カテゴリー Ⅰ 日本建築学会構造系論文集第 82 巻第 734 号, ,2017 年 4 月 J. Struct. Constr. Eng., AIJ, Vol. 82 No. 734, , Apr., 2017 DOI

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1 カテゴリー Ⅰ 日本建築学会構造系論文集第 8 巻第 734 号, ,7 年 4 月 J. Sruc. Consr. Eng., AIJ, Vol. 8 No. 734, , Apr., 7 DOI hp://doi.org/.33/aijs リカレントニューラルネットワークによる材料構成則の構築に関する基礎的研究 BASICAL STUDY ON HYSTERETIC MODELING BY USING RECURRENT NEURAL NETORK 鈴木琢也 * **, 松岡康友 Takua SUZUKI and Yasuomo MATSUOKA In nonlinear srucural analsis, i is ver imporan o use an accurae hsereic model. However, here are some maerials and srucural members for which he human developmen and applicaion of a hsereic model are oo complex. Such siuaions can apparenl be addressed using a recurren neural nework (RNN) ssem. An RNN is a pe of neural nework (NN) ha can be changed b a ssem based on previous hseresis inpus and oupus. In he presen sud, we confirmed he applicabili of RNN o he developmen of a normal bilinear model. Firsl, we idenified he appropriae RNN model using raining daa comprising heoreical bilinear hisorical displacemen as inpu and force as oupu daa. The resuls confirmed ha he idenified RNN model could be applied o he ssem, and ha i was equivalen o a heoreical bilinear model. Kewords : Recurren Neural Nework, Hseresis Model, Srucural Analsis.. Ramberg-Osgood ) ) 3). NN 4)5) NN NN 6)-9) ) ) ) 3) 4),5) NN NN Fig.(a) NN NN * ** 竹中工務店技術研究所主任研究員博士 ( 工学 ) 竹中工務店技術研究所研究主任修士 ( 学際情報学 ) Chief Researcher, R&D Insiue, Takenaka Corporaion, Dr. Eng. Assoc. Chief Researcher, R&D Insiue, Takenaka Corporaion, M. Informaion Sudies 543

2 Force(Curren) Force(Curren) Force(=) Force(=) Force(=n) Inpu for nex ime sep = Disp. (Curren) Min. Disp. (Pas) Max. Disp. (Pas) Inpu seleced b Human Disp.(Curren) Disp.(=) Disp.(=) Disp.(=n) (a) Neural Nework (b) Recurren Neural Nework Fig. Concep of RNN Force(Curren) Modeled B RNN Process A Process B Process C Check Curren Sae Correc Curren Sae Disp.(Curren) Fig. Targe Process o be modeled b RNN Analsis Resuls of Member b Deailed FE Model Idenified RNN Member Model Fig.3 Applicaion Example of RNN Model High-accurac Frame Model Using RNN Model.3 NN RNNRNN NN 6) NN NN Fig.(b)RNN RNN Fig.(b) NN Elman nework 7) Echo sae nework 8) Time dela neural nework 9) Nework Fig. ProcessAC NN ProcessAC RNN FEM FEM Fig.3 RNN NN ),) RNN RNN RNN RNN RNN.. RNN 544

3 F F K F F (F old, old ) K K -F Fig.4 Bi-Linear Model (kinemaic hardening) Table Parameers of Bi-Linear Model Iniial Siffness Yield Force Second Siffness K (kn/m) F (kn) K (kn/m).. 5. F K F K F K old Fold K F K F where ( K ( K old old -F F F old old ) ( K K) F ) ( K K) F Fig.5 Cording Example of Kinemaic Hardening Bi-Linear Model K K Fig.4 K F K 3 Table Fig.5 F 3 K 3 old F old Fig.4 RNN NN. RNN.. RNN RNN Fig.6 RNN,,4 NN L=3 LSTM Uni L= L= (L=)(L=3) L=L=3 NN u u u () L L u () L3 L3 Force(Curren) L=3 {} L b L= {4} 3, L3 {} {} {} {} {4} {4} {4} {4} L= {} L b u L=3 {} u L= {6}, L u L= {} Disp.(Curren) Fig.6 RNN archiecure Recurren Loop - L= {4} 3 545

4 ..3 (L=) LSTMLong Shor Term Memor LSTM RNN ),3) LSTM Fig.7 LSTM NN 3 4 u u IGu OGu FG u IGu OG u FG InpuGaeOupuGae FogeGae s s gig f ( u ) gfg s (3) Forge Gae u FG Oupu() h + g u Inpu (4) Oupu Gae Inpu Gae u IG u OG + g h LEGEND connecion wihou ime-lag connecion wih ime-lag Memor Cell muliplicaion sum over all inpus Gae acivaion funcion (logisic sigmoid) inpu acivaion funcion (hperbolic angen) oupu acivaion funcion (hperbolic angen) g IG g FG u g /( IG IG e ) (4) u g /( FG FG e ) (5) f anh -+ f ( u ) anh( u ) (6) g OG gog s (7) g OG u g /( OG OG e ) (8) LSTM 4 LSTM 4 4 4=6 4 Fig.7 LSTM block..4 Fig.6 u b u (9) L L { L, L} bl u () L3 L 3 { L} bl 3 b RNN = 64, , LSTM 4 6 LSTM 4.3 RNN Fig.5 Chainer 4) Chainer GPU PCInel Core i7-48mq(.7gh), GPU Nvidia GeForce GT 73M, Main Memor 6GBCUDA 7., cudnn

