Fat Latin Hypercube Sampling and Efficient Sparse Polynomial Chaos Expansion for Uncertainty Propagation on Finite Precision Models: Application to 2D Deep Drawing Process

2016 ◽  
pp. 185-213
Author(s):  
Jérémy Lebon ◽  
Guénhaël Le Quilliec ◽  
Piotr Breitkopf ◽  
Rajan Filomeno Coelho ◽  
Pierre Villon
Keyword(s):  
Deep Drawing ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Latin Hypercube Sampling ◽  
Chaos Expansion ◽  
Drawing Process ◽  
Latin Hypercube ◽  
Finite Precision ◽  
Deep Drawing Process ◽  
Sparse Polynomial

scholarly journals Optimized Sparse Polynomial Chaos Expansion With Entropy Regularization

2021 ◽  
Author(s):  
SiJie Zeng ◽  
XiaoJun Duan ◽  
JiangTao Chen ◽  
Liang Yan
Keyword(s):  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Entropy Change ◽  
Optimization Method ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Sparse Polynomial ◽  
Output Uncertainty ◽  
Sparse Polynomial Chaos Expansion ◽  
Fitting In

Abstract Sparse Polynomial Chaos Expansion(PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviate the problem of dimensionality curse. However, current sparse PCE techniques focus on choosing features with the largest coefficients, which may ignore uncertainties propagated with high order features. Hence, this paper proposes the idea of selecting polynomial chaos basis based on information entropy, which aims to retain the advantages of existing sparse techniques while considering entropy change as output uncertainty. A novel entropy-based optimization method is proposed to update the state-of-the-art sparse PCE models. This work further develops an entropy-based synthetic sparse model, which has higher computational efficiency. Two benchmark functions and a CFD experiment are used to compare the accuracy and efficiency between the proposed method and classical methods. The results show that entropy-based methods can better capture the features of uncertainty propagation, and the problem of over-fitting in existing sparse PCE methods can be avoided.

Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability

AIAA Journal ◽  
2004 ◽  
Vol 42 (6) ◽  
pp. 1191-1198 ◽  
Author(s):  
Seung-Kyum Choi ◽  
Ramana V. Grandhi ◽  
Robert A. Canfield ◽  
Chris L. Pettit
Keyword(s):  
Polynomial Chaos ◽  
Latin Hypercube Sampling ◽  
Polynomial Chaos Expansion ◽  
Response Variability ◽  
Chaos Expansion ◽  
Latin Hypercube

scholarly journals Effect of Tool Geometry Parameters on the Formability of a Camera Cover in the Deep Drawing Process

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3993
Author(s):  
Thanh Trung Do ◽  
Pham Son Minh ◽  
Nhan Le
Keyword(s):  
Deep Drawing ◽  
Thickness Distribution ◽  
Metal Flow ◽  
Sheet Thickness ◽  
Side Wall ◽  
Tool Geometry ◽  
Drawing Process ◽  
Nose Radius ◽  
Deep Drawing Process

The formability of the drawn part in the deep drawing process depends not only on the material properties, but also on the equipment used, metal flow control and tool parameters. The most common defects can be the thickening, stretching and splitting. However, the optimization of tools including the die and punch parameters leads to a reduction of the defects and improves the quality of the products. In this paper, the formability of the camera cover by aluminum alloy A1050 in the deep drawing process was examined relating to the tool geometry parameters based on numerical and experimental analyses. The results showed that the thickness was the smallest and the stress was the highest at one of the bottom corners where the biaxial stretching was the predominant mode of deformation. The problems of the thickening at the flange area, the stretching at the side wall and the splitting at the bottom corners could be prevented when the tool parameters were optimized that related to the thickness and stress. It was clear that the optimal thickness distribution of the camera cover was obtained by the design of tools with the best values—with the die edge radius 10 times, the pocket radius on the bottom of the die 5 times, and the punch nose radius 2.5 times the sheet thickness. Additionally, the quality of the camera cover was improved with a maximum thinning of 25% experimentally, and it was within the suggested maximum allowable thickness reduction of 45% for various industrial applications after optimizing the tool geometry parameters in the deep drawing process.

Blank shape optimization in the deep drawing process by sun method

2021 ◽  
Author(s):  
Hamidreza Gharehchahi ◽  
Mohammad Javad Kazemzadeh-Parsi ◽  
Ahmad Afsari ◽  
Mehrdad Mohammadi
Keyword(s):  
Shape Optimization ◽  
Deep Drawing ◽  
Drawing Process ◽  
Deep Drawing Process ◽  
Blank Shape Optimization ◽  
Blank Shape

scholarly journals Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

Production of Tapered Cups by Sequential Deep Drawing of Sheet Metals Using Drawn Cups as a Part of Punch

1993 ◽  
Vol 115 (2) ◽  
pp. 224-229 ◽  
Author(s):  
K. Yamaguchi ◽  
K. Kanayama ◽  
M. H. Parsa ◽  
N. Takakura
Keyword(s):  
Deep Drawing ◽  
Drawing Ratio ◽  
Drawing Process ◽  
Sheet Metals ◽  
Deep Drawing Process ◽  
Drawing Method

A new deep drawing process of sheet metals is developed to facilitate small-lot production of deep cups with large drawing ratio. In this process, unlike the conventional deep drawing method, a few drawn cups are always stacked on the punch and used as a part of punch for the subsequent deep drawing of a given blank. Before drawing a new blank, a drawn cup which is in contact with the punch is stripped off. The repetition of such stripping and drawing operations makes it possible to carry out both the first-stage drawing and the subsequent slight redrawings in one drawing operation using only one pair of punch and die. In this paper, this new deep drawing process is applied to the production of tapered cups and the main feature of the process is shown.

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