Prediction of solitary wave attenuation by emergent vegetation using genetic programming and artificial neural networks
Introduction
Tsunamis, as highly destructive waves, can cause serious damage to coastal areas. (Chen et al., 2013). Emergent vegetation in coastal wetlands is an important components of coastal ecosystems. The intertidal aquatic plants represented by mangroves can effectively reduce wave energy, and the resistance of their roots, trunks and canopy to wave makes them an effective and novel ecological wave attenuation measure (Augustin et al., 2009; Huang et al., 2011; Chen et al., 2018; Wang et al., 2019). Therefore, optimizing the cultivation of coastal vegetation and predicting the wave height after vegetation is of significant importance.
Wave attenuation by emergent vegetation, which is mainly affected by the hydrodynamic parameters and the vegetation characteristics, can be calculated by semi-empirical or empirical methods. However, the interaction between variables and the complex nonlinear relationship has impeded the accurate wave attenuation prediction. Generally, the performance of wave attenuation by vegetation is characterized by drag coefficient CD (e.g. Thuy et al., 2012) and wave transmission coefficient Kt (e.g. Arnaud et al., 2017). CD is a function of the vegetation configurations, Reynolds number, and other wave factors, which can be calculated by drag force and velocity according to the Morison equation. Once CD is obtained, the wave attenuation height can be calculated by using a wave elimination model such as Dalrymple et al. (1984) or Kobayashi et al. (1993). However, measuring the water particle velocity beside vegetation is indefinable and fallible because of the difference in depth and the location of the measuring point. Furthermore, the attenuation law used by different models is discrepant due to the simplification of the model. In addition, Kt ignores the variation of wave height in the vegetation field, and that can be directly determined according to the ratio of the transmitted wave to incident wave. Therefore, Kt is more suitable to establish the prediction formula in the case of no drag force and water particle velocity.
So far, scholars have done extensive research works on the influencing factors of wave attenuation and have accumulated a large number of high-quality, multi-element, and multi-scale data (Hashim and Catherine., 2013; Liu et al., 2015; Hoque et al., 2018). The common approach to derive empirical equation is through multivariate non-linear regression (MNLR). Türker et al. (2006) derived an empirical relation that defines the amount of erosion under the protection of emergent vegetation. Chen et al. (2016) obtained a formula for predicting the Kt of a surface vegetated platform based on numerical experiments and laboratory data. He et al. (2019) proposed an empirical equation by using MNLR on the basis of experimental data for predicting wave attenuation by the stem, root, and canopy of vegetation. However, the complex plant structure composed of roots and leaves and multiple data structures results in poor performance of wave attenuation prediction using MNLR methods.
Genetic Programming (GP) and Artificial Neural Networks (ANNs) are robust, simple and universal, and have a strong ability to solve complex nonlinear problems. Abbaspour et al. (2013) used GP and ANNs as alternative tools to characterize hydraulic jumps. Furthermore, GP and ANNs have been successfully applied for the prediction of wave-induced scour depth around breakwaters (Pourzangbar et al., 2017), flow resistance caused by flexible vegetation (Babovic and Keijzer, 2000), and channel Chèzy resistance coefficient (Giustolisi, 2004). These aforementioned works showed that GP and ANNs could obtain more concise and accurate relationships, and these approaches have not been implemented for the prediction of the Kt.
Therefore, solitary wave attenuation tests by three kinds of artificial vegetation models were carried out in wave flume. One of the aims of this study is to predict the wave attenuation using a more accurate empirical equation of Kt, and we used GP and ANNs as the intelligent method to contrast with classical MNLR methods. Another aim of this study is to understand the main influencing factors of emergent vegetation over wave attenuation. However, it is noted that, unlike GP and MNLR, ANNs cannot obtain explicit functional relationships. Experimental data of different types of plant models cannot be unified at present. Hence, each vegetation model has a corresponding Kt prediction formula and result.
This paper is organized as follows: Section 2 shows the overview of Kt governing parameters and the modeling approach; The detailed experimental setup and pre-processing of experimental data are reported in Section 3; The results of prediction and discussions are given in Section 4 and the sensitivity analysis is presented in Section 5. The main conclusions of this study are drawn in Section 6.
