Frequency Domain Model Reduction Based on Principal Component Analysis

A new frequency response based model reduction technique is presented for use in the mid-frequency range. The reduction was designed to avoid the use of modal based correlation metrics, which are known to fail in systems with high modal density. A transformation matrix based on a set of complex shapes extracted from the frequency response is used to reduce the impedance matrix to the sensor locations. The sensor locations are selected using the frequency domain effective independence sensor placement technique. Correlation measures that evaluate the test or FEM frequency response data directly with the reduced impedance matrix are used in the frequency domain model validation. The correlation metrics provide a consistency check between the measured response and the complete finite element model. Two numerical examples are included to illustrate the effectiveness of the new model reduction technique. NOMENCLATURE [M] : Mass matrix D : Dominant set [K] : Stiffness matrix R : Residual set [C] : Damping matrix o : Omitted degrees of freedom [Z] : Impedance matrix s : Sensor / kept degrees of freedom [h] : Frequency response ωj : j forcing frequency [H] : Frequency response data matrix a : input locations [ψ ] : Principal direction matrix [T] : Transformation matrix [S] : Singular value matrix [O] : Frequency domain orthogonality [V] : Right singular vector matrix [φ ] : Mode shape matrix