Inverse Calculation of Wave-Absorbing Structure Dimensions Based on Extended ANFIS Model

A new wave energy dissipation structure is proposed, aiming to optimize the dimensions of the structure and make the reflection of the structure maintain a low level within the scope of the known frequency band. An optimal extended ANFIS model combined with the wave reflection coefficient analysis for the estimation of the structure dimensions is established. In the premise of lower wave reflection coefficient, the specific sizes of the structure are obtained inversely, and the contribution of each related parameter on the structural reflection performance is analyzed. The main influencing factors are determined. It is found that the optimal dimensions of the proposed structure exist, which make the wave absorbing performance of the structure reach a perfect status under a wide wave frequency band.


Introduction
Wave dissipation structures are used to protect coastal areas from wave attacking. Varieties of wave dissipating structures have been proposed and studied, which include horizontal plate/plates, perforated caisson or wall. Horizontal plate/plates wave dissipation structures have been studied by Cheong and Patarapanich (1992), Usha and Gayathri (2005) and Neelaman and Gayathri (2006). Wang et al. (2016) concluded that the main wave energy dissipation mechanisms of plates were shallow water effect, wave breaking and more intensive turbulent vortices generated by plates. Lalli et al. (2012) investigated the effectiveness of the submerged flat plate breakwater, and studied the behavior of a dual plate array in different layouts and geometric configuration on the hydrodynamic performance. Li (2014) concluded that the effect of dissipating waves for the horizontal double-plate system was better than that of single horizontal plate normally and was not worse than that of multiple horizontal plates in most cases.
Since the early study of Jarlan (1961) on the effect of a perforated wall, several researchers have investigated the interaction of waves with double-layer and even multiple-layer perforated-wall caisson breakwater. Fugazza and Natale (1992) studied the reflection characteristics of multiple-lay-er perforated breakwaters based on the linear wave theory. Huang (2006) studied the reflection of multi-chamber perforated structures based on the linear velocity potential theory. Lee and Shin (2014) studied the reflection of partially perforated wall caisson structures with single and double chambers in a wave flume. Kakuno et al. (2003) proposed double slit-wall breakwater to overcome the "narrow-band" effect of single slit-wall breakwater which meant low reflection only for waves of the specific frequency band, and low wave reflection in wider frequency range can be attained through optimizing the dimensions of the structure. Hiraishi (2006) pointed out that the slit caisson was effective to reduce the reflection coefficient of the shorter period waves. Zhu (2013) investigated the hydrodynamic nonlinear characteristics of regular wave interacted with a double-layer perforated-wall caisson breakwater, and the study shown that the reflection coefficients of double-layer perforatedwall caisson breakwater can be reduced and the effective frequency band can be widened if the structural parameters and the wave parameters were combined effectually.
So far, most studies have been focused on the hydraulic characteristics of the structures. Only a few studies dwelt on the methodologies that could reasonably estimate the structural parameters in view of a wave dissipation structure sys-tem. Therefore, this study attempts to compute the structural parameters inversely through the hydraulic characteristics of the structures to make the structure have lower reflection for a wide range of wave frequency.
The neural network systems are usually used to model complex relationships between inputs and outputs or find patterns in available data. The prediction problem has been contemplated by numerous researchers utilizing neural network systems techniques, for example, Lee et al. (2009) and Malekmohamadi et al. (2011). The use of fuzzy set theory allows the user to include the unavoidable imprecision in the data. The fuzzy modeling approach is a weighted average of several linear models, which are introduced by the rules. Utilizing the fuzzy modeling approach, one can make useful interpretations by considering the fuzzy rule base. Özger and Şen (2007) adopted fuzzy logic inference system (FIS) to predict the significant wave height by the wind speed, showing that the fuzzy logic was more efficient than other traditional approach in linking the multiple inputs to a single output in a non-linear domain. Kazeminezhad et al. (2005), Özger and Şen (2007) and Mahjoobi et al. (2008) used the FIS to forecast the wave parameters.
