Prediction of high-strength concrete: high-order response surface methodology modeling approach


In the concrete industry, compressive strength is the most essential mechanical property. Therefore, insufficient compressive strength may lead to dangerous failure and, thus, becomes very difficult to repair. Consequently, early, and precise prediction of concrete strength is a major issue facing researchers and concrete designers. In this study, high-order response surface methodology (HORSM) is used to develop a prediction model to accurately predict the compressive strength of high-strength concrete (HSC). Different polynomial degrees order ranging from 2 to 5 is used in this model. The HORSM, with five-order polynomial degree, model outperforms several artificial intelligence (AI) modeling approaches which are carried out widely in the prediction of HSC compression strength. Besides, support vector machine (SVM) model was developed in this study and compared with the HORSM. The HORSM models outperformed the SVM models according to different statistical measures. Additionally, HORSM models managed to perfectly predict the HSC compressive strength in less than one second to accomplish the learning processes. While, other AI models including SVM much longer time. Lastly, the use of HORSM for the first time in the concrete technology field provided much accurate prediction results and it has great potential in the field of concrete technology.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Carrasquillo RL, Nilson AH (1981) Slate FO properties of high strength concrete subject to short-term loads. J Proc 3:171–178

    Google Scholar 

  2. 2.

    Russell HG (1999) ACI defines high-performance concrete. Concr Int 21(2):56–57

    Google Scholar 

  3. 3.

    Mbessa M, Péra J (2001) Durability of high-strength concrete in ammonium sulfate solution. Cement Concr Res 31(8):1227–1231

    Article  Google Scholar 

  4. 4.

    Sobhani J, Najimi M, Pourkhorshidi AR, Parhizkar T (2010) Prediction of the compressive strength of no-slump concrete: a comparative study of regression, neural network and ANFIS models. Constr Build Mater 24(5):709–718

    Article  Google Scholar 

  5. 5.

    Bharatkumar B, Narayanan R, Raghuprasad B, Ramachandramurthy D (2001) Mix proportioning of high performance concrete. Cement Concr Compos 23(1):71–80

    Article  Google Scholar 

  6. 6.

    Papadakis V, Tsimas S (2002) Supplementary cementing materials in concrete: Part I: efficiency and design. Cement Concr Res 32(10):1525–1532

    Article  Google Scholar 

  7. 7.

    Prasad BR, Eskandari H, Reddy BV (2009) Prediction of compressive strength of SCC and HPC with high volume fly ash using ANN. Constr Build Mater 23(1):117–128

    Article  Google Scholar 

  8. 8.

    Bhanja S, Sengupta B (2002) Investigations on the compressive strength of silica fume concrete using statistical methods. Cement Concr Res 32(9):1391–1394

    Article  Google Scholar 

  9. 9.

    Yeh I-C, Lien L-C (2009) Knowledge discovery of concrete material using genetic operation trees. Expert Syst Appl 36(3):5807–5812

    Article  Google Scholar 

  10. 10.

    Hameed MM, AlOmar MK (2020) Prediction of compressive strength of high-performance concrete: hybrid artificial intelligence technique. In: Applied computing to support industry: innovation and technology. Springer International Publishing, Cham, pp 323–335

  11. 11.

    Topcu IB, Sarıdemir M (2008) Prediction of compressive strength of concrete containing fly ash using artificial neural networks and fuzzy logic. Comput Mater Sci 41(3):305–311

    Article  Google Scholar 

  12. 12.

    Velay-Lizancos M, Perez-Ordoñez JL, Martinez-Lage I, Vazquez-Burgo P (2017) Analytical and genetic programming model of compressive strength of eco concretes by NDT according to curing temperature. Constr Build Mater 144:195–206

    Article  Google Scholar 

  13. 13.

    Behnood A, Olek J, Glinicki MA (2015) Predicting modulus elasticity of recycled aggregate concrete using M5′ model tree algorithm. Constr Build Mater 94:137–147

    Article  Google Scholar 

  14. 14.

    Golafshani EM, Behnood A (2018) Automatic regression methods for formulation of elastic modulus of recycled aggregate concrete. Appl Soft Comput 64:377–400

    Article  Google Scholar 

  15. 15.

