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Applied Soft Computing 13 (2013) 3449–3458

Contents lists available at SciVerse ScienceDirect

Applied Soft Computing

j ourna l h o mepage: www.elsev ier .com/ locate /asoc

hybrid artificial intelligence model for river flow forecasting

arlos H. Fajardo Toro ∗, Silvana Gómez Meire, Juan F. Gálvez, Florentino Fdez-Riverolascuela Superior de Ingeniería Informática, University of Vigo, Edificio Politécnico, Campus Universitario As Lagoas s/n, 32004 Ourense, Spain

r t i c l e i n f o

rticle history:eceived 5 July 2010eceived in revised form5 September 2012ccepted 19 April 2013vailable online 2 May 2013

a b s t r a c t

A hybrid hydrologic estimation model is presented with the aim of performing accurate river flow fore-casts without the need of using prior knowledge from the experts in the field. The problem of predictingstream flows is a non-trivial task because the various physical mechanisms governing the river flowdynamics act on a wide range of temporal and spatial scales and almost all the mechanisms involvedin the river flow process present some degree of nonlinearity. The proposed system incorporates bothstatistical and artificial intelligence techniques used at different stages of the reasoning cycle in order to

eywords:iver flow forecastingydrologic modelslack-box approachesase-based reasoningybrid forecasting system

calculate the mean daily water volume forecast of the Salvajina reservoir inflow located at the Departmentof Cauca, Colombia. The accuracy of the proposed model is compared against other well-known artifi-cial intelligence techniques and several statistical tools previously applied in time series forecasting. Theresults obtained from the experiments carried out using real data from years 1950 to 2006 demonstratethe superiority of the hybrid system.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

River flow modelling and prediction is one of the earliest fore-asting problems to have attracted the interest of a good numberf scientists. Given the importance of estimating flows for theivelihoods of inhabitants located near rivers, it has been neces-ary to record and study the flow data from early historical times.n fact, the ancient Egyptians established several mechanisms to

easure river flows, even using this knowledge to predict floods1].

Nowadays, the availability of an accurate river flow forecast-ng method can help in the resolution of relevant tasks such asi) the optimal design of water storage and drainage networks, (ii)he management of extreme events such as floods and droughts,iii) the planning of future expansion or reduction of reser-oir capacities, (iv) improving the efficiency of power generationnd (v) aiding in the prevention and comprehension of hydro-ogic hazards like the change of hydro-climatic regime, erosionnd sediment movement, mud flows or environmental pollutants

2,3].

In the context of time series studies, prediction methods are usu-lly based on the analysis, representation and projection of existing

∗ Corresponding author at: ESEI: Escuela Superior de Ingeniería Informática, Edi-cio Politécnico, Campus Universitario As Lagoas s/n, 32004 Ourense, Spain.el.: +34 988 387028; fax: +34 988 387001.

E-mail addresses: cfajardo@uvigo.es (C.H.F. Toro), sgmeire@uvigo.esS. Gómez Meire), galvez@uvigo.es (J.F. Gálvez), riverola@uvigo.es (F. Fdez-Riverola).

568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.asoc.2013.04.014

time series data [4]. In this situation, obtaining an accurate fore-cast is particularly difficult when the target system is governed bydynamic processes under chaotic and stochastic conditions. To dealwith this scenario in our problem domain, traditional approacheslike statistical tools and specific hydrological models have been pre-viously applied with different levels of success [5,6]. Nevertheless,relatively recent works apply artificial intelligence (AI) methodslike artificial neural networks (ANNs) and hybrid systems to theproblem of river flow forecasting in order to generate more accuratemodels [7–9].

Based on our previous experience developing hybrid forecastingsystems [10,11], here we present the definition of a novel hybridAI model able to predict the behaviour of a reservoir flow influxlocated in the Department of Cauca (Colombia). The aims for devel-oping the proposed system are twofold: it should allow a preciseestimation of the electricity production as well as provide adequateflood control in the zone.

The implemented system uses a case-based reasoning (CBR)model that incorporates a hierarchical clustering technique and aFourier frequency analysis method to perform the initial selectionand filter of similar data values, an Elman and a Modular ANN togenerate a primitive forecast, and a final auto configurable weight-ing schema able to adjust the definitive prediction.

