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Employing TLBO and SCE for optimal prediction of the compressive strength of concrete

  • Zhao, Yinghao (Guangzhou Institute of Building Science Co., Ltd.) ;
  • Moayedi, Hossein (Institute of Research and Development, Duy Tan University) ;
  • Bahiraei, Mehdi (Faculty of Engineering, Razi University) ;
  • Foong, Loke Kok (Department for Management of Science and Technology Development, Ton Duc Thang University)
  • Received : 2020.03.22
  • Accepted : 2020.10.18
  • Published : 2020.12.25

Abstract

The early prediction of Compressive Strength of Concrete (CSC) is a significant task in the civil engineering construction projects. This study, therefore, is dedicated to introducing two novel hybrids of neural computing, namely Shuffled Complex Evolution (SCE) and Teaching-Learning-Based Optimization (TLBO) for predicting the CSC. The algorithms are applied to a Multi-Layer Perceptron (MLP) network to create the SCE-MLP and TLBO-MLP ensembles. The results revealed that, first, intelligent models can properly handle analyzing and generalizing the non-linear relationship between the CSC and its influential parameters. For example, the smallest and largest values of the CSC were 17.19 and 58.53 MPa, and the outputs of the MLP, SCE-MLP, and TLBO-MLP range in [17.61, 54.36], [17.69, 55.55] and [18.07, 53.83], respectively. Second, applying the SCE and TLBO optimizers resulted in increasing the correlation of the MLP products from 93.58 to 97.32 and 97.22%, respectively. The prediction error was also reduced by around 34 and 31% which indicates the high efficiency of these algorithms. Moreover, regarding the computation time needed to implement the SCE-MLP and TLBO-MLP models, the SCE is a considerably more time-efficient optimizer. Nevertheless, both suggested models can be promising substitutes for laboratory and destructive CSC evaluative models.

Keywords

References

  1. Al-Shamiri, A.K., Kim, J.H., Yuan, T.F. and Yoon, Y.S. (2019), "Modeling the compressive strength of high-strength concrete: An extreme learning approach", Constr. Build. Mater., 208, 204-219. https://doi.org/10.1016/j.conbuildmat.2019.02.165.
  2. Asteris, P.G. and Mokos, V.G. (2019), "Concrete compressive strength using artificial neural networks", Neural Comput. Appl., 2019, 1-20. https://doi.org/10.1007/s00521-019-04663-2.
  3. Bui, D.T., Ghareh, S., Moayedi, H. and Nguyen, H. (2019), "Fine-tuning of neural computing using whale optimization algorithm for predicting compressive strength of concrete", Eng. Comput., 2019, 1-12. 10.1007/s00366-019-00850-w.
  4. Chao, L., Zhang, K., Li, Z., Zhu, Y., Wang, J. and Yu, Z. (2018), "Geographically weighted regression based methods for merging satellite and gauge precipitation", J. Hydrol., 558, 275-289. https://doi.org/10.1016/j.jhydrol.2018.01.042.
  5. Chen, H.L., Wang, G., Ma, C., Cai, Z.N., Liu, W.B. and Wang, S.J. (2016), "An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson's disease", Neurocomput., 184, 131-144. https://doi.org/10.1016/j.neucom.2015.07.138.
  6. Chen, H., Heidari, A.A., Chen, H., Wang, M., Pan, Z. and Gandomi, A.H. (2020), "Multi-population differential evolution-assisted Harris hawks optimization: Framework and case studies", Future Gener. Comput. Syst., 111, 175-198. https://doi.org/10.1016/j.future.2020.04.008.
  7. Cook, R., Lapeyre, J., Ma, H. and Kumar, A. (2019), "Prediction of compressive strength of concrete: Critical comparison of performance of a hybrid machine learning model with standalone models", J. Mater. Civ. Eng., 31(11), 04019255. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002902.
  8. Dao, D.V., Adeli, H., Ly, H.B., Le, L.M., Le, V.M., Le, T.T. and Pham, B.T. (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. 10.3390/su12030830. https://doi.org/10.3390/su12030830.
