A Hierarchical Neural Hybrid Method for Failure Probability Estimation

Li, Ké; Tang, Kejun; Li, Jinglai; Wu, Tianfan; Liao, Qifeng

doi:10.1109/access.2019.2934980

Cited by 13 publications

(11 citation statements)

References 33 publications

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“…A comparative study using various mathematical examples shows that the method can obtain a more accurate percentile value estimation. Li et al [42] presented a novel hierarchical neural hybrid method to efficiently compute failure probabilities of challenging high-dimensional problems. Multi-fidelity surrogates are constructed based on two-hidden layer MLP with different levels of layers, so expensive high-fidelity surrogates are adapted only when the parameters are in the suspicious domain.…”

Section: Mlp-based Mcsmentioning

confidence: 99%

Deep learning-based methods in structural reliability analysis: a review

Afshari

Zhao

Zhuang

et al. 2023

Meas. Sci. Technol.

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One of the most significant and growing research fields in mechanical and civil engineering is Structural Reliability Analysis (SRA). A reliable and precise SRA usually has to deal with complicated , aand numerically expensive problems. Artificial intelligence-based (AI) nd specifically, Deep learning-based (DL) methods, have been applied to the SRA problems to reduce the computational cost and to improve the accuracy of reliability estimation as well. This article reviews the recent advances in using DL models in SRA problems. The review includes the most common categories of DL-based methods used in SRA. More specifically, the application of supervised methods, unsupervised methods, and hybrid deep learning methods in SRA are explained. In this paper, the supervised methods for SRA are categorized as Multi-Layer Perceptron (MLP), Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN ), Long short-term memory (LSTM), Bidirectional (Bi-LSTM) and Gated recurrent units (GRU). For the unsupervised methods, we have investigated methods such as Generative Adversarial Network (GAN), Autoencoders (AE), Self-Organizing Map (SOM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We have made a comprehensive survey of these methods in SRA. Aiming towards an efficient SRA, deep learning-based methods applied for approximating the limit state function (LSF) with First/Second Order Reliability Methods (FORM/SORM), Monte Carlo simulation (MCS), or MCS with importance sampling (IS). Accordingly, the current paper focuses on the structure of different DL-based models and the applications of each DL method in various SRA problems. This survey helps researchers in mechanical and civil engineering, especially those who are engaged with structural and reliability analysis or dealing with quality assurance problems.

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Section: Mlp-based Mcsmentioning

confidence: 99%

Deep learning-based methods in structural reliability analysis: a review

Afshari

Zhao

Zhuang

et al. 2023

Meas. Sci. Technol.

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“…If we consider equal offline sample sizes, number of blocks and training epochs, N i = N off , B i = B off , T i = T off for all subdomains {D i } p i=1 , then total cost can be written as pN off B off T off C solve . The total cost is decreased by employing the idea of hierarchical neural networks [29,17]. Remark 2.…”

Section: D3m Summarymentioning

confidence: 99%

D3M: A Deep Domain Decomposition Method for Partial Differential Equations

Tang

et al. 2020

IEEE Access

Self Cite

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A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization problem, and we design a multi-fidelity neural network framework to solve this optimization problem. Our contribution is to develop a systematical computational procedure for the underlying problem in parallel with domain decomposition. Our analysis shows that the D3M approximation solution converges to the exact solution of underlying PDEs. Our proposed framework establishes a foundation to use variational deep learning in large-scale engineering problems and designs. We present a general mathematical framework of D3M, validate its accuracy and demonstrate its efficiency with numerical experiments.

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“…Fernandez et al 3 employed artificial neural networks as a surrogate model to transfer atomistic grain boundary decohesion data to continuum scale modeling of intergranular fracture in Aluminum. Li et al 4 developed a hierarchical neural hybrid method to efficiently compute failure probabilities in high dimensional problems employing the multifidelity approach introduced by Aydin et al 1 . They showed that for achieving an accurate estimate of the rare failure probability, a traditional Monte Carlo method needs to solve the equations significantly more frequently than the proposed hierarchical neural hybrid method.…”

Section: Introductionmentioning

confidence: 99%

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Mianroodi

Siboni²,

Raabe

2021

npj Comput Mater

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We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.

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A Hierarchical Neural Hybrid Method for Failure Probability Estimation

Cited by 13 publications

References 33 publications

Deep learning-based methods in structural reliability analysis: a review

Deep learning-based methods in structural reliability analysis: a review

D3M: A Deep Domain Decomposition Method for Partial Differential Equations

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

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