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

Time delay arises in a variety of real-world complex systems. A high-fidelity simulation generally renders high accuracy to simulate the dynamic evolution of such complex systems and appraise quantity of interest for process design and response optimization. Identification of limit states exemplifies such applications, which outlines the boundary that separates distinct regions (e.g., stability region) in parameter space. While design of experiments is the common procedure to evaluate decision functions to sketch the boundary, it crucially relies on the quantity and quality of sampling points. This has made it infeasible to explore a large parameter design space with expensive-to-evaluate high-fidelity simulations. Furthermore, the complex contour of stability region in time-delay systems nullifies most existing sequential design paradigms, including adaptive classification approaches. On the other hand, low-fidelity surrogate modeling efficiently emulates a high-fidelity simulation, albeit at the expense of accuracy, not ideal to inspect the system behavior near the critical boundary. In this study, we investigate a multifidelity approach to delineate the stability region in a sequential fashion: sampling points are first evaluated by the low-fidelity surrogate modeling, and only those selected according to the exploration-exploitation trade-off principle are then assessed by a high-fidelity simulation to approximate the stability boundary. The application in a numerical case study of the delayed Mathieu equation as well as a real-world machining process corroborates the proposed approach.