Application of a Large Scale State Estimator to the Vibrational Response of a Mechanical Structure

摘要

The SEALS (State Estimator for Large Systems) computer code was applied to the estimation of displacement time histories of points on a vibrating mechanical structure given noisy measurements at two locations on the structure. The goal was to demonstrate the feasibility of determining the motion of internal members of the structure given only noisy measurements from the exterior and a finite-element model of the structure. This study was done in four distinct phases, i.e., model development; simulation of displacements vs time; acquisition of noisy measurement data (computer simulated); and estimation of displacements from measurements. The model was developed from the geometry of the structure using the ZONE finite-element mesh generator to produce an axi-symmetric finite-element model consisting of 15 elements and 32 nodes. The SAP4 code was used to translate the geometry and material properties into a 2nd order matrix differential equation (with matrices of size 87 by 87) which was then transformed into 174 state space equations (i.e., first order differential equations) for input to the SEALS state estimation code. A model check feature of SEALS was used to simulate displacement time histories at all the nodes of the finite-element model given an initial displacement for one of the nodes. Noisy measurements at two exterior locations on the structure were simulated by adding Gaussian white noise to the appropriate simulation waveforms. The standard deviation of the noise was chosen to given an approximate signal-to-noise ratio of 40. The SEALS code was used to reconstruct the displacement time histories of all the nodes of the model given the measurements, and erroneous initial value for both the initial condition displacement and the measurement noise covariance. Plots of displacement time histories at selected nodes of the model for simulation, measurement, and state estimation (reconstruction) are given. (ERA citation 06:011383)