Model for forecasting expressway surface temperature in snowy areas

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1 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 Model for forecasing expressway surface emperaure in snowy areas Masafumi Horii* and Takayuki Hayami** * Deparmen of Civil Engineering, College of Engineering, Nihon Universiy ** Saku Office, Nexco-Mainenance Kano Company Ld. (Received: May. 2, 216 Acceped :Sep. 28, 216 ) ABSTRACT We proposed a forecas model ha uses a neural nework o predic wha he winer road surface emperaure will be afer hree hours in order o increase he efficiency of ani-icing programs. In order o esablish he forecas model, learning models of he road surface emperaure using hree ses of inpu variables a a specific sie were creaed. These learning models were hen applied o oher sies along an expressway, and he correc of he road surface emperaure was examined. The resuls of he presen sudy revealed ha he road surface emperaure along an expressway can be prediced hree hours in advance more han 76% of he ime by applying a learning model o he ime series variaion of he road surface emperaure and oher variables, such as he hourly raffic volume and he effec of spreading aniicing chemicals. Keywords: forecas of road surface emperaure, neural nework, discriminan analysis 1. Inroducion In snowy areas, highway mainenance auhoriies ofen spread chemicals such as sodium chloride (sal) on he road surface in order o increase safey during winer condiions. However, hese chemicals damage he soil, plans, vehicles, and roadside srucures. The amoun of sal used has increased yearly, increasing he financial burden for hese services. Therefore, a forecas model of he road surface emperaure ha enables sal o be spread before he road surface freezes would be beneficial. The model should be simple and easy o apply in daily roue-based road mainenance using only exising basic sensor measuremens. However, no such pracical forecas model has been esablished. Several sudies on forecas models of he road surface emperaure have been conduced. These sudies can be classified ino wo ypes: 1) mehods using hea balance models and 2) saisical mehods. Hea balance models have been repored by Rayer (1987), Shao e al. (1993), and Voldborg (1993), and hese models have improved he accuracy of he road surface emperaure predicion. However, hese models are difficul o apply in all locaions for which effecive winer road mainenance is needed because hey require several ypes of equipmen for he observaion of meeorological variables, such as solar radiaion, radiaion balance, and albedo. Wih respec o saisical mehods, Suzuki e al. (1993) consruced a forecas model of he road surface emperaure ha uses muliple regression analysis and repored ha a fairly accurae forecas model could be obained. Shao (1998) and Almkvis and Waler (26) invesigaed he forecasing of he road surface emperaure using a neural nework model. These mehods also require several ypes of equipmen for measuring meeorological variables. Under hese condiions, we proposed a forecas model ha uses a neural nework o predic road surface emperaures hree hours in advance a a specific sie on an expressway based on measuremens 49

2 M.HORII, T.HAYAMI using exising basic sensors and obained accepably accurae resuls. Moreover, we confirmed ha he neural nework model has an accuracy similar o ha of muliple regression models (Suzuki e al., 1993) by comparing he resuls (Horii and Fukuda, 2). Furhermore, Horii (213) applied a forecas model o sies on a naional highway and esablished a roue-based forecas model having sufficien accuracy for pracical applicaion. In our previous sudies, we consruced he model by inpuing he imes series daa for only one variable, ha is, road surface emperaure. In he presen paper, however, we apply he proposed model (Horii, 213) o an expressway by changing he inpu variables. We examine he effec of he inpu variables of he forecas model and evaluae he difference in precision beween he various ses of inpu variables of he roue-based model in order o increase he efficiency of ani-icing programs (Horii and Hayami, 215). 2. Forecas model Arificial neural neworks are compuer models ha are inspired by componens of he human brain and are powerful ools ha can be used o solve complex problems. The neural nework used in he presen sudy is a mulilayer nework, as shown in Fig. 1. A neural nework consiss of hree layers: an inpu layer, a hidden layer, and an oupu layer. The inpu neurons receive signals from ouside he model and send heir oupus o he hidden neurons. The oupu neurons receive signals from he hidden neurons and produce he final oupus. w ji l w kj u i j k Inpu layer Hidden layer Oupu layer Figure 1. Mulilayered neural nework The oupus of he hidden and oupu neurons, denoed by o j and y k, respecively, are given by o y j k I = f i= 1 l ( uj) = f w x (1) J = f j= 1 ( ) u zk = f w o (2) kj ji j i where u j is he inpu o he jh neuron in he hidden layer, z k is he inpu o he kh neuron in he oupu layer, w ji l is he connecion weigh beween he jh neuron in he hidden layer and he ih neuron in he inpu layer, 5

