Prediction of seasonal maximum wave height for unevenly spaced time series by Black Widow Optimization algorithm

doi:10.1016/j.marstruc.2021.103005

Marine Structures

Volume 78, July 2021, 103005

https://doi.org/10.1016/j.marstruc.2021.103005 Get rights and content

Highlights

•
The obtained results indicated that the BWO and PSO algorithms increased the accuracy of ANFIS and SVR.
•
The results indicate that the BWO acted better in SVR than the PSO.
•
The performance of the models was poorer in summer than in the other seasons.
•
The models can predict the maximum wave height for winter more accurately than other seasons.

Abstract

The present study aimed to predict the maximum seasonal wave height by new integrative data driven methods. For this purpose, two data-driven techniques, that are, the Adaptive Neuro-Fuzzy Inference System (ANFIS) and the Support Vector Regression (SVR), were applied, and a BWO algorithm was used as an integrated method (ANFIS-BWO and SVR-BWO). In addition, the Particle Swarm Optimization (PSO) algorithm was used as a method integrated with SVR and ANFIS (SVR-PSO and ANFIS-PSO) to compare the performance of the newly developed methods (ANFIS-BWO and SVR-BWO). The wave data were collected in different seasons by a buoy station deployed in the southern Baltic Sea by the Institute of Hydro-Engineering of the Polish Academy of Sciences. Seasonal simulations were performed to investigate the effect of seasons on the maximum wave height. The wave data constituted an unevenly spaced time series. The maximum wave height was modeled using the maximum wave height period (T_max), the significant wave height (H_s), the significant wave period (T_s), and time steps (Δt). The results showed that the application of BWO and PSO algorithms increased the accuracy of ANFIS and SVR by about 18.45%. Moreover, the results show that PSO increased the accuracy of ANFIS and SVR by about 17.98% and 21.59%, respectively. The results of different runs indicated that the BWO is more stable to reach the global solution than PSO. The results also show that show that SVR-BWO is the most accurate model.

Introduction

Wave features are the most significant factors in determining the geometric characteristics of beaches. The design of marine and coastal structures, waterways, and seaports is based on wave features, such as the maximum wave height, a significant wave height, and a wave period. The maximum wave height has been used frequently in the design of coastal and offshore structures [1]. Thus, in order to secure the sustainability of shoreline structures, such as breakwaters, groins, seawalls, etc., it is of fundamental importance to find a reliable method of estimating the maximum wave height accurately. Researchers have made numerous attempts to model wave characteristics using meteorological data and other factors that influence the process of wave formation. The application of stochastic methods such as extreme value methods to model sea wave characteristics has been reported in many studies [[2], [3], [4]]. Nowadays, data-driven techniques are recognized as powerful tools for tackling intricate problems in engineering and science. The application of data-driven methods in predicting hydraulic and hydrological parameters has been successfully attempted by various researchers [[5], [6], [7], [8], [9]]. Furthermore, previous studies indicate that meta-heuristic optimization algorithms may improve the accuracy of data-driven techniques [[10], [11], [12]].

Numerous studies have been performed to predict wave parameters by data-driven methods [[13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]]. Malekmohamadi et al. [15] evaluated the performance of different data-driven methods for wave height prediction, namely, Support Vector Machines (SVMs), Adaptive Neuro-Fuzzy Inference System (ANFIS), Artificial Neural Networks (ANNs), and Bayesian Networks (BNs). The data set included wave height and wind data collected in Lake Superior in the United States by the National Data Buoy Center. The results confirmed the reliability of ANN, SVM, and ANFIS methods in predicting the wave height, whereas the outcomes from the designed BNs were untrustworthy. Cornejo-Bueno et al. [16] suggested a methodology for the estimation of the significant wave height on the basis of the Support Vector Regression (SVR) algorithm. The data sets consist of X-band marine radar data for three different stations in the North Sea and South Africa. The outcomes indicated that the accuracy of SVR in predicting a significant wave height is higher than that of the available standard procedures. Kumar et al. [18] used a group of Extreme Learning Machine (Ens-ELM) for forecasting the daily wave height in 10 different stations in Brazil and Korean waters, and the Gulf of Mexico. The accuracy of Ens-ELM was assessed by comparison with SVR, ELM, and Online Sequential ELM (OS-ELM) methods. The results indicated the superiority of Ens-ELM over the other techniques in predicting the wave height. Akbarifard and Radmanesh [21] attempted to predict the wave height in hourly and daily time frames using the Symbiotic Organisms Search (SOS) algorithm and compared the outcomes with those from Particle Swarm Optimization (PSO) algorithm and Imperialist Competitive Algorithm (ICA), data-driven approaches containing ANN, SVR, and the Simulating Waves Nearshore (SWAN) dynamic model, and the hybrid SWAN-SOS model. The results showed a greater accuracy of SOS and SWAN-SOS models in wave height prediction in comparison with the other methods. Karabulut and Ozmen Koca [24] used regression methods, including Linear, Gaussian Regression, Decision Tree, Ensemble (Boosted Tree and Bagged Tree), and SVM models, to predict the offshore wave height using a flow velocity variable at two locations in the Mediterranean Sea in Turkey. They obtained R-square values of 0.86 and 0.95, proving the reliability of the proposed techniques. Table 1 summarizes some other studies on the prediction of wave features e.g. wave height and wave period.