  9. Dong, Q., Cui, L. and Si, S. (2020), "Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes", Appl. Math. Model., 79, 414-433. https://doi.org/10.1016/j.apm.2019.10.044.
  10. Duan, Q., Gupta, V.K. and Sorooshian, S. (1993), "Shuffled complex evolution approach for effective and efficient global minimization", J. Optim. Theory Appl., 76(3), 501-521. https://doi.org/10.1007/BF00939380.
  11. Dutta, D. and Barai, S.V. (2019), Recent Advances in Structural Engineering, Springer, USA.
  12. Felix, E.F., Possan, E. and Carrazedo, R. (2019), "Analysis of training parameters in the ANN learning process to mapping the concrete carbonation depth", J. Build. Pathol. Rehab., 4(1), 16. https://doi.org/10.1007/s41024-019-0054-8.
  13. Feng, D.C., Liu, Z.T., Wang, X.D., Chen, Y., Chang, J.Q., Wei, D.F. and Jiang, Z.M. (2020), "Machine learning-based compressive strength prediction for concrete: An adaptive boosting approach", Constr. Build. Mater., 230, 117000. https://doi.org/10.1016/j.conbuildmat.2019.117000.
  14. Golafshani, E.M., Behnood, A. and 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. https://doi.org/10.1016/j.conbuildmat.2019.117266.
  15. Guan, Z., Xing, Q., Xu, M., Yang, R., Liu, T. and Wang, Z. (2019), "MFQE 2.0: A new approach for multi-frame quality enhancement on compressed video", IEEE Trans. Pattern Anal. Mach. Intell., 2019, 1902. https://doi.org/10.1109/TPAMI.2019.2944806.
  16. Han, I.J., Yuan, T.F., Lee, J.Y., Yoon, Y.S. and Kim, J.H. (2019), "Learned prediction of compressive strength of GGBFS concrete using hybrid artificial neural network models", Materials, 12(22), 3708. https://doi.org/10.3390/ma12223708.
  17. Hornik, K., Stinchcombe, M. and White, H. (1989), "Multilayer feedforward networks are universal approximators", Neural Netw., 2(5), 359-366. https://doi.org/10.1016/0893-6080(89)90020-8
  18. Hu, L., Hong, G., Ma, J., Wang, X. and Chen, H. (2015), "An efficient machine learning approach for diagnosis of paraquat-poisoned patients", Comput. Biol. Med., 59, 116-124. https://doi.org/10.1016/j.compbiomed.2015.02.003.
  19. Hu, P., Cao, L., Su, J., Li, Q. and Li, Y. (2020), "Distribution characteristics of salt-out particles in steam turbine stage", Energy, 192, 116626. https://doi.org/10.1016/j.energy.2019.116626.
  20. Ira, J., Hasalova, L. and Jahoda, M. (2015), "The use of optimization in fire development modeling, the use of optimization techniques for estimation of pyrolysis model input parameters", Proceedings of the International Conference, Prague, Czech, April.
  21. Ji, X., Ye, H., Zhou, J., Yin, Y. and Shen, X. (2017), "An improved teaching-learning-based optimization algorithm and its application to a combinatorial optimization problem in foundry industry", Appl. Soft Comput., 57, 504-516. https://doi.org/10.1016/j.asoc.2017.04.029.
  22. Jiang, Q., Shao, F., Gao, W., Chen, Z., Jiang, G. and Ho, Y. (2019), "Unified no-reference quality assessment of singly and multiply distorted stereoscopic images", IEEE Trans. Image Process., 28(4), 1866-1881. https://doi.org/10.1109/TIP.2018.2881828.
  23. Lei, Z., Hao, S., Yang, J. and Dan, X. (2020), "Study on solid waste pyrolysis coke catalyst for catalytic cracking of coal tar", Int. J. Hydro, Energy., 45(38), 19280-19290. https://doi.org/10.1016/j.ijhydene.2020.05.075.
  24. Li, C., Hou, L., Sharma, B.Y., Li, H., Chen, C., Li, Y., Zhao, X., Huang, H., Cai, Z. and Chen, H. (2018), "Developing a new intelligent system for the diagnosis of tuberculous pleural effusion", Comput. Methods Programs Biomed., 153, 211-225. https://doi.org/10.1016/j.cmpb.2017.10.022.
