Operational Modal Analysis of Aeronautical Structures via Tangential Interpolation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. While the title explicitly highlights “via Tangential Interpolation,” the Abstract does not clearly demonstrate how this method is implemented or reflected.
2. The research object of this paper is helicopter rotor blades, which operate in a rotating condition in practical service. However, the experiments were conducted under a stationary state. It is recommended to supplement modal tests under rotating conditions to make the research more consistent with practical engineering scenarios.
3. Damping characteristics are particularly crucial for modal identification. The results indicate that the proposed method has low accuracy in identifying damping characteristics, and further improvement and refinement are required in this aspect.
4. The evaluation of high-order modes is questionable: it is unreasonable to simply define frequencies above 50 Hz as high-order modes, and the definition of high-order modes is not clearly specified in the paper. In addition, the paper only attributes the poor identification performance of high-frequency modes to insufficient excitation energy without conducting quantitative verification. Neither the impacts of sensor layout and modal coupling characteristics on high-order mode identification nor the discussion on strategies to improve the identification performance of high-order modes are provided.
5. Add discussions on the robustness of the NExT-LF method, including its identification performance under different excitation levels and various noise conditions.
6. Clarify the theoretical and experimental basis for the number, selection principles and relevant setting details of interpolation points in the Loewner Framework (LF).
7. Improve the formatting standards for figures and tables in accordance with academic norms, such as Figure 11 and Table 4.
8. It is recommended to cite the necessary references, such as > > 10.2514/1.J066336

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

I would like to underline that the presented manuscript addresses an important and timely topic, and indeed represents a valuable addition to the current state of knowledge concerning advancements in Operational Modal Analysis. Please consider the comments and questions outlined below, which are intended to further improve the already good quality of your manuscript.

 

 

1. Please clarify the rationale for using three different types of accelerometers. Was the use of the PCB Model 356B18 1000 mV/g accelerometer technically necessary, or was it primarily chosen for convenience? In addition, the mass and structural characteristics of the tested rotor blade were not reported (materials, overall mass, internal construction, etc.). Reference [50] is indicated as the source of supplementary information, but no DOI is provided. The manuscript should include the blade’s mass and material composition to allow the reader to assess potential mass‑loading effects.
2. Lines 359–361:
   “The H135 BMR blade specimen considered here, see Figure 7(b), is an unserviceable item, still in relatively good shape, which has been dynamically tested, via AVT, in the former Cranfield University project BladeSense.”
   This description is vague and should be revised. For instance, how many service hours had the blade accumulated? More precise contextual information about its operational history is required.
3. Table 3: Natural frequencies and damping ratios obtained with different methods for the Airbus Helicopters H135 BMR blade. Values in parentheses indicate the relative difference (%) w.r.t. [25].
   Please clarify why the relative difference was calculated with respect to AOMA. A justification is needed, as EMA data may serve as a more appropriate benchmark.
4. Lines 512–513:
   “To the authors’ knowledge, this is the first time in the literature that NExT‑LF is applied for the OMA of aeronautically relevant systems.”
   Rather than emphasising the “first‑time” application, it would be more elegant to state that although the application of NExT‑LF to aeronautical configurations has not previously been reported in the literature, the results obtained here are comparable to those produced by established methods.
5. Lines 520–521:
   “The identification of the damping ratios exhibits a significantly larger dispersion across methods and benchmark data, with comparatively high relative errors observed for all considered modes, particularly in the helicopter blade case.”
   Once again, please comment on the decision to compute relative differences with respect to AOMA.
6. The conclusions section should be expanded to include a discussion of future research directions and potential practical applications of the presented method.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper studies modal analysis for output-only identification, Operational Modal Analysis (OMA), Stochastic Subspace Identification (SSI) methods and the Natural Excitation Technique combined with the Eigensystem Realization Algorithm (NExT-ERA). The authors investigates an OMA frequency-domain formulation for aeronautical structures by coupling the Loewner Framework (LF) with NExT, yielding the proposed NExT-LF method. The method exploits the computational efficiency of LF together with the impulse response function retrieval enabled by NExT. NExT-LF is assessed on two experimental benchmarks.

1. The paper shows a solid work on modal analysis; however, the novelty seems a kind data post processing since the LF is used to assist NExT.

2. The identified modal parameters are compared against available experimental references and results obtained via SSI with Canonical Variate Analysis and NExT-ERA. The results show that the modes identified by NExT-LF correlate well with benchmark data, However, how is NExT-LF better than existing methods ?

3. How to explain the errors of modal damping ratios are high?

4. For high-amplitude low-frequency range, the identification performance is fine; however, the difficulty is low-amplitude high-frequency identification.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It can be accepted

Reviewer 3 Report

Comments and Suggestions for Authors

Accept in present form.