Skip to main content
Erschienen in:

08.04.2022 | Original Article

A novel deep unsupervised learning-based framework for optimization of truss structures

verfasst von: Hau T. Mai, Qui X. Lieu, Joowon Kang, Jaehong Lee

Erschienen in: Engineering with Computers | Ausgabe 4/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, an efficient deep unsupervised learning (DUL)-based framework is proposed to directly perform the design optimization of truss structures under multiple constraints for the first time. Herein, the members’ cross-sectional areas are parameterized using a deep neural network (DNN) with the middle spatial coordinates of truss elements as input data. The parameters of the network, including weights and biases, are regarded as decision variables of the structural optimization problem, instead of the member’s cross-sectional areas as those of traditional optimization algorithms. A new loss function of the network model is constructed with the aim of minimizing the total structure weight so that all constraints of the optimization problem via unsupervised learning are satisfied. To achieve the optimal parameters, the proposed model is trained to minimize the loss function by a combination of the standard gradient optimizer and backpropagation algorithm. As soon as the learning process ends, the optimum weight of truss structures is indicated without utilizing any other time-consuming metaheuristic algorithms. Several illustrative examples are investigated to demonstrate the efficiency of the proposed framework in requiring much lower computational cost against other conventional methods, yet still providing high-quality optimal solutions.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Kaveh A, Mahjoubi S (2019) Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints. Eng Comput 35:1443–1462 Kaveh A, Mahjoubi S (2019) Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints. Eng Comput 35:1443–1462
2.
Zurück zum Zitat Ho-Huu V, Vo-Duy T, Luu-Van T, Le-Anh L, Nguyen-Thoi T (2016) Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme. Autom Constr 68:81–94 Ho-Huu V, Vo-Duy T, Luu-Van T, Le-Anh L, Nguyen-Thoi T (2016) Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme. Autom Constr 68:81–94
3.
Zurück zum Zitat Kaveh A, Talatahari S (2009) Size optimization of space trusses using big bang-big crunch algorithm. Comput Struct 87:1129–1140 Kaveh A, Talatahari S (2009) Size optimization of space trusses using big bang-big crunch algorithm. Comput Struct 87:1129–1140
4.
Zurück zum Zitat Khot N (1983) Nonlinear analysis of optimized structure with constraints on systemstability. AIAA J 21:1181–1186MATH Khot N (1983) Nonlinear analysis of optimized structure with constraints on systemstability. AIAA J 21:1181–1186MATH
5.
Zurück zum Zitat Khot N, Kamat M (1985) Minimum weight design of truss structures with geometric nonlinear behavior. AIAA J 23:139–144MATH Khot N, Kamat M (1985) Minimum weight design of truss structures with geometric nonlinear behavior. AIAA J 23:139–144MATH
6.
Zurück zum Zitat El-Sayed ME, Ridgely BJ, Sandgren E (1989) Nonlinear structural optimization using goal programming. Comput Struct 32:69–73MATH El-Sayed ME, Ridgely BJ, Sandgren E (1989) Nonlinear structural optimization using goal programming. Comput Struct 32:69–73MATH
7.
Zurück zum Zitat Saka M, Ulker M (1992) Optimum design of geometrically nonlinear space trusses. Comput Struct 42:289–299 Saka M, Ulker M (1992) Optimum design of geometrically nonlinear space trusses. Comput Struct 42:289–299
8.
Zurück zum Zitat Shin M-K, Park K-J, Park G-J (2007) Optimization of structures with nonlinear behavior using equivalent loads. Comput Methods Appl Mech Eng 196:1154–1167MATH Shin M-K, Park K-J, Park G-J (2007) Optimization of structures with nonlinear behavior using equivalent loads. Comput Methods Appl Mech Eng 196:1154–1167MATH
9.
Zurück zum Zitat Miguel LFF, Miguel LFF (2012) Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms. Expert Syst Appl 39:9458–9467 Miguel LFF, Miguel LFF (2012) Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms. Expert Syst Appl 39:9458–9467
10.
Zurück zum Zitat Lieu QX, Do DT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112 Lieu QX, Do DT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112
11.
Zurück zum Zitat Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968 Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968
12.
Zurück zum Zitat Kaveh A, Zolghadr A (2014) Democratic pso for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21 Kaveh A, Zolghadr A (2014) Democratic pso for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21
13.
