## 1 Introduction  
With the fast advancement of microprocessors, miniature sensors, wired and wireless digital transmission networks, and contemporary monitoring devices are able to collect an enormous amount of signals exhibited from bridge structures. However, it is well known that complex bridge structures show high-level nonlinear and non-stationary behaviors due to a variety of causes such as continuous ambient vibrations, vehicle-bridge coupling effect, cumulative crack growth, and degradation of columns, joints, and beams [1]. This brings considerable challenges for civil engineers to inspect the time-varying performance of complex bridge structures. It is of great significance to consider the characteristics of bridge structure signals for detecting the inherent non-stationary and nonlinear nature of signals. Conventional stationary analysis methodologies and linear statistical approaches tend to have limitations to capture the nonlinear and nonstationary variations in the signals [2]. For example, the fast Fourier transformation cannot provide the temporal localization of the frequency components and assumes that spectral components are stationary. Furthermore, linear statistical methods, e.g., regression models or the analysis of variance, have certain difficulties to capture the nonlinearityand non-stationarity of signals. As a result, linear and stationary methods lead to less realistic characterization and estimation of time series from real-world bridge structures. In recent decades, the recurrence plot (RP) and the recurrence quantification analysis (RQA) has already become a commonly powerful tool for its better understanding and interpretation of complex dynamic behaviors [3]. RP is usually utilized to give a qualitative visual impression of the dynamics of a given system. It is essentially a global probabilistic autocorrelation function that consider the relative frequencies at which a system returns to a given dynamic state [4]. Based on the recurrence point density, the diagonal and vertical line distribution in RP [4], RQA [5] is proposed to quantify the structures displayed by RP. Compared with many classical signal-processing methods, e.g., Fourier transform-based methods, RP and RQA have the distinct advantage of sensitivity to some varying dynamic properties and is relatively immune to noise [5]. In recent years, RP and RQA or their variations, like cross recurrence plot [6], the ordinal patterns recurrence plot [7], the multivariate recurrence plot [8], and the recurrence network [9] have been widely and successfully applied to test the nonlinearity and non-stationarity of the signal from the real world in various branches of science and technology, such as in physiology [9; 10; 11; 12], economy [13; 14], chemistry [15; 16], and engineering [17; 18]. [PERSON] et al. [1] and [PERSON] et al. [19] presented excellent reviews of the earlier studies on RP and RQA. In addition, recent reviews by [PERSON] et al. and [PERSON] et al., covering detailed and extensive theories and various application, are available in References [6; 20]. Although powerful in testing the properties of nonlinear and nonstationary signals, the success of RP and RQA application is mainly on the signal from the numerical simulation or small-scale and controlled laboratory experiments [6; 20]. In these research studies, the influencing factors of the experiments are controllable and RP patterns of the signals are simple. However, when being used in the measured signals from bridge structures, RP and RQA faces several requirements of the bridge dynamic signal processing [21]: (1) high-level noise, (2) multi-mode and closely spaced mode, and (3) data-driven. On one hand, as summarized above, RP and RQA are usually effective when dealing with the signal with a single recurrence mode and low-level noise. However, bridge structures are generally large and complex systems.