its performance and efficiency. Integrating these new technologies has resulted in more interconnections and interdependencies between the physical and cyber components of the grid. Natural disasters and man-made perturbations have begun to threaten grid integrity more often. Urban infrastructure networks are highly reliant on the electric grid and consequently, the vulnerability of infrastructure networks to electric grid outages is becoming a major global concern. In order to minimize the economic, social, and political impacts of power system outages, the grid must be resilient. The concept of a power system cyber-physical resilience centers around maintaining system states at a stable level in the presence of disturbances. Resilience is a multidimensional property of the electric grid, it requires managing disturbances originating from physical component failures, cyber component malfunctions, and human attacks. In the electric grid community, there is not a clear and universally accepted definition of cyber-physical resilience. This paper focuses on the definition of resilience for the electric grid and reviews key concepts related to system resilience. This paper aims to advance the field not only by adding cyber-physical resilience concepts to power systems vocabulary, but also by proposing a new way of thinking about grid operation with unexpected disturbances and hazards and leveraging distributed energy resources.