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An alternative approach for the prediction of significant wave heights based on classification and regression trees

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An alternative approach for the prediction of significant wave heights based on classification and regression trees
  Author's personal copy Applied Ocean Research 30 (2008) 172–177 Contents lists available at ScienceDirect Applied Ocean Research  journal homepage: An alternative approach for the prediction of significant wave heights based onclassification and regression trees  J. Mahjoobi a,b , A. Etemad-Shahidi b, ∗ a Ministry of Energy, Water Research Institute, Hakimieh, Tehran, P.O.Box: 16765-313, Iran b School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, P.O. Box 16765-163, Iran a r t i c l e i n f o  Article history: Received 23 March 2008Received in revised form29 October 2008Accepted 1 November 2008Available online 11 December 2008 Keywords: Wave predictionData miningMachine learningClassificationDecision treesRegression treesC5 algorithmCART a b s t r a c t Inthisstudy,theperformancesofclassificationandregressiontreesforthepredictionofsignificantwaveheights were investigated. The data set used in this study is comprised of 5 years of wave and wind datagathered from a deep water location in Lake Michigan. Training and testing data include wind speed andwind direction as the input variables and significant wave heights ( H  s ) as the output variable. To buildthe classification trees, a C5 algorithm was invoked. Then, significant wave heights for the whole dataset were grouped into wave height bins of 0.25 m and a class was assigned to each bin. For evaluationof the developed model, the index of each predicted class was compared with that of the observed data.The CART algorithm was employed for building and evaluating regression trees. Results of decision treeswere then compared with those of artificial neural networks (ANNs). The error statistics of decision treesand ANNs were nearly similar. Results indicate that the decision tree, as an efficient novel approach withan acceptable range of error, can be used successfully for prediction of   H  s . It is argued that the advantageof decision trees is that, in contrast to neural networks, they represent rules. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction Waves, the most significant maritime phenomenon, due totheir complicated and stochastic behavior are known as one of the most difficult subject in coastal and maritime engineeringpractice. The effect of waves on coastal and marine activitiesurges us to identify the wave characteristics. Different approachessuch as field measurements, theoretical studies and numericalsimulations have been used for this purpose. Coastal and offshoreengineers generally use these approaches to identify wave climateand extreme wave characteristics as well as annual attributes of waves. Different methods such as empirical, numerical and softcomputing approaches have been proposed for significant waveheight prediction.Soft computing techniques such as artificial neural networkshave been widely used to predict wave parameters [e.g. [1–5]].A review of neural network applications in ocean engineering isgiven in [6]. Recently, other soft computing techniques such astheFuzzyInferenceSystem(FIS)andtheAdaptive-Network-basedFuzzy Inference System (ANFIS) have been used to develop wave ∗ Corresponding author. Tel.: +98 21 7391 3170; fax: +98 21 77454053. E-mail addresses: (J. Mahjoobi), Etemad-Shahidi). prediction models (e.g. [7,8]). These studies have shown that the wind speed is the most important parameter in wave parameter’sprediction. Recently, Mahjoobi et al. [9] compared different softcomputing methods such as Artificial Neural Networks (ANNs),theFuzzyInferenceSystem(FIS)andtheAdaptive-Network-basedFuzzy Inference System (ANFIS) to hindcast wave parameters.Their results showed that the performances of these methodsare nearly the same. Furthermore, using sensitivity analysis, theyshowed that the wind speed and direction are the most importantparameters for wave hindcasting.As mentioned before, the prediction of significant wave heightthat is essentially an uncertain and random process is noteasy to accomplish by using deterministic equations. Therefore,it is ideally suited to decision trees since they are primarilyaimed at the recognition of a random pattern in a given setof input values. Decision trees are helpful in predicting thevalue of the output of a system from its corresponding randominputs as the application of decision trees does not requireknowledge of the underlying physical process as a precondition.Examples of decision tree applications include potential profitanalysis of new drugs in pharmaceutical companies [10], medicaldiagnosis [11] and risk management analysis in petroleumpipeline construction [12]. However, to the authors’ knowledgethis method has not been applied in wave prediction. In thiswork, the performances of classification and regression trees as 0141-1187/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2008.11.001
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