3 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 w kj u is he connecion weigh beween he kh neuron in he oupu layer and he jh neuron in he hidden layer, x i is he inpu o he ih neuron in he inpu layer, and I and J are he numbers of neurons in he inpu and he hidden layer, respecively. The mos commonly used acivaion funcion is a sigmoid funcion: f 1 1+ e ( x) = (3) x Neural neworks can be rained by adjusing he connecion weighs in order o absrac he relaionships beween he inpu daa and he oupu daa. This learning procedure can be achieved by minimizing he error beween he desired oupus and he acual oupus: E = 1 2 K ( y k y dk ) k= 1 2 (4) where y dk is he desired oupu signal of he kh neuron in he oupu layer, and K is he number of neurons in he oupu layer. In general, he error backpropagaion algorihm is applied in order o minimize his error funcion. However, he backpropagaion learning algorihm has some problems. The backpropagaion process requires oo many learning cycles o converge o he correc weighs, and he learning process becomes suck a a local minimum of he error. In he presen paper, a learning algorihm ha is based on an exended Kalman filer has been inroduced (Murase e al., 1994). We assume he following nonlinear sae model (Kaayama, 1983): w = f + ( w ) v (5) + 1 ( w ) n (6) y = h + where w is he n-dimensional sae vecor a ime, y is he p-dimensional observaion vecor, f (w ) and h (w ) are he n- and p-dimensional nonlinear vecor funcions, respecively, v is he zero-mean m-dimensional plan noise, and n is he zero-mean p-dimensional observaion noise wih covariance marices v E n T T Q ( v n ) = (7) τ τ δ τ in which Q is a marix of size m m, R is a marix of size p p, and δ τ is he Kronecker dela. Here, since he connecion weighs are he elemens of he sae vecor and are assumed o be ime invarian, he plan noise is no aken ino consideraion. Therefore, in place of Equaion 5, he sae equaion can be expressed as follows: R w = Iw + 1 (8) where I is he ideniy marix. Since h (w ) is a nonlinear funcion, his funcion is linearized around he esimae of he sae as follows: h ( w ) h wˆ ) + H ( w wˆ ) (9) = ( / 1 / 1 51

4 M.HORII, T.HAYAMI Then, an exended Kalman filer algorihm can be applied o he esimaes of he saes. By subsiuing Equaion 9 ino Equaion 6, we can derive he following expression o replace Equaion 6: η = H w + n (1) where η h ( ˆ ) ˆ w / 1 + Hw / 1 = y (11) and H is he gradien marix ha resuls from linearizing he nework and is defined as follows: H h = w w= wˆ / 1 (12) Using he sae and observaion equaions, a mehod for updaing he esimaors of he sysem can be derived. The updaed equaions are [ y h ( wˆ )] (13) w ˆ ˆ / = w / 1 + K / 1 w ˆ ˆ + / = w / 1 (14) K T 1 ( H P H R ) (15) T = P / 1H / 1 + / = P / 1 KHP / 1 P P = P + 1/ / (17) (16) where w ˆ / is he Kalman filer esimae of he sae a ime based on is one-sep predicion, K is he Kalman gain, and P / is an esimaion error covariance marix. 3. Applicaion 3.1. Learning model of road surface emperaure We applied a neural nework model based on he exended Kalman filer o forecas road surface emperaures a hree sies of he Ban-Esu expressway in Fukushima prefecure. Sie A (99.1 kp, aliude: meers) and Sie C (121.5 kp, aliude: 19.4 meers) are locaed in embankmen secions, and Sie B (15.3 kp, aliude: 57.8 meers) is locaed in a cu secion. Here, kp refers o kilo-poss and indicaes he disance from he origin of a roue. Observaion daa from December 213 o March 214 were provided by he Tohoku Regional Head Office of he Eas Nippon Expressway Company (NEXCO Eas, ). These daa consis of air emperaure, road surface emperaure, emperaures a 5 and 1 cenimeers underground, wind velociy, amouns of rainfall and snowfall per hour, raffic volume, and repors on operaions of spreading ani-icing chemicals. Furhermore, he grid poin value (GPV) daa a he neares poin of hree sies a 37.6 degrees norh laiude and 14. degrees eas longiude were colleced. The GPV daa were provided by he Japan Meeorological Agency and were calculaed using he Global Specral Model. 52

