A Methodology for Optimal Sensor Locations for Identification of Dynamic Systems

Abstract

The problem of optimally positioning sensors in lumped and distributed parameter dynamic systems for the purpose of system identification from time-domain input-output data is formulated and a methodology for its solution is presented. A linear relation between small perturbations in a finite-dimensional representation of the system parameters and a finite sample of observations of the system time response is used to determine approximately the covariance of the parameter estimates. The locations of a given number of sensors are then determined such that a suitable norm of the covariance matrix is minimized. The methodology is applied to the problem of optimally locating a single sensor in a building structure modeled by a shear beam, such that the estimates of the stiffness distributions, obtained from the records of strong ground shaking and the building response at the sensor location, are least uncertain.

On the optimal location of sensors for parametric identification of linear structural systems

“…If i t is assumed that the N measurements inelucled in the vector Y are dependent then by taking the expectation in (3) the Fisher information matrix becomes (18) It is seen from (18) that a N x Ns-dimensional integral has to be solved if the Fisher information matrix is to be estimated directly from the definition which is much more cumbersome than using (17). To see the difference between calculating the Fisher information matrix from (17) and from (18) it is assumed that an observation is taken only once at each measuring point simultaneously.…”

Posterior Robust Optimization for Design Update Based on Measurements

“…The first step is the optimization of the locations of the sensors [1,2,3,4,5,6] so that the experiments to be committed will be as much informative as possible for the identification of parameters. The minimization of the information entropy is sought in this step, which, based on asymptotic approximations, depends on the differentiation of the quantities to be measured with respect to the parameters to be identified.…”

Bayesian Optimal Sensor Placement for Modal Identification of Civil Infrastructures

“…In the past, notable contributions to the sensor placement problem for modal identification have been provided by the effective indepen-E dence (EFI) method [8] for uniaxial and triaxial sensors [9,10] . Information theory measures, based on scalar measures of the Fisher information matrix (FIM) [11,12] and on information entropy [13][14][15] , proposed in the past for structural parameter estimation problems, have been extended to be used for modal identification [16] as well. An optimal sensor placement design for modal identification based on FIM was proposed by Kammer [17] .…”