Robust Optimization of a Compressor Blade Through Combination of an Adjoint-Based Multistart Approach and Global Gaussian Process Regression

Abstract The real geometry of compressor blades naturally deviates from the intended design due to the finite accuracy of manufacturing processes as well as abrasion and deformation in operation. Consequently, a deterministic design approach causes an inevitable performance degradation. Robust design optimization captures this effect by defining a probabilistic objective that is subject to uncertain geometrical features. However, the required process complexity inherently entails an increase in computational cost, which narrows the pool of available methods in the industrial context due to the extensive usage of costly three-dimensional computational fluid dynamics in aerodynamic investigation. The adjoint method provides a means for the cheap acquisition of gradient information and thus lays the foundation for efficient gradient-based local search procedures. Furthermore, a global approximation of the search space can be achieved by surrogate modeling techniques enabling a better understanding of the system behavior and guidance towards the global optimum. This paper presents the development and application of a hybrid robust optimization algorithm to compressor aerodynamics through the combination of the respective advantages of an efficient gradient-based search methodology incorporating the adjoint method and the Gaussian process regression. As such, the proposed algorithm aims for the balance of local and global optimization. For this purpose, a favorable interaction between the involved methods was targeted while accounting for geometrical uncertainty determined from optical measured blades. The performance of the employed methods as well as their ensemble within the complete algorithm was validated and analyzed on a low- and high-dimensional test function. In addition, the algorithm was compared to the efficient global optimization algorithm (EGO) where the behavior and overall results were evaluated by suitable criteria regarding the compressor application case. Following the established strategy, robust design optimization of a rotor blade from a state-of-the-art high-pressure compressor was conducted. The algorithm’s decisions and especially the surrogate model were monitored and analyzed. Validation by means of a design of experiments resolving the uncertainty space revealed the nonlinear character of the compressor performance with respect to geometrical uncertainty. The applied algorithm yielded a robust optimum, which is superior to those acquired by previous local searches under equal conditions. Ultimately, the optimal blade aerodynamics were analyzed and compared to the nominal design, disclosing a systematic reduction of loss caused by secondary flow and supersonic effects. A definite adaptation to the operating point under investigation was observed, leading to a shortened characteristic, albeit with improvement in a wide operating range.