Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFrom Generalized Gauss Bounds to Distributionally Robust Fault Detection with Unimodality Information
375
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Probabilistic methods have attracted much interest in fault detection design, but its need for complete distributional knowledge is seldomly fulfilled. This has spurred endeavors in distributionally robust fault detection (DRFD) design, which secures robustness against inexact distributions by using moment-based ambiguity sets as a prime modelling tool. However, with the worst-case distribution being implausibly discrete, the resulting design suffers from over-pessimisim and can mask the true fault. This paper aims at developing a new DRFD design scheme with reduced conservatism, by assuming unimodality of the true distribution, a property commonly encountered in real-life practice. To tackle the chance constraint on false alarms, we first attain a new generalized Gauss bound on the probability outside an ellipsoid, which is less conservative than known Chebyshev bounds. As a result, analytical solutions to DRFD design problems are obtained, which are less conservative than known ones disregarding unimodality. We further encode bounded support information into ambiguity sets, derive a tightened multivariate Gauss bound, and develop approximate reformulations of design problems as convex programs. Moreover, the derived generalized Gauss bounds are broadly applicable to versatile change detection tasks for setting alarm thresholds. Results on a laborotary system shown that, the incorporation of unimodality information helps reducing conservatism of distributionally robust design and leads to a better tradeoff between robustness and sensitivity.
rate research
Read More
In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide an exact reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.
We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our approach is computationally as tractable as the standard (without side information) Wasserstein-metric-based DRO and enjoys performance guarantees. Furthermore, our DRO framework can be conveniently used to address data-driven decision-making problems under contaminated samples and naturally produces distributionally robu
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a tractable reformulation of the optimization over the chosen model ambiguity set, which is generally infinite dimensional. Previous works have solved this problem in the case where the objective functional is an expected value. In this paper we study objective functionals that are the sum of an expected value and a variance penalty term. We prove that the corresponding variance-penalized DRO problem over an $f$-divergence neighborhood can be reformulated as a finite-dimensional convex optimization problem. This result also provides tight uncertainty quantification bounds on the variance.
We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point problem. The performance of the method is demonstrated on both synthetic and real data.
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first partial moment) bounds, and semideviation (second partial moment) in one dimension are investigated. The infinite dimensional primal problems are formulated and the simpler finite dimensional dual problems are derived. A principal motivating question is how does data-driven distributional ambiguity affect the moment bounds. Towards answering this question, some theory is developed and computational experiments are conducted for specific problem instances in inventory control and portfolio management. Finally some open questions and suggestions for future research are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
