Application of fixed-lag Kalman smoother for nonlinear state estimation

During their lifetime, civil structures and infrastructures are subjected to environmental and human-induced hazards that may lead to structural damages or, in some cases, to full collapse. Such failures are associated with increased risk for life and limb, while also environmental and monetary losses may be triggered with adverse societal footprint. Consequently, it is highly relevant to screen reliably the condition of the structural systems and, if necessary, to intervene to safeguard the structural integrity and avoid undesirable failures. To this end, several structural health monitoring schemes are becoming a key element for various structures and infrastructure systems, enabling the continuous assessment of their state. The latter, in turn, can allow for detecting damages at an early age, avoiding extensive failures or even sudden collapse. In order to identify the failures due to excessive loading events, measured time-varying responses are frequently used as the basis for damage detection. However, in reality, practical restrictions exist in mounting sensors on all the locations of the structure that an engineer would prefer to know the structural response. For example, sensing data from the submerged part of an offshore platform is commonly not available, while the latter is also valid for various locations in bridges where the access is limited to apply and operate sensors. Therefore, the available measured data is mostly incomplete since only a limited number of sensors can be employed. Additionally, various noise sources usually pollute the sparsely measured responses, and the overall quality is compromised. As a remedy to this challenge, a new framework is proposed herein to aid in estimating reliably the nonlinear dynamic response of a structural system with the use of limited and noisy measurements. Especially, a Kalman smoothing technique called the fixed-lag algorithm is coupled with an augmented extended Kalman filter, and such an integrated scheme is anticipated to increase the state estimation accuracy. The current study adopts a simulation framework as the testbed for the proposed scheme. The use of the FE software OpenSees allows the numerical nonlinear modeling of the structural system subjected to time-varying loads. Compared with the ones calculated directly from nonlinear response history analysis, the estimated responses based on the proposed scheme are found to be associated with increased accuracy.