  25. Li, T., Xu, M., Zhu, C., Yang, R., Wang, Z. and Guan, Z. (2019), "A deep learning approach for multi-frame in-loop filter of HEVC", IEEE Trans. Image Process., 28(11), 5663-5678. https://doi.org/10.1109/TIP.2019.2921877.
  26. Li, Z., Zhou, H., Hu, D. and Zhang, C. (2020), "Yield criterion for rocklike geomaterials based on strain energy and CMP model", Int. J. Geomech., 20(3), 04020013. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001593.
  27. Ling, H., Qian, C., Kang, W., Liang, C. and 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. https://doi.org/10.1016/j.conbuildmat.2019.02.071.
  28. Liu, S., Chan, F.T. and Ran, W. (2016), "Decision making for the selection of cloud vendor: An improved approach under group decision-making with integrated weights and objective/subjective attributes", Exp. Syst. Appl., 55, 37-47. https://doi.org/10.1016/j.eswa.2016.01.059.
  29. Liu, C., Deng, X., Liu, J., Peng, T., Yang, S. and Zheng, Z. (2020a), "Dynamic response of saddle membrane structure under hail impact", Eng. Struct., 214, 110597. https://doi.org/10.1016/j.engstruct.2020.110597.
  30. Liu, C., Wang, F., Deng, X., Pang, S., Liu, J., Wu, Y. and Xu, Z. (2020b), "Hailstone-induced dynamic responses of pretensioned umbrella membrane structure", Adv. Struct. Eng., 1369433220940149. https://doi.org/10.1177/1369433220940149.
  31. Liu, C., Wang, F., He, L., Deng, X., Liu, J. and Wu, Y. (2020c), "Experimental and numerical investigation on dynamic responses of the umbrella membrane structure excited by heavy rainfall", J. Vib. Control, 2020, 1077546320932691. https://doi.org/10.1177/1077546320932691.
  32. Lu, H., Kang, Y., Liu, L. and Li, J. (2019a), "Comprehensive groundwater safety assessment under potential shale gas contamination based on integrated analysis of reliability-resilience-vulnerability and gas migration index", J. Hydrol., 578, 124072. https://doi.org/10.1016/j.jhydrol.2019.124072.
  33. Lu, H., Tian, P. and He, L. (2019b), "Evaluating the global potential of aquifer thermal energy storage and determining the potential worldwide hotspots driven by socio-economic, geo-hydrologic and climatic conditions", Renew. Sustain. Energy Rev., 112, 788-796. https://doi.org/10.1016/j.rser.2019.06.013.
  34. Lv, Z., Li, X., Lv, H. and Xiu, W. (2020), "BIM big data storage in WebVRGIS", IEEE Trans. Ind. Inf., 16(4), 2566-2573. https://doi.org/10.1109/TII.2019.2916689.
  35. Ma, X., Foong, L.K., Morasaei, A., Ghabussi, A. and Lyu, Z. (2020), "Swarm-based hybridizations of neural network for predicting the concrete strength", Smart Struct. Syst., Int. J., 26(2), 241-251. https://doi.org/10.12989/sss.2020.26.2.241.
  36. Mirjalili, S. and Lewis, A. (2016), "The whale optimization algorithm", Adv. Eng. Softw., 95, 51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008
  37. Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H. and Mirjalili, S.M. (2017), "Salp swarm algorithm: A bio-inspired optimizer for engineering design problems", Adv. Eng. Softw., 114, 163-191. https://doi.org/10.1016/j.advengsoft.2017.07.002.
  38. Moayedi, H., Nguyen, H. and Safuan, A.R.A. (2019), "Novel metaheuristic classification approach in developing mathematical model-based solutions predicting failure in shallow footing", Eng. Comput., 36, 1-8. https://doi.org/10.1007/s00366-019-00819-9.
