Performance of artificial neural networks in nearshore wave power prediction

Applied Soft Computing 23 (2014) 194–201

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

Performance of artificial neural networks in nearshore wave power prediction ˜ d A. Castro a,∗ , R. Carballo b , G. Iglesias c , J.R. Rabunal a

Univ. of Santiago de Compostela, EPS, Transportation Eng., Campus Univ. s/n, 27002 Lugo, Spain Univ. of Santiago de Compostela, EPS, Hydraulic Eng, Campus Univ. s/n, 27002 Lugo, Spain School of Marine Science and Engineering, University of Plymouth, Plymouth PL4 8AA, UK d Univ. of A Coru˜ na, Dept Information & Communications Technologies, 15071 A Coru˜ na, Spain b c

a r t i c l e

i n f o

Article history: Received 26 October 2012 Received in revised form 24 March 2014 Accepted 21 June 2014 Available online 28 June 2014 Keywords: Wave energy Artificial intelligence Neural network Numerical model Wave propagation SWAN

a b s t r a c t In this paper the assessment of the wave energy potential in nearshore coastal areas is investigated by means of artificial neural networks (ANNs). The performance of the ANNs is compared with in situ measurements and spectral numerical modelling (the conventional tool for wave energy assessment). For this purpose, 13 years of records of two buoys, one offshore and one inshore, with an hourly frequency are used to develop an ANN model for predicting the nearshore wave power. The best suited architecture was selected after assessing the performance of 480 ANN models involving twelve different architectures. The results predicted by the ANN model were compared with the measured data and those obtained by means of the SWAN (Simulating Waves Nearshore) spectral model. The quality in the predictions of the ANN model shows that this type of artificial intelligence models constitutes a powerful tool to forecast the wave energy potential at particular coastal site with great accuracy, and one that overcomes some of the disadvantages of the conventional tools for nearshore wave power prediction. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Fossil fuels, energy dense and relatively inexpensive, supply nowadays the majority of the global energy consumption. Nevertheless, it is clear that, in the short to medium term, they should be replaced to a great extent by carbon-free renewable sources [1]. While wind and solar energy exploitation have matured over the last decades and are increasingly being installed today, ocean wave energy exploitation is still unproven at a commercial scale. However, its enormous potential explains the intensive research currently dedicated to the development of wave energy conversion systems [2–8] and to the assessment of the wave resource in various regions [9–11]. In spite of their importance, the technological considerations are not the only factor to be considered in bringing wave energy to a commercial stage. Another crucial aspect is the spatial and temporal variability of the resource, which is particularly significant in the nearshore – the area with the greatest practical interest; thus, the first step to exploiting wave energy is understanding the resource

∗ Corresponding author. Tel.: +34 982 285900; fax: +34 982 285926. E-mail addresses: [email protected], [email protected] (A. Castro). http://dx.doi.org/10.1016/j.asoc.2014.06.031 1568-4946/© 2014 Elsevier B.V. All rights reserved.

and being able to perform a thorough and accurate assessment of the energy available at a site of interest [12]. There exist different methodologies and data sources to carry out a wave resource assessment which have been implemented in different coastal regions. Wave buoy data are indeed very useful, but the wave buoys may be too expensive to maintain for the periods of time needed for long-term wave climate assessment. The back-scattered signal from satellite altimeters can provide relatively cheaply [13] enormous amounts of wave data with nearly the same accuracy as a wave buoy if correctly interpreted [14]. These data, together with data obtained from global wind-wave models, are an effective approximation to the wave power in deepwater. However, they provide a poor estimate of the wave power at nearshore locations, where the complex bathymetry and coastline gives rise to shoaling, refraction and diffraction and thus to significant variations in the distribution of wave energy over small areas. Currently, spectral numerical models are the most popular tool to investigate these wave transformations and thus the available wave energy resource in the nearshore. These models compute accurately the propagation of swell in nearshore areas [15–17] without the need of an important investment of resources as it is the case of in situ measurements. However, they have some critical disadvantages, they are very time consuming, need of care and

A. Castro et al. / Applied Soft Computing 23 (2014) 194–201

195

43.7

43.6 Vilán−Sisargas buoy 1000 m

Latitude(º)

