An Introduction to Rare Event Simulation and Importance Sampling

Biondini, Gino

doi:10.1016/b978-0-444-63492-4.00002-2

Cited by 15 publications

(8 citation statements)

References 36 publications

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“…ANN (an SLFNN model) is used to predict the RUL for Li-ion batteries online (Wu et al, 2016). The input to the SLFNN are eleven points from the CC charging voltage curve selected by the importance sampling (IS) method (Biondini, 2015;Sadowsky, 1990), whereas the output of the SLFNN is the equivalent circle life (ECL). Then the RUL is calculated by subtracting the cycle number when the battery reaches its end of life by the ECL.…”

Section: Ll Open Accessmentioning

confidence: 99%

Machine learning toward advanced energy storage devices and systems

Gao

2021

iScience

118

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Technology advancement demands energy storage devices (ESD) and systems (ESS) with better performance, longer life, higher reliability, and smarter management strategy. Designing such systems involve a trade-off among a large set of parameters, whereas advanced control strategies need to rely on the instantaneous status of many indicators. Machine learning can dramatically accelerate calculations, capture complex mechanisms to improve the prediction accuracy, and make optimized decisions based on comprehensive status information. The computational efficiency makes it applicable for real-time management. This paper reviews recent progresses in this emerging area, especially new concepts, approaches, and applications of machine learning technologies for commonly used energy storage devices (including batteries, capacitors/supercapacitors, fuel cells, other ESDs) and systems (including battery ESS, hybrid ESS, grid and microgrid-containing energy storage units, pumped-storage system, thermal ESS). The perspective on future directions is also discussed.

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Section: Ll Open Accessmentioning

confidence: 99%

Machine learning toward advanced energy storage devices and systems

Gao

2021

iScience

118

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“…In this section, a sequential CE algorithm for the estimation of overload probabilities of a distribution network asset is described, adapted from [6]. For a more a general discussion of the CE method, the interested reader is referred to [5], [10].…”

Section: Application Of the Cross-entropy Methodsmentioning

confidence: 99%

Efficient Assessment of Electricity Distribution Network Adequacy with the Cross-Entropy Method

Betge

Droste²,

Heres³

et al. 2021

2021 IEEE Madrid PowerTech

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Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using probabilistic models of future demand. However, computational cost can become a severe challenge when evaluating large probabilistic electricity demand forecasting models with long forecasting horizons. In this paper, Monte Carlo methods are developed to increase the computational efficiency of obtaining asset overload probabilities from a bottom-up stochastic demand model. Cross-entropy optimised importance sampling is contrasted with conventional Monte Carlo sampling. Benchmark results of the proposed methods suggest that the importance sampling-based methods introduced in this work are suitable for estimating rare overload probabilities for assets with a small number of customers.

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“…For an efficient and reliable estimation of the failure probability with IS, the sampling density needs to be chosen carefully. In fact, there exists an optimal IS density, whose PDF is [13]:…”

Section: Cross Entropy Methodsmentioning

confidence: 99%

“…(30) and (31) with Eq. (13) shows that obtaining the MLE estimate of the parameters of a parametric density with pre-selected samples according to the indicator function used in the CE method is equivalent to solving the CE optimization problem. This equivalence has also been discussed in [4].…”

Section: Maximum Likelihood Estimation Of Distribution Parametersmentioning

confidence: 99%

Cross entropy-based importance sampling using Gaussian densities revisited

2019

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The computation of the probability of a rare (failure) event is a common task in structural reliability analysis. In most applications, the numerical model defining the rare event is nonlinear and the resulting failure domain often multimodal. One strategy for estimating the probability of failure in this context is the importance sampling method. The efficiency of importance sampling depends on the choice of the importance sampling density. A near-optimal sampling density can be found through application of the cross entropy method. The cross entropy method is an adaptive sampling approach that determines the sampling density through minimizing the Kullback-Leibler divergence between the theoretically optimal importance sampling density and a chosen parametric family of distributions. In this paper, we investigate the suitability of the multivariate normal distribution and the Gaussian mixture model as importance sampling densities within the cross entropy method. Moreover, we compare the performance of the cross entropy method to sequential importance sampling, another recently proposed adaptive sampling approach, which uses the Gaussian mixture distribution as a proposal distribution within a Markov Chain Monte Carlo algorithm. For the parameter updating of the Gaussian mixture within the cross entropy method, we propose a modified version of the expectation-maximization algorithm that works with weighted samples. To estimate the number of distributions in the mixture, the density-based spatial clustering of applications with noise (DBSCAN) algorithm is adapted to the use of weighted samples. We compare the performance of the different methods in several examples, including component reliability problems, system reliability problems and reliability in varying dimensions. The results show that the cross entropy method using a single Gaussian outperforms the cross entropy method using Gaussian mixture and that both distribution types are not suitable for high dimensional reliability problems.

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An Introduction to Rare Event Simulation and Importance Sampling

Cited by 15 publications

References 36 publications

Machine learning toward advanced energy storage devices and systems

Machine learning toward advanced energy storage devices and systems

Efficient Assessment of Electricity Distribution Network Adequacy with the Cross-Entropy Method

Cross entropy-based importance sampling using Gaussian densities revisited

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