Information Theoretic Optimal Sensor Placement In Structural Health Monitoring

As most of civil structures are rather gigantic and complicated, it is impossible, unfeasible and unnessesary to install too many sensors in order to diagnose the degeneration. Optimal sensor placement becomes the elementary part for the well-design of structural health monitoring system. An objective we always try to fullfil is to use fewer sensors to obtain enough information about the health condition of structures; therefore, the data recorded should be sensitive to the potential damage to aid the damage identification and prognosis. Information theory has been widely applied for the sensor placement in parameter identification and modal identification. It is also the method we want to introduce in the optimal sensor placement for damage identification. In this thesis, an overall, systematic application was illustrated through the generalization, expansion and creation. Main contents and conclusions are as follows:(1)A through description of Fisher information criterion for sensor placement was prensented, including the popular D-optimality and T-optimality. Maximizing the Fisher information matrix is equivalent to minimizing the estimation error of damage parameters, i.e. to achieve the efficiency. The physical meanings of D-optimality and T-optimality are to minimize the volume and root mean square of semi-axis of the confidence ellipsoid, respectively. If the covariance matrix is assumed to be a diagnal matrix, the optimal solution of T-optimality must be obtained through the greedy algorithm, while this algorithm has no guarantee on the optimization of D-optimality; the greedy algorithm combined with principle subset selection, which could get a large determinant of Fisher information matrix while assure the rank of the sensitivity matrix, shows a good performance in the deployment of accelerometers.(2)The conditional entropy was applied in the sensor placement aiming at damage identification. It was proved that the conditional entropy is the lower bound of error entropy, which reflects the accuracy of the parameter estimation. The asymptotic approximation of conditional entropy was acquired based upon the Bernstein-von Mises theorem; then, the convex optimization was employed to find the optimal sensor locations. Conditional entropy criterion stands even in the condition of non-Gaussian and nonlinear form. Under the assumption of Gaussian noise, conditional entropy criterion is identical to the D-optimality or the effective independence method in modal identification. The influence of covariance matrix, of which the diagonal elements were the DPR, is quite similar to that of the EI-DPR method. The convex optimization shows high efficiency, and the upper bound obtained has a certain guiding significance.(3)The K-L divergence criterion, a load and damage dependent criterion, was pioneered in sensor placement. The physical meaning of K-L divergence is to minimize the distance between the identification results via partial measuring points and those through full points. In order to avoid the selection of the load and damage, the expectation of K-L divergence was utilized in the real case. The cross entropy optimization was adopted to determine the optimal positions for sensors. The K-L divergence is a versatile criterion, for SA_K-L and S_K-L focus on the unbiasedness of estimation, while the ASK-L prefers the efficiency, equivalent to the conditional entropy criterion. The measurement error and model error impact heavily on the criterion all the aforementioned:according to the assumption made in this thesis, measurement errors keep the optimal locations nearer to the ones with high kinetic energy, and model errors disperse the clustered measuring points. The cross entropy optimization manifests strong convergence, and the optimization problem could be solved within a short time in most cases.