###### Abstract  
Composite materials are extensively used in aircraft structures, wherein they are subjected to cyclic loads and subsequently impact-induced damages. Progressive fatigue degradation can lead to catastrophic failure. This highlights the need for an efficient prognostic framework to predict crack propagation in the field of structural health monitoring (SHM) of composite structures to improve functional safety and reliability. However, achieving good accuracy in crack growth prediction is challenging due to uncertainties in the material properties, loading conditions, and environmental factors. This paper presents a particle-filter-based online prognostic framework for damage prognosis of composite laminates due to crack-induced delamination and fiber breakage. An optimized Paris law model is used to describe the damage propagation in glass-fiber-reinforced polymer (GFRP) laminates subject to low-velocity impacts. Our proposed methodology deduces the jump energy/inflection point online wherein the damage growth switches from rapid degradation to slow degradation. The prediction results obtained are compared with the conventional Paris law model to validate the need for an optimized bimodal crack growth propagation model. The root mean square error (RMSE) and remaining useful life (RUL) prediction errors are used as the prognostic metrics. damage prognosis; particle filters; remaining useful life; composite materials; crack propagation; delamination +
Footnote †: journal: Medicalstochasticity and predict the remaining useful life of materials. In general, damage prognosis methodologies are broadly categorized as physics-based, data-driven, and hybrid methods. Physics-based methods rely on mathematical/physical models formulated by understanding the root cause of the underlying failure mechanisms. These models help to forecast the failure progression by estimating the model parameters. The accuracy of the model-based methods depends on the relevance of the physical model (and its inherent assumptions and hypothesis) that best describes the failure/degradation mechanism. In literature, there are several research works on probability-based methods for structural prognosis. Bayesian estimation techniques are popular choices for prognosis for non-linear components/devices owing to their ability to address uncertainties. Additionally, Bayesian estimation methods do not make assumptions of linearity and Gaussian noise [5; 6]. To list a few, [PERSON] et al. [7] considered two degradation parameters, namely, micro-crack density and stiffness loss simultaneously, and formulated a damage propagation model for the composite laminate structures. Subsequently, a particle-filter-based prognostic approach with stochastic embedding was used to deduce the remaining useful life (RUL). The proposed methodology was tested on data collected from run-to-failure tension-tension experiments on carbon-fiber-reinforced polymer (CFRP) cross-ply laminates. The authors further extended their work to address the model uncertainty by choosing five different candidate models [8]. These models were parameterized using global sensitivity analysis and then ranked based on the accuracy of predictions using a Bayesian framework. The authors concluded from their investigation that a simple shear-lag model was the most effective. Similarly, [PERSON] et al. [9] considered four different degradation models for fatigue crack growth: Paris-Erdogan, polynomial, global function-based, and curve fitting models. The authors proposed an ensemble strategy to combine all the four degradation models using Best-Worst Weighted Vote (BWWV) strategy and then predicted the remaining fatigue life using the particle filter framework once again. However, their methodology has not been tested and validated on a real dataset to evaluate its robustness and prediction accuracy. In contrast, data-driven methods rely on available condition monitoring data and do not require any physical model for RUL prediction.