Wave Time Series Research Articles

Data-driven fast reliability assessment of offshore structures based on real-time sensor data

With the advancement of monitoring technologies for offshore structures, sensor data are becoming increasingly available in real-time. The objective of this paper is to develop fast methods for reliability assessment of offshore structures for the extreme and fatigue failure modes, based on the latest real-time sensor data, assumed to be four months. The continuously updated assessment informs operators on the failure probability over the next few years. Reliability analysis using real-time data is challenging owing to the need to extrapolate the observed data to more severe sea states and across many orders of magnitudes of probabilities, and there is a lack of related studies. Here, the environment comprises the short-term and long-term wave characteristics. Three data-driven reliability approaches are developed for three types of wave sensor data. The first approach applies statistical models to the response when wave data are unavailable. The second relies on Gaussian Process Regression (GPR) when only the wave spectral parameters are known. The third applies the Gaussian-experienced NARX network to predict the response time series when the wave time series are recorded. The proposed approaches are applied to a jack-up platform, and implementation of benchmark reliability analysis is enabled by establishing an emulator trained from dynamic simulations for fast generation of synthetic sensor data. The GPR approach is found to show good extrapolation capabilities and able to provide relatively accurate and robust reliability predictions.

Sediment dynamic on the tidal flat sheltered by artificial engineering: A case study on eddies

Tidal flats are important ecological and terrestrial resources. With the increasing development of coastal engineering projects, it is important to understand the dynamic response of tidal flats to human activities. Hence, the time series of wave, current, and suspended sediment during the spring tide from April 30, 2013 to May 1, 2013 were recorded by three tripod observation systems placed on the upper, middle, and lower parts of the tidal flats south of a constructed harbor in Wanggang, Jiangsu, China. The results showed that eddies formed south of the reclamations during flood tides. The directions of local tidal currents changed from their original southwest to the present northwest, and the ebb tides also changed but continued to flow northeast. The sediment transport process was basically consistent with the currents. The total net sediment fluxes during the tidal cycle (mean values of two tides) on the mudflat were two orders of magnitude larger than those on the salt marsh. Most of the sediments on both the mudflat and the salt marsh were transported northward alongshore, and a small portion of the sediments was transported seaward on the mudflat but shoreward on the salt marsh. The portion of the tidal flat with an elevation >1 m was wide in the north but narrow in the south, as determined by analysis of LiDAR elevation data, which coincided with the local sediment dynamics. The sediments were transported northward from southern deep waters during flood tides, which assisted in the expansion of the tidal flats in the north. This phenomenon reflected unique local sediment dynamics that were highly constrained by reclamations and Dafeng Harbor in the north as well as seawalls in the west. The tidal flat influenced by eddies can extend up to approximately 10 km south of the Dafeng Harbor. This case study has significant implications for the protection of tidal flats and the construction of coastal artificial engineering projects.

Advancing weather predictions for offshore wind farm maintenance through deep learning

Historical met-ocean data are widely used in the decision support tools to evaluate different operations & maintenance (O&M) strategies for offshore wind energy. Although effective, they are often very limited, which may not be able to represent prolonged offshore weather conditions at the wind farm sites. This hinders their application to the O&M planning. In this paper, a deep learning approach is proposed to build up the stochastic weather generator, in which the long short-term memory neural network is leveraged to simulate wind and wave time series data. The neural network is trained using the (limited) historical met-ocean dataset to accurately capture the statistical characteristics of wind and wave conditions. The results demonstrate the effectiveness of the proposed stochastic weather generator in delivering both open-loop and closed-loop forecasting for wind speed and significant wave height data, thereby supporting both corrective and preventive maintenance activities. The case study reveals that the open-loop forecast excels in short-term hourly met-ocean parameter predictions, while the closed-loop forecast proficiently captures the met-ocean patterns within a predefined window. Although the closed-loop forecast for wave parameters generally follows the measurements trend, it diverges from the actual measurements; a discrepancy likely due to the complex spatial-temporal dynamics of waves not completely captured by the LSTM model. The proposed LSTM model, considered as a complementary but connected solution, is able to enhance the utility of the limited historical data in O&M planning.