Adaptive neuro-fuzzy inference system (ANFIS), developed on the basis of artificial neural network and fuzzy logic, is first introduced by Jang (1993). ANFIS has high speed of training, the most effective learning algorithm and is simple in terms of the structure (Vairappan et al., 2009). To the best knowledge of the authors, several simplified wave prediction methods have been presented in the literature, such as Kazeminezhad et al. (2005), Lin and Chang (2008) applied the ANFIS method to predict wave parameters. Bateni and Jeng (2007) developed ANFIS models to predict the scour depth and scour width for a group of piles supporting a pier. Bakhtyar et al. (2008b) established an ANFIS model which had supervised-learning capabilities and can be explained and understood to estimate the wave runup in landward sea, and the results show that the proposed ANFIS modeling approach could provide high accuracy and reliability for the wave runup estimation. Bakhtyar et al. (2008a) have concluded that the ANFIS model was more flexible than the FIS model with more options for incorporating the fuzzy nature of the real world system. Soltani et al. (2010) combined a water quality simulation model which is based on an ANFIS and a hybrid genetic algorithm to determine optimal operating policies for different reservoir outlets. Malekmohamadi et al. (2011) used various soft computing-based models to map wind data to the wave height, and the results showed that ANFIS can provide acceptable predictions for wave heights.
The applications of ANFIS in coastal engineering structures are few, and Patil et al. (2011) developed ANFIS model which was trained by the data set obtained from the experimental wave transmission to predict the wave transmission through floating breakwaters. Nikoo et al. (2014) de-veloped a data-driven simulation modeling based on AN-FIS, which can model the relationship among the wave parameters, to determine the optimized dimension of Double-layered perforated wall breakwaters by finding the best agreed-upon design point on the trade-off curve from wave transmission and reflection point of view. This study was the first to consider the wave reflection and transmission indices in optimum design of perforated-wall breakwaters to optimize the breakwater structure.
Planning and design of wave eliminating structures require information about the performance characteristics of the structure in reducing the wave energy. A prominent parameter indicating the reflection characteristics of the structure is the wave reflected coefficient. The wave reflection coefficient is crucial to understand the wave climate at the seaside of the structure. Therefore, it is necessary to predict the reflection coefficient in the targeted area. Everybody knows that the wave reflection is affected by the configuration and sizes of the structures to a great extent, and the size of the structures also depends on the level of the required wave attenuation. The relation between the wave reflection coefficient and the sizes of the structures is complex and includes many uncertainties. The main uncertainties in this area include the nonlinear transformation of waves in breaking turbulence, multiple wave reflection and the effects of infragravity waves. Researchers have carried out tremendous work dealing with an absorbing structure, but they failed to give a simple mathematical model for these structures to foreknow the wave reflection and to predict the sizes of the structural system. Contemporarily, AN-FIS has been accepted as the potentially valuable tool for modeling and forecasting complex nonlinear systems containing many uncertainties. The main advantage of ANFIS is that it can recognize the highly nonlinear relations in systems, thus this method is still a modern technique for solving complicated problems which either does not have a specific algorithm, or using conventional methods to find their solution is very difficult.
The wave reflection coefficient before the structure is the end product of numerous complex time-and space-dependent interactions between fluid and the boundaries of obstacles. These interactions cannot be resolved completely by deterministic models since most of the intervening steps in the existing models are adhoc and unverified. Since the influence relation of the structural sizes to the wave reflection coefficient is still unknown, it is necessary to solve the nonlinear problem. This is an inverse problem that the structural sizes are required to determine explicitly in the level of the desired wave attenuation. Therefore, as the potential function extension to ANFIS model is extremely feasible for the interaction between waves and structure, it should also have a refinement capability that can estimate the sizes of the structure within the scope of known eliminating-wave level.
From what has been discussed above, the first goal of this paper is to design a new-type absorbing wave structure that can attenuate waves to the minimum height for a prevailing wave climate. Secondly, an expanded ANFIS model is also developed to forecast the sizes of the special combination structures through the unknown relationship between the wave reflection and the sizes of the structure. Finally, an additional originality for this work is the optimization procedure which will be performed for a wide range of wave periods.
