Title:
Artificial Intelligence to Investigate Modulus of Elasticity of Recycled Aggregate Concrete
Author(s):
Seyedhamed Sadati, Leonardo Enzo Brito da Silva, Donald C. Wunsch II, and Kamal H. Khayat
Publication:
Materials Journal
Volume:
116
Issue:
1
Appears on pages(s):
51-62
Keywords:
artificial intelligence; machine learning; modulus of elasticity; neural networks; recycled concrete aggregate; sustainable infrastructure
DOI:
10.14359/51706948
Date:
1/1/2019
Abstract:
Modulus of elasticity (MOE) is one of the main factors that affect the deformation characteristics and serviceability of concrete in the hardened state. The use of recycled concrete aggregate (RCA) in concrete production can lead to a significant reduction in the MOE. An artificial neural network (ANN) was employed to quantify the effect of coarse RCA on the concrete’s MOE. A database summarizing over 480 data series obtained from 52 technical publications was developed and analyzed using ANN. Concrete mixture proportions and aggregate properties were considered input parameters. The rate of reduction in 28-day MOE was considered the output parameter. An additional data set of 43 concrete mixtures obtained from laboratory investigation of concrete with well-known properties was used to validate the established model. Several combinations of input parameters and ANN architectures were considered in the analysis. Results indicated that the performance of the system was acceptable, with a coefficient of correlation ranging from 0.71 to 0.95 for the training, validation, and testing of the model with a mean square error limited to 0.008. The developed model was incorporated for a case study on a typical concrete used for rigid pavement construction. Contour graphs were developed to showcase the effect of up to 100% coarse RCA replacement on the variations in the MOE of concrete made with 0.40 water-cementitious materials ratio (w/cm) and 323 kg/m3 (545 lb/yd3) of a binary cement, designated for rigid pavement construction. The results indicated that depending on the RCA quality, a reduction of 10 to 30% in the MOE of pavement concrete made with 50% RCA can be expected. However, the reduction in the MOE will be limited to 10% when RCA with water absorption limited to 2.5% and an oven-dry specific gravity of over 2500 kg/m3 (156 lb/ft3) is used.
Related References:
1. United States Environmental Protection Agency, “RCRA in Focus: Construction, Demolition, and Renovation,” Washington, DC, 2004, https://www.epa.gov/hwgenerators/resource-conservation-and-recovery-act-rcra-focus-hazardous-waste-generator-guidance. (last accessed Jan. 29, 2019)
2. United States Environmental Protection Agency, “Advancing Sustainable Materials Management: 2013 Fact Sheet,” Washington, DC, 2015, https://www.epa.gov/sites/production/files/2015-09/documents/2013_advncng_smm_fs.pdf. (last accessed Jan. 29, 2019)
3. United States Environmental Protection Agency, “Advancing Sustainable Materials Management: 2014 Fact Sheet,” Washington, DC, 2016, https://www.epa.gov/sites/production/files/2016-11/documents/2014_smmfactsheet_508.pdf. (last accessed Jan. 29, 2019)
4. Gonzalez, G. P., and Moo-Young, H. K., “Transportation Applications of Recycled Concrete Aggregate,” FHWA State of the Practice National Review, Federal Highway Administration, Washington, DC, 2004, 47 pp.
5. National Academies of Sciences, Engineering, and Medicine, “Recycled Materials and Byproducts in Highway Applications—Reclaimed Asphalt Pavement, Recycled Concrete Aggregate, and Construction Demolition Waste,” V. 6, The National Academies Press, Washington, DC, 2013. /https://doi.org/10.17226/22547.10.17226/22547
6. Monteiro, P., Concrete: Microstructure, Properties, and Materials, McGraw-Hill Publishing, New York, 2006.
7. Knaack, A. M., and Kurama, Y. C., “Behavior of Reinforced Concrete Beams with Recycled Concrete Coarse Aggregates,” Journal of Structural Engineering, ASCE, V. 141, No. 3, 2015, p. B4014009 doi: 10.1061/(ASCE)ST.1943-541X.0001118
8. Fonseca, N.; De Brito, J.; and Evangelista, L., “The Influence of Curing Conditions on the Mechanical Performance of Concrete Made with Recycled Concrete Waste,” Cement and Concrete Composites, V. 33, No. 6, 2011, pp. 637-643. doi: 10.1016/j.cemconcomp.2011.04.002
9. Vieira, J. P. B.; Correia, J. R.; and De Brito, J., “Post-Fire Residual Mechanical Properties of Concrete Made with Recycled Concrete Coarse Aggregates,” Cement and Concrete Research, V. 41, No. 5, 2011, pp. 533-541. doi: 10.1016/j.cemconres.2011.02.002
10. Eurocode 2:1992, “European Standard EN 1992-1-1: Eurocode 2: Design of Concrete Structures: Part 1-1: General Rules and Rules for Buildings,” Stage 51 Draft, Comite Europeen de Normalisation, Brussels, Belgium, Dec. 2003.
