Neural Computing and Applications

, Volume 31, Issue 10, pp 6535–6548 | Cite as

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

  • Sujeet KumarEmail author
  • Arun Prasad
Original Article


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.


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



Average absolute error


Artificial neural network


Box–Behnken designed ANN


Circumscribed central composite


Central composite designed ANN


Conventional designed ANN


Face-centered composite design


Feed forward back propagation artificial neural network


Fuzzy interface system


Genetic algorithms


Inscribed central composite


Maximum absolute error


Mean absolute percentage error


Mean square error


One factor at time


Root-mean-square error


Response surface methodology


Scanning electron micrograph


Support vector machine


Bayesian regularization training function


Unconfined compressive strength (qu)


X-ray diffraction

List of symbols


Bias at the kth neuron in the hidden layer


Bias at the output layer


Number of hidden layers


Number of neurons


Lime content


Number of hidden neurons


Porosity/volumetric lime ratio


Measured unconfined compressive strength (UCS)


Predicted maximum unconfined compressive strength


Predicted minimum unconfined compressive strength


Predicted unconfined compressive strength


Coefficient of correlation (R-squared)


Normalized predicted unconfined compressive strength


Curing time


Moisture content


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


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


Normalized input variable i


Activation function


Dry density of the specimen


Number of input factors


Specific gravity of lime


Specific gravity of bauxite residue


Density of water


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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