Data-driven methodologies have found increasing usage in the last decade for remaining useful life (RUL) prognostics of composite materials utilizing structural health monitoring (SHM) data. Of particular interest is the reliable RUL prediction in cases where the end-of-life is not in between the extreme values within the testing dataset. For example, when unexpected phenomena that severely compromise the structural integrity occur during the service life. Such cases are often referred as outliers and the RUL prognosis based on a data-driven model that learns from past data is often erroneous. This study addresses this challenge by proposing a new stochastic model; the Similarity Learning Hidden Semi Markov Model (SLHSMM), an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). Through the utilization of a nonparametric discrete distribution, which characterizes the similarity between the testing structure and the training structures, a dynamic re-estimation process is employed. This process assigns higher importance to the training structures that display greater similarity to the testing one. As a result, the estimated parameters effectively capture the specific characteristics of the testing structure. The training and testing SHM data sets consist of strain measurements collected from a case study where carbon–epoxy single-stringered panels, are subjected to constant, variable, and random amplitude fatigue loading until failure. RUL estimations from the SLHSMM, the NHHSMM, and the Gaussian Process Regression (GPR) are compared. The SLHSMM clearly outperforms its classical counterpart and GPR providing more accurate outlier and inlier prognostics, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data into a prognostic platform.

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In recent years, prognostics gained attention in various industries by optimizing maintenance, boosting operational efficiency, and preventing costly downtime. Central to prognostics is the Remaining Useful Life (RUL), representing the critical time before system failure. Deep learning advancements facilitate RUL forecasting by extracting features from diverse data formats such as time series, images, or sequences thereof, in one, two, or three dimensions, respectively. Yet, predicting RUL from image sequences often relies heavily on resource-intensive techniques like digital image correlation, complicating data acquisition. To address challenges with high-dimensional data and unreliable models, this study introduces ISTRUST, an innovative Transformer-based architecture. ISTRUST (Interpretable Spatiotemporal TRansformer for Understanding STructures) tackles the dual challenges posed by high-dimensional data and the black-box nature of existing models. Leveraging Transformers’ attention mechanism, ISTRUST breaks down the spatiotemporal domain, effectively realizing interpretable RUL predictions under uncertainty using only sparse raw image sequences as input. Evaluated on fatigue-loaded composite samples showcasing crack propagation, ISTRUST interprets the relation between cracks and RUL via the attention mechanism. The results substantiate its capacity to interpret and clarify instances in which predictions may exhibit variability in accuracy. Through the attention mechanism, a strong correlation between the model’s spatiotemporal focus and the RUL predictions is established, making it, to the best of our knowledge, the first model to provide interpretable stochastic RUL predictions directly from sequential images of this nature.@en

An increasing interest for Structural Health Monitoring has emerged in the last decades. Acoustic emission (AE) is one of the most popular and widely studied methodologies employed for monitoring, due to its capabilities of detecting, locating and capturing the evolution of damage. Most literature so far, has employed AE for characterizing damage mechanisms and monitoring propagation, while only a few employ it for real time monitoring and even fewer for Remaining Useful Life (RUL) prognosis. In the present work, we demonstrate a methodology for leveraging AE recordings for prognostics of composite aerospace structures. Single stiffened CFRP panels are subjected to a variety of compressive fatigue loadings, while AE sensors monitor the panels’ degradation in real time. Several AE features, both from the time and frequency domains, are utilized to identify features capable of capturing the degradation and used as Health Indicators for RUL prognosis. The choice of Health Indicators is predominantly made based on three prognostic attributes, i.e. monotonicity, trend and prognosability, which can overall affect the prognostic performance. RUL prediction of the panels is performed by employing two prominent machine learning algorithms, i.e. Gaussian Process Regression and Artificial Neural Networks. It is evidenced that the proposed AE-based methodology is highly capable to be utilized for RUL prediction of composite structures under variable loading conditions.

