## 1 Introduction  
Numerical methods play a vital role in the design and analysis of engineering structures. In traditional structural numerical analysis, parameters are typically treated as deterministic quantities. However, in real-world engineering problems, uncertainties abound in various aspects such as material properties, geometric parameters, and loads, due to factors such as manufacturing and assembly errors as well as variations in operating conditions [1; 2; 3]. These uncertainties are small, but their cumulative effect can have a significant impact on the structural response. Therefore, it is crucial to fully consider the effects of uncertainty in the numerical calculation of structures to ensure the accuracy and reliability of the results. Currently, three main mathematical models are used to represent uncertainty: stochastic/probabilistic models, fuzzy models, and interval models. Stochastic/probabilistic models [4] treat uncertainties as random variables and employ probability and statistical methods to analyze uncertainty. However, these models necessitate ample empirical data to establish accurate probability density functions that describe the uncertain parameters. Fuzzy models [5] are part of fuzzy mathematics, and determining fuzzy membership functions also relies on substantial data support. Interval models [6; 7] represent uncertain variables as intervals and address uncertainty by specifying a range of intervals. Compared with other models, interval models do not require extensive data and have lower demands for structural information. Therefore, in situations with inadequate or ambiguous information, interval models have emerged as a popular tool for studying uncertainty and exhibit significant potential for widespread applications. Since [PERSON]'s seminal work [8] on interval analysis in 1966, many scholars have further developed the fundamental theory of interval analysis [9; 10], leading to the continuous evolution of interval analysis methods. Subsequently, the application of interval analysis methods to solve structural response problems has become a popular research field and has been widely utilized to guide structural design [11; 12]. Currently, the interval analysis methods used to solve structural uncertainty response can be classified into two categories: intrusive and non-intrusive methods [13]. The scanning method (SM) [14] is a simple non-intrusive approach that samples uniformly in the input parameter space to obtain the uncertainty range of the output response. The results of the Monte Carlo method and SM tend to converge as the number of samples increases. Furthermore, the vertex combination method (VM) based on the monotonicity assumption theory was proposed by [PERSON] et al. [15], which obtains results by computing all possible combinations of input interval bounds. However, for high-dimensional parameter problems and limited computational resources, these methods may not be applicable. The polynomial chaos method replaces the system model with interpolated polynomial functions to perform an uncertainty propagation analysis. [PERSON] et al. [16] used a tensor product to construct multidimensional Chebyshev polynomials for studying nonlinear dynamical systems under uncertainty conditions. [PERSON] et al. [17] employed a non-intrusive analysis method based on Legendre polynomial collocation to investigate uncertainty propagation in the dynamic response of misaligned rotors. [PERSON] et al. [18] analyzed the uncertainty in aerodynamics and heating characteristics of hypersonic vehicles using Bernstein polynomials. However, polynomial-based methods may introduce extra errors. In contrast, Gaussian process regression [19] is a non-parametric regression method based on Bayesian inference that can infer the uncertainty of the output response and provide results for uncertainty propagation analysis. This approach is flexible and robust and can handle more complex system models.