Zurück zum Zitat Toğan V, Daloğlu AT (2006) Optimization of 3d trusses with adaptive approach in genetic algorithms. Eng Struct 28:1019–1027 Toğan V, Daloğlu AT (2006) Optimization of 3d trusses with adaptive approach in genetic algorithms. Eng Struct 28:1019–1027
14.
Zurück zum Zitat Zuo W, Bai J, Li B (2014) A hybrid oc-ga approach for fast and global truss optimization with frequency constraints. Appl Soft Comput 14:528–535 Zuo W, Bai J, Li B (2014) A hybrid oc-ga approach for fast and global truss optimization with frequency constraints. Appl Soft Comput 14:528–535
15.
Zurück zum Zitat Pierezan J, dos Santos Coelho L, Mariani VC, de Vasconcelos Segundo EH, Prayogo D (2021) Chaotic coyote algorithm applied to truss optimization problems. Comput Struct 242:106353 Pierezan J, dos Santos Coelho L, Mariani VC, de Vasconcelos Segundo EH, Prayogo D (2021) Chaotic coyote algorithm applied to truss optimization problems. Comput Struct 242:106353
16.
Zurück zum Zitat Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798 Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798
17.
Zurück zum Zitat Buntara G, Takahiro H, Aylie H, Alisjahbana S, As’ad S (2017) Evolutionary aco algorithms f or truss optimization problems. Proc Eng 171:1100–1107 Buntara G, Takahiro H, Aylie H, Alisjahbana S, As’ad S (2017) Evolutionary aco algorithms f or truss optimization problems. Proc Eng 171:1100–1107
18.
Zurück zum Zitat Kaveh A, Zakian P (2018) Improved gwo algorithm for optimal design of truss structures. Eng Comput 34:685–707 Kaveh A, Zakian P (2018) Improved gwo algorithm for optimal design of truss structures. Eng Comput 34:685–707
19.
Zurück zum Zitat Degertekin S (2012) Improved harmony search algorithms for sizing optimization of truss structures. Comput Struct 92:229–241 Degertekin S (2012) Improved harmony search algorithms for sizing optimization of truss structures. Comput Struct 92:229–241
20.
Zurück zum Zitat Le-Duc T, Nguyen Q-H, Nguyen-Xuan H (2020) Balancing composite motion optimization. Inf Sci 520:250–270MathSciNet Le-Duc T, Nguyen Q-H, Nguyen-Xuan H (2020) Balancing composite motion optimization. Inf Sci 520:250–270MathSciNet
21.
Zurück zum Zitat Fan H-Y, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129MathSciNetMATH Fan H-Y, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129MathSciNetMATH
22.
Zurück zum Zitat Koo B, Jung R, Yu Y (2021) Automatic classification of wall and door bim element subtypes using 3d geometric deep neural networks. Adv Eng Inform 47:101200 Koo B, Jung R, Yu Y (2021) Automatic classification of wall and door bim element subtypes using 3d geometric deep neural networks. Adv Eng Inform 47:101200
23.
Zurück zum Zitat Thorat Z, Mahadik S, Mane S, Mohite S, Udugade A (2019) Self driving car using raspberry-pi and machine learning. IRJET 06:969–972 Thorat Z, Mahadik S, Mane S, Mohite S, Udugade A (2019) Self driving car using raspberry-pi and machine learning. IRJET 06:969–972
24.
Zurück zum Zitat De Bruijne M (2016) Machine learning approaches in medical image analysis: from detection to diagnosis. Med Image Anal 33:94–97 De Bruijne M (2016) Machine learning approaches in medical image analysis: from detection to diagnosis. Med Image Anal 33:94–97
25.
Zurück zum Zitat Na H, Kim S (2021) Predicting stock prices based on informed traders’ activities using deep neural networks. Econ Lett 204:109917MATH Na H, Kim S (2021) Predicting stock prices based on informed traders’ activities using deep neural networks. Econ Lett 204:109917MATH
26.
Zurück zum Zitat Jokar M, Semperlotti F (2021) Finite element network analysis: a machine learning based computational framework for the simulation of physical systems. Comput Struct 247:106484 Jokar M, Semperlotti F (2021) Finite element network analysis: a machine learning based computational framework for the simulation of physical systems. Comput Struct 247:106484
27.
