Using the idea of integral

the curved case was considered to be accumulated by a number of cylindrical cases. The mode shape data were interpolated into a three-dimensional pixel space of circle×points×layer

which can realize the identification of the mode shape of curved case by radial axial Tchebichef moment (RAT moment). The feature moment set was extracted from the mode shape data by using the RAT moment function to achieve compression of the mode shape data. Correlation analysis based on RAT moment can well describe the double modes phenomenon

which can make up for the defects of traditional modal assurance critertiom （MAC）values for double modes description. The eigenvalue of the moment was used as the objective function instead of the mode data

which was applied to model verification. The data amount of the moment eigenvalue was much smaller than the mode shape data

which can improve the calculation efficiency and avoid the non-convergence of the updating result. Considering that most engineering components were not completely axisymmetric

an aero-engine casing with an asymmetric boss was taken as an example. Based on RAT moments for mode calculation

correlation analysis and model updating

it was found that both frequency and RAT moments were used for model verification. Correlation was significantly improved

for example

the correlation of the ninth-order mode was increased from 35.35% to 67.21%. The frequency difference of each mode pair was also significantly reduced

and the maximum frequency difference was reduced from 14.56% to 9.09%. It was proved that the RAT moment function can be used in the model confirmation of asymmetrical three-dimensional surface.