Improving Ship Response Estimation using Neural Networks

The feasibility of a data-adaptive multi-fidelity seakeeping model is assessed for use in early stage design in this study. Data adaptive tuning (or correction) of lower-fidelity model predictions are implemented based on training with higher fidelity ship motion response data. Long Short-Term Memory (LSTM) neural networks are incorporated as part of a multi-fidelity approach for prediction of 6 degree of freedom (6-DOF) ship motion responses in waves. LSTM networks are trained and tested with Large Amplitude Motion Program (LAMP)simulations as a target, and SimpleCode simulations and wave time series as inputs. LSTM networks improve the fidelity of SimpleCode seakeeping predictions relative to LAMP, while retaining the computational efficiency of a lower-fidelity simulation tool.

Overtopping Flow Velocity Characterisation Of Focused Waves On Promenades Using The Bubble Image Velocimetry Technique

This study characterises the flow velocity of individual extreme waves that overtop promenades using the bubble image velocimetry (BIV) technique (Ryu et al., 2005). Experimental tests were carried out in the small-scale wave flume CIEMito, at the Marine Engineering Laboratory (LIM) of the Universitat Politècnica de Catalunya – BarcelonaTech (UPC), and the obtained images were post-processed to calculate the flow velocities. The ultimate objective of the experimental campaign is to develop more precise models for forecasting wave overtopping of structures with an emergent toe, commonly found on sandy beaches and frequently utilized as promenades or waterfronts in most urbanized coastal environments. The NewWave theory (Tromans et al., 1991) was used to simulate the extreme individual wave overtopping in a real random sea state. The NewWave theory establishes a correlation between the expected form of a large wave in a linear sea state and the bulk characteristics of the sea state. Using focused wave groups instead of long-duration irregular wave time series offers several benefits. It improves the ability to repeat experiments and enhances measurement capabilities by providing greater temporal resolution in models used to investigate significant wave interactions (Hofland et al., 2014). Additionally, due to the compactness of focused wave groups, wave absorption becomes unnecessary. The research identifies two distinct case studies with varying wave forcing, tidal regimes and coastal layouts. This work presents a case study of a typical Mediterranean Sea configuration, which is a micro-tidal environment with steep and relatively short foreshores and pocket beaches. The study aims to characterize the overtopping flow velocity on the selected structure, and the feasibility of non-intrusive measurements such as a BIV technique has been investigated. The work includes preliminary results.

Spatial and temporal variability of wave energy resource in the eastern Pacific from Panama to the Drake passage

We analyse the wave energy resource available along the Pacific coast of South America from Panama from the latitude of 8°N to the Drake Passage at 55°S. The analysis is based on wave time series over 63 years (1959–2021) from the European Union Copernicus database constructed using the WAM wave model for the entire Pacific forced by wind information from ERA5. The novel features are the analysis of temporal variations in the wave energy flux, quantification of the contribution of swells and wind-seas into the wave energy potential, establishing properties of the most energy-carrying wave conditions, and evaluation of the role of El Niño and La Niña in the wave energy potential. The annual average wave energy flux increases from about 2 kW/m just to the north of the equator on the Colombian Pacific coast to 20–50 kW/m in the central and southern mainland of Chile and up to 80 kW/m near the Drake Passage. The wave energy resource to the north of latitude 32°S is almost entirely provided by swells. To the south of 44°S wind-seas predominate among the most energetic wave conditions and the maxima of energy flux by wind-seas up to 20 times exceed the already high average energy flux. The temporal variation in the wave energy flux follows the same pattern. It is fairly small at lower latitudes and increases rapidly from the forties. The magnitude of seasonal variation in terms of monthly mean wave energy flux is commonly from −47% to +32% from the long-term mean. The calmest time that contains 1% of the total annual energy flux is 10–20 days, about 10% of energy is contained in the 100 calmest days, while 50% of the annual energy flux arrives during the 100 days with strongest waves in the entire study area. The typical height of waves that provide the largest contribution to wave energy is about 1–1.5 m in the very north, around 1 m near the equator, gradually increases to the South and reaches 3.5–4 m on the shores of southern Chile. The associated wave periods are about 10 s in the entire study area. The wave energy flux has been almost constant over the 63 years near the equator but has increased at a rate up to 0.6 kW/m per year in the nearshore of Chile. For the evaluated time scales in coastal areas of South America, the interchange of El Niño and La Niña does not have detectable impact on the wave energy resource.

