Health indicators (HIs) are central to diagnosing and prognosing the condition of aerospace composite structures, enabling efficient maintenance and operational safety. However, extracting reliable HIs remains challenging due to variability in material properties, stochastic damage evolution, and diverse damage modes. Manufacturing defects (e.g. disbonds) and in-service incidents (e.g. bird strikes) further complicate this process. This study presents a comprehensive data-driven framework that learns HIs via two learning approaches integrated with multi-domain signal processing. Because ground-truth HIs are unavailable, a semi-supervised and an unsupervised approach are proposed: (i) a diversity deep semi-supervised anomaly detection (Diversity-DeepSAD) approach augmented with continuous auxiliary labels used as hypothetical damage proxies, which overcomes the limitation of prior binary labels and enables modelling of intermediate degradation, and (ii) a degradation-trend-constrained variational autoencoder (DTC-VAE), in which the monotonicity criterion is embedded via an explicit trend constraint. Guided waves with multiple excitation frequencies are used to monitor single-stiffener composite structures under fatigue loading. Time, frequency, and time–frequency representations are explored, and per-frequency HIs are fused via unsupervised ensemble learning to mitigate frequency dependence and reduce variance. Using fast Fourier transform features, the models achieved fitness scores of 81.6% (Diversity-DeepSAD) and 92.3% (DTC-VAE), indicating improved monotonicity and consistency over existing baselines. The proposed history-independent framework, supported by prognostic metrics–guided Bayesian optimisation and excitation frequency-agnostic HI fusion, enables the estimation of more robust HIs for aeronautical composite structures.

Predicting the remaining useful life (RUL) of composite structures is particularly challenging in impact-damaged carbon fiber–reinforced polymers (CFRPs) under compressive fatigue, where delamination growth with complex morphology and stochastic progression often governs failure. Guided wave–based structural health monitoring (GW-SHM) enables sensitive damage characterization, yet RUL prediction remains difficult due to the strong dependence of GW–delamination interactions on excitation frequency and damage geometry. Physics-based models often struggle to generalize beyond specific configurations, whereas purely data-driven models can capture complex patterns but typically lack consistency with the underlying physical mechanisms. This study introduces a multi-level, frequency-aware prognostic framework that combines the adaptability of deep learning with the physical interpretability of engineered features. GW signals acquired at multiple excitation frequencies are transformed into time- and time–frequency representations, while damage indicators are derived through temporal segmentation. These indicators are correlated with delamination growth measured by C-scan inspections, providing a link between signal-derived features and physical damage evolution. The multi-level architecture integrates convolutional neural networks, multilayer perceptrons, and long short-term memory layers to capture complementary aspects of degradation. Experimental assessment on seven specimens demonstrates that the proposed framework achieves a minimum mean absolute percentage error (MAPE) of 1.904, corresponding to 11% and 55% improvements over the highest- and lowest-performing single-frequency baselines at 160 kHz and 100 kHz, respectively. The results confirm that integrating GW signal processing with deep learning yields robust and physically consistent RUL predictions for impact-damaged CFRPs, while enhancing the interpretability of prognostic outcomes.

Monitoring the structural integrity of aeronautical structures is critical for safety, reducing maintenance costs, and enabling predictive maintenance. However, raw structural health monitoring (SHM) data are often noisy, high-dimensional, and difficult to interpret. To enable condition-based maintenance, it is essential to extract health indicators (HIs)—quantitative representations of structural degradation that evolve consistently over time. Accurately extracting HIs for composite structures is particularly challenging due to complex material behavior and multiple damage sources. While deep learning models offer potential, their application is limited by the lack of run-to-failure data and ground-truth HI labels. To address these challenges, this study proposes a novel approach that divides HI modeling into two tasks: time-independent (spatial) and time-dependent (temporal). This separation allows more effective data utilization, especially in the time-independent case. A semi-supervised spatial model is first developed and fine-tuned using a Bayesian algorithm with a coupled physics-based loss function that integrates both prognostic criteria and simulated labels—explicitly through the former and implicitly through the latter—embedding degradation physics into training. The study also introduces a new adaptive standardization technique for fatigue-based SHM and systematically evaluates principal component analysis (PCA)-based methods for dimensionality reduction prior to spatial and temporal modeling, simplifying subsequent network architectures. In the final stage, following time-based resampling, a semi-supervised temporal model captures HI evolution, with ensemble learning enhancing robustness. Validation on single-stiffener composite panels under fatigue loading, monitored via acoustic emission sensors, confirms the framework's generalizability and performance—achieving up to 90% (±2%) accuracy in prognostic metrics.