5 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 The model srucure is a hree-layer nework, as shown in Fig. 2. We used he ime series variaion of daa as inpus o he inpu neurons and he road surface emperaures afer hree hours as oupus o he oupu neurons. Three hours corresponds o he amoun of ime required for a sal spreader o depar from a snow removal saion and complee he spreading operaion. Presen inpus Inpus of 1 hour before Inpus of 2 hours before Inpus of 3 hours before Oupus of 3 hours ahead Inpus of 4 hours before Figure 2. Basic archiecure for forecasing road surface emperaures In he presen paper, we seleced hree ses of inpu variables: 1) road surface emperaure, 2) road surface emperaure, hourly raffic volume, and effeciveness of spreading ani-icing chemicals, and 3) seleced variables by sepwise discriminan analysis. The sepwise discriminan analysis for variable was carried ou by adding and deleing variables from he equaion according o he parial F values in order o find he appropriae discriminan equaion. Refer o, for example, Afifi and Clark (1984) for deails. Here, he daa on he effeciveness of spreading ani-icing chemicals can be represened by a dummy variable ha akes one of wo values: 1, indicaing chemicals on a road surface are effecive, and, indicaing oherwise. We assume ani-icing chemicals on a road surface o be effecive for hree hours afer sal spreader operaion. The selecion of he model srucure was based on he learning and esing resuls. Here, he daa se for learning was a period of 31 days, from January 1 o January 31 of 214, and he daa se for esing was a period of 9 days, from December 1 o December 31 of 213 and from February 1 o March 31 of 214. Firsly, we consruced he learning model by varying he inpu neurons and hidden neurons for each inpu variable. We hen prediced he oupus of hese models using he esing daa se, which had no been previously presened o he models. Finally, we decided he forecas model srucure of he road surface emperaure wih he bes resuls of he learning and esing. The number of ieraions for learning was fixed a 1, for he sake of pracicaliy (Horii and Fukuda, 2). A he same ime, discriminan analysis was used o examine wheher he road surface emperaures could be adequaely prediced by he neural nework model. Discriminan analysis was used o assign a new sample belonging o wo or more groups in order o minimize he probabiliy of mis. Evaluaion of he resuls was conduced in erms of 1) oal correc, including correc of he road surface emperaures for above-zero and below-zero condiions, and 2) criical correc for dangerous road condiions, ha is, below-zero road surface emperaures. Tables 1 and 2 show he bes resuls of he correc for he learning and esing daa obained using he firs se of inpu variables a Sie A. In his case, he inpu variables are he ime series 53

6 M.HORII, T.HAYAMI variaion of he road surface emperaure for six hours, and he number of hidden neurons is nine. Tables 3 and 4 show he same resuls obained using he second se of inpu variables, which are he ime series variaion of he road surface emperaure for six hours, he hourly raffic volume, and he effeciveness of spreading ani-icing chemicals for hree hours, a Sie A. The number of hidden neurons in his case is again nine. In boh cases, he percenages of overall correc for he learning and esing daa were high: 88.4% (firs se, learning), 84.1% (firs se, esing), 89.2% (second se, learning), and 77.6%. (second se, esing). Table 1. Learning resuls for road surface emperaure using he firs se of inpu variables (January of 214, Sie A). Prediced Measured condiions condiions Below Above Below zero % Above zero % 91.5% 79.2% 88.4% Table 2. Tasing resuls for road surface emperaure using he firs se of inpu variables (Oher hree monhs, Sie A). Prediced Measured condiions condiions Below Above Below zero % Above zero % 81.9% 86.9% 84.1% Table 3. Learning resuls for road surface emperaure using he second se of inpu variables (January of 214, Sie A). Measured Prediced condiions condiions Below zero Above zero Below zero % Above zero % 92.5% 79.9% 89.2% 54

7 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 Table 4. Tasing resuls for road surface emperaure using he second se of inpu variables (Oher hree monhs, Sie A). Prediced Measured condiions condiions Below Above Below zero % Above zero % 72.7% 86.3% 77.6% Table 5 shows he discriminan funcions for wo groups of daa: daa for below-zero road surface emperaures and daa for above-zero road surface emperaures. The predicor variables in his able were seleced based on he resuls of he sepwise discriminan analysis. A new sample is assigned o he group wih he higher discriminan funcion score. Table 5. Discriminan funcions Coefficiens of discriminan Parial F funcions value Predicor Below Above variables Road surface emperaure Hourly raffic volume Surface emperaure (GPV) Relaive humidiy a hpa (GPV) Consan Tables 6 and 7 show he resuls of correc for he learning and esing daa obained using he hird se of inpu variables, which consiss of he ime series variaion of he road surface emperaure for eigh hours, he hourly raffic volume for hree hours, he surface emperaure for wo hours, and he relaive humidiy a 5 hpa for one hour, all a Sie A. In his case, he number of hidden neurons is seven. We obained fairly high percenages of overall correc for he learning (93.4%) and esing daa (84.7%). The hree forecas model srucures are summarized in Table 8. 55