Zurück zum Zitat Lee S, Kim H, Lieu QX, Lee J (2020) Cnn-based image recognition for topology optimization. Knowl Based Syst 198:105887 Lee S, Kim H, Lieu QX, Lee J (2020) Cnn-based image recognition for topology optimization. Knowl Based Syst 198:105887
28.
Zurück zum Zitat Papadopoulos V, Soimiris G, Giovanis D, Papadrakakis M (2018) A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities. Comput Methods Appl Mech Eng 328:411–430MathSciNetMATH Papadopoulos V, Soimiris G, Giovanis D, Papadrakakis M (2018) A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities. Comput Methods Appl Mech Eng 328:411–430MathSciNetMATH
29.
Zurück zum Zitat Zhuang X, Guo H, Alajlan N, Zhu H, Rabczuk T (2021) Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. Eur J Mech A Solids 87:104225MathSciNetMATH Zhuang X, Guo H, Alajlan N, Zhu H, Rabczuk T (2021) Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. Eur J Mech A Solids 87:104225MathSciNetMATH
30.
Zurück zum Zitat Truong TT, Dinh-Cong D, Lee J, Nguyen-Thoi T (2020) An effective deep feedforward neural networks (dfnn) method for damage identification of truss structures using noisy incomplete modal data. J Build Eng 30:101244 Truong TT, Dinh-Cong D, Lee J, Nguyen-Thoi T (2020) An effective deep feedforward neural networks (dfnn) method for damage identification of truss structures using noisy incomplete modal data. J Build Eng 30:101244
31.
32.
Zurück zum Zitat Truong TT, Lee J, Nguyen-Thoi T (2021) Joint damage detection of structures with noisy data by an effective deep learning framework using autoencoder-convolutional gated recurrent unit. Ocean Eng 243:110142 Truong TT, Lee J, Nguyen-Thoi T (2021) Joint damage detection of structures with noisy data by an effective deep learning framework using autoencoder-convolutional gated recurrent unit. Ocean Eng 243:110142
33.
Zurück zum Zitat Le HQ, Truong TT, Dinh-Cong D, Nguyen-Thoi T (2021) A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy. Front Struct Civ Eng 15:1453–1479 Le HQ, Truong TT, Dinh-Cong D, Nguyen-Thoi T (2021) A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy. Front Struct Civ Eng 15:1453–1479
34.
Zurück zum Zitat Truong TT, Lee S, Lee J (2020) An artificial neural network-differential evolution approach for optimization of bidirectional functionally graded beams. Compos Struct 233:111517 Truong TT, Lee S, Lee J (2020) An artificial neural network-differential evolution approach for optimization of bidirectional functionally graded beams. Compos Struct 233:111517
35.
Zurück zum Zitat Shariati M, Mafipour MS, Mehrabi P, Shariati A, Toghroli A, Trung NT, Salih MN (2021) A novel approach to predict shear strength of tilted angle connectors using artificial intelligence techniques. Eng Comput 37:2089–2109 Shariati M, Mafipour MS, Mehrabi P, Shariati A, Toghroli A, Trung NT, Salih MN (2021) A novel approach to predict shear strength of tilted angle connectors using artificial intelligence techniques. Eng Comput 37:2089–2109
36.
Zurück zum Zitat Lee S, Vo TP, Thai H-T, Lee J, Patel V (2021) Strength prediction of concrete-filled steel tubular columns using categorical gradient boosting algorithm. Eng Struct 238:112109 Lee S, Vo TP, Thai H-T, Lee J, Patel V (2021) Strength prediction of concrete-filled steel tubular columns using categorical gradient boosting algorithm. Eng Struct 238:112109
37.
Zurück zum Zitat Hajela P, Berke L (1991) Neurobiological computational models in structural analysis and design. Comput Struct 41:657–667MATH Hajela P, Berke L (1991) Neurobiological computational models in structural analysis and design. Comput Struct 41:657–667MATH
38.
Zurück zum Zitat Hajela P, Berke L (1991) Neural network based decomposition in optimal structural synthesis. Comput Syst Eng 2:473–481MATH Hajela P, Berke L (1991) Neural network based decomposition in optimal structural synthesis. Comput Syst Eng 2:473–481MATH
39.