The structure of the paper is as follows: first, we present a briefoverview of past efforts and recent approaches related with river

flow forecasting; then the hybrid forecasting system is explainedand the results obtained with the proposed model are discussedand analyzed; finally, the main conclusions are summarized andfuture work is outlined.

3450 C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458

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Fig. 1. Simplified hydro cl

. River flow forecasting: past efforts and recentpproaches

In hydrology, river flow forecasting is one of the most fre-uently analyzed problems. For this reason, different predictiveodels coming from several areas of knowledge under different

pproaches and with specific goals have been developed resultingn various levels of success. Although many of them are variations ofNN architectures and neuro-fuzzy approaches, numerous hydro-

ogical models and black-box alternatives are also available. Thisection presents a general overview of existing approaches previ-usly used in hydrology that are related to the problem of river floworecasting.

.1. Classical forecasting methods: hydrological and black-boxodels

During the last decades, a large number of papers focusedn modelling and forecasting of river flow dynamics have beenublished [12–18]. This is because, previous to the develop-ent and general application of AI tools in the field, hydrologists

nd researchers had to appeal to some expert-based forecastingethods or to develop new models according to the intrinsic char-

cteristics of the problem domain. Many techniques currently usedn both approaches assume linear relationships amongst the vari-bles. These techniques can be classified into two main groups: (i)ydrological models and (ii) black-box approaches.

Hydrological models can be understood from three differenterspectives: (i) based on spatial representation [19], (ii) based on

representation of the hydrological processes [20] and (iii) basedn the temporal extension in which the model can be applied [12].

The classification based on spatial representation considershree types of models: (i) aggregated (ii) semi-distributed and (iii)istributed models. In the first type, a uniform spatial rain distri-ution is assumed and all the hydrological variables are consideredlobal and constant in time for the whole basin. The second typellows some variability in both the spatial distribution of rain andhe hydrological variables. The last type permits variability in thearameters and the spatial distribution of rain, dividing the basin

nto cells and simulating hydrological processes for each one.Taking into account the classification based on the representa-

ion of hydrological processes, there are three main categories: (i)

hysically based models [13,14], (ii) conceptual models [15] andiii) metric models [16,17]. The first one is specifically designedo mathematically simulate or approximate the general internalub-processes and physical mechanisms that govern the river flow

model (physically based).

process. The input is represented by the precipitation values thatare partitioned into components and routed through the sub-processes to the watershed outlet as stream flow, to the surfaceand deep storages or to the atmosphere as evaporation [13]. Fig. 1shows a simplified hydrological model that incorporates five phys-ical variables (incoming shortwave and outgoing longwave; ozoneabsorption and emission; H2O and CO2 absorption and emission;latent and sensible heat fluxes; precipitation) together with theirinteractions.

In the case of conceptual models, parameters must be estimatedfrom fitting the model to historical rainfall-runoff data. Fig. 2 showsa typical structure of a conceptual watershed hydrological modeladapted from [21]. Therefore, a conceptual model can not be usedin engaged watersheds where historical rainfall-runoff data are notavailable.

Finally, metric models are those that, after performing a searchon the observed data are able to characterize the system response.The characterization is performed by an information extractionmethod applied over the existing data. These models are built withminimal or no consideration of the physical processes that occur inthe hydrological system, and they use the simplest watershed rep-resentation. Their main advantage is that they require minimumdata, but their utilization is limited because of both the variabil-ity of the observed data and their inability to consider watershedchanges.

The classification based on temporal extension distinguishestwo main categories: (i) event-driven models, developed for shorttime simulations with a unique rain episode, and (ii) continuousmodels, which allows daily, monthly and seasonal runoff simula-tions.

While physically based models are very useful to understandthe physical mechanisms involved in river flow dynamics or anyother hydrological process, they are difficult to apply. The maindrawbacks originate from the fact that they require a large numberof parameters to model the complexity of river flow dynamics andthe difficulties associated with the extension of a particular modelto even slightly different situations.

