Skip to main content

On the modeling of the annual corrosion rate in main cables of suspension bridges using combined soft computing model and a novel nature-inspired algorithm


Suspension bridges are critical components of transport infrastructure around the world. Therefore, their operating conditions should be effectively monitored to ensure their safety and reliability. However, the main cables of suspension bridges inevitably deteriorate over time due to corrosion, as a result of their operational and environmental conditions. Thus, accurate annual corrosion rate predictions are crucial for maintaining reliable structures and optimal maintenance operations. However, the corrosion rate is a chaotic and complex phenomenon with highly nonlinear behavior. This paper proposes a novel predictive model for the estimation of the annual corrosion rate in the main cables of suspension bridges. This is a hybrid model based on the multilayer perceptron (MLP) technique optimized using marine predators algorithm (MPA). In addition, well-known metaheuristic approaches such as the genetic algorithm (GA) and particle swarm algorithm (PSO) are employed to optimize the MLP. In order to implement the proposed model, a comprehensive database composed of 309 sample tests on the annual corrosion rate from all around the world, including various factors related to the surrounding environmental properties, is utilized. In addition, several input combinations are proposed for investigating the trigger factors in modeling the annual corrosion rate. The performance of the proposed models is evaluated using various statistical and graphical criteria. The results of this study demonstrate that the proposed hybrid MLP-MPA model provides stable and accurate predictions, while it transcends the previously developed approaches for solving this problem. The effectiveness of the MLP-MPA model shows that it can be used for further studies on the reliability analysis of the main cables of suspension bridges.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. 1.

    Barton SC, Vermaas GW, Duby PF, West AC, Betti R (2000) Accelerated corrosion and embrittlement of high-strength bridge wire. J Mater Civ Eng 12:33–38

    Article  Google Scholar 

  2. 2.

    Chavel BW, Leshko BJ. (2012) Primer for the inspection and strength evaluation of suspension bridge cables. Government Printing Office

  3. 3.

    Mayrbaurl RM, Camo S (2004) Guidelines for inspection and strength evaluation of suspension bridge parallel-wire cables, vol 534. Transportation Research Board, Washington

    Google Scholar 

  4. 4.

    El Amine Ben Seghier M, Keshtegar B, Elahmoune B (2018) Reliability analysis of low, mid and high-grade strength corroded pipes based on plastic flow theory using adaptive nonlinear conjugate map. Eng Fail Anal.

    Article  Google Scholar 

  5. 5.

    Bagheri M, Peng Z-P, El Amine BSM, Ben KB (2020) Hybrid intelligent method for fuzzy reliability analysis of corroded X100 steel pipelines. Eng Comput.

    Article  Google Scholar 

  6. 6.

    Kim H-K, Lee M-J, Chang S-P (2002) Non-linear shape-finding analysis of a self-anchored suspension bridge. Eng Struct 24:1547–1559

    Article  Google Scholar 

  7. 7.

    Revie RW (2008) Corrosion and corrosion control: an introduction to corrosion science and engineering. John Wiley, Hoboken

    Book  Google Scholar 

  8. 8.

    Saha JK (2012) Corrosion of constructional steels in marine and industrial environment: frontier work in atmospheric corrosion. Springer Science & Business Media, Berlin

    Google Scholar 

  9. 9.

    Betti R, Yanev B (1999) Conditions of suspension bridge cables: New York City case study. Transp Res Rec 1654:105–112

    Article  Google Scholar 

  10. 10.

    Bieniek M, Betti R (1998) Cable conditions for New York City bridges. New York City Department of Transportation, New York

    Google Scholar 

  11. 11

    Eiselstein LE, Caligiuri RD (1987) Atmospheric corrosion of the suspension cables on the Williamsburg Bridge. In: Dean S, Lee T (eds) Degradation of metals in the atmosphere. ASTM International, West Conshohocken

    Google Scholar 

  12. 12.

    Stahl FL, Gagnon CP (1995) Cable corrosion in bridges and other structures: causes and solutions. American Society of Civil Engineers, New York

    Google Scholar 

  13. 13.

    Suzumura K, Nakamura S (2004) Environmental factors affecting corrosion of galvanized steel wires. J Mater Civ Eng 16:1–7

    Article  Google Scholar 

  14. 14.

    Deeble Sloane MJ, Betti R, Marconi G, Hong AL, Khazem D (2013) Experimental analysis of a nondestructive corrosion monitoring system for main cables of suspension bridges. J Bridg Eng 18:653–662

    Article  Google Scholar 

  15. 15.

    De la Fuente D, Castano JG, Morcillo M (2007) Long-term atmospheric corrosion of zinc. Corros Sci 49:1420–1436

    Article  Google Scholar 

  16. 16.

