Distilling middle-age cement hydration kinetics from observed data using phased hybrid evolution


The hydration of cement is of great importance to the formation of the microstructure and development of strength. However, the complex nature of cement hydration results in that the existing manually derived model from some assumptions that are made to simplify the problem and make it mathematically and computationally tractable is not satisfactory in comparison with experimental results. In this paper, the middle-age hydration kinetics is distilled from observed data reversely using phased hybrid evolution method. The task that distils the hydration kinetics is divided into two phases and combines different algorithms. Furthermore, some strategies are also adopted for enhancement. To solve the problem of high time complexity, the searching process is accelerated by graphics processing units in parallel. The middle-age cement hydration kinetics model is distilled successfully from observed data. Studies show that the simulation result is close to the same with experimental results according to the distilled kinetics.

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    These specimens were provided by The Cement Quality Supervision and Inspection Station of Shandong Province, China.


  1. Anderson C (2008) The End of Theory: The Data Deluge Makes the Scientific Method Obsolete. http://www.wired.com/science/discoveries/magazine/16-07/pb_theory/

  2. Avrami M (1939) Kinetics of phase change. J Chem Phys 7:1103–1112

    Article  Google Scholar 

  3. Bae H, Jeon TR, Kim S, Han SS (2010) Modified genetic programming combining with particle swarm optimization and performance criterion in solar cell fabrication. Int J Control Autom Syst 8:841–849

    Article  Google Scholar 

  4. Bentz DP (2011) Critical observations for the evaluation of cement hydration models. Int J Adv Eng Sci Appl Math 2:75–82

    Article  Google Scholar 

  5. Bogue RH (1955) The chemistry of Portland cement. Reinhold Publishing Corporation, pp 245–268

  6. Box GEP, Hunter JS, Hunter WG (2005) Statistics for experiments: design, innovation, and discovery, 2nd edn. Wiley, New York

    MATH  Google Scholar 

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

    Google Scholar 

  8. CUDA (2009) CUDA programming guide version 2.3.1, NVIDIA

  9. Du X, Ding L, Jia L (2008) Asynchronous distributed parallel gene expression programming based on estimation of distribution algorithm. In: Proceedings 4th international conference national computing, pp 433–437

  10. Dabic P, Krstulovic R, Rusic D (2000) A new approach in mathematical modelling of cement hydration development. Cem Concr Res 30:1017–1021

    Article  Google Scholar 

  11. Fan WG, Gordon MD, Pathak P (2004) Discovery of context-specific ranking functions for effective information retrieval using genetic programming. IEEE Trans Knowl Data Eng 16:523–527

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  13. Floares AG (2007) Automatic reverse engineering algorithm for drug gene regulating networks. In: Proceedings of 11th Iasted International Conference Artificial Intelligence Soft Computing, pp 238–243

  14. Guan W, Szeto KY (2013) Topological effects on the performance of island model of parallel genetic algorithm. In: Proceedings international work conference artificial neural network, pp 11–19

  15. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, second edn. MIT Press, University of Michigan Press, p 1992

  16. Huang Z, Lu X, Duan H (2012) A task operation model for resource allocation optimization in business process management. IEEE Trans Syst Man Cybern Part A Syst Hum 42:1256–1270

    Article  Google Scholar 

  17. Iba H (2008) Inference of differential equation models by genetic programming. Inf Sci 178:4453–4468

    Article  Google Scholar 

  18. Johnson WA, Mehl RF (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Eng 135:416

    Google Scholar 

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

  20. Kondo R, Kodama M (1967) On the hydration kinetics of cement. Semento Gijutsu Nenpo 21:77–82 (in Japanese)

    Google Scholar 

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

    MATH  Google Scholar 

  22. Krogmann K, Kuperberg M, Reussner R (2010) Using genetic search for reverse engineering of parametric behavior models for performance prediction. IEEE Trans Softw Eng 36:865–877

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Lin F, Meyer C (2009) Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure. Cem Concr Res 39:255–265

