A strategy for input estimation with sensitivity analysis

The estimation of unknown excitation or input signals from measured response is essentially the solution of an optimization problem; a function representing the input is sought such that the discrepancy between measured and simulated response is minimized. From the view of optimization it is convenient to consider the general situation where the governing differential equations may be time-variant and non-linear. Moreover, the choice of parameterization for the sought input, sampling instances of measurement data and discretization of the state problem are all decoupled, in contrast to standard methods such as Dynamic Programming. In this paper, the optimization problem is solved by seeking a stationary point of the pertinent Lagrangian functional, resulting in a Newton-type iterative algorithm. Moreover, the sensitivity of the solution with respect to measurement noise may also be estimated from a perturbation analysis of the optimality conditions. Two numerical examples show that the approach produces results in agreement with those of standard methods, however, with the additional advantage the numerical properties of the considered problem may be investigated. In particular, such knowledge may be used for choosing a proper amount of regularization. Copyright q 2006 John Wiley & Sons, Ltd.