In contrast to hydrological models, black-box approaches aredesigned to identify the connection between inputs and outputswithout analyzing the internal structure of the physical process[18]. In this approach, stochastic models are fitted to historicalrecords in order to forecast the short and long term behaviour of

hydrological variables that represent the states of the hydrologicalphenomena. In this sense, black-box models may not necessarilylead to a better understanding of the river flow process, but theydo have the advantage of being easy to apply even under different

C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458 3451

erived

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Fig. 2. Conceptual watershed hydrological model. D stands for the flow d

onditions since the modelling and forecasting procedures aresually similar. Moreover, the analysis of characteristic parame-ers of black-box models can furnish useful information about theynamics of the phenomenon under study.

In the black-box approach, AR (Autoregressive) models are theost widely used, especially ARMA (Autoregressive Moving Average)

nd ARIMA (Autoregressive Integrated Moving Average) techniques22,23]. Some other simple methods such as moving average, expo-ential smoothing or regression models (simple and multiple)ould be also used depending on the number of available vari-bles and their correlation. Moreover, previous hydrological studiesuggest the utilization of some techniques according to the char-cteristics of the series. For single and multiple stationary timeeries, it is recommended to use AR, ARMA and ARIMA modelss well as the GAR (Gamma Autoregressive) approach [18]. In thease of single and multiple periodic time series, the usage of PARPeriodic Autoregressive), PARMA (Periodic Autoregressive Movingverage) and periodic GAR models are appropriate [18]. However,hese models represent the nonlinear characteristics of hydrologi-al processes assuming ‘causes’ no change, which is something thatoes not usually happen within the hydrological domain.

.2. More recent trends: AI approaches

As already mentioned, almost all the hydrological variables androcesses exhibit highly non-linear behaviour and, in many cases,esearchers represent those variables and processes using classi-

al physically based models. The use of conventional or statisticalechniques is not appropriate because of the poor understanding ofhe relations and the complex interactions between the processes.ence, there is a need for improvement in forecasting techniques.

from one tank to another. H represents the available water in each tank.

In this sense, AI offers flexible structures and non-parametric algo-rithms capable of identifying and capturing the complex non-linearrelationships between input and output data sets [2].

During the last 20 years there has been a growing interest inapplying various AI techniques to both time series prediction ingeneral and hydrological forecasting in particular. These techniquesinclude neural networks [23] (comprising multi-layer perceptrons(MLP), radial basis function (RBF) networks, modular networks andrecurrent neural networks) [24–31], fractal analysis [32,33], geneticalgorithms [34,35] and fuzzy logic [36–38]. These techniques havebeen mainly used for simulating, forecasting and predicting thepossible behaviour of different hydrological variables [22,39].

From all the previous successful soft computing methods andtechniques, ANNs are particularly suitable for dealing with theintrinsic characteristics commonly present in hydrological pro-cesses [40]. In this sense, neural networks have the ability tocorrectly handle extremely noisy and prone to error time series.Moreover, hydrological processes are highly non-linear in nature,a situation that can be alleviate by the flexible mathematical struc-ture of ANNs, able to identify complex relationships between inputand output data. A final advantage of ANNs with application intime series forecasting is that the statistical distribution of the rawdata need not be known in advance, because the non-stationaritiespresent in the time series (e.g., trends and seasonal variations)are implicitly accounted for by the internal structure of the neuralnetworks.

In contrast with previous hydrological forecasting studies that

use simple models or ensemble alternatives based on ANNs[23–31,40], the proposed system hybridizes two different neuralnetworks (i.e., Elman and Modular) working in parallel as copro-cessors in order to generate an initial but precise forecast. This

3452 C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458

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Fig. 3. Hybrid CBR system

pproach is enclosed by a previous historical filtering phase ableo select similar data and a later process of weight modificationhich ensures continuous learning. Such integration is a distinc-

ive characteristic of the proposed system that will be responsibleor its accurate results.

. Hybrid system for river flow forecasting

As already mentioned, a novel CBR system is proposed for calcu-ating the mean daily water volume forecast of a reservoir inflow.he main reason for using a CBR approach is that this methodologyasily allows the combination and fusion of different AI algorithmsnd statistical techniques, resulting in more scalable and accurateybrid models.

In this context, CBR systems define four sequential stages thatre invoked every time a new problem (prediction) needs to beolved: (i) retrieval of previous cases that are more similar to the

resent one, (ii) reuse (adaptation) of those situations in order toenerate a feasible solution to the present problem, (iii) review ofhe initial solution proposed by the system and (iv) retain (learning)he final solution as a new case for future reuse [41,42].

ecture and data workflow.

