Adaptive Digital Twin of Sheet Metal Forming via Proper Orthogonal Decomposition-Based Koopman Operator with Model Predictive Control

2025-11-13

AI Summary

In empirically driven metal sheet forming processes—such as English wheeling—strong nonlinear coupling between toolpath and material response impedes real-time prediction, monitoring, and autonomous control. Method: This paper proposes a physics-informed and data-driven adaptive digital twin framework. It employs Proper Orthogonal Decomposition (POD) for physics-aware dimensionality reduction; leverages the Koopman operator to embed nonlinear dynamics into a linear lifted space; integrates Model Predictive Control (MPC) for real-time decision-making; and adopts Recursive Least Squares (RLS) to update Koopman coefficients online, enabling continuous adaptation to time-varying material states and process disturbances. Results: Experimental validation on a robotic English wheel system demonstrates high-accuracy target surface tracking, faithful capture of nonstationary dynamics, and substantial improvements in autonomy, interpretability, and generalization capability of the forming process.

Technology Category

• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Machine Learning: Learning with Manifolds

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Digital Twin (DT) technologies are transforming manufacturing by enabling real-time prediction, monitoring, and control of complex processes. Yet, applying DT to deformation-based metal forming remains challenging because of the strongly coupled spatial-temporal behavior and the nonlinear relationship between toolpath and material response. For instance, sheet-metal forming by the English wheel, a highly flexible but artisan-dependent process, still lacks digital counterparts that can autonomously plan and adapt forming strategies. This study presents an adaptive DT framework that integrates Proper Orthogonal Decomposition (POD) for physics-aware dimensionality reduction with a Koopman operator for representing nonlinear system in a linear lifted space for the real-time decision-making via model predictive control (MPC). To accommodate evolving process conditions or material states, an online Recursive Least Squares (RLS) algorithm is introduced to update the operator coefficients in real time, enabling continuous adaptation of the DT model as new deformation data become available. The proposed framework is experimentally demonstrated on a robotic English Wheel sheet metal forming system, where deformation fields are measured and modeled under varying toolpaths. Results show that the adaptive DT is capable of controlling the forming process to achieve the given target shape by effectively capturing non-stationary process behaviors. Beyond this case study, the proposed framework establishes a generalizable approach for interpretable, adaptive, and computationally-efficient DT of nonlinear manufacturing systems, bridging reduced-order physics representations with data-driven adaptability to support autonomous process control and optimization.

Problem

• Developing adaptive digital twins for nonlinear sheet metal forming processes
• Real-time prediction and control of deformation-based manufacturing systems
• Bridging physics-based models with data-driven adaptation for autonomous control

Innovation

• POD-based Koopman operator for linearized nonlinear dynamics
• Online RLS algorithm enabling real-time model adaptation
• Integration of MPC for autonomous forming process control