Paper description: the paper proposes the validation of a recently published method for the identification of short-term damping and natural frequencies of time-varying structures under operational and environmental conditions, using output-only data. The method is presented and then it is applied using different sets of experimental data obtained from a laboratory test rig (a three-storey shear frame with controllable electromagnetic dampers) and a full-scale wind turbine (under unstable dynamic conditions).  The natural frequencies and damping ratios associated with the first three modes of the three-storey shear frame are estimated using the proposed approach (GP-TARMA model) under variable damping conditions (controlled with the electromagnetic dampers) to simulate variable operational and environmental conditions. The estimation of damping and natural frequencies is also performed with and without the additional electromagnetic damping using well-established methods such as the hammer test and  Stochastic Subspace Identification (SSI) method. The damping ratios and natural frequency identified with the GP-TARMA approach are shown to be in very good agreement with the estimation provided by the SSI method and standard hammer test. Then, the GP-TARMA approach is used to estimate the natural frequencies and damping ratios of two whirling modes of a full-scale wind turbine under unstable conditions. The identified parameters are shown to be meaningful and in agreement with previous studies.

Comments:  The paper clearly describes the proposed methodology and demonstrates, through experimental analyses, the validity of the proposed method for identifying short-term damping in time-varying vibrating structures under nonstationary operating conditions. I therefore advise the editor to accept the paper after a minor revision.

With the intent to improve the quality of the paper, I would like to recommend the authors the following modifications:

• The paper should briefly discuss the limitations of the proposed methodology, e.g. problems that might occur in the presence of strongly nonlinear properties in the considered structure.
• In section 3.2 the model orders (Nc and Na) of the ARMA model are selected for the three-storey shear frame using the procedure outlined in section 2.4 and Table 1.  Figure 4 shows the trend of the BIC and RSS/SSS indices for different model orders, nonetheless, it is not completely clear how this figure is used to identify the convergence of the model order adopting the proposed procedure of section 2.4. The authors should improve the description of this step in section 3.2.
• Figure 5 shows the stabilization diagram for the three-storey shear frame: despite the convergence of RSS/SSS and BIC indices occurs at a model order equal to Nc = 2 and the stabilization diagram seems to show stable poles for all the considered modes at Nc = 3 /  Nc = 4, a model order Nc = 8 has been used in the final ARMA model. The authors should justify this choice, highlighting their motivations.

The manuscript presents two experimental validations of a Gaussian Process Time-dependent Auto-Regressive Moving Average (GP-TARMA) model recently proposed by some of the authors for estimating short-term damping and natural frequency of vibrating structures under varying environmental and operational conditions. The model is tested on a laboratory small-scale three-storey frame structure and on a full scale 7MW wind turbine. As for the wind turbine, the model is used to estimate short-term, linear (equivalent) modal damping of two edgewise rotor modes deliberately driven to flutter-like instability, which cause negative damping values. While results are very accurate for the three-storey frame structure, some inaccuracies are found in the results for the wind turbine, see Fig. 13 in particular. However, potential issues motivating the inaccuracies are discussed as well as potential improvements of the proposed GP-TARMA model.

In the reviewer’s opinion, the manuscript is well organized and well written. Publication is recommended before minor revisions addressing the following issues:

1. According to the authors’ comments on Figure 11 in Section 4.2, the time series of the model residuals is not a stationary white noise. Consequently, the authors state that “The residual analysis implies that the NID assumption of the innovations is violated, i.e., the model does not completely represent the statistical structure of the response”. Does it mean that the time series of the model residuals shall always be a stationary white noise for the GP-TARMA model to be accurate? This seems to contradict Section 2.3, where the GP-TARMA model residuals can be non-stationary and a “whiteness” test of the model residuals is possible also in the non-stationary case (see Eq.(16)). Please clarify.
2. A model validation strategy discussed in Section 2.3 is the “cross-validation”. Can the authors apply it to the wind turbine for double-checking the results of the residual analysis?