In order to forecast the inflow of the target reservoir one dayin advance, a problem descriptor (case) has been defined on aquarterly basis, so each case represents the daily reservoir inflowcorresponding to the previous three months. The proposed quarterrepresentation is conceptually justified by a hydrological con-cept called ‘seasonal regime’, which explains the phenomena thataffect the fluvial network, being tightly related with seasons innorthern and southern zones defined by the temperature changes[43].

In the proposed hybrid model, the forecasted values areobtained using different techniques at different stages of the CBRlife cycle. In this context, Fig. 3 presents the general architecture anddata workflow of the developed model. Both, the proposed archi-tecture and life cycle are based on the previous successful work ofFdez-Riverola and Corchado [10,11].

The forecasting model represented in Fig. 3 incorporates (i) ahierarchical clustering algorithm and a Fourier frequency analysismethod to perform the initial selection and filter of similar past

cases, (ii) an Elman and a Modular ANN for in line generation of aprimitive forecast, (iii) an auto configurable weighting schema ableto adjust the final prediction of the model and (iv) a learning proce-dure for automatically updating the knowledge base. In the middle

C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458 3453

Table 1Summary of the technologies comprising the hybrid CBR system.

CBR phase Technology Input Output Process

Retrieval Quarter extractionalgorithm

- Problem descriptor Historical quarters fromprevious years belonging to thesame period (season) offorecasting

Based on the forecasting date,historical data is divided into quartersand filtered taking into considerationthe forecasting season

(ad-hoc procedure) - Historical daily record of riverflow volume (in m3/sec)

Hierarchicalagglomerative

- Last quarter existing in thecase base (containing theproblem descriptor)

Ranked dendogram identifyingmost similar quarters withrespect to the problemdescriptor

The distance measure characterizingWard’s method is based on thevariance criterion (small variancewithin each cluster and large variancebetween the clusters)

clustering - Historical quarters belongingto the same period (season)

(Ward distance)Fourier FrequencyAnalysis

Most similar quarters (withminimal variance)

Filtered historical daily recordof river flow volume belongingto those similar quartersshowing the same periodicity

Spectral density analysis of similarquarters for detecting time seriesperiodicity

(FFT algorithm)Reuse Elman ANN - Problem descriptor Initial solution for the problem

descriptor (river flow volumein m3/sec)

Semi-recurrent neural network baseon a Jordan ANN (7 × [20] × 1)

Modular ANN - Raw training data (historicaldaily record of river flowvolume) belonging to quarterswith minimal variance andsame periodicity

Initial solution for the problemdescriptor (river flow volumein m3/sec)

2 MutiLayer Perceptrons working inparallel with two hidden layers eachone (7 × [16 × 8] × 1)

Revise Weighted votingalgorithm

- Initial solutions provided bythe Elman and Modular ANNs

- Final adjusted forecast The MAE index is used to weight eachANN model for computing the finalforecast. The confidence interval iscalculated using the weighted MSE andthe final forecast

- Performance assessment ofeach ANN (historical MSE andMAE)

- Confidence interval

Retain Elman ANN - Problem descriptor Hydrology series case base andthreshold weights updated

A new case (forecasted situation) isadded to the case base and thethreshold weights are updated

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Modular ANN - Forecasting error

f Fig. 3 there is the hydrology series case base that implements theemory of the CBR system by storing all the time series data.

.1. System operation

Every time a new prediction needs to be made, the proposedystem evolves from phase 1 (retrieval) to phase 4 (retain). Table 1etails the techniques used to implement each phase comprisinghe whole CBR life cycle.

The retrieval stage is carried out using three sequential steps: (i)uarter extraction, (ii) hierarchical clustering and (iii) spectral den-ity analysis. In the first step, all the quarters from previous yearshat correspond with the same weeks of the problem descriptor arenitially selected. Then, a hierarchical clustering algorithm based onhe Ward distance is used to identify those historical quarters mostimilar to the present situation. Finally, a spectral density analysisased on the Fourier frequency is applied to the selected quarters inrder to choose those cases with similar frequency (retrieval phasen Table 1).

