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.

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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.

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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.

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Segregation of granular materials is a critical challenge in many industries, often aimed at being controlled or minimised. The discrete element method (DEM) offers valuable insights into this phenomenon. However, calibrating DEM models is a crucial, albeit time-consuming, step. Recently, using machine learning (ML)-based surrogate models (SMs) in the calibration process has emerged as a promising solution. Nevertheless, developing such SMs is challenging due to the high number of DEM simulations required for training. Additionally, choosing a suitable ML model is not trivial. This study aims to develop SMs that effectively link particle-particle and particle-wall DEM interaction parameters to segregation of a multi-component mixture. We evaluate several ML models, ranging from artificial neural networks to ensemble learning, that are trained on a very cost-effective dataset, employing Bayesian optimisation with cross-validation to tune their hyperparameters. Next, we introduce a novel transfer learning (TL)-based approach that leverages knowledge from a few scenarios to handle new “unseen” ones. This method enables the construction of adaptive SMs for unseen scenarios, such as a new initial configuration (IC) of granular mixtures, without the need for a full-sized dataset. Our findings indicate that Gaussian process regression (GPR) efficiently builds accurate SMs on a very small dataset. We also demonstrate that only a few samples are required to build an accurate SM for the unseen IC, which significantly reduces the data preparation burden. By incorporating one and five samples from unseen scenarios to update the TL-GPR-based surrogate model, the SM’s performance (based on ) on unseen scenarios improves by 17 and 47%, respectively. The insights and methodology presented in this study will facilitate and accelerate the development of accurate SMs for DEM calibration, assisting in developing reliable DEM models in a shorter timeframe.@en

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.

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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.

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In a wide range of disciplines, such as aeronautical, automotive, and structural engineering, infrared thermography (IRT) has demonstrated promising performance for inspecting and monitoring structures. This chapter provides a survey of IRT as a nondestructive assessment method for composite materials subjected to impact loads that cause critical damage scenarios inside the structure. The chapter starts with a general overview of the principles of IRT and its historical evolution. Various methodologies of thermography inspection, such as optically, mechanically, and inductively stimulated thermography, are described for the evaluation of impact damage in composite structures. In the heating waveforms and data processing section, the relevant processing techniques and data analysis algorithms for each type of the above-mentioned thermography methodologies based on the applied waveform are presented. Case studies of composite specimens suffering from impact damage are provided at the end of the chapter to demonstrate the applicability and performance of IRT inspection.@en

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.

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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.

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Health indicators are indices that act as intermediary links between raw SHM data and prognostic models. An efficient HI should satisfy prognostic requirements such as monotonicity, trendability, and prognosability in such a way that it can be effectively used as an input in a prognostic model for remaining useful life estimation. However, discovering or designing a suitable HI for composite structures is a challenging task due to the inherent complexity of the evolution of damage events in such materials. Previous research has shown that data-driven models are efficient for accomplishing this goal. Large labeled datasets, however, are normally required, and the SHM data can only be labeled, respecting prognostic requirements, after a series of nominally identical structures are tested to failure. In this paper, a semi-supervised learning approach based on implicitly imposing prognostic criteria is adopted to design a novel HI suitable. To this end, single-stiffener composite panels were subjected to compression-compression fatigue loading and monitored using acoustic emission (AE). The AE data after signal processing and feature extraction were fused using a multi-layer LSTM neural network with criteria-based hypothetical targets to generate an intelligent HI. The results confirm the performance of the proposed scenario according to the prognostic criteria.

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Acousto-ultrasonic composite transducers (AUCT), which are made of piezoceramic materials embedded in a reinforced polymeric matrix, are promising for the health monitoring of composite structures. However, when they are integrated into highly loaded thermoplastic composite structures, ensuring proper joining properties is a challenge. The conventional approach of attaching the AUCT using adhesive may not be sufficiently reliable in aeronautic applications for low surface energy materials such as polyaryletherketone composites, where surface treatments are needed for adhesion. Welding techniques can be used to create a joint in which the interface material interfuses with the AUCT embedment and the structure matrix, resulting in a homogeneous interface with properties comparable to the host structure matrix throughout its service life. With this in mind, the main objective of the present work is to investigate the viability of attaching AUCT to low-melting polyaryletherketone carbon fiber reinforced thermoplastic composite structures using the ultrasonic welding (UW) procedure and characterize the joint performance. The ultrasonic welded joint using an external energy director in the interface is investigated by comparing the findings to those of a reference AUCT system integrated into the structure with autoclave co-consolidation. Infrared thermography is employed to monitor the process, and a parameter study of the UW process is carried out. The AUCT survivability during the UW process is determined by measuring the capacitance, and C-scan is used to assess joint quality. The results show the challenges of attaching AUCT to thermoplastic composite structures using UW and surviving the procedure.@en