2 Proposal of the type of absorbing wave structure 2.1 Layout and research schemes of the COMBLOC system Waves have an important influence on coastal dissipating structures, in turn the pattern of the structure usually affects the shapes of the reflected waves, and the pattern of the dissipating waves system is also important to reduce the wave reflection before the structures. By considering the waves conditions and the dimensions of the structure, it is possible to identify the reflection behavior of the wave-dissipating structure, and the wave conditions and the size of the structure are crucial and can directly affect wave reflection coefficient of the structure.
Zero reflection can be achieved with horizontal plates under certain conditions, especially for short waves. However, low reflection is gained only for waves of the specific frequency. By reviewing the previous work it is found that the bandwidth of dissipating waves of double-layer perforated-wall structure can be broadened obviously if the structure parameters and hydraulic parameters are effectually combined. In order to overcome the disadvantage of the narrow-band effect of horizontal plates and maximize the damping wave energy of the dissipating system in a wider frequency range, this study proposes a composite wave elimination structure composed of two horizontal plates and two rows of vertical block structure attached to the back of the plates-COMBLOC, as shown in Fig. 1. It is expected that the horizontal double-plate system damps short waves and the double-layer perforated-wall structure damps long wave as much as possible.
The horizontal plates have the function of restraining wave vertical movement and the flow beneath the plates is forced into the advection movement dominated by the horizontal motion, and part of the incident wave energy therefore gets dissipation due to the change of the motion state. The wave length of waves propagated through plates will be shorter and will interact with vertical blocks with different boundary shapes in the rear of the plates, and eventually the energy of waves is further diminished. The boundaries of the vertical block structure can be of circular arc, straight flange or other shapes. These different types of boundaries can form various types of cavity structures. The wave energy gets dissipation due to the waves in cavities generating reflection, refraction or plug flow. So various types of fluid cavity channels in the fluid domain are built by the block structure, and the waves in the cavity channels conduct periodic motion repeatedly, which can dissipate the rest of the wave. At the same time the front panel structure and the back block structure are not in the same plane, and consequently the complex wave height before the COMBLOC can be reduced by the phase difference.

Verification of numerical model and calculated results of reflection coefficient
To compare the wave-eliminating performance of every structure scheme of the COMBLOC system, a well-known parameter characterized the hydrodynamic characteristics of the structure is the wave reflected coefficient. The calculations of the wave reflection coefficients need the wave surface history at least at two points in front of the structures. The time series of the wave surface of monitoring points is obtained through a vertically two-dimensional numerical model which is based on the open code FLUENT. The accuracy of the model for calculating the wave reflection coefficients is verified against the physical model test data of arc plate breakwater and horizontal plate breakwater (Wang et al., 2016) before the numerical simulation. The experiment was conducted in a water tank of 22.00 m×0.45 m×0.60 m. The model test setup, test wave conditions and the final comparison results are shown in Fig. 2. It can be seen in Fig. 2 that the numerical results of the present model involving the wave reflected coefficients and wave transmission coefficients agree well with Wang et al.'s (2016) experimental data. Therefore, the present two-dimensional numerical model can be employed to simulate the interaction between waves and structures.

Model framework system
The wave reflection is affected by the configuration and dimensions of the structures. The dimensions of the structures generally depend on their applications and the level of the required wave attenuation. The relations between the wave reflection coefficient and the sizes of the structures are complex, and include many uncertainties such like wave TIAN Zheng-lin et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 501-513 breaking, air entrainment and turbulence. The complex relations between the wave reflection coefficient and the sizes of the structures can be modeled by a valuable tool ANFIS. Therefore, in this section an advanced ANFIS model is developed to predict the sizes of the structure based on the changes of the wave reflection coefficients in front of the wave dissipating system inversely. The wave reflection coefficients of the COMBLOC under various parameter conditions are obtained through the FLUENT code numerical simulations. The extended ANFIS models are trained by these reflection coefficients to let the COMBLOC with suitable dimensions have lower wave reflection coefficients in a wider wave frequency band.

