## 1 Introduction  
Modal parameters (frequency, mode shape, and damping) reflect the dynamic characteristics of a structure, which are important references for structural damage identification and vibration control. Therefore, modal identification is an indispensable part in the fields of structural health monitoring and vibration attenuation. For a civil structure, its performance under traffic, wind, and other loads depends on its stiffness, mass and damping characteristics, and their distribution. In this case, the modal model consisting of frequency, mode shape, and damping ratio is identified from vibration data. Traditionally, parameter estimation methods can be used to obtain experimental models based on measurable input and output data. However, it is difficult to measure the environmental excitation of civil structures, and the available information for system identification algorithms is the output. Ambient excitation is an important phenomenon in civil structures, which plays a vital role in their health monitoring. Nevertheless, measuring such excitation reliably poses practical challenges, making the output the only means to obtain relevant information for system identification algorithms. In circumstances where direct measurements of ambient excitation are not possible, output-only measurement, also referred to as ambient vibration testing, provides a practical alternative for stimulating the structure. This approach leverages the effects of various environmental factors, including wind, traffic, and environmental loads, to induce vibrations in the structure [1; 2; 3; 4; 5]. Despite its limitations, such as human structure interaction [6] and wind structure interaction [7], ambient vibration testing remains a valuable tool in assessing the dynamic behavior of civil structures, especially when direct excitation is unattainable. With the development of modern signal processing technology, blind source separation [8; 9; 10] has rapidly developed as a powerful signal processing method. It is a combination of statistical signal processing, artificial neural networks, and information theory. Its main task is to separate and reconstruct the input signal or identify the system only by the output information of the system (the mixed signal), when the input information is unknown. The blind source separation technique [11] has been extensively utilized in various application domains, including communications [12], image processing [13], biomedical signal processing [14] and geospatial information processing [15]. In comparison to the traditional method which relies on the model assumption of the system, the blind source separation method has the advantages of simplicity, high computational efficiency, non-parameterization, no need to assume the behavior, and no prior information of the system. Consequently, BSS techniques were introduced for mechanical vibration signal processing [16], and a physical interpretation of the BSS problem for structural dynamics was later developed by expressing the system responses in terms of vibration modes and treating the modal responses as virtual sources to be extracted [17]. Under the assumption of independent source statistics, two common BSS algorithms, independent component analysis (ICA) [11] and second-order blind identification (SOBI) [18], were proposed for output-only identification of mechanical and structural systems, and their effectiveness was demonstrated through simulated data and experimental measurements [19; 20]. However, these two BSS methods have some limitations. The ICA method is limited to undamped or lightly damped structures [21; 22]; the SOBI method assumes a fixed source, which cannot meet the close modes and non-diagonalized damping cases in the practical application of civil infrastructure [23; 24; 25]. For handling the aforementioned issues in modal identification, a novel BSS method-complexity pursuit using temporal predictability proposed in [26] was first applied to structural identification [27].