Abstract: Remaining useful life predictions depend on the quality of health indicators (HIs) generated from condition monitoring sensors, evaluated by predefined prognostic metrics such as monotonicity, prognosability, and trendability. Constructing these HIs requires effective models capable of automatically selecting and fusing features from pertinent measurements, given the inherent noise in sensory data. While deep learning approaches have the potential to automatically extract features without the need for significant specialist knowledge, these features lack a clear (physical) interpretation. Furthermore, the evaluation metrics for HIs are nondifferentiable, limiting the application of supervised networks. This research aims to develop an intrinsically interpretable ANN, targeting qualified HIs with significantly lower complexity. A semi-supervised paradigm is employed, simulating labels inspired by the physics of progressive damage. This approach implicitly incorporates nondifferentiable criteria into the learning process. The architecture comprises additive and newly modified multiplicative layers that combine features to better represent the system’s characteristics. The developed multiplicative neurons are not restricted to pairwise actions, and they can also handle both division and multiplication. To extract a compact HI equation, making the model mathematically interpretable, the number of parameters is further reduced by discretizing the weights via a ternary set. This weight discretization simplifies the extracted equation while gently controlling the number of weights that should be overlooked. The developed methodology is specifically tailored to construct interpretable HIs for commercial turbofan engines, showcasing that the generated HIs are of high quality and interpretable.

Prognostic methods broadly fall into two categories—model-based and data-driven—both of which have shown effectiveness across a range of engineering applications. Model-based approaches require an explicit representation of the degradation process, defining failure as the point when the physical damage state exceeds a predetermined threshold. Data-driven methods, on the other hand, leverage sensor data to directly predict end-of-life (EOL) or related prognostic information. Although both approaches offer insights that could be complementary and potentially fused, most existing fusion methods either combine the outputs from multiple methods or adopt a data-driven method to assist the model-based method. To further enhance the prognostic performance, this study proposes a fusion-based prognostic approach in which the output of one method is actively used to update the model of the other through either the crossover operator or the likelihood function. The proposed approach is validated using both an aluminum fatigue dataset and the Prognostics and Health Management (PHM) 2010 cutter wear dataset, demonstrating improved prognostic accuracy compared to either method used independently.

Damage imaging plays a crucial role in structural health monitoring (SHM) systems for fast and efficient damage assessment. Delay-and-sum (DAS) beamforming is a widely used algorithm in non-destructive testing for damage imaging, but its effectiveness is often compromised by the use of sparse ultrasonic transducer arrays and the difficulty in detecting progressive delamination larger than the wavelength using guided wave-based methods under fatigue loading. Although X-ray imaging offers detailed assessments of progressive delamination, its application is still limited due to the need to interrupt fatigue loading cycles and its high operational cost. To this end, we propose a novel Damage Imaging framework that uses the fine-tuned Conditional Diffusion Model for SHM systems (DI-CDM). Leveraging the powerful image generation capabilities of diffusion models, the framework was fine-tuned by combining DAS beamforming images derived from ultrasonic sparse array data with X-ray images captured during fatigue loading cycles of the composite structures. The proposed approach can generate damage images that reveal the progression of delamination size in the fatigue loading process. The framework was validated through numerical simulations and experimental data from NASA datasets for composite structures, demonstrating its potential and effectiveness by applying diffusion models in SHM applications to enable fast, high-resolution damage imaging.

Designing health indicators (HIs) for aerospace composite structures that demonstrate their health comprehensively, including all types of damage that can be adaptively updated, is challenging, especially under complex conditions like impact and compression-fatigue loadings. This paper introduces a new AI-based approach to designing reliable HIs (fulfilling requirements—monotonicity, prognosability, and trendability—referred to as ’Fitness’) for single-stiffener composite panels under fatigue loading using acoustic emission sensors. It incorporates complete ensemble empirical mode decomposition with adaptive noise for feature extraction, semi-supervised base deep learner models made of long short-term memory layers for information fusion, and a semi-supervised paradigm to simulate labels inspired by the physics of progressive damage. In this way, nondifferentiable prognostic criteria are implicitly implemented into the learning process. Ensemble learning, especially using a semi-supervised network built with bidirectional long short-term memory, improves HI quality while reducing deep learning randomness. The Fitness function equation has been modified to provide a more trustworthy foundation for comparison and enhance the practical reliability of the standard in prognostics and health management. Ablation experiments are conducted, including variations in dataset division and leave-one-out cross-validation, confirming the generalizability of the approach.

Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-024-78455-7, published online 06 November 2024 The original version of this Article contained typographical errors in Equations. In Equation 8, where now reads: In Equation 17, where now reads: In Equation 18, where now reads: In Equation 24, where now reads: The original Article has been corrected.