5 .3. Fig.5 Fig.8 RNN K-neKiK-ne gal 6gal 869.,.,.5,.,., 5., Fig.5 Fig.9 RNN RNN x nd n ne(w) MSE N E( ) dn ( x n ; w) N w () n w Ew E w w E () w w. epoch.3 5 Epoch.4 5) 6) 6) RNN BPTT back-propagaion hrough ime 7),8) RNN Fig. RNN Inpu Disp. His. ou in x Theoreical Bi-Linear Modeled b Human Training Daa Oupu Force. His. Fig. 8 Training Daa made b Theoreical Bi-linear Model Ts =.~. [sec] Inpu Acc. Disp. Response Fig. 9 Inpu Disp. Hisor Daa from Single Node Dnamic ou in x in x mini bach Sochasic gradien descen : SGD 9) w N w w E (3) N N w w E (4) N ' ou in 3 x 5 5 mini bach Sep mini bach SGD.5 3 ou 3 ou in x 3 Fig. Expand of RNN for BPTT 547

6 .5.5 L=L=35% 3) 5% 5%.3.3 RNN RNN Fig.5 RNN Fig. ElcenroNS T=.(s) m Fig. RNN () 3 4 se N L=5 4, 5 4, 7 4 se RNN Fig.3 N L=5 4 sep 35sep RNN N L=5 4 sep 35sep N L=7 4 Fig.4 RNN N L=5 4 RNN N L=7 4 RNN Acc.(m/s ) Time (sec) 5 Fig. Time Hisor of Inpu AcceleraionElcenroNS RNN 4) ReLU 3) Fig.5 N L=7 4 m.m 5 RNN N L=7 4 Fig.6 N L=7 4 m Fig.5 RNN RNN NN 4),),4) 548

7 Mean Squared Error Training Perplexi Validaion Perplexi Calculaed Force(kN) 5 Theoreical Model RNN Model Learned Daase (x 4 ) Calculaed Force(kN) 5 Fig. Learning Curve Theoreical Model RNN Model Disp.(m) Calculaed Force(kN) 5 (a) N L=5 4 se Theoreical Model RNN Model Sep 5 Calculaed Force(kN) 5 (a) N L=5 4 se Theoreical Model RNN Model Sep 5 Calculaed Force(kN) 5 (b) N L= 5 4 se Theoreical Model RNN Model Sep 5 (c) N L= 7 4 se Fig.3 Comparison of Oupu Force Hisor beween RNN and Theoreical bi-linear Disp.(m) Calculaed Force(kN) 5 (b) N L= 5 4 se Theoreical Model RNN Model Disp.(m) (c) N L= 7 4 se Fig.4 Comparison of force-disp. relaionship beween RNN and Theoreical bi-linear 549

8 ave Tpe Inpu Disp. ave ( uni : m ) Oupu Force ave ( uni : kn ) Theoreical Model RNN Model (a) Equal ampliude - - (b) Gradual-increase - - (c) Gradual-decrease - - (d) Gradual-decrease afer Gradual-increase - - (e) Gradual-increase afer Gradual-decrease - - (f) Shif - - (g) Gradual-shif - - Fig.5 Validaion Tes of RNN model b various displacemen waves (N L= 7 4 se, in arge range) ave Tpe Inpu Disp. ave ( uni : m ) Oupu Force ave ( uni : kn ) Theoreical Model RNN Model (a) Equal ampliude - - (b) Gradual-increase - - (c) Gradual-decrease - - (d) Gradual-decrease afer Gradual-increase - - (e) Gradual-increase afer Gradual-decrease - - (f) Shif - - (g) Gradual-shif - - Fig.6 Validaion es of RNN model b various displacemen waves (N L= 7 4 se, beond arge range) 8 55

9 Frequenc 3 N=6 ( x 6) Frequenc N=64 (4 x 6) Frequenc 3 N=4 (4 x ) Value Value Value (a) L=, Curren (b) L=, Recurren (c) L=3 Fig.7 Hisogram of RNN weigh coefficien (N L= 7 4 ) (c) RNN RNN RNN 3. RNN Fig.6 L= L=3 RNN RNN Fig.7 L=(sie:4 6) L=3(sie:4 ) L= sie: 6(a) sie:4 6(b) (a)(b) L= (b) RNN RNN Fig.6 LSTM LSTM OupuGae (c) L=3 5% 5% RNN RNN RNN RNN RNN NN 3) NN ),) RNN RNN RNN NN RNN 9 55

