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

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## 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*/*L*_{v′}) 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 (

*q*_{u})- XRD
X-ray diffraction

## List of symbols

*b*_{hk}Bias at the

*k*th neuron in the hidden layer*b*_{o}Bias at the output layer

*H*Number of hidden layers

*K*Number of neurons

*L*Lime content

*m*Number of hidden neurons

*η*/*L*_{v′}Porosity/volumetric lime ratio

*q*_{u}Measured unconfined compressive strength (UCS)

*q*_{umax}Predicted maximum unconfined compressive strength

*q*_{umin}Predicted minimum unconfined compressive strength

*q*_{up}Predicted unconfined compressive strength

*R*^{2}Coefficient of correlation (R-squared)

*q*_{un}Normalized predicted unconfined compressive strength

*t*Curing time

*w*Moisture content

*w*_{ik}Connection weight between

*i*th input variable and*k*th neuron in hidden layer*w*_{k}Connection weight between

*k*th neuron in hidden layer and single output neuron*X*_{i}Normalized input variable

*i**f*Activation function

*γ*_{d}Dry density of the specimen

*Z*Number of input factors

*G*_{L}Specific gravity of lime

*G*_{RM}Specific gravity of bauxite residue

*γ*_{w}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

## References

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