It should be noted that the data-driven methods in the present study were trained and evaluated using unevenly spaced time series data. One of the works that used this type of time series was a study by Mukherjee and Ramachandran [25], who modeled a hydraulic phenomenon. They employed ANN, SVR, and linear regression methods to predict groundwater levels using unevenly spaced time series data. The results revealed that the output from SVR and ANN was better than that from linear regression.

The BWO is a new evolutionary optimization algorithm developed by Hayyolalam and Pourhaji Kazem [26]. Hayyolalam and Pourhaji Kazem [26] used 45 mathematical benchmark functions to evaluate the BWO performance. The results of BWO were also compared with 9 other optimization algorithms. Their results confirmed the advantages of BWO. Sarath and Sekar [24] used the BWO algorithm for the optimal design of an LLC resonant converter. The BWO was assessed along with other optimization methods, and the performance of BWO in designing the LLC-RC model was satisfactory. Tightiz et al. [28] determined power transformer fault based on the integrative ANFIS-BWO classification method. The results revealed a suitable performance of BWO to optimize the ANFIS parameters.

The aim of the present study is to predict maximum wave height by new integrative methods. The BWO is a new meta-heuristic algorithm and its high performance in solving complex optimization problems was confirmed in past studies [[26], [27], [28]]. However, to the best of our knowledge, the application of the BWO algorithm as an integrative method with SVR and ANFIS to predict wave variables has not been investigated. In this study, the performance of BWO is evaluated in solving low-dimensional problems (SVR, D = 3) and high-dimensional problems (ANFIS, D = 230). Finally, the particle swarm optimization (PSO) algorithm is used to compare the results of the new integrative methods.

Section snippets

Methods

In this study, two main data-driven methodologies, ANFIS and SVR, are applied in modeling the maximum wave height. Furthermore, BWO and PSO algorithms are used in combination with ANFIS and SVR to optimize their parameters. All these methods are described briefly in the following sections.

Study area and data preparation

The wave data for the present study were acquired at the Coastal Research Station in Lubiatowo (IHE PAS) in the southern part of the Baltic Sea. A buoy station is situated 5 km offshore. The location of the buoy station is shown in Fig. 2.

The data were recorded by a Directional Waverider (DWR) buoy. The frequency measurement was set to 1.28 Hz. Free-surface elevations were recorded for 20 min for each raw data. Seasonal models of wave data were created to investigate the effect of seasons on

Model input selection

To model a time series of the maximum wave height, it is essential to obtain the time delay (lag) between the input and output parameters. In this study, autocorrelation and cross-correlation functions were used to acquire the time delay for H_max and input variables, respectively. The values of these functions and the lag number of all parameters for different seasons are presented in Table 4. In addition, to visualize the results from Table 4, the autocorrelation and cross-correlation function

Evaluation criteria

The performance of the models is assessed by statistical indices, namely, the coefficient of determination (R²), the standard mean absolute error (SMAE), the standard root mean square error (SRMSE), the index of agreement (IA), and the Nash–Sutcliffe model efficiency (NSE), as follows: $R^{2} = \frac{(\sum_{i = 1}^{N} (x_{m, i} - \overline{x_{m}}) {(x_{o, i} - \overline{x_{o}})}^{2})}{\sum_{i = 1}^{N} {(x_{m, i} - \overline{x_{m}})}^{2} \sum_{i = 1}^{N} {(x_{o, i} - \overline{x_{o}})}^{2}}$ $S M A E = \frac{\frac{1}{N} \sum_{i = 1}^{N} | x_{m, i} - x_{o, i} |}{\overline{x_{o}}}$ $S R M S E = \frac{\sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(x_{m, i} - x_{o, i})}^{2}}}{\overline{x_{o}}}$ $I A = 1 - \frac{\sum_{i = 1}^{N} {(x_{m, i} - x_{o, i})}^{2}}{\sum_{i = 1}^{N} {(| x_{m, i} - \overline{x_{m}} | + | x_{o, i} - \overline{x_{o}} |)}^{2}}$ $N S E = 1 - \frac{\sum_{i = 1}^{N} {(x_{m, i} - x_{o, i})}^{2}}{\sum_{i = 1}^{N} {(x_{o, i} - \overline{x_{o}})}^{2}}$ where $x$

Results and discussion

As mentioned before, all data were divided into three categories including training, validation, and testing datasets. Table 5 presents the values of SRMSE, R², and IA evaluation criteria for the training and validation phases.