Once the most similar quarters with uniform frequency haveeen selected, the reuse stage is carried out by training with theseata two different neural networks: an Elman ANN [44,45], which

mplements a semi-recurrent neural network based on a JordanNN [46], and a Modular neural network [9]. The Elman network

s composed of seven neurons in the input layer (representing therevious week), one hidden layer with 20 neurons and one neuron

n the output layer. The Modular neural network comprises twoLPs working in parallel with seven neurons in the input layer,

two hidden layers with sixteen and eight neurons respectively, andan output layer with one neuron. Both networks are responsible forgenerating an initial solution that will be combined to obtain a finalforecast through a weighting process mechanism (Reuse phase inTable 1).

The revision stage performs the weighting of the initial fore-cast generated by the two neural networks and establishes the finalconfidence interval. Threshold weights are initially defined by thepercentage of times each neural network has obtained the best fore-cast based on the Mean Square Error (MSE) and Mean Absolute Error(MAE) efficiency indexes (revise phase in Table 1).

Finally, in the learning stage a new case is stored in the hydrol-ogy series case base and the threshold weights are subsequentlyupdated taking into consideration the efficiency indexes (retainphase in Table 1).

4. Experimental setup and results

The raw data used for the present study was taken from themonitoring network of the Cauca Valley Regional Autonomous Cor-poration (CVC) that maintains more than 150 hydrometric andrainfall stations which perform the measurement and control ofwater resources in the valley and north of river Cauca. Under anagreement with the Pacific Power Company (EPSA), the CVC super-

vises the Salvajina reservoir for energy production. In this context,one of the CVC goals is to determine the amount of water that maybe used for power generation, while restricting the reservoir dropsto critical levels.

3454 C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458

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Fig. 4. Salvajina reservoir inflow

.1. Study area and dataset pre-processing

Available data is received and processed daily in the Salva-ina hydrometric station located at the Department of Cauca, inolombia (see Fig. 4). This information represents the daily recordf river flow volume (m3/s), level of rainfall (ml/m2) and temper-ture (◦C) from ground measurements provided by CVC from theears 1950 to 2006.

In order to generate a ready-to-use dataset for training, vali-ation and testing purposes, it was necessary to previouslyre-process and analyze available raw data. The first step carriedut was the treatment of wrong and missing values. In the case ofissing values corresponding to river flow and rainfall level vari-

bles, time series were completed using a weighting procedure inhich the new values were calculated taking into consideration

heir relative importance for the current month when comparedith the whole year. For the temperature, the new value was esti-ated as the mean between the day before and after the target date.rong values were processed in the same way as missing variables.The second processing step was the execution of a correlation

nalysis between filtered and adjusted variables. At first, it was car-ied out with data in the original order, but later the rainfall levelecords were advanced by one day to evaluate the assumption that

ne day average rainfall influence next day average flows. Based onhe experimental results obtained, temperature was discarded asnput variable due to its low correlation with regard to river flowolume.

artment of Cauca – Colombia).

The final step involved the execution of several simulations withstandard neural networks using both the level of rainfall and theriver flow volume as input variables. The results obtained showedthat in all the situations, the neural networks performed well onlywith the river flow variable as input, so the level of rainfall was alsofinally discarded.

As a result of all the previous data pre-processing operations, afinal debugged case base was generated containing only the dailyrecord of river flow volume (in m3/s) belonging to the Salvajinahydrometric station from year 1950 up to 2006. The final hydrologyseries case base incorporates a total amount of 224 quarters (56years) with more than 20,000 individual points.

4.2. Reservoir inflow forecasting results

In order to validate the proposed approach, we have tested ourhybrid system using the previous generated case base. In all theexperiments we have utilized 60% of the available data to trainthe models (134 quarters), 15% to estimate the best configura-tion parameters (34 previously unseen quarters) and the remaining25% of unseen data for testing purposes (56 quarters). This vali-dation schema and distribution is commonly accepted for testingthe performance of different approaches in time series forecast-

ing problems [47]. Fig. 5 summarizes the dataset pre-processingcarried out and how the experimental configuration was setup.