43.5

43.4 200 m

Langosteira buoy Ría de A Coruña

43.3 100 m

43.2

Cape Touriñan

43.1

SPAIN

43

−9.6

−9.4

−9.2

−9

−8.8

−8.6

−8.4

Longitude(º) Fig. 1. Map of the study area with the location of offshore buoy (Vilán-Sisargas) and the inshore buoy (Langosteira).

expertise when implementing the model, and are very sensitive to different parameters (as it may be the bathymetric data). For these reasons, in the last years, different attempts have been made to supplement or replace numerical results with other techniques [13,18,19]. In this paper, a new approach to characterising the wave energy resource at a particular coastal point based on Artificial intelligence (AI) is presented. In particular, the AI tool developed is an Artificial neural network (hereafter ANN) model, which is capable of predicting wave power at a nearshore location. Artificial neural networks have proven to be a very powerful technique capable of resolving complex physical problems [20–23]. Indeed, they have already been applied to other Coastal engineering problems with excellent results, such as the forecasting of wind and wave climate time series [13,24], wave reflection at submerged breakwaters [25], floating boom performance [26], headland-bay beach planforms [27–29] or rubble-mound breakwater stability [30]. These works have shown that ANN modelling presents key advantages such as computational efficiency or potentially predictive power, but without the need of testing numerous physical and numerical parameters or to obtain detailed geographic information [31]. The final aim of this work is to assess the performance of the ANN model and its suitability for nearshore wave power prediction. For this purpose the model results are compared with those obtained from in situ measurements and from a state-of-art spectral numerical model.

more important type of gaps are those spanning longer periods of time, from days to, in some cases, months. These gaps occur predominantly during winter months, when high energetic sea states prevail, leading to permanent failures and unfavourable climatic conditions for repair operations. Owing to this fact and the need for simultaneous data records from both buoys – a key point towards the validation of the ANN and spectral wave models – a previous step towards the development of the ANN model was to apply a filter to the original wave records of each buoy with the objective of identifying the gaps and selecting only the time periods in which both buoys were operating simultaneously. As a result of this process a total number of 72,747 valid datapoints were finally selected. The fundamental parameters for wave energy characterisation which can be obtained from buoy records were the significant wave height (Hm0 ) and the energy period (Te ) at both the offshore and nearshore buoys and the mean wave direction ( m ) at the offshore buoy. The nearshore wave power at the Langosteira buoy corresponding to each sea state is determined according to:

JBuoy =

g 2 g 2 H cg = H cn 16 m0 16 m0

(1)

where  is the seawater density, g is the gravitational acceleration, cg is the group velocity, c is the phase velocity and n is the ratio c/cg . Both c and n are calculated following linear wave theory as,

2. Wave data and wave energy characterisation The data used in this work were obtained from two types of buoys operated by Spain’s State Ports: one offshore (Vilán-Sisargas) and one nearshore (Langosteira) (Fig. 1), covering nearly 13 years (from 13/5/1998 to 8/4/2011) with an hourly frequency. The offshore and nearshore buoys are located at water depths of 386 m and 40 m, respectively. The data records from the buoys present gaps of different nature. First, there exist an important number of small gaps of a few hours which are presumably due to errors in the transmission of the data, maintenance issues or specific device failures. Another

c=

gT L = tanh(kh) T 2

n=

1 2



1+

2kh sinh(2kh)

(2)

 (3)

where L is the wave length, k = 2/L is the wave number and h the local water depth. The above equations were solved for each sea state recorded by the nearshore buoy.