11. Japan Society of Civil Engineers, “Standard Specification for Concrete Structure (JSCE No. 15),” Tokyo, Japan, 2007.
12. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 520 pp.
13. Behnood, A.; Olek, J.; and Glinicki, M. A., “Predicting Modulus Elasticity of Recycled Aggregate Concrete Using M5′ Model Tree Algorithm,” Construction and Building Materials, V. 94, 2015, pp. 137-147. doi: 10.1016/j.conbuildmat.2015.06.055
14. Ravindrarajah, R. S., and Tam, C. T., “Properties of Concrete Made with Crushed Concrete as Coarse Aggregate,” Magazine of Concrete Research, V. 37, No. 130, 1985, pp. 29-38. doi: 10.1680/macr.1985.37.130.29
15. Dhir, R. K.; Limbachiya, M. C.; and Leelawat, T., “Suitability of Recycled Aggregate for Use in BS 5328 Designated Mixes,” Proceedings of the Institution of Civil Engineers. Structures and Buildings, V. 134, No. 3, 1999, pp. 257-274. doi: 10.1680/istbu.1999.31568
16. Dillmann, R., “Concrete with Recycled Concrete Aggregate,” Proceedings of International Symposium on Sustainable Construction: Use of Recycled Concrete Aggregate, Dundee, UK, 1998, pp. 239-253.
17. Mellmann, G., “Processed Concrete Rubble for the Reuse as Aggregate,” Proceedings of the International Seminar on Exploiting Waste in Concrete, Dundee, UK, 1999, pp. 171-178.
18. Kakizaki, M.; Harada, M.; Soshiroda, T.; Kubota, S.; Ikeda, T.; and Kasai, Y., “Strength and Elastic Modulus of Recycled Aggregate Concrete,” Proceedings of the Second International RILEM Symposium on Demolition and Reuse of Concrete and Masonry, Tokyo, Japan, 1988, pp. 565-574.
19. Zilch, K., and Roos, F., “An Equation to Estimate the Modulus of Elasticity of Concrete with Recycled Aggregates,” Civil Engineering (New York, N.Y.), V. 76, No. 4, 2001, pp. 187-191. (only available in German)
20. Corinaldesi, V., “Mechanical and Elastic Behaviour of Concretes Made of Recycled-Concrete Coarse Aggregates,” Construction and Building Materials, V. 24, No. 9, 2010, pp. 1616-1620. doi: 10.1016/j.conbuildmat.2010.02.031
21. Xiao, J. Z.; Li, J. B.; and Zhang, C., “On Relationships between the Mechanical Properties of Recycled Aggregate Concrete: An Overview,” Materials and Structures, V. 39, No. 6, 2007, pp. 655-664. doi: 10.1617/s11527-006-9093-0
22. Deng, F.; He, Y.; Zhou, S.; Yu, Y.; Cheng, H.; and Wu, X., “Compressive Strength Prediction of Recycled Concrete Based on Deep Learning,” Construction and Building Materials, V. 175, 2018, pp. 562-569. doi: 10.1016/j.conbuildmat.2018.04.169
23. Naderpour, H.; Rafiean, A. H.; and Fakharian, P., “Compressive Strength Prediction of Environmentally Friendly Concrete Using Artificial Neural Networks,” Journal of Building Engineering, V. 16, 2018, pp. 213-219. doi: 10.1016/j.jobe.2018.01.007
24. Adams, M. P.; Fu, T.; Cabrera, A. G.; Morales, M.; Ideker, J. H.; and Isgor, O. B., “Cracking Susceptibility of Concrete Made with Coarse Recycled Concrete Aggregates,” Construction and Building Materials, V. 102, 2016, pp. 802-810. doi: 10.1016/j.conbuildmat.2015.11.022
25. Akbarnezhad, A.; Ong, K. C. G.; Zhang, M. H.; Tam, C. T.; and Foo, T. W. J., “Microwave-Assisted Beneficiation of Recycled Concrete Aggregates,” Construction and Building Materials, V. 25, No. 8, 2011, pp. 3469-3479. doi: 10.1016/j.conbuildmat.2011.03.038
26. Andreu, G., and Miren, E., “Experimental Analysis of Properties of High Performance Recycled Aggregate Concrete,” Construction and Building Materials, V. 52, 2014, pp. 227-235. doi: 10.1016/j.conbuildmat.2013.11.054