  39. More, J.J. (1978), Numerical Analysis, Springer, USA.
  40. Naseri, H., Jahanbakhsh, H. and Moghadas Nejad, F. (2019), "Developing a novel machine learning method to predict the compressive strength of fly ash concrete in different ages", AUT J. Civ. Eng., 2019, 16124. https://doi.org/10.22060/AJCE.2019.16124.5569.
  41. Ni, T., Xu, Q., Huang, Z., Liang, H., Yan, A. and Wen, X. (2020), "A cost-effective TSV repair architecture for clustered faults in 3D IC", IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 1, 1. https://doi.org/10.1109/TCAD.2020.3025169.
  42. Onat, O. and Gul, M. (2018), "Application of Artificial Neural Networks to the prediction of out-of-plane response of infill walls subjected to shake table". Smart Struct. Syst., Int. J., 21(4), 521-535. https://doi.org/10.12989/sss.2018.21.4.521.
  43. Pham, A.D., Hoang, N.D. and Nguyen, Q.T. (2016), "Predicting compressive strength of high-performance concrete using metaheuristic-optimized least squares support vector regression", J. Comput. Civ. Eng., 30(3), 06015002. https://doi.org/10.1061/%28ASCE%29CP.1943-5487.0000506.
  44. Prayogo, D. (2018), "Metaheuristic-based machine learning system for prediction of compressive strength based on concrete mixture properties and early-age strength test results", Civ. Eng. Dimen., 20(1), 21-29. https://doi.org/10.9744/ced.20.1.21-29.
  45. Qiu, C., Gong, S. and Gao, W. (2019), "Three artificial intelligence-based solutions predicting concrete slump", UPB Sci. Bull. Series C, 81(4), 2019.
  46. Rao, R. (2016), "Review of applications of TLBO algorithm and a tutorial for beginners to solve the unconstrained and constrained optimization problems", Dec. Sci. Lett., 5(1), 1-30. https://doi.org/10.5267/j.dsl.2015.9.003.
  47. Rao, R.V., Savsani, V.J. and Vakharia, D. (2011), "Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems", Comput. Aided Des., 43(3), 303-315. https://doi.org/10.1016/j.cad.2010.12.015.
  48. Sadowski, L., Nikoo, M., Shariq, M., Joker, E. and Czarnecki, S. (2019), "The nature-inspired metaheuristic method for predicting the creep strain of green concrete containing ground granulated blast furnace slag", Materials, 12(2), 293. https://doi.org/10.3390/ma12020293.
  49. Sai, G.J. and Singh, V.P. (2019), "Prediction of compressive strength using support vector regression", Mendel, 2019, 51-56. https://doi.org/10.13164/mendel.2019.1.051.
  50. Saldarriaga, M.V., Mahfoud, J., Steffen, V. and Hagopian, J.D. (2009), "Adaptive balancing of highly flexible rotors by using artificial neural networks". Smart Struct. Syst., Int. J., 5(5), 507-515. https://doi.org/10.12989/sss.2009.5.5.507.
  51. Shahbazi, Y., Delavari, E. and Chenaghlou, M.R. (2014), "Predicting the buckling load of smart multilayer columns using soft computing tools", Smart Struct. Syst., Int. J., 13(1), 81-98. https://doi.org/10.12989/sss.2013.13.1.081.
  52. Shariati, M., Mafipour, M.S., Mehrabi, P., Ahmadi, M., Wakil, K, Trung, N.T. and Toghroli, A. (2020), "Prediction of concrete strength in presence of furnace slag and fly ash using Hybrid ANN-GA (Artificial neural network-genetic algorithm)", Smart Struct. Syst., Int. J., 25(2), 183-195. https://doi.org/10.12989/sss.2020.25.2.183.
  53. Shen, C.Q., Wang, D., Liu, Y.B., Kong, F.R. and Tse, P.W. (2014), "Recognition of rolling bearing fault patterns and sizes based on two-layer support vector regression machines", Smart Struct. Syst., Int. J., 13(3), 453-471. https://doi.org/10.12989/sss.2014.13.3.453.
