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Gas insulated switchgear (GIS) is essential for the reliability and stability of power systems, requiring precise recognition of its operating conditions, which are typically represented by voiceprint data. Traditional methods, predominantly based in Euclidean space, often struggle to differentiate specific intricate operating conditions in GIS. Addressing this gap, this paper proposes a novel method anchored in Riemannian space. Specifically, this method begins by employing Mel frequency cepstral coefficient (MFCC) and singular value decomposition (SVD) to extract features from voiceprint data. Subsequently, it projects these features within Riemannian space and maps them onto a Grassmann manifold, effectively capturing its intricate and nonlinear characteristics. A key innovation of this method is the use of three kernel functions, namely projection, Binet-Cauchy, and canonical correlation, optimized via empirical kernel alignment techniques to select the most suitable adaptive parameters, thereby enhancing classification accuracy. Further refinement is achieved through kernel linear discriminant analysis (KLDA), which integrates the aligned kernel into a lower-dimensional subspace for more efficient classification. Experiments on real data from ZF23-126 type GIS, encompassing 20 different operational conditions, show our method achieves an accuracy of 95.21%, precision of 95.38%, specificity of 99.75%, and F1-score of 95.22%, significantly outperforming all baseline methods. Moreover, the method demonstrates robust performance across various classifiers, with accuracy consistently exceeding 90%. Additional ablation experiments confirm its effectiveness and generalizability.