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In the past decade, data-driven methodologies have gained increasing popularity, offering a foundation for predicting the remaining useful life (RUL) of engineering systems and structures using condition monitoring (CM) data. A particularly intriguing challenge lies in accurately predicting the RUL of systems that exhibit exceptional performance, whether underperforming or overperforming, owing to unforeseen phenomena occurring during their operational life. These unique systems, often referred to as outliers, pose a formidable challenge for RUL prediction. This research addresses this challenge by introducing a novel data-driven model, which is known as the Similarity Learning Hidden Semi-Markov Model (SLHSMM) and extends the capabilities of the Non-Homogeneous Hidden Semi-Markov Model (NHHSMM). The training dataset comprises strain data obtained from open-hole carbon-epoxy specimens exposed solely to fatigue loading. In contrast, the validation-testing dataset includes strain data from two specimens subjected to both fatigue and in-situ impact loading, representing an unexpected and previously unseen event in the training data. The study compares RUL estimations generated by the SLHSMM and NHHSMM. The results indicate that the SLHSMM outperforms the NHHSMM, offering superior accuracy in predicting outliers' RUL. This underscores its capability to adapt to unexpected phenomena and seamlessly incorporate unforeseen data into prognostics.

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We present a generic methodology for developing a Health Indicator out of strain-based Structural Health Monitoring data suitable for implementation in prognostic tasks. For this purpose, an in-house test campaign is launched. Single-stringered composite panels are subjected to compression-compression fatigue with the strains being monitored with Fiber Bragg Grating sensors located along the stringers’ feet. Three different fatigue scenarios with increased complexity are investigated i.e. constant amplitude fatigue, variable amplitude fatigue and finally random amplitude (spectrum) fatigue. In this paper, we propose a fusion scheme based on Genetic Algorithms, with the resulted fused Health Indicator achieving high monotonicity and prognosability, both crucial attributes for an enhanced performance of prognostic algorithms. Finally, a popular machine learning algorithm, i.e. Gaussian Process Regression, is employed in order to predict the Remaining Useful Life of the panels in the test set. It is evidenced that the newly proposed fused Health Indicator predicts the Remaining Useful Life far more accurately as several popular performance metrics indicate. The methodology retains a data agnostic character able to be applied in Structural Health Monitoring data from different sensing technologies.

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Prognosis of the Remaining Useful Life (RUL) of a structure from Structural Health Monitoring data is the ultimate level in the SHM hierarchy. Reliable prognostics are key to a Condition Based Maintenance paradigm for aerospace systems and structures. In the present work, we propose a methodology for RUL prognosis of generic aeronautical elements i.e. single stringered composite panels subjected to compression/compression fatigue. Strain measurements are utilized in this direction via FBG sensors bonded to the stiffener feet. The strain data collected during the fatigue life are processed and used for the RUL prognosis. In order to accomplish this task, it is essential to produce Health Indicators (HIs) out of raw strain that can properly capture the degradation process. To create such HIs a new pre/post-processing technique is employed and a variety of different HIs are developed. The quality of the HIs can enhance the performance of the prognostic algorithms, hence a fusion methodology is proposed using genetic algorithms. The resulted fused HI is used for the RUL estimation of the SSCPs. Gaussian processes and Hidden Semi Markov Models are employed for RUL prognosis and their performance is compared. Despite the complexity the raw data we demonstrate the feasibility of successful RUL prognostics in a SHM-data driven approach.

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We investigate the performance of three different data-driven prognostic methodologies towards the Remaining Useful Life estimation of commercial aircraft brakes being continuously monitored for wear. The first approach utilizes a probabilistic multi-state deterioration mathematical model i.e. a Hidden Semi Markov model whilst the second utilizes a nonlinear regression approach through classical Artificial Neural Networks in a Bootstrap fashion in order to obtain prediction intervals to accompany the mean remaining life estimates. The third approach attempts to leverage the highly linear degradation data over time and uses a simple linear regression in a Bayesian framework. All methodologies, when properly trained with historical degradation data, achieve excellent performance in terms of early and accurate prediction of the remaining useful flights that the monitored set of brakes can safely serve. The paper presents a real-world application where it is demonstrated that even in non-complex linear degradation data the inherent data stochasticity prohibits the use of a simple mathematical approaches and asks for methodologies with uncertainty quantification.

