Strain estimation of truss structures based on augmented Kalman filtering and modal expansion

Introduction

Structural health monitoring (SHM) takes a breakthrough of care and maintenance of engineering structure by making use of structural and environmental information and measurement technologies to make the structure have self-sensing and self-diagnostic abilities. Truss structures are commonly used as the support skeletons such as aircraft wings, crane booms, derricks, scaffolds, transmission towers, offshore platforms, and steel bridges.^1,2 It is an inevitable problem to implement the SHM strategy and extract response data from a large number of members and joints of a truss structure. However, due to the cost of the sensors, the inaccessibility of some locations and the sensor damage subject to harsh service environments in practical cases, it is difficult or sometimes impossible to acquire the required data on the truss structure.^3,4

In some cases, vibration data from a limited number of sensors are used to estimate input information by field experiences⁵ or by system inversion techniques⁶ and then to extrapolate indirectly responses at unmeasured locations. The problem of load inversion is often ill-posed,⁷ and the results are sensitive to measurement noises and modeling errors. Recently, the Bayesian filter approaches have been proposed in the literature to provide a series of recursive solutions that may be the input and the unobservable system states with the corresponding uncertainties. Ching and Beck⁸ estimated the unknown state of a structure using incomplete output data and uncertain dynamic loading. Bernal⁹ proposed a damage detection method to employ the whiteness test based on linear Kalman filter (KF) innovations. To lower the impact on the accuracy of the state estimation due to the unknown input, Gillijns and De Moor¹⁰ have proposed a KF-based joint input-state estimation algorithm where the input estimation is performed prior to the state estimation step. The algorithm was then introduced in structural dynamics by Lourens et al.,¹¹ extending the algorithm in combination with reduced-order models. Maes et al.¹² developed the algorithm by considering the inherent correlation between process noises and measurement noises. The standard KF is used by Papadimitriou et al.¹³ to estimate strain responses at unmeasured members using acceleration measurements. Jo and Spencer ¹⁴ verified that the combination of acceleration and strain measurements for the standard KF could obtain better estimates....