## 1 Introduction
As a consequence of this kind of flow condition, the vibration may lead to guide wall cracking near the base and eventual failure and removal of the wall. Regarding the safety of the guide wall, several studies on the guide wall stability have been proposed with different topics. Regarding the flow pattern, the computational fluid dynamic (CFD) tool is widely applied [14] to assess the geometry of the guide wall to guarantee the stability of the flow. Physical models are also employed in flow pattern optimization [15]. With regard to fluctuating pressure and vibrational characteristics, conventional research techniques include theoretical derivation [16], model tests [13], prototype tests [17], and numerical simulation [18]. There have also been various damage diagnosis algorithms presented for the guide wall [19; 20]. The above studies are focused on structural optimizations and excitations; however, for the vibration mechanism and dynamic response of the guide wall, conventional research methods are inadequate. As mentioned above, the two main methods for the FIV mechanism are model tests and prototype tests. Both of the methods will produce a large number of vibration signals, which contain complex signal components, resulting in the necessity of signal processing. Conventional vibration analyses usually employ the Fourier Transform (FT) to obtain the vibrational characteristics [21]. Another common signal processing method is Empirical Mode Decomposition (EMD), and its various modifications are widely applied in the analysis of vibrations [22]. In recent years, the wavelet transform (WT) technique and its modifications have become widely utilized in signal processing. Extended from WT, the cross-wavelet transform (XWT) is a new method to evaluate the relationship between two signals. This method is more common in meteorological [23], hydrological [24] and medical [25] fields, and is demonstrated to be an efficient method of analyzing the vibrational correlation between two structures [26]. In conclusion, the studies on the FIV of spillway guide walls are inadequate, as the conventional methods usually focus on the vibrations caused by flow excitations, but the influence of dam vibration is always ignored, leading to the inaccuracy and irrationality of vibration analyses. In this paper, according to prototype tests and structural characteristics of a typical guide wall, a new perspective of associated-forced coupled vibration (AFCV) is proposed. Considering the lightweight characteristic of the guide wall, it can be deemed to be an accessory structure installed in the large-scale primary structure, constituting the associated vibration (AV) system. Then, considering the connection between the guide wall and the foundation, the AV system was modified to be an AFCV system, with the establishment of a two-degrees-of-freedom theoretical model. The proposed theoretical model is subsequently verified based on prototype tests. By employing the signal processing method XWT and numerical simulation, the vibration mechanism can be clarified in detail utilizing the theoretical model, and simultaneously demonstrates the reasonability and correctness of the theoretical model. In practice, this investigation aims at contributing to the design, monitoring, and maintenance of spillway guide walls, and is beneficial to the vibrational control of similar lightweight hydraulic structures.