    Article  Google Scholar 

  25. Luo GH, Huang SK, Chang YS, Yuan SM (2014) A parallel Bees Algorithm implementation on GPU. J Syst Archit 60:271–279

    Article  Google Scholar 

  26. Oltean M, Dumitrescu D (2002) Multi expression programming. Technical report, UBB-01-2002, Babes-Bolyai University

  27. Park KB, Noguchib 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 

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

    Article  Google Scholar 

  29. Qian L, Wang H, Dougherty ER (2008) Inference of noisy nonlinear differential equation models for gene regulatory networks using genetic programming and Kalman filtering. IEEE Trans Signal Process 56:3327–3339

    MathSciNet  Article  Google Scholar 

  30. Robilliard D, Poty VM, Fonlupt C (2009) Genetic programming on graphics processing units. Genet Program Evol Mach 10:447–471

    Article  Google Scholar 

  31. Sanz SS, Roldan FC, Heneghan C, Yao X (2007) Evolutionary design of digital filters with application to subband coding and data transmission. IEEE Trans Signal Process 55:1193–1203

    MathSciNet  Article  Google Scholar 

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

    Google Scholar 

  33. Schmidt M, Lipson H (2009) Distilling free-form natural laws from experimental data. Science 324:81–85

    Article  Google Scholar 

  34. Thomas JJ, Biernacki JJ, Bullard JW, Bishnoi S, Dolado JS, Scherer GW, Luttge A (2011) Modeling and simulation of cement hydration kinetics and microstructure development. Cem Concr Res 41:1257–1278

    Article  Google Scholar 

  35. Tomosawa F (1997) Development of a kinetic model for hydration of cement. In: Proceedings of tenth international congress chemistry of cement, pp 2ii051

  36. Vega FF, Gil GG, Pulido JAG, Guisado JL (2004) Control of bloat in genetic programming by means of the island model. In: Proceedings of international conference parallel prob solv nat, pp 263–271

  37. Wang L, Yang B, Zhao XY, Chen YH, Chang J (2010) Reverse extraction of early-age hydration kinetic equation from observed data of Portland cement. Sci China Technol Sci 53:1540–1553

    Article  Google Scholar 

  38. Wang L, Yang B, Chen YH, Zhao XY, Chang J, Wang HY (2012) Modeling early-age hydration kinetics of Portland cement using flexible neural tree. Neural Comput Appl 21:877–889

  39. Wang L, Yang B, Chen YH, Zhao XY (2012) Predict the hydration of Portland cement using differential evolution. In: Proceedings of IEEE congress evolution computer, pp 3388–3392

  40. Wang PM, Feng SX, Liu XP (2005) Research approaches of cement hydration degree and their development. J Build Mater 8:646–652 (in Chinese)

    Google Scholar 

  41. Yan LP, Zeng JC (2006) Using particle swarm optimization and genetic programming to evolve classification rules. In: Proceedings of 6th world congress intelligence control automation, pp 3415–3419

  42. Yang ZY, Li XL, Bowers CP, Schnier T, Tang K, Yao X (2012) An efficient evolutionary approach to parameter identification in a building thermal model. IEEE Trans Syst Man Cybern Part C Appl Rev 42:957–969

    Article  Google Scholar 

  43. Zhang S, He Z (2009) Implementation of parallel genetic algorithm based on CUDA. In: Proceedings of international symposium intelligence computer application, pp 24–30

  44. Zheng L, Lu Y, Guo M, Guo S, Xu CZ (2014) Architecture-based design and optimization of genetic algorithms on multi- and many-core systems. Future Gener Comput Syst 38:75–91

    Article  Google Scholar 

  45. Zhou Y, Tan Y (2009) GPU-based Parallel Particle Swarm Optimization. In: Proceedings of IEEE congress evolution computer, pp 1493–1500

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This work was supported by National Natural Science Foundation of China under Grant No. 61203105, No. 61173078, No. 61373054, No. 61173079, No. 81301298, No.61302128. Shandong Provincial Natural Science Foundation, China, under Grant No. ZR2012FQ016, No. ZR2012FM010. National Key Technology Research and Development Program of the Ministry of Science and Technology under Grant 2012BAF12B07-3.

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Correspondence to Bo Yang.

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Communicated by V. Loia.

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Wang, L., Yang, B. & Abraham, A. Distilling middle-age cement hydration kinetics from observed data using phased hybrid evolution. Soft Comput 20, 3637–3656 (2016). https://doi.org/10.1007/s00500-015-1723-4

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  • Evolutionary computation
  • Cement hydration kinetics
  • Reverse modeling