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Modeling early-age hydration kinetics of Portland cement using flexible neural tree


The early-age hydration of Portland cement paste has an important impact on the formation of microstructure and development of strength. However, manual derivation of analytic kinetic equation for hydration process is very difficult because there are multi-phased, multi-sized and interrelated complex chemical and physical reactions during cement hydration. In this paper, a flexible neural tree structure is built as the right-hand side of kinetics instead of traditional analytic expression. Two evolutionary algorithms gene expression programming and particle swarm optimization are used to evolve tree structure and rules’ parameters, respectively. In order to reduce the computing time, GPUs are used for acceleration in parallel. Studies have shown that according to the established model, simulation curve of early-age hydration is in good accordance with the observed experimental data. Furthermore, this model still has a good generalization ability even changing chemical composition, particle size and curing conditions.

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  1. Yuan R (1996) Cementing material science (in Chinese). Wuhan University of Technology Press, Wuhan

    Google Scholar 

  2. Chen W, Brouwers HJH (2008) Mitigating the effects of system resolution on computer simulation of Portland cement hydration. Cem Concr Compos 30:779–787

    Article  Google Scholar 

  3. Tomosawa F (1974) Kinetic hydration model of cement. In: Proceedings of cement and concrete, pp 53–57

  4. Krstulovic R, Dabic P (2000) A conceptual model of the cement hydration process. Cem Concr Res 30:693–698

    Article  Google Scholar 

  5. Pignat C, Navi P, Scrivener K (2005) Simulation of cement paste microstructure hydration, pore space characterization and permeability determination. Mater Struct 38:459–466

    Google Scholar 

  6. Park K-B, Noguchi T, Plawsky J (2005) Modeling of hydration reactions using neural networks to predict the average properties of cement paste. Cem Concr Res 35:1676–1684

    Article  Google Scholar 

  7. Yan P, Zheng F (2006) Kinetics model for the hydration mechanism of cementitious materials (in Chinese). J Chin Ceram Soc 34:555–559

    Google Scholar 

  8. Ozbay E, Gesoglu M, Guneyisi M (2008) Empirical modeling of fresh and hardened properties of self-compacting concretes by genetic programming. Constr Build Mater 22:1831–1840

    Article  Google Scholar 

  9. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge

    MATH  Google Scholar 

  10. Baykasoglu A, Dereli T, Tanis S (2004) Prediction of cement strength using soft computing techniques. Cem Concr Res 34:2083–2090

    Article  Google Scholar 

  11. Subasi A, Yilmaz AS, Binici H (2009) Prediction of early heat of hydration of plain and blended cements using neuro-fuzzy modelling techniques. Expert Syst Appl 36:4940–4950

    Article  Google Scholar 

  12. Trtnik G, Kavcic F, Turk G (2008) The use of artificial neural networks in adiabatic curves modeling. Autom Constr 18:10–15

    Article  Google Scholar 

  13. Chen Y, Yang B, Dong J, Abraham A (2005) Time-series forecasting using flexible neural tree model. Inf Sci 174:219–235

    Article  MathSciNet  Google Scholar 

  14. Bahrololum M, Salahi E, Khaleghi M (2009) Machine learning techniques for feature reduction in intrusion detection systems: a comparison. In: Proceedings of the 4th international conference on computer sciences and convergence information technology, pp 1091–1095

  15. Chen Y, Abraham A, Yang B (2007) Hybrid flexible neural tree based intrusion detection systems. Int J Intell Syst 22:337–352

    Article  MATH  Google Scholar 

  16. Qi F, Liu X, Ma Y (2009) Housing price index forecasting using neural tree model. In: Proceedings of the 2nd ISECS international colloquium on computing, communication, control and management, pp 467–470

  17. Chen Y, Abraham A, Yang B (2006) Feature selection and classification using flexible neural tree. Neurocomputing 70:305–313

    Article  Google Scholar 

  18. Pan Y, Liu Y, Zheng Y-W (2007) Face recognition using kernel PCA and hybrid flexible neural tree. In: Proceedings of international conference on wavelet analysis and pattern recognition, pp 1361–1366

  19. Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Com Syst 13:87–129

    MATH  Google Scholar 

  20. Kennedy J, Eberhart RC (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39–43

  21. Wang P, Feng S, Liu X (2005) Research approaches of cement hydration degree and their development (in Chinese). J Bldg Mater 8:646–652

    Google Scholar 

  22. Schindler AK, Folliard KJ (2005) Heat of hydration models for cementitious materials. ACI Mater J 102:24–33

    Google Scholar 

  23. Bogue RH (1955) The chemistry of Portland cement. Reinhold Publishing Corporation, New York

    Google Scholar 

  24. Salustowicz R, Schmidhuber J (1997) Probabilistic incremental program evolution. Evol Comput 5:123–141

    Article  Google Scholar 

  25. Oltean M, Grosan C (2003) Evolving evolutionary algorithms using multi expression programming. In: Proceedings of the 7th European conference on artificial life, pp 651–658

  26. Chen L (2005) Optimal design for machinery: genetic algorithm (in Chinese). Machinery Industry Press, Beijing

  27. NVIDIA (2009) CUDA programming guide version 2.3.1. Online at

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This work was supported by National Basic Pre-Research Program of China (973 Program) under Grant No. 2010CB635117. National Natural Science Foundation of China under Grant No. 60873089, No. 60573065, No. 61070130, No. 60903176, No. 60673130, and No. 90818001. Provincial Natural Science Foundation for Outstanding Young Schoolers of Shandong under Grant No. JQ200820. Program for New Century Excellent Talents in University under Grant No. NCET-10-0863.

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Correspondence to Bo Yang.

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Wang, L., Yang, B., Chen, Y. et al. Modeling early-age hydration kinetics of Portland cement using flexible neural tree. Neural Comput & Applic 21, 877–889 (2012).

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  • Neural network
  • Flexible neural tree
  • Portland cement
  • Hydration kinetics