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A machine learning approach for ball milling of alumina ceramics

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Abstract

In this work, machine learning approach based on polynomial regression was explored to analyze the optimal processing parameters and predict the target particle sizes for ball milling of alumina ceramics. Data points were experimentally collected by measuring the particle sizes. Prediction interval (PI)-based optimization methods using polynomial regression analysis are proposed. As a first step, functional relations between processing parameters (inputs) and quality responses (outputs) are derived by applying the regression analysis. Later, based on these relations, objective functions to be maximized are defined by desirability approach. Finally, the proposed PI-based methods optimize both parameter points and intervals of the target mill for accomplishing user-specified target responses. The optimization results show that the PI-based point optimization methods can select and recommend statistically reliable optimized parameter points even though unique solutions for the objective functions do not exist. From the results of confirmation experiments, it is established that the optimized parameter points can produce desired final powders with quality responses quite similar to the target responses.

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Data availability

All data generated or mentioned in this study are included in this published article.

Code availability

No code was provided in this manuscript.

Abbreviations

L :

Number of quality responses (inputs)

p :

Number of processing parameters (outputs)

y l, x j :

lTh output, and jth input

\(\hat{y}_{l} ({\mathbf{x}})\) :

Regression function for lth output yl

\(\hat{y}_{l} ({\mathbf{x}}_{{{\text{new}}}} )\) :

Output of lth regression function for new input vector xnew

\([PI_{LB}^{l} ({\mathbf{x}}_{{{\text{new}}}} ),PI_{UB}^{l} ({\mathbf{x}}_{{{\text{new}}}} )]\) :

Prediction interval for \(\hat{y}_{l} ({\mathbf{x}}_{{{\text{new}}}} )\)

\(PI_{k}^{l}\) :

Length of prediction interval \([PI_{LB}^{l} ({\mathbf{x}}_{k}^{*} ),PI_{UB}^{l} ({\mathbf{x}}_{k}^{*} )]\)

PI k :

Total length of L prediction intervals obtained by summing all the standardized values of \(PI_{k}^{1} ,...,PI_{k}^{L}\)

\({\mathbf{I}}_{{{\text{imp}}{.}}} \in \Re^{L \times p}\) :

Importance matrix that consists of importance values of p inputs for L outputs

d l(∙):

Desirability function for lth output yl

y l ,target :

Target value for lth output yl

y l ,min, y l ,max :

Lower and upper limits of lth output yl

D(x):

Overall desirability function (objective function for multiple response optimization problem)

\({\mathbf{x}}^{*} = [x_{1}^{*} ,...,x_{p}^{*} ]^{T}\) :

Optimized parameter point

\({\mathbf{x}}_{LB}^{*} ,{\mathbf{x}}_{UB}^{*}\) :

Lower and upper bounds for defining optimized parameter intervals

\([x_{LB,j}^{*} ,x_{UB,j}^{*} ]\) :

Optimized parameter interval for jth input

J L × p :

L By p matrix of ones

δ l :

Small positive increment

W lj, \(\overline{W}_{lj}\) :

(l, j)Th element of W = JL×p − Iimp., and standardized values of Wlj

\(\times_{j = 1}^{p} [x_{j}^{*} - \delta_{l} \overline{W}_{lj} ,x_{j}^{*} + \delta_{l} \overline{W}_{lj} ]\) :

p-Dimensional hyper-rectangle centered at x*

v m, V :

Vertices of hyper-rectangle, and vertex set composed of all vm

ML:

Machine learning

PI:

Prediction interval

ANN:

Artificial neural networks

PSD:

Particle size distribution

RSM:

Response surface method

GA:

Genetic algorithm

AVOVA:

Analysis of variance

CCD:

Central composite design

MRO:

Multiple response optimization

MC:

Monte Carlo

PSO:

Particle swarm optimization

RMSE:

Root mean squared error

ECDF:

Empirical cumulative distribution function

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Funding

This work was supported by the Ministry of Trade, Industry and Energy (MOTIE) and the Korea Evaluation Institute of Industrial Technology (KEIT) research funding (Grant No. 20003891), and in part by Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government [22ZD1120, Regional Industry ICT Convergence Technology Advancement and Support Project in Daegu-Gyeongbuk].

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Authors and Affiliations

  1. Electronics and Telecommunications Research Institute, Daegu-Gyeongbuk Research Center, Daegu, 42994, South Korea

    Jungwon Yu & Youngjae Lee

  2. School of Advanced Materials Science and Engineering, Kumoh National Institute of Technology, Gumi, Gyeongbuk, 39177, South Korea

    Kati Raju, So-Hyun Jin & Hyun-Kwuon Lee

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  1. Jungwon Yu
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  2. Kati Raju
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Correspondence to Hyun-Kwuon Lee.

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Yu, J., Raju, K., Jin, SH. et al. A machine learning approach for ball milling of alumina ceramics. Int J Adv Manuf Technol 123, 4293–4308 (2022). https://doi.org/10.1007/s00170-022-10430-w

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