Morphodynamic Response of Open and Embayed Beaches to Winter Conditions: Two Case Studies from the North Atlantic Iberian Coast

The morphological responses of two mesotidal beaches located in different coastal settings (embayed and open sandy beaches) on the northwestern Iberian coast were monitored during the winter of 2018/19. The offshore wave time series analysis is related to high-resolution topo-bathymetric measurements to explore spatial-temporal morphological variability at monthly to seasonal scales. Both locations are subjected to the North Atlantic wave climate which exhibits a pronounced seasonality. Throughout the last decade (2010–2020), significant wave heights reached values of up to Hs~9 m during winters and up to Hs~6 m during summers. On average, approximately 12 storms occurred annually in this region. The results clearly reveal divergent morphological responses and sediment transport behaviors at the upper beach and the intertidal zone during the winter for each location. In the embayed beach (Patos), sediment transport in the nearshore is governed by cross-shore processes between the beach berm and a submerged sandbar. In contrast, the open beach (Mira) showed dynamic sediment exchanges and three-dimensional morphologies alternating between accumulation and erosion zones. Overall, both beaches exhibited an erosional trend after the winter, particularly concerning berm erosion and the subaerial beach volume/shoreline retreat. This study highlights the contrasting morphodynamic response on open and embayed beaches to winter conditions, integrating both the subaerial and submerged zones. Local geological and environmental factors, as well as the coastal management strategies applied, will influence how the beach responds to winter wave events. Monitoring and understanding these responses are essential for effective coastal management and adaptation to changing climate.

Reduced wave time series for long-term morphodynamic applications

Shoreline models have usually been recognized by professionals as the most appropriate tool for reproducing the long-term morphodynamic evolution of the shoreline of sandy beaches. Despite their underlying simplifications, the simulation of shoreline evolution at large temporal and spatial scales may imply significant computational efforts. Hence, to reduce computational costs, many approaches aimed to optimize the size of the input wave datasets have been proposed so far. A simplified novel method to reduce long-term offshore wave series is proposed herein. The rationale of the approach is to build reduced series that induce the same morphodynamic effects in the long-term as the ones induced by the whole, and more computationally expensive, original series. The method is conceived to define offshore reduced time series with the same chronological order of the complete series and is able to represent the bi-modal features of the wave climate. In-depth hydrodynamic and morphodynamic parametric analyses have been performed and it has been demonstrated that the method is capable to get reliable reduced offshore wave time series for reproducing the long-term evolution of sandy beaches with decreased computational costs.

Multi-fidelity data-adaptive autonomous seakeeping

Safe operation of a ship in heavy weather and high sea states requires accounting for the risk of extreme ship motion responses in stochastic ocean waves. Excessive ship motions can lead to hazardous and unsafe conditions such as pure loss of stability, surf-riding and broaching. Mitigation of these risks can be performed through selection of ship speeds and headings for a given seaway, and avoiding conditions likely to lead to severe motions. To address this challenge, a robust, fast, data-adaptive model is a prospective enabling capability for onboard autonomous seakeeping. In this study, data-adaptive Long Short-Term Memory (LSTM) neural networks are investigated as part of a multi-fidelity approach incorporating Large Amplitude Program (LAMP), and a reduced-order model known as SimpleCode. An assessment of this multi-fidelity approach focuses on prediction of ship motion responses in waves. LSTM networks are trained and tested with LAMP simulations as a target, and SimpleCode simulations and wave time-series as inputs. LSTM networks are shown to improve the fidelity of SimpleCode seakeeping predictions relative to LAMP, while retaining the computational efficiency of a reduced-order model. Potential areas of application include unmanned and reduced-crew vessels, operator guidance for manned systems, and weather-informed ship route planning.

