Research Article
BibTex RIS Cite
Year 2023, Volume: 41 Issue: 2, 302 - 321, 30.04.2023

Abstract

References

  • REFERENCES
  • [1] Kam M, Saruhan H. Vibration damping capac-ity of deep cyrogenic treated AISI 4140 steel shaft supported by rolling element bearings. Mater Test 2021;63:742−747. [CrossRef]
  • [2] Hirane H, Belarbi MO, Houari MSA, Tounsi A. On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Eng Comput 2021;38:3. [CrossRef]
  • [3] Kam M. Effects of deep cyrogenic treatment on machinability, hardness and microstructure in dry tuning process of tempered steels. P I Mech Eng E-J Pro 2020;235:927−936. [CrossRef]
  • [4] Do VNV, Lee CH. Static bending and free vibration analysis of multilayered composite cylindrical and spherical panels reinforced with graphene platelets by using isogeometric analysis method. Eng Struct 2020; 215:110682. [CrossRef]
  • [5] Kam M, Demirtaş M. Experimental analysis of the effect of mechanical properties and microstruc-ture on tool vibration and surface quality in dry tuning of hardened AISI 4340 steels. Surf Rev Lett 2021;28:1−13. [CrossRef]
  • [6] He JH. Generalized variational principles for buckling analysis of circular cylinders. Acta Mech 2020;231:899−906. [CrossRef]
  • [7] Kam M, Demirtaş M. Analysis of tool vibration and surface roughness during turning process of tem-pered steel samples using Taguchi method. P I Mech Eng E-J Pro 2021;235:1429−1438. [CrossRef]
  • [8] Bagheri B, Abdollahzadeh A, Sharifi F, Abbasi M. The role of vibration and pass number on micro-structure and mechanical properties of AZ91/SiC composite layer during friction stir processing. P I Mech ENG C-J Mech Eng Sci 2022;236:2312−2326.[CrossRef]
  • [9] Kam M, Şeremet M. Experimental and statistical inves-tigation of surface roughness and vibration during fin-ish turning of AISI 4140 steel workpiece under cooling method. Surf Rev Lett 2021;28:10. [CrossRef]
  • [10] Şengül Ö, Kam M. Analysis of radial tire design and dynamic analysis for sustainable production. IMASCON 2019; Kocaeli, Turkey.
  • [11] Daş DB, Birant D. Ordered physical human activity recognition based on ordinal classification.Turk J Electr Comput Sci 2021;29:2416−2436. [CrossRef]
  • [12] Zhan Z, Li H. A novel approach based on the elas-toplastic fatigue damage and machine learning models for life prediction of aerospace alloy parts fabricated by additive manufacturing. Int J Fatigue 2021;145:106089. [CrossRef]
  • [13] Kardani N, Zhou A, Nazem M, Shen SL. Estimation of Bearing Capacity of Piles in Cohesionless Soil Using Optimised Machine Learning Approaches. Geotech Geol Eng 2020;38:2271−2291. [CrossRef]
  • [14] Boiangiu M, Ceausu V, Untaroiu CD. A transfer matrix method for free vibration analysis of eul-er-bernoulli beams with variable cross section. J Vib Cont 2016;22:2591−2602. [CrossRef]
  • [15] Chen M, Jin G, Zhang, Y, Niu F, Liu Z. Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thick-ness. Comp Struct 2019;207:304−322. [CrossRef]
  • [16] Pradhan KK, Chakraverty S. Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions. J Braz Soc Mech Sci 2017;39:3295−3313. [CrossRef]
  • [17] Hong CC. Free vibration frequency of thick FGM spherical shells with simply homogeneous equation by using TSDT. J Braz Soc Mech Sci 2020;42:159.[CrossRef]
  • [18] Laory I, Trinh TN, Smith IFC, Brownjohn JMW. Methodologies for predicting natural frequency variation of a suspension bridge. Eng Struct 2014;80:211−221. [CrossRef]
  • [19] Avcar M, Saplioglu K. An artificial neural network application for estimation of natural frequencies of beams. Int J Adv Comput Sci Appl 2015;6:94−102. [CrossRef]
  • [20] Dey S, Mukhopadhyay T, Spickenheuer A, Gohs U, Adhikari S. Uncertanity quantification in nat-ural frequency of composite plates - an artificial neural network based approach. Adv Comp Lett 2016;25:43−48. [CrossRef]
  • [21] Banerjee A, Pohit G, Panigrahi B. Vibration anal-ysis and prediction natural frequencies of cracked timoshenko beam by two optimization techniques-cascade ann and anfis. Mater Today Proceed 2017;4:9909−9913. [CrossRef]
  • [22] Nikoo M, Hadzima-Nyarko M, Nyarko EK, Nikoo M. Determining the natural frequency of cantilever beams using ann and heuristic search. Appl Artif Intelligence 2018;32:309−334. [CrossRef]
  • [23] Karsh PK, Mukhopadhyay T, Dey S. Stochastic investigation of natural frequency for function-ally graded plates. IOP Conf Ser Mater Sci Eng 2018;326:012003. [CrossRef]