Adaptive Network based on the Fuzzy Inference System
The ANFIS, which uses the back-propagation learning and the least mean squares hybrid algorithm to modulate the premise parameters and consequent parameters, is a new fuzzy inference system structure combined fuzzy logic and neural network organically. It is functionally equivalent to a fuzzy interference system consisting of a set of rules, it can construct an input-output mapping based on the fuzzy ifthen rules or the stipulated input-output data pairs (Soltani et al., 2010). ANFIS employs the neural network training procedure to adjust the membership function and the associated parameters. The fuzzification of the input and output variables, the inference engine and defuzzification of fuzzy control three basic processes all use neural network to realize, and the neural network is embedded in a complete fuzzy structure. In the process of solving, the neural network learning mechanism is used to extract rules from input and output sample data automatically, and constitute the adaptive neural fuzzy controller, which conduct the self-adjusting of fuzzy reasoning of control rules through training and learning, and eventually making the system itself develop towards adaptive, self-organizing, self-learning direction.
The ANFIS is powerful in terms of extracting nonlinear and illdefined relations that may exist in the data (Bakhtyar et al., 2008b). In fuzzy set theory and neural networks, if the input-output data include the information on uncertainty and main features (even highly nonlinear) of the real-world system to be controlled by ANFIS, ANFIS is expected to be successful in the real-world simulation. The ANFIS modeling method is based on the data, so the establishment of the system is not dependent on the object model, but rather depends on the expert knowledge. The if-then fuzzy rules in the system are generated through the study of the known data automatically, rather than determined by the experience or intuition. This is particularly important for the systems whose characteristics are still not fully understood by people or is very complex. For example, in our problem the uncertainty of the wave reflection characteristics and the effect of the structural sizes, as important characteristics of the system behavior, are converted to nonlinearity in data, which are then used by the ANFIS through generating different input parameters and different structural sizes, respectively.
Since the ANFIS is a universal approximator, one can refer to the literatures (Bakhtyar et al., 2008b;Soltani, 2010;Malekmohamadi et al., 2011;Patil et al., 2011) for a detailed description of the model and its theoretical background. The architecture of the ANFIS consists of five layers (see Fig. 3), and the operating principle of the model is given next. Let denote the output of the node i in Layer l and x i is the i-th input of the ANFIS, i=1, 2, …, m.
Layer 1: Nodes are adaptive and the fuzzification of the inputs is achieved in this layer. Membership functions (MFs) of the input variables are used as the node fuzzy The role of the node functions M 1 , M 2 , …, M m here is the same as the membership functions used in the regular fuzzy systems, and m is the number of nodes for each input. Generalized bell member-ship function is the typical choice and is given by: where , , and are the parameters of the membership function, governing the shape of MFs with the minimum and maximum equal to 0 and 1, respectively. ω i Layer 2: Nodes are fixed and each node in this layer estimates the firing strength ( ) of a rule by applying the AND operator. Firing strength means the degrees to which the antecedent part of a fuzzy rule is satisfied and it shapes the output function for the rule. The output of every node of this layer is the product of all the incoming signals from Layer 1. . (3) Layer 3: Each node output represents the firing strength of the reasoning rule. Each of these firing strengths of the rule is compared with the sum of all the firing strengths. Therefore, the normalized firing strengths are compared in this layer as: Layer 4: The Sugeno-type inference system, i.e. a linear combination of the input variables of an ANFIS x 1 , x 2 , …, x m plus constant terms c 1 , c 2 , …, c m , from the output of each IF-THEN rule, is employed in this layer. The output of the node is a weighted sum of these intermediate outputs: where the parameters P 1 , P 2 , …, P m and c 1 , c 2 , …, c m , are referred to as the consequent parameters in this layer . Layer 5: This layer aggregates the qualified consequents to produce a crisp output. The node in this layer produces the sum of its inputs, i.e. the defuzzification process of the fuzzy system (using weighted average method) and is obtained as: There are two adaptive layers (Layers 1 and 4) in the ANFIS structure. The aim of the training or learning algorithm is to adjust all the modifiable parameters to make the ANFIS output emulate the given training data. A hybrid algorithm combining the least squares method and gradient descent method is usually adopted to solve this nonlinear system problem. There are two steps in the hybrid-learning procedure for the ANFIS. In the first step, the output of the ANFIS is calculated by employing the consequent parameters, functional signals go forward until Layer 4 and the consequent parameters are identified by the least-squares estimate. In the second pass, the output error rates propagate backward and the premise parameters are updated by a standard error backpropagation algorithm (the gradient descent). A detailed coverage of an ANFIS can be found in Jang (1993).
