Na Lu

Zhihao Kong, Amirhossein Mollaali, Christian Moya et al.

Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended DeepONet to allow multiple input functions in different Banach spaces. MIONet offers flexibility in training dataset grid spacing, without constraints on output location. However, it requires offline inputs and cannot handle varying sequence lengths in testing datasets, limiting its real-time application in dynamic complex systems. This work redesigns MIONet, integrating Long Short Term Memory (LSTM) to learn neural operators from time-dependent data. This approach overcomes data discretization constraints and harnesses LSTM's capability with variable-length, real-time data. Factors affecting learning performance, like algorithm extrapolation ability are presented. The framework is enhanced with uncertainty quantification through a novel Bayesian method, sampling from MIONet parameter distributions. Consequently, we develop the B-LSTM-MIONet, incorporating LSTM's temporal strengths with Bayesian robustness, resulting in a more precise and reliable model for noisy datasets.

Hanxuan Wang, Na Lu, Yinhong Liu et al.

The success of deep learning in transient stability assessment (TSA) heavily relies on high-quality training data. However, the label information in TSA datasets is vulnerable to contamination through false label injection (FLI) cyberattacks, resulting in degraded performance of deep TSA models. To address this challenge, a Multi-Module Robust TSA method (MMR) is proposed to rectify the supervised training process misguided by FLI in an unsupervised manner. In MMR, a supervised classification module and an unsupervised clustering module are alternatively trained to improve the clustering friendliness of representation leaning, thereby achieving accurate clustering assignments. Leveraging the clustering assignments, we construct a training label corrector to rectify the injected false labels and progressively enhance robustness and resilience against FLI. However, there is still a gap on accuracy and convergence speed between MMR and FLI-free deep TSA models. To narrow this gap, we further propose a human-in-the-loop training strategy, named MMR-HIL. In MMR-HIL, potential false samples can be detected by modeling the training loss with a Gaussian distribution. From these samples, the most likely false samples and most ambiguous samples are re-labeled by a TSA experts guided bi-directional annotator and then subjected to penalized optimization, aimed at improving accuracy and convergence speed. Extensive experiments indicate that MMR and MMR-HIL both exhibit powerful robustness against FLI in TSA performance. Moreover, the contaminated labels can also be effectively corrected, demonstrating superior resilience of the proposed methods.

Hanxuan Wang, Na Lu, Zixuan Wang et al.

Deep learning based transient stability assessment (TSA) has achieved great success, yet the lack of interpretability hinders its industrial application. Although a great number of studies have tried to explore the interpretability of network solutions, many problems still remain unsolved: (1) the difference between the widely accepted power system knowledge and the generated interpretive rules is large, (2) the probability characteristics of the neural network have not been fully considered during generating the interpretive rules, (3) the cost of the trade-off between accuracy and interpretability is too heavy to take. To address these issues, an interpretable power system Transient Stability Assessment method with Expert guiding Neural-Regression-Tree (TSA-ENRT) is proposed. TSA-ENRT utilizes an expert guiding nonlinear regression tree to approximate the neural network prediction and the neural network can be explained by the interpretive rules generated by the tree model. The nonlinearity of the expert guiding nonlinear regression tree is endowed with the extracted knowledge from a simple two-machine three-bus power system, which forms an expert knowledge base and thus the generated interpretive rules are more consistent with human cognition. Besides, the expert guiding tree model can build a bridge between the interpretive rules and the probability prediction of neural network in a regression way. By regularizing the neural network with the average decision length of ENRT, the association of the neural network and tree model is constructed in the model training level which provides a better trade-off between accuracy and interpretability. Extensive experiments indicate the interpretive rules generated by the proposed TSA-ENRT are highly consistent with the neural network prediction and more agreed with human expert cognition.