AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

Echard, Benjamin; Gayton, Nicolas; Lemaire, Maurice

doi:10.1016/j.strusafe.2011.01.002

Cited by 1,428 publications

(894 citation statements)

References 27 publications

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“…In practice, this can be obtained by concentrating the I/O training observations of the real model in the proximity of the CRs and of their limit surfaces. Sequential adaptive training strategies have been recently developed to this aim (Echard et al, 2011;Picheny et al, 2010). In what follows, the fundamental concepts of Kriging are recalled, with a focus on the adaptive strategy exploited for training the meta-model.…”

Section: Meta-modelingmentioning

confidence: 99%

“…In particular, it is important that the meta-model is capable of discriminating the CR from the normal conditions; thus, instead of using an a-priori fixed DOE, a sequential one (where the experimental observations are iteratively and adaptively added to increase the accuracy of the meta-model around the regions of interest) is preferable. The Adaptive Kriging Monte Carlo Simulation (AK-MCS) (Echard et al, 2011) is here employed to this aim. In the AK-MCS, an initial Kriging model is trained with a small set of I/O observations, e.g., sampled according to LHS scheme; then, the algorithm proceeds iteratively according to the following steps: i) randomly sample a large set of input configurations • = c , … , k 8‚ƒ g, e.g., by means of LHS; ii) evaluate the associated responses using the Kriging metamodel " z = cj … , … , j … k 8‚ƒ g; iii) check if a convergence criterion has been reached: if so, the meta-model is sufficiently accurate; otherwise, iv) select, according to a predefined learning function/criterion, the best candidate subset • * ⊂ • to add to the current DOE and evaluate the corresponding real model output " * ; v) retrain a new Kriging meta-model by adding the • * , " * to the training set and go back to step i).…”

Section: Meta-modelingmentioning

confidence: 99%

“…As learning function (step iv above), we consider the so-called U-function, which is based on the concept of misclassification (Echard et al, 2011):…”

Section: Meta-modelingmentioning

confidence: 99%

See 2 more Smart Citations

Simulation-based exploration of high-dimensional system models for identifying unexpected events

Turati

Pedroni

Zio

2017

Reliability Engineering & System Safety

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. Simulation-based exploration of highdimensional system models for identifying unexpected events. Reliability Engineering and System Safety.http://dx.doi.org/10.1016/j.ress.2017.04.004Simulation-based exploration of high-dimensional system models for identifying unexpected events AbstractMathematical numerical models are increasingly employed to simulate system behavior and identify sequences of events or configurations of the system's design and operational parameters that can lead the system to extreme conditions (Critical Region, CR). However, when a numerical model is: i) computationally expensive, ii) high-dimensional, and iii) complex, these tasks become challenging.In this paper, we propose an adaptive framework for efficiently tackling this problem: i) a dimensionality reduction technique is employed for identifying the factors and variables that most affect the system behavior; ii) a meta-model is sequentially trained to replace the computationally expensive model with a computationally cheap one; iii) an adaptive exploration algorithm based on Markov Chain Monte Carlo is introduced for exploring the system state space using the meta-model; iv) clustering and other techniques for the visualization of high dimensional data (e.g., parallel coordinates plot) are employed to summarize the retrieved information.The method is employed to explore a power network model involving 20 inputs. The CRs are properly identified with a limited computational cost, compared to another exploration technique of literature (i.e., Latin Hypercube Sampling).

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Section: Meta-modelingmentioning

confidence: 99%

Section: Meta-modelingmentioning

confidence: 99%

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Simulation-based exploration of high-dimensional system models for identifying unexpected events

Turati

Pedroni

Zio

2017

Reliability Engineering & System Safety

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“…Such adaptive techniques have been developed e.g. with Kriging [5][6][7]), SVM [8][9][10][11][12] and polynomial chaos expansions [13,14]. This paper proposes an adaptive technique for assessing low failure probabilities based on SVM surrogates used in regression.…”

Section: Introductionmentioning

confidence: 99%

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Bourinet¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Reliability assessment in the context of rare failure events still suffers from its computational cost despite some available methods widely accepted by researchers and engineers. Monte Carlo simulation methods even in their most efficient version such as subset simulation often require a large number of samples for an acceptable accuracy on the failure probability of interest. For low to moderately high dimensional problems and under the assumption of a rather smooth limit-state function, surrogate models a.k.a. metamodels or response surfaces represent interesting alternative solutions. This paper presents an adaptive method based on SVM surrogates used in regression. The SVM formulation hinges on the -insensitive loss function and a Gaussian RBF kernel. The key idea of the proposed method is to iteratively construct SVM surrogates which become more accurate as they get closer to the limit-state surface. Subset simulation is applied to the constructed SVM surrogates for assessing probabilities with respect to intermediate threshold values of the LSF and more importantly for generating new training points. The efficiency of the method is tested on several examples featuring various challenges: a parallel system, a highly curved limit-state surface at a single most probable failure point and a smooth high-dimensional limit-state surface with equal curvatures. The paper puts an emphasis on the key role of an optimal selection of SVM surrogate hyperparameters. This is achieved in the present work by minimizing an estimate of the leave-one-out error using the cross-entropy method.652

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“…Compared to other metamodels, Kriging metamodel is particularly useful for reliability analysis due to the direct availability of error estimation that allows one to deploy active learning strategy [21,22,23] (i.e., Kriging with adaptive sampling). Active learning works by adding more samples so as to increase the accuracy of the metamodel near the region of interest, that is, the limit state.…”

mentioning

confidence: 99%

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Palar

Zuhal

Shimoyama

et al. 2018

Reliability Engineering & System Safety

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The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations are required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the lowfidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.

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AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

Cited by 1,428 publications

References 27 publications

Simulation-based exploration of high-dimensional system models for identifying unexpected events

Simulation-based exploration of high-dimensional system models for identifying unexpected events

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

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