A multi-condition spectral proper orthogonal decomposition approach for reconstruction of transient temperature fields in turbine blades - Mi, Jin; Qiu, Lu; Tong, Zi-Xiang; Zhang, Yimin; Zhu, Jianqin (Applied thermal engineering, 2025)
•A multi-condition SPOD method is developed for transient field reconstruction.•Frequency-aware SPOD modes are extracted from five types of thermal scenarios.•Reconstruction is performed under unknown inlet conditions using sparse sensors.•SPOD modal coefficients are estimated via compressed-sensing formulation.•Method achieves high accuracy and robustness in unseen transient scenarios. Reconstructing temperature fields based on sparse measurement is crucial for the design, operation, and life assessment of turbine blades. When reconstructing transient temperature fields using a data-driven gappy Proper Orthogonal Decomposition (POD) algorithm, the POD modes do not inherently capture the transient dynamics of the temperature field. This limitation can lead to reduced reconstruction accuracy. Spectral Proper Orthogonal Decomposition (SPOD) algorithm is an extension of POD in the frequency domain. SPOD modes exhibit both spatial correlation within the same time instant and temporal correlation across different time instants. In this paper, a multi-condition SPOD framework is proposed to enable accurate reconstruction under unknown and complex operating conditions using sparse measurement data. The method builds a frequency-aware and condition-robust modal basis by decomposing multiple representative transient scenarios, and formulates the reconstruction task as a compressed sensing inverse problem, where modal coefficients are estimated using least-squares projection. To enhance the reconstruction accuracy for unknown operating conditions, this paper investigates the guidelines for dataset construction by comparing and analyzing the types and durations of datasets. Additionally, two sets of sparse measurement data are designed to validate the reconstruction accuracy of the multi-condition SPOD algorithm. Comparisons with the traditional gappy POD algorithm reveal that the multi-condition SPOD algorithm achieves an average reconstruction error of 0.12% under the same measurement conditions, which is a significant improvement compared to the 1.04% error of the gappy POD algorithm. This advancement suggests that the multi-condition SPOD algorithm has promising applications in the practical reconstruction of turbine blade temperature fields under varying operating conditions.