    Alamilla JL, Sosa E (2008) Stochastic modelling of corrosion damage propagation in active sites from field inspection data. Corros Sci 50:1811–1819.

    Article  Google Scholar 

  17. 17.

    Valor A, Caleyo F, Alfonso L, Velazquez JC, Hallen JM (2013) Markov chain models for the stochastic modeling of pitting corrosion. Math Probl Eng.

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Romanoff M (1957) Underground corrosion. US Government, Washington

    Google Scholar 

  19. 19.

    Kamrunnahar M, Urquidi-Macdonald M (2010) Prediction of corrosion behavior using neural network as a data mining tool. Corros Sci 52:669–677

    Article  Google Scholar 

  20. 20.

    Yu X, Jiang F, Du J, Gong D (2019) A cross-domain collaborative filtering algorithm with expanding user and item features via the latent factor space of auxiliary domains. Pattern Recognit 94:96–109

    Article  Google Scholar 

  21. 21.

    Dashtipour K, Gogate M, Li J, Jiang F, Kong B, Hussain A (2020) A hybrid Persian sentiment analysis framework: integrating dependency grammar based rules and deep neural networks. Neurocomputing 380:1–10

    Article  Google Scholar 

  22. 22.

    Ben SMEA, Gao X-Z, Jafari-Asl J, Thai D-K, Ohadi S, Trung N-T (2021) Modeling the nonlinear behavior of ACC for SCFST columns using experimental-data and a novel evolutionary-algorithm. Structures 30:692–709

    Article  Google Scholar 

  23. 23.

    Yu X, Yang J, Xie Z (2014) Training SVMs on a bound vectors set based on fisher projection. Front Comput Sci 8:793–806

    MathSciNet  Article  Google Scholar 

  24. 24.

    Keshtegar B, Ben SMEA, Zio E, Correia JAFO, Zhu S-P, Trung N-T (2021) Novel efficient method for structural reliability analysis using hybrid nonlinear conjugate map-based support vector regression. Comput Methods Appl Mech Eng 381:113818

    MathSciNet  Article  Google Scholar 

  25. 25.

    Yu X, Chu Y, Jiang F, Guo Y, Gong D (2018) SVMs classification based two-side cross domain collaborative filtering by inferring intrinsic user and item features. Knowledge-Based Syst 141:80–91

    Article  Google Scholar 

  26. 26.

    Mai SH, Ben SMEA, Nguyen PL, Jafari-Asl J, Thai D-K (2020) A hybrid model for predicting the axial compression capacity of square concrete-filled steel tubular columns. Eng Comput.

    Article  Google Scholar 

  27. 27.

    Ben SMEA, Ouaer H, Ghriga MA, Menad NA, Thai D-K (2020) Hybrid soft computational approaches for modeling the maximum ultimate bond strength between the corroded steel reinforcement and surrounding concrete. Neural Comput Appl 33:1–16

    Google Scholar 

  28. 28.

    Jafari-Asl J, Ohadi S, Ben Seghier MEA, Trung N-T (2021) Accurate structural reliability analysis using an improved line-sampling-method-based slime mold algorithm. ASCE-ASME J Risk Uncertain Eng Syst Part A Civ Eng 7:4021015

    Article  Google Scholar 

  29. 29.

    Wen YF, Cai CZ, Liu XH, Pei JF, Zhu XJ, Xiao TT (2009) Corrosion rate prediction of 3C steel under different seawater environment by using support vector regression. Corros Sci 51:349–355.

    Article  Google Scholar 

  30. 30.

    Chou JS, Ngo NT, Chong WK (2017) The use of artificial intelligence combiners for modeling steel pitting risk and corrosion rate. Eng Appl Artif Intell 65:471–483.

    Article  Google Scholar 

  31. 31.

    El M, Ben A, Keshtegar B, Fah K, Zayed T, Abbassi R et al (2020) Prediction of maximum pitting corrosion depth in oil and gas pipelines. Eng Fail Anal 112:104505.

    Article  Google Scholar 

  32. 32.

    Ben SMEA, Keshtegar B, Taleb-Berrouane M, Abbassi R, Trung N-T (2021) Advanced intelligence frameworks for predicting maximum pitting corrosion depth in oil and gas pipelines. Process Saf Environ Prot 147:818–833

    Article  Google Scholar 

  33. 33.

    Lv Y, Wang J, Wang JJ, Xiong C, Zou L, Li L et al (2020) Steel corrosion prediction based on support vector machines. Chaos, Solitons Fractals 136:109807

    Article  Google Scholar 

  34. 34

    Karanci E, Betti R (2018) Modeling corrosion in suspension bridge main cables. I: annual corrosion rate. J Bridg Eng 23:4018025

    Article  Google Scholar 

  35. 35.