A health indicator (HI) serves as an intermediary link between structural health monitoring (SHM) data and prognostic models, and an efficient HI should meet prognostic criteria, i.e., monotonicity, trendability, and prognosability. However, designing a proper HI for composite structures is a challenging task due to the complex damage accumulation process during operational conditions. Additionally, designing a HI that is independent of historical SHM data (i.e., from the healthy state until the current state) is even more challenging as HI and remaining useful life prediction are time-dependent phenomena. A reliable SHM technique is required to extract informative time-independent data, and a powerful model is necessary to construct a proper HI from that data. The lamb wave (LW) technique is a useful SHM method that can extract such time-independent data. However, translating the LW data at each time step to the appropriate HI value is a challenge. AI—deep learning in this case—offers significant mathematical potential to meet this difficulty. A semi-supervised learning approach is developed to train the model using the simulated ideal HIs as the targets. The model uses the current LW data, without prior or subsequent data, to output the current HI value. Prognostic criteria are then calculated using the entire HI trajectory until the end-of-life. To validate the proposed approach, aging experiments from NASA’s prognostics data repository are used, which include composite specimens subjected to a tension-tension fatigue loading and monitored using the LW technique. The LW data is first processed using the Hilbert transform, and then, upper and lower signal envelopes in two states – baseline and current time – are used to feed the deep learning model. The results confirm the effectiveness of the proposed approach according to the prognostic criteria. The effect of different triggering frequencies of the LW system on the results is also discussed in terms of the prognostic criteria. @en

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.

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Under in-plane compressive load conditions, the growth of a delamination initially induced by an impact can be followed by a fast growth after a threshold level, which leads to a catastrophic failure in composite structures. To avoid reaching this critical level, it is essential to uncover the delamination size and growth pattern in real time. Ultrasonic Guided Waves (UGW) have a strong capability to interrogate and monitor the structure in real-time and thus track the growth of damage, which may occur during the flight cycles. Although various types of damage affect the monitored UGW signals, it is challenging to determine from the UGW signals what types of damage and at what rate of growth are occurring within the structure. UGW signals can be acquired at defined intervals and then analysed to possibly detect different types of damages, such as delamination, and to quantify the rate of damage growth over fatigue cycles. However, correlating the UGW-based Damage Indicators (DIs) with the specific type of damage, such as delamination, and damage growth is a challenging task as the relation between these DIs and the actual damage state is very complex. Therefore, in this study, a supervised Deep Neural Network-based (DNN) prediction model is proposed aiming to diagnose the delamination size of the composite structure by correlating the UGW-based DIs with the quantified time-varying delamination size. UGW data is collected through a network of permanently installed piezoelectric transducers (PZTs). The delamination size is obtained through ultrasonic C-Scan technique at defined cycles. DIs are extracted in time, frequency, and time-frequency domains and used as the input for the DNN-based regression model. Each sensor-actuator path is considered as an independent set of indicators, which are separated for training, validation, and testing purposes. The effect of the different paths on the delamination size prediction is presented along with the model performance on measured delamination growth in woven type composite sample. @en

The infrared thermography (IRT) technique has shown great potential with many applications in a variety of fields, such as aerospace, petroleum, civil engineering, and so forth. This chapter is designed to provide an overview of the method of IRT in non-destructive material evaluation. It begins with the general introduction and development of the IRT. It follows the basic principles of the electromagnetic spectrum and radiative energy concepts. Following the introduction of different types of thermography, applications in the non-destructive testing fields are provided. The next section focuses on recent trends and developments, in particular the integration of IRT with other technologies namely ultrasonic, acoustic emission, and so on. By assigning a data analysis section, data processing techniques are described by dividing them into two conventional and advanced categories. The numerical modeling and simulation of the IRT inspection process are then presented as beneficial applications. In addition, the relevant standards have been specified in a short separate section. To testify to the effectiveness of the IRT, a case study of a steel sample inspection is provided at the end of the chapter itself.