In general, the more input-output pairs and the more generated rules, and as the number of rules increases, the difference between the predicted and experimental values decreases, and more complex relations can be modeled with a large number of rules. However, if the number of rules is larger, the over-fitting phenomenon will appear and the approximation results will distort. Thus, it is important that ANFIS is kept as fast and efficient as possible, we tune a FIS with a small number of fuzzy rules.

Principal component analysis
In order to determine the main influencing factors, the influence of input parameters is assessed using the principal component analysis (PCA). PCA can be used to extract relevant information from confusing data sets (Patil et al., 2011), and the major contributing components can be observed. In coastal engineering, there are many factors affecting the hydrodynamic performance of wave dissipating facilities, such as the wave height, wave steepness belonging to wave conditions and submerged depth belonging to the structural parameters. If one knows which factors influence the characteristics of hydrodynamics more, the more attention can be paid to the main factors in planning and design of wave eliminating structures.
3.3 Reverse procedure of the structure size For an effective design of the wave dissipating structure, it is necessary to study the hydrodynamic performance characteristics of this structure. An intensive and comprehensive study on the wave reflection of the wave dissipating structure would provide a proper size to the structure. The relationships between the wave reflection coefficient and main influential parameters are highly nonlinear. In order to study the influential relationships between the wave reflection and influential parameters, the fuzzy reasoning model which is used to invert the influential parameters based on the ANFIS modeling mechanism is built.
Till now, there has not been an available simple mathematical model to predict the size parameters of the structure by considering the hydrodynamic characteristics. This is due to the complexity and vagueness associated with many of the governing factors and their effects on the performance of the structure. By considering waves conditions and structures dimensions, it is possible to identify the reflected behavior of the system. These factors are important and can directly affect the wave reflection coefficient of the system. The proposed extended ANFIS method can be useful as a tool for hindcast problems by taking the advantage of the ANFIS. The extended ANFIS can predict the future structural sizes directly from the wave reflection coefficients. In the present paper, the extended ANFIS, which is an implementation of a representative fuzzy inference system using a back-propagation neural network-like structure with limited mathematical representation of the system, is developed.
Programming to solve the modeling problem in MAT-LAB environment, an extended ANFIS model used to speculate the sizes of the COMBLOC is designed, and a rigorous procedure of the program design is provided based on the ANFIS method. In order to back-determine the sizes of the structure, the wave reflection coefficients are proposed as training data to train the extended ANFIS model. In the following sections, the main components of the proposed methodology are described in detail.
The implementing process of the extended ANFIS fuzzy modeling can be divided into the following steps.
(1) The factors affecting the wave reflection are analyzed, the data required are gathered and the main performance objectives are selected, eventually the training data and testing data sets are formed; (2) A series of stipulated input-output data pairs are constituted, such as [(d n , H n , T n , …), (Rf n )], where n=1, 2, 3, …, (d n , H n , T n , …) are the inputs of the network and (Rf n ) is the corresponding outputs; (3) The model architecture with the specified paramet-ers is determined, the method of learning is assigned, and an initial FIS structure is generated by the genfis1 command, which specifies the membership function type and the number of the membership functions associated with each input; (4) The parameters of the FIS model for training are set; (5) The outputs of the FIS model are exported; (6) The graphs of the results are set and the outputs are exported; (7) The wave bandwidth whose wave reflection coefficient is smaller than 0.4 is outputted; (8) The optimal sizes of the structure whose wave reflection coefficient is smaller than 0.4 are gained crisply. The codes are written in MATLAB R2016b. The flowchart of the extended ANFIS procedure used in the present paper is shown in Fig. 4.