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This paper presents the results for an experimental campaign of in-situ impact during tension-tension fatigue loading for open-hole carbon fibre reinforced polymer specimens. High-speed low energy impact was introduced to the specimen with the use of a canon, which was attached to testing bench enabling the impact without the need to remove the specimens from the test bench. Digital Image Correlation, C-scan and Acoustic Emission were utilized to record health monitoring data for damage diagnostics. A strain-based criterion was used to identify a common threshold for the timing of impact ensuring a fair comparison between the different tests. The results indicate that while an impact causes the total amount of damage to increase as one would expect, it does not necessarily increase the damage level in the critical area where final fracture occurs. A dependence on the moment of impact with the fatigue failure was found for specimens subjected to impact before the initiation of the fatigue loading. In contrast, impacting specimens in the presence of fatigue damage had no detrimental effect on the fatigue life, although it was observed that the damaged area was enlarged. Overall, the paper showcases the need to study systemically the effect of in-situ impact on the fatigue life in order to understand better the implications that may be introduced to the integrity of a composite structure.

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Data driven probabilistic methodologies have found increasing use the last decade and provide a platform for the remaining useful life (RUL) prediction of composite structures utilizing health-monitoring data. Of particular interest is the RUL prediction of composite structures that either underperform or outperform due to unexpected phenomena that might occur during their service life. These composite structures are referred as outliers and the prediction of their RUL is a challenge. This study addresses this challenge by proposing a new data-driven model; the Adaptive Non-Homogenous Hidden Semi Markov Model (ANHHSMM), which is an extension of the NHHSMM. The ANHHSMM uses diagnostic measures, which are estimated based on the training and testing data, and it adapts the trained parameters of the NHHSMM. The training data set consists of acoustic emission data collected from open-hole carbon–epoxy specimens, subjected to fatigue loading, while the testing data set consists of acoustic emission data collected from specimens, subjected to fatigue and in-situ impact loading, which can be considered as an unseen event for the training process. ANHHSMM provides better predictions in comparison to the NHHSMM for all the cases, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data to the prognostics course.

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In this paper, temperature measurements are utilized to develop health indicators based on principal component analysis toward the probabilistic estimation of the remaining useful life (RUL) of reciprocating compressors in service. Temperature degradation histories obtained from 13 actual valve failure cases constitute the training data in a data-driven prognostic approach. Two data-driven prognostic methodologies are presented and proposed based on probabilistic mathematical models, i.e., gradient boosted trees and nonhomogeneous hidden semi-Markov models. The training and testing process of all models is described in detail. RUL prognostics in unseen data are obtained for all models. Beyond the mean estimates of the RUL, the uncertainty associated with the point prediction is quantified and upper/lower confidence bounds are also estimated. Prediction estimates for 12 real-life failure cases are presented and the pros and cons of each model's performance are highlighted. Several metrics are utilized to assess the performance of the prognostic algorithms and conclusions are drawn regarding the prognostic capabilities of each of them.

