Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

Menz, Morgane; Gogu, Christian; Dubreuil, Sylvain; Bartoli, Nathalie; Mitard, J.

doi:10.1016/j.ress.2019.106771

Cited by 15 publications

(3 citation statements)

References 44 publications

(56 reference statements)

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“…The estimation of reliability constraints, outside of any optimization, with the help of Gaussian processes has received a lot of attention [54,55,56,57]. Such reliability analyses based on metamodels have then been included within optimization searches.…”

Section: Bayesian Optimization Under Uncertaintymentioning

confidence: 99%

Coupling and selecting constraints in Bayesian optimization under uncertainties

Pelamatti¹,

Riche²,

Helbert³

et al. 2022

Preprint

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We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the number of evaluations and makes this type of problems particularly challenging. In such a context, it is common to rely on Bayesian optimization algorithms. Assuming, without loss of generality, that the uncertainty comes from some of the inputs, it becomes possible to build a Gaussian process model in the joint space of design and uncertain variables. A two-step acquisition function is then used to provide, both, promising optimization variables associated to relevant uncertain samples. Our overall contribution is to correlate the constraints in the GP model and exploit this to optimally decide, at each iteration, which constraint should be evaluated and at which point. The coupled Gaussian model of the constraints relies on an output-as-input encoding. The constraint selection idea is developed by enabling that each constraint can be evaluated for a different uncertain input, thus improving the refinement efficiency. Constraints coupling and selection are gradually implement in 3 algorithm variants which are compared to a reference Bayesian approach. The results are promising in terms of convergence speed, accuracy and stability as observed on a 2, a 4 and a 27-dimensional problems.

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Section: Bayesian Optimization Under Uncertaintymentioning

confidence: 99%

Coupling and selecting constraints in Bayesian optimization under uncertainties

Pelamatti¹,

Riche²,

Helbert³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Xiao et al 16 used a back-propagation neural network to construct surrogate models for the reliability analysis of structural systems, in order to alleviate the computational burden and improve efficiency. Similarly, Menz et al 17 developed a method which adaptively couples kriging based active learning and reduced basis modeling for reliability analysis. Wang and Shaeezadeh 18 used adaptive kriging to establish a high-delity reliability updating model for the reliability assessment of structural systems, which was reported to be effective in computational efficiency enhancement and achieving high accuracy.…”

Section: Introductionmentioning

confidence: 99%

A machine learning methodology for reliability evaluation of complex chemical production systems

Zhao

et al. 2020

RSC Adv.

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“…Menz et al formalized the method of giving it the ability to address geostatistical problems. (13) However, owing to the limited number and uneven distribution of monitoring stations on the ground, the kriging method cannot accurately estimate the PM 2.5 concentration in areas without monitoring stations. Moreover, it does not consider the impact of time and space dimensions on air pollutants, making it difficult to meet the requirements for the study of the spatiotemporal distribution of the PM 2.5 concentration.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Seasonal Geographically and Temporally Weighted Regression Model for Accurate Estimation of Seasonal PM2.5 Concentrations in Beijing–Tianjin–Hebei Region

Zhou¹,

Wang²,

Du³

et al. 2020

Sensors and Materials

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Particulate matter with a diameter of less than 2.5 µm (PM 2.5 ) has a significant impact on air pollution, atmospheric visibility, and human health. The most basic and important step of regional air pollution control is to obtain air pollution data in different seasons from both satellite sensors and ground-level observations. The aim of this paper is to accurately estimate the PM 2.5 concentration in the Beijing-Tianjin-Hebei urban area in different seasons by establishing a seasonal geographically and temporally weighted regression (S-GTWR) model that integrates multiple complex factors. Using a greedy algorithm, the model results were optimized by selecting the characteristic variables that contributed to the accuracy of the model in different seasons. The measured and estimated PM 2.5 concentrations were compared and the cross-validation results were used as a basis for evaluating the accuracy of the model. The results showed that the accuracy of the S-GTWR model that combined the optimal characteristic variables was higher than that of the geographically weighted regression (GWR) model and the kriging method. The mean prediction error (ME), relative prediction error (RPE), and root mean square error (RMSE) of the S-GTWR model were small, and the coefficient of determination (R 2 ) of the model exceeded 0.86 for each season. The accuracy of the S-GTWR model in estimating the PM 2.5 concentration was highest in summer and lowest in winter. In addition, the proposed model can accurately estimate PM 2.5 concentrations in areas without monitoring sites. The results can provide a scientific basis for the study of pollution control and PM 2.5 exposure in large urban agglomerations.

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Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

Cited by 15 publications

References 44 publications

Coupling and selecting constraints in Bayesian optimization under uncertainties

Coupling and selecting constraints in Bayesian optimization under uncertainties

A machine learning methodology for reliability evaluation of complex chemical production systems

Optimization of Seasonal Geographically and Temporally Weighted Regression Model for Accurate Estimation of Seasonal PM2.5 Concentrations in Beijing–Tianjin–Hebei Region

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