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Facing stochastic variations of the loads due to an increasing penetration of renewable energy generation, online decision making under uncertainty in modern power systems is capturing power researchers' attention in recent years. To address this issue while achieving a good balance between system security and economic objectives, we propose a surrogate-enhanced scheme under a joint chance-constrained (JCC) optimal power-flow (OPF) framework. Starting from a stochastic-sampling procedure, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo (MC) method, we propose to use a polynomial-chaos-based surrogate that allows us to efficiently evaluate the power-system model at non-Gaussian distributed sampled values with a negligible computing cost. Learning from the MC simulated samples, we further proposed a hybrid adaptive approach to overcome the conservativeness of the JCC-OPF by utilizing correlation of the system states, which is ignored in the traditional Boole's inequality. The simulations conducted on the modified Illinois test system demonstrate the excellent performance of the proposed method.
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Uncertainty Quantification and Optimal Robust Design for Machining Operations
Abstract In this study, we carry out robust optimal design for the machining operations, one key process in wafer polishing in chip manufacturing, aiming to avoid the peculiar regenerative chatter and maximize the material removal rate (MRR) considering the inherent material and process uncertainty. More specifically, we characterize the cutting tool dynamics using a delay differential equation (DDE) and enlist the temporal finite element method (TFEM) to derive its approximate solution and stability index given process settings or design variables. To further quantify the inherent uncertainty, replications of TFEM under different realizations of random uncontrollable variables are performed, which however incurs extra computational burden. To eschew the deployment of such a crude Monte Carlo (MC) approach at each design setting, we integrate the stochastic TFEM with a stochastic surrogate model, stochastic kriging, in an active learning framework to sequentially approximate the stability boundary. The numerical result suggests that the nominal stability boundary attained from this method is on par with that from the crude MC, but only demands a fraction of the computational overhead. To further ensure the robustness of process stability, we adopt another surrogate, the Gaussian process, to predict the variance of the stability index at unexplored design points and identify the robust stability boundary per the conditional value at risk (CVaR) criterion. Therefrom, an optimal design in the robust stable region that maximizes the MRR can be identified.
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- Award ID(s):
- 2119334
- PAR ID:
- 10410835
- Date Published:
- Journal Name:
- Journal of Computing and Information Science in Engineering
- Volume:
- 23
- Issue:
- 1
- ISSN:
- 1530-9827
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4055039
