# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 1 Introduction
Utilizing a limited amount of sample data generated by physical model tests and numerical analysis, it can establish mathematical models to improve computational efficiency under the premise of a certain accuracy level [9]. In recent years, the surrogate model has received extensive research attention. Numerous surrogate models, including Polynomial Response Surface (PRS) models [10], Kriging models [11], Support Vector Regression (SVR) models [12], Radial Basis Function (RBF) models [13], and Artificial Neural Network models [14], were proposed. [PERSON] et al. [15] proposed a new failure-related analysis strategy based on the Kriging model, conducting reliability assessments on high-pressure turbine rotors and enhancing computational efficiency. [PERSON] et al. [7] established a stress probability analysis model for aviation engine turbine rotors' critical locations using response surface methods, demonstrating high efficiency and accuracy. [PERSON] et al. [16] proposed a Multi-Fidelity Successive Response Surface (MF-SRS) model for collision testing, demonstrating superior accuracy and effectiveness in predictions when compared to the Successive Response Surface Method (SRSM). [PERSON] et al. [17] introduced a machine learning-based method for predicting the lifespan of a turbine blade and predicted the remaining useful life through five start-stop cycles of a gas turbine. [PERSON] et al. [17] used a Kriging surrogate model to capture input data uncertainty and successfully obtained better performance variability in a robust optimization considering design uncertainties for pulse-corrected ballistic trajectories. [PERSON] et al. [4] constructed a neural network model for conducting sensitivity analysis on the multidisciplinary system of a turbine blade, reducing computational workload. The application of surrogate models in the optimization of a high-pressure cooling turbine blade addresses challenges posed by the complexity of multidisciplinary interactions, computational demands, and information exchange. While the surrogate model offers various advantages, the suitability of different surrogate models for diverse problems varies. Given the absence of prior knowledge regarding the multidisciplinary design optimization of the cooling turbine blade, finding appropriate and highly precise surrogate models for practical engineering problems proves challenging. A common approach to address this challenge involves constructing an ensemble surrogate model, which integrates two or more independent surrogate models by introducing weight factors. The concept of the ensemble surrogate model traces back to the 1990s and has become a current research focus. In a study by [PERSON] et al. [18],a robust combination surrogate model was proposed through weighted combination, resulting in enhanced model accuracy. [PERSON] et al. [19] introduced a new weighting factor and established a new ensemble surrogate model named EM-MROWF, demonstrating superior performance compared to a single-surrogate model. [PERSON], et al. [20] conducted a study on composite surrogate models from the aspects of selecting the model, calculating weight, and compensating residuals, proposing the OSF-TLPE composite surrogate model method and demonstrating its more flexible and reliable performance through testing. Combining the advantages of regression surrogate models and interpolation surrogate models, the authors of [21] proposed a regression/interpolation combination surrogate model to leverage the global trend-fitting capability of regression surrogate models and the local accuracy prediction advantage of interpolation surrogate models, which can effectively enhance the accuracy and robustness of surrogate models. However, this surrogate model has not yet been applied in practical engineering optimization to demonstrate its utility. This study focuses on the design optimization of a two-stage high-pressure turbine blade in a specific aeroengine.