Multi-fidelity modeling in sequential design for stability identification in dynamic time-delay systems

Area of Science:

• Complex Systems Dynamics
• Computational Engineering
• Control Theory

Background:

• Time delays are prevalent in complex systems, necessitating accurate simulation for design and optimization.
• Identifying limit states, such as stability boundaries, is crucial but challenging with expensive high-fidelity simulations.
• Existing methods struggle with large parameter spaces and complex stability contours in time-delay systems.

Purpose of the Study:

• To develop an efficient multifidelity approach for sequentially delineating stability regions in time-delay systems.
• To overcome the limitations of expensive high-fidelity simulations and complex parameter spaces.
• To accurately approximate stability boundaries using a combination of simulation fidelities.

Main Methods:

• A sequential multifidelity approach is proposed, integrating low-fidelity surrogate modeling and high-fidelity simulations.
• Sampling points are initially evaluated using low-fidelity models.
• Selected points balancing exploration and exploitation are then assessed with high-fidelity simulations to refine the stability boundary.

Main Results:

• The multifidelity approach effectively delineates stability regions in a computationally efficient manner.
• The method successfully approximates the complex stability boundary of time-delay systems.
• Validation was performed using a numerical case study (delayed Mathieu equation) and a real-world machining process.

Conclusions:

• The proposed multifidelity strategy offers a robust and efficient solution for stability region identification in complex time-delay systems.
• This approach enhances the feasibility of exploring large parameter spaces with high-fidelity simulations.
• The findings have significant implications for process design and optimization in systems with time delays.