The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force models (GPLFMs) are hybrid models that combine differential equations representing a physical system with data-driven non-parametric Gaussian process models. In this work, the unknown input forces acting on a structure are modelled as Gaussian processes with some chosen covariance functions which are combined with the mechanistic differential equation representing the structure to construct a GPLFM. The GPLFM is then conveniently formulated as an augmented stochastic state-space model with additional states representing the latent force components, and the joint input and state inference of the resulting model is implemented using Kalman filter. The augmented state-space model of GPLFM is shown as a generalization of the class of input-augmented state-space models, is proven observable, and is robust compared to conventional augmented formulations in terms of numerical stability. The hyperparameters governing the covariance functions are estimated using maximum likelihood optimization based on the observed data, thus overcoming the need for manual tuning of the hyperparameters by trial-and-error. To assess the performance of the proposed GPLFM method, several cases of state and input estimation are demonstrated using numerical simulations on a 10-dof shear building and a 76-storey ASCE benchmark office tower. Results obtained indicate the superior performance of the proposed approach over conventional Kalman filter based approaches.

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Summary Identifying mode shapes of bridge structures typically require a dense array of stationary sensors to accurately capture mode shapes with appropriate spatial resolution. An alternative approach is developed here, which requires only a single pair of actuator and sensor. The mode shape identification involves, first, identifying the natural frequencies and modal damping ratios, followed by an estimation of the mass normalized mode shapes components at the excited and measured degrees of freedom. An input–output balance is employed with a series of inputs and outputs obtained from a sequence of tests. The sequence of tests include exciting and measuring at different locations along the bridge, using either a roving actuator and/or a roving sensor; the requirement for a unique identification is that the roving actuator and sensor must be collocated in at least one of the tests. The performance of the proposed method using different types of responses, namely, displacement, velocity, and acceleration, is assessed using numerical simulations. The effect of different types of errors in the identification process is also studied. The method is finally applied to experimental data obtained from laboratory scale tests.

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