Detection and quantification of wave trends in the Mediterranean basin

A study of a 42-year (1979–2020) long wave time series was performed for the Mediterranean Sea to detect and quantify trends in two relevant wave parameters adopted for coastal and offshore engineering purposes: significant wave height, Hs and peak period, Tp. The high resolution MeteOcean Re-Analysis database by the Department of Civil, Chemical and Environmental Engineering (DICCA) was used. At yearly and seasonal scales, the trends of the mean and maximum values were detected by the Mann–Kendall test, choosing a significance level equal to 90%. The slope or increase/decrease trends in Hs and Tp were assessed by the Theil–Sen estimator. For the mean values of Hs and Tp, increasing trends were detected for the Libyan, Levantine and Aegean seas, while for the maximum values this increasing trend was observed in a large part of the Mediterranean Sea. Finally, for the different marginal seas of the Mediterranean basin, a running trend analysis was applied in order to quantify the effect of the time window in the trend detection. The obtained results can be significant for flooding and erosion control strategies, ship and port operations, design and verification of structures, installations of Wave Energy Converters, in a hot spot for climate change such as the Mediterranean basin.

Statistical assessment of the wave loads at walls through two-phase CFD modeling of the effects of air compressibility

The modeling of wave impacts against coastal structures requires the analysis of hundreds or thousands of waves to be statistically meaningful. Long irregular wave attacks, when affordable, can be performed experimentally, but may be inadequate to track the air entrapment and account for air compressibility, which, instead, plays a key role in the wave impacts. On the other hand, long simulations are generally avoided in numerical modeling for computational effort and numerical stability reasons, even more so when two-phase flows and air compressibility are involved. In such a context, this paper presents, for the first time, the application of a plug-in suite developed in the OpenFOAM® environment to the representation of long time series of irregular waves impacting against coastal defenses while solving two compressible fluids. To this purpose, such a plug-in compressible suite was applied to reproduce recent 2D experiments of wave overtopping and wave impacts at smooth dikes with crown walls. The numerical stability of the compressible solver and its adequacy to accurately reproduce the wave reflection and the wave overtopping are first verified by comparing the numerical results with the laboratory tests. Second, the improved representation of the wave pressures and wave forces at the walls obtained with the plug-in compressible suite is shown by comparing its results with the corresponding ones obtained with the incompressible solver. Specifically, the plug-in suite—accounting for the effects of the air compressibility during the impact events—outperforms the incompressible native solver in the capture of the pressure peaks, in the reproduction of the time–pressure trace, and in the statistical analysis of the pressure distribution along the crown wall.

Experimental observation on wave propagation and geomorphological evolution in a sandbar-lagoon system

The sandbar-lagoon coast, one of the most productive and valuable ecosystems, has been strongly exposed to severe degradation. Excessive erosions aggravate the fragility of sandbar-lagoon systems. In order to seek adaptable solutions for ecological restoration, it is essential to study the hydrodynamic and morphodynamic characteristics. In this study, a series of flume experiments are conducted to investigate the wave propagation and geomorphological evolution in a typical sandbar-lagoon system. The time-series of swell and infragravity waves are obtained by a simple time-domain separation method, where wave reflection coefficient, skewness and asymmetry are calculated separately. The following conclusions can be drawn. To quantitatively assess the experimental results, a critical parameter ζ is introduced involving the incident wave height, the water depth and the sandbar freeboard. There is a linear relationship between wave attenuation and ζ. Further, a linear dependence on the maximum erosion thickness of foredune is achieved, and the maximum erosion thickness of sandbar increases with the increasing incident wave height by a superb linear correlation. Additionally, the shape transition of foredune scarp is significantly correlated with the dramatic change of the water level rise in the lagoon and the infragravity wave reflection. These findings promote better understanding for the morphodynamics of typical sandbar-lagoon systems and provide fundamental and scientific evidences on further coastal engineering.

