STRUCTURAL MODEL UPDATING USING VIBRATION MEASUREMENTS

Abstract. A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Paret

Optimal sensing for fish school identification

Fish schooling implies an awareness of the swimmers for their companions. In flow mediated environments, in addition to visual cues, pressure and shear sensors on the fish body are critical for providing quantitative information that assists the quantification of proximity to other swimmers. Here we examine the distribution of sensors on the surface of an artificial swimmer so that it can optimally identify a leading group of swimmers. We employ Bayesian experimental design coupled with two-dimensional Navier Stokes equations for multiple self-propelled swimmers. The follower tracks the school using information from its own surface pressure and shear stress. We demonstrate that the optimal sensor distribution of the follower is qualitatively similar to the distribution of neuromasts on fish. Our results show that it is possible to identify accurately the center of mass and even the number of the leading swimmers using surface only information

Optimal experimental design in structural dynamics.

Theoretical and computational issues arising in experimental design for model identification and parameter estimation in structural dynamics are addressed. The objective is to optimally locate sensors in a structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling. The information entropy, measuring the uncertainty in the parameters of a structural model class, is used as a performance measure of a sensor configuration. For a single model class, the optimal sensor location problem is formulated as an information entropy minimization problem. For model class selection and/or damage detection applications, the problem is formulated as a multi-objective optimization problem of finding the Pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices related to multiple model classes and/or probable damage scenarios. Asymptotic estimates for the information entropy, valid for large number of measured data, are presented that rigorously justify that the selection of the optimal experimental design can be based solely on the nominal structural model from a class, ignoring the details of the measured data that are not available in the experimental design stage. The effect of the measurement and model prediction error variances on the optimal sensor location design is examined. Finally, heuristic algorithms are proposed for constructing effective sensor configurations that are superior, in terms of accuracy and computational efficiency, to the sensor configurations provided by genetic algorithms

Structural model updating using vibration measurements

A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Pareto optimal structural models that are consistent with the measured data and the residuals used to measure the discrepancies between the measured and the finite element model predicted characteristics. The relation between the multi-objective identification method, Bayesian in-ference method, and conventional single-objective weighted residuals methods for model up-dating is discussed. Computational algorithms for the efficient and reliable solution of the resulting optimization problems are presented. The algorithms are classified to gradient-based, evolutionary strategies and hybrid techniques. In particular, efficient algorithms are introduced for reducing the computational cost involved in estimating the gradients of the ob-jective functions representing the modal residuals. Specifically, a formulation requiring the solution of the adjoint problem is presented, avoiding the explicit estimation of the gradients of the modal characteristics. The adjoint method is also extended to carry out efficiently the estimation of the Hessian of the objective function. The computational cost for estimating the gradients and Hessian is shown to be independent of the number of structural model parame-ters. The methodology is particularly efficient to system with several number of model param-eters and large number of DOFs where repeated gradient and Hessian evaluations are computationally time consuming. Component mode synthesis methods dividing the structure to linear substructural components with fixed properties and linear substructural components with uncertain properties are incorporated into the methodology to further reduce the compu-tational effort required in optimization problems. The linear substructures with fixed proper-ties are represented by their lower contributing modes which remain unchanged during the model updating process. The method is particular effective for finite element models with large number of DOF and for parameter estimation in localized areas of a structure. Theoret-ical and computational developments are illustrated by updating finite element models of a laboratory building using impact hammer measurements and multi-span reinforced concrete bridges using ambient vibration measurements

Statistical Methodology for Optimal Sensor Locations for Damage Detection in Structures

A Bayesian statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting the most information about the model parameters which can be used in model updating and in damage detection and localization. This statistical approach properly handles the unavoidable uncertainties in the measured data as well as the uncertainties in the mathematical model used to represent the structural behavior. The optimality criterion for the sensor locations is based on information entropy which is a measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by the Bayesian statistical methodology and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. Results presented illustrate how both the minimum entropy of the parameters and the optimal sensor configuration depend on the location of sensors, number of sensors, number and type of contributing modes and the structural parameterization (substructuring) scheme used