As can be observed from Table 5 the accuracy of the proposed methods in predicting the seasonal maximum wave height was acceptable for all simulations, R²>0.8. The outcomes indicate that in the training stage, the integration of SVR with the BWO and PSO algorithms

Conclusions

In this study, the maximum seasonal wave height was predicted by the ANFIS and SVR methods. The variables of these methods were optimized using the Black Widow Optimization (BWO) algorithm. The outcomes of the new integrative methods (ANFIS-BWO and SVR-BWO) were compared with the particle swarm optimization algorithm (PSO) in combination with ANFIS and SVR. Wave data were collected with a Directional Waverider (DWR) buoy by the Institute of Hydro-Engineering of the Polish Academy of Sciences

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors are indebted to the reviewers for valuable comments.

References (45)

H. Chun et al.
Empirical formulas for estimating maximum wave height and period in numerical wave hindcasting model
Ocean Eng
(2019)
G. Feld et al.
Design conditions for waves and water levels using extreme value analysis with covariates
Ocean Eng
(2019)
M.H. Moeini et al.
Wave modeling and extreme value analysis off the northern coast of the Persian Gulf
Appl Ocean Res
(2010)
A. Niroomandi et al.
Extreme value analysis of wave climate in Chesapeake Bay
Ocean Eng
(2018)
V. Wolfs et al.
A data driven approach using Takagi–Sugeno models for computationally efficient lumped floodplain modelling
J Hydrol
(2013)
M.K. Goyal et al.
Modeling of daily pan evaporation in sub tropical climates using ANN, LS-SVR, Fuzzy Logic, and ANFIS
Expert Syst Appl
(2014)
I. Malekmohamadi et al.
Evaluating the efficacy of SVMs, BNs, ANNs and ANFIS in wave height prediction
Ocean Eng
(2011)
L. Cornejo-Bueno et al.
Accurate estimation of significant wave height with support vector regression algorithms and marine radar images
Coast Eng
(2016)
L. Cornejo-Bueno et al.
Significant wave height and energy flux prediction for marine energy applications: a grouping genetic algorithm–Extreme Learning Machine approach
Renew Energy
(2016)
N.K. Kumar et al.
Ocean wave height prediction using ensemble of Extreme Learning Machine
Neurocomputing
(2018)

N.K. Kumar et al.

Regional ocean wave height prediction using sequential learning neural networks

Ocean Eng

(2017)

S. Akbarifard et al.

Predicting sea wave height using Symbiotic Organisms Search (SOS) algorithm

Ocean Eng

(2018)

A. Mukherjee et al.

Prediction of GWL with the help of GRACE TWS for unevenly spaced time series data in India: analysis of comparative performances of SVR, ANN and LRM

J Hydrol

(2018)

V. Hayyolalam et al.

Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems

Eng Appl Artif Intell

(2020)

M.A. Boyacioglu et al.

An adaptive network-based fuzzy inference system (ANFIS) for the prediction of stock market return: the case of the istanbul stock exchange

Expert Syst Appl

(2010)

B. Chen et al.

Wind turbine pitch faults prognosis using a-priori knowledge-based ANFIS

Expert Syst Appl

(2013)

H. Ansari et al.

Robust method based on optimized support vector regression for modeling of asphaltene precipitation

J Petrol Sci Eng

(2015)

K. Bi et al.

An intelligent SVM modeling process for crude oil properties prediction based on a hybrid GA-PSO method

Chin J Chem Eng

(2019)

R. Salat et al.

New approach to predicting proconvulsant activity with the use of Support Vector Regression

Comput Biol Med

(2012)

S. Verma et al.

Activation soil moisture accounting (ASMA) for runoff estimation using soil conservation service curve number (SCS CN) method

J Hydrol

(2020)

H.M. Azamathulla et al.

Machine learning approach to predict sediment load – a case study

Clean

(2010)

M.C. Aydin et al.