Developing comprehensive health indicators (HIs) for composite structures encompassing various damage types is challenging due to the stochastic nature of damage accumulation and uncertain events (like impact) during operation. This complexity is amplified when striving for HIs independent of historical data. This paper introduces an AI-driven approach, the Hilbert transform-convolutional neural network under a semi-supervised learning paradigm, to designing reliable HIs (fulfilling requirements, referred to as 'fitness'). It exclusively utilizes current guided wave data, eliminating the need for historical information. Ensemble learning techniques were also used to enhance HI quality while reducing deep learning randomness. The fitness equation is refined for dependable comparisons and practicality. The methodology is validated through investigations on T-single stiffener CFRP panels under compression-fatigue and dogbone CFRP specimens under tension-fatigue loadings, showing high performance of up to 93% and 81%, respectively, in prognostic criteria.

The prognostic of the Remaining Useful Life (RUL) of composite structures remains a critical challenge as it involves understanding complex degradation behaviors while it is emerging for maintaining the safety and reliability of aerospace structures. As damage accumulation is the primary degradation indicator from the structural integrity point of view, a methodology that enables monitoring the damage mechanisms contributing to the structure's failure may facilitate a reliable and effective RUL prognosis. Therefore, in this study, an integrated methodology has been introduced by targeting the RUL and progressive delamination state via Deep Neural Network (DNN) trained with Guided wave-based damage indicators (GW-DIs). These GW-DIs are obtained via signal processing, Hilbert transform, and Continuous Wavelet Transform. This work uses GW-DIs to train and test the proposed model within two frameworks: one focusing on individual sample analysis to explore path dependency in RUL and delamination prognosis and another on an ensembled dataset to propose a generic model across varying stress scenarios. Results from the study indicate that proposed DNN frameworks are capable of encapsulating fast and slow degradation scenarios to evaluate the RUL prediction with associated delamination progress, which could contribute to ensuring the integrity and longevity of critical life-safe structures.

In this research, a generalized machine learning (ML) framework is proposed to estimate the fatigue life of epoxy polymers and additively manufactured AlSi10Mg alloy materials, leveraging their failure surface void characteristics. An extreme gradient boosting algorithm-based ML framework encompassing Synthetic Minority Over-sampling TEchnique (SMOTE), categorical data encoding, and external loop cross-validation is developed to evaluate the fatigue life across materials. The influence of different training strategies based on materials, input features, encoding method, and data standardization on the model performance is explored. Additionally, the importance of anti-data-leakage and anti-overfitting measures over the ML model performance is addressed. The result shows that the data-leakage-free, external loop cross-validated model can estimate the fatigue life of selective epoxy polymers and metal alloys with an average R² of 0.71 ± 0.06 using a mere 12 to 27 experimental data points per material category. Whereas the model trained with data-leakage and overfitting results in high R² of 0.9.

Acousto-ultrasonic composite transducers (AUCTs), comprising piezoceramic materials in a reinforced polymeric matrix, show promise for structural health monitoring in composite structures. Challenges arise when integrating AUCTs onto highly loaded thermoplastic composites, especially low-surface-energy materials like polyaryletherketone composites. To address this, the study explores the viability of attaching AUCTs to low-melting polyaryletherketone carbon fiber-reinforced thermoplastic composite structures using ultrasonic welding. This welding technique forms a joint where the interface material fuses with the AUCT embedment and the structure matrix, providing a reliable and automatable process. The investigation includes a comparative analysis of an ultrasonic welded joint with an external energy director and a reference AUCT system integrated using a vacuum bagging oven procedure. Results highlight the potential of AUCT configurations integrated by ultrasonic welding as an alternative solution, acknowledging challenges that persist for further development and increased reliability in structural health monitoring applications.

A health indicator (HI) is a valuable index demonstrating the health level of an engineering system or structure, which is a direct intermediate connection between raw signals collected by structural health monitoring (SHM) methods and prognostic models for remaining useful life estimation. An appropriate HI should conform to prognostic criteria, i.e., monotonicity, trendability, and prognosability, that are commonly utilized to measure the HI's quality. However, constructing such a HI is challenging, particularly for composite structures due to their vulnerability to complex damage scenarios. Data-driven models and deep learning are powerful mathematical tools that can be employed to achieve this purpose. Yet the availability of a large dataset with labels plays a crucial role in these fields, and the data collected by SHM methods can only be labeled after the structure fails. In this respect, semi-supervised learning can incorporate unlabeled data monitored from structures that have not yet failed. In the present work, a semi-supervised deep neural network is proposed to construct HI by SHM data fusion. For the first time, the prognostic criteria are used as targets of the network rather than employing them only as a measurement tool of HI's quality. In this regard, the acoustic emission method was used to monitor composite panels during fatigue loading, and extracted features were used to construct an intelligent HI. Finally, the proposed roadmap is evaluated by the holdout method, which shows a 77.3% improvement in the HI's quality, and the leave-one-out cross-validation method, which indicates the generalized model has at least an 81.77% score on the prognostic criteria. This study demonstrates that even when the true HI labels are unknown but the qualified HI pattern (according to the prognostic criteria) can be recognized, a model can still be built that provides HIs aligning with the desired degradation behavior.