The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions

Girolami, Mark; Febrianto, Eky; Yin, Guofu; Cirak, Fehmi

doi:10.1016/j.cma.2020.113533

Cited by 49 publications

(51 citation statements)

References 37 publications

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“…This time, the objective function is composed exclusively of the second term of the right-hand side of Equation ( 5) and its minimization is sought. Following this training scheme, during the first step, the discriminator learns to distinguish between real and generated images and the generator to generate images that the discriminator classifies as real and (as shown in Goodfellow et al, 2014) to have probability distribution similar to the real data.…”

Section: Vanilla Gansmentioning

confidence: 99%

“…Since a cGAN is able to generate manifolds of data as a function of a code vector, it fits the desired functionality of a mirror, as described in the current work. Moreover, as stated in Goodfellow et al (2014), the generator learns, apart from generating data that look real, to generate data close to the distribution of the original data. The same results are expected herein by the use of a cGAN.…”

Section: Cgan As Mirrors Of a Structurementioning

confidence: 99%

“…For the purposes of using generative models as mirrors of structures, a very recently developed neural network architecture is used here. The core algorithm is the generative adversarial network (GAN) (Goodfellow et al, 2014) and a variation of it, the cGAN (Mirza and Osindero, 2014). The latter algorithm is used exactly in the same way as an SFE model is used.…”

Section: Generative Adversarial Networkmentioning

confidence: 99%

“…The training of the discriminator is carried out by maximizing the probability that it assigns the correct label ("real" or "fake") to the samples. At the same time, the training of the generator, G, is accomplished by trying to minimize the probability that the discriminator classifies the generated samples as fake, that is, minimization of log Goodfellow et al (2014), the objective function L can be interpreted as a two-player game explained by,…”

Section: Vanilla Gansmentioning

confidence: 99%

“…In terms of white generative models, a fairly basic implementation of the stochastic FE method has been presented here, based on the early polynomial-chaos formulation of Ghanem and Spanos (2003); however, more recent variants, like the stochastic Galerkin approach (Augustin and Rentrop, 2012), have advantages like more general expansion bases for the stochastic space. A very recent methodology StatFEM (Duffin et al, 2021;Girolami et al, 2021), provides an elegant Bayesian framework for both building and updating generative FE models. In terms of generative black-box models, GANs are by no means the only option; in fact, one alternative-the variational auto-encoder (Kingma and Welling, 2014)-has already proved to be generally useful in engineering problems; particularly in condition monitoring problems (e.g., Mylonas et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

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On generative models as the basis for digital twins

Tsialiamanis

Wagg

Dervilis

et al. 2021

DCE

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A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modeling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modeling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modeling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperforms the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.

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Section: Vanilla Gansmentioning

confidence: 99%

Section: Cgan As Mirrors Of a Structurementioning

confidence: 99%

Section: Generative Adversarial Networkmentioning

confidence: 99%

Section: Vanilla Gansmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On generative models as the basis for digital twins

Tsialiamanis

Wagg

Dervilis

et al. 2021

DCE

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A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling

Rouse

Kerfriden

Hamadi

2022

Numerical Meth Engineering

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The present work proposes a computational approach that recovers full finite element error fields from a small number of estimates of errors in scalar quantities of interest. The approach is weakly intrusive and is motivated by large scale industrial applications wherein modifying the finite element models is undesirable and multiple regions of interest may exist in a single model. Error estimates are developed using a Zhu-Zienkiewicz estimator coupled with the adjoint methodology to deliver goal-oriented results. A Bayesian probabilistic estimation framework is deployed for full field estimation. An adaptive, radial basis function based reduced order modeling strategy is implemented to reduce the cost of calculating the posterior. The Bayesian reconstruction approach, accelerated by the proposed model reduction technology, is shown to yield good probabilistic estimates of full error fields, with a computational complexity that is acceptable compared to the evaluation of the goal-oriented error estimates. The novelty of the work is that a set of computed error estimates are considered as partial observations of an underlying error field, which is to be recovered. Future improvements of the method include the optimal selection of goal-oriented error measures to be acquired prior to the error field reconstruction.

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Research on Digital Twin for Building Structure Health Monitoring

Jincheng

2021

Lecture Notes on Data Engineering and Communications Technologies

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Existing buildings are vulnerable to damage due to adverse factors such as multi-field coupling, material degradation, and corrosion. With the help of the big data provided by the health monitoring system, the digital twin uses data analysis to diagnose the current state of the building, predict the future performance of the building, and give real-time decisions on the operations to be taken in the future according to the information provided by the data. The technical system of the digital twin, theoretical, and technical composition of structural health monitoring are described. The key problems and research paradigms of building structure health management are combed based on the digital twin model. With the breakthrough of technology, the accumulation of data, and the improvement of computing power, digital twins for building structure health management will become a trend.

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The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions

Cited by 49 publications

References 37 publications

On generative models as the basis for digital twins

On generative models as the basis for digital twins

A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling

Research on Digital Twin for Building Structure Health Monitoring

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