A prediction method for the ultimate load of composite corrugated sandwich structures (CCSS) was established based on the dimension-reduction method and Chebyshev polynomial. First, an ultimate load response function of the CCSS was reduced in dimension on basis of the univariate method. The original response function was converted to the sum of univariate functions of all random variables. Chebyshev polynomial was used to fit all univariate functions, and the univariate Chebyshev approximate model (UCAM) of the response function was obtained. Second, the fitting accuracy of the UCAM was analytically compared with the Kriging model, radial basis function, and response surface methodology. Finally, the effect of the order on the fitting accuracy of UCAM was studied. The UCAM has higher fitting accuracy and calculation efficiency compared with the other three approximate models. When the order of UCAM is lower than ninth-order, the larger the order, the higher the fitting accuracy. And the order and the fitting accuracy are no longer positively correlated when the order exceeds ninth-order. The order is recommended to choose an odd-order when using UCAM to solve the uncertainty problem.
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