## 1 Introduction  
With the expansion of computational capabilities and the surge in data accumulation, optimization challenges in various scientific and industrial domains have become increasingly complex. The evolutionary algorithms (EAs) have emerged as an outperform optimization technique within this region, capable of handling the aforementioned complexities [1]. However, the mechanism of EAs is rooted in population-based iteration, which requires an extensive iterative phase to determine the fitness values of a large population. In many engineering fields, to evaluate these fitness functions for complex optimization tasks is a significant computational overhead, and this is classified as an expensive optimization problem (EOP) [2; 3; 4], such as in the field of aerodynamic design optimization. To achieve consistency between a design's aerodynamic metrics in computational fluid dynamics simulations, the real-world aerodynamic performance can be time-consuming, which may take anywhere from minutes to potentially hours for a single evaluation. Due to the challenges mentioned, the academic community has shifted towards the surrogate-assisted evolutionary algorithm (SAEA) [5], and the SAEA has gained significant scholarly interest [6; 7; 8]. The SAEA has proven to be effective for EOPs [9; 10], as it can reduce computational overheads. Based on the available dataset, either singular [11] or composite models [12] are used to assess the feasibility of potential solutions. Contemporary methodologies, such as polynomial regression [13], support vector machines [14], radial basis function networks [14; 15], artificial neural networks [16], and Gaussian processes (also known as Kriging model) [17; 18], are commonly used in surrogate model. The SAEA commonly uses global surrogate models to improve search capability [19; 20; 21]. [PERSON] et al. proposed harnessing Gaussian functions for surrogate model articulation to enhance the SAEA's prowess in curating a robust global surrogate construct [18]. By utilizing sample mapping techniques, the dimensionality of decision variables obtains a contraction [22]. To redress the algorithm's tapering exploratory vigor in its mature phases, [PERSON] et al. provided a global model governance blueprint [23], in which optimal fitness values concerned with ambiguous solutions are discerned through the amalgamated surrogate model. However, in recent years, there has been a focus on local surrogate models. These models explore the proximity of the global optimal solution's locus. Based on the latent potential of historic datasets, [PERSON] et al. proposed an avant-garde strategy to use semi-supervised learning, optimally harnessing both annotated and non-annotated datasets to amplify algorithmic precision [24]. [PERSON] et al. provided a social learning particle swarm optimization method for granular, localized spatial exploration [25]. Additionally, cooperation between global and local surrogate models comes into prominence as a new optimization method. [PERSON] et al. proffered archival samples to cultivate both global and local surrogate models. The strategy meticulously calibrates a balance between the dual models to minimize the computational impositions of the genuine objective function. Despite the widespread use of global and local surrogate models, there is a lack of effective control mechanisms during global and local surrogate model transitions. Additionally, due to constraints in single evaluation metrics, it is difficult to precisely describe the state of surrogate models, which can impact their effectiveness during transformation. Both of these reduce the effectiveness of the local surrogate model and its ability to explore locally. Based on the above considerations, this paper firstly presents a new methodology to address situations with high levels of uncertainty. To navigate these complexities, we record points with significant uncertainty and use them to formulate a normal distribution function, which enables the self-adaptive modulation of parameters.