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Prognostics is an emerging field of research that enables the real-time health assessment of an engineering system and the prediction of its future state based on up-to-date information. This field integrates various scientific disciplines including physics/mechanics, computational statistics and probabilistic modeling, machine learning and sensing technologies. The main goal is the prediction of the remaining useful life (RUL) of the engineering system while it is in-service. Lately, there is an effort to study and predict the future status of engineering systems that exhibit a complex degradation process. The availability of condition monitoring (CM) data, the constantly increasing computational power, the development of machine learning algorithms and the advancements on the physics/mechanics for several engineering systems form a solid foundation to achieve that goal. Among the engineering systems that exhibit a complex degradation process are composite structures. Composite structures have made a significant mark in numerous industries, driven by advantages in structural efficiency, performance, versatility and cost. It is well known that the damage accumulation process of composite structures depends on several parameters, i.e. the type of material and the lay-up, the loading frequency and sequence, the manufacturing process. Additionally, the multi-phase nature of composites and the variation of defects result in a stochastic activation of the different failure mechanisms. So, one expects that the long-term behaviour of two comparable composites structures, subjected to comparable environmental and loading conditions, will differ and that makes the fatigue damage analysis, and consequently the prediction of RUL, very complex tasks. This difference is profound especially when unexpected phenomena may occur. The goal of this research is to develop a new RUL prediction model that is able to learn from unexpected phenomena and adapt its parameters accordingly. The model is composed of three elements; 1) sensing techniques to acquire online CM data, 2) machine learning algorithm for developing a damage modelling strategy and 3) stochastic modelling for uncertainty quantification. Based on the literature review, it was concluded that a frequentist data-driven model has the potential to fulfil the research goal and an extension of the Non-Homogenous Hidden Semi Markov model (NHHSMM) is a good candidate. The first step was to design the structure of the RUL prediction model and define its elements. The next step was to develop the extension of the NHHSMM, and verify its correctness and robustness, utilizing simulated Monte-Carlo (MC) data. A series of assumptions was necessary in order to frame the applicability of the model towards composite structures and to achieve an efficient prediction process. @en

This chapter presents a data-driven probabilistic framework for the in-situ prognostics of composite structures subjected to fatigue loading. The framework deals with the real-time estimation of the remaining useful life based on health monitoring data and a multistate degradation model, the nonhomogeneous hidden semi-Markov model. The motivation of this work lays on the need to predict the remaining useful life accounting for the complex phenomenon of fatigue damage accumulation and the numerous uncertainties that affect it. The methodology was demonstrated during fatigue tests of open-hole carbon epoxy specimens under R = 0. Acoustic emission and strain data were used to extract features sensitive to the fatigue degradation process and a data fusion process was proposed aiming to enhance the prognostics performance. Eight metrics were used to compare the performance between the acoustic emission data, strain and fused data. It was found that based on the selected data fusion process, strain data provided the best predictions.

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In this paper, the discharge voltage is utilized as a critical indicator towards the probabilistic estimation of the Remaining Useful Life until the End-of-Discharge of the Lithium-Polymer batteries of unmanned aerial vehicles. Several discharge voltage histories obtained during actual flights constitute the in-house developed training dataset. Three data-driven prognostic methodologies are presented based on state-of-the-art as well as innovative mathematical models i.e. Gradient Boosted Trees, Bayesian Neural Networks and Non-Homogeneous Hidden Semi Markov Models. The training and testing process of all models is described in detail. Remaining Useful Life prognostics in unseen data are obtained from all three methodologies. Beyond the mean estimates, the uncertainty associated with the point predictions is quantified and upper/lower confidence bounds are also provided. The Remaining Useful Life prognostics during six random flights starting from fully charged batteries are presented, discussed and the pros and cons of each methodology are highlighted. Several special metrics are utilized to assess the performance of the prognostic algorithms and conclusions are drawn regarding their prognostic capabilities and potential.

