Open Access

Engineering structures experience performance degradation due to progressive damage throughout their lifespan. Factors responsible for this include mechanical loading, electrochemical processes such as corrosion, and manufacturing and material defects introduced during construction, among others. Typically, damage manifests as cracks, failed prestressing cables, and similar issues, which can eventually lead to structural failure. The onset of damage is characterised by a localised reduction in stiffness in the affected area. By using current data from the structure within its computational model, predictions about its ongoing damage state can be made, helping to prevent failures. Additionally, it is necessary to provide probabilistic estimates of these predictions, considering the presence of model discrepancy and noise in the data. Uncertainty propagation within the Bayesian inference framework helps in getting these estimates. The aim of this study is the stochastic localisation and quantification of damage. Parameters of a computer model that characterise structural damage are estimated using modal response data derived from Stochastic Subspace Identification (SSI) performed on acceleration measurements. An inverse problem is formulated and solved using Bayesian inference. A linear elastic Finite Element (FE) computer model is used, reparameterised to incorporate damage parameters. A damage zone is defined as a sub-domain with a spatially varying damage field that models a reduction in the nominal Young’s modulus within that sub-domain. An arbitrary number of such zones are assumed to exist within the domain. Sparsity-promoting priors are applied to each zone, serving as a switch to signify the presence (on) or absence (off) of the respective zone [Hirsh et al.]. During inference, these priors prevent over-parameterisation of the model and assist in model selection. The locations of damage zones, their number, and the local reduction in Young’s modulus together constitute the inferred parameter set. A reduced-order model for the sensed locations within the domain is created using the Iterative Improved Reduction System (IIRS) method [Friswell et al.]. The likelihood function favors minimal errors in the eigenvalue problem when modal data, combined with the damage parameterised reduced-order model matrices, are inserted into the eigenvalue problem. Modal data, along with its uncertainty estimates, is obtained from SSI. The uncertainty is then propagated using the delta method to determine the uncertainty in the eigenvalue problem error. The posterior distribution of the damage parameters is sampled using Markov Chain Monte Carlo (MCMC) sampling. Experimental acceleration data from a T-shaped reinforced concrete structure is used to test the method. The structure is progressively damaged through increasing load cycles. Acceleration measurements are taken after each load cycle, and simultaneously, the locations of observed cracks on the structure are documented. The damage locations identified in the computer model are then compared with the experimental observations. Although the proposed scheme is applied to cracks in this case, it can be extended to other forms of failure modes, which would be parameterised differently in the model.

Computer models of civil structures like wind turbines, dams, bridges etc., find their use in predicting the structure’s behaviour under different loading conditions. The structure response might change over a period of time for the same loading conditions if some form of damage, e.g., cracks build up in the structure. A previously calibrated model thus won’t produce reliable results in this situation. The model needs to account for the damage to make reliable predictions. The goal here is to predict the location of cracks i.e., damage regions and the corresponding magnitude of damage in these regions. The response e.g., strain, eigenfrequency of a structure that has undergone damage if measured could be used to identify regions of damage in it. In order to perform this identification, the Bayesian inference is deployed. Each crack is modelled as a function that approximates the failure mechanics. A certain number of these cracks are assumed to be distributed in the domain. Their positions and their corresponding damage magnitude are put in as priors. The latter is defined as a sparsifying prior [1] that promotes sparsity in the set of inferred parameters. Therefore, on performing the inference some of the initially assumed cracks are discarded and the remaining cracks are identified and located. The modal data providing the eigenfrequency response of a concrete slab under an increasing load is used for the inference problem. The increasing damage is marked by a decreasing eigenfrequency response of the slab. Horizontal cracks that appear as the slab undergoes damage are identified, located and their contribution to the overall damage magnitude is identified.