    Behnood A, Verian KP, Gharehveran MM (2015) Evaluation of the splitting tensile strength in plain and steel fiber-reinforced concrete based on the compressive strength. Constr Build Mater 98:519–529

    Article  Google Scholar 

  16. 16.

    Dao DV, Adeli H, Ly H-B, Le LM, Le VM, Le T-T, Pham BT (2020) A sensitivity and robustness analysis of GPR and ANN for high-performance concrete compressive strength prediction using a Monte Carlo simulation. Sustainability 12(3):830

    Article  Google Scholar 

  17. 17.

    Ling H, Qian C, Kang W, Liang C, Chen H (2019) Combination of support vector machine and K-Fold cross validation to predict compressive strength of concrete in marine environment. Constr Build Mater 206:355–363

    Article  Google Scholar 

  18. 18.

    Tsai H-C, Liao M-C (2019) Knowledge-based learning for modeling concrete compressive strength using genetic programming. Comput Concr 23(4):255–265

    Google Scholar 

  19. 19.

    Al-Shamiri AK, Kim JH, Yuan T-F, Yoon YS (2019) Modeling the compressive strength of high-strength concrete: an extreme learning approach. Constr Build Mater 208:204–219

    Article  Google Scholar 

  20. 20.

    Golafshani EM, Behnood A, Arashpour M (2020) Predicting the compressive strength of normal and high-performance concretes using ANN and ANFIS hybridized with grey wolf optimizer. Constr Build Mater 232:117266

    Article  Google Scholar 

  21. 21.

    Gholampour A, Mansouri I, Kisi O, Ozbakkaloglu T (2020) Evaluation of mechanical properties of concretes containing coarse recycled concrete aggregates using multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) models. Neural Comput Appl 32(1):295–308.

    Article  Google Scholar 

  22. 22.

    Singh B, Sihag P, Tomar A, Sehgal A (2019) Estimation of compressive strength of high-strength concrete by random forest and M5P model tree approaches. J Mater Eng Struct JMES 6(4):583–592

    Google Scholar 

  23. 23.

    Tien Bui D, MaM A, Ghareh S, Moayedi H, Nguyen H (2019) Fine-tuning of neural computing using whale optimization algorithm for predicting compressive strength of concrete. Eng Comput.

    Article  Google Scholar 

  24. 24.

    Afan HA, El-Shafie A, Yaseen ZM, Hameed MM, Wan Mohtar WHM, Hussain A (2015) ANN based sediment prediction model utilizing different input scenarios. Water Resour Manag 29(4):1231–1245.

    Article  Google Scholar 

  25. 25.

    Hameed M, Sharqi SS, Yaseen ZM, Afan HA, Hussain A, Elshafie A (2017) Application of artificial intelligence (AI) techniques in water quality index prediction: a case study in tropical region. Malays Neural Comput Appl 28(1):893–905.

    Article  Google Scholar 

  26. 26.

    Yaseen ZM, El-Shafie A, Afan HA, Hameed M, Mohtar WHMW, Hussain A (2016) RBFNN versus FFNN for daily river flow forecasting at Johor River. Malays Neural Comput Appl 27(6):1533–1542.

    Article  Google Scholar 

  27. 27.

    AlOmar MK, Hameed MM, Al-Ansari N, AlSaadi MA (2020) Data-driven model for the prediction of total dissolved gas: robust artificial intelligence approach. Adv Civ Eng 2020:6618842.

    Article  Google Scholar 

  28. 28.

    Chen S, Gu C, Lin C, Wang Y, Hariri-Ardebili MA (2020) Prediction, monitoring, and interpretation of dam leakage flow via adaptative kernel extreme learning machine. Measurement 166:108161.

    Article  Google Scholar 

  29. 29.

    Zhang G, Ali ZH, Aldlemy MS, Mussa MH, Salih SQ, Hameed MM, Al-Khafaji ZS, Yaseen ZM (2020) Reinforced concrete deep beam shear strength capacity modelling using an integrative bio-inspired algorithm with an artificial intelligence model. Eng Comput.

    Article  Google Scholar 

  30. 30.

    Alnaqi AA, Moayedi H, Shahsavar A, Nguyen TK (2019) Prediction of energetic performance of a building integrated photovoltaic/thermal system thorough artificial neural network and hybrid particle swarm optimization models. Energy Convers Manag 183:137–148.

