Physics-Informed Neural Network Framework for Input Load Estimation and Virtual Sensing of Offshore Wind Turbines

Physics-Informed Neural Ordinary Differential Equations for Parameter Estimation in Rotating Generators

Accurate estimation of dynamic parameters of generators is crucial for constructing high-fidelity models for dynamic studies and ensuring the reliable operation of power systems. This paper develops a physics-informed neural ordinary differential equations (ODE) approach to learn the parameters of a generator’s dynamic model using grid sensor data. A physics-informed neural network is designed to represent the ODEs governing power system dynamics. A loss function is defined as the discrepancy between the dynamic response generated by the physics-informed neural network and synthesized grid sensor data, which mimics real-world measurements. The model parameters are iteratively updated using neural ODEs and the adjoint method. Unlike moving window-based approaches, the proposed neural ODE framework enhances parameter estimation by leveraging a longer observation period with a mini-batch scheme. Numerical studies on a 3-machine 9-bus system demonstrate that the proposed model significantly outperforms state-of-the-art baseline methods in dynamic parameter estimation accuracy.

Deep learning empowered stochastic dynamics analysis of single-tower cable-stayed bridge with nonlinear tuned inerter dampers

A Physics-Informed Neural Network Framework Leveraging Deterministic Learning and Statistical Constraints for Bearing Fault Diagnosis

Recently, physics-informed learning-based intelligent bearing fault diagnosis methods have demonstrated great potential in improving diagnostic accuracy and physical consistency. Nevertheless, the practical deployment of conventional physics-informed neural networks typically relies on explicit partial differential equations (PDEs), which are generally difficult to acquire in real industrial scenarios. To address this limitation, a PDE-free physics-informed bearing fault diagnosis framework is proposed based on deterministic learning and statistical constraints. In the proposed framework, deterministic learning is adopted to extract nonlinear dynamic trajectories from multi-directional bearing vibration signals. The residuals between sample dynamic trajectories and class-specific standard trajectories are further converted into probabilistic statistical soft constraints. Accordingly, the system evolution mechanism embedded with physical dynamic characteristics is incorporated into the model training process, eliminating the need for explicit PDE constraints. In addition, a composite loss function is constructed by integrating the supervised classification loss with dynamic trajectory-based statistical constraint terms. This enables the network optimization process to be jointly guided by classification error and physical dynamic consistency. Finally, the effectiveness of the proposed method is validated through simulation and experimental studies. The results reveal that the average discernibility of dynamic trajectories reaches 0.3614, representing respective improvements of 122% and 68.6% over time-domain and frequency-domain signals. The proposed method achieves an effective balance among diagnostic accuracy, inference speed, and model complexity, with its average parameter volume reduced by approximately 93.9% relative to the comparative methods. These results demonstrate that the proposed method is applicable to bearing fault diagnosis scenarios where explicit PDE information is unavailable.

Multi-domain physics-informed neural networks for dynamic yaw-induced wind farm wake reconstruction

Wind turbine wakes significantly influence wind farm performance, particularly under active yaw control used for wake redirection. Accurate wake reconstruction requires resolving the large spatial extent and multi-scale variability of wind-farm flows, making single-network training computationally demanding. A multi-domain formulation addresses this challenge by decomposing the global domain into smaller subregions, allowing localized learning while remaining compatible with sparse offshore measurements. Accordingly, a multi-domain physics-informed neural network (md-PINN) framework is developed for reconstructing unsteady wake fields of offshore wind turbines subjected to active yaw control. We begin by developing a standard PINN to reconstruct the wake behind a single wind turbine, incorporating Navier–Stokes constraints to enforce physical consistency. Building on this, a domain decomposition strategy is applied to divide the wind farm into multiple subdomains, each modeled using an independent PINN, thus forming the md-PINN framework. Validation against large eddy simulation (LES) data shows that the md-PINN framework accurately reconstructs velocity fields, wake trajectories, wake widths, and power outputs in downstream regions affected by complex wake interactions, while exhibiting improved robustness compared to a single full-domain PINN. In addition, the proposed framework naturally supports parallel training of sub-models, leading to a significant reduction in computational cost and enhanced scalability for sparse-data-based wake reconstruction in large wind farms.

Structural parameter identification with hybrid physics informed neural network

System identification (SI) is critical for ensuring the reliability of structural and mechanical components across engineering applications. Traditional model-based SI methods often struggle with complex dynamics and the scarcity of accurate physical models, while purely data-driven, model-free approaches though simple and fast lack physical interpretability and suffer from poor generalization. Recent advances such as physics-informed neural networks (PINNs) combine data and physics to overcome these limitations and have shown strong promise for structural health monitoring (SHM). However, most existing methods still require knowledge of the input force, which limits their practical use for parameter estimation. To address this challenge, an input-robust hybrid physics informed neural network (rHPINN) framework is proposed that integrates physics-based system dynamics with the temporal learning capability of HPINN. An output-injection strategy enables rejection of unknown input forces, allowing accurate estimation of system states and spatial health parameters without input force measurements. By explicitly preserving temporal dependencies often overlooked in conventional PINNs the method achieves stable, physics-consistent system identification. Numerical simulations on systems demonstrate that rHPINN remains robust under unknown excitation, measurement noise, sparse data, and varying damage scenarios, highlighting its potential for real-world SHM under uncertain conditions.

A physics-constrained temporal modeling framework for robust short-term wind power forecasting

Accurate short-term wind power prediction plays a critical role in ensuring stable grid operation, effective energy management, and the large-scale integration of renewable energy systems under highly variable wind conditions. Although data-driven and deep learning models have demonstrated promising forecasting capability, many existing approaches suffer from performance degradation during rapid wind fluctuations due to the lack of embedded physical constraints and the high computational complexity associated with recurrent architectures. To address these limitations, this article proposes a Physics-Guided Residual Temporal Convolutional Network (PG-ResTCN) for short-term wind power forecasting. The proposed framework integrates dilated temporal convolutional learning with residual connections to effectively capture multiscale temporal dependencies in wind power time series while avoiding the sequential computation of recurrent neural networks, thereby improving computational efficiency. Furthermore, a physics-based smoothness constraint is incorporated into the training loss function to enforce physically consistent power ramping behavior that reflects the inherent operational dynamics and inertia of wind turbines, reducing unrealistic fluctuations in predicted power outputs. The effectiveness of the proposed model is validated using a large real-world dataset containing approximately 140,161 hourly samples collected from five wind farm locations, including meteorological variables and corresponding turbine power outputs. Comprehensive experiments are conducted by comparing the proposed method with widely used benchmark models, including Support Vector Regression, Random Forest, Extreme Gradient Boosting, and Long Short-Term Memory networks. Results demonstrate that the proposed PG-ResTCN model achieves superior forecasting performance, obtaining a root mean square error of 0.0359, mean absolute error of 0.0296, and R 2 of 0.9759, outperforming all baseline models. The integration of physics-guided constraints with the temporal convolutional architecture significantly enhances prediction accuracy, stability, and generalization capability. In addition, the proposed framework maintains high computational efficiency and robustness, making it suitable for real-time wind energy forecasting applications, intelligent energy management systems, and microgrid power system operations.