## 1 Introduction  
The finite element model (FEM) has been extensively used in various areas by the engineering community: structural health monitoring (SHM) [1, 2], risk and reliability analysis [3, 4] and structural dynamics and response control [5, 6]. However, the errors between analytical responses from the FEM and their counterparts from a real structure are always unavoidable due to (1) measurement errors caused by signal quality, measurement devices and human operation, (2) modeling errors such as idealization assumption and improper discretization and (3) erroneous assumptions in material properties and dimensions [7, 8]. Therefore, the FE model updating (FEMU) is in great demand and practical value for enhancing the fidelity of FEM. FEMU is essentially the process to minimize the discrepancy between analytical prediction and test results in such a way that progressively adjusts physical parameters until the FEM reproduces the measured data to a satisfactory level [9, 10]. Generally, FEMU techniques can be divided into deterministic and stochastic approaches. Deterministic approaches only update the parameter of a single model using one set of measured data [8], yielding a unique solution. In the scope of deterministic approaches, swarm intelligence optimization methods have been widely used to seek the optimal parameters for structural damage identification--see, for example, the whale optimization algorithm and its variants [11, 12, 13], but optimization algorithm and its modifications [14, 15], particle swarm optimization [16; 17], moth-flame optimization [18; 19] and genetic algorithm [20; 21]. However, civil engineering applications by deterministic approaches are still limited in practice due to the unavailability of uncertainties induced by measurement noise and modeling errors. On the other hand, stochastic approaches enable to identify model parameters with either a range or probability density function (PDF) and thus parameter uncertainty can be straightforwardly quantified [9]. A wide range of stochastic approaches have developed to more reasonably identify model parameters accounting for different sources of uncertainties [22; 23; 24; 25; 26]. A comprehensive overview of stochastic approaches is available in the literature [9]. The Bayesian model updating approach (BMUA), as a representative of stochastic FEMU, has attracted great attention and achieved satisfactory practical real-world applications in recent years, e.g., buildings [27; 28], bridges [7; 29] and lab-scale structures [30; 31]. In the BMUA, model parameters are random variables identified as their most probable values (MPVs) and, along with the PDF, give measured data and model class. The BMUA provides a robust and rigorous framework to characterize parameter uncertainty, as the identified PDF serves as a natural measure of parameter uncertainty. The prominent strength of the Bayesian approach is to incorporate all available data information and efficiently treat incomplete measured data and uncertainty errors. [PERSON] et al. [32; 33] are pioneers in establishing the BMUA's fundamental theory. Later, the derivations and improvements to promote the Bayesian approach's capability were only developed for stiffness updating [31; 34; 35; 36]. However, all aforementioned BMUA work (herein, traditional BMUA) generally only focuses on stiffness updating and is performed based on the classical eigenequation,  
\[(\mathbf{K}-\lambda\mathbf{M})\boldsymbol{\phi}=0 \tag{1}\]  
where \(\mathbf{M}\) is a mass matrix; \(\mathbf{K}\) is a stiffness matrix; \(\lambda\) are eigenvalues (the square of natural frequencies); \(\boldsymbol{\phi}\) are eigenvectors (the mode shapes). As seen in Equation (1), it is unidentifiable to simultaneously update mass and stiffness because of an unlimited combination of mass and stiffness, giving the same natural frequency [22] (herein, the coupling effect of mass and stiffness).