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

## 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

- 1.Li J, Xu L, Sun P, Zhai P, Chen X, Zhang H et al (2017) Novel application of red mud: Facile hydrothermal-thermal conversion synthesis of hierarchical porous AlOOH and Al
_{2}O_{3}microspheres as adsorbents for dye removal. Chem Eng J 321(Supplement C):622–634CrossRefGoogle Scholar - 2.Sutar H, Mishra SC, Sahoo SK, Maharana H (2014) Progress of bauxite residue utilization: an overview. Am Chem Sci J 4(3):255–279CrossRefGoogle Scholar
- 3.Khale D, Chaudhary R (2007) Mechanism of geopolymerization and factors influencing its development: a review. J Mater Sci 42(3):729–746CrossRefGoogle Scholar
- 4.Klauber C, Gräfe M, Power G (2011) Bauxite residue issues: II. options for residue utilization. Hydrometallurgy 108(1):11–32CrossRefGoogle Scholar
- 5.Liu R-X, Poon C-S (2016) Utilization of red mud derived from bauxite in self-compacting concrete. J Clean Prod 112:384–391CrossRefGoogle Scholar
- 6.Thakur R, Sant B (1983) Utilization of red mud. 2. Recovery of alkali, iron, aluminum, titanium and other constituents and the pollution problems. J Sci Ind Res 42(8):456–469Google Scholar
- 7.Vangelatos I, Angelopoulos G, Boufounos D (2009) Utilization of ferroalumina as raw material in the production of ordinary portland cement. J Hazard Mater 168(1):473–478CrossRefGoogle Scholar
- 8.Satayanarayana P, Naidu G, Adiseshu S, Rao C (2012) Characterization of lime stabilized redmud mix for feasibility in road construction. Int J Eng Res Dev 3(7):20–26Google Scholar
- 9.Deelwal K, Dharavath K, Kulshreshtha M (2014) Evaluation of characteristic properties of bauxite residue for possible use as a geotechnical material in civil construction. Int J Adv Eng Technol 7(3):1053–1059Google Scholar
- 10.Kushwaha S, Kishan D (2016) Stabilization of bauxite residue by lime and gypsum and investigating its possible use in geoenvironmental engineering. Geo Chic 2016:978–988Google Scholar
- 11.Sabat AK, Mohanta S (2015) Efficacy of dolime fine stabilized bauxite residue-fly ash mixes as subgrade material. ARPN J Eng Appl Sci 10(14):5918–5923Google Scholar
- 12.Kumar S, Prasad A (2017) Parameters controlling strength of red mud-lime mix. Eur J Environ Civil Eng 1–15. https://doi.org/10.1080/19648189.2017.1304280
- 13.Mozumder RA, Laskar AI (2015) Prediction of unconfined compressive strength of geopolymer stabilized clayey soil using artificial neural network. Comput Geotech 69:291–300CrossRefGoogle Scholar
- 14.Narendra B, Sivapullaiah P, Suresh S, Omkar S (2006) Prediction of unconfined compressive strength of soft grounds using computation[20]al intelligence techniques: a comparative study. Comput Geotech 33(3):196–208CrossRefGoogle Scholar
- 15.Das SK, Samui P, Sabat AK (2011) Application of artificial intelligence to maximum dry density and unconfined compressive strength of cement stabilized soil. Geotech Geol Eng 29(3):329–342CrossRefGoogle Scholar
- 16.Güllü H, Fedakar HI (2017) On the prediction of unconfined compressive strength of silty soil stabilized with bottom ash, jute and steel fibers via artificial intelligence. Geomech Eng 12(3):441–464CrossRefGoogle Scholar
- 17.Suman S, Mahamaya M, Das SK (2016) Prediction of maximum dry density and unconfined compressive strength of cement stabilised soil using artificial intelligence techniques. Int J Geosynth Ground Eng 2(2):1–11CrossRefGoogle Scholar
- 18.Kalkan E, Akbulut S, Tortum A, Celik S (2009) Prediction of the unconfined compressive strength of compacted granular soils by using inference systems. Environ Geol 58(7):1429–1440CrossRefGoogle Scholar
