Application of supervised machine learning as a method for identifying DEM contact law parameters

Piotr Klejment; Piotr Klejment

doi:10.3934/mbe.2021370

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 7490-7505. doi: 10.3934/mbe.2021370

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Research article Special Issues

Application of supervised machine learning as a method for identifying DEM contact law parameters

Piotr Klejment ^,

Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

Received: 26 June 2021 Accepted: 17 August 2021 Published: 01 September 2021

Calibration of Discrete Element Method (DEM) models is an iterative process of adjusting input parameters such that the macroscopic results of simulations and experiments are similar. Therefore, selecting appropriate input parameters of a model effectively is crucial for the efficient use of the method. Despite the growing popularity of DEM, there is still an ongoing need for an efficient method for identifying contact law parameters. Commonly used trial and error procedures are very time-consuming and unpractical, especially in the case of models with many parameters to calibrate. It seems that machine learning may offer a new approach to that problem. This research aims to apply supervised machine learning to figure out the dependencies between specific microscopic and macroscopic parameters. More than 6000 DEM simulations of uniaxial compression tests gathered the data for two algorithms - Multiple Linear Regression and Random Forest. Promising results with an accuracy of over 99% give good hope for finding a universal relation between input and output parameters (for a specific DEM implementation) and reducing the number of simulations required for the calibration procedure. Another pertinent question concerns the size of the DEM models used during calibration based on the uniaxial compression test. It has been proven that calibration of certain parameters can be done on smaller samples, where the critical threshold is around 30% of the radius of the original model.

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Citation: Piotr Klejment. Application of supervised machine learning as a method for identifying DEM contact law parameters[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7490-7505. doi: 10.3934/mbe.2021370

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Abstract

A correction on

Numerical investigation and improvement of the aerodynamic performance of a modified elliptical-bladed Savonius-style wind turbine. By Sri Kurniati, Sudirman Syam and Arifin Sanusi. AIMS Energy, 2023, Volume 11, Issue 6: 1211–1230. Doi: 10.3934/energy.2023055

The authors would like to make the following corrections to the published paper [1].

On page 1213, we updated the contents of "one symbol statement: ρ" in section 2. The updated contents are as follows:

- ρ is the the density of air,

On page 1215, we updated the contents of "Eq 16" in section 2. The updated contents are as follows:

$\frac{{{\bf{∂}} {\bf{ \pmb{\mathsf{ ϕ}} }}}_{{\bf{ℓ}}}}{{\bf{∂}} \boldsymbol{t}}+{\bf{∇}} \left({{\varnothing }}_{{\bf{ℓ}}}\overrightarrow{\boldsymbol{V}}\right)-{\bf{∇}} \left({\bf{\Gamma }}_{{\bf{ℓ}}}\overrightarrow{\boldsymbol{V}}{{\varnothing }}_{{\bf{ℓ}}}\right) = {\boldsymbol{R}}_{{\bf{ℓ}}}$

(16)

On page 1216, we updated the contents of "Table 2" in section 2. The updated contents are as follows:

Table 2. The terms in the general transfer equation Eq 16.

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \frac{{\partial {\rm{ \mathsf{ ϕ} }}}_{\ell }}{\partial t}+\nabla \left({\varnothing }_{\ell }\overrightarrow{V}\right)-\nabla \left({\mathrm{\Gamma }}_{\ell }\overrightarrow{V}{\varnothing }_{\ell }\right)={R}_{\ell } \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(16)$
$l$	${\varnothing }_{\ell }$	${\mathrm{\Gamma }}_{\ell }$
1	U	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial x}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial x}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial x}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial x}\right)+gx$
2	V	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial y}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial y}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial y}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial y}\right)+gy$
3	W	$vt$	$-\frac{1}{\rho }\frac{\partial \rho }{\partial z}+\frac{\partial }{\partial x}\left(vt\frac{\partial u}{\partial z}\right)+\frac{\partial }{\partial y}\left(vt\frac{\partial v}{\partial z}\right)+\frac{\partial }{\partial z}\left(vt\frac{\partial w}{\partial z}\right)+gz$
4	1	0	0
5	K	$vt/$	$G-\varepsilon$
6	$\varepsilon$	$vt/$	${C}_{1}\frac{\varepsilon }{k}G-{c}_{2}\frac{\varepsilon }{k}\varepsilon$

| Show Table

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Conflict of interest

All authors declare no conflicts of interest in this paper.

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