8 M.HORII, T.HAYAMI Table 6. Learning resuls for road surface emperaure using he hird se of inpu variables (January of 214, Sie A). Prediced Measured condiions condiions Below Above Below zero % Above zero % 96.9% 84.5% 93.4% Table 7. Tasing resuls for road surface emperaure using he hird se of inpu variables (Oher hree monhs, Sie A). Prediced Measured condiions condiions Below Above Below zero % Above zero % 84.7% 84.8% 84.7% Table 8. Summary of forecas model srucures Se No. of inpu Inpu neurons Number of hidden variables Variable name hours neurons Firs se Road surface emperaure 6 9 Second se Road surface emperaure Hourly raffic volume Spreading resuls of ani-icing chemicals Third se Road surface emperaure Hourly raffic volume Surface emperaure (GPV) Relaive humidiy a 5 hpa (GPV) Figures 3 and 4 show he learning and esing resuls, respecively, obained using he firs se of inpu variables for Sie A. Figures 5 and 6 show he same resuls obained using he second se of inpu variables, and Figs. 7 and 8 show he same resuls obained using he hird se of inpu variables. In every case, he prediced values follow he observed values. Therefore, we can obain hree models ha enable high-precision learning and esing

9 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 Road surface emperaure( ) ( Sie A) Observed values Prediced values Dae Figure 3. Learning resuls for road surface emperaures using he firs se of inpu variables (December of 214, Sie A) Road surface emperaure( ) ( Sie A) Observed values Prediced values Dae Figure 4. Tesing resuls for road surface emperaures using he firs se of inpu variables (December of 213, Sie A) 57

10 M.HORII, T.HAYAMI Raod surface emperaue( ) ( Sie A) Observed values Prediced values Dae Figure 5. Learning resuls for road surface emperaures using he second se of inpu variables (January of 214, Sie A) Road surface emperaure( ) ( Sie A) Observed values Prediced values Dae Figure 6. Tesing resuls for road surface emperaures using he second se of inpu variables (December of 213, Sie A) 58

11 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 Raod surface emperaure( ) ( Sie A) Observed values Prediced values Dae Figure 7. Learning resuls for road surface emperaures using he hird se of inpu variables (January of 214, Sie A) ( Sie A) Road syrface emperaure( ) Observed values Prediced values Dae Figure 8. Tesing resuls for road surface emperaures using he hird se of inpu variables (December of 213, Sie A) 3.2. Forecasing road surface emperaure for oher sies along he expressway Nex, we examined he possibiliy of forecasing road surface emperaures a oher sies along he expressway using he learning model of he road surface emperaure a Sie A (99.1 kp). 59

12 M.HORII, T.HAYAMI Tables 9, 1, and 11 show he forecas resuls obained using he ime series variaion of he firs, second, and hird ses of inpu variables, respecively, a Sie B, which is locaed 6.2 kilomeers from Sie A. Tables 12, 13, and 14 show he same resuls for Sie C, which is locaed 22.4 kilomeers from Sie A. For he wo sies, he percenages of criical correc resuls obained using he firs se of inpu variables and he hird se of inpu variables were 94.5% (Sie B, firs se), 93.3% (Sie B, hird se), 89.6% (Sie C, firs se), and 91.% (Sie C, hird se), which are exremely high for below-zero condiions. Furhermore, he percenages of correc resuls obained using he second se of inpu variables were 85.6% (Sie B, second se) and 86.4% (Sie C, second se). These percenages are considerably high for overall predicion. Therefore, when considering he correc for overall predicion, we should use he second se of inpu variables, and when considering he correc for criical condiion, ha is, below-zero road surface emperaures, we should use he firs or hird se of inpu variables. Thus, he expressway mainenance auhoriies would selec he forecas model according o he raffic volume, weaher condiions, and financial burden for hese services. Table 9. Forecas resuls for road surface emperaure using he firs se of inpu variables (four monhs, Sie B). Prediced Measured condiions condiions Below Above Below zero % Above zero % 74.% 93.% 81.3% Table 1. Forecas resuls for road surface emperaure using he second se of inpu variables (four monhs, Sie B). Prediced Measured condiions condiions Below Above Below zero % Above zero % 85.7% 85.5% 85.6% 6

13 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp49-64 Table 11. Forecas resuls for road surface emperaure using he hird se of inpu variables (four monhs, Sie B). Prediced Measured condiions condiions Below Above Below zero % Above zero % 68.7% 9.5% 76.2% Table 12. Forecas resuls for road surface emperaure using he firs se of inpu variables (four monhs, Sie C). Prediced Measured condiions condiions Below Above Below zero % Above zero % 69.8% 92.2% 81.2% Table 13. Forecas resuls for road surface emperaure using he second se of inpu variables (four monhs, Sie C). Prediced Measured condiions condiions Below Above Below zero % Above zero % 82.5% 88.8% 86.4% 61