Prediction of discharge capacity over two-cycle labyrinth side weir using ANFIS

J Irrigat Drain Eng

(2016)

Cited by (23)

Development of pyramid neural networks for prediction of significant wave height for renewable energy farms
2024, Applied Energy
Significant wave height (H_s) is a critical parameter in the design, operation, and maintenance of nearshore and offshore wind and wave farms. In this study, the original pyramid neural network (PNN) was introduced and applied to predict H_s for North Sea renewable energy farms. The performance of PNN was compared with state-of-the-art algorithms. The results show that the machine learning (ML) models trained by the network datasets can accurately predict Hs at any point of nearshore or offshore energy farms, significantly reducing wave monitoring costs. The PNN models predict H_s with high accuracy. The results predicted by PNN, with SRMSE of 0.256 and R² of 0.873, are more accurate than the corresponding results obtained by the deep neural network (DNN) model, which show that PNNs with their far simpler structures and lower number of parameters are attractive alternatives for complex and time-consuming DNN models. The ensemble of regular models, with SRMSE of 0.247, is ranked as the most accurate method. The results also show that the applied state-of-the-art algorithms including MLR, SNN, DNN, ANFIS, and SVR models predict non-physical negative values of H_s. The PNNs developed in this study predict H_s with positive values. Moreover, the analysis shows that the scatter of the results obtained by the derived nonlinear models is less pronounced than the scatter of corresponding results obtained by other methods. The results also show that to evaluate the performance of nonlinear ML methods for large datasets, the analysis of standard statistical indices is not sufficient. For large datasets standard statistical indices provide inadequate or insufficient information and additional calculations, and statistical analysis are required.
Development of clustered machine learning technique for the modeling of scour profile induced by propeller jets
2023, Ocean Engineering
In this study novel clustered machine learning (CML) models were developed by applying different base learners including multi linear regression (MLR), adaptive neuro-fuzzy inference system (ANFIS), classification and regression trees (CART), least-squares boosting (LSBoost), and random forest (RF) to predict scour profile induced by the jet of a propeller. Moreover, the results of CML models were compared with regular ML algorithms. The results show that the tree-based ensemble models, RF and LSBoost, are more accurate than CART. The ANIFS has the worst performance compared with other regular nonlinear methods, RMSE = 17.414 mm. The performance of MLR is also weak, RMSE = 35.63 mm and R2 = 0.088. However, the implementation of CML drastically increases the performance of MLR, RMSE = 15.053 mm, and R2 = 0.871. The CANFIS with RMSE = 8.757 mm, R2 = 0.976, and SI = 0 is ranked as the most accurate model. The results show that CLM enhances the performance of regular ML by up to 59.90%. The application of clustered ML is recommended for other complex problems. Finally, the results show that the derived models trained by other datasets very well predict measured scour profiles which datasets were not used in the training process.
Left-right brain interaction inspired bionic deep network for forecasting significant wave height
2023, Energy
As a promising source of clean energy in carbon neutrality, ocean wave energy generation depends heavily on forecasting significant wave height (SWH), whose evolution is too complex to accurately model due to multi-factor mixed effects. Additionally, most existing deep models present intelligent fitting via making some tricks and further have mining-extraction capabilities of hidden features, while they ignore the support of biologically-inspired ideas. An important and interesting open issue is how to utilize SWH data characteristics with advanced brain structures and functions to construct its high-performance forecasting network. Specifically, from SWH data analysis, the overall framework of the proposed network separately extracts autocorrelation and causality via two brain-interaction-inspired (BII) modules at first, and then integrates them via the attention fusion module, which coincides with the idea of “divide and conquer”. From a micro view, 1) through imitating both structures and functions in left-right brain interaction, the designed BII module stacks the one-dimensional convolutions and gate mechanisms to implement the gate, collaboration, and inhibition functions for capturing long short-term dependencies. 2) The attention mechanism with dynamic weights is designed to integrate captured information and real-timely grasp the main features for making high-accuracy forecasts. The proposed network not only has some interpretability in the design process but also effectively enhances the feature completeness. In six experiments of two real-world datasets, the proposed network improves the root mean squared error by averages of 26.3% and 23.7% compared with 11 baselines, respectively.
Hourly significant wave height prediction via singular spectrum analysis and wavelet transform based models
2023, Ocean Engineering