The LISA Data Challenge Radler analysis and time-dependent ultra-compact binary catalogues

Context. Galactic binaries account for the loudest combined continuous gravitational wave signal in the Laser Interferometer Space Antenna (LISA) band, which spans a frequency range of 0.1 mHz–1 Hz. Aims. A superposition of low frequency Galactic and extragalactic signals and instrument noise comprise the LISA data stream. Resolving as many Galactic binary signals as possible and characterising the unresolved Galactic foreground noise after their subtraction from the data are a necessary step towards a global fit solution to the LISA data. Methods. We analysed a simulated gravitational wave time series of tens of millions of ultra-compact Galactic binaries hundreds of thousands of years from merger. This dataset is called the Radler galaxy and is part of the LISA Data Challenges. We used a Markov chain Monte Carlo search pipeline specifically designed to perform a global fit to the Galactic binaries and detector noise. Our analysis was performed for increasingly larger observation times of 1.5, 3, 6 and 12 months. Results. We show that after one year of observing, as many as ten thousand ultra-compact binary signals are individually resolvable. Ultra-compact binary catalogues corresponding to each observation time are presented. The Radler galaxy is a training dataset, with binary parameters for every signal in the data stream included. We compare our derived catalogues to the LISA Data Challenge Radler catalogue to quantify the detection efficiency of the search pipeline. Included in the appendix is a more detailed analysis of two corner cases that provide insight into future improvements to our search pipeline.

Effects of projected wave climate changes on the sizing and performance of OWCs: a focus on the Mediterranean and Atlantic European coastal waters

Reliable estimations of the Annual Energy Production (AEP) achievable with a certain Wave Energy Converter (WEC) are among the fundamental elements for a sound evaluation of the related Levelized Cost of Energy (LCOE) that plays a crucial role in the investment decision-making process. The lack of reliability in estimates of the device productivity can be a result of the uncertainty in the assessment of the available wave energy resource since the geometry of the device which maximizes the AEP is dependent on the specific wave climate at the foreseen installation site.
 The Climate Data Store of the Copernicus Climate Change Service delivers projections of the wave climate along the 20 m bathymetric contours of the whole European coastlines, covering the period 2040-2100, under two Representative Concentration Pathway (RCP) scenarios (RCP4.5 and RCP8.5) [1].
 This work addresses the effect of such long-term wave climate changes on the optimal sizing and performances of Oscillating Water Column (OWC) WECs to be installed along the Atlantic European coastline, expanding a previously published work in which the Mediterranean coastline was investigated [2]. The capture width of the OWC WEC under different wave conditions is computed using an empirical model [3] capable of predicting the device performance with acceptable accuracy and limited computational time.
 The results show that the optimal geometry of the OWC WEC varies significantly in the different geographical locations, and that the long-term changes in the wave energy resource could cause a slight modification of the optimal geometry in each potential installation site. The AEP of the OWC WEC in the projected wave climate scenario can be significantly different compared to the present one, potentially contributing to reducing the LCOE of this wave energy conversion technology in some geographical locations.
 REFERENCES:
 [1] Caires, S., Yan, K., 2022. Ocean surface wave time series for the European coast from 1976 to 2100 derived from climate projections. (Accessed on Feb. 2022) DOI: 10.24381/cds.572bf382. Copernicus Climate Change Service (C3S) Climate Data Store (CDS)
 [2] Simonetti, I., Cappietti, L., 2023, Mediterranean coastal wave-climate long-term trend in climate change scenarios and effects on the optimal sizing of OWC wave energy converters, Coastal Engineering, 173, 104247.
 [3] Simonetti, I., Cappietti, L., Oumeraci, H., 2018. An empirical model as a supporting tool to optimize the main design parameters of a stationary oscillating water column wave energy converter. Appl. Energy 231, 1205–1215.