27. Arezoumandi, M.; Drury, J.; Volz, J. S.; and Khayat, K. H., “Effect of Recycled Concrete Aggregate Replacement Level on Shear Strength of Reinforced Concrete Beams,” ACI Materials Journal, V. 112, No. 4, July-Aug. 2015, pp. 559-568. doi: 10.14359/51687766
28. Bravo, M.; de Brito, J.; Pontes, J.; and Evangelista, L., “Mechanical Performance of Concrete Made with Aggregates from Construction and Demolition Waste Recycling Plants,” Journal of Cleaner Production, V. 99, 2015, pp. 59-74. doi: 10.1016/j.jclepro.2015.03.012
29. Cachim, P. B., “Mechanical Properties of Brick Aggregate Concrete,” Construction and Building Materials, V. 23, No. 3, 2009, pp. 1292-1297. doi: 10.1016/j.conbuildmat.2008.07.023
30. Casuccio, M.; Torrijos, M. C.; Giaccio, G.; and Zerbino, R., “Failure Mechanism of Recycled Aggregate Concrete,” Construction and Building Materials, V. 22, No. 7, 2008, pp. 1500-1506. doi: 10.1016/j.conbuildmat.2007.03.032
31. Choi, W. C., and Yun, H. D., “Compressive Behavior of Reinforced Concrete Columns with Recycled Aggregate under Uniaxial Loading,” Engineering Structures, V. 41, 2012, pp. 285-293. doi: 10.1016/j.engstruct.2012.03.037
32. Cui, H. Z.; Shi, X.; Memon, S. A.; Xing, F.; and Tang, W., “Experimental Study on the Influence of Water Absorption of Recycled Coarse Aggregates on Properties of the Resulting Concretes,” Journal of Materials in Civil Engineering, ASCE, V. 27, No. 4, 2015, p. 04014138 doi: 10.1061/(ASCE)MT.1943-5533.0001086
33. Dapena, E.; Alaejos, P.; Lobet, A.; and Pérez, D., “Effect of Recycled Sand Content on Characteristics of Mortars and Concretes,” Journal of Materials in Civil Engineering, ASCE, V. 23, No. 4, 2011, pp. 414-422. doi: 10.1061/(ASCE)MT.1943-5533.0000183
34. De Juan, M. S., and Gutiérrez, P. A., “Influence of Recycled Aggregate Quality on Concrete Properties,” Conference on Use of Recycled Materials in Building and Structures, 2004, pp. 9-11.
35. Debieb, F.; Courard, L.; Kenai, S.; and Degeimbre, R., “Mechanical and Durability Properties of Concrete Using Contaminated Recycled Aggregates,” Cement and Concrete Composites, V. 32, No. 6, 2010, pp. 421-426. doi: 10.1016/j.cemconcomp.2010.03.004
36. Dilbas, H.; Şimşek, M.; and Çakır, Ö., “An Investigation on Mechanical and Physical Properties of Recycled Aggregate Concrete (RAC) with and without Silica Fume,” Construction and Building Materials, V. 61, 2014, pp. 50-59. doi: 10.1016/j.conbuildmat.2014.02.057
37. Dong, J. F.; Wang, Q. Y.; and Guan, Z. W., “Structural Behaviour of Recycled Aggregate Concrete Filled Steel Tube Columns Strengthened by CFRP,” Engineering Structures, V. 48, 2013, pp. 532-542. doi: 10.1016/j.engstruct.2012.11.006
38. Duan, Z. H., and Poon, C. S., “Properties of Recycled Aggregate Concrete Made with Recycled Aggregates with Different Amounts of Old Adhered Mortars,” Materials & Design, V. 58, 2014, pp. 19-29. doi: 10.1016/j.matdes.2014.01.044
39. Etxeberria, M.; Vázquez, E.; Marí, A.; and Barra, M., “Influence of Amount of Recycled Coarse Aggregates and Production Process on Properties of Recycled Aggregate Concrete,” Cement and Concrete Research, V. 37, No. 5, 2007, pp. 735-742. doi: 10.1016/j.cemconres.2007.02.002
40. Geng, Y.; Wang, Y.; and Chen, J., “Time-Dependent Behaviour of Steel Tubular Columns Filled with Recycled Coarse Aggregate Concrete,” Journal of Constructional Steel Research, V. 122, 2016, pp. 455-468. doi: 10.1016/j.jcsr.2016.04.009
41. Gómez-Soberón, J. M., “Porosity of Recycled Concrete with Substitution of Recycled Concrete Aggregate: An Experimental Study,” Cement and Concrete Research, V. 32, No. 8, 2002, pp. 1301-1311. doi: 10.1016/S0008-8846(02)00795-0