    Karanci E, Betti R (2018) Modeling corrosion in suspension bridge main cables. II: long-term corrosion and remaining strength. J Bridg Eng 23:4018026

    Article  Google Scholar 

  36. 36.

    Sexton RS, Gupta JND (2000) Comparative evaluation of genetic algorithm and backpropagation for training neural networks. Inf Sci (Ny) 129:45–59

    Article  Google Scholar 

  37. 37.

    Sexton RS, Dorsey RE, Johnson JD (1998) Toward global optimization of neural networks: a comparison of the genetic algorithm and backpropagation. Decis Support Syst 22:171–185

    Article  Google Scholar 

  38. 38.

    Seiffert U. (2001) Multiple layer perceptron training using genetic algorithms. In: ESANN, Citeseer, p. 159–64

  39. 39.

    Jafari-Asl J, Ben SMEA, Ohadi S, van Gelder P (2020) Efficient method using whale optimization algorithm for reliability-based design optimization of labyrinth spillway. Appl Soft Comput 101:107036

    Article  Google Scholar 

  40. 40.

    Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22:1–15

    Article  Google Scholar 

  41. 41.

    Rakitianskaia AS, Engelbrecht AP (2012) Training feedforward neural networks with dynamic particle swarm optimisation. Swarm Intell 6:233–270

    Article  Google Scholar 

  42. 42.

    Ouaer H, Hosseini AH, Amar MN, El M, Ben A, Ghriga MA et al (2020) Rigorous connectionist models to predict carbon dioxide solubility in various ionic liquids. Appl Sci.

    Article  Google Scholar 

  43. 43.

    Nait M, Abdelfetah M, Ouaer H, El Ben MA (2020) Modeling viscosity of CO2 at high temperature and pressure conditions. J Nat Gas Sci Eng.

    Article  Google Scholar 

  44. 44.

    Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377

    Article  Google Scholar 

  45. 45

    Yu G, Meng Z, Ma H, Liu L (2021) An adaptive Marine predators algorithm for optimizing a hybrid PV/DG/Battery system for a remote area in China. Energy Rep 7:398–412

    Article  Google Scholar 

  46. 46.

    Ebeed M, Alhejji A, Kamel S, Jurado F (2020) Solving the optimal reactive power dispatch using marine predators algorithm considering the uncertainties in load and wind-solar generation systems. Energies 13:4316

    Article  Google Scholar 

  47. 47.

    Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Kluwer Academic Publishers, New York

    Google Scholar 

  48. 48

    Ohadi S, Jafari-Asl J (2020) Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs. Flow Meas Instrum 77:101787

    Article  Google Scholar 

  49. 49.

    Kennedy J, Eberhart R. (1995) Particle swarm optimization. In: Neural Networks, 1995 Proceedings, IEEE Int Conf 4 :1942–8.

  50. 50.

    Jafari-Asl J, Kashkooli BS, Bahrami M (2020) Using particle swarm optimization algorithm to optimally locating and controlling of pressure reducing valves for leakage minimization in water distribution systems. Sustain Water Resour Manag 6:1–11

    Article  Google Scholar 

  51. 51.

    Moayedi H, Mehrabi M, Mosallanezhad M, Rashid ASA, Pradhan B (2019) Modification of landslide susceptibility mapping using optimized PSO-ANN technique. Eng Comput 35:967–984

    Article  Google Scholar 

  52. 52.

    Ben Seghier MEA, Carvalho H, Keshtegar B, Correia JAFO, Berto F (2020) Novel hybridized adaptive neuro-fuzzy inference system models based particle swarm optimization and genetic algorithms for accurate prediction of stress intensity factor. Fatigue Fract Eng Mater Struct 43:2653–2667

    Article  Google Scholar 

  53. 53.

    Keshtegare B, El Seghier MAB (2018) Modified response surface method basis harmony search to predict the burst pressure of corroded pipelines. Eng Fail Anal 89:177–199.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mohamed El Amine Ben Seghier.

Ethics declarations

Conflict of interest

The authors of the manuscript confirm that there are no conflicts of interest regarding its publication.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ben Seghier, M.E.A., Corriea, J.A.F.O., Jafari-Asl, J. et al. On the modeling of the annual corrosion rate in main cables of suspension bridges using combined soft computing model and a novel nature-inspired algorithm. Neural Comput & Applic 33, 15969–15985 (2021).

Download citation


  • Suspension bridges
  • Main cables
  • Annual corrosion rate
  • Artificial intelligence
  • Multilayer perceptron
  • Marine predators algorithm