Hysteresis is a ubiquitous phenomenon in magnetic materials; its modeling and identification are crucial for understanding and optimizing the behavior of electrical machines. Such machines often operate under uncertain conditions, necessitating modeling methods that can generalize across unobserved scenarios. Traditional recurrent neural architectures struggle to generalize hysteresis patterns beyond their training domains. This paper mitigates the generalization challenge by introducing a physics-aware recurrent neural network approach to model and generalize the hysteresis manifesting in sequentiality and history-dependence. The proposed method leverages ordinary differential equations (ODEs) governing the phenomenological hysteresis models to update hidden recurrent states. The effectiveness of the proposed method is evaluated by predicting generalized scenarios, including first-order reversal curves and minor loops. The results demonstrate robust generalization to previously untrained regions, even with noisy data, an essential feature that hysteresis models must have. The results highlight the advantages of integrating physics-based ODEs into recurrent architectures, including superior performance over traditional methods in capturing the complex, nonlinear hysteresis behaviors in magnetic materials.

Manufacturing imperfections are an inherent aspect of the production process, affecting the reliability and performance of all engineered components, including actuators. This work investigates the effects of manufacturing uncertainty in coil assembly. Given the manufacturing tolerances of geometrical and material properties of wires and coils, the coil’s electrical response is studied from a probabilistic perspective. While many researchers acknowledge these uncertainties, they often do not quantify their effects on the system’s response. We propose the use of copulas to model nonlinear relationships and quantify the probabilistic dependence between design variables (i.e., wire and coil’s properties) and their effects on electrical responses. Additionally, tolerances of the design variables are determined through unstructured expert elicitation. The results show the impact of the thickness of the wire’s insulation in the performance of the coil. Furthermore, we establish a design space that is studied probabilistically, allowing for probabilistic design optimization.

Nonlinear hysteresis modeling is essential for estimating, controlling, and characterizing the behavior of piezoelectric material-based devices. However, current deep-learning approaches face challenges in generalizing effectively to previously unseen voltage profiles. This Letter tackles the limitation of generalization by introducing the notion of neural operators for modeling the nonlinear constitutive laws governing inverse piezoelectric hysteresis, specifically focusing on the relationship between voltage inputs and displacement responses. The study utilizes two neural operators—Fourier neural operator and the deep operator network—to predict material responses to unseen voltage profiles that are not part of the training data. Numerical experiments, including butterfly-shaped hysteresis curves, show that in accuracy and generalization to unseen voltage profiles, neural operators outperform traditional recurrent neural network-based models, including conventional gated networks. The findings highlight the potential of neural operators for modeling hysteresis in piezoelectric materials, offering advantages over existing methods in varying voltage scenarios.