  54. Shen, L., Chen, H., Yu, Z., Kang, W., Zhang, B., Li, H., Yang, B. and Liu, D. (2016), "Evolving support vector machines using fruit fly optimization for medical data classification", Knowl. Based Syst., 96, 61-75. https://doi.org/10.1016/j.knosys.2016.01.002.
  55. Song, J., Zhong, Q., Wang, W., Su, C., Tan, Z. and Liu, Y. (2020), "FPDP: Flexible privacy-preserving data publishing scheme for smart agriculture", IEEE Sensors J., 1, 1. https://doi.org/10.1109/JSEN.2020.3017695.
  56. Togan, V. (2012), "Design of planar steel frames using teachinglearning based optimization", Eng. Struct., 34, 225-232. https://doi.org/10.1016/j.engstruct.2011.08.035.
  57. Trung, N.T., Alemi, N., Haido, J..H, Shariati, M., Baradaran, S. and Yousif, S.T. (2019), "Reduction of cement consumption by producing smart green concretes with natural zeolites", Smart Struct. Syst., Int. J., 24(3), 415-425. https://doi.org/10.12989/sss.2019.24.3.415.
  58. Tsai, Y.H., Wang, J., Chien, W.T., Wei, C.Y., Wang, X. and Hsieh, S.H. (2019), "A BIM-based approach for predicting corrosion under insulation", Auto. Constr., 107, 102923. https://doi.org/10.1016/j.autcon.2019.102923.
  59. Vu, D.T. and Hoang, N.D. (2016), "Punching shear capacity estimation of FRP-reinforced concrete slabs using a hybrid machine learning approach", Struct. Infrastruct. Eng., 12(9), 1153-1161. https://doi.org/10.1080/15732479.2015.1086386.
  60. Wang, M. and Chen, H. (2020), "Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis", Appl. Soft Comput. J., 88, 105946. https://doi.org/10.1016/j.asoc.2019.105946.
  61. Wang, S.J., Chen, H.L., Yan, W.J., Chen, Y.H. and Fu, X. (2014), "Face recognition and micro-expression recognition based on discriminant tensor subspace analysis plus extreme learning machine", Neural Process. Lett., 39(1), 25-43. https://doi.org/10.1007/s11063-013-9288-7.
  62. Wang, M., Chen, H., Yang, B., Zhao, X., Hu, L., Cai, Z., Huang, H. and Tong, C. (2017), "Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses", Neurocomputing, 267, 69-84. https://doi.org/10.1016/j.neucom.2017.04.060.
  63. Wu, C., Wang, X., Chen, M. and Kim, M.J. (2019), "Differential received signal strength based RFID positioning for construction equipment tracking", Adv. Eng. Inf., 42, 100960. https://doi.org/10.1016/j.aei.2019.100960.
  64. Xia, J., Chen, H., Li, Q., Zhou, M., Chen, L., Cai, Z., Fang, Y. and Zhou, H. (2017), "Ultrasound-based differentiation of malignant and benign thyroid nodules: An extreme learning machine approach", Comput. Methods Programs Biomed., 147, 37-49. https://doi.org/10.1016/j.cmpb.2017.06.005.
  65. Xu, X. and Chen, H.L. (2014), "Adaptive computational chemotaxis based on field in bacterial foraging optimization", Soft Comput., 18(4), 797-807. https://doi.org/10.1007/s00500-013-1089-4.
  66. Xu, M., Li, T., Wang, Z., Deng, X., Yang, R. and Guan, Z. (2018), "Reducing complexity of HEVC: A deep learning approach", IEEE Trans. Image Process., 27(10), 5044-5059. https://doi.org/10.1109/TIP.2018.2847035.
  67. Xu, M., Li, C., Chen, Z., Wang, Z. and Guan, Z. (2019a), "Assessing visual quality of omnidirectional videos", IEEE Trans. Circuits Syst. Video Technol., 29(12), 3516-3530. https://doi.org/10.1109/TCSVT.2018.2886277.
  68. Xu, Y., Chen, H., Luo, J., Zhang, Q., Jiao, S. and Zhang, X. (2019b), "Enhanced moth-flame optimizer with mutation strategy for global optimization", Inf. Sci., 492, 181-203. https://doi.org/10.1016/j.ins.2019.04.022.
