TEMPERATURE PREDICTION IN TIMBER USING ARTIFICIAL NEURAL NETWORKS

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1 TEMPERATURE PREDICTION IN TIMBER USING ARTIFICIAL NEURAL NETWORKS Paulo Cachm ABSTRACT: Neural networks are a owerful tool used to model roertes and behavour of materals n many areas of cvl engneerng alcatons. In the resent aer, the models n artfcal neural networks for redctng the temeratures n tmber under fre loadng have been develoed. For buldng these models, tranng and testng usng the avalable numercal results obtaned usng desgn methods of Eurocode 5 have been used. The data used n the multlayer feed forward neural network models are arranged n a format of three nut arameters that cover the densty of tmber, the tme of fre exosure and the dstance from exosed sde. Wth these nut arameter used n the multlayer feed forward neural network models the temeratures n tmber are redcted. The tranng and testng results n the neural network model have shown that neural networks can accurately calculate the temerature n tmber members subected to fre. KEYWORDS: Instructons to authors, Proceedngs, WCTE 00 INTRODUCTION Artfcal neural networks (ANN) have become a very oular technque n many felds such as medcne, fnance, economcs, engneerng, etc. The tyes of roblems to whch they are aled to are also extensve and vary from classfcaton and redcton to data vsualzaton and comresson. The number of neuro-lke models and schemas as well as ways to mlement neural models s ermanently ncreasngly. Wthn the feld of constructon ndustry, has mostly beng used for estmatng concrete roertes such as strength, slum or modulus of elastcty [-6]. If neural networks could adequately model the temerature felds wthn a tmber member then, after network learnng, the results of the network can be used n numercal calculatons wthout the need to use smultaneously a thermal and mechancal analyss. Consequently, temeratures n tmber can be smly calculated by alyng the network to the arorate nut values. The am of ths artcle s to descrbe the alcablty of artfcal neural networks for the redcton of temeratures n tmber under fre loadng. ARTIFICIAL NEURAL NETWORKS. BASICS An artfcal neural network s bascally a large number of hghly nterconnected dealzed neurons that receves Paulo Cachm, Deartment of Cvl Engneerng & LABEST, Unversty of Avero, Avero, Portugal. Emal: cachm@ua.t nut from the neurons to whch t s connected, comutes an actvaton level, and transmts that actvaton to other rocessng neurons. The core of neural network comutatons s actvaton. Each nut neuron actvates one or several addtonal neurons wth dfferent levels of effcency. Subsequently these actvated neurons wll actvate other neurons untl an outut was reached. The fnal result, the outut, of the betwork s strongly nfluenced by the nterconnecton between neurons,.e., the strength and layout of the connectons. An ANN must be traned n order to learn and roduce meanngful results. After the learnng rocess, the network s able to erform comutatons. The learnng rocess can be contnuous n whch case the network s contnuously adatng tself for the new data. In a feed forward neural network, as used n ths work, the artfcal neurons are groued n layers. In each layer, all the neurons are connected to all the neurons n the next layer (see Fgure ). No connecton exsts between neurons of the same layer or the neurons whch are not n successve layers. Bascally, a mnmum of three layers of neurons must exst: () one nut layer; () at least one hdden layer; and () one outut layer of neurons. Each connecton between artfcal neurons s characterzed by a weght value. Each neuron of the nut layer receves nformaton (data from exerments or analyss) that wll be the outut of ths layer and asses t to the neurons of the followng layer weghted by the weght of the connecton layer (see Fgure ). In all of the subsequent layers, each neuron comutes the weghtng sum of all the n neurons of the recedent layer, s, accordng to equaton (). At ths stage a bas, b, can be ntroduced.

