What is Nonlinear Estimation

The chapter proposes structural condition monitoring for buildings and mechanical structures using a new nonlinear filtering method under the name Derivative-Free Nonlinear Kalman Filtering. The filter makes use of exact linearization of the structure's dynamical model in accordance to differential flatness theory and of an inverse transformation that enables one to obtain estimates for the state vector elements of the initial model. The response of the structure is compared to the response generated by the filter under the assumption of a damage-free model. Moreover, the filter provides estimates of the state vector elements of the structure, which cannot be directly measured, while it can also give estimates of unknown excitation inputs. By comparing the two signals, residuals sequences are generated. The statistical processing of the residuals provides an indication about the existence of parametric changes (damages) in the structure that otherwise could not have been detected.