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Composite structures are highly valued for their strength-to-weight ratio, durability, and versatility, making them ideal for a variety of applications, including aerospace, automotive, and infrastructure. However, potential damage scenarios like impact, fatigue, and corrosion can lead to premature failure and pose a threat to safety. This highlights the importance of monitoring composite structures through structural health monitoring (SHM) and prognostics and health management (PHM) to ensure their safe and reliable operation. SHM provides information on the current state of the structure, while PHM predicts its future behavior and determines necessary maintenance. Health indicators (HIs) play a crucial role in both SHM and PHM, providing information on structural health and behavior, but accurate determination of these indicators can be challenging due to the complexity of material behavior and multiple sources of damage in composite structures. In the present work, a model containing a developed adaptive standardization, a dimension reduction sub-model, a time-independent sub-model, and a time-dependent sub-model is introduced to address this challenge. First, the raw data collected by the acoustic emission technique monitoring composite structures under fatigue loading is processed to provide plenty of statistical features. The extracted features are adaptively standardized according to the available data until the current time. Then, the principal component analysis algorithm is employed to reconstruct a few yet highly informative features out of those statistical features. An artificial neural network is used to regress the principal components to the HI that meets the prognostic criteria. Finally, the last sub-model takes into account the time dependency of HI values during fatigue loading. In comparison to other models, the results show superior performance.@en

Recently, companies all over the world have been focusing on the improvement of autonomous health management systems in order to enhance performance and reduce downtime costs. To achieve this, the remaining useful life predictions have been given remarkable attention. These predictions depend on the proper designing process and the quality of health indicators (HI) generated from structural health monitoring sensors based on prior established multiple prognostic evaluation criteria. Constructing such HIs from noisy sensory data demands powerful models that enable the automatic selection and fusion of features taken from those relevant measurements. Deep learning models are promising to autonomously extract features in scenarios with a huge volume of data without requiring considerable domain expertise. Nonetheless, the features established by artificial neural networks are complicated to comprehend and cannot be regarded as physical system characteristics. In this regard, the goal of this paper is to extend a new model; an interpretable artificial neural network that enables the automatic selection and fusion of features to construct the most appropriate HIs with remarkably fewer parameters. This model consists of additive and multiplicative layers that provide a feature fusion that better reflects the system’s physical properties. Additionally, the weights are discretized in two ways: a) using a ternary form with values {-1, 0, 1}, and b) relaxing the aforementioned ternary form by rounding the weights at the first decimal point in the range of [-1, 1]. Both discretization techniques have the ability to softly control the number of parameters that should be ignored. This trick guarantees interpretability for the neural network by extracting simple yet powerful equations representing the constructed HIs. Finally, the model’s performance is evaluated and compared with other approaches using a practical case study. The results show that the proposed approach's designed HIs are both interpretable and of high quality according to the criteria of the HI's evaluation.@en

Assessment of cultural heritage assets is now extremely important all around the world. Non-destructive inspection is essential for preserving the integrity of artworks while avoiding the loss of any precious materials that make them up. The use of Infrared Thermography is an interesting concept since surface and subsurface faults can be discovered by utilizing the 3D diffusion inside the object caused by external heat. The primary goal of this research is to detect defects in artworks, which is one of the most important tasks in the restoration of mural paintings. To this end, machine learning and deep learning techniques are effective tools that should be employed properly in accordance with the experiment’s nature and the collected data. Considering both the temporal and spatial perspectives of step-heating thermography, a spatiotemporal deep neural network is developed for defect identification in a mock-up reproducing an artwork. The results are then compared with those of other conventional algorithms, demonstrating that the proposed approach outperforms the others.@en

Assessment of cultural heritage assets is now extremely important all around the world. Non-destructive inspection is essential for preserving the integrity of the artworks while avoiding the loss of any precious materials that make it up. The use of Infrared Thermography (IRT) is an interesting concept since surface and subsurface faults can be discovered by utilizing the 3D diffusion inside the object caused by external heat. The primary goal of this research is to detect defects in artworks, which is one of the most important tasks in the restoration of mural paintings. To this end, a spatiotemporal deep neural network (STDNN) is utilized for defect identification in a mock-up reproducing an artwork, taking into account both the temporal and spatial perspectives of step-heating (SH) thermography. Finally, the outcomes are compared to those of other conventional algorithms.@en