  69. Xu, M., Li, C., Zhang, S. and Callet, P.L. (2020), "State-of-the-art in 360° video/image processing: Perception, assessment and compression", IEEE J. Select. Topics Signal Process., 14(1), 5-26. https://doi.org/10.1109/JSTSP.2020.2966864.
  70. Yang, R., Xu, M., Liu, T., Wang, Z. and Guan, Z. (2019), "Enhancing quality for HEVC compressed videos", IEEE Trans. Circuits Syst. Video Technol., 29(7), 2039-2054. https://doi.org/10.1109/TCSVT.2018.2867568.
  71. Yang, Y., Liu, J., Yao, J., Kou, J., Li, Z., Wu, T., Zhang, K., Zhang, L. and Sunm, H. (2020), "Adsorption behaviors of shale oil in kerogen slit by molecular simulation", Chem. Eng. J., 387, 124054. https://doi.org/10.1016/j.cej.2020.124054.
  72. Yeh, I.C. (2007), "Modeling slump flow of concrete using second-order regressions and artificial neural networks", Cement Concrete Compos., 29(6), 474-480. https://doi.org/10.1016/j.cemconcomp.2007.02.001.
  73. Yi, T.H., Li, H.N. and Sun, H.M. (2013), "Multi-stage structural damage diagnosis method based on energy-damage theory", Smart Struct. Syst., Int. J., 12(3-4), 345-361. https://doi.org/10.12989/sss.2013.12.3_4.345.
  74. Zhang, K., Wang, Q., Chao, L., Ye, J., Li, Z., Yu, Z., Yang, T. and Ju, Q. (2019), "Ground observation-based analysis of soil moisture spatiotemporal variability across a humid to semi-humid transitional zone in China", J. Hydrol., 574, 903-914. https://doi.org/10.1016/j.jhydrol.2019.04.087.
  75. Zhang, Y., Liu, R., Wang, X., Chen, H. and Li, C. (2020), "Boosted binary Harris hawks optimizer and feature selection"., Eng. Comput., 2020, 1-13. https://doi.org/10.1007/s00366-020-01028-5.
  76. Zhao, X., Li, D., Yang, B., Ma, C., Zhu, Y. and Chen, H. (2014), "Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton", Appl. Soft Comput., 24, 585-596. https://doi.org/10.1016/j.asoc.2014.07.024.
  77. Zhao, X., Li, D., Yang, B., Chen, H., Yang, X., Yu, C. and Liu, S. (2015), "A two-stage feature selection method with its application", Comput. Elec. Eng., 47, 114-125. https://doi.org/10.1016/j.compeleceng.2015.08.011.
  78. Zhao, X., Zhang, X., Cai, Z., Tian, X., Wang, X., Huang, Y., Chen, H. and Hu, L. (2019), "Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients", Comput. Biol. Chem., 78, 481-490. https://doi.org/10.1016/j.compbiolchem.2018.11.017.
  79. Zheng, S., Lyu, Z. and Foong, L.K. (2020), "Early prediction of cooling load in energy-efficient buildings through novel optimizer of shuffled complex evolution", Eng. Comput., 2020, 1-15. https://doi.org/10.1007/s00366-020-01140-6.
  80. Zhu, J., Wang, X., Chen, M., Wu, P. and Kim, M.J. (2019), "Integration of BIM and GIS: IFC geometry transformation to shapefile using enhanced open-source approach", Auto. Constr., 106, 102859. https://doi.org/10.1016/j.autcon.2019.102859.
  81. Zuo, C., Chen, Q., Tian, L., Waller, L. and Asundi, A. (2015), "Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective", Opt. Lasers Eng., 71, 20-32. https://doi.org/10.1016/j.optlaseng.2015.03.006.
  82. Zuo, C., Sun, J., Li, J., Asundi, A. and Chen, Q. (2020), "Wide-field high-resolution 3d microscopy with fourier ptychographic diffraction tomography", Opt. Lasers Eng., 128, 106003. https://doi.org/10.1016/j.optlaseng.2020.106003.