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In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two‐dimensional four‐branch function, a four‐dimensional function with a disjoint contour of interest and a time‐delay dynamic system. [ABSTRACT FROM AUTHOR]

The interconnectivity between constituent nodes gives rise to cascading failure in most dynamic networks, such as a traffic jam in transportation networks and a sweeping blackout in power grid systems. Basin stability (BS) has recently garnered tremendous traction to quantify the reliability of such dynamical systems. In power grid networks, it quantifies the capability of the grid to regain the synchronous state after being perturbated. It is noted that detection of the most vulnerable node or generator with the lowest BS or N-1 reliability is critical toward the optimal decision making on maintenance. However, the conventional estimation of BS relies on the Monte Carlo (MC) method to separate the stable and unstable dynamics originated from the perturbation, which incurs immense computational cost particularly for large-scale networks. As the BS estimate is in essence a classification problem, we investigate the relevance vector machine and active learning to locate the boundary of stable dynamics or the basin of attraction in an efficient manner. This novel approach eschews the large number of sampling points in the MC method and reduces over 95% of the simulation cost in the assessment of N-1 reliability of power grid networks.

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.