MS18.11 - System Identification and Damage Detection

The importance of uncertainty quantification has become increasingly more apparent, particularly in the field of system identification and modal analysis. The stochastic nature of the forcing in operational modal analysis (OMA) lends itself to variable identification performance. The need to quantify the uncertainty and therefore encapsulate this variability introduced by the data and the method itself, is highly sought by many a modern dynamicist to aid decision making. Often atypical observations in time series data can further compound this issue and even lead to the misidentification of the system. At time of writing, no method currently exists capable of quantifying the uncertainty in a Bayesian sense, whilst remaining statistically robust to outliers. Covariance-driven stochastic subspace identification (SSI) is frequently employed in OMA applications as a reliable means of recovering the modal properties of a structural dynamic system. At the heart of this method lies a mathematical concept known as canonical correlation analysis (CCA) which seeks to find the correlation between Hankel matrices of the future and the past observations, from a set of response sensors, measuring a dynamic system. In earlier work by the authors, a probabilistic formulation of SSI was presented that saw the replacement of traditional CCA with a probabilistic equivalent, using the theory of latent variable models. This change in formulation provides new insight into this well established technique. Subsequently, the authors extended this to a statistically robust approach, with the inclusion of a Student’s-T distributed noise model. This robust extension saw improved identification performance over standard SSI when confronted with atypical observations in time series responses. Following the success of this work, the probabilistic interpretation of SSI was further extended to a, so-called, fully Bayesian approach, capable of recovering the posterior distributions over the modal properties. The availability of this posterior uncertainty provides additional information to the dynamicist, which can impact future decision making or modelling exercises. This paper combines the two work packages and presents a Robust Bayesian formulation of SSI using a statistically robust, variational Bayesian approach capable of approximating the posterior distributions over the modal properties. This robust Bayseian approach demonstrates a number of improvements, most notably the ability to recover posterior distributions over the modal properties, whilst remaining statistically robust to atypical observations.

Among the compendium of highway civil infrastructures built in the last decades, many repetitive or quasi-periodic configurations can be found, such as multi-span simply supported bridges. Structural Health Monitoring (SHM) strategies for this kind of structures should properly consider such structural periodicity. Of specific interest to this paper are SHM methods based on Operational Modal Analysis (OMA). These techniques allow inferring the presence of damage by means of persistent variations in the modal features extracted from response time histories under ambient excitation. Literature studies already demonstrated that multi-span bridges are particularly challenging target structures for OMA. Such difficulties arise from the fact that the modal properties of the spans typically appear as dense clusters of poles with closely spaced frequencies and mode shapes with similar wavelengths. Hence, this circumstance considerably hinders the identification of physical poles using standard stabilization diagrams. Only slight differences arise as a result of the imperfect independence between spans, which is typically due to weak deck/asphalt connections and/or imperfect expansion joints. In this context, the coupling degree of spans manifests through global mode shapes and frequencies spanning between the limit cases of simply supported and continuous multi-span conditions. In this light, this paper proposes a novel method to interpret the results of OMA of partially continuous multi-span bridges. The proposed method is based on the analytical modal solution to the free vibration problem of multi-span beams with weak rotational coupling between adjacent spans. Through comparison analyses against experimental results from OMA, the developed model can be used to infer the elastic coupling between adjacent spans and the location/severity of damage. The developed formulation is validated against finite element simulations, and numerical results and discussion are presented to evidence its potential for the modal identification of a real-world in-operation multi-span reinforced-concrete girder bridge.

Dynamic properties of ships, especially damping, are important for predicting fatigue damage from wave-induced vibrations. Operational modal analysis (OMA) is useful for characterising the dynamics of structures through the identification of a modal model from vibration measurements. A modal model comprising five modes is obtained by performing OMA on full-scale measurements conducted during purposefully-executed test sequences of a slamming-prone polar vessel. Close inspection of features in the measurements indicate that the hydro-elastic responses of the ship are associated with periodic, non-stationary wave excitation, and strong fluid-structure interaction. This violates many fundamental assumptions of OMA and introduces both bias and random errors in the identified modal model. A harmonic removal technique is investigated to suppress the influence of periodic inputs in the vibration signals, while random errors are quantified through a first-order sensitivity analysis. Removal of periodic components result in improved identification of weakly excited lateral bending and torsional modes, and increases damping estimates of two-node and three-node vertical bending estimates by as much as 800 % and 400 %, respectively. Comparison of modal estimates from test sequences at varying speeds indicate speed dependency of natural frequency and damping. The natural frequency tends to decrease, and damping ratio increases. Both natural frequency and damping estimates are found to have lower variances at higher ship speeds, which corresponds to measurements that match the underlying OMA assumptions more closely. The relative variances of natural frequency estimates are generally all below 0.008, while damping estimates are more uncertain with relative variances as high as 1.5. Vertical bending modes, which are well-excited, have lower variances, while weakly-excited modes that are buried in noisy measurements have higher variances.

A growing number of urban structures, such as quay walls and bridges, are reaching the end of their operational life, while the cost of fully replacing these structures is often prohibitive. Consequently, asset owners face the challenge of having to perform manual assessment based on engineering models, structural codes and expert judgment, for a large number of structures. The necessary expertise and large cost involved makes this type of assessment infeasible for large numbers of structures. In recent years, the wider adoption of structural health monitoring methods combined with advancements in sensor technology have enabled the collection of large amounts of data, with high spatial and temporal resolution. Additionally, multiple heterogeneous sources of data may be available. Utilizing spatially and temporarily correlated measurement data from heterogeneous sources to perform inference, model calibration and prediction for structures presents several challenges. In this work, an evolving, probabilistic, physics informed machine learning model based on Bayesian statistical model updating is proposed. We devise an approach for defining prior distributions on uncertain parameters that leverages the framework of imprecise probabilities to describe information obtained from highly varied sources, including prior knowledge and data, and expert opinion and physical constraints in terms of bounds on statistical expectations. This enhanced prior description is combined with measurement data and a physics-based model to yield the posterior distribution of uncertain, unobservable parameters. The feasibility of the proposed approach is demonstrated by investigating a synthetic problem of a quay wall.