Zurück zum Zitat Adeli H, Park HS (1995) Optimization of space structures by neural dynamics. Neural Netw 8:769–781 Adeli H, Park HS (1995) Optimization of space structures by neural dynamics. Neural Netw 8:769–781
40.
Zurück zum Zitat Kang H-T, Yoon CJ (1994) Neural network approaches to aid simple truss design problems. Comput Aid Civ Infrastruct Eng 9:211–218 Kang H-T, Yoon CJ (1994) Neural network approaches to aid simple truss design problems. Comput Aid Civ Infrastruct Eng 9:211–218
41.
Zurück zum Zitat Ramasamy J, Rajasekaran S (1996) Artificial neural network and genetic algorithm for the design optimization of industrial roofs-a comparison. Comput Struct 58:747–755MATH Ramasamy J, Rajasekaran S (1996) Artificial neural network and genetic algorithm for the design optimization of industrial roofs-a comparison. Comput Struct 58:747–755MATH
42.
Zurück zum Zitat Iranmanesh A, Kaveh A (1999) Structural optimization by gradient-based neural networks. Int J Numer Methods Eng 46:297–311MATH Iranmanesh A, Kaveh A (1999) Structural optimization by gradient-based neural networks. Int J Numer Methods Eng 46:297–311MATH
43.
Zurück zum Zitat Mai HT, Kang J, Lee J (2021) A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior. Finite Elem Anal Des 196:106461MathSciNet Mai HT, Kang J, Lee J (2021) A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior. Finite Elem Anal Des 196:106461MathSciNet
44.
Zurück zum Zitat Nguyen LC, Nguyen-Xuan H (2020) Deep learning for computational structural optimization. ISA Trans 103:177–191 Nguyen LC, Nguyen-Xuan H (2020) Deep learning for computational structural optimization. ISA Trans 103:177–191
46.
Zurück zum Zitat Truong TT, Lee J, Nguyen-Thoi T (2021) Multi-objective optimization of multi-directional functionally graded beams using an effective deep feedforward neural network-smpso algorithm. Struct Multidiscip Optim 63:2889–2918MathSciNet Truong TT, Lee J, Nguyen-Thoi T (2021) Multi-objective optimization of multi-directional functionally graded beams using an effective deep feedforward neural network-smpso algorithm. Struct Multidiscip Optim 63:2889–2918MathSciNet
47.
Zurück zum Zitat Li B, Huang C, Li X, Zheng S, Hong J (2019) Non-iterative structural topology optimization using deep learning. Comput Aided Des 115:172–180 Li B, Huang C, Li X, Zheng S, Hong J (2019) Non-iterative structural topology optimization using deep learning. Comput Aided Des 115:172–180
48.
Zurück zum Zitat White DA, Arrighi WJ, Kudo J, Watts SE (2019) Multiscale topology optimization using neural network surrogate models. Comput Methods Appl Mech Eng 346:1118–1135MathSciNetMATH White DA, Arrighi WJ, Kudo J, Watts SE (2019) Multiscale topology optimization using neural network surrogate models. Comput Methods Appl Mech Eng 346:1118–1135MathSciNetMATH
49.
Zurück zum Zitat Deng H, To AC (2021) A parametric level set method for topology optimization based on deep neural network. J Mech Des 143:091702 Deng H, To AC (2021) A parametric level set method for topology optimization based on deep neural network. J Mech Des 143:091702
50.
Zurück zum Zitat Abueidda DW, Koric S, Sobh NA (2020) Topology optimization of 2d structures with nonlinearities using deep learning. Comput Struct 237:106283 Abueidda DW, Koric S, Sobh NA (2020) Topology optimization of 2d structures with nonlinearities using deep learning. Comput Struct 237:106283
51.
Zurück zum Zitat Nguyen-Thanh VM, Zhuang X, Rabczuk T (2020) A deep energy method for finite deformation hyperelasticity. Eur J Mech A/Solids 80:103874MathSciNetMATH Nguyen-Thanh VM, Zhuang X, Rabczuk T (2020) A deep energy method for finite deformation hyperelasticity. Eur J Mech A/Solids 80:103874MathSciNetMATH
52.
