Tightening the bound estimate of structural reliability under imprecise probability information

Structural reliability analysis is typically performed based on the identification of distribution types of random inputs. However, this is often not feasible in engineering practice due to limited available probabilistic information (e.g., limited observed samples or physics-based inference). In this paper, a linear programming-based approach is developed to perform structural reliability analysis subjected to incompletely informed random variables. The approach converts a reliability analysis into a standard linear programming problem, which can make full use of the probabilistic information of the variables. The proposed method can also be used to construct the best-possible distribution function bounds for a random variable with limited statistical information. Illustrative examples are presented to demonstrate the applicability and efficiency of the proposed method. It is shown that the proposed approach can provide a tighter estimate of structural reliability bounds compared with existing interval Monte Carlo methods which propagate probability boxes.This research has been supported by the Faculty of Engineering and IT PhD Research Scholarship (SC1911) from the University of Sydney. This support is gratefully acknowledged

Optimising the Reliability that can be Claimed for a Software-based System based on Failure-free Tests of its components

This paper describes a numerical method for optimising the conservative confidence bound on the reliability of a system based on statistical testing of its individual components. It provides an alternative to the sub-optimal test plan algorithms identified by the authors in an earlier research paper. For a given maximum number of component tests, this numerical method can derive an optimal test plan for any arbitrary system structure. The optimisation method is based on linear programming which is more efficient than the alternative integer programming approach. In addition, the optimisation process need only be performed once for any given system structure as the solution can be re-used to compute an optimal integer test plan for a different maximum number of component tests. This approach might have broader application to other optimisation problems

Automatic programming methodologies for electronic hardware fault monitoring

This paper presents three variants of Genetic Programming (GP) approaches for intelligent online performance monitoring of electronic circuits and systems. Reliability modeling of electronic circuits can be best performed by the Stressor - susceptibility interaction model. A circuit or a system is considered to be failed once the stressor has exceeded the susceptibility limits. For on-line prediction, validated stressor vectors may be obtained by direct measurements or sensors, which after pre-processing and standardization are fed into the GP models. Empirical results are compared with artificial neural networks trained using backpropagation algorithm and classification and regression trees. The performance of the proposed method is evaluated by comparing the experiment results with the actual failure model values. The developed model reveals that GP could play an important role for future fault monitoring systems.This research was supported by the International Joint Research Grant of the IITA (Institute of Information Technology Assessment) foreign professor invitation program of the MIC (Ministry of Information and Communication), Korea

Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs---in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.Comment: 42 pages, 10 figure