    Article  Google Scholar 

  31. 31.

    Moayedi H, Raftari M, Sharifi A, Jusoh WAW, Rashid ASA (2020) Optimization of ANFIS with GA and PSO estimating α ratio in driven piles. Eng Comput 36(1):227–238.

    Article  Google Scholar 

  32. 32.

    Nguyen H, Mehrabi M, Kalantar B, Moayedi H, MaM A (2019) Potential of hybrid evolutionary approaches for assessment of geo-hazard landslide susceptibility mapping. Geomat Nat Hazards Risk 10(1):1667–1693.

    Article  Google Scholar 

  33. 33.

    Zhou G, Moayedi H, Bahiraei M, Lyu Z (2020) Employing artificial bee colony and particle swarm techniques for optimizing a neural network in prediction of heating and cooling loads of residential buildings. J Clean Prod 254:120082.

    Article  Google Scholar 

  34. 34.

    Moayedi H, Tien Bui D, Gör M, Pradhan B, Jaafari A (2019) The feasibility of three prediction techniques of the artificial neural network, adaptive neuro-fuzzy inference system, and hybrid particle swarm optimization for assessing the safety factor of cohesive slopes. ISPRS Int J Geo-Inf 8(9):391

    Article  Google Scholar 

  35. 35.

    Shariati M, Mafipour MS, Ghahremani B, Azarhomayun F, Ahmadi M, Trung NT, Shariati A (2020) A novel hybrid extreme learning machine–grey wolf optimizer (ELM-GWO) model to predict compressive strength of concrete with partial replacements for cement. Eng Comput.

    Article  Google Scholar 

  36. 36.

    Xu C, Nait Amar M, Ghriga MA, Ouaer H, Zhang X, Hasanipanah M (2020) Evolving support vector regression using Grey Wolf optimization; forecasting the geomechanical properties of rock. Eng Comput.

    Article  Google Scholar 

  37. 37.

    Keshtegar B, MeAB S (2018) Modified response surface method basis harmony search to predict the burst pressure of corroded pipelines. Eng Fail Anal 89:177–199

    Article  Google Scholar 

  38. 38.

    Heddam S, Keshtegar B, Kisi O (2019) Predicting total dissolved gas concentration on a daily scale using kriging interpolation, response surface method and artificial neural network: case study of Columbia River Basin Dams, USA. Nat Resour Res 1–18

  39. 39.

    Keshtegar B, Heddam S (2018) Modeling daily dissolved oxygen concentration using modified response surface method and artificial neural network: a comparative study. Neural Comput Appl 30(10):2995–3006.

    Article  Google Scholar 

  40. 40.

    Fiyadh SS, AlSaadi MA, AlOmar MK, Fayaed SS, Mjalli FS, El-Shafie A (2018) BTPC-based DES-functionalized CNTs for As3+ removal from water: NARX neural network approach. J Environ Eng 144(8):04018070.

    Article  Google Scholar 

  41. 41.

    AlOmar MK, Hameed MM, AlSaadi MA (2020) Multi hours ahead prediction of surface ozone gas concentration: robust artificial intelligence approach. Atmos Pollut Res 11(9):1572–1587.

    Article  Google Scholar 

  42. 42.

    Keshtegar B, Kisi O (2017) Modified response-surface method: new approach for modeling pan evaporation. J Hydrol Eng 22(10):04017045

    Article  Google Scholar 

  43. 43.

    Keshtegar B, Kisi O, Zounemat-Kermani M (2019) Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration. Hydrol Sci J 64(6):720–730

    Article  Google Scholar 

  44. 44.

    Hammoudi A, Moussaceb K, Belebchouche C, Dahmoune F (2019) Comparison of artificial neural network (ANN) and response surface methodology (RSM) prediction in compressive strength of recycled concrete aggregates. Constr Build Mater 209:425–436

    Article  Google Scholar 

  45. 45.

    Keshtegar B, Mert C, Kisi O (2018) Comparison of four heuristic regression techniques in solar radiation modeling: kriging method vs RSM, MARS and M5 model tree. Renew Sustain Energy Rev 81:330–341

    Article  Google Scholar 

  46. 46.