42. Gonzalez-Corominas, A., and Etxeberria, M., “Properties of High Performance Concrete Made with Recycled Fine Ceramic and Coarse Mixed Aggregates,” Construction and Building Materials, V. 68, 2014, pp. 618-626. doi: 10.1016/j.conbuildmat.2014.07.016
43. Gonzalez-Corominas, A., and Etxeberria, M., “Effects of Using Recycled Concrete Aggregates on the Shrinkage of High Performance Concrete,” Construction and Building Materials, V. 115, 2016, pp. 32-41. doi: 10.1016/j.conbuildmat.2016.04.031
44. Gonzalez-Corominas, A.; Etxeberria, M.; and Poon, C. S., “Influence of Steam Curing on the Pore Structures and Mechanical Properties of Fly-Ash High Performance Concrete Prepared with Recycled Aggregates,” Cement and Concrete Composites, V. 71, 2016, pp. 77-84. doi: 10.1016/j.cemconcomp.2016.05.010
45. González-Fonteboa, B., and Martínez-Abella, F., “Recycled Aggregates Concrete: Aggregate and Mix Properties,” Materiales de Construcción, V. 55, No. 279, 2005, pp. 53-66.
46. González-Fonteboa, B.; Martínez-Abella, F.; Eiras-López, J.; and Seara-Paz, S., “Effect of Recycled Coarse Aggregate on Damage of Recycled Concrete,” Materials and Structures, V. 44, No. 10, 2011, pp. 1759-1771. doi: 10.1617/s11527-011-9736-7
47. Henry, M.; Pardo, G.; Nishimura, T.; and Kato, Y., “Balancing Durability and Environmental Impact in Concrete Combining Low-Grade Recycled Aggregates and Mineral Admixtures,” Resources, Conservation and Recycling, V. 55, No. 11, 2011, pp. 1060-1069. doi: 10.1016/j.resconrec.2011.05.020
48. Ignjatović, I. S.; Marinković, S. B.; Mišković, Z. M.; and Savić, A. R., “Flexural Behavior of Reinforced Recycled Aggregate Concrete Beams under Short-Term Loading,” Materials and Structures, V. 46, No. 6, 2013, pp. 1045-1059. doi: 10.1617/s11527-012-9952-9
49. Kang, T. H.; Kim, W.; Kwak, Y. K.; and Hong, S. G., “Flexural Testing of Reinforced Concrete Beams with Recycled Concrete Aggregates,” ACI Structural Journal, V. 111, No. 3, May-June 2014, pp. 607-615. doi: 10.14359/51686622
50. Katz, A., “Properties of Concrete Made with Recycled Aggregate from Partially Hydrated Old Concrete,” Cement and Concrete Research, V. 33, No. 5, 2003, pp. 703-711. doi: 10.1016/S0008-8846(02)01033-5
51. Kou, S. C., and Poon, C. S., “Long-Term Mechanical and Durability Properties of Recycled Aggregate Concrete Prepared with the Incorporation of Fly Ash,” Cement and Concrete Composites, V. 37, 2013, pp. 12-19. doi: 10.1016/j.cemconcomp.2012.12.011
52. Kou, S. C.; Poon, C. S.; and Chan, D., “Influence of Fly Ash as Cement Replacement on the Properties of Recycled Aggregate Concrete,” Journal of Materials in Civil Engineering, ASCE, V. 19, No. 9, 2007, pp. 709-717. doi: 10.1061/(ASCE)0899-1561(2007)19:9(709)
53. Kou, S. C.; Poon, C. S.; and Chan, D., “Influence of Fly Ash as a Cement Addition on the Hardened Properties of Recycled Aggregate Concrete,” Materials and Structures, V. 41, No. 7, 2008, pp. 1191-1201. doi: 10.1617/s11527-007-9317-y
54. Kou, S. C.; Poon, C. S.; and Wan, H. W., “Properties of Concrete Prepared with Low-Grade Recycled Aggregates,” Construction and Building Materials, V. 36, 2012, pp. 881-889. doi: 10.1016/j.conbuildmat.2012.06.060
55. Koulouris, A.; Limbachiya, M. C.; Fried, A. N.; and Roberts, J. J., “Use of Recycled Aggregate in Concrete Application: Case studies.” Proceedings of the International Conference on Sustainable Waste Management and Recycling: Challenges and Opportunities, Thomas Telford, London, UK, pp. 245-257.
