## 1 Introduction
It was shown that SPCE was advantageous over PCE in terms of the number of analyses required to make an accurate prediction. In a following study, [PERSON] and [PERSON] [14] combined SPCE with an adaptive algorithm to automatically determine the important polynomial coefficients. Comparing the results of the adaptive SPCE method with full PCE and stepwise SPCE demonstrated that the adaptive SPCE method could represent high-dimensional problems with fewer data. [PERSON] and [PERSON] [3] performed a reliability analysis for high-dimensional models using LRA, where the number of unknown coefficients increased linearly depending on the problem size. It was concluded that the LRA method outperformed the SPCE method while also using fewer analysis results. [PERSON] et al. [15] integrated the PCE method with the PLS method to approximate unknown orthogonal polynomial coefficients for high-dimensional problems and found that the PCE-PLS method provides more accurate estimations compared to the LRA method when a small number of simulations results are used. Recently, [PERSON] and [PERSON] [16] integrated the generalised dimension reduction algorithm with the PCE method for efficient uncertainty quantification of non-standard distribution types and [PERSON] et al. [17] performed reliability analysis using the Kriging method integrated with the PLS algorithm instead of orthogonal polynomial-based methods for high-dimensional problems. Among multi-fidelity applications, [PERSON] et al. [18] applied the multi-fidelity Monte Carlo (MFMC) method and [PERSON] et al. [19] performed high-dimensional uncertainty quantification studies using the multi-level Monte Carlo method. High-fidelity engineering simulations are usually computationally expensive, and uncertainty quantification processes using high-fidelity engineering models struggle with extreme computational cost. Multi-fidelity methods leverage both high-fidelity and low-fidelity data to reduce the high computational or experimental costs by achieving high accuracy simultaneously. As multi-fidelity surrogate modelling methods reduce the computational cost of simulations with an acceptable accuracy, this approach can be a remedy for uncertainty quantification processes [2]. In uncertainty quantification studies, orthogonal polynomial-based surrogate models such as multi-fidelity PCE [20] and SPCE [21] can be preferred since they successfully represent the general behaviour of computational models. In [20; 21] studies, additive and multiplicative correction terms were used to extend the multi-fidelity versions of PCE and SPCE. In addition, there are studies in which multi-fidelity extensions of these methods are made with the Gaussian process such as [22]. Other widely used multi-fidelity methods are kernel-based methods such as the multi-fidelity Gaussian process [23], coKriging [24], and Stochastic Radial Basis function [25]. These methods are preferred in optimisation studies due to their success in capturing local properties and are also used in uncertainty analysis. In addition, there are methods such as Polynomial Chaos-coKriging [26] and Sparse Polynomial Chaos-Kriging [27], which combine the ability to capture global features of orthogonal-based methods with the ability to capture local features of kernel-based methods. Regarding the uncertainty quantification for a low-boom aircraft design, the effects of uncertainties in flight conditions and atmospheric profile at the sonic boom level were studied by [PERSON] et al. [28] using a mixed uncertainty quantification and second-order probability method; they performed the uncertainty quantification for flow analysis through a PCE surrogate model, which significantly increased the computational demand. [PERSON] and [PERSON] [29] and [PERSON] et al. [30] studied the effect of aeroelastic impacts on sonic boom using the non-intrusive PCE method. [PERSON] et al. [30] examined the effect of uncertainties due to the material properties on the sonic boom and reduced the number of uncertain parameters by performing sensitivity analysis.