MIMO Input Derivations, Optimizing Input Force Against Output Accuracy

Abstract

Multi-Input-Multi-Output (MIMO) vibration testing is considered more representative of the true loading environment (flight or wind induced vibration) where the inputs are not through a single point. The derivation of N inputs for testing typically involves matching the response at M locations (outputs). This involves inversion of a N × M Transfer Functions (TRF) matrix corresponding to the N input and M output locations. The matrix inversion is affected by both mathematical and physical parameters (ill-conditioned matrix, structural modes, signal noise).

Tikhonov regularization is commonly used in inverting an ill-conditioned N × M matrix. A low value of the Tikhonov regularization parameter minimizes the distortion of the original equations while a higher value can minimize error. In practice this introduces an interesting dilemma where obtaining realistic input loads and maintaining accuracy of output are often pitted against each other. A study was conducted using data synthesized from a simply-supported plate structure with known vibration modes with added noise at outputs. The objective of the study was to understand how noise or errors in the output and the Transfer function affect the input. This leads to a more judicious choice of the Tikhonov parameter that can achieve a balance between reducing input loads while preserving desired accuracy of output vibration.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

“This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.”