Section snippets
Transmission coefficient
In the wave flume, the wave with the incident wave height of Hi propagates through the vegetation zone, and its wave energy can be divided into three parts: one part of the energy propagates through the plant in the form of transmitted wave Ht; The other part of the energy is blocked by the vegetation and forms the reflected wave; The remaining energy is dissipated due to turbulence and frictional heat generated by the interaction between waves and vegetation zones and boundaries.
Experimental set-up
To further understand the wave attenuation by vegetation, three kinds of nonbreaking waves, artificial, rigid, and emergent vegetation experiments were performed in a 40.0 m long, 0.5 m wide, and 0.8 m deep wave flume (Fig. 2). The designed solitary waves were generated by a piston-type wave generator on one side of the flume, while a porous, clival wave absorber was constructed at the opposite end to reduce reflection. The vegetation field was placed in the middle of the flume. Wave gauges
Results of VM-Ⅰ
A total number of 150 datasets of VM-Ⅰ have been used for the prediction of the transmission coefficient using the GP, ANNs and MNLR models. The transmission coefficient (Kt) as the dependent variable, and the relative wave height (RH), relative width (RB), relative height (α), and solid volume fraction (ϕ) as the independent variables. The steps in exploiting a model with GP and ANNs are discussed in section 2.
Table 4 shows the solution equations at different sizes by using the GP method, and
GP results
It can be seen from Table 4 that the dimensionless factors may or may not appear in an optimal formula of a certain size, and they may occur once or more. Among them, the solid volume fraction (ϕ) appears most frequently, the relative width (RB) and the relative height (α) of the model appeared less frequently, and the relative wave height (RH) appeared least frequently.
The performance of a dimensionless factor in the GP results is measured by the number of times that a factor appears in all
Conclusions
The experiments studied three non-flooded rigid plant models, and the influence of the relative wave height, relative width, relative height, and solid volume fraction on the transmission coefficient was considered. Using multivariate non-linear regression, genetic programming and artificial neural networks to perform formula fitting and weight analysis of each factor, and the following conclusions were obtained:
- (1)
The formulas of transmission coefficient and relative wave height, relative width,
CRediT authorship contribution statement
Shangpeng Gong: Conceptualization, Methodology, Data curation, Writing – original draft. Jie Chen: Validation, Writing – review & editing. Changbo Jiang: Supervision, Funding acquisition. Sudong Xu: Software. Fei He: Investigation, Visualization. Zhiyuan Wu: Resources, Validation, Supervision.
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.
Acknowledgments
The study is financially supported by the National Natural Science Foundation of China (Grant No. 51839002 & 51979014). Partial support also comes from the Hunan Education Department Scientific Research Projects of China (Grant No. 18A123).
References (26)
- et al.
Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming
Water Sci. Eng.
(2013) - et al.
Wave propagation through dense vertical cylinder arrays: interference process and specific surface effects on damping
Appl. Ocean Res.
(2017) - et al.
Numerical simulations of wave propagation over a vegetated platform
Coast. Eng.
(2016) - et al.
A laboratory study on wave reduction by mangrove forests
APCBEE Procedia
(2013) - et al.
Interaction of solitary waves with emergent, rigid vegetation
Ocean Eng.
(2011) - et al.
Numerical simulation estimating effects of tree density distribution in coastal forest on tsunami mitigation
Ocean Eng.
(2012) - et al.
Coastal forest effects on tsunami run-up heights
Ocean Eng.
(2009) - et al.
Periodic water waves through an aquatic forest
Coast. Eng.
(2015) - et al.
Tsunami wave interaction with mangrove forests: a 3-D numerical approach
Coast. Eng.
(2015) - et al.
Prediction of non-breaking wave induced scour depth at the trunk section of breakwaters using Genetic Programming and Artificial Neural Networks
Coast. Eng.
(2017)
Analysis of coastal damage of a beach profile under the protection of emergent vegetation
Ocean Eng.
Laboratory measurements of wave attenuation and wave setup by vegetation
Genetic programming as a model induction engine
J. Hydroinf.
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