Modified Particle Swarm Optimization-Artificial Neural Network and Gene Expression Programing for Predicting High Temperature Oxidation Behavior of Ni–Cr–W-Mo Alloys

Document Type : Original Article


1 Department of Materials Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Metal, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran


This paper is an attempt to model the oxidation behavior of Ni-base alloys by considering the alloying elements, i.e., Cr, W, Mo, as variables. Modified particle swarm optimization-artificial neural network (MPSO-ANN) and gene expression programming (GEP) techniques were employed for modeling. Data set for construction of (MPSO-ANN) and GEP models selected from 66 cyclic oxidation performed in the temperature range of 400-1150 ᵒC for 27 different Ni-based alloy samples at various amounts of Cr, W, and Mo. The weight percent of alloying elements selected as input variables and the changes of weight during the oxidation cycle considered as output. To analyze the performance of proposed models, various statistical indices, viz. root mean squared error (RMSE) and the correlation coefficient between two data sets (R2) were utilized. The collected data of GEP randomly divided into 21 training sets and 6 testing sets. The results confirmed that the possibility of oxidation behavior modeling using GEP by R2 = 0.981, RMSE =0.0822. By consideration of oxidation resistance as criteria, Cr, Mo, and W enhanced the oxidation resistance of Ni-based alloys. The results showed that in the presence of Cr as alloying element, especially at Cr contents higher than 22 wt.%, the effect of W and Mo were negligible. However, the same trend was reversed at the sample with Cr content lower than 20 wt.%. In these cases, the effect of W and Mo on oxidation resistance were significantly enhanced.


1.     Yun, D. W., Seo, S. M., Jeong, H. W., Kim, I. S., and Yoo, Y. S. “Modelling high temperature oxidation behaviour of Ni-Cr-W-Mo alloys with Bayesian neural network.” Journal of Alloys and Compounds, Vol. 587, (2014), 105–112.
2.     Smola, G., Gawel, R., Kyziol, K., Miszczak, M., and Grzesik, Z. “Influence of Nickel on the Oxidation Resistance at High Temperatures of Thin Chromium Coatings.” Oxidation of Metals, Vol. 91, No. 5–6, (2019), 625–640.
3.     Cho, S. H., Lee, S. K., Kim, D. Y., Lee, J. H., and Hur, J. M. “Effects of alloying elements of nickel-based alloys on the hot-corrosion behavior in an electrolytic reduction process.” Journal of Alloys and Compounds, Vol. 695, (2017), 2878–2885.
4.     Tawancy, H. M. “On the behaviour of minor active elements during oxidation of selected Ni-base high-temperature alloys.” Materials at High Temperatures, Vol. 34, No. 1, (2017), 22–32.
5.     Olivares, R. I., Young, D. J., Nguyen, T. D., and Marvig, P. “Resistance of High-Nickel, Heat-Resisting Alloys to Air and to Supercritical CO2 at High Temperatures.” Oxidation of Metals, Vol. 90, No. 1–2, (2018), 1–25.
6.     Kim, H. S., Park, S. J., Seo, S. M., Yoo, Y. S., Jeong, H. W., and Jang, H. J. “High temperature oxidation resistance of Ni-(5∼13)Co-(10∼16)Cr-(5∼9)W-5Al-(1∼1.5)Ti-(3∼6)Ta alloys.” Metals and Materials International, Vol. 22, No. 5, (2016), 789–796.
7.     Duan, R., Jalowicka, A., Unocic, K., Pint, B. A., Huczkowski, P., Chyrkin, A., Grüner, D., Pillai, R., and Quadakkers, W. J. “Predicting Oxidation-Limited Lifetime of Thin-Walled Components of NiCrW Alloy 230.” Oxidation of Metals, Vol. 87, No. 1–2, (2017), 11–38.
8.     Sadeghimeresht, E., Reddy, L., Hussain, T., Huhtakangas, M., Markocsan, N., and Joshi, S. “Influence of KCl and HCl on high temperature corrosion of HVAF-sprayed NiCrAlY and NiCrMo coatings.” Materials and Design, Vol. 148, (2018), 17–29.
9.     Yun, D. W., Seo, S. M., Jeong, H. W., and Yoo, Y. S. “Effect of refractory elements and Al on the high temperature oxidation of Ni-base superalloys and modelling of their oxidation resistance.” Journal of Alloys and Compounds, Vol. 710, (2017), 8–19.
10.   Gandomi, A. H., and Roke, D. A. “Assessment of artificial neural network and genetic programming as predictive tools.” Advances in Engineering Software, Vol. 88, (2015), 63–72.
