A Unified Physics-Constrained Deep Reinforcement Learning Framework for Parameter Identification of Nonlinear Hysteretic Models

Neural Parameter Calibration for Identification of Nonlinear Hysteretic Behavior in Bolted Joints

A neural calibration framework is presented for estimating the nonlinear hysteretic behavior of jointed structures using the parameters of the Bouc-Wen model, which serves as a reduced-order representation of bolted joints under dynamic excitation. This methodology integrates data-driven modeling, physics-based representation, and ensemble-based variability analysis to achieve robust parameter estimation and to propagate parameter dispersion into response-level uncertainty envelopes. A feed-forward neural network is employed to minimize the discrepancy between simulated and measured responses, with multiple random initializations producing an ensemble of calibrations. This ensemble quantifies variability resulting from both neural initialization and experimental repetitions under identical boundary conditions. Experimental validation was performed on a beam testbed subjected to different vibration regimes and various torque-tightening levels. The results demonstrate that the calibrated models capture key hysteretic features, such as stiffness degradation and energy dissipation, while yielding physically admissible parameter sets and consistent uncertainty envelopes across repeated measurements. The evolution of these parameters may serve as health indicators for structural health monitoring (SHM), facilitating the development of uncertainty-aware digital shadows for nonlinear structural systems.

Physics-Constrained Residual Learning for Refined Dynamic Identification and Robust Torque Estimation

Accurate dynamic modeling of industrial robots is essential for high-performance control and estimating torque. However, traditional physics-based models often fail to capture unmodeled dynamics such as complex friction, payload variations, and gearbox-induced distortions. This article refines a physics-based modeling framework with a data-driven residual learning policy to compensate for unmodeled dynamics. We first employ a nested optimization strategy using multistart sequential quadratic programming (MS-SQP) and QR-based base parameter extraction to identify identifiable inertial and Stribeck friction parameters. To compensate for remaining systematic errors, we integrate the residual error policy model using physics-aware feature engineering. The proposed method is validated on both synthetic datasets and a real-world six-DOF industrial manipulator across various trajectories (including Fourier, chirp, and trapezoidal excitations) and payload conditions. A friction modeling ablation study confirms that richer friction representations progressively reduce the residual space, with the Stribeck backbone achieving 2.32-Nm root-mean-square error (RMSE) compared to 3.89 Nm for the rigid-body-only baseline. Experimental results demonstrate that the proposed physics-imbued residual framework improves torque prediction RMSE 31.5 % in real-world trajectories and 31.7 % in unseen synthetic payload testing. The results confirm that the framework effectively captures complex unmodeled dynamics while maintaining physical interpretability and generalization capabilities essential for industrial instrumentation and measurement applications.

Physics-Guided Neural ODEs for Building Thermal Prediction and Model Predictive Control

Building supervisory control requires accurate, prior-consistent, and computationally tractable thermal models. This study proposes a physics-guided neural ordinary differential equation (PG-NODE) framework for thermal prediction and model predictive control (MPC). It combines a resistance–capacitance (RC)-inspired reference, a neural residual, RC-prior directional regularization, and validation-based checkpoint selection; the selected predictor remains fixed during MPC operation. Using 30 min EnergyPlus data from five zones, the framework was evaluated through held-out prediction, Gaussian noise and control-input-mismatch tests, ablation, and surrogate-based closed-loop experiments. Long short-term memory achieved the lowest prediction root mean square error (RMSE), whereas PG-NODE achieved the lowest RMSE among the evaluated neural ODE models and the lowest directional inconsistency rate among learned nonlinear models. In five-seed × five-window BACK SPACE experiments using independently trained, fixed PG-NODE surrogate environments rather than direct EnergyPlus interaction, fixed-block analysis supported lower reference-tracking RMSE for PG-NODE-MPC than for rule-based control and lower tariff-weighted normalized control effort than for the extended Kalman filter-based RC-MPC benchmark. This benchmark achieved the lowest descriptive mean reference-tracking RMSE and total objective. Mean PG-NODE-MPC optimization time was 0.86 s. Results suggest the potential for low-frequency building management system supervisory decision support, subject to physical command mapping and staged field validation.

A Hybrid Finite Element–Deep Learning Framework for Bearing Structure Optimization

The groove curvature coefficient plays a critical role in determining the thermo-mechanical performance of angular-contact ball bearings. However, its optimization remains challenging due to strong nonlinear coupling among stress, stiffness, heat generation, and fatigue capacity. To address this issue, this study proposes a hybrid optimization framework integrating a corrected two-dimensional axisymmetric finite element method (2D-AxFEM) model, a deep learning surrogate model, and a genetic algorithm. Firstly, an efficient 2D-AxFEM model calibrated by a bearing dynamic model is developed to accurately predict key performance metrics, including contact stress, stiffness, heat generation, and dynamic load rating, with significantly reduced computational cost compared to the conventional 3D FEM model. Based on the generated data, a multi-layer perceptron deep learning surrogate model is trained to establish a fast nonlinear mapping between groove curvature coefficients and performance indicators. The model achieves high accuracy, with R2 values of 0.9745, 0.9414, and 0.9756 at three different rotational speeds, as well as significantly improved computational efficiency. Building upon this, single- and multi-constraint optimization problems are solved using a genetic algorithm. The results reveal clear trade-offs among stiffness, heat generation, and load capacity. Under stiffness constraints, optimal solutions consistently converge to the constraint boundary, indicating its dominant role in thermal optimization. Under multiple constraints, the framework effectively identifies feasible design regions, enabling reduced heat generation while maintaining acceptable stress and load capacity. Overall, the proposed framework enables efficient exploration of multi-physics design spaces and provides a scalable solution for high-speed bearing optimization.

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

Data-Driven Prediction of Friction Hysteresis Loops Using Temporal Deep Learning Models

Friction hysteresis loops are critical for characterizing the nonlinear dynamic behavior of jointed structures. However, their complex nonlinear characteristics make efficient prediction challenging. In this study, a public high-frequency experimental dataset covering diverse operating conditions is adopted to investigate data-driven friction hysteresis loop prediction. Temporal datasets are constructed based on historical displacement information, and temporal deep learning models are developed for one-step-ahead friction force prediction. The prediction performance of TCN and GRU was evaluated across nine operating conditions, demonstrating their capability to accurately model friction hysteresis responses. Both models achieved comparable performance, with average R2 values exceeding 0.997 across all test conditions. TCN delivers marginally better overall accuracy and physical consistency, while GRU yields more stable predictions. Furthermore, physics-oriented metrics, including energy dissipation error and stiffness preservation error, are introduced to evaluate the physical consistency of predicted hysteresis responses. The proposed framework provides an effective data-driven approach for friction hysteresis prediction and offers potential support for nonlinear modeling and digital twin applications.