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Strength retrieval of artificially cemented bauxite residue using machine learning: an alternative design approach based on response surface methodology

  • Sujeet Kumar
  • Arun Prasad
Original Article

Abstract

The aim of the present study is to propose an alternative artificial neural network model based on response surface methodology over conventional approach to estimate the unconfined compressive strength of artificially cemented bauxite residue. The artificial neural network model uses molding moisture content (w), curing time (t) and porosity/volumetric lime (η/Lv′) as input parameters and unconfined compressive strength as the output parameter. Bayesian regularization as training function with sigmoid and pure linear at hidden and output layers is used for modeling the artificial neural network. The proposed response surface methodology designed ANN model is comparable with the conventional designed ANN model and can be used effectively with significantly less number of data set. Sensitivity analysis, to make out the significant input factors based on connection-weight approach, is also discussed. Further, neural interpretation diagram is incorporated to study the effects of individual input parameters over the response. Finally, a predictive equation is presented based on response surface methodology designed artificial neural network model for the range of parameters studied.

Keywords

Bauxite residue Unconfined compressive strength Artificial neural network Sensitivity analysis Response surface methodology 

Abbreviations

AAE

Average absolute error

ANN

Artificial neural network

BBDANN

Box–Behnken designed ANN

CCC

Circumscribed central composite

CCDANN

Central composite designed ANN

CONVDANN

Conventional designed ANN

FCCD

Face-centered composite design

FFBPANN

Feed forward back propagation artificial neural network

FIS

Fuzzy interface system

GA

Genetic algorithms

ICC

Inscribed central composite

MAE

Maximum absolute error

MAPE

Mean absolute percentage error

MSE

Mean square error

OFAT

One factor at time

RMSE

Root-mean-square error

RSM

Response surface methodology

SEM

Scanning electron micrograph

SVM

Support vector machine

trainbr

Bayesian regularization training function

UCS

Unconfined compressive strength (qu)

XRD

X-ray diffraction

List of symbols

bhk

Bias at the kth neuron in the hidden layer

bo

Bias at the output layer

H

Number of hidden layers

K

Number of neurons

L

Lime content

m

Number of hidden neurons

η/Lv′

Porosity/volumetric lime ratio

qu

Measured unconfined compressive strength (UCS)

qumax

Predicted maximum unconfined compressive strength

qumin

Predicted minimum unconfined compressive strength

qup

Predicted unconfined compressive strength

R2

Coefficient of correlation (R-squared)

qun

Normalized predicted unconfined compressive strength

t

Curing time

w

Moisture content

wik

Connection weight between ith input variable and kth neuron in hidden layer

wk

Connection weight between kth neuron in hidden layer and single output neuron

Xi

Normalized input variable i

f

Activation function

γd

Dry density of the specimen

Z

Number of input factors

GL

Specific gravity of lime

GRM

Specific gravity of bauxite residue

γw

Density of water

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest with any organization or entity with any financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Supplementary material

521_2018_3482_MOESM1_ESM.docx (53 kb)
Supplementary material 1 (DOCX 54 kb)

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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology (BHU)VaranasiIndia

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