A centrifugal compressor is required to increase aerodynamic efficiency, ensure structural integrity, and reduce processing costs. This paper presents a dimension reduction technique based on proper orthogonal decomposition (POD) in combination with an adaptive sampling method to reduce computational costs. Design of experiment (DOE) is first used to choose initial sampling points. Then, parts of the sampling points are selected to format the snapshot matrix. Subsequently, the number of principal components to be retained is determined after POD analysis. An adaptive sampling point adding approach is used to increase new sampling points. The approach places more points around the regions of initial optimum designs by learning the information from previous data through POD analysis. Finally, the POD coefficients are selected to act as new design variables in the following multidisciplinary design optimization process. The method is first tested by three mathematical benchmark functions. The proposed method is then used to optimize a centrifugal compressor, of which the results are verified by tests. A normalized isentropic efficiency improvement of 3.7% and 3.0% in the maximum speed state and cruise state has been obtained after optimization. Additionally, the processing costs are reduced by about 30% owing to the number of blades reduced.

The conventional resonance conditions are derived based on the conventionally designed impellers without splitter blades. This paper proposes the resonance conditions for impellers under the excitation from the impeller–diffuser interaction with attention paid on the influence of splitter blades. A lumped parameter model is established and the modal analysis is carried out. The blade-based representative modal vector (RMV) is defined. The influence of splitter blades on the impeller’s traits of modes is investigated by analyzing the spatial harmonic contents of the RMV. Then, given the specific form of the diffuser-induced engine order excitation acting on the main and splitter blades, the resonance conditions are derived. Tuned and mistuned cases are provided for a practical impeller. The resonance conditions are verified by harmonic response calculations. The applications of the proposed resonance conditions in resonance identification and hazard evaluation of different excitations are given. The differences between the proposed resonance conditions and the conventional ones are discussed. The research indicates that even the RMV of the tuned impeller contains two harmonic components due to the existence of splitter blades. When the excitation frequency equals the natural frequency of the impeller and the excitation order matches with either harmonic index of the two harmonics, the resonance occurs. The results of case studies show that the harmfulness of various engine orders of excitation can be exactly evaluated by the joint use of the spatial harmonic contents analysis result and the proposed resonance conditions; however, analyzing based on the conventional resonance conditions may lead to the misjudgment of the harmfulness of the excitations.