56. Laserna, S., and Montero, J., “Influence of Natural aggregates Typology on Recycled Concrete Strength Properties,” Construction and Building Materials, V. 115, 2016, pp. 78-86. doi: 10.1016/j.conbuildmat.2016.04.037
57. Limbachiya, M.; Meddah, M. S.; and Ouchagour, Y., “Performance of Portland/Silica Fume Cement Concrete Produced with Recycled Concrete Aggregate,” ACI Materials Journal, V. 109, No. 1, Jan.-Feb. 2012, pp. 91-100.
58. Pedro, D.; De Brito, J.; and Evangelista, L., “Influence of the Use of Recycled Concrete Aggregates from Different Sources on Structural Concrete,” Construction and Building Materials, V. 71, 2014, pp. 141-151. doi: 10.1016/j.conbuildmat.2014.08.030
59. Pedro, D.; De Brito, J.; and Evangelista, L., “Performance of Concrete Made with Aggregates Recycled from Precasting Industry Waste: Influence of the Crushing Process,” Materials and Structures, V. 48, No. 12, 2015, pp. 3965-3978. doi: 10.1617/s11527-014-0456-7
60. Rahal, K., “Mechanical Properties of Concrete with Recycled Coarse Aggregate,” Building and Environment, V. 42, No. 1, 2007, pp. 407-415. doi: 10.1016/j.buildenv.2005.07.033
61. Rao, M. C.; Bhattacharyya, S. K.; and Barai, S. V., “Influence of Field Recycled Coarse Aggregate on Properties of Concrete,” Materials and Structures, V. 44, No. 1, 2011, pp. 205-220. doi: 10.1617/s11527-010-9620-x
62. Folino, P., and Xargay, H., “Recycled Aggregate Concrete—Mechanical Behavior under Iniaxial and Triaxial Compression,” Construction and Building Materials, V. 56, 2014, pp. 21-31. doi: 10.1016/j.conbuildmat.2014.01.073
63. Salem, R. M.; Burdette, E. G.; and Jackson, N. M., “Resistance to Freezing and Thawing of Recycled Aggregate Concrete,” ACI Materials Journal, V. 100, No. 3, May-June 2003, pp. 216-221.
64. Schubert, S.; Hoffmann, C.; Leemann, A.; Moser, K.; and Motavalli, M., “Recycled Aggregate Concrete: Experimental Shear Resistance of Slabs without Shear Reinforcement,” Engineering Structures, V. 41, 2012, pp. 490-497. doi: 10.1016/j.engstruct.2012.04.006
65. Seara-Paz, S.; González-Fonteboa, B.; Martínez-Abella, F.; and González-Taboada, I., “Time-Dependent Behaviour of Structural Concrete Made with Recycled Coarse Aggregates. Creep and Shrinkage,” Construction and Building Materials, V. 122, 2016, pp. 95-109. doi: 10.1016/j.conbuildmat.2016.06.050
66. Thomas, C.; Setién, J.; Polanco, J.; Alaejos, P.; and De Juan, M. S., “Durability of Recycled Aggregate Concrete,” Construction and Building Materials, V. 40, 2013, pp. 1054-1065. doi: 10.1016/j.conbuildmat.2012.11.106
67. Wang, W. L.; Kou, S. C.; and Xing, F., “Deformation Properties and Direct Shear of Medium Strength Concrete Prepared with 100% Recycled Coarse Aggregates,” Construction and Building Materials, V. 48, 2013, pp. 187-193. doi: 10.1016/j.conbuildmat.2013.06.065
68. Xiao, J.; Li, J.; and Zhang, C., “Mechanical Properties of Recycled Aggregate Concrete under Uniaxial Loading,” Cement and Concrete Research, V. 35, No. 6, 2005, pp. 1187-1194. doi: 10.1016/j.cemconres.2004.09.020
69. Yang, K. H.; Chung, H. S.; and Ashour, A. F., “Influence of Type and Replacement Level of Recycled Aggregates on Concrete Properties,” ACI Materials Journal, V. 105, No. 3, May-June 2008, pp. 289-296.