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3. Nearshore wave power prediction 3.1. ANN model An ANN [32,33] is an information-processing system based on neural biology capable of storing observed knowledge related to some physical problem and making it applicable to new cases. It consists of a certain number of artificial neurons linked by means of interneuron connections simulating the structure of a human brain. An ANN learns from its environment through a training process and stores the acquired knowledge in the interneuron connections by means of synaptic weights in the same way as a human brain does. In this work a specific type of ANN called multilayer feedforward neural network is used [34]. It consists of several layers of artificial neurons (input layer, hidden layers and output layers) linked by means of feedforward connections, permitting the transmission of the information only on a layer-by-layer basis, without feedback or information exchange between neurons of the same layer. Within each neuron, the information received is modified by means of a transfer or activation function before being transmitted to the following layer. The activation function must be continuous and differentiable [33], being selected in this case the hyperbolic tangent sigmoid and the linear function as transfer functions for the neurons of the hidden layers and linear layer respectively. Two different processes have to be conducted in order to develop an ANN model: the training or learning process and the testing process. During the training process the model acquires the knowledge about the problem in question. The method commonly used to train this kind of ANN is a gradient descent technique known as the backpropagation algorithm [35]. This method minimises the error of the model through an iterative procedure which adjusts progressively the synaptic weights of the ANN model. Each iteration consists of two basic steps: first, the error between the desired output (the target) and the actual output provided by the model is computed; and second, the error obtained is propagated backward from the output layer to the input layer, adjusting the synaptic weights. This process is repeated over and over until either a maximum number of iterations or a satisfactory error level is reached. In this case, the error function used during the training process was the mean square error (MSE). However, in order to select the most appropriate ANN architecture for this application (Section 4.1) the normalised mean square error (NMSE) was used to carry out a representative comparison among the ANN architectures considered. In addition, with the objective of ensuring over-fitting or underfitting the technique called Early Stopping was used. The data used for training is divided into two subsets: the training subset used to determine the best parameters of the ANN model and the validation subset. During the training process the errors on the training subset and validation subset are monitored. Initially, the validation error decreases as the training error does. When the ANN model begins to over-fit the data the validation error typically increases. When the validation error increases during a certain number of iterations the training process is automatically stopped, being the parameters of the ANN model returned to the values corresponding to the minimum validation error. Once the model has been trained, a subsequent testing process is carried out with the objective of assessing its capability to generalise the knowledge acquired during the training process to unknown cases. A crucial step in the development of an ANN model is the selection of the input and output variables. In this case, the objective is to predict the value of wave power at a nearshore point and therefore it must be considered as the output variable of the model. As regards the selection of the input variables, it is necessary to keep in mind that the wave power at a specific coastal location is determined, in addition to the local bathymetry, by the offshore wave

conditions in front of the coastal region of interest. Conventional models (spectral numerical models) being currently implemented to assess the wave power at a certain coastal location, compute the nearshore wave power by propagating the spectrum of the offshore wave conditions defined by means of the following parameters: the significant wave height (Hm0 ), the energetic period (Te ) (or the peak period), and the mean wave direction ( m ), which are in turn the most representative parameters defining a given wave spectrum. Taking this fact into account, these parameters are also selected as input variables of the ANN model so as to conduct a reliable comparison between the results obtained by the ANN model and conventional models. The next step in the process consists in dividing the total data into two different datasets: the training dataset and the testing dataset, in order to carry out the training and the testing process. Each of the 72,747 hourly wave data provides one data point (xj , yj ), consisting of an input vector xj = (Hm0 , Te ,  m )j of offshore wave conditions and an output vector yj = Jj of nearshore wave power (the super index j designates hourly wave data). These data were distributed into a training dataset with 48,746 datapoints (67% of the total data) corresponding to the period between 13/5/1998 and 31/12/2006, and a testing dataset with 24,001 datapoints (33% of the total data) recorded from 1/1/2007 to 8/4/2011.

3.2. Spectral numerical model The conventional tool to assess the wave patterns and thus the wave energy resource at a particular coastal location is the spectral numerical model. In this case, the SWAN model (simulating waves nearshore) [36] is used to determine the wave power at the nearshore point of interest (Langosteira). This model computes the evolution of the wave spectrum by using the action balance equation, which reads:

∂ ∂ ∂ S N + ∇ · (→ CN) + (C N) + (C N) =  ∂t ∂ ∂

(6)

where N is the wave action density (N = E/),  the relative frequency, C the propagation velocity in the geographical space (→ C = → C g + → U, with → U as the ambient current), C the propagation velocity in the -space and C the propagation velocity in the -space. Finally, the term S on the right-hand side is the source term representing the effects of generation, dissipation and wave–wave interactions. In this case, the model was implemented on a Cartesian grid covering a coastal area in the north-western corner of the Iberian ˜ ˜ (Fig. 2). The grid to Ria de A Coruna Peninsula, from Cape Tourinan had 18,872 cells (M = 242; N = 109) with a varying size, approximately 600 m offshore and 200 m nearshore. The water depth was digitised and interpolated onto the numerical grid from nautical Charts 927, 928 and 412 of the Spanish Hydrographic Institute and Chart 1111 of the United Kingdom Hydrographic Office. The resulting bathymetry is shown in Fig. 3. The offshore records at Vilán-Sisargas buoy were used as boundary conditions. After running the model, the wave power for each sea state at the grid point closest to Langosteira buoy (M = 43, N = 71) is computed from:



2



JSWAN = g

∞

E(f, )Cg (f, h)dfd 0

0

(7)

A. Castro et al. / Applied Soft Computing 23 (2014) 194–201

197

Input layer

Hidden layers

Output layer

Hm0

JANN

Te

θm

Fig. 4. Architecture of the ANN model. Fig. 2. Computational grid for the spectral model. For clarity, only one in three coordinate lines is shown.

4. Results 4.1. ANN model The architecture of an ANN model is defined by means of its number of layers and its number of neurons per layer. For a given problem, the number of neurons of the input and output layer must be equal to the number of input and output variables, respectively. Therefore, in this specific case the input layer consists of three input neurons corresponding to the three input variables at the offshore location (Hm0 , Te and  m ) and the output layer must consist of one output neuron corresponding to the output variable (JANN ) at the nearshore location. Once the number of input neurons and output have been established, the subsequent step in order to define the architecture of the ANN model (Fig. 4) is to determine the number of hidden layers and the number of neurons in each hidden layer that optimise the ANN model performance. Unfortunately, there are no well-developed rules to determine the most favourable values of these parameters for a specific problem. In this case, these values were determined by means of an experimental study in which the performance of twelve different architectures (six with one hidden layer and six with two hidden layers) were compared. In order to represent the different architectures in a clear and simplified way the following notation was used: [3-hn-hn-1], which represents an architecture with three neurons in the input layer, two hidden layers with hn hidden neurons in each

one of them, and finally one neuron in the output layer. The architectures considered present the same number of neurons in each hidden layer, varying from one to six. Therefore, the architectures with one hidden layer were [3-1-1], [3-2-1], [3-3-1], [3-4-1], [3-51] and [3-6-1]; and the architectures with two hidden layers were [3-1-1-1], [3-2-2-1], [3-3-3-1], [3-4-4-1], [3-5-5-1] and [3-6-6-1]. In order to assess the performance of each architecture the normalised mean square error (NMSE) was used. Denoting the desired output for the ith energy data (obtained from the nearshore buoy records) by di , and the actual output of the ANN model by ai , the NMSE is given by the following expression, NMSE =

1 N a¯ d¯

N 

2

(ai − di ) ,

(8)

i=1

where: 1 i a, N N

a¯ =

(9)

i=1

and 1 i d¯ = d, N N

(10)

i=1

where N is the total number of data in the dataset considered. The results obtained with a given architecture can be very sensitive to the initial values of the synaptic weights established before the training process. This means that the same architecture

Fig. 3. 3D bathymetry of the study area as interpolated in the computational grid.

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trained with the same dataset may produce different outputs. Taking this fact into account, the performance of each architecture was assessed based on the results obtained not with one ANN model [37] but with a number of them (40 in this case). Each model was trained with a different set of initial synaptic weights randomly set at the beginning of the process. In this manner, the comparative study carried out with the twelve architectures involved training and testing 480 different ANN models. Once the NMSE values of the ANN models were computed for both the training and the testing dataset, the performance of the twelve architectures were compared taking into account the best result achieved with each of them. This comparison was carried out in terms of minimum NMSE obtained for the testing data, being this parameter more significant than the corresponding to the training data, as they measure the ability of the ANN model to deal with unknown data. The minimum NMSE obtained with the testing data and their respective values for the training data are shown in Figs. 5 and 6 for architectures with one and two hidden layers, respectively. In both cases, it can be observed that the values obtained with the training dataset are lower than those corresponding to the testing dataset, as it could be expected. In general terms, the value of NMSE obtained decreases as the number of neurons per layer increases.

