## 5 Conclusions  
Due to the complexity of environmental excitations, such as gusts, earthquakes, and impact loads, which are borne by large civil engineering structures, these excitations cannot usually be assumed to be white noise, which leads to the problem of false modes and mode omissions in the traditional stochastic subspace identification method. Therefore, this paper combines the random decrement technique (RDT) under non-stationary excitation with the covariance-driven stochastic subspace identification (SSI) method to propose the improved RDT-SSI method. Under non-stationary environmental excitation, the random decrement technique uses a new trigger that increases by 0.1 standard deviation (\(\sigma\)) of the response signal, starting from 1.0 \(\sigma\), until at least 500 sub-samples are obtained, to obtain the free-decay response. This response is then used to construct the Hankel matrix, with covariance as the statistic. The non-correlation between the signal and noise is utilized to remove the noise, and finally, the singular value decomposition technique is applied to identify the modal parameters of the structure. This method solves the problem of identifying the modal parameters of the structure under non-stationary excitation of the stochastic subspace identification (SSI) method. The recognition accuracy of frequency and vibration mode is high, while the damping ratio identification is less effective compared to frequency identification, but it meets the requirement of accuracy. The method proposed in this paper is applied to the actual engineering of stadium grids. Using traditional SSI-COV and improved RDT-SSI methods, the data collected by the accelerometer are processed separately. The results show that for non-stationary excitation of the environment, the improved RDT-SSI method proposed in this paper improved the accuracy of frequency and vibration mode identification, and improved computational efficiency, providing a valuable reference for the identification of modal parameters in large-scale practical engineering.  
Conceptualization, J.W. and G.S.; methodology, J.H., [PERSON] and [PERSON]. ([PERSON]); software, [PERSON] ([PERSON]) and [PERSON]; investigation, [PERSON] ([PERSON]); resources, [PERSON] and [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON] ([PERSON]) and [PERSON]; writing--review and editing, [PERSON]; supervision, [PERSON] All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Opening Funds of State Key Laboratory of Building Safety and Built Environment & National Engineering Research Center of Building Technology (BSBE2022-03) and National Key Research and Development Program of China (grant number 2023 YFC380560203).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors gratefully acknowledge the supported by the Opening Funds of State Key Laboratory of Building Safety and Built Environment & National Engineering Research Center of Building Technology (BSBE2022-03) and National Key Research and Development Program of China (grant number 2023 YFC380560203).  
Author [PERSON] was employed by the company China Academy of Building Research Co., Ltd. Author [PERSON] was employed by the company Shaanxi Academy of Building Research Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.