70. Zega, C. J., and Di Maio, A. A., “Recycled Concretes Made with Waste Ready-Mix Concrete as Coarse Aggregate,” Journal of Materials in Civil Engineering, ASCE, V. 23, No. 3, 2011, pp. 281-286. doi: 10.1061/(ASCE)MT.1943-5533.0000165
71. Omary, S.; Ghorbel, E.; and Wardeh, G., “Relationships between Recycled Concrete Aggregates Characteristics and Recycled Aggregates Concretes Properties,” Construction and Building Materials, V. 108, 2016, pp. 163-174. doi: 10.1016/j.conbuildmat.2016.01.042
72. Khayat, K. H., and Sadati, S., “High-Volume Recycled Materials for Sustainable Pavement Construction, Final Report No. crm17-006, Missouri Department of Transportation, Jefferson City, MO, 2016.
73. González-Taboada, I.; González-Fonteboa, B.; Martínez-Abella, F.; and Carro-López, D., “Study of Recycled Concrete Aggregate Quality and its Relationship with Recycled Concrete Compressive Strength Using Database Analysis,” Materiales de Construcción, V. 66, No. 323, 2016, pp. 1-18.
74. ASTM C143/C143M-15, “Standard Test Method for Slump of Hydraulic-Cement Concrete,” ASTM International, West Conshohocken, PA, 2015, 4 pp.
75. ASTM C231/C231-14, “Standard Test Method for Air Content of Freshly Mixed Concrete by the Pressure Method,” ASTM International, West Conshohocken, PA, 2014, 9 pp.
76. ASTM C39/C39M-01, “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 2001, 5 pp.
77. ASTM C469/C469M-10, “Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression,” ASTM International, West Conshohocken, PA, 2010, 5 pp.
78. Duan, Z.; Poon, C. S.; and Xiao, J., “Using Artificial Neural Networks to Assess the Applicability of Recycled Aggregate Classification by Different Specifications,” Materials and Structures, V. 50, No. 2, 2017, pp. 107-116. doi: 10.1617/s11527-016-0972-8
79. Ghafari, E.; Bandarabadi, M.; Costa, H.; and Júlio, E., “Prediction of Fresh and Hardened State Properties of UHPC: Comparative Study of Statistical Mixture Design and an Artificial Neural Network Model,” Journal of Materials in Civil Engineering, ASCE, V. 27, No. 11, 2015, p. 04015017 doi: 10.1061/(ASCE)MT.1943-5533.0001270
80. Werbos, P. J., The Roots of Backpropagation: From Ordered Derivatives to Neural Networks and Political Forecasting, Wiley Interscience, 1994, 319 pp.
81. Levenberg, K., “A Method for the Solution of Certain Non-linear Problems in Least Squares,” Quarterly of Applied Mathematics, V. 2, No. 2, 1944, pp. 164-168. doi: 10.1090/qam/10666
82. Marquardt, D. W., “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal of the Society for Industrial and Applied Mathematics, V. 11, No. 2, 1963, pp. 431-441. doi: 10.1137/0111030
83. Hagan, M. T., and Menhaj, M. B., “Training Feedforward Networks with the Marquardt Algorithm,” IEEE Transactions on Neural Networks, V. 5, No. 6, 1994, pp. 989-993. doi: 10.1109/72.329697
84. Fu, X.; Li, S.; Fairbank, M.; Wunsch, D. C. II; and Alonso, E., “Training Recurrent Neural Networks with the Levenberg–Marquardt Algorithm for Optimal Control of a Grid-Connected Converter,” IEEE Transactions on Neural Networks and Learning Systems, V. 26, No. 9, 2015, pp. 1900-1912. doi: 10.1109/TNNLS.2014.2361267
85. Haykin, S., Neural Networks and Learning Machines, Pearson Education, Upper Saddle River, NJ, 2009.
86. Eiben, A. E., and Smith, J. E., Introduction to Evolutionary Computing, Springer-Verlag, Berlin Heidelberg, 2007.
87. Duda, R. O.; Hart, P. E.; and Stork, D. G., Pattern Classification, second edition, Wiley, Hoboken, NJ, 2000.
88. Sadati, S., and Khayat, K. H., “Field Performance of Concrete Pavement Incorporating Recycled Concrete Aggregate,” Construction and Building Materials, V. 126, 2016, pp. 691-700. doi: 10.1016/j.conbuildmat.2016.09.087