Validation of the extended ANFIS model
In order to verify the correctness of the program, the training data and testing data are two basic requirements for the extended ANFIS model. The measured cave depth data (Lee et al., 2009) Lee et al.'s (2009) testing data, thus, our present model can be used to carry out the following work.
In order to concretely explain the present procedure, we consider a simple demonstrative example in which the data are used from Tanimoto and Yoshimoto (1982) who stud- ied the reflection performance of double slit-wall breakwaters, and a goal reflection coefficient of 0.4 as the optimization target value is chosen like Kakuno et al. (2003), and the details are shown below.
Firstly, make the relative width B/L of slit-wall breakwaters and the wave reflection coefficients of Tanimoto and Yoshimoto (1982) match to input-output pairs, and the relative width B/L, the wave reflection coefficients are set as inputs of the extended ANFIS and the corresponding outputs respectively. Secondly, the type of the membership function is designated as gbellmf, and the number of the membership function which has a great influence on the model simulating results is adjusted to 6. Finally, the simulating results of the extended ANFIS trained by the experimental data is displayed in Fig. 6, and the wave bandwidth that the reflection coefficient is smaller than 0.4 is shown in Fig. 7 after operating the program of the extended ANFIS. In Fig. 7, it is observed obviously that the reflection coefficients when B/L between 0.117-0.2673 are always smaller than 0.4. Normally, the wave length of incident waves is known in advance, and then the specific values of the breakwater width B are determined promptly.

Optimal design of the structure sizes
The wave reflection before the complex structure system is a well-known topic which has been studied for many years. However, as a result of complicated features such as wave breaking, air entrainment and turbulence, the study of the wave reflection is still a thorny problem, and the prediction of the wave reflection coefficient is also a tough problem. Reflected wave height and wave motion fluctuations can show strongly hydrodynamic characteristics of the system where the reflection coefficient depends not only on the wave climate, but also on previous internal physical dimensions. Usually, a structure has a steady wave reflected coefficient, and one can obtain the wave reflected coefficient through the CFD simulated calculation conveniently. But, if the wave reflected coefficient is known in advance, there is still not a current effective methodology to determine the sizes of the structure. Based on the wave reflection coefficients, the prediction of the sizes of the COMBLOC structure is necessary in order to design an excellent absorbing structure. Since the ANFIS is an adaptive system with human feeling and the cognitive component, the ANFIS can be used to map the wave reflected coefficient to the sizes of the structure, and the ANFIS can predict various future structure parameters directly from the wave reflected coefficient. The objective of this section is to examine the technique that has been developed to evaluate the wave reflection coefficient before the structure system. Note that the models selected are not intended to be inclusive, but merely representative of the classes of models.
Waves have an important effect on harbors, breakwaters, shore protection measures, coastal structures, and the other coastal works, meanwhile, these structures similarly have an important effect on waves, i.e. waves characteristics. In reality, waves often have variable shapes because they are under the influence of the structures. For the design of wave eliminating structure, it is desired to forecast the reflection performance of the structure in advance, on the basis of that to design and optimize the structure to reduce the wave reflection of the structure in the actual sea. In the following, the combinatorial optimization of the COMB-LOC structure will be conducted step by step and the final optimized results of the sizes of the COMBLOC structure will be shown.