However, beyond a certain number of hidden neurons the results obtained do not present significant improvements. Focusing on the architectures with one hidden layer (Fig. 5) the best results are obtained by the architecture [3-5-1] in terms of both training and testing NMSE, with values of 0.27 and 0.33, respectively. As mentioned before, in spite of introducing an additional neuron in the hidden layer (architecture [3-6-1]) the results do not improve. In the case of models with two hidden layers (Fig. 6) the architecture [3-5-1] provides the lowest error with the training data (NMSE = 0.24), improving the result obtained by the best one hidden layer model. However, with the testing data the architecture [3-4-4-1] provides better results than architecture [3-5-5-1] and also the architecture [3-5-1]. The training and testing NMSE obtained with the architecture [3-4-4-1] are 0.25 and 0.32, respectively. Taking this fact into account, the architecture [3-4-4-1] was selected as definitive architecture for the ANN model. In addition to the NMSE results, a linear regression analysis was carried out with the selected architecture in order to further assess its performance. The results for the training and testing dataset are shown in Figs. 7 and 8 respectively. In the first case, the best linear fit obtained is a = 0.912d + 2.099

(11)

900

0,50 Training dataset Testing dataset

700

a (ANN model)

0,45

0,40

NMSE

a=d Training y = 0.91*x + 2.1data Best linear fit

800

0,35

600

500

400

300

0,30 200

100

0,25

0

0,20

0

1

2

3

4

5

100

200

300

400

500

600

700

800

900

d (Langosteira buoy)

6

NEURONS PER LAYER Fig. 7. Linear regression analysis with the training dataset. Fig. 5. Minimum NMSE values obtained with the architectures with one hidden layer.

900

a=d Test data Best linear fit

800

0,50 Training dataset Testing dataset

700

0,45

a (ANN model)

600

NMSE

0,40

0,35

500

400

300

0,30

200

0,25 100

0,20

1

2

3

4

5

6

NEURONS PER LAYER

0

0

100

200

300

400

500

600

700

d (Langosteira buoy)

Fig. 6. Minimum NMSE values obtained with the architectures with two hidden layers.

Fig. 8. Linear regression analysis with the testing dataset.

800

900

A. Castro et al. / Applied Soft Computing 23 (2014) 194–201

199

1

1

1

0.8

0.8

0.8

JANN 0.6

0.6

0.6

40%

0.4

0.4

0.4

80%

values between 110 – 180 degrees

20% 60% 100%

0.2

0.2 0

0

0.2

0.6

0.4

0.8

1

0

0

0.2

0.2

0.4

0.6

0.8

1

0

0

0.2

0.4

0.6

0.8

1

θm

Te

Hm0

Fig. 9. Sensitivity analysis of the ANN output to each input. Splits represent the quantile values at which the remaining inputs were held constant.

with a correlation coefficient R equal to 0.96 (R2 = 0.91), which shows that the model has properly acquire the knowledge about the problem from the training dataset. The results obtained from the regression analysis with the testing dataset are also good (R = 0.96 and R2 = 0.91), showing a excellent response to new cases. In this case, the equation of the best fit line has the following expression: a = 0.850d + 4.101

(12)

4.2. Sensitivity analysis of the ANN model In order to study the effect of each input on the output predicted by the ANN model a sensitivity analysis was carried out by means of the method called “Profile” [38]. This method consists in obtaining the ANN outputs corresponding to the possible values across the range of a specific input while the values of the remaining inputs are keeping constant inside a given set of values. This process is carried out for different sets covering all the range of variation of the input. As a result of this process, a set of response curves for each input are obtained covering their corresponding range of variation (Fig. 9). The response curves show different behaviours as a function of the input. The curves corresponding to the significant wave height Hm0 show the importance of this variable on the predictions, being the influence of the energetic period Te less important. In the case of the mean wave direction  m a significant change on the behaviour of the ANN prediction can be observed in the range of values between 110 and 180◦ . This values correspond to a few cases included in the dataset (54 cases) in which the offshore buoy detected waves coming from the coast originated by the wind regimen in this area, and represents a change in the behaviour of the

nearshore wave power in the Langosteira buoy registers, in relation with the inputs values. As it can be seen in Fig. 9, the ANN uses the wave direction input to detect this feature and adapt the output to make a right prediction. This sensitivity analysis also permits to quantify the influence of each parameter on the ANN response. In this case, the average contribution to the output of each input in terms of percentage is 53.2% in the case of the significant wave height Hm0 , 25.4% in the case of the energetic period Te and finally 21.4% in the case of the mean wave direction  m . These results indicate that all the inputs have a significant influence on the prediction, being the significant wave height Hm0 the most significant variable in the prediction process.

