Bayesian networks for comprehensive uncertainty quantification in multi-scale, multi-physics reliability analysis

Author(s):  
Y Ling ◽  
S Mahadevan
2009 ◽  
Vol 31 (10) ◽  
pp. 1814-1825 ◽  
Author(s):  
Dong LIU ◽  
Chun-Yuan ZHANG ◽  
Wei-Yan XING ◽  
Rui LI

Author(s):  
Zequn Wang ◽  
Mingyang Li

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.


Author(s):  
Zhuo Wang ◽  
Chen Jiang ◽  
Mark F. Horstemeyer ◽  
Zhen Hu ◽  
Lei Chen

Abstract One of significant challenges in the metallic additive manufacturing (AM) is the presence of many sources of uncertainty that leads to variability in microstructure and properties of AM parts. Consequently, it is extremely challenging to repeat the manufacturing of a high-quality product in mass production. A trial-and-error approach usually needs to be employed to attain a product with high quality. To achieve a comprehensive uncertainty quantification (UQ) study of AM processes, we present a physics-informed data-driven modeling framework, in which multi-level data-driven surrogate models are constructed based on extensive computational data obtained by multi-scale multi-physical AM models. It starts with computationally inexpensive metamodels, followed by experimental calibration of as-built metamodels and then efficient UQ analysis of AM process. For illustration purpose, this study specifically uses the thermal level of AM process as an example, by choosing the temperature field and melt pool as quantity of interest. We have clearly showed the surrogate modeling in the presence of high-dimensional response (e.g. temperature field) during AM process, and illustrated the parameter calibration and model correction of an as-built surrogate model for reliable uncertainty quantification. The experimental calibration especially takes advantage of the high-quality AM benchmark data from National Institute of Standards and Technology (NIST). This study demonstrates the potential of the proposed data-driven UQ framework for efficiently investigating uncertainty propagation from process parameters to material microstructures, and then to macro-level mechanical properties through a combination of advanced AM multi-physics simulations, data-driven surrogate modeling and experimental calibration.


2019 ◽  
Vol 188 ◽  
pp. 178-187 ◽  
Author(s):  
Miguel Angel Mendoza-Lugo ◽  
David Joaquín Delgado-Hernández ◽  
Oswaldo Morales-Nápoles

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