Modal Assurance Criterion for Evaluating the Quality of Mode Shapes in Modal Analysis

The Modal Assurance Criterion (MAC) is a widely adopted method for evaluating the quality of mode shapes in modal analysis. It also serves to quantify the similarity between two vectors. This criterion is computed based on the inner product of modal vectors and their corresponding frequencies, making it effective for assessing the accuracy and correlation of mode shapes. In computational implementations, MAC values are typically calculated using matrix operations where the MAC matrix elements represent the normalized scalar product between mode shape vectors. The formula is commonly implemented as MAC(i,j) = |φ_i^T φ_j|^2 / (|φ_i^T φ_i||φ_j^T φ_j|), where φ_i and φ_j represent different mode shape vectors. Additionally, the Modal Assurance Criterion can identify potential errors and uncertainties during the modal analysis process, thereby enhancing the reliability and precision of mode shape analysis. When performing mode shape analysis, utilizing the MAC for evaluation and comparison enables a more comprehensive understanding of the characteristics and performance of mode shapes. Algorithmically, MAC values range from 0 (no correlation) to 1 (perfect correlation), with threshold values typically set above 0.9 indicating high consistency between compared mode shapes.