Study on the Intelligent Modeling of the Blade Aerodynamic Force in Compressors Based on Machine Learning

Round 1

Reviewer 1 Report

This paper details the use of the XGBoost algorithm on a previously constructed CFD simulation data set.  The goal of the approach is to help speed up simulation/modeling of aerodynamic forces on compressor blades through the creation of a reduced-order model.

 

Strengths:

-Important topic. Accurate simulation of multistage compressors requires time-consuming transient analyses which involve fluid-structure interactions.  Any methods that allow for reduction in computational power/time will be helpful to the field.

-Interesting and novel approach.  ML/AI in fluids is a rapidly developing field, I appreciated the focus on using recently published works in the introduction and background to help add context.

Weaknesses:

-3D plots are difficult to read/interpret and are thus rarely helpful to the reader.  The presentation of the same data could have been achieved without plotting the data in 3D space.

-Grammar and word usage need more attention.  There were multiple occurrences of words/grammar that could leave readers interpreting results in an unintended way.  The first few paragraphs in the introduction have multiple instances, but they can be found throughout.

-More information and description on the CFD simulation database could have been provided.  I appreciated the concise description of the CFD setup, but was left wondering more about the specifics of the data set that was created for training/testing. 

 

 

Author Response

Thank you very much for the suggestions for our draft. We have replied point by point to your comments, along with a clear indication of red color at the location of the revised paper. The comments and replies can be summarized as follows:  Q: 3D plots are difficult to read/interpret and are thus rarely helpful to the reader. The presentation of the same data could have been achieved without plotting the data in 3D space.  A: The purpose of this paper is to predict the aerodynamic force on the blade surface at its modal location. The 3D plots show the distribution of aerodynamic force at blade surface in the space position. So this presentation of data is adopted in this paper to draw a 3D graph. Thanks for your kind advice.  Q: Grammar and word usage need more attention. There were multiple occurrences of words/grammar that could leave readers interpreting results in an unintended way. The first few paragraphs in the introduction have multiple instances, but they can be found throughout.  A: The typographical and grammatical errors had been revised most in the revised paper. We have made the correction accordingly.  Q: More information and description on the CFD simulation database could have been provided. I appreciated the concise description of the CFD setup, but was left wondering more about the specifics of the data set that was created for training/testing.  A: The fluid-structure coupled simulations are conducted in the ANSYS Package. The structural equations for mechanical blade are solved by finite element method. Within each time step, the flow equations and the structural equations are solved simultaneously, exchanging information on the fluid-structure interface. This procedure is repeated until the flow and displacements are converged, before proceeding to the next time step. After the convergence of simulation, the results computed by the commercial CFD software is used for the current data learning. The snapshot data of the unsteady flow is captured at each time step, including pressure and aerodynamic force of the blades with three-dimensional modal coordinate. The data set for training/testing is composed with five variables, such as Cartesian coordinates, pressure and aerodynamic force. Thanks again for your advice.

Author Response File: Author Response.docx

Reviewer 2 Report

This article provides an interesting application of the XGBoost algorithm of machine learning aimed at obtaining a reduced order model for the characterization of the aerodynamic loads acting on vibrating blades in compressor.

In the past few years, we have experienced an increasing number of ML application studies in fluid mechanics. In particular, with respect to classical reduced order model, such as POD or DMD, the great advantage of this procedure is to overcome the difficulty of capture transient, intermittent and or multiscale phenomenon of those.  Therefore, the argument analysed in this paper is of interest for many applications and it could be worthy of publications, but in my opinion the manuscript requires some modifications, which address the readability of the paper, that are listed below.

• In the introduction, the bibliography is sometimes limited and difficult to obtain, such as doctoral thesis or article difficult to find on web, while important papers and review are omitted. Moreover, since the main goal of the paper is the achievement of a reduced order model for the aerodynamical load, methods like POD and DMD should be mentioned.
• The choice of the symbols in the equations is sometimes misleading: as an example in the definition of the loss function (eq.2) the experiment value of the i-th label and the prediction in the integration model of the XGBoost system are defined using the same parameter y_i .
• Some additional information on the analysed fluid structure model should be added, in particular concerning the structural model and which kind of coupling is used between the structural and the CFD code.
• In figure 7, where the prediction error is depicted, it would be interesting to show also a percentage error. In the paper the authors affirm that the pressure predicted by XGBoost model doesn’t match very well with cfd data at the root of the blade. But looking at figure 7, it is evident that the difference is not limited to root region but extend till 40% of the span. How do you explain this behaviour?
• There are also a number of lapses in style, as an example paragraphs 2 and 3 are both named Introduction, which is correct only for the first paragraph, while for the second one the author should write something like Overview of XGBoost algorithm .

Author Response

Thank you very much for the suggestions for our draft. We have replied point by point to your comments, along with a clear indication of red color at the location of the revised paper. The comments and replies can be summarized as follows:  Q: In the introduction, the bibliography is sometimes limited and difficult to obtain, such as doctoral thesis or article difficult to find on web, while important papers and review are omitted. Moreover, since the main goal of the paper is the achievement of a reduced order model for the aerodynamical load, methods like POD and DMD should be mentioned.  A: Based on the input and output data, the XGBoost model adopted in this paper establishes the mathematical mapping relationship between the input and output, which is belong to the system identification method. POD and DMD are two typical modal decomposition methods, which have been widely used in the study of fluid problems. According to your suggestion, the references which are difficult to obtain are deleted. And the relevant literatures of modal decomposition have been added in the paper.  Q: The choice of the symbols in the equations is sometimes misleading: as an example in the definition of the loss function (eq.2) the experiment value of the i-th label and the prediction in the integration model of the XGBoost system are defined using the same parameter yi.  A: to avoid the missing symbol, the parameter has been redefined. And the symbols in other equations are also corrected.  Q: Some additional information on the analysed fluid structure model should be added, in particular concerning the structural model and which kind of coupling is used between the structural and the CFD code.  A: The fluid-structure coupled simulations are conducted in the ANSYS Package. The structural equations for mechanical blade are solved by finite element method. Within each time step, the flow equations and the structural equations are solved simultaneously, exchanging information on the fluid-structure interface. This procedure is repeated until the flow and displacements are converged, before proceeding to the next time step. After the convergence of simulation, the results computed by the commercial CFD software is used for the current data learning. This part has been added in line 207-210.  Q: In figure 7, where the prediction error is depicted, it would be interesting to show also a percentage error. In the paper the authors affirm that the pressure predicted by XGBoost model doesn’t match very well with cfd data at the root of the blade. But looking at figure 7, it is evident that the difference is not limited to root region but extend till 40% of the span. How do you explain this behaviour?  A: The error shown in figure 7 is the absolute error, which refers to the difference between the predicted results and CFD data at each grid point. In this paper, the coefficient of determination R2 and RMSE are introduced to measure the error level instead of paying attention to the errors at specific points. So this paper does not show the percentage error. The representation of error at the root of the blade is discussed in generalities. This statement is revised as “there are still errors located under 40% of span” in line 311.  Q: There are also a number of lapses in style, as an example paragraphs 2 and 3 are both named Introduction, which is correct only for the first paragraph, while for the second one the author should write something like Overview of XGBoost algorithm.  A: Sorry for the mistake. The second part has been corrected as Description of the Machine Learning Algorithm. The typographical and grammatical errors had been revised most in the revised paper. We have made the correction accordingly. Thanks again for your advice.

Author Response File: Author Response.docx