# Uncertainty Representation of Natural Frequency for
Generally, the surrogate model technology includes three basic steps: design of experiment (DOE), model construction and model validation. Rational DOE can quickly determine optimal parameter combination, effectively improve the modeling efficiency and robustness of optimization design [22; 23]. To make the factor level balanced matching and the distribution of sample points more uniform, the orthogonal array, Latin hypercube sampling and optimal Latin hypercube sampling are proposed [24]. The optimal Latin hypercube sampling method can ensure that all design points are evenly distributed in the entire design space, and the spatial filling and equilibrium are stronger than other design methods, which is conductive to the construction of a surrogate model with higher accuracy [25; 26]. In terms of surrogate model construction, the most common surrogate models are the response surface model (RSM) [27; 28], radial basis function model (RBF) [29; 30], Kriging model [31; 32], artificial neural network model (ANN) [33; 34], support vector regression (SVR) [35]. The Kriging model is an unbiased estimation model with the minimum approximate evaluation variance, and the distribution of function response values at unknown points can be better predicted by using the correlation function, which has faster training speed and higher accuracy than other types of surrogate models and is widely applied to replace the original objective function to solve complicated uncertainty analysis problems [36]. [PERSON] proposed a Kriging surrogate model for analyzing the vibration characteristics of the composite shallow hyperbolic shells, which improved the calculation accuracy and efficiency compared with original Monte Carlo simulation (MCS) [37; 38]. [PERSON] presented an effective hybrid optimization algorithm based on the adaptive Kriging surrogate model and improved partial swarm optimization algorithm to predict the buckling characteristics of composite laminate plates [39]. [PERSON] used the Kriging surrogate method to analyze the random response of homogenization elastic tensor and homogenization elastic constants of unidirectional fiber reinforced composites [40; 41]. [PERSON] studied the damage prediction of a composite plate based on the Kriging surrogate model under edge constraint conditions, and took the natural frequency and vibration change as the main research indexes, which can greatly reduce the calculation time [42]. The above literatures have verified the validity of the Kriging model acting on laminated composite plates. When the uncertain random variables and distribution parameters meet the probability distribution, it is crucial to establish the calculation method of natural frequency of laminated composite cylindrical shells based on the Kriging surrogate model. The corresponding results of the proposed method are compared with the MCS results to verify the validity of the Kriging model in laminated composite cylindrical shells [36]. In view of the uncertainty analysis problems of input variables of laminated composite cylindrical shells, the available data obtained by the experiments are converted to probabilistic variables or interval variables [43]. Using the four statistical moments method, cubic normal distribution functions are acquired, and the PDF and CDF of uncertainty input variables are transformed [18]. To increase the accuracy and computational efficiency of uncertainty analysis of natural frequency for laminated composite cylindrical shells, the uncertainty representation method for natural frequency based on the Kriging surrogate model is proposed. Considering the uncertainty of probabilistic and interval variables, the corresponding performance functions are selected to construct the initial Kriging surrogate model, and the new sample points are selected based on the maximum prediction interval criterion. The constructed Kriging surrogate model improves the accuracy of the uncertainty result and reduces the computational cost.