Probability of failure sensitivity with respect to decision variables

Lacaze, Sylvain; Brevault, Loïc; Missoum, Samy; Balesdent, Mathieu

doi:10.1007/s00158-015-1232-1

Cited by 31 publications

(22 citation statements)

References 16 publications

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“…comprised by the developments presented in [21,35,37,40]. First, assuming that g < 0 indicates failure of the system under study, the probability of failure can be defined as follows:…”

Section: Probability Of Failure Sensitivitymentioning

confidence: 99%

“…Moreover, the high computational effort also leads to the utilization of gradient-based optimization algorithms for the solution of these problems. However, it is worth to point out that sensitivity analysis of probability of failure with respect to design variables is not a trivial task when dealing with sampling approaches [21,35].…”

Section: Introductionmentioning

confidence: 99%

“…Besides, evaluation of probabilities of failure and its sensitivities is made using PCE [14,40,46,48] that ensures accuracy of the results. The concepts regarding sensitivity analysis of probability of failure have mostly been developed in previous works [19,21,35,38,40]. It is worth to highlight that the limitation of the proposed RO scheme is closely linked to the limitation of the PCE, i.e., the stochastic dimension of the problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A gradient-based polynomial chaos approach for risk and reliability-based design optimization

Torii

López

Miguel

2017

J Braz. Soc. Mech. Sci. Eng.

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This paper presents an approach for the solution of risk and reliability-based design optimization problems using gradient-based algorithms together with polynomial chaos expansions (PCE) for probability of failure evaluation and sensitivity analysis. The approach is intended to alleviate the computational burden required by such problems with accurate evaluation of probabilities of failure. Benchmark problems from the literature are solved to assess the effectiveness of the proposed approach and the results show that it is able to obtain accurate solutions with tractable computational effort. The main limitation of the proposed approach, inherited from the PCE, is that the computational effort grows very fast for an increasing number of random variables.

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“…comprised by the developments presented in [21,35,37,40]. First, assuming that g < 0 indicates failure of the system under study, the probability of failure can be defined as follows:…”

Section: Probability Of Failure Sensitivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A gradient-based polynomial chaos approach for risk and reliability-based design optimization

Torii

López

Miguel

2017

J Braz. Soc. Mech. Sci. Eng.

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show abstract

“…Estimating the probability of failure based on computational simulation models is a challenging problem in several engineering applications including device and system design [3,4,5,6], structural and reliability analysis [7,8,9], fault-tree analysis [10,11,12], and financial systems [13,14,15].…”

Section: Problem Statementmentioning

confidence: 99%

POF-Darts: Geometric adaptive sampling for probability of failure

Ebeida

Mitchell

Swiler

et al. 2016

Reliability Engineering & System Safety

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We introduce a novel technique, POF-Darts, to estimate the Probability Of Failure based on random disk-packing in the uncertain parameter space. POF-Darts uses hyperplane sampling to explore the unexplored part of the uncertain space. We use the function evaluation at a sample point to determine whether it belongs to failure or non-failure regions, and surround it with a protection sphere region to avoid clustering. We decompose the domain into Voronoi cells around the function evaluations as seeds and choose the radius of the protection sphere depending on the local Lipschitz continuity. As sampling proceeds, regions uncovered with spheres will shrink, improving the estimation accuracy. After exhausting the function evaluation budget, we build a surrogate model using the function evaluations associated with the sample points and estimate the probability of failure by exhaustive sampling of that surrogate. In comparison to other similar methods, our algorithm has the advantages of decoupling the sampling step from the surrogate construction one, the ability to reach target POF values with fewer samples, and the capability of estimating the number and locations of disconnected failure regions, not just the POF value. We present various examples to demonstrate the efficiency of our novel approach.

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“…Estimating the probability that a system breaks up or fails is crucial for decision and control applications. This problem was widely addressed for offline risk of failure analysis of critical systems [1], [2], [3], [4]. Knowing the failure probability is also essential for real time applications in the presence of uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Online failure probability estimation under state estimation error and its application to angle of attack control of a reentry vehicle

Merlinge

Cantou

Dahia

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Knowing the probability of failure in real timei.e. the probability that a system violates some constraintsis decisive for aerospace applications in the presence of state uncertainty. However, it often involves stochastic prediction of the constraints on the upcoming system's trajectory, which is computationally demanding. In addition, the trajectory prediction depends on the accuracy of the current state estimate, e.g. the navigation system, whose errors are usually not accounted for. This paper studies the impact of the state estimate error on the failure probability calculation, obtained by Monte Carlo trajectory sampling. The failure probability error is first shown to be made of two terms depending on the current state estimation error and the number of Monte Carlo samples. Then, an iterative Least Square estimator is introduced to refine the failure probability estimation without significantly increasing the computational load. It is theoretically shown to converge and lowers the failure probability estimation error of 33% in simulation. The approach is illustrated on a constrained stochastic control application: the atmospheric reentry of a vehicle inspired from SpaceX's Starship (SXS). The proposed method allows the failure probability estimate to be more accurate despite the unavoidable disturbances yielded by the state estimation algorithm and the Monte Carlo discrete sampling, in particular when the available computational load is limited onboard.

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Probability of failure sensitivity with respect to decision variables

Cited by 31 publications

References 16 publications

A gradient-based polynomial chaos approach for risk and reliability-based design optimization

A gradient-based polynomial chaos approach for risk and reliability-based design optimization

POF-Darts: Geometric adaptive sampling for probability of failure

Online failure probability estimation under state estimation error and its application to angle of attack control of a reentry vehicle

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