The length of the first wave chamber B 1 , the length of the second wave chamber B 2 , the length of the third wave   (Tanimoto and Yoshimoto, 1982). TIAN Zheng-lin et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 501-513 chamber B 3 , the plate length l, the submerged depth of the first horizontal plate d 1 , the thickness of the plate t 1 , and the gap of the two horizontal plates g are found to have a major effect on the wave reflection under investigation. The main purpose of this methodology is to give a procedure for determining the above design parameters of the COMBLOC giving the values of incident wave period. Thus, seven parameters, including B 1 , B 2 , B 3 , l, d 1 , t 1 , and g are selected as the inputs for the ANFIS, and the one output is the wave reflection coefficient. The ANFIS model is then applied to estimate the sizes of the structure based on the wave reflection coefficient stated above.

Optimized results of the wave chamber width
Firstly, the input parameters that influence the wave reflection (K r ) of the COMBLOC B 1 , B 2 , and B 3 are considered, and the relations between the wave chamber width and the wave reflection coefficient are presented in Figs. 8-10. Observing the simulated results, one can know that almost all the wave reflection coefficients are larger than 0.4 when the wave chamber widths B 1 , B 2 , and B 3 change in the range of 0.1 to 0.5 m. There is an interesting and inspiring tendency from Fig. 9 and Fig. 10 that the impact trend of the wave chamber widths B 2 and B 3 on the wave reflection coefficient are the same more or less. As the wave reflection coefficient curves do not appear the transit that the reflection coefficient shuttle in 0.4 up and down, the wave reflection coefficients obtained by the CFD numerical model are not very befitting for the extended ANFIS model. Actually, this situation that all the calculating results are not entirely satisfactory, that is the perfect data we want, however, exists. The considered maximum of B 1 , B 2 , and B 3 are all 0.5 m in this study, and the sum is 1.5 m that is one half of the wavelength when the period of wave is 1.6 s and the water depth is 0.5 m, but that is 1.5 times the wavelength when the period of wave is 0.8 s and the water depth is 0.5 m. If the sum of the wave chamber widths B 1 , B 2 , and B 3 is added the length of plates, the total length of the COMBLOC structure gets longer, this is not thrifty in actual engineering. In such situation, we choose the optimal wave chamber width under the action of long period waves preferentially, and it needs to be emphasized that there is no rigid rules here. The wave chamber widths B 1 , B 2 , and B 3 are set as 0.4 m, 0.5 m, and 0.5 m through the comprehensive analysis respectively. Fig. 11 displays the relations between the plate length and the wave reflection coefficient under the action of different periods of waves. From the curves of the simulated results, it can be seen clearly that all the wave reflection coefficients are smaller than 0.4 when the length of the plate in the range from 0.11 to 0.21 m. Compared with the simulated results of wave chamber width, this group of simulated results are very perfect since the wave reflection coefficient curves show the transit that the reflection coefficient

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TIAN Zheng-lin et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 501-513 shuttles in 0.4 up and down. The extended ANFIS model does not seek to reproduce the detailed flow patterns in and around the structure, which are strong effects of the structural geometry, but rather seek  TIAN Zheng-lin et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 501-513 509 to provide, through a rational analysis procedure, a method to obtain the sizes of the structure reversely through the farfield reflected wave amplitude. This result simulated by the extended ANFIS model confirms that the wave reflection coefficient can be utilized to estimate the sizes of the structure system. And an optimal COMBLOC structure exists, which can be designed for a wide range of frequencies.
4.3 Optimized results of the submerged depth of plates Fig. 12 displays the relations between the submerged depth of plates and the wave reflection coefficient under the action of different periods of waves. From the curves of the simulated results, it can be seen clearly that all the wave reflection coefficients are smaller than 0.4 when the submerged depths of plates in the range from 0.011 to 0.021 m. Compared with the simulated results of the wave chamber width, this group of the simulated results are very perfect as the wave reflection coefficient curves demonstrate the transit that the reflection coefficient shuttles in 0.4 up and down. Fig. 13 displays the relations between the plate thickness and the wave reflection coefficient under the action of different periods of waves. From the simulated results curves, it can be seen that the thickness of the plates has certain effects on the wave reflection coefficients, but the effects is not very significant in the range of the considered plate thicknesses. This group of the simulated wave reflec-tion coefficient curves do not demonstrate the transit that the reflection coefficient shuttles in 0.4 up and down, but the minimum wave reflection coefficient is obtained when the plate thickness is 0.02 m.

