## 3 Method of Constructing Global POD ROM
### CV-Voronoi Sequence Sampling Method  
A robust CV-Voronoi sequence sampling method has been proposed [32] to use the information of existing sample configurations more completely and, in effect, to adaptively increase sample configurations. It mainly consists of three steps: design space partition, sensitive Voronoi identification, and determination of new sample configuration. Step 1: Design space partition. Voronoi is a polygon composed of perpendicular bisectors of the current sample configuration and neighboring sample configurations. The Voronoi in two-dimensional space is shown in Figure 1. By the set of sample configurations \(\mathbf{P}=\{\mathbf{p}_{1},\mathbf{p}_{2},\ldots,\mathbf{p}_{k}\}\in\mathbf{\Omega}^{d\times k}\), where \(d\) is the number of single configuration design variables, the design space is divided into a series of Voronoi elements \(\mathbb{C}{=\{C_{1},C_{2},\ldots,C_{m}\}}\). The space of the \(i\)th element \(C_{i}\) is defined as:  
\[dom(\mathbf{p}_{i},\mathbf{p}_{j}) =\Big{\{}\mathbf{p}\in\mathbb{R}^{d}\Big{|}\Big{|}\Big{|}\mathbf{p}-\mathbf{p }_{i}\Big{|}\Big{|}_{2}\leq\Big{|}\Big{|}\mathbf{p}-\mathbf{p}_{j}\Big{|}\Big{|}_{2} \Big{\}}, \tag{13}\] \[C_{i} =\underset{\mathbf{p}_{j}\in\mathbb{P}/\mathbf{p}_{i}}{\cap}dom(\mathbf{p}_{ i},\mathbf{p}_{j}), \tag{14}\]  
where the \(dom(\mathbf{p}_{i},\mathbf{p}_{j})\) is the point in the design space that is closer to the sample configuration \(\mathbf{p}_{i}\) than any other sample configuration \(\mathbf{p}_{j}\). In two-dimensional space, a Voronoi element is a closed region bounded by the vertical bisectors of the \(i\)th sample configuration and the neighboring sample configurations. The boundary of Voronoi is difficult to describe analytically in high-dimensional space, so the Monte Carlo method is used to describe Voronoi elements. The geometric distances from Monte Carlo points to sample configurations are calculated and compared to determine the attribution of each Monte Carlo point to their original sample configuration. Monte Carlo points are numerous and random, and the Voronoi element described by Monte Carlo points is shown in Figure 1, where \(\times\) represents the sample configuration and \(\triangle\) is the Monte Carlo point. Step 2: Sensitive Voronoi identification. Using cross-validation, the \(i\)th sample configuration is selected as the test sample \(\mathbf{p}_{i}\), and other \(k-1\) samples are used as the sample set for constructing the reduced basis matrix:  
\[\mathbf{T}_{k-1}^{(-i)}=\Big{\{}\mathbf{v}_{k-1}^{j}\Big{\}}(j=1,2,\ldots,r_{k-1}), \tag{15}\]  
where, \(\mathbf{v}_{k-1}^{j}\) represents the POD basis vector constructed based on \(k-1\) sample configurations. \(\mathbf{T}_{k-1}^{(-i)}\) is used to reduce the stiffness matrix, mass matrix, and damping matrix of the test sample configuration \(\mathbf{p}_{i}\). Then, the Root Mean Square Error (RMSE) of the dynamic responses calculated based on the FOM (\(f(\mathbf{p}_{i})\)) and the ROM (\(\hat{f}_{\mathbf{P}/\mathbf{p}_{i}}(\mathbf{p}_{i})\)) are obtained as error evaluation metrics for ROM and the truncation threshold of sampling. \[e(\mathbf{p}_{i})=\text{RMSE}= \sqrt{\frac{1}{n}\sum_{i=1}^{n}\big{(}f(\mathbf{p}_{i})-\hat{f}_\mathbf{{P}/\mathbf{p}_{i}}(\mathbf{p}_{i})\big{)}^{2}}. \tag{16}\]  
\(k\) sample configurations are traversed by the above steps to obtain \(k\) RMSE values \(e(\mathbf{p}_{i})(i=1,2,\ldots,k)\) of dynamic response. The sample configuration with the largest RMSE value is the sensitive sample configuration \(\mathbf{p}_{\text{sensitive}}\), and the corresponding Voronoi element is the sensitive Voronoi element \(C_{\text{sensitive}}\). Step 3: Determination of new sample configuration. The new sample configuration is selected from \(C_{\text{sensitive}}\).