4.3. ANN model vs. spectral model The performance of the ANN model was compared with the results obtained by means of the SWAN spectral model. The period (February, 2011) was selected so that it covered a wide range of wave conditions, including low, mean and powerful sea states (with a heavy storm occurred during 15/02/11–17/02/11) (Fig. 10), and thus the performance of the ANN model can be reliably assessed. The results obtained are shown in Fig. 11 and the corresponding statistics are presented in Table 1. It can be observed that overall there is very good agreement throughout the whole simulation period, and in particular during the most energetic seas states – Hm0 values varying from 2 to 5 m at deep water (Fig. 10), which correspond to energetic periods of Te = 9–14 s [39,40]–of crucial importance to perform an accurate energy characterisation at the coastal site of interest.

Hm0(m)

10 8 6 4 2 0 01/02

04/02

07/02

10/02

13/02

16/02

19/02

22/02

25/02

28/02

Date Fig. 10. Significant wave height at the offshore buoy during February 2011.

5

10

x 10

JBuoy

J(W/m)

8

JANN

6

JSWAN

4 2 0 01/02

04/02

07/02

10/02

13/02

16/02

19/02

22/02

25/02

28/02

Date Fig. 11. Nearshore wave power obtained from the Langosteira buoy (JBuoy ), from ANN model (JANN ) and from SWAN spectral model (JSWAN ).

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Table 1 Correlation coefficient (R) and Normalised Mean Square Error (NMSE) between wave power computations obtained from ANN model, buoy measurements and SWAN model.

R NMSE

ANN vs Buoy

SWAN vs Buoy

ANN vs SWAN

0.94 0.23

0.89 0.23

0.96 0.17

The performance of the ANN model is even better than that the achieved by SWAN model (similar NMSE and higher R) with the exception of the most powerful peak (Fig. 11). It is also important to note the excellent agreement obtained between the ANN and SWAN models, which may indicate that the behaviour of the ANN model reproduces that of the numerical model. This fact may also indicate the possibility of the presence of some not-so-accurate in situ measurements either from the offshore or nearshore buoys, in particular during the storm peaks during which both models present the less accurate results.

5. Conclusions In this work, an ANN model for predicting the nearshore wave power has been developed. It uses as input three offshore parameters: significant wave height, energy period and mean wave direction. In order to select the most appropriate ANN architecture for this specific problem, a thorough experimental study involving twelve different architectures with one and two hidden layers was conducted. The performance of each architecture was characterised in terms of minimum NMSE obtained after 40 training processes with the training and testing dataset. The best result was provided by the architecture [3-4-4-1], with three input neurons, two hidden layers with four neurons per layer, and one output neuron. An excellent agreement between the field data and the results of the ANN model was achieved, with very high correlation coefficients for both training and testing data (R = 0.96 and R2 = 0.91). A sensitivity analysis was also carried out in order to study the effect of each input on the output predicted by the ANN model. The results showed that the significant wave height Hm0 is the most important input variable with a contribution of 53.2% to the output, while the energetic period Te and the mean wave direction  m contribute with 25.4% and 21.4% respectively. Finally, the performance of the ANN model was compared with a state-of-the-art spectral model (SWAN model). For this purpose a period of time covering a wide range of wave conditions was selected. The results obtained show that the ANN model is capable of yielding very accurate wave power predictions (R = 0.93; NMSE = 0.23), even more precise than a conventional spectral wave model. Furthermore, during the more energetic sea states (Hm0 = 2–5 m; Te = 9–14 s) the ANN model showed an excellent behaviour, reproducing the nearshore wave power calculated from the buoy measurements very precisely. The ANN model developed in this work constitutes a powerful tool to compute quickly and with great accuracy the wave power at a nearshore coastal location without the computational cost associated to a spectral wave model. Furthermore, the results obtained indicate that the ANN model can be used to determine the actual wave power output of a WEC at the coastal point of interest with nearly the same (or even the same) accuracy as with a wave buoy, for the bulk of the energy is provided by sea states for which the behaviour of the ANN model is almost perfect, but without the high costs associated to the maintenance of the buoy.

