Optimal Design of a U-Shaped Oscillating Water Column Device Using an Artificial Neural Network Model

Round 1

Reviewer 1 Report

The paper deals with an interesting problem on the optimization of a WEC.

The authors in order to improve the readability of the paper should:

1)improve fig.1 (is really too schematic);

2)state explicitly the cost function to be optimized (lines 459-461). It is not clear if one can maximize the efficiency and minimize the force or some kind of trade-off is needed;

3)clarify the algorithm used to build the databases (lines 475-480).

Author Response

The authors appreciate constructive comments by the reviewer to strengthen the overall quality of the article. We tried our best to respond and incorporate the suggestions required by the reviewer.

1)improve fig.1 (is really too schematic);

A matched eigenfunction expansion method (MEEM), adopted as an analytical tool, has a limitation for application, different from the general numerical schemes. It is applicable to the simple geometric model, which can be expressed by the Cartesian and Cylindrical coordinate system. Fig.1 may seem to be too schematic to the reviewer, but is enough to involve the all information for the application of a MEEM.

2)state explicitly the cost function to be optimized (lines 459-461). It is not clear if one can maximize the efficiency and minimize the force or some kind of trade-off is needed;

A U-shaped OWC is a new conceptual design for increasing performance by adding a vertical barrier in front of the conventional OWC. We found out that the barrier's geometry (height, distance) and submergence depth of the chamber wall affect the performance of a U-shaped OWC through the parametric study shown in section 3. Our initial intention is to search for the optimal input features (barrier's geometry and submergence depth of the chamber wall) for maximizing power generation. However, we couldn't ignore the structural safety of a bottom-mounted vertical barrier. For this reason, we are forced to select two output features (conversion efficiency and wave force on a barrier). The optimal design of input features was mainly performed to focus on enhancing the conversion efficiency and the wave force is considered for reference.    

3)clarify the algorithm used to build the databases (lines 475-480).

We mentioned the LHS sampling method to build the databases and already explained its detail below Eq. (4.1) in the manuscript.

Reviewer 2 Report

George et al. used an analytical model to study the hydrodynamic performance of a 2D U-OWC in irregular waves. The manuscript is well researched and well presented. I suggest a few recommendations before further consideration of the paper.

1- the introduction lacks proper citation. Some statements are given without mentioning the source, for instance, lines 100-105. This is more evident in section 2. Analytical model. The equations borrowed from literature should have proper citations.

2- why did you validate the MEEM solutions with Evans and Porter (1995)? This may not be clear to some of readers.

3- how did you choose values for non-dimensional chamber length and submerged depth?

4- the Numerical calculation section is not clear. You need to bring the detailed information about the procedure.

5- section 4.1 does not provide enough information. How did you choose these values to build the dataset? For instance, for three input features?

6- how did you conduct the parametric study to build the dataset?

7- again section 4.4 lacks citations. Please look for the rest.

8- figure 16, you need to provide x, and y axis legends.

9- modify the conclusion to better present the findings.

Author Response

The authors would like to thank the reviewer’s valuable suggestions. The manuscript has been revised as suggested by the reviewer. The modifications in the text have been marked in yellow color.

1. the introduction lacks proper citation. Some statements are given without mentioning the source, for instance, lines 100-105. This is more evident in section 2. Analytical model. The equations borrowed from literature should have proper citations.

Thanks for the suggestion. Some references were cited and added in the reference.

2. why did you validate the MEEM solutions with Evans and Porter (1995)? This may not be clear to some of readers.

The present article was initiated with a basis of Evans and Porter's OWC model and extended to a U-shaped OWC by adding the vertical barrier in front of the chamber. The methodology is almost the same as that of Evans and Porter. We couldn't found out a more appropriate one for comparison than Evans and Porter. For these reasons, we compared our analytical results with Evans and Porter's (1995) results by setting the height of barrier zero(without a barrier).

3. how did you choose values for non-dimensional chamber length and submerged depth?

In the present U-shaped OWC model, there exist too many geometric parameters. Therefore, some having low importance to the conversion efficiency were taken as fixed values(e.g. water depth (h=10m), chamber length (a=5m)). The barrier height (d1), submergence depth of a chamber wall (d2), and barrier distance (b) between them were set as key input parameters for the application of an ANN model and its range of each parameter for optimization was also chosen from numerical results in section 3.

4. the Numerical calculation section is not clear. You need to bring the detailed information about the procedure.

The numerical calculation (section 3) is related to the numerical results and discussions obtained by using a MEEM that was described in detail in section 2. This part is a preparatory stage for the generation of datasets for the application of an ANN model. First, we did the validation test of the developed MEEM through a comparison with Evans and Porter (1995)’s results. And then we identified the key design input features and discussed their effects on the conversion efficiency and wave forces on the front barrier.

5. section 4.1 does not provide enough information. How did you choose these values to build the dataset? For instance, for three input features?

The details of the dataset creation are included in section 4.1. The sample space of each input feature for creating the dataset was determined by conducting a parametric study using the analytical model which is detailed in section 3.2.

6. how did you conduct the parametric study to build the dataset?

Key input design features of a U-OWC and their space of identified input feature were determined through the parametric study using the analytical model. Then, the dataset containing input and output features was created using the Latin Hypercube Sampling method.

7. again section 4.4 lacks citations. Please look for the rest.

Thanks for the suggestion. Some references were cited as pointed

8. figure 16, you need to provide x, and y axis legends.

Corrected as you pointed.

9. modify the conclusion to better present the findings.

Thanks for the suggestion. Some addition and modification were included in the revised manuscript.

Reviewer 3 Report

the authors presented an analytical model for hydrodynamic perfromance of a U-shap wave energy convertors. The authors decsripe the formulations of the model very well with good descriptions on the parameters and teh concepts, The model suported with good results. moreover, they included a seperate section regarding the design of the energy convertor using the ANN. Although the ANN model is a conventional model, the authors interestingly presented an integrated framework with their analytical model and uncertainty model to estimat the optimum design paramter. In overall, the manuscript has good quality for consideration of the publication in the journal. I do not feel any further changes is need to be done for this manuscript.

Author Response

The authors thank the reviewer's positive estimation.

Round 2

Reviewer 2 Report

The manuscript can be accepted for publication.