Entropy-Based Optimal Sensor Location for Structural Model Updating

Abstract

A statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting from the measured data the most information about the parameters of the model used to represent structural behavior. The methodology can be used in model updating and in damage detection and localization applications. It properly handles the unavoidable uncertainties in the measured data as well as the model uncertainties. The optimality criterion for the sensor locations is based on information entropy, which is a unique measure of the uncertainty in the model parameters. The uncertainty in these parameters is computed by a Bayesian statistical methodology, and then the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. The information entropy measure is also extended to handle large uncertainties expected in the pretest nominal model of a structure. In experimental design, the proposed entropy-based measure of uncertainty is also well-suited for making quantitative evaluations and comparisons of the quality of the parameter estimates that can be achieved using sensor configurations with different numbers of sensors in each configuration. Simplified models for a shear building and a truss structure are used to illustrate the methodology.

Optimal Wave Propagation-Based Nondestructive Test Design for Quantitative Damage Characterization

“…Furthermore, optimal NDT design can provide guidance for implementation of specific NDE, helping to answer questions such as how many sensors are needed to inversely characterize the material properties for a particular NDT system. In recent years, several optimal NDT design approaches for damage detection and identification were introduced and developed [34,35,36,37,27,38,39,40].…”

“…In [38,39] a methodology to optimize damage detection and localization applications was introduced based on minimizing the information entropy with respect to the uncertainty in the model parameters. GA was employed to search for the "best" locations of sensors with the minimum information entropy.…”

Sensor Placement Optimization Using Ensemble Kalman Filter and Genetic Algorithm

“…Therefore the equation of motion is expressed as (11) where M is the mass matrix, C is the damping matrix, Kel and Kin are respectively the elastic and inelastic stiffness matrices, is ratio of the post yielding stiffness to the elastic stiffness, τ is an influence vector, u is the displacement vector, x is the inter-story drift vector, and z is the evolutionary hysteretic vector of dimension n and whose ith component is expressed by the Bouc-Wen model by (12) where A, , are the Bouc-Wen model parameters, whose values are shown in the On the other side, the predicted values of the displacements and velocities are calculated using an inverse model that is used to detect the behavior of the system under consideration. The inverse model is expressed by the following equation…”

“…C. Papadimitriou et al proposed a methodology where the Bayesian approach is used to compute the uncertainty in the parameters, then the GA is applied to minimize the information entropy over the set of possible sensor configurations [11]. The methodology proposed was applied on two numerical examples, a 9-story building and a 29-DOF truss structure.…”

System Identification of Constructed Facilities: Challenges and Opportunities across Hazards

“…System identification of constructed facilities should look toward methods that provide a framework to quantify the uncertainties of model parameters [e.g., Beck and Katafygiotis, 1998]. Such methods would better reflect the inherent uncertainty in measurements and models for direct incorporation into reliability analyses and may even help determine improved sensor deployment strategies and design networks with increased sensitivity and efficiency [e.g., Papadimitriou, et al, 2000].…”