11.   Karahan, I. H., and Özdemir, R. “A comparison for grain size calculation of Cu-Zn alloys with genetic programming and neural networks.” Acta Physica Polonica A, Vol. 128, No. 2, (2015), 427–431.
12.   Coşkun, M. İ., and Karahan, İ. H. “Modeling corrosion performance of the hydroxyapatite coated CoCrMo biomaterial alloys.” Journal of Alloys and Compounds, Vol. 745, (2018), 840–848.
13.   Ashtiani, H. R. R., and Shahsavari, P. “A comparative study on the phenomenological and artificial neural network models to predict hot deformation behavior of AlCuMgPb alloy.” Journal of Alloys and Compounds, Vol. 687, (2016), 263–273.
14.   Xu, D. S., Wang, H., Zhang, J. H., Bai, C. G., and Yang, R. “Titanium Alloys: From Properties Prediction to Performance Optimization.” In Handbook of Materials Modeling (pp. 113–151), Springer International Publishing, 2020.
15.   Shakiba, M., Khayati, G. R., and Zeraati, M. “State-of-the-art predictive modeling of hydroxyapatite nanocrystallite size: a hybrid density functional theory and artificial neural networks.” Journal of Sol-Gel Science and Technology, Vol. 92, No. 3, (2019), 641–651.
16.   Mahdavi Jafari, M., and Khayati, G. R. “Prediction of hydroxyapatite crystallite size prepared by sol–gel route: gene expression programming approach.” Journal of Sol-Gel Science and Technology, Vol. 86, No. 1, (2018), 112–125.
17.   Jafari, M. M., Khayati, G. R., Hosseini, M., and Danesh-Manesh, H. “Modeling and Optimization of Roll-bonding Parameters for Bond Strength of Ti/Cu/Ti Clad Composites by Artificial Neural Networks and Genetic Algorithm.” International Journal of Engineering Transactions C: Aspects, Vol. 30, No. 12, (2017), 1885–1893.
18.   Xu, C., Rangaiah, G. P., and Zhao, X. S. “Application of Artificial Neural Network and Genetic Programming in Modeling and Optimization of Ultraviolet Water Disinfection Reactors.” Chemical Engineering Communications, Vol. 202, No. 11, (2015), 1415–1424.
19.   Vakili, M., Khosrojerdi, S., Aghajannezhad, P., and Yahyaei, M. “A hybrid artificial neural network-genetic algorithm modeling approach for viscosity estimation of graphene nanoplatelets nanofluid using experimental data.” International Communications in Heat and Mass Transfer, Vol. 82, (2017), 40–48.
20.   Raza, M. Q., and Khosravi, A. “A review on artificial intelligence based load demand forecasting techniques for smart grid and buildings.” Renewable and Sustainable Energy Reviews, Vol. 50, (2015), 1352-1372.
21.   khosrojerdi, S., Vakili, M., Yahyaei, M., and Kalhor, K. “Thermal conductivity modeling of graphene nanoplatelets/deionized water nanofluid by MLP neural network and theoretical modeling using experimental results.” International Communications in Heat and Mass Transfer, Vol. 74, (2016), 11–17.
22.   Mahdavi, M., and Khayati, G. R. “Artificial Neural Network Based Prediction Hardness of Al2024-Multiwall Carbon Nanotube Composite Prepared by Mechanical Alloying.” International Journal of Engineering Transactions C: Aspects, Vol. 29, No. 12, (2016), 1726–1733.
23.   Kalidass, S., and Mathavaraj Ravikumar, T. “Cutting Force Prediction in End Milling Process of AISI 304 Steel Using Solid Carbide Tools.” International Journal of Engineering, Transactions A:  Basics, Vol. 28, No. 7, (2015), 1074–1081.
24.   shafaei, A., and Khayati, G. R. “A predictive model on size of silver nanoparticles prepared by green synthesis method using hybrid artificial neural network-particle swarm optimization algorithm.” Measurement: Journal of the International Measurement Confederation, Vol. 151, (2020), 107199.
25.   da Silva, I. N., Hernane Spatti, D., Andrade Flauzino, R., Liboni, L. H. B., dos Reis Alves, S. F., da Silva, I. N., Hernane Spatti, D., Andrade Flauzino, R., Liboni, L. H. B., and dos Reis Alves, S. F. “Artificial Neural Network Architectures and Training Processes.” In Artificial Neural Networks (pp. 21–28). Springer International Publishing, 2017.
26.   Maleki, E., and Kashyzadeh, K. R. “Effects of the hardened nickel coating on the fatigue behavior of CK45 steel: Experimental, finite element method, and artificial neural network modeling.” Iranian Journal of Materials Science and Engineering, Vol. 14, No. 4, (2017), 81–99.