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This paper examines diagnostics and prognostics of Lithium-Polymer (Li-Po) batteries for unmanned aerial vehicles (UAVs). Several discharge voltage histories obtained during actual indoor flights constitute the training data for a data-driven approach, utilizing the Non-Homogenous Hidden Semi Markov model (NHHSMM). NHHSMM is a suitable candidate as it has a rich mathematical structure, which is capable of describing the discharge process of Li-Po batteries and providing diagnostic and prognostic measures. Diagnostics and prognostics in unseen data are obtained and compared with the actual remaining flight time in order to validate the effectiveness of the selected model.@en

The procedure of fatigue damage accumulation in composite structures is still unknown and depends on several parameters such as type and frequency of loading, stacking sequence and material properties. Additionally, the nonhomogeneous and anisotropic nature of composites result to a stochastic activation of the different failure mechanisms and make the estimation of remaining useful life (RUL) very complex but interesting task. Data driven probabilistic methodologies have found increasing use the last decade and provide a platform for reliable estimations of RUL utilizing condition monitoring (CM) data. However, the fatigue life of a specific composite structure has a quite significant scatter, with specimens that either underperform or outperform. These specimens are often referred as outliers and the estimation of their RUL is challenging. This study proposes a new RUL probabilistic model, the Extreme Non-Homogenous Hidden Semi Markov Model (ENHHSMM) which is an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). The ENHHSMM uses dynamic diagnostic measures, which are estimated based on the training and testing CM data and adapts dynamically the trained parameters of the NHHSMM. The available CM data are acoustic emission data recorded throughout fatigue testing of open-hole carbon–epoxy specimens. RUL estimations from the ENHHSMM and NHHSMM are compared. The ENHHSMM is concluded as the preferable option since it provides more accurate outlier prognostics.@en

A novel framework to fuse structural health monitoring (SHM) data from different in-situ monitoring techniques is proposed aiming to develop a hyper-feature towards more effective prognostics. A state-of-the-art Non-Homogenous Hidden Semi Markov Model (NHHSMM) is utilized to model the damage accumulation of composite structures, subjected to fatigue loading, and estimate the remaining useful life (RUL) using conventional as well as fused SHM data. Acoustic Emission (AE) and Digital Image Correlation (DIC) are the selected in-situ SHM techniques. The proposed methodology is applied to open hole carbon/epoxy specimens under fatigue loading. RUL estimations utilizing features extracted from each SHM technique and after data fusion are compared, via established and newly proposed prognostic performance metrics.@en

A new structural health monitoring (SHM) data fusion methodology is proposed in order to produce features with strong prognostic capability. The Non-Homogenous Hidden Semi Markov model (NHHSMM) is utilized to estimate the remaining useful life (RUL) of composite structures using conventional as well as fused SHM data. The proposed data fusion methodology and NHHSMM are applied to open hole carbon/epoxy specimens under fatigue loading. During the specimens’ lifetime, acoustic emission (AE) and digital image correlation (DIC) techniques were used in order to capture the inherently dynamic and multi-scale character of damage. This work investigates the prognostic performance of the fused data in comparison to the performance of the conventional AE and DIC data. Prognostic performance metrics were used and as it was found fused data has potential to provide better prognostics.

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The procedure of fatigue damage accumulation in composite structures, is a complex phenomenon due to the multiphase nature of composites, the variation of inherent manufacturing defects, the randomness of loads, the stochastic activation of different damage mechanisms and an incomplete knowledge about the physics behind the evolution and interaction of damage mechanisms. In order to develop a robust model, which will reliably estimate the remaining useful life of the structure, we hypothesize that the damage accumulation process is of a stochastic nature and we propose a framework that combines a stochastic model with structural health monitoring data. In this study, the Non-Homogenous Hidden Semi Markov model and acoustic emission and strain data extracted from fatigue tests of open-hole quasi-isotropic carbon fibre reinforced polymers are selected. The damage accumulation is a hidden process and the goal of the framework is to correlate the structural health monitoring data with the parameters of the model and identify the hidden relationship. In conclusion, the remaining useful life estimations of each structural health monitoring technique are compared with the actual remaining useful life and based on performance metrics it was found that the strain data provided more accurate predictions.@en

The present study utilizes a state-of-the-art stochastic modeling with structural health monitoring (SHM) data derived from strain measurements, in order to assess the remaining useful life (RUL) online in