Table 2 displays the values for those commonly used efficiencyindices obtained by the hybrid system during the test period. After

C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458 3455

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obtained from using five different ANN alternatives: (i) a Feed-forward neural network, (ii) a Radial Basis Function (RBF), (iii) a

Fig. 5. Dataset pre-processin

he whole training of the CBR model and the configuration of theest parameters for the ANNs implementing the reuse phase, thenal weight assigned to the Elman and Modular ANNs was 0.59 and.41, respectively. All the experiments including the whole training,alidation and test processes carried out by the hybrid system werexecuted on a personal computer with Intel Core 2 Quad 3 GHzrocessor and 4 GB RAM. The computation time for all the tasksas about 47 min.

Further experiments were carried out to compare the perfor-ance of the CBR hybrid system with several other forecasting

pproaches. These include standard statistical forecasting algo-ithms (from Statgraphics Centurion software) and the applicationf several neural networks methods (available in NeuroSolutionsuite 5.0). Tables 3 and 4 show the results obtained by the sta-istical approaches during the estimation and validation periods,espectively.

The error series produced by the previous statistical tech-iques and the proposed CBR system did not present a normalehaviour when the Kolmogorov–Smirnov and Shapiro–Wilk testsere applied, so this fact tends to invalidate the results obtained

y any parametric test. In order to deal with this situation, a non-arametric Kruskall–Wallis test was executed. Since the P-value is

ess than 0.01 there is a statistically significant difference amonghe models at the 99.0% confidence level. Fig. 6 shows a standardox-and-Whisker plot for the different alternatives.

From Fig. 6 it can be seen that the proposed CBR system shows higher concentration of data (i.e., error values calculated fromhe predicted outcomes), which means that although the efficiency

able 2ummary of results using the proposed CBR system.

Model Mean standarderror

Mean absoluteerror

Mean absolutepercentage error

CBR system 702.1845 17.1141 16.0500

experimental configuration.

indices are similar between the analyzed models, data dispersion islower (dot lines from left and right of the middle box) and therebythe forecast value and its confidence interval is more reliable.

In order to complement the comparison and gain a deeperinsight, Table 5 shows some alternative indexes which reflect thebehaviour of the analyzed model. This table includes the standarddeviation of the error (SD), the maximum and minimum values forthe predictions carried out and the range between these values.From Table 5 it can be seen that the smallest standard deviationand range are obtained using the proposed CBR system.

Finally, Table 6 shows a multiple comparison procedure(Mann–Whitney test) used to determine which models are signif-icantly different from the others. It can be seen in Table 6 that theproposed CBR system presents statistically significant differencesto the rest of the models.

In order to complete the experimental evaluation of the pro-posed CBR system, its accuracy was compared with the results

Fig. 6. Box-and-Whisker plot for model comparison.

3456 C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458

Table 3Summary of results using statistical techniques during the estimation period.

Model Mean standard error Mean absolute error Mean absolutepercentage error

Naive 1129.4438 19.8274 12.9296Mean = 142.671 7581.8640 62.9098 58.9123Linear trend = 155.513–0.00237375 t 7527.5925 62.6878 58.6839Simple exponential smoothing = 0.8486 1110.4556 19.9675 13.1051Brown’s exponential smoothing 1348.0646 22.4015 14.8328˛ = 0.3889Holt’s exponential smoothing = 0.5232 and = 0.0001 1203.5834 20.9570 13.7028ARIMA (1,0,2) with constant 1060.4075 19.8012 13.8273ARIMA (2,0,2) with constant 1054.9309 19.7602 13.7125ARIMA (2,1,1) 1066.1857 19.8419 13.1862ARIMA (2,1,2) 1065.3891 19.8434 13.2040

Table 4Summary of results using statistical techniques during the validation period.

Model Mean standard error Mean absolute error Mean absolutepercentage error

Naive 791.5163 17.1849 12.8427Mean = 142.671 5630.2062 59.0764 67.5159Linear trend = 155.513–0.00237375 t 5496.6506 54.0124 52.1165Simple exponential smoothing = 0.8486 784.1232 17.4110 13.1021Brown’s exponential smoothing = 0.3889 969.2512 19.8070 15.0185Holt’s exponential smoothing 865.2128 18.7143 14.1887˛ = 0.5232 and = 0.0001ARIMA (1,0,2) with constant 752.7615 17.4916 14.1176ARIMA (2,0,2) with constant 745.4756 17.3674 13.9272ARIMA (2,1,1) 750.2833 17.2026 13.0810ARIMA (2,1,2) 749.8889 17.1978 13.0876

Table 5Behaviour of the statistical techniques and the proposed CBR system.