ENVIRONMENTAL CONTOUR ESTABLISHMENT BASED ON OPENLY AVAILABLE EMODNET WAVE AND WIND DATA FOLLOWING HEFFERNAN AND TAWN METHODOLOGIES

In this paper, I present methodologies and routines for inference of environmental contours based on openly available data from the European EMODnet service, specifically wind and wave timeseries from oil platform 6200146. The conditional marginal distribution models, known as environmental contours, is established based on measured wind and wave heights, at platform 6200146 located in the North Sea. The data is provided through the openly available data platform, EMODnet. The environmental contour model is established by fitting univariate distributions to each data-series independently, whereafter an extremal dependence structure is established following methodologies outlined in (Janet E. heffernan, 2004).

Performance based assessment of a small-scale artificially nourished beach

In coastal engineering studies, coastal protection procedures can be provided by hard and soft methods. Soft methods applied using the right techniques and methods are not only long-lasting but also adapt to the natural structure of the coast. This study aims to present monitoring the development of a small-scale artificial nourished beach between the groins for 15 months and analyze its performance. For this purpose, field studies were carried out with land and sea observations taken once before nourishment and at 8 different times after nourishment. The seabed and profile variations observed at different sections were analyzed after processing field data. For determining the characteristics of the natural beach and borrow area before nourishment a sieve analysis was done for sediment samples taken from the shoreline, beach face, and 1-m depth on the nourished area. Sediment transportation of nourished material was observed by monitoring the amount of material remaining in 3 sub-regions (a nearshore region between the groins - A, a region representing the seaward end of the groins - B, and a region offshore of the groins - C) in the nourished region over time. The relationship between this behavior and waves was examined by considering the wave roses and time series of wave parameters produced as a result of wave simulations performed with the third-generation wave hindcast model SWAN. Lastly, as well as the variation of the mean layer thickness, the retreat of coastline, and mean beach width on the nourished area by the time were extracted for 8 different surveys. The results show that artificial beach nourishment materials were eroded in less than five months and the beach width returned to its initial position. The nourished material transported out groin-protected area moved eastward due to north-west dominated waves and the eastward longshore transport.

Uncertainties in wave-driven longshore sediment transport projections presented by a dynamic CMIP6-based ensemble

In this study four experiments were conducted to investigate uncertainty in future longshore sediment transport (LST) projections due to: working with continuous time series of CSIRO CMIP6-driven waves (experiment #1) or sliced time series of waves from CSIRO-CMIP6-Ws and CSIRO-CMIP5-Ws (experiment #2); different wave-model-parametrization pairs to generate wave projections (experiment #3); and the inclusion/exclusion of sea level rise (SLR) for wave transformation (experiment #4). For each experiment, a weighted ensemble consisting of offshore wave forcing conditions, a surrogate model for nearshore wave transformation and eight LST models was used. The results of experiment # 1 indicated that the annual LST rates obtained from a continuous time series of waves were influenced by climate variability acting on timescales of 20-30 years. Uncertainty decomposition clearly reveals that for near-future coastal planning, a large part of the uncertainty arises from model selection and natural variability of the system (e.g., on average, 4% scenario, 57% model, and 39% internal variability). For the far future, the total uncertainty consists of 25% scenario, 54% model and 21% internal variability. Experiment #2 indicates that CMIP6 driven wave climatology yield similar outcomes to CMIP5 driven wave climatology in that LST rates decrease along the study area’s coast by less than 10%. The results of experiment #3 indicate that intra- and inter-annual variability of LST rates are influenced by the parameterization schemes of the wave simulations. This can increase the range of uncertainty in the LST projections and at the same time can limit the robustness of the projections. The inclusion of SLR (experiment #4) in wave transformation, under SSP1-2.6 and SSP5-8.5 scenarios, yields only meagre changes in the LST projections, compared to the case no SLR. However, it is noted that future research on SLR influence should include potential changes in nearshore profile shapes.