2 layer, and the weghts are adusted based on some learnng strateges so as to reduce the network error. In ths study results of numercal fnte element smulatons were used as data for the network. Basc arameters of the model were selected and used as nut neurons whle the results, temeratures n tmber, are used as oututs. For each case, a random number of avalable onts were selected to serve as data for neural network tranng whle the remanng results were used to test and valdate the model. Detals secfc for each networks are gven below, deendng on the analysed roblem. In ths study, the error occurred durng the tranng and testng of the network was exressed as a root mean squared error (RMSE) and as a mean absolute error (MAE) that can be calculated by equatons (3) and (4), where t s the desred outut (numercal results), o s the redcted outut (calculated by the network) and s the number of onts where the temeratures have been calculated. RMSE ( t o ) (3) Fgure : Feed forward neural network scheme (to) and ndvdual neuron calculaton scheme (bottom) Afterwards each neuron actvates the outut, o, by usng an actvaton functon, f. One of the most used actvaton functons s the sgmod functon leadng to an outut as descrbed n equaton (), where α s a arameter controllng the rate of changng of the sgmod. In a feed forward network, the nuts and outut varables are normalzed to be n the range [0, ]. For ractcal uroses, however, the alcable range s usually [0., 0.9] to avod small sloes of the actvaton functon. s b + n w o () MAE t o In addton, accuracy of the network redctons were also assessed by the coeffcent of dstrbuton (R ) and by the mean absolute ercentage error (MAPE) calculated accordng to equatons (5) and (6), resectvely. In equaton (5), t reresents the average of desred oututs. R ( t o ) ( t t) (4) (5) o f ( s ) + ex ( α s ) () MAPE t o t (6). CHOICE OF NETWORK Because there s no relable method for decdng the number of neural unts requred for a artcular roblem, the choce of the number of hdden layers and of neurons er layer must be based on exerence and a few number of trals s usually necessary to determne the best confguraton of the network. Back roagaton algorthm, as one of the most wellknown tranng algorthms for the multlayer ercetron, s a gradent descent technque to mnmze the error for a artcular tranng attern n whch t adusts the weghts by a small amount at a tme. The network error s assed backwards from the outut layer to the nut 3 TIMBER TEMPERATURES UNDER FIRE LOADING In ths work, the temerature evoluton wthn a tmber member under fre loadng was calculated usng the conductve model resented n Eurocode 5, Part - (EC5) [7]. The conductve model resented n EC5 s based on the calculaton of the two- or threedmensonal, transent, heat transfer dfferental equaton, ncororatng thermal roertes that vary wth temerature. Effects such as mass transfer wthn the structure, reacton energy released nsde the wood due to yrolyss or degradaton of materal, crackng of charcoal, whch ncreases the heat transfer of the char layer are not accounted for. Thus, EC5 rooses

3 roertes that are equvalent roertes takng these effects nto account. The coeffcent of heat transfer by convecton on unexosed surfaces was consdered 9 W/m K and on heated surfaces wth standard temerature-tme curves 5 W/m K, as defned n Eurocode, Part - [7]. The surface emssvty of wood used n calculatons was 0.8 [8]. Thermal conductvty, secfc heat caacty and densty rato were used wth values defned n EC5 (Fgure and 3). Mosture content of wood was consdered equal to 0.. The calculaton of temeratures n tmber was erformed by usng a fnte element mesh wth square elements (sde s 5 mm); ths wll allow an adequate characterzaton of the thermal feld wthn tmber. Default EC5 thermal roertes for tmber as descrbed n revous secton were used. Numercal fnte element calculatons were carred out usng the fnte element code SAFIR [9], whch s a secal urose fnte element code, develoed at Unversty of Lege for studyng structures subected to fre. Fgure 4 shows the temerature dstrbuton for t 30 mnutes and 450 kg/m 3 densty wth the abscssa dstance measured from the face exosed to fre obtaned usng SAFIR and standard roertes of EC5. Fgure : Secfc heat n tmber [7] Fgure 4: Temerature rofle n tmber for t 30 and 60 mnutes and 450 kg/m 3 densty Fgure 3: Relatve densty and conductvty [7] 4 PREDICTION OF TEMPERATURES IN TIMBER UNDER FIRE LOADING USING ARTIFICIAL NEURAL NETWORKS The use of artfcal neural networks to redct temeratures n tmber members wll be resented n ths artcle by usng the followng aroach: a) for a secfc tmber densty, several network models were tested by tranng them usng randomly selected data; b) for the network model wth best tranng results addtonal nformaton regardng network behavour was nvestgated. To assess the ossblty of usng artfcal neural networks for redcton of temerature n tmber, several networks were tested. The nut arameters were the tme of exosure, t; (and the dstance from exosed surface, s. Outut was defned by a sngle neuron that reresents the temerature n tmber, T. The rocedure was defned as follows. Temeratures were calculated every 60 seconds durng one hour, meanng that a total of 60 tme onts are avalable. Snce the fnte element mesh had elements wth 5 mm sde and the maxmum dstance from exosed surface s 00 mm a total of 4 onts where temeratures were calculated exsted. Thus, a total of 460 tme-dstance-temerature onts are avalable. For network tranng, 30 % of these onts were randomly selected. The remander were used for network assessment. Snce there s no rule of thumb for the selecton of artfcal network layouts, several (n ths case ) network layouts were tested where the number of hdden layers and the number of neurons n these layers were changed (see Table ). For network tranng, sgmod actvaton functons were used wth the α- arameter equal to, the number of teratons was 00000, the learnng rate was 0.3 and the momentum was 0.. Tmber densty used for assessng the ablty of artfcal neural networks for temerature redcton was 450 kg/m 3.