  • [24] Ali F, Chowdary BV. Natural frequency prediction of fdm manufactured parts using ann approach. IFAC-PapersOnLine 2019;52:403−408. [CrossRef]
  • [25] Atilla D, Sencan C, Goren Kiral B, Kiral Z. Free vibration and buckling analyses of laminated composite plates with cutout. Arch Appl Mech 2020;11:2433−2448. [CrossRef]
  • [26] Jayasundara N, Thambiratnam DP, Chan THT, Nguyen A. Damage detection and quantification in deck type arch bridges using vibration based meth- ods and artificial neural networks 2020;109:104265.[CrossRef]
  • [27] Saeed RA, Galybin AN, Popov V. Crack identifica-tion in curvilinear beams by using ann and anfis based on natural frequencies and frequency response funcitons. Neural Comput Appl 2012;21:1629−1645. [CrossRef]
  • [28] Hakim SJS, Razak HA. Structural damage detection of steel bridge girder using artificial neural net-works and finite element models. Steel Comp Struct 2013;14:367−377. [CrossRef]
  • [29] Yan B, Cui Y, Zhang L, Zhang C, Yang Y, Bao Z, Ning G. Beam structure damage identification based on bp neural network and support vector machine. Math Prob Eng 2014;2014:850141. [CrossRef]
  • [30] De Fenza A, Sorrentino A, Vitello P. Application of artificial neural networks and probability ellipse methods for damage detection using lamb waves. Comp Struct 2015;133:390−403. [CrossRef]
  • [31] Satpal SB, Guha A, Banerjee S. Damage identification in aluminum beams using support vector machine: numerical and experimental studies. Struct Cont Health Monitor 2015;23:446−457. [CrossRef]
  • [32] Ghiasi R, Torkzadeh P, Noori M. A machine-learn-ing approach for structural damage detection using least square support vector machine based on a new combinational kernel function. Struct Health Monitor 2016;15:302−316. [CrossRef]
  • [33] Neves AC, Gonzalez I, Leander J, Karoumi R. Structural health monitoring of bridges: a mod-el-free ann-based approach to damage detection. J Civil Struct Health Monitor 2017;7:689−702.[CrossRef]
  • [34] Kourehli SS. Prediction of unmeasured mode shapes and structural damage detection using least squares support vector machine. Struct Monitor Maint 2018;5:379−390.
  • [35] Hassan AKF, Mohammed LS, Abdulsamad HJ. Experimental and artificial neural network ann investigation of bending fatigue behavior of glass fiber/polyester composite shafts. J Braz Soc Mech Sci Eng 2018;40:201. [CrossRef]
  • [36] Ghiasi R, Ghasemi MR, Noori M. Comparative studies of metamodeling and ai-based techniques in damage detection of structures. Adv Eng Soft 2018;125:101−112. [CrossRef]
  • [37] Tan ZX, Thambiratnam DP, Chan THT, Gordan M, Razak HA. Damage detection in steel-concrete composite bridge using vibration characteris-tics and artificial neural network. Struct Infra Eng 2020;16:1247−1261. [CrossRef]
  • [38] Tran-Ngoc H, Khatir S, De Roeck G, Bui-Tien T, Wahab MA. An efficient artificial neural network for damage detection in bridges and beam-like struc-tures by improving training parameters using cuckoo search algorithm. Eng Struct 2019;199:109637.[CrossRef]
  • [39] He M, Wang Y, Ramakrishnan KR, Zhang Z. A comparison of machine learning algorithms for assessment of delamination in fiber-reinforced polymer composite beams. Struct Health Monitor 2020;20:1997−2012. [CrossRef]
  • [40] Gan BS. An isogenometric approach to beam struc-tures. Cham, Springer; 2018. [CrossRef]
  • [41] Frank E. Fully supervised training of gaussian radial basis function networks in WEKA. 2014.
  • [42] Breiman L. Random forests. Mach Learn 2001;45:5−32. [CrossRef]
  • [43] Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. New York, Springer-Verlag, NY:Springer; 2009. [CrossRef]
  • [44] Stathakis D. How many hidden layers and nodes?. Int J Remote Sens 2007;30:2133−2147. [CrossRef]
  • [45] Uzair M, Jamil N. Effects of hidden layers on the efficiency of neural networks. 2020 IEEE 23rd Int Multitopic Conf. [CrossRef]
  • [46] Tran TTK, Lee T, Kim JS. Increasing neurons or deepening layers in forecasting maximum tempera-ture time series?. Atmoshpere 2020;11:1072. [CrossRef]
  • [47] Smola AJ, Schölkopf B. A tutorial on support vector regression. Stat Comput 2004;14:199−222. [CrossRef]
  • [48] Üstün B, Melssen WJ, Buydens LMC. Facilitating the application of support vector regression by using a universal pearson vii function based kernel. Chemometr Intell Lab Syst 2006;81:29−40. [CrossRef]