Acknowledgements This work was supported by project DPI2009-14546-C02-02 (“Assessment of Renewable Energy Resources”) of the Spanish Ministry of Science and Innovation and the project “Development of a geospatial database for the exploitation of the energy resource along the Galician Coast” funded by the Barrie de la Maza Foundation. The authors are indebted to Puertos del Estado (Spain’s State Ports), in particular to Dr. I. Rodríguez-Arévalo, Dr. E. Fanjul, Ms. P. Gil and Ms. S. Pérez, for kindly providing the wave data.

References [1] P. Lenee-Bluhm, R. Paasch, H.T. Özkan-Haller, Characterizing the wave energy resource of the US Pacific Northwest, Renew. Energy 36 (2011) 2106–2119. [2] A.J. Caska, T.D. Finnigan, Hydrodynamic characteristics of a cylindrical bottompivoted wave energy absorber, Ocean Eng. 35 (2008) 6–16. [3] J.M.B.P. Cruz, A.J.N.A. Sarmento, Sea state characterisation of the test site of an offshore wave energy plant, Ocean Eng. 34 (2007) 763–775. [4] A.F.d.O. Falcão, Wave energy utilization: a review of the technologies, Renew. Sustain. Energy Rev. 14 (2010) 899–918. [5] M.F.P. Lopes, J. Hals, R.P.F. Gomes, T. Moan, L.M.C. Gato, A.F.d.O. Falcão, Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter, Ocean Eng. 36 (2009) 386–402. [6] G.S. Payne, J.R.M. Taylor, T. Bruce, P. Parkin, Assessment of boundary-element method for modelling a free-floating sloped wave energy device. Part 1: Numerical modelling, Ocean Eng. 35 (2008) 333–341. [7] C. Beels, P. Troch, J.P. Kofoed, P. Frigaard, J. Vindahl Kringelum, P. Carsten Kromann, et al., A methodology for production and cost assessment of a farm of wave energy converters, Renew. Energy 36 (2011) 3402–3416. [8] C. Beels, P. Troch, G. De Backer, M. Vantorre, J. De Rouck, Numerical implementation and sensitivity analysis of a wave energy converter in a time-dependent mild-slope equation model, Coast. Eng. 57 (2010) 471–492. [9] G. Iglesias, R. Carballo, Choosing the site for the first wave farm in a region: a case study in the Galician Southwest (Spain), Energy 36 (2011) 5525–5531. [10] G. Iglesias, R. Carballo, Wave resource in El Hierro—an island towards energy self-sufficiency, Renew. Energy 36 (2011) 689–698. [11] G. Iglesias, R. Carballo, Wave power for La Isla Bonita, Energy 35 (2010) 5013–5021. [12] R.C. Ertekin, X. Yingfan, Preliminary assessment of the wave-energy resource using observed wave and wind data, Energy 19 (1994) 729–738. [13] R. Kalra, M.C. Deo, Derivation of coastal wind and wave parameters from offshore measurements of TOPEX satellite using ANN, Coast. Eng. 54 (2007) 187–196. [14] S. Barstow, G. Mork, L. Lonseth, J.P. Mathisen, WorldWaves wave energy resource assessments from the deep ocean to the coast, in: Proceedings of the 8th European Wave and Tidal Energy Conference, Uppsala, Sweden, 2009. [15] G. Iglesias, R. Carballo, Wave energy resource in the Estaca de Bares area (Spain), Renew. Energy 35 (2010) 1574–1584. [16] G. Iglesias, R. Carballo, Offshore and inshore wave energy assessment: Asturias (N Spain), Energy 35 (2010) 1964–1972. [17] G. Iglesias, R. Carballo, Wave energy and nearshore hot spots: the case of the SE Bay of Biscay, Renew. Energy 35 (2010) 2490–2500. [18] T. Kobayashi, T. Yasuda, Nearshore wave prediction by coupling a wave model and statistical methods, Coast. Eng. 51 (2004) 297–308. [19] A.R. Rambekar, M.C. Deo, Wave prediction using genetic programming and model trees, J. Coast. Res. 28 (2012) 43–50. [20] D. Chen, C. Gao, Soft computing methods applied to train station parking in urban rail transit, Appl. Soft Comput. 12 (2012) 759–767. [21] E. Karadurmus, M. Cesmeci, M. Yuceer, R. Berber, An artificial neural network model for the effects of chicken manure on ground water, Appl. Soft Comput. 12 (2012) 494–497. [22] D. Niu, H. Shi, D.D. Wu, Short-term load forecasting using Bayesian neural networks learned by Hybrid Monte Carlo algorithm, Appl. Soft Comput. 12 (2012) 1822–1827. [23] S. Pandey, D.A. Hindoliya, R. Mod, Artificial neural networks for predicting indoor temperature using roof passive cooling techniques in buildings in different climatic conditions, Appl. Soft Comput. 12 (2012) 1214–1226. [24] O. Makarynskyy, A.A. Pires-Silva, D. Makarynska, C. Ventura-Soares, Artificial neural networks in wave predictions at the west coast of Portugal, Comput. Geosci. 31 (2005) 415–424. [25] A. Castro, F.T. Pinto, G. Iglesias, Artificial intelligence applied to plane wave reflection at submerged breakwaters, J. Hydraul. Res. 49 (2011) 465–472. [26] G. Iglesias, A. Castro, J.A. Fraguela, Artificial intelligence applied to floating boom behavior under waves and currents, Ocean Eng. 37 (2010) 1513–1521. [27] G. Iglesias, I. López, A. Castro, R. Carballo, Neural network modelling of planform geometry of headland-bay beaches, Geomorphology 103 (2009) 577–587. [28] G. Iglesias, I. López, R. Carballo, A. Castro, Headland-bay beach planform and tidal range: a neural network model, Geomorphology 112 (2009) 135–143. [29] G. Iglesias, G. Diz-Lois, F.T. Pinto, Artificial intelligence and headland-bay beaches, Coast. Eng. 57 (2010) 176–183.