Zurück zum Zitat Li W, Bazant MZ, Zhu J (2021) A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches. Comput Methods Appl Mech Eng 383:113933MathSciNetMATH Li W, Bazant MZ, Zhu J (2021) A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches. Comput Methods Appl Mech Eng 383:113933MathSciNetMATH
53.
54.
Zurück zum Zitat Panghal S, Kumar M (2020) Optimization free neural network approach for solving ordinary and partial differential equations. Eng Comput 37:2989–3002 Panghal S, Kumar M (2020) Optimization free neural network approach for solving ordinary and partial differential equations. Eng Comput 37:2989–3002
55.
Zurück zum Zitat Wang S, Wang H, Perdikaris P (2021) On the eigenvector bias of fourier feature networks: from regression to solving multi-scale pdes with physics-informed neural networks. Comput Methods Appl Mech Eng 384:113938MathSciNetMATH Wang S, Wang H, Perdikaris P (2021) On the eigenvector bias of fourier feature networks: from regression to solving multi-scale pdes with physics-informed neural networks. Comput Methods Appl Mech Eng 384:113938MathSciNetMATH
56.
Zurück zum Zitat Jin X, Cai S, Li H, Karniadakis GE (2021) Nsfnets (navier-stokes flow nets): physics-informed neural networks for the incompressible navier-stokes equations. J Comput Phys 426:109951MathSciNetMATH Jin X, Cai S, Li H, Karniadakis GE (2021) Nsfnets (navier-stokes flow nets): physics-informed neural networks for the incompressible navier-stokes equations. J Comput Phys 426:109951MathSciNetMATH
57.
Zurück zum Zitat Zhu Q, Liu Z, Yan J (2021) Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput Mech 67:619–635MathSciNetMATH Zhu Q, Liu Z, Yan J (2021) Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput Mech 67:619–635MathSciNetMATH
58.
Zurück zum Zitat Chandrasekhar A, Suresh K (2021) Tounn: topology optimization using neural networks. Struct Multidiscip Optim 63:1135–1149MathSciNet Chandrasekhar A, Suresh K (2021) Tounn: topology optimization using neural networks. Struct Multidiscip Optim 63:1135–1149MathSciNet
60.
Zurück zum Zitat Kaveh A, Ghazaan MI (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147 Kaveh A, Ghazaan MI (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147
61.
Zurück zum Zitat Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized css-bbbc algorithm with trap recognition capability. Comput Struct 102:14–27 Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized css-bbbc algorithm with trap recognition capability. Comput Struct 102:14–27
62.
Zurück zum Zitat Kaveh A, Azar BF, Talatahari S (2008) Ant colony optimization for design of space trusses. Int J Space Struct 23:167–181 Kaveh A, Azar BF, Talatahari S (2008) Ant colony optimization for design of space trusses. Int J Space Struct 23:167–181
63.
Zurück zum Zitat Sonmez M (2011) Artificial bee colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418 Sonmez M (2011) Artificial bee colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418
64.
Zurück zum Zitat Hasançebi O (2008) Adaptive evolution strategies in structural optimization: enhancing their computational performance with applications to large-scale structures. Comput Struct 86:119–132 Hasançebi O (2008) Adaptive evolution strategies in structural optimization: enhancing their computational performance with applications to large-scale structures. Comput Struct 86:119–132
65.
Zurück zum Zitat Cao X, Sugiyama Y, Mitsui Y (1998) Application of artificial neural networks to load identification. Comput Struct 69:63–78MATH Cao X, Sugiyama Y, Mitsui Y (1998) Application of artificial neural networks to load identification. Comput Struct 69:63–78MATH
67.
Zurück zum Zitat Camarda CJ, Adelman HM (1984) Static and dynamic structural-sensitivity derivative calculations in the finite-element-based engineering analysis language (eal) system. No. NASA-TM-85743 Camarda CJ, Adelman HM (1984) Static and dynamic structural-sensitivity derivative calculations in the finite-element-based engineering analysis language (eal) system. No. NASA-TM-85743
68.
Zurück zum Zitat Chandrasekhar A, Sridhara S, Suresh K (2021) Auto: a framework for automatic differentiation in topology optimization. arXiv:2104.01965 Chandrasekhar A, Sridhara S, Suresh K (2021) Auto: a framework for automatic differentiation in topology optimization. arXiv:​2104.​01965
69.
