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Delamination is a failure mechanism which is intrinsic of laminated fibre-reinforced plastics and possibly one of the major concerns of laminated composite structures, since, under certain conditions, delaminations can grow up to an hazardous extent without visible traces. In order to keep pace with recent condition-based maintenance requirements, proper validated diagnostic and prognostic methods which should be capable of operating on-line and in real time are required. In this respect, particle filters provide a consistent Bayesian framework, where the posterior distribution of the system degradation status is recursively approximated based on a time-growing stream of observations measuring the system response. However, the real-time operation capability of such methods is hindered by their requirements in terms of analysis time, which is mainly due to the complexity of the models they rely upon. Within this work, a particle filter framework, able to deal with the inherent stochasticity of fatigue delamination growth – while simultaneously relieving the computational burden associated with the evaluation of the trajectory likelihoods – is provided, leveraging on surrogate modelling strategies. Simultaneous diagnosis and prognosis of a simulated carbon fibre-reinforced plastics double cantilever beam specimen subject to fatigue delamination growth are performed, based on the observation of the strain field pattern acquired at some specific locations. The posterior probability density function of the delamination extent during propagation is updated at each inspection time as well as the probability density function of the remaining useful life. Ultimately, the adoption of the augmented state formulation allows for the estimation and updating of the joint probability density function of the parameters driving the stochastic delamination propagation model. Results demonstrate the feasibility and potential of the proposed approach as a tool able to monitor the progressing delamination while simultaneously providing estimates about the remaining useful life of composite structures.

Despite the promising application of Distributed Optical Fiber Sensors (DOFS) in monitoring damage in composite structures, their implementation outside academia is still unsatisfactory due to the lack of a systematic approach to assessing their damage detection performance. The existing tool developed for non-destructive evaluation, Probability of Detection (POD) curves, needs to be adapted for structural health monitoring applications to account for spatial and temporal dependency. Damage detection performance with DOFS is deeply related to the inherent variability sources of the system, the strain transfer properties of the optical fiber, and the loading conditions, which determine the damage-induced strain on the structure. This paper establishes a systematic approach based on the Length at Detection (LaD) method to qualify DOFS for damage detection in composites under different scenarios. Specifically, this study considers two DOFS with different strain transfer properties for monitoring delamination in carbon fiber reinforced polymers double-cantilever beam specimens under mode I quasi-static and fatigue loading. The POD curves derived from the LaD method confirm that this methodology can quantify the change in the detection performance due to the DOFS type and the loading conditions. The study also proposes a practical solution to compare POD curves obtained with different sample sizes, by introducing the concept of virtual specimens to simulate the lower confidence bound convergence.

Transverse cracking and crack induced delaminations growth are generally considered as the most relevant damage modes developing during the fatigue loading of composite laminates. So far, non-interactive damage progression schemes have been considered, arguing that transverse cracks saturate before the initiation of induced delaminations, despite concurrent damage accumulation has been experimentally acknowledged, also suggesting mutual interaction. In the present paper a simultaneous and interactive damage progression scheme based on fracture mechanics is proposed. A two-dimensional variational mechanics analysis approach is used to obtain the individual energy release rates and the interaction between damage modes is theoretically acknowledged. Also, a unique parameter is proposed accounting for both the damage modes accumulation levels, ruling the growth rates of the individual damage modes, and the characteristic damage state is questioned. Theoretical findings are then verified using multi-scale fatigue damage data from GFRP cross-ply laminate specimens subjected to uniaxial fatigue loading.

A key issue affecting the performances of every human-conceived engineering system is its degradation, fatigue crack growth being one of the major structural deterioration phenomena. Fatigue crack growth is usually modelled as a stochastic process: uncertainty sources lie both in the item and in the physical degradation process variability. Fatigue crack growth deserves close attention, especially considering that condition-based maintenance methodologies are recently experiencing a major drive to increase their technology readiness level, requiring validated diagnostic and prognostic methodologies which should be capable of operating online and in real-time. In this regard, particle filters provide a consistent Bayesian framework, where the posterior distribution of the system degradation state is recursively approximated based on a time-growing stream of observations measuring the system response, enabling, in general, increasingly informed lifetime estimates. However, the real-time operation capability of such methods is hindered by their requirements in terms of computational power, which is mainly due to the complexity of the structural models they rely upon. Within this work, a comprehensive particle filter framework, able to deal with fatigue crack growth uncertainty sources while simultaneously addressing the computational burden issue, is proposed. The algorithm structure enables to simultaneously perform the diagnosis and prognosis of fatigue crack growth, while the adoption of the augmented state formulation allows to address scenarios where the degradation process of fatigue crack growth fails to meet the degradation model ruling the particle filter. Artificial neural networks–based surrogate modelling is adopted at different stages and embedded within the particle filter algorithm, relieving the computational burden associated with the evaluation of the trajectory likelihoods as well as enabling a fast estimation of the remaining useful life. Both simulated and experimental data sets regarding fatigue crack growth in an aluminium aeronautical panel are used for the algorithm testing, additionally proving the validity and effectiveness thereof by means of common prognostic performance metrics.

Bayesian model updating has proven to be successful for inverse problem solutions, such as for the evaluation of the posterior probability distribution of the parameters of interest, conditional on the observations of some damagedependent features. Specifically, the sequential Monte-Carlo procedure generates possible damage evolution trajectories based on available process models and then assigns each trajectory a weight according to its likelihood. However, for realistic structures, computationally expensive numerical simulations might be required for the evaluation of the trajectory likelihoods. In this work, the computational problem is addressed by leveraging on surrogate modeling, while particle filtering provides the sequential Bayesian framework for performing simultaneous diagnosis and prognosis of a composite double cantilever beam specimen subject to fatigue delamination growth, based on observations of the strain field pattern acquired at some specific locations. The algorithm is successfully tested with respect to a case study of a propagating delamination.