Prediction of the natural frequencies of various beams using regression machine learning models

Year 2023, Volume: 41 Issue: 2, 302 - 321, 30.04.2023

Abstract

Machine learning models are widely used for decades in various engineering applications, such as structural health monitoring, optimization of the properties of engineering systems or structures. For instance, in structural engineering, researchers have investigated machine learning techniques for the prediction of the natural frequencies, damage detection, and de-sign optimization of beams, frames, plates, and many other structures. Using machine learn-ing is advantageous since machine learning can reduce the cost and time consumption to solve real-world problems. These techniques do not require powerful computers and soft-ware, unlike numerical analysis methods to solve such problems. To benefit such positive as-pects of the machine learning techniques, the prediction of the first ten natural frequencies of aluminum and steel very thin, thin, and thick beam structures under fixed-free, fixed-sim-ply supported, and simply supported boundary conditions by using Radial Basis Function Regressor, Random Forest Regressor, Multilayer Perceptrons Regressor, and Support Vector Machine Regressor with Pearson VII Universal Function Kernel (Puk) has been presented. The dataset required for the analysis is obtained via the Finite Element Analysis considering Euler-Bernoulli and Timoshenko Beam Theories. The performance of the machine learning models has been investigated and compared by examining (i) the thickness-length ratio, (ii) boundary conditions, and (iii) natural frequencies of the beam structures. Results indicate that the considered regression machine learning models are effective in predicting the natural frequencies of beam structures. Among all four regression machine learning models, Support Vector Machine Regressor with Puk and Random Forest models are robust and accurately predict the natural frequency values of the structures by an average accuracy of 98.78% and 98.88% regardless of the boundary conditions and thickness-length ratio of beam structures. On the other hand, Radial Basis Function Regressor and Multilayer Perceptron Regressors predict the first ten natural frequencies by 96.36% and 94.17%, respectively.

