# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 1 Introduction  
High-pressure cooling turbine blades play a critical role in aero engines, operating under harsh conditions characterized by high temperature, high pressure, and high rotational speeds, which significantly influence the overall performance of the aero engine [1]. During the service life of the blade, several disciplines such as aerodynamics, heat transfer, and structural strength are intricately interrelated and heavily influenced. Therefore, the design of the high-pressure cooling turbine blade is a typical multidisciplinary and complex work of system engineering. In high-temperature environments, conventional blade materials often struggle to maintain optimal performance. Employing high-temperature materials alongside thermal barrier coatings can enhance the thermal protection capabilities of blades to some extent. Furthermore, utilizing cooling mediums like low-temperature gas for heat exchange or employing insulation film cooling represent highly effective cooling strategies. However, the adoption of such cooling methods can lead to heightened string stress conditions [2; 3]. Therefore, achieving an advanced turbine blade design requires comprehensive consideration of the interplay and synergistic effects between multiple disciplines, including aerodynamics, heat transfer, structure, and strength. Traditional methods for designing a cooled turbine blade typically involve sequential analyses of aerodynamics, heat transfer, and structural strength. These methods often require multiple iterations to meet comprehensive performance criteria. However, relying on iterative design and verification, traditional methods have limited exploration capabilities for performance and struggle to identify optimal blade configurations. In contrast, Multi-disciplinary Design Optimization (MDO) technology provides a solution by synchronizing considerations of various disciplines. It fully utilizes advanced optimization techniques to coordinate conflicts between discipline indicators in real time, thereby obtaining themost comprehensive blade design scheme [4]. In recent years, MDO technology has found widespread application in turbine blade design optimization. For example, [PERSON] et al. [5] conducted a multidisciplinary analysis of a cooling turbine blade using time-sequential conjugate heat transfer analysis and temperature-pressure interpolation strength analysis. Their study significantly improved the performance of the cooling turbine blade by integrating multiple disciplines and optimizing the blade design. [PERSON] et al. [6] and [PERSON] et al. [7] established reliability models for a cooling turbine blade using fluid-thermal-structural coupled analysis methods. Compared to traditional models with failure-independent assumptions, such models demonstrate higher efficiency and accuracy. [PERSON] et al. [4] proposed a sensitivity analysis method for a cooling turbine blade considering surface thickness uncertainty, combining mesh deformation, neural network models, and multidisciplinary analysis. [PERSON] et al. [8] established a multidisciplinary coupled analysis model for aerodynamics, heat transfer, and thermodynamics, effectively enhancing cooling performance through internal heat transfer reinforcement and external membrane cooling improvements. These studies offer compelling evidence supporting the feasibility and effectiveness of MDO-based optimization in engineering applications for cooled turbine blades, underscoring its substantial value. The analysis of cooling turbine blades within a single discipline is already quite complex. When considering comprehensive optimization across multiple disciplines, challenges arise in terms of model complexity, computational complexity, and information exchange complexity. To address these challenges in practical engineering, surrogate models are often employed to replace intricate multidisciplinary system analyses. The surrogate model, which is also known as the metamodel, is one of the core technologies of MDO.