Model Standard deviation MIN value MAX value Range

Naive 27.6304 −193.0000 259.0000 452.0000Mean = 142.671 72.0325 −121.6710 496.0290 617.7000Linear trend = 155.513–0.00237375 t 71.9059 −90.3923 531.4530 621.8460Simple exponential smoothing 40.5259 −440.3480 355.5710 795.9190˛ = 0.8486Brown exponential smoothing 41.5129 −461.2510 355.7910 817.0410˛ = 0.3889Holt’s exponential smoothing 37.4661 −382.7790 359.8710 742.6500˛ = 0.5232 and = 0.0001ARIMA (1,0,2) with constant 39.6646 −404.9110 358.9860 763.8970ARIMA (2,0,2) with constant 39.6646 −404.9110 358.9860 763.8970

M(

s

TMs

ARIMA (2,1,1) 39.9354

ARIMA (2,1,2) 39.9565

CBR system 26.4847

ulti-Layer Perceptron (MLP), a (iv) Modular neural network and

v) an Elman model.

All the networks, except Modular and Elman that maintain theame configuration as in the hybrid system, have seven neurons

able 6ann–Whitney test for multiple comparison. An asterisk (*) indicates that these pairs sho

ign (=) express absence of differences in the performance of the models.

ARIMA (1,0,2) ARIMA (2,0,2) ARIMA (2,1,1) ARIMA (2,1,2)

ARIMA (1,0,2)ARIMA (2,0,2) =ARIMA (2,1,1) * *ARIMA (2,1,2) * * =Naive * * * *Simple mean * * * *

Brown * * * *

Holt * = * *

Linear = = * *

CBR system * * * *

Simple * * * *

−420.0080 356.4790 776.4870−419.720 356.0470 775.7670−175.872 265.288 441.160

in the input layer and one neuron in the output layer. The MLP has

two hidden layers with sixteen and eight neurons, respectively. TheRBF has one hidden layer with 100 centres, and the Feedforward ahidden layer with 16 neurons. The same validation framework was

w statistically significant differences at the 99.0% confidence level whilst an equals

Naive Simple mean Brown Holt Linear CBR system Simple

** ** * *= * * ** * * * ** * * = * *

C.H.F. Toro et al. / Applied Soft Computing 13 (2013) 3449–3458 3457

Table 7Behaviour of individual neural networks and the proposed CBR system.

Model Mean absolute error Standard deviation MIN value MAX value Range

Feedforward forecast 18.6992 27.2168 −194.5447 311.5183 506.0630Elman 17.3345 26.9856 −160.8456 305.8964 466.7420RBF 24.0911 39.1129 −316.1634 427.0840 743.2482

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Multilayer 55.3210 75.7700

Modular 18.6232 27.8964

CBR system 17.1141 26.4847

pplied as in the previous experimentation: 60% of the data wassed for training, 15% for parameter estimation and the remaining5% for testing. All the networks were trained with a maximum of000 iterations. Table 7 summarizes the results obtained.

As can be observed from Table 7, the proposed CBR systemenerates better results than the other selected models. However,lman and Modular neural networks were close to the CBR sys-em but with a greater standard deviation and range. In ordero statistically validate the results obtained, a non-parametricruskall–Wallis test was also executed. The results showed that,lso in this occasion, there is a statistically significant differencemong the models at the 99.0% confidence level (P-value < 0.001).

. Conclusions and future work

This paper has presented a hybrid AI system together with itspplication to a river flow forecasting problem as a prototype exam-le of a chaotic and non-linear environment. In the current work,e have used different data mining techniques together with AI

lgorithms to build the final hybrid CBR system. In the retrievaltage, a hierarchical clustering algorithm is used to build a rank-ng of quarters based on the dissimilarities between them. Then,

spectral density technique based on Fourier frequency analy-is is applied to compare time series in the frequency domain.n order to implement the reuse stage of the hybrid system twoeural networks architectures have been used: an Elman ANNnd a Modular ANN composed by two MLPs. Their outputs arenally combined by a weighting schema based on MSE and MAEalues.

