## 1 Introduction  
The dynamic analyses of complex structures provided by finite element (FE) models have become increasingly important, especially for complex structures working in adverse conditions and costing a lot for experimentation [1; 2; 3]. The discrepancies between initial FE analyses and experimental results inevitably exist due to some factors such as structural simplification, inaccurate material parameters, unreasonable boundary conditions, and unknown damping characteristics [4; 5]. Therefore, the dynamic FE model updating is a common practice to decrease these discrepancies [6; 7; 8; 9]. On the other hand, the data obtained from experimental models are often incomplete due to many limitations, including the limited number, position or direction of measuring points, limitation of the measurable frequency range, and the increasing modal density with frequency increasing [10; 11]. Hence, it is very difficult to pair the correlated modes between inaccurate analytical modal data and incomplete experimental modal data purely based on frequencies or/and modal assurance criterion (MAC) thresholds [12; 13; 14; 15]. Generally, the following situations are encountered:  
1. The correlation between analytical and experimental modes can be uniquely established by frequencies or/and MAC thresholds, denoted as case 1\(\leftrightarrow\)1 in this paper. 2. Similarly, there is a one-to-many or many-to-one correlation between analytical and experimental modes established by frequencies or/and MAC thresholds. This type of situation is denoted as case 1\(\leftrightarrow\)n.
3. Compared with measuring data, one or several analytical modes are missing. Alternatively, one or several experimental modes are missing compared with numerical results. This type of situation is denoted as case 0\(\leftrightarrow\)n.  
Obviously, for case 1\(\leftrightarrow\)1, the correlated mode pairings (CMPs) can be determined unquestionably. Since the objective function values calculated by the analytical and experimental modal data residuals can be obtained directly, routine updating methods [5; 10] work well. However, case 1\(\leftrightarrow\)n and case 0\(\leftrightarrow\)n are ignored and occur commonly in dynamic model updating of the complex structures, which may cause significant discrepancies in certain circumstances because some valuable analytical or experimental modal data are not fully exploited. Improved methods by specifying correlated modes based on pre-analysis are employed to overcome the above shortages. Case 1\(\leftrightarrow\)n could be transformed into the ideal case 1\(\leftrightarrow\)1 by specifying the one-to-one CMPs manually based on appropriate frequencies or/and MAC thresholds after pre-analysis. For example, three CMPs were specified to transform case 1\(\leftrightarrow\)n into case 1\(\leftrightarrow\)1 in the beam model updating of the GARTEUR structure by [PERSON] and [PERSON] [16]. Similar improved methods were adopted by many researchers, such as the plate model updating of the GARTEUR structure by [PERSON] and [PERSON] [17], the aero-engine casing model updating by [PERSON] et al. [18; 19] and [PERSON] et al. [20], the Podgorica footbridge model updating by [PERSON] [21], and the Guadalquivir bridge model updating by [PERSON] [22]. [PERSON] proposed a model updating method by using uncorrelated modes (MUUM) [23]. The correlated and uncorrelated modes were determined after pre-analysis. The objective function was innovatively defined as the quadratic sum of the relative errors in the correlated modes plus the geometric mean for the relative errors in the uncorrelated modes. Thus, uncorrelated modes of experimental data are used to simplify the specifying of CMPs and avoid manual mistakes when unreasonable updating parameter values are assigned in pre-analysis. [PERSON] et al. developed a hierarchical model updating strategy [24] and parametric modeling-based model updating strategy [25] concerning uncorrelated modes.