27.   Ansari, A., Heras, M., Nones, J., Mohammadpoor, M., and Torabi, F. “Predicting the performance of steam assisted gravity drainage (SAGD) method utilizing artificial neural network (ANN).” Petroleum, (2019). (In press)
28.   Gara, S., and Tsoumarev, O. “Optimization of cutting conditions in slotting of multidirectional CFRP laminate.” International Journal of Advanced Manufacturing Technology, Vol. 95, No. 9–12, (2018), 3227–3242.
29.   Gupta, I. K., Choubey, A., and Choubey, S. “Particle swarm optimization with selective multiple inertia weights.” In 8th International Conference on Computing, Communications and Networking Technologies, (2017), 1-6.
30.   Kumar, N., and Kumar Sharma, S. “Inertia weight controlled pso for task scheduling in cloud computing.” In 2018 International Conference on Computing, Power and Communication Technologies, (2018), 155–160.
31.   Nouiri, M., Bekrar, A., Jemai, A., Niar, S., and Ammari, A. C. “An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem.” Journal of Intelligent Manufacturing, Vol. 29, No. 3, (2018), 603–615.
32.   Ebrahimzade, H., Khayati, G. R., and Schaffie, M. “A novel predictive model for estimation of cobalt leaching from waste Li-ion batteries: Application of genetic programming for design.” Journal of Environmental Chemical Engineering, Vol. 6, No. 4, (2018), 3999–4007.
33.   Mansouri, I., Kisi, O., Sadeghian, P., Lee, C.-H., and Hu, J. “Prediction of Ultimate Strain and Strength of FRP-Confined Concrete Cylinders Using Soft Computing Methods.” Applied Sciences, Vol. 7, No. 751, (2017), 1–14.
34.   Ferreira, C. “Gene Expression Programming in Problem Solving.” In Soft Computing and Industry (pp. 635–653). Springer London, 2002.
35.   Hoseinian, F. S., Faradonbeh, R. S., Abdollahzadeh, A., Rezai, B., and Soltani-Mohammadi, S. “Semi-autogenous mill power model development using gene expression programming.” Powder Technology, Vol. 308, (2017), 61–69.
36.   Mansouri, I., Chacón, R., and Hu, J. W. “Improved predictive model to the cross-sectional resistance of CFT.” Journal of Mechanical Science and Technology, Vol. 31, No. 8, (2017), 3887–3895.
37.   Mahdavi jafari, M., and Reza Khayati, G. “Adaptive neuro-fuzzy inference system and neural network in predicting the size of monodisperse silica and process optimization via simulated annealing algorithm.” Journal of Ultrafine Grained and Nanostructured Materials, Vol. 51, No. 1, (2018), 43–52.
38.   Al-Mosawe, A., Kalfat, R., and Al-Mahaidi, R. “Strength of Cfrp-steel double strap joints under impact loads using genetic programming.” Composite Structures, Vol. 160, (2017), 1205–1211.
39.   Mansouri, I., Hu, J., and Kisi, O. “Novel Predictive Model of the Debonding Strength for Masonry Members Retrofitted with FRP.” Applied Sciences, Vol. 6, No. 337, (2016), 1–13.
40.   Gholampour, A., Gandomi, A. H., and Ozbakkaloglu, T. “New formulations for mechanical properties of recycled aggregate concrete using gene expression programming.” Construction and Building Materials, Vol. 130, (2017), 122–145.
41.   Khandelwal, M., Armaghani, D. J., Faradonbeh, R. S., Ranjith, P. G., and Ghoraba, S. “A new model based on gene expression programming to estimate air flow in a single rock joint.” Environmental Earth Sciences, Vol. 75, No. 9, (2016), 1–13.
42.   Bakhsheshi-Rad, H. R., Abdellahi, M., Hamzah, E., Ismail, A. F., and Bahmanpour, M. “Modelling corrosion rate of biodegradable magnesium-based alloys: The case study of Mg-Zn-RE-xCa (x = 0, 0.5, 1.5, 3 and 6 wt%) alloys.” Journal of Alloys and Compounds, Vol. 687, (2016), 630–642.
43.   Birks, N., Meier, G. H., and Pettit, F. S. Introduction to the High Temperature Oxidation of Metals. Cambridge University Press, 2006. Retrieved from
44.   Park, S.-J., Seo, S.-M., Yoo, Y.-S., Jeong, H.-W., and Jang, H. “Statistical Study of the Effects of the Composition on the Oxidation Resistance of Ni-Based Superalloys” Journal of Nanomaterials, Vol. 2015, (2015), 1–11.