    Samuel OD, Okwu MO (2019) Comparison of response surface methodology (RSM) and artificial neural network (ANN) in modelling of waste coconut oil ethyl esters production. Energy Sources Part A Recov Utiliz Environ Effects 41(9):1049–1061.

    Article  Google Scholar 

  47. 47.

    Keshtegar B, Allawi MF, Afan HA, El-Shafie A (2016) Optimized river stream-flow forecasting model utilizing high-order response surface method. Water Resour Manag 30(11):3899–3914.

    Article  Google Scholar 

  48. 48.

    Keshtegar B, Heddam S, Kisi O, Zhu S-P (2019) Modeling total dissolved gas (TDG) concentration at Columbia river basin dams: high-order response surface method (H-RSM) vs. M5Tree, LSSVM, and MARS. Arab J Geosci 12(17):544

    Article  Google Scholar 

  49. 49.

    Azimi-Pour M, Eskandari-Naddaf H, Pakzad A (2020) Linear and non-linear SVM prediction for fresh properties and compressive strength of high volume fly ash self-compacting concrete. Constr Build Mater 230:117021

    Article  Google Scholar 

  50. 50.

    Çelik SB (2019) Prediction of uniaxial compressive strength of carbonate rocks from nondestructive tests using multivariate regression and LS-SVM methods. Arab J Geosci 12(6):193.

    Article  Google Scholar 

  51. 51.

    Ghanizadeh AR, Abbaslou H, Amlashi AT, Alidoust P (2019) Modeling of bentonite/sepiolite plastic concrete compressive strength using artificial neural network and support vector machine. Front Struct Civ Eng 13(1):215–239.

    Article  Google Scholar 

  52. 52.

    Tanyildizi H (2018) Prediction of the strength properties of carbon fiber-reinforced lightweight concrete exposed to the high temperature using artificial neural network and support vector machine. Adv Civ Eng

  53. 53.

    Vn V (1995) The nature of statistical learning theory. Springer, New York

    Google Scholar 

  54. 54.

    Park JY, Yoon YG, Oh TK (2019) Prediction of concrete strength with P-, S-, R-Wave velocities by support vector machine (SVM) and artificial neural network (ANN). Appl Sci 9(19):4053

    Article  Google Scholar 

  55. 55.

    Cw L, Huang Xh, Jj M, Gz Ba (2019) Modification of finite element models based on support vector machines for reinforced concrete beam vibrational analyses at elevated temperatures. Struct Control Health Monit 26(6):e2350

    Article  Google Scholar 

  56. 56.

    Masino J, Pinay J, Reischl M, Gauterin F (2017) Road surface prediction from acoustical measurements in the tire cavity using support vector machine. Appl Acoust 125:41–48

    Article  Google Scholar 

  57. 57.

    Li L, Zheng W, Wang Y (2019) Prediction of moment redistribution in statically indeterminate reinforced concrete structures using artificial neural network and support vector regression. Appl Sci 9(1):28

    Article  Google Scholar 

  58. 58.

    Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222

    MathSciNet  Article  Google Scholar 

  59. 59.

    Chou J-S, Tsai C-F, Pham A-D, Lu Y-H (2014) Machine learning in concrete strength simulations: Multi-nation data analytics. Constr Build Mater 73:771–780

    Article  Google Scholar 

  60. 60.

    Momeni E, Nazir R, Jahed Armaghani D, Maizir H (2014) Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN. Measurement 57:122–131.

    Article  Google Scholar 

  61. 61.

    Ji X, Liang SY (2017) Model-based sensitivity analysis of machining-induced residual stress under minimum quantity lubrication. Proc Inst Mech Eng Part B J Eng Manuf 231(9):1528–1541.

    Article  Google Scholar 

Download references


The authors would like to express their thanks to ALMaarif University College (AUC) for funding this research.

Author information



Corresponding author

Correspondence to Mohamed Khalid AlOmar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hameed, M.M., AlOmar, M.K., Baniya, W.J. et al. Prediction of high-strength concrete: high-order response surface methodology modeling approach. Engineering with Computers (2021).

Download citation


  • High-order response surface methodology
  • Support vector machine
  • High-strength concrete
  • Compressive strength test
  • Machine learning