Optimized results of the distance between plates
Fig. 14 displays the relations between the plate spacing and the wave reflection coefficient under the action of different periods of waves. From the curves of simulated results, it can be seen that the gap of the plates almost has some small but discernable effects on the wave reflection coefficient, and the simulated wave reflection coefficient curves are almost in a straight line. And this group of the simulated wave reflection coefficient curves also do not show the transit that the reflection coefficient shuttles in 0.4 up and down.

Analysis results based on the PCA
The input parameters that influence the wave reflection (K r ) of the COMBLOC, such as L 1 , d 1 , B 1 , B 2 , B 3 , t 1 and g 1 are considered. Based on the above input parameters, the calculation results of the PCA are shown in Table 1.
From Table 1, some important information can be seen explicitly. The first component alone accounts for 46.63% of the total variance, the second component alone accounts for 26.68% and the 3rd, 4th and 5th components account for 9.16%, 7.82% and 7.55% respectively, and the last 6th and 7th components together account for smaller than 2%. Ac- cording to the PCA, the first five components together account for more than 98%. This shows that L 1 , d 1 , B 1 , B 2 , and B 3 have more important effects on the wave reflection coefficients, and the last two principal components have less im-  TIAN Zheng-lin et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 501-513 511 portant effects on the wave reflection coefficients. In fact, the first principal component reflects the plate length on the influence of the reflection coefficient, the second principal component reflects the submerged depths of plates on the influence of the reflection coefficient and B 1 , B 2 , and B 3 , commonly reflect the width of the wave chamber on the influence of the reflection coefficient. From this study it is observed that the plate thickness t 1 and plate spacing g 1 are the least influential parameters. Thus, we know that L 1 , d 1 , B 1 , B 2 , and B 3 have more important effects on the wave reflection coefficients, and more attentions should be paid to the main factors in planning and design of wave eliminating structures.

Conclusions
For an actual sea suffered by the waves of certain period range from 0.8 to 1.6 s, an optimal structure that can eliminate the most energy of incident wave within the scope of the known wave period is designed. The original intention of this structure is based on the thought that the horizontal double-plate system damps short wave and the double-layer perforated-wall structure damps long wave in eliminating wave aspect. Therefore, a new kind of the energy dissipation system COMBLOC consisting of the horizontal double-plate and double-layer perforated-wall structure is proposed. The extended ANFIS model is developed to design the dimensions of structure, and the extended ANFIS models are trained by the wave reflection coefficients which are gained through the numerical simulations to approach the highly nonlinear system interacted by the wave reflection coefficients, wave parameters and structural parameters, eventually make the extended ANFIS model possess the function that back-calculates the sizes of structure based on the known wave reflection coefficients. In the premise of lower wave reflection coefficient, the sizes of the structure are obtained inversely, and an optimal size of the structure that can be applicable for a wide range of wave periods is found in this article. Demonstration optimizations for the extended ANFIS model are given, and the first-rank sizes of the COMBLOC are obtained accurately.
With the proper plate length, submerged depth and relative breakwater width, it is possible to achieve a considerable and effective attenuation of waves. Based on the PCA, it is also concluded the lengths of plates and the submerged depths of plates are the most significant parameters, followed by the wave chamber widths, and whereas the thicknesses of plates and the gap between plates are the least influencing parameters and the effect of the gap between plates is negligible. Eventually, it can be concluded that the constructed ANFIS model has a great ability to learn and build up a neuro-fuzzy inference system for prediction, and the forecasting results provide a useful guidance or reference for the structure sizes. Although the proposed methodology can be effectively utilized for determining the optimal dimension of the COMBLOC structure, this method has some drawbacks, for example, it requires considerable training data and the simulated results reasonably rely on training data. In future works, the methodology presented in this paper can be extended to include more parameters or more available training data and incorporate the main existing uncertainties in inputs and parameters of the simulation models.