- 19.Besalatpour A, Hajabbasi M, Ayoubi S, Afyuni M, Jalalian A, Schulin R (2012) Soil shear strength prediction using intelligent systems: artificial neural networks and an adaptive neuro-fuzzy inference system. Soil Sci Plant Nutr 58(2):149–160CrossRefGoogle Scholar
- 20.Sharma LK, Singh R, Umrao RK, Sharma KM, Singh TN (2017) Evaluating the modulus of elasticity of soil using soft computing system. Eng Comput 33(3):497–507CrossRefGoogle Scholar
- 21.Sakizadeh M, Mirzaei R, Ghorbani H (2017) Support vector machine and artificial neural network to model soil pollution: a case study in Semnan Province, Iran. Neural Comput Appl 28(11):3229–3238CrossRefGoogle Scholar
- 22.Moayedi H, Rezaei A (2017) An artificial neural network approach for under-reamed piles subjected to uplift forces in dry sand. Neural Comput Appl. https://doi.org/10.1007/s00521-017-2990-z
- 23.Erzin Y, Gul TO (2014) The use of neural networks for the prediction of the settlement of one-way footings on cohesionless soils based on standard penetration test. Neural Comput Appl 24(3):891–900CrossRefGoogle Scholar
- 24.Yilmaz I, Marschalko M, Bednarik M, Kaynar O, Fojtova L (2012) Neural computing models for prediction of permeability coefficient of coarse-grained soils. Neural Comput Appl 21(5):957–968CrossRefGoogle Scholar
- 25.Erzin Y, Turkoz D (2016) Use of neural networks for the prediction of the CBR value of some Aegean sands. Neural Comput Appl 27(5):1415–1426CrossRefGoogle Scholar
- 26.Erzin Y, Ecemis N (2017) The use of neural networks for the prediction of cone penetration resistance of silty sands. Neural Comput Appl 28(1):727–736CrossRefGoogle Scholar
- 27.Edincliler A, Cabalar AF, Cagatay A, Cevik A (2012) Triaxial compression behavior of sand and tire wastes using neural networks. Neural Comput Appl 21(3):441–452CrossRefGoogle Scholar
- 28.Ikizler SB, Vekli M, Dogan E, Aytekin M, Kocabas F (2014) Prediction of swelling pressures of expansive soils using soft computing methods. Neural Comput Appl 24(2):473–485CrossRefzbMATHGoogle Scholar
- 29.Tsai H-C, Tyan Y-Y, Wu Y-W, Lin Y-H (2013) Determining ultimate bearing capacity of shallow foundations using a genetic programming system. Neural Comput Appl 23(7):2073–2084CrossRefGoogle Scholar
- 30.Buragohain M, Mahanta C (2008) A novel approach for ANFIS modelling based on full factorial design. Appl Soft Comput 8(1):609–625CrossRefGoogle Scholar
- 31.Güllü H, Fedakar Hİ (2017) Response surface methodology for optimization of stabilizer dosage rates of marginal sand stabilized with sludge ash and fiber based on UCS performances. KSCE J Civil Eng 21(5):1717–1727CrossRefGoogle Scholar
- 32.Güllü H, Fedakar Hİ (2016) Use of factorial experimental approach and effect size on the CBR testing results for the usable dosages of wastewater sludge ash with coarse-grained material. Eur J Environ Civil Eng 22(1):42–63CrossRefGoogle Scholar
- 33.Dutta JR, Dutta PK, Banerjee R (2004) Optimization of culture parameters for extracellular protease production from a newly isolated Pseudomonas sp. using response surface and artificial neural network models. Process Biochem 39(12):2193–2198CrossRefGoogle Scholar
- 34.Olgun M (2013) The effects and optimization of additives for expansive clays under freeze–thaw conditions. Cold Reg Sci Technol 93:36–46CrossRefGoogle Scholar
- 35.Bayramov F, Taşdemir C, Taşdemir M (2004) Optimisation of steel fibre reinforced concretes by means of statistical response surface method. Cement Concr Compos 26(6):665–675CrossRefGoogle Scholar
- 36.Chavalparit O, Ongwandee M (2009) Optimizing electrocoagulation process for the treatment of biodiesel wastewater using response surface methodology. J Environ Sci 21(11):1491–1506CrossRefGoogle Scholar
