# An EEMD-BiLSTM Algorithm Integrated with Boruta Random Forest Optimiser for Significant Wave Height Forecasting along Coastal Areas of Queensland, Australia

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.2. Data Preparation

#### 2.3. Data Normalisation

#### 2.4. Data Decomposition by Ensemble Empirical Mode Decomposition (EEMD)

- The n-dimensional length either has an equal number of extrema and zero crossings, or they differ at most by one.
- The mean value at any point which is defined by local maxima and the envelope defined by the local minima are zero.

- The white noise series are added to the wave data;
- Wave dataset is then decomposed with added white noise into its IMFs (see Figure 2);
- Steps 1 and 2 are repeated with different Gaussian white noise series.
- Since the mean value of added noise is zero, the average over all corresponding IMFs will be the final decomposition.

#### 2.5. Feature Selection by Boruta Random Forest Optimiser (BRF)

- the information system is extended by the addition of all variables in consideration, minimum of five shadow attributes are added;
- the added attributes are shuffled so that their correlation with the response are removed;
- the random forest classifier is applied to gather the z-scores;
- the maximum z-score among the shadow attributes is found and every attribute that has a better score than this is taken as a hit;
- a two-sided test of equality is performed with attributes that attained an undetermined importance;
- the attributes that have significantly lower z-score than the maximum z-score among the shadow attributes are removed;
- the attributes that have significantly higher z-score are selected;
- all shadow attributes are then removed.

#### 2.6. Modal Development

#### 2.6.1. Bidirectional Long Short-Term Memory (BiLSTM) Model Development

#### 2.6.2. Support Vector Regression (SVR) Model Development

#### 2.6.3. Bi-Directional Long Short-Term Memory (BiLSTM) Architecture

**C**= penalty parameter, $\mathit{\epsilon}$ = an insensitive loss function and ${\mathit{\xi}}_{\mathit{i}},{\mathit{\xi}}_{\mathit{i}}{}^{*}$ = slack variables.

## 3. Results and Discussion

- Pearson’s Correlation Coefficient (R)

- 2
- Nash-Sutcliffe Coefficient (NS)

- 3
- Willmott’s Index of agreement (WI)

- 4
- Root Mean Square Error (RMSE)

- 5
- Mean Absolute Error (MAE)

- 6
- Mean Absolute Percentage Error (MAPE)

^{2}and a small residual error.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Partial autocorrelation function (PACF) plot of the Hs time series exploring the antecedent behaviour in terms of the lag of Hs in hours.

**Figure 4.**Correlogram showing the covariance between the objective variable (Hs) in terms of the cross-correlation coefficient (rcross) for Cairns.

**Figure 5.**Boruta feature selection output for Cairns. The intrinsic mode functions (IMFs) are compared with shadow attributes and declared as confirmed (hit) or rejected (removed) using the Boruta algorithm in R package.

**Figure 6.**Workflow detailing the steps in the model designing phase, as for the proposed hybrid EEMD-BiLSTM predictive models. Note: BiLSTM = Bidirectional Long Short-Term Memory, BRF = Boruta Random Forest Optimiser.

**Figure 7.**A snapshot taken within the BiLSTM model development phase; it shows the layers through which the information flows for learning in the network.

**Figure 9.**The long short-term memory (LSTM) cell block representation on how the input is processed within the architecture.

**Figure 10.**The BiLSTM cell structure at time step $\mathit{t}$. The architecture has the forward and backward flow arrangement of connected LSTM layers.

**Figure 11.**The SVR model structure shows how the error and the hyperplane are arranged around the data points.

**Figure 12.**Taylor diagram representing correlation coefficient together with the standard deviation difference for proposed hybrid EEMD-BiLSTM vs. benchmark models for Cairns and Gold Coast.

**Figure 13.**Scatter plot of forecasted vs. observed Hs of Cairns and Gold Coast sites. A least square regression line and coefficient of determination (R

^{2}) with a linear fit equation are shown in each sub-panel.

**Figure 14.**Histograms of absolute forecasting error (PE) generated by EEMD-BiLSTM and the benchmark models for (

**a**) Cairns and (

**b**) Gold Coast data sites.

Data Site | Geographical Location |
---|---|

Gold Coast | 27°57′53.9319″ S, 153°20′58.1543″ E |

Cairns | 16°55′34.4124″ S, 145°46′27.0667″ E |

Partition | Training (60%) | Validation (20%) | Testing (20%) |
---|---|---|---|

Dataset | January 2014–July 2017 | August 2017–July 2018 | August 2018–August 2019 |

**Table 3.**Augmented Dickey Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) analysis results.

ADF Statistic: −17.44 | KPSS Statistic: 0.29 |
---|---|

Critical Values: | Critical Values |

5%: −2.862 | 5%: 0.463 |

10%: −2.567 | 10%: 0.347 |

Input Wave Features | Description |
---|---|

Hmax | Wave Height |

Tz | Zero up crossing wave period |

Tp | Peak energy wave period |

SST | Sea surface temperature |

Optimizer | Activation Function | Weight Regularization | Dropout | Early Stopping |
---|---|---|---|---|

Adam | Rectified Linear Unit | L1 = 0, L2 = 0.01 | 0.1 | Mode = Minimum, Patience = 20 |

**Table 6.**Optimal values obtained from grid search for ε, γ, and C in the support vector regression (SVR) model.

Epsilon (ε) | Gamma (γ) | Parameter (C) | Kernel |
---|---|---|---|

0.1 | 1 × 10^{−7} | 1.0 | Radial Basis Function |

Model | Cairns | Gold Coast | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R | WI | NS | RMSE | MAE | MAPE | R | WI | NS | RMSE | MAE | MAPE | |

EEMD-BiLSTM | 0.9961 | 0.9979 | 0.9912 | 0.0214 | 0.0133 | 2.8609 | 0.9965 | 0.9983 | 0.9931 | 0.0413 | 0.0293 | 2.5258 |

BiLSTM | 0.9911 | 0.9873 | 0.9873 | 0.0248 | 0.0187 | 3.3921 | 0.9903 | 0.9945 | 0.9772 | 0.075 | 0.0553 | 5.5633 |

EEMD-SVR | 0.9852 | 0.9913 | 0.9647 | 0.043 | 0.0313 | 8.6412 | 0.9953 | 0.9976 | 0.9906 | 0.0481 | 0.034 | 3.0422 |

SVR | 0.9801 | 0.9879 | 0.9508 | 0.0507 | 0.0357 | 9.8301 | 0.9935 | 0.9967 | 0.9868 | 0.057 | 0.042 | 3.9214 |

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**MDPI and ACS Style**

Raj, N.; Brown, J.
An EEMD-BiLSTM Algorithm Integrated with Boruta Random Forest Optimiser for Significant Wave Height Forecasting along Coastal Areas of Queensland, Australia. *Remote Sens.* **2021**, *13*, 1456.
https://doi.org/10.3390/rs13081456

**AMA Style**

Raj N, Brown J.
An EEMD-BiLSTM Algorithm Integrated with Boruta Random Forest Optimiser for Significant Wave Height Forecasting along Coastal Areas of Queensland, Australia. *Remote Sensing*. 2021; 13(8):1456.
https://doi.org/10.3390/rs13081456

**Chicago/Turabian Style**

Raj, Nawin, and Jason Brown.
2021. "An EEMD-BiLSTM Algorithm Integrated with Boruta Random Forest Optimiser for Significant Wave Height Forecasting along Coastal Areas of Queensland, Australia" *Remote Sensing* 13, no. 8: 1456.
https://doi.org/10.3390/rs13081456