Zurück zum Zitat Lee S, Ha J, Zokhirova M, Moon H, Lee J (2018) Background information of deep learning for structural engineering. Arch Comput Methods Eng 25:121–129MathSciNetMATH Lee S, Ha J, Zokhirova M, Moon H, Lee J (2018) Background information of deep learning for structural engineering. Arch Comput Methods Eng 25:121–129MathSciNetMATH
71.
Zurück zum Zitat Khatibinia M, Naseralavi SS (2014) Truss optimization on shape and sizing with frequency constraints based on orthogonal multi-gravitational search algorithm. J Sound Vib 333:6349–6369 Khatibinia M, Naseralavi SS (2014) Truss optimization on shape and sizing with frequency constraints based on orthogonal multi-gravitational search algorithm. J Sound Vib 333:6349–6369
72.
Zurück zum Zitat Degertekin S, Bayar GY, Lamberti L (2021) Parameter free jaya algorithm for truss sizing-layout optimization under natural frequency constraints. Comput Struct 245:106461 Degertekin S, Bayar GY, Lamberti L (2021) Parameter free jaya algorithm for truss sizing-layout optimization under natural frequency constraints. Comput Struct 245:106461
73.
Zurück zum Zitat Camp CV (2007) Design of space trusses using big bang-big crunch optimization. J Struct Eng 133:999–1008 Camp CV (2007) Design of space trusses using big bang-big crunch optimization. J Struct Eng 133:999–1008
74.
Zurück zum Zitat Li L, Huang Z, Liu F, Wu Q (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85:340–349 Li L, Huang Z, Liu F, Wu Q (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85:340–349
75.
Zurück zum Zitat Degertekin S, Hayalioglu M (2013) Sizing truss structures using teaching-learning-based optimization. Comput Struct 119:177–188 Degertekin S, Hayalioglu M (2013) Sizing truss structures using teaching-learning-based optimization. Comput Struct 119:177–188
76.
Zurück zum Zitat Lamberti L (2008) An efficient simulated annealing algorithm for design optimization of truss structures. Comput Struct 86:1936–1953 Lamberti L (2008) An efficient simulated annealing algorithm for design optimization of truss structures. Comput Struct 86:1936–1953
77.
Zurück zum Zitat Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208 Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208
78.
Zurück zum Zitat Mallipeddi R, Suganthan PN, Pan Q-K, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11:1679–1696 Mallipeddi R, Suganthan PN, Pan Q-K, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11:1679–1696
79.
Zurück zum Zitat Pan Q-K, Suganthan PN, Wang L, Gao L, Mallipeddi R (2011) A differential evolution algorithm with self-adapting strategy and control parameters. Comput Oper Res 38:394–408MathSciNetMATH Pan Q-K, Suganthan PN, Wang L, Gao L, Mallipeddi R (2011) A differential evolution algorithm with self-adapting strategy and control parameters. Comput Oper Res 38:394–408MathSciNetMATH
80.
Zurück zum Zitat Rao RV, Kalyankar V, Waghmare G (2014) Parameters optimization of selected casting processes using teaching-learning-based optimization algorithm. Appl Math Model 38:5592–5608 Rao RV, Kalyankar V, Waghmare G (2014) Parameters optimization of selected casting processes using teaching-learning-based optimization algorithm. Appl Math Model 38:5592–5608
81.
Zurück zum Zitat Wang D, Tan D, Liu L (2018) Particle swarm optimization algorithm: an overview. Soft Comput 22:387–408 Wang D, Tan D, Liu L (2018) Particle swarm optimization algorithm: an overview. Soft Comput 22:387–408
82.
Zurück zum Zitat Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Comput Struct 165:59–75 Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Comput Struct 165:59–75
83.
Zurück zum Zitat Yam JY, Chow TW (2000) A weight initialization method for improving training speed in feedforward neural network. Neurocomputing 30:219–232 Yam JY, Chow TW (2000) A weight initialization method for improving training speed in feedforward neural network. Neurocomputing 30:219–232
Metadaten
Titel
A novel deep unsupervised learning-based framework for optimization of truss structures
verfasst von
Hau T. Mai
Qui X. Lieu
Joowon Kang
Jaehong Lee
Publikationsdatum
08.04.2022
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 4/2023
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-022-01636-3