Accelerating Predictions of Morphological Bed Evolution by Combining Numerical Modelling and Artificial Neural Networks
2. Materials and Methods
2.1. Theoretical Aspects
2.2. Methodology Outline
- Three idealized alongshore uniform bathymetries were set up, each characterized by a different value of the bed slope tanβ, namely 1:5, 1:25, and 1:50.
- Determination of a number of combinations of the Input Parameters (IP) of to be inserted in the numerical modelling simulations.
- For each set of IP, nearshore wave propagation simulations were carried out utilizing a spectral version of a nonlinear parabolic mild slope wave model and the resulting radiation stresses were then inserted as forcing input to a flow model based on the depth-averaged Shallow Water Equations, providing the current speed and current direction.
- Subsequently calculations of the value of over a wave cycle were carried out for a cross-section in the middle of the domain in the alongshore direction through a post-processing algorithm. The value of is taken as the average value computed shoreward the maximum depth where initiation of breaking occurs, according to the criterion of , out of all the 3200 distinct wave records. The set of IP are consequently linked to a unique value of the Output Parameter (OP) . The corresponding values of IP and OP are provided for the training and validation of an ANN, which will predict for any values within the ranges defined in Table 1.
- Through Equations (8) and (9) estimation of follows. Each wave record that satisfies the condition is eliminated, since it is considered unable to initiate sediment motion and thus produce significant morphological changes. Each eliminated wave record is considered to contribute to the “calm conditions” (i.e., waves from directions exiting the numerical domain) hence it retains its individual frequency of occurrence . After elimination, a reduced dataset containing only the sea-states satisfying the Shield’s criterion of incipient sediment motion is obtained.
- Utilizing the reduced dataset as input and implementing Equations (12) and (13) a set of annual “equivalent” wave characteristics are defined. The equivalent wave characteristics are used to force the coastal area model and obtain predictions of the coastal bed evolution. In our implementations, we used a combination of a parabolic mild slope wave model (PMS) a hydrodynamic model (HYD), and an initial sedimentation/erosion and morphological model (SDT).
2.3. Overview of the Numerical Models
2.3.1. The Parabolic Mild Slope Wave Model (PMS)
2.3.2. The Hydrodynamic Model (HYD)
2.3.3. The Sediment Transport and Morphological Model (SDT)
2.4. ANN Parametrization and Training
- An input layer sending input data to the network
- A hidden layer composed of 32 units and a rectified linear unit (relu) activation function
- A hidden layer composed of 64 units using also a reLU activation function
- An output layer with an identity function
3. Methodology Implementation
3.1. Idealized Test Case Validation
- A “brute force” simulation set (BF) containing a detailed representation of the wave climate composed of 36 sea-states propagating from the dominant wave directions.
- A simulation set with the elimination of sea-states considered unable to initiate sediment motion by implementing the developed ANN to reduce the input dataset. Thereafter seven “annual equivalent” wave representatives are obtained from the reduced dataset, one for each dominant wave direction and are used to force the integrated models. This simulation will be thereafter denoted as “EW w/ANN”
- A simulation set with the forcing conditions being the seven “annual equivalent” wave representatives considering the full wave climate. This simulation will be thereafter denoted as “EW”
3.2. Real-Field Test Case
- A “brute force” simulation set (BF) containing a robust representation of the wave climate composed of 78 sea-states.
- A simulation set with the elimination of sea-states considered unable to initiate sediment motion by implementing the developed ANN to reduce the input dataset. This simulation set will be thereafter denoted as “EW w/ANN” and contains a representative sea-state for each dominant wave direction.
- A simulation set with the forcing conditions being the seven “annual equivalent” wave representatives after the elimination of wave records by employing an arbitrary threshold of < 0.5. This simulation will be thereafter denoted as “EW w/threshold”.
4. Results and Discussion
4.1. Idealized Test Case
4.1.1. Obtained Representative Wave Conditions
4.1.2. Morphological Modelling Results and Evaluation
4.2. Real-Field Case Study
4.2.1. Obtained Representative Wave Conditions
4.2.2. Morphological Modelling Results and Evaluation
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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|He (m)||Te (s)||MWD (°)||f (%)||He (m)||Te (s)||MWD (°)||f (%)|
|Test ID||EW w/ANN||EW|
|IC1||0.92 (E)||0.65 (E)|
|IC2||0.77 (E)||0.24 (G)|
|IC3||0.65 (E)||0.22 (G)|
|IC4||0.86 (E)||0.45 (G)|
|IC5||0.86 (E)||0.19 (R/F)|
|IC6||0.72 (E)||0.04 (P)|
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Papadimitriou, A.; Chondros, M.; Metallinos, A.; Tsoukala, V. Accelerating Predictions of Morphological Bed Evolution by Combining Numerical Modelling and Artificial Neural Networks. J. Mar. Sci. Eng. 2022, 10, 1621. https://doi.org/10.3390/jmse10111621
Papadimitriou A, Chondros M, Metallinos A, Tsoukala V. Accelerating Predictions of Morphological Bed Evolution by Combining Numerical Modelling and Artificial Neural Networks. Journal of Marine Science and Engineering. 2022; 10(11):1621. https://doi.org/10.3390/jmse10111621Chicago/Turabian Style
Papadimitriou, Andreas, Michalis Chondros, Anastasios Metallinos, and Vasiliki Tsoukala. 2022. "Accelerating Predictions of Morphological Bed Evolution by Combining Numerical Modelling and Artificial Neural Networks" Journal of Marine Science and Engineering 10, no. 11: 1621. https://doi.org/10.3390/jmse10111621