Generation of significant wave height (SWH) is considered as a complex and stochastic dynamical process whose prediction is vital for effective marine, ocean engineering, sustainable development and scientific phenomena. Based on literature review, despite numerous research attempts to forecast significant wave height with short prediction time horizons, they are incapable in yielding accurate SWH predictions. To achieve this end wavelet techniques have been intensively employed as data pre-processing tools and, have been incorporated with soft computing based approaches to improve the prediction performance of developed models. However, wavelet algorithm has some limitations such as shift sensitivity, poor directionality and lack of phase information. In addition, this technique suffers from time consuming complicated mathematical procedures. In the present study, as a way of addressing the shortcomings of wavelet tool and enhancing prediction accuracy with extended time horizons, singular spectrum analysis (SSA) is proposed as a decomposition procedure. The prediction accuracy of the three distinct models is contrasted by means of diagnostic metrics, Mean Square Error (MSE), the Nash-Sutcliffe Coefficient of efficiency (CE) and determination of coefficient (R²). With its lowest MSE and highest CE value SSA-Fuzzy model clearly outperformed the stand alone Fuzzy and W-Fuzzy models in predicting hourly SWH for all stations and future time horizons. This implies that SSA technique has the utmost capability to decompose measured data effectively into its deterministic and stochastic components.
Application of nested artificial neural network for the prediction of significant wave height
2023, Renewable Energy
Significant wave height is the most important parameter in feasibility studies and the design of wave energy converters. In this study, the novel nested artificial neural networks were developed and applied to predict significant wave height at twenty selected locations of the North Sea. A nested artificial neural network applies nonlinear machine learning models as transfer functions in the neurons of networks. Two input parameters comprising wind speed and wind direction were implemented to train the derived models. The results show that the derived nonlinear machine learning models are about 18.39% more accurate than the linear regression technique. The statistical indices confirm that the nested artificial neural network may increases the accuracy of traditional models by up to 34%. Among all applied models, the nested artificial neural network developed based on the integration of particle swarm optimization algorithm and adaptive neuro-fuzzy inference system, with RMSE = 0.525m and R² = 0.84, provides the most accurate prediction of wave heights. The high accuracy of the results indicates that if computational time is not a very critical factor for users, then the application of nested artificial neural networks may be recommended for the modeling of wave parameters and other complex problems.
Analyzing wave direction scenarios for large waves in deep water and its impact on littoral drift
2023, Ocean Engineering
Citation Excerpt :
The development of detection and remote sensing technology has helped in the research progress on the directional characteristics of wind waves. Collection of wave direction data at an observation station and analysis of satellite images have been reported (e.g., Carter, 1982; Young, 1994; Mahjoobi and Mosabbeb, 2009; Hofland et al., 2017; Kumar et al., 2017; Osawa et al., 2020; Memar et al., 2021; Woo and Park, 2021). Numerical models such as the Wave Model (WAM) and Simulating Waves at Nearshore (SWAN) are used to simulate various spectral characteristics of wave energy and wind wave direction (The Wamdi Group, 1988; Booij et al., 1997; Chun and Suh, 2018, 2019; Wornom et al., 2001; Zijlema, 2010).
In this study, four types of wave direction scenarios in large waves greater than 3 m in deep water are examined by analyzing NOAA's wave hindcast data spanning over 40 years. The results reveal that wave direction changes at the starting, peak and ending of large/storm waves, accompanying by changing wave heights with wave direction becoming in perpendicular to the coastal orientation when waves reaching a peak. Within the bulk of NOAA wave data which last 1.65 days, 55.1% of the large/storm waves had wave direction returning to the starting direction on the wane of the waves, while the remaining 44.9% reversed to the opposite side of the starting direction. Based on this finding, littoral drift is calculated for each scenario by the CERC equation, on the basis of deep water wave parameters. The resulting littoral drift is then used in a numerical model to calculate shoreline changes at Jeongdongjin Beach in Korea, where a natural groin block the longshore sediment transport. The result of shoreline change in the vicinity of the groin suggests beach may become stable about one day after the end of a short-term large wave/storm event, or 2 days after the peak wave height.

View all citing articles on Scopus

View full text

Prediction of seasonal maximum wave height for unevenly spaced time series by Black Widow Optimization algorithm

Highlights

Abstract

Introduction

Section snippets

Methods

Study area and data preparation

Model input selection

Evaluation criteria

Results and discussion

Conclusions

Declaration of competing interest

Acknowledgements

Ocean Eng

Ocean Eng

Appl Ocean Res

Ocean Eng

J Hydrol

Expert Syst Appl

Ocean Eng

Coast Eng

Renew Energy

Neurocomputing

Ocean Eng

Ocean Eng

J Hydrol

Eng Appl Artif Intell

Expert Syst Appl

Expert Syst Appl

J Petrol Sci Eng

Chin J Chem Eng

Comput Biol Med

J Hydrol

Machine learning approach to predict sediment load – a case study

Clean

Prediction of discharge capacity over two-cycle labyrinth side weir using ANFIS

J Irrigat Drain Eng