14 M.HORII, T.HAYAMI Table 14. Forecas resuls for road surface emperaure using he hird se of inpu variables (four monhs, Sie C). Prediced Measured condiions condiions Below zero Above zero Below zero % Above zero % 63.6% 92.4% 76.7% Figures 9 and 1 show he forecas resuls for he road surface emperaure a Sies B and C obained using he learning model for Sie A and he observaions of ime series variaion of he hird se of inpu variables a Sies B and C, which has exremely high percenages of correc for below-zero condiions. In boh cases, he prediced road surface emperaures follow he observed values for near-zero condiions. In conras, larger errors occur a higher road surface emperaures. However, his is no problemaic, because his emperaure range is no subjec o ice formaion. 4 ( Sie B) Observed values Prediced values Road surface emperaure( ) Dae Figure 9. Forecas resuls for road surface emperaure using he hird se of inpu variables (four monhs, Sie B). 62

15 Journal of Naural Disaser Science, Volume 37,Number 2,216,pp ( Sie C) Observed values Prediced values Road surface emperaure( ) Dae Figure 1. Forecas resuls for road surface emperaure using he hird se of inpu variables (four monhs, Sie C). 4. Conclusion In he presen paper, we aemped o esablish a forecas model of he road surface emperaure along an expressway. The resuls are as follows: 1. The neural nework model has he abiliy o forecas road surface emperaure wih high precision. 2. We examined he abiliy of he learning model o forecas he road surface emperaure a oher sies along he expressway, i.e., roue-based forecasing of he road surface emperaure. 3. We obained hree models ha have he abiliy o forecas road surface emperaures for overall condiions or road surface emperaures in below-zero condiions along he expressway using differen inpu variables. For expressway mainenance in winer, i is of paricular imporance o carefully mainain safe road surface condiions by using an appropriae forecas model of he road surface emperaure when below-zero condiions migh exis. We hope o esablish a roue-based forecas model for he road surface condiions by combining he proposed model and a model for deecing waer on road surfaces. This model uses a discriminan analysis and a neural nework o predic dry versus oher road surface condiions hree hours in advance (Horii and Fukuda, 21). Acknowledgmens The presen research was suppored in par by a Gran from he Minisry of Educaion, Culure, Spors, Science, and Technology (No ). We are graeful o he saff of Koriyama and Aizu Office of Eas Nippon Expressway Company. REFERENCES Afifi, A. A. and Clark, V., Compuer-aided mulivariae analysis, Lifeime Learning Publicaion. Almkvis, S. E. and Waler, M., 26. Which variables should be measured a a road weaher saion 63

16 M.HORII, T.HAYAMI Arificial inelligence gives he answer, SIRWEC, Horii, M. and Fukuda, T., 2. Forecas model of road surface emperaure in snowy areas using neural nework, Proceedings of he Fourh Inernaional Conference on Snow Engineering, Horii, M. and Fukuda, T., 21. Pavemen ice predicion sysem in winer mainenance, Journal of Maerials, Concree Srucures and Pavemens, 669, Horii, M., 213. Forecas model of road surface emperaure along naional highway in snowy area, Journal of Snow Engineering of Japan, 29 (1), Horii, M. and Hayami, T., 215. Forecas model of road surface emperaure along expressway, Summaries of JSSI & JSSE Join Conf. on Snow and Ice Research, 99. Kaayama, T., Applied Kalman Filer, Asakura Publishing Co., Ld. Murase, H., Koyama, S., and Ishida, R., Kalman neuro compuing by personal compuer, Morikia Publishing Co., Ld. NEXCO Eas, Meeorological and Traffic Survey Daa. Rayer, P. J., The Meeorological Office forecas road surface emperaure model, Meeorological Magazine, 116, Shao, J., Thornes, J. E., and Liser, P. J., Descripion and verificaion of a road ice predicion model, Transporaion Research Record, 1387, Shao, J., Improving nowcass of road surface emperaure by a backpropagaion neural nework, Weaher and Forecasing, 13, Suzuki, T., Amano, T., and Hirama, S., Research on new sysem for predicion freezing on road surfaces, Repor of Research Cener of Japan Highway Public Corporaion, Vol. 3, Voldborg, H., On he predicion of road condiions by a combined road layer-amospheric model in winer, Transporaion Research Record, 1387,