Cross entropy-based importance sampling using Gaussian densities revisited

Geyer, Sebastian; Papaioannou, Iason; Straub, Daniel

doi:10.1016/j.strusafe.2018.07.001

Cited by 84 publications

(43 citation statements)

References 19 publications

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“…

\max_{ω_{e}, μ_{e}, {normalΣ}_{e} e = 1, \dots, n_{normalGS}} \frac{1}{m} \sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) \ln g (x_{cv, k}) .

Equation (22) can be solved by the expectation‐maximisation algorithm adopted in ref. [28]. The solution in the l ‐th iteration is given as

r_{e, k}^{(l)} = \frac{ω_{e}^{(l - 1)} φ false(x_{normalcv, k}; μ_{e}^{false(l - 1 false)}, Σ_{e}^{false(l - 1 false)} false)}{\sum_{e = 1}^{n_{GM}} ω_{e}^{false(l - 1 false)} φ (x_{cv, k}; μ_{e}^{(l - 1)}, {normalΣ}_{e}^{(l - 1)})} .

ω_{e}^{(l)} = \frac{\sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) r_{e, k}^{false(l false)} x_{normalcv, k}}{\sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) r_{e, k}^{...}}

…”

Section: Methodology Of Truncated Gaussian Mixture Model Based Cross ...mentioning

confidence: 99%

Capacity value evaluation of wind farms considering the correlation between wind power output and load

Cai

2021

IET Generation Trans & Dist

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A method of capacity value evaluation for wind farms considering the correlation between wind power and load is presented. The paper starts with defining the metric of capacity value called capacity credit, and its basic evaluation process. Then the core part of capacity credit evaluation, which is the reliability assessment of power systems, is focused on. In this core part, two limitations of the frequently used cross entropy based importance sampling method are analysed. To solve the problems, an improved method is proposed by using truncated Gaussian mixture model as the proposal distribution of the cross entropy based importance sampling methods. This improved method is adopted to speed up the reliability assessment of composite power systems in the capacity credit evaluation. Finally, several numerical tests are designed and performed on the IEEE-RTS 79 and IEEE-RTS 96 test systems. The results show that the improved method is faster than traditional cross entropy based importance sampling methods when assessing the reliability of power system. Besides, the efficiency of the improved method is almost impervious to the correlation of load and wind power output, which ensures its applicability in different scenarios. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…

\max_{ω_{e}, μ_{e}, {normalΣ}_{e} e = 1, \dots, n_{normalGS}} \frac{1}{m} \sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) \ln g (x_{cv, k}) .

Equation (22) can be solved by the expectation‐maximisation algorithm adopted in ref. [28]. The solution in the l ‐th iteration is given as

r_{e, k}^{(l)} = \frac{ω_{e}^{(l - 1)} φ false(x_{normalcv, k}; μ_{e}^{false(l - 1 false)}, Σ_{e}^{false(l - 1 false)} false)}{\sum_{e = 1}^{n_{GM}} ω_{e}^{false(l - 1 false)} φ (x_{cv, k}; μ_{e}^{(l - 1)}, {normalΣ}_{e}^{(l - 1)})} .

ω_{e}^{(l)} = \frac{\sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) r_{e, k}^{false(l false)} x_{normalcv, k}}{\sum_{k = 1}^{m} I (x_{k}) Q (x_{k}) r_{e, k}^{...}}

…”

Section: Methodology Of Truncated Gaussian Mixture Model Based Cross ...mentioning

confidence: 99%

Capacity value evaluation of wind farms considering the correlation between wind power output and load

Cai

2021

IET Generation Trans & Dist

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“…For GR-PMC, the multinomial resampling breaks down if all N K samples have zero weight, in which case we reweight all the samples evenly with weight 1/N K and proceed as the algorithm intended. In CE-PMC when updating the covariances of a Gaussian distribution one or several dimensions may flatten resulting in a singular matrix, especially when approaching a linear function [21,Sec. 6.3].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…First we examine three examples taken from structural reliability literature [1], [21]. The target distributions are all proportional to I {Si(x)≤γ} π(x), where π(x) = π(x 1 , x 2 ) is given by a standard multivariate Gaussian distribution, and…”

Section: A Structural Reliability Examplesmentioning

confidence: 99%

Rare Events via Cross-Entropy Population Monte Carlo

Miller,

Corcoran,

Schneider

2021

Preprint

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We present a Cross-Entropy based population Monte Carlo algorithm. This methods stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on numerical examples show that the algorithm can outperform existing resampling population Monte Carlo methods, especially for higher-dimensional problems.

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“…This approach will fail when scaling to high dimensional problems. This is discussed in (Geyer et al, 2019) in the context of reliability estimation problems.…”

Section: Estimation Of Distribution Algorithms (Edas)mentioning

confidence: 99%

GACEM: Generalized Autoregressive Cross Entropy Method for Multi-Modal Black Box Constraint Satisfaction

Hakhamaneshi¹,

Settaluri²,

Abbeel³

et al. 2020

Preprint

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In this work we present a new method of blackbox optimization and constraint satisfaction. Existing algorithms that have attempted to solve this problem are unable to consider multiple modes, and are not able to adapt to changes in environment dynamics. To address these issues, we developed a modified Cross-Entropy Method (CEM) that uses a masked auto-regressive neural network for modeling uniform distributions over the solution space. We train the model using maximum entropy policy gradient methods from Reinforcement Learning. Our algorithm is able to express complicated solution spaces, thus allowing it to track a variety of different solution regions. We empirically compare our algorithm with variations of CEM, including one with a Gaussian prior with fixed variance, and demonstrate better performance in terms of: number of diverse solutions, better mode discovery in multi-modal problems, and better sample efficiency in certain cases.For the rest of this article, in section 2, background informa-

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Cross entropy-based importance sampling using Gaussian densities revisited

Cited by 84 publications

References 19 publications

Capacity value evaluation of wind farms considering the correlation between wind power output and load

Capacity value evaluation of wind farms considering the correlation between wind power output and load

Rare Events via Cross-Entropy Population Monte Carlo

GACEM: Generalized Autoregressive Cross Entropy Method for Multi-Modal Black Box Constraint Satisfaction

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