4 Table : ANN characterzaton Network name Number of hdden layers Neurons n hdden layer 3 H H H H H H H H H H H rocess. The results of the testng are shown n Table 3. Agan t can be observed that network H570 gves the best results wth a RMSE of 3.5 ºC and an R equal to In Fgure 5 the results calculated usng SAFIR are comared wth the oututs of the network H570. It can be observed that a very good corresondence between both results was acheved. Table resents the errors and accuracy measures for the analysed cases. It can be shown that the network H570 gves the best results for the tranng rocess. Ths network has two hdden layers wth 5 neurons n the frst layer and 7 neurons n the second hdden layer. It can also be observed that one layer networks gve the worst results. Table : Tranng results Network name MAE MAPE RMSE R ºC - ºC - H H H H H H H H H H H Fgure 5: Comarson of SAFIR calculated temeratures and ANN outut temeratures for H570 network The evoluton of the error durng the teraton rocess can be observed n Fgure 6. It can be observed that the convergence rocess s relatvely effcent. It should be noted that, snce the ntal estmaton of the network arameters are randomly selected and then corrected through the teratve rocess, two sequental runs of the rocess may lead to dfferent network arameters and error values (although smlar). Table 3: Testng results Network name MAE MAPE RMSE R ºC - ºC - H H H H H H H H H H H After tranng, the network was tested by usng the remander 70% of the results not used for the tranng Fgure 6: Evoluton of the error durng the teratve rocess for H570 network 5 CONCLUSIONS Artfcal neural networks are a owerful tool for solvng some of the comlex cvl engneerng roblems because

5 they can learn and generalze from examles and exerences. In ths study, usng these benefcal roertes, artfcal neural networks are used n order to redct the temeratures n tmber under fre loadng. The use of artfcal neural networks allow desgners to easly calculate the temeratures n a tmber member at any tme and to use these results nto structural analyss and desgn wthout the need to use a thermal and mechancal model. REFERENCES [] Toçu, IB, C Karakurt, and M SarIdemr, Predctng the strength develoment of cements roduced wth dfferent ozzolans by neural network and fuzzy logc. Materals & Desgn, (0): [] SarIdemr, M, Predcton of comressve strength of concretes contanng metakaoln and slca fume by artfcal neural networks. Advances n Engneerng Software, (5): [3] Das, WPS and SP Poolyadda, Neural networks for redctng roertes of concretes wth admxtures. Constructon and Buldng Materals, 00. 5(7): [4] Ashu, J, J Saneev Kumar, and M Sudhr, Modelng and Analyss of Concrete Slum Usng Artfcal Neural Networks. Journal of Materals n Cvl Engneerng, (9): [5] Demr, F, Predcton of elastc modulus of normal and hgh strength concrete by artfcal neural networks. Constructon and Buldng Materals, 008. (7): [6] Özcan, F, et al., Comarson of artfcal neural network and fuzzy logc models for redcton of long-term comressve strength of slca fume concrete. Adv. Eng. Softw., (9): [7] CEN, EN 995--:004: Eurocode 5: Desgn of tmber structures - Part -: General - Structural fre desgn, CEN, Edtor. 004: Brussels, Belgum. [8] CEN, EN 99--:00. Eurocode : Actons on structures - Part -: General actons - Actons on structures exosed to fre, CEN, Edtor. 00: Brussels, Belgum. [9] Franssen, J-M, SAFIR. A Thermal/Structural Program Modellng Structures under Fre. Engneerng Journal, (3):