- 37.Güneyisi E, Gesoğlu M, Algın Z, Mermerdaş K (2014) Optimization of concrete mixture with hybrid blends of metakaolin and fly ash using response surface method. Compos B Eng 60:707–715CrossRefGoogle Scholar
- 38.Kobya M, Demirbas E, Bayramoglu M, Sensoy M (2011) Optimization of electrocoagulation process for the treatment of metal cutting wastewaters with response surface methodology. Water Air Soil Pollut 215(1–4):399–410CrossRefGoogle Scholar
- 39.Murugesan K, Dhamija A, Nam I-H, Kim Y-M, Chang Y-S (2007) Decolourization of reactive black 5 by laccase: optimization by response surface methodology. Dyes Pigments 75(1):176–184CrossRefGoogle Scholar
- 40.ASTM D1633-00 (2000) Standard test method for compressive strength of molded soil-cement cylinders. ASTM International. West Conshohocken. https://compass.astm.org/EDIT/html_annot.cgi?D1633+17. Accessed 15 Apr 2017
- 41.Gupta D, Kumar P, Mishra V, Prasad R, Dikshit P, Dwivedi S (2015) Bistatic measurements for the estimation of rice crop variables using artificial neural network. Adv Space Res 55(6):1613–1623CrossRefGoogle Scholar
- 42.Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366CrossRefzbMATHGoogle Scholar
- 43.Witek-Krowiak A, Chojnacka K, Podstawczyk D, Dawiec A, Pokomeda K (2014) Application of response surface methodology and artificial neural network methods in modelling and optimization of biosorption process. Biores Technol 160:150–160CrossRefGoogle Scholar
- 44.Salchenberger LM, Cinar E, Lash NA (1992) Neural networks: a new tool for predicting thrift failures. Decis Sci 23(4):899–916CrossRefGoogle Scholar
- 45.Boger Z, Guterman H (1997) Knowledge extraction from artificial neural network models. Systems, man, and cybernetics. In: 1997 IEEE international conference on computational cybernetics and simulation, pp 3030–3035. IEEEGoogle Scholar
- 46.Sheela KG, Deepa SN (2013) Review on methods to fix number of hidden neurons in neural networks. Math Probl Eng 425740:1–10CrossRefGoogle Scholar
- 47.Shibata K, Ikeda Y (2009) Effect of number of hidden neurons on learning in large-scale layered neural networks. In: ICCAS-SICE, 2009, pp 5008–5013. IEEEGoogle Scholar
- 48.Xu S, Chen L (2008) A novel approach for determining the optimal number of hidden layer neurons for FNN’s and its application in data mining. In: 5th international conference on information technology and applications (ICITA 2008), pp 683–686Google Scholar
- 49.Murata N, Yoshizawa S (1994) Amari S-i. Network information criterion-determining the number of hidden units for an artificial neural network model. IEEE Trans Neural Netw 5(6):865–872CrossRefGoogle Scholar
- 50.Kulkarni P, Londhe S, Deo M (2017) Artificial neural networks for construction management: a review. Soft Comput Civil Eng 1(2):70–88Google Scholar
- 51.Consoli NC, da Silva Lopes L Jr, Heineck KS (2009) Key parameters for the strength control of lime stabilized soils. J Mater Civ Eng 21(5):210–216CrossRefGoogle Scholar
- 52.Wei TK, Manickam S (2012) Response Surface Methodology, an effective strategy in the optimization of the generation of curcumin-loaded micelles. Asia Pac J Chem Eng 7:S125–S133CrossRefGoogle Scholar
- 53.Miličević I, Šipoš TK (2017) Prediction of properties of recycled aggregate concrete. Građevinar 69(05):347–357Google Scholar
- 54.David FW (1992) Contouring: a guide to the analysis and display of spatial data with programs on diskette, 1st edn. Computer methods in the geosciences. Pergamon Press, Oxford, New YorkGoogle Scholar
- 55.Das SK, Basudhar PK (2006) Undrained lateral load capacity of piles in clay using artificial neural network. Comput Geotech 33(8):454–459CrossRefGoogle Scholar