10 RNN ) LSTM 3 RNN RNN ) RNN RNN LSTM FEM RNN K-NET, KiK-ne ) 9 ) : No. 36, pp.8-4, ) H Vol.74No.636pp ) No.5pp ) 38App.85-94, 99 6) No.458, pp.7-77, ) No.47, pp.93-99, ) No.473, pp.7-5, ) No.496, pp.37-4, ) No.53, pp.53-6, 998. ) No.458, pp.79-89, ) No.555, pp.69-76,.5 3) No.5, pp.9-98, ) No.58, pp.73-8, 4.8 5) No.589, pp.89-96, 5.3 6) 5 7) J. L. Elman. : Finding srucure in ime, Cogniive Science, 4:79-,99 8) H. Jaeger : The echo sae approach o analing and raining reccuren neural neworks, Technical Repor GMD Repor 48, German Naional Research Cener for Informaion Technolog, 9) K. J. Lang, A. H. aibel, and G. E. Hinon : A ime-dela neural nework archiecure for isolaed word recogniion, Neural Neworks, 3():3-43, 99 ) Deep Learning 9 C3-OS-6b- 5.6 ) Laurens van der Maaen and G.E. Hinon: Visualiing Daa Using -SNE, Journal of Machine Learning Research, 9, pp , 8. ) A. Graves: Supervised Sequence Labelling wih Recurren Neural Neworks, PhD hesis, Technische Univ. Munchen, 8 3) S. Hochereier and J. Schmidhuber : Long shor-erm memor, Neural Compuaion, 9(8), pp , 997 4) Preferred Neworks, inc. : Chainer, hp://chainer.org/ (6.. ) 5) Sanford Univ.: CS3n: Convoluional Neural Neworks for Visual Recogniion (Lecure 5), hp://cs3n.sanford.edu/sllabus.hml (6.. ) 6) James Bergsra and Yoshua Bengio: Random Search for Hper-Parameer Opimiaion, Journal of Machine Learning Research, 3, pp. 8-35,. 7) P.erbos: Backpropagaion hrough Time: ha i does and how o do i, Proc. of he IEEE, 78(), pp.55-56, 99 8) R. J. illiams and D. Zisper: Gradien Based Learning Algorihms for Recurren Neworks and heir Compuaional Complexi, Back-propagaion: Theor, Archiecures and Applicaions, pp , 995 9) H. Robbins and S. Monro: A sochasic approximaion mehod, Ann. Mah. Sais., (3): pp.4-47, 95 3) N. Srivasava, G. E. Hinon, A. Krihevsk, I. Suskever, and R. Salakhudinov: Dropou : A simple wa o preven neural neworks from over fiing, Journal of Machine Learning Research, 5, pp , 4 3) X. Gloro, A. Bordes and Y. Bengio : Deep Sparse Recifier Neural Neworks, Proc. of AISTATS-. 5, pp.35-33, 3) 4 No.493, pp.33-38,

11 BASICAL STUDY ON HYSTERETIC MODELING BY USING RECURRENT NEURAL NETORK Takua SUZUKI * and Yasuomo MATSUOKA ** * Chief Researcher, R&D Insiue, Takenaka Corporaion, Dr. Eng. ** Assoc. Chief Researcher, R&D Insiue, Takenaka Corporaion, M. Informaion Sudies In nonlinear srucural analses, i is ver imporan o use an accurae hsereic model. However, here are some maerials and srucural members for which he human developmen and applicaion of a hsereic model are oo complex. Such siuaions can apparenl be addressed using a recurren neural nework (RNN) ssem. An RNN is a pe of neural nework (NN) ha can be changed b a ssem based on previous hseresis inpus and oupus. The objecive of he presen sud was o confirm he applicabili of RNN modeling o he normal bilinear modeling of ver complex nonlinear hseresis. Firs, we idenified he appropriae long shor-erm memor (LSTM) RNN model using raining daa comprising bilinear hisorical displacemen as inpu and force as oupu daa. I was confirmed ha he idenified RNN model could be applied o he ssem, and ha i was equivalen o a heoreical bilinear model. Following is a summar of he sud findings: () A hree-laered RNN model wih LSTM unis is required for a bilinear ssem. This was deermined using raining daa comprising heoreical bilinear inpu-oupu daa. Comparison of he oupu of he idenified RNN model wih ha of a heoreical model revealed good agreemen. The changeabili of an RNN b a ssem based on previous hseresis inpus and oupus was confirmed in he case of basic hsereic bilinear model, which is ofen used for srucural seismic design. () The sparsi of he weigh marix of he idenified RNN model was invesigaed. The marix was no found o exhibi sparsi when is laer conained drop ou. This indicaed ha he RNN model was ver large and had man weigh coefficiens, which would make is analsis ver difficul. The findings of his sud confirm he applicabili of RNN modeling o srucural hseresis. There is, however, he need for furher improvemen of he procedure. (6 年 8 月 9 日原稿受理,6 年月 7 日採用決定 ) 553

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