Risk-based tsunami early warning using random forest

A new risk-based tsunami early warning method is developed using Random Forest (RF) with an extensive tsunami monitoring network (S-net) deployed off the Northeastern region of Japan. To consider a wide range of possible tsunami waves that may occur in the future, the RF model is developed using simulated 4000 tsunami wave time series at the S-net sensors. The response variable is the total aggregate loss of buildings caused by the tsunami, and the explanatory variables include earthquake information (magnitude, epicenter latitude, and epicenter longitude) and tsunami wave amplitudes at the S-net sensors. Unlike the conventional tsunami early warning method for predicting the tsunami wave amplitude along the shoreline, the response variable adopted in this study is a tsunami risk metric that reflects the tsunami impact to people and assets in coastal areas. The RF model is suitable for predicting highly nonlinear and scattered tsunami loss due to its characteristics of nonparametric regression and ensemble learning. The result indicates that compared with conventional linear regression-based algorithms, RF predicts the tsunami loss significantly better, reducing the mean square error by 90%. Furthermore, RF does not rely heavily on earthquake information, making it useful for announcing early warning for tsunamis generated by other sources.

A deep learning method for the prediction of focused waves in a wave flume

Rogue waves pose a significant risk to marine safety, emphasizing the need to accurately predict their occurrence in the open ocean. However, the complexity of their evolution, which may involve nonlinear physical phenomena such as wave-wave interaction and modulation instability, makes this task challenging. Currently the reconstruction of rogue waves involves generating focused waves through the superposition of different spectral components of irregular waves that are in phase at the focusing point. Despite its effectiveness, this approach is limited. The paper introduces a deep learning method based on Long short-term memory (LSTM) to predict focused waves generated in a Computational Fluid Dynamics (CFD) flume in the time domain. The model is trained on 60% of the generated wave time series, with the remaining 40% used for both validation and testing. The results demonstrate that the proposed method can assist with the prediction of focused waves at various observation points, indicating its potential as a promising approach for predicting rogue wave behaviour in the ocean.

Application of Empirical Mode Decomposition and Hodrick Prescot filter for the prediction single step and multistep significant wave height with LSTM

The study discusses the application of the Empirical Model Decomposition (EMD) and Hodrick Prescot (HP) filter for significant wave height prediction. Long Short-Term Memory (LSTM) is applied for sequence predictions in Natural Language Processing (NLP). LSTM can also be modeled to time series forecasting, particularly for cyclic data since LSTM learns from experience to forecast the data. The time series signal is a combination of frequencies or spectra, when the LSTM is applied to the raw signal the prediction is lagged, to reduce the lag in the forecast the noise in the time series signal is filtered. Since, the time series consists of various frequency components, filtering the higher-frequency components is required to reduce the delay in prediction from the LSTM neural network model. The EMD is applied to the original time series wave data to split the signal into several frequencies in time series or Intrinsic Mode Functions (IMFs). Similarly, when the HP filter is applied to the original wave data or time series signal it gives a trend and cycle. The LSTM is applied to the IMFs and HP filter trend time series to predict the EMD-IMFs and Trend respectively. All the predicted IMFs are summed to compare with the original raw time series. The single step and multistep prediction or forecasting is carried out for 1-h interval, 6-h, 12-h, and 24 h interval. With the increase in forecasting interval the error values also increased and changing the lambda parameter of HP filter played a critical step for the multistep prediction. The EMD-LSTM is computationally expensive as it takes higher amount time to predict each IMF compared to HP-LSTM. Finally, the results are compared with between normal LSTM, EMD-LSTM and HP-LSTM.