As in other real data forecasting studies, the appropriate appli-ation of correct pre-processing steps are of crucial importanceor obtaining accurate results. In this context, (i) the treatment ofrong and missing values, (ii) the execution of previous correla-

ion analysis between filtered and adjusted variables and (iii) thenitial execution of several simulations with standard techniqueslay an important role in identifying those features with a majoriscriminant power.

Regarding the benefits of our hybrid model, the proposed CBRystem is able to generate a forecast with an acceptable degreef accuracy outperforming previous approaches. The prediction isade for the short term (one day in advance), but the results could

e extrapolated to produce forecasts further ahead using the sameechnique. The hybrid system can be used to make predictionsn situations in which univariate time series exist but taking intoccount that a daily update of the case base is required and suffi-ient records are necessary to guarantee the accuracy of the neuraletworks.

Moreover, the adoption of the CBR paradigm as design method-logy to develop the hybrid model eases its reutilization for otheriver modelling problems. Both the proposed general architectures well as the different techniques used for implementing eachhase of the whole life cycle can be reused ‘as is’, or minimally

dapted in order to fit new specific requirements. In addition,

given technique can also be fully replaced by an alternativepproach in order to obtain a better performance of the model forolving a particular problem.

[

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−95.4736 525.5702 621.0430−178.2365 312.2589 490.4954−175.8720 265.2880 441.1600

With regard to future work, development of new mechanismsable to automatically tune the parameters that govern the opera-tion of the neural networks will be a focus. In this sense, relatedtopics of importance are the effective differentiation between esti-mation and prediction [48] and the consideration of differentpredictivity measures [49]. Moreover, the integration of fuzzy logicmay dramatically improve the capabilities of the proposed system.In this direction, there are previous interesting works by Castilloand Melin [50] and Pulido et al. [51] that can contribute to thisgoal.

Acknowledgments

This work was made possible by the collaboration of the Cor-poración Autónoma Regional del Valle del Cauca (CVC), Colombia,who kindly provided the historical data necessary to perform thisstudy. The authors also want to acknowledge the support lent bythis institution.

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C.H. Fajardo Toro obtained Ph.D. from the University of Vigo, Spain. He was born inCali, Colombia in 1968. He worked as an associate and full time professor at the IcesiUniversity in Cali, Colombia from 1994 to 2001, and as an associate professor at theComputer Science Department of the University of Vigo from 2001. He collaboratesas researcher with the SING group (Computer Systems of New Generation) belongingto the University of Vigo and the IREHISA group belonging to the Universidad delValle in Colombia. Currently, his main topic of interest is the study of AI hybridmethods and their application to real problems, although he has also worked intopics related with software quality and project management focused on softwaredevelopment.

S. Gómez-Meire obtained Ph.D. from the University of Vigo, Spain. She was bornin Ourense, Spain in 1972. She is a full time professor in the Computer ScienceDepartment of the University of Vigo. From there she collaborates as researcherwith the SING group and the GIG (Computer Graphics and Multimedia) group, bothbelonging to the University of Vigo. In her research, she is mainly interested in thestudy of data mining techniques applied to music transcription and signal analysis.

J.F. Gálvez obtained Ph.D. from the University of Vigo, Spain. He was born in Granada,Spain in 1968. He is a full time professor in the Computer Science Department ofthe University of Vigo. He collaborates as researcher with the SING research groupand the LIA (Laboratory of Applied Computer Science) group, both belonging to theUniversity of Vigo. Although his present research is related to the field of Rough Setstheory and its application to real problems, previous work was on topics related toclassification and image analysis.

F. Fdez-Riverola obtained Ph.D. from the University of Vigo, Spain. He was born inLangen-Hessen, Germany, in 1973. He is Director of the CITI research Centre and afull time professor in the Computer Science Department of the University of Vigo. He

is also the principal investigator of the SING group and collaborates with the BISITE(Biomedicine, Intelligent Systems & Educational Technology) group belonging to theUniversity of Salamanca. He is a joint author of several books and book chapters, aswell as the author of numerous articles published by well-known houses such asthe Springer-Verlag, Ios Press, and Kluwer (http://sing.ei.uvigo.es/).