A. Castro et al. / Applied Soft Computing 23 (2014) 194–201 ˜ M.A. Losada, H. Pachón, A. Castro, R. Carballo, A virtual lab[30] G. Iglesias, J. Rabunal, oratory for stability tests of rubble-mound breakwaters, Ocean Eng. 35 (2008) 1113–1120. [31] M. Browne, D. Strauss, B. Castelle, M. Blumenstein, R. Tomlinson, C. Lane, Empirical estimation of nearshore waves from a global deep-water wave model, IEEE Geosci. Remote Sens. Lett. 3 (2006) 462–466. [32] R.P. Lippman, An introduction to computing with neural nets, IEEE 4 (2) (1987) 4–22, ISSN: 0740-7467. [33] M.T. Hagan, H.B. Demuth, M.H. Beale, Neural Network Design, PWS Publishing, Boston, 1996. [34] S. Haykin, Neural Networks, Prentice Hall, New Jersey, 1999. [35] E.M. Johansson, F.U. Dowla, D.M. Goodman, Backpropagation learning for multi-layer feed-forward neural networks using the conjugate gradient method, Int. J. Neural Syst. 2 (1991) 291–301.

201

[36] N. Booij, R.C. Ris, L.H. Holthuijsen, A third-generation wave model for coastal regions 1. Model description and validation, J. Geophys. Res. C: Oceans 104 (1999) 7649–7666. [37] H.R. Maier, G.C. Dandy, Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications, Environ. Model. Softw. 15 (2000) 101–124. [38] M. Gevrey, I. Dimopoulos, S. Lek, Review and comparison of methods to study the contribution of variables in artificial neural network models, Ecol. Model. 160 (2003) 249–264. [39] G. Iglesias, R. Carballo, Wave energy potential along the Death Coast (Spain), Energy 34 (2009) 1963–1975. [40] R. Carballo, G. Iglesias, A methodology to determine the power performance of wave energy converters at a particular coastal location, Energy Convers. Manag. 61 (2012) 8–18.