References

  • REFERENCES
  • [1] Kam M, Saruhan H. Vibration damping capac-ity of deep cyrogenic treated AISI 4140 steel shaft supported by rolling element bearings. Mater Test 2021;63:742−747. [CrossRef]
  • [2] Hirane H, Belarbi MO, Houari MSA, Tounsi A. On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Eng Comput 2021;38:3. [CrossRef]
  • [3] Kam M. Effects of deep cyrogenic treatment on machinability, hardness and microstructure in dry tuning process of tempered steels. P I Mech Eng E-J Pro 2020;235:927−936. [CrossRef]
  • [4] Do VNV, Lee CH. Static bending and free vibration analysis of multilayered composite cylindrical and spherical panels reinforced with graphene platelets by using isogeometric analysis method. Eng Struct 2020; 215:110682. [CrossRef]
  • [5] Kam M, Demirtaş M. Experimental analysis of the effect of mechanical properties and microstruc-ture on tool vibration and surface quality in dry tuning of hardened AISI 4340 steels. Surf Rev Lett 2021;28:1−13. [CrossRef]
  • [6] He JH. Generalized variational principles for buckling analysis of circular cylinders. Acta Mech 2020;231:899−906. [CrossRef]
  • [7] Kam M, Demirtaş M. Analysis of tool vibration and surface roughness during turning process of tem-pered steel samples using Taguchi method. P I Mech Eng E-J Pro 2021;235:1429−1438. [CrossRef]
  • [8] Bagheri B, Abdollahzadeh A, Sharifi F, Abbasi M. The role of vibration and pass number on micro-structure and mechanical properties of AZ91/SiC composite layer during friction stir processing. P I Mech ENG C-J Mech Eng Sci 2022;236:2312−2326.[CrossRef]
  • [9] Kam M, Şeremet M. Experimental and statistical inves-tigation of surface roughness and vibration during fin-ish turning of AISI 4140 steel workpiece under cooling method. Surf Rev Lett 2021;28:10. [CrossRef]
  • [10] Şengül Ö, Kam M. Analysis of radial tire design and dynamic analysis for sustainable production. IMASCON 2019; Kocaeli, Turkey.
  • [11] Daş DB, Birant D. Ordered physical human activity recognition based on ordinal classification.Turk J Electr Comput Sci 2021;29:2416−2436. [CrossRef]
  • [12] Zhan Z, Li H. A novel approach based on the elas-toplastic fatigue damage and machine learning models for life prediction of aerospace alloy parts fabricated by additive manufacturing. Int J Fatigue 2021;145:106089. [CrossRef]
  • [13] Kardani N, Zhou A, Nazem M, Shen SL. Estimation of Bearing Capacity of Piles in Cohesionless Soil Using Optimised Machine Learning Approaches. Geotech Geol Eng 2020;38:2271−2291. [CrossRef]
  • [14] Boiangiu M, Ceausu V, Untaroiu CD. A transfer matrix method for free vibration analysis of eul-er-bernoulli beams with variable cross section. J Vib Cont 2016;22:2591−2602. [CrossRef]
  • [15] Chen M, Jin G, Zhang, Y, Niu F, Liu Z. Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thick-ness. Comp Struct 2019;207:304−322. [CrossRef]
  • [16] Pradhan KK, Chakraverty S. Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions. J Braz Soc Mech Sci 2017;39:3295−3313. [CrossRef]
  • [17] Hong CC. Free vibration frequency of thick FGM spherical shells with simply homogeneous equation by using TSDT. J Braz Soc Mech Sci 2020;42:159.[CrossRef]
  • [18] Laory I, Trinh TN, Smith IFC, Brownjohn JMW. Methodologies for predicting natural frequency variation of a suspension bridge. Eng Struct 2014;80:211−221. [CrossRef]
  • [19] Avcar M, Saplioglu K. An artificial neural network application for estimation of natural frequencies of beams. Int J Adv Comput Sci Appl 2015;6:94−102. [CrossRef]
  • [20] Dey S, Mukhopadhyay T, Spickenheuer A, Gohs U, Adhikari S. Uncertanity quantification in nat-ural frequency of composite plates - an artificial neural network based approach. Adv Comp Lett 2016;25:43−48. [CrossRef]
  • [21] Banerjee A, Pohit G, Panigrahi B. Vibration anal-ysis and prediction natural frequencies of cracked timoshenko beam by two optimization techniques-cascade ann and anfis. Mater Today Proceed 2017;4:9909−9913. [CrossRef]
  • [22] Nikoo M, Hadzima-Nyarko M, Nyarko EK, Nikoo M. Determining the natural frequency of cantilever beams using ann and heuristic search. Appl Artif Intelligence 2018;32:309−334. [CrossRef]
  • [23] Karsh PK, Mukhopadhyay T, Dey S. Stochastic investigation of natural frequency for function-ally graded plates. IOP Conf Ser Mater Sci Eng 2018;326:012003. [CrossRef]
  • [24] Ali F, Chowdary BV. Natural frequency prediction of fdm manufactured parts using ann approach. IFAC-PapersOnLine 2019;52:403−408. [CrossRef]
  • [25] Atilla D, Sencan C, Goren Kiral B, Kiral Z. Free vibration and buckling analyses of laminated composite plates with cutout. Arch Appl Mech 2020;11:2433−2448. [CrossRef]
  • [26] Jayasundara N, Thambiratnam DP, Chan THT, Nguyen A. Damage detection and quantification in deck type arch bridges using vibration based meth- ods and artificial neural networks 2020;109:104265.[CrossRef]
  • [27] Saeed RA, Galybin AN, Popov V. Crack identifica-tion in curvilinear beams by using ann and anfis based on natural frequencies and frequency response funcitons. Neural Comput Appl 2012;21:1629−1645. [CrossRef]
  • [28] Hakim SJS, Razak HA. Structural damage detection of steel bridge girder using artificial neural net-works and finite element models. Steel Comp Struct 2013;14:367−377. [CrossRef]
  • [29] Yan B, Cui Y, Zhang L, Zhang C, Yang Y, Bao Z, Ning G. Beam structure damage identification based on bp neural network and support vector machine. Math Prob Eng 2014;2014:850141. [CrossRef]
  • [30] De Fenza A, Sorrentino A, Vitello P. Application of artificial neural networks and probability ellipse methods for damage detection using lamb waves. Comp Struct 2015;133:390−403. [CrossRef]
  • [31] Satpal SB, Guha A, Banerjee S. Damage identification in aluminum beams using support vector machine: numerical and experimental studies. Struct Cont Health Monitor 2015;23:446−457. [CrossRef]
  • [32] Ghiasi R, Torkzadeh P, Noori M. A machine-learn-ing approach for structural damage detection using least square support vector machine based on a new combinational kernel function. Struct Health Monitor 2016;15:302−316. [CrossRef]
  • [33] Neves AC, Gonzalez I, Leander J, Karoumi R. Structural health monitoring of bridges: a mod-el-free ann-based approach to damage detection. J Civil Struct Health Monitor 2017;7:689−702.[CrossRef]
  • [34] Kourehli SS. Prediction of unmeasured mode shapes and structural damage detection using least squares support vector machine. Struct Monitor Maint 2018;5:379−390.
  • [35] Hassan AKF, Mohammed LS, Abdulsamad HJ. Experimental and artificial neural network ann investigation of bending fatigue behavior of glass fiber/polyester composite shafts. J Braz Soc Mech Sci Eng 2018;40:201. [CrossRef]
  • [36] Ghiasi R, Ghasemi MR, Noori M. Comparative studies of metamodeling and ai-based techniques in damage detection of structures. Adv Eng Soft 2018;125:101−112. [CrossRef]
  • [37] Tan ZX, Thambiratnam DP, Chan THT, Gordan M, Razak HA. Damage detection in steel-concrete composite bridge using vibration characteris-tics and artificial neural network. Struct Infra Eng 2020;16:1247−1261. [CrossRef]
  • [38] Tran-Ngoc H, Khatir S, De Roeck G, Bui-Tien T, Wahab MA. An efficient artificial neural network for damage detection in bridges and beam-like struc-tures by improving training parameters using cuckoo search algorithm. Eng Struct 2019;199:109637.[CrossRef]
  • [39] He M, Wang Y, Ramakrishnan KR, Zhang Z. A comparison of machine learning algorithms for assessment of delamination in fiber-reinforced polymer composite beams. Struct Health Monitor 2020;20:1997−2012. [CrossRef]
  • [40] Gan BS. An isogenometric approach to beam struc-tures. Cham, Springer; 2018. [CrossRef]
  • [41] Frank E. Fully supervised training of gaussian radial basis function networks in WEKA. 2014.
  • [42] Breiman L. Random forests. Mach Learn 2001;45:5−32. [CrossRef]
  • [43] Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. New York, Springer-Verlag, NY:Springer; 2009. [CrossRef]
  • [44] Stathakis D. How many hidden layers and nodes?. Int J Remote Sens 2007;30:2133−2147. [CrossRef]
  • [45] Uzair M, Jamil N. Effects of hidden layers on the efficiency of neural networks. 2020 IEEE 23rd Int Multitopic Conf. [CrossRef]
  • [46] Tran TTK, Lee T, Kim JS. Increasing neurons or deepening layers in forecasting maximum tempera-ture time series?. Atmoshpere 2020;11:1072. [CrossRef]
  • [47] Smola AJ, Schölkopf B. A tutorial on support vector regression. Stat Comput 2004;14:199−222. [CrossRef]
  • [48] Üstün B, Melssen WJ, Buydens LMC. Facilitating the application of support vector regression by using a universal pearson vii function based kernel. Chemometr Intell Lab Syst 2006;81:29−40. [CrossRef]
There are 49 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section Research Articles
Authors

Oğuzhan Daş 0000-0001-7623-9278

Publication Date April 30, 2023
Submission Date August 18, 2021
Published in Issue Year 2023 Volume: 41 Issue: 2

Cite

Vancouver Daş O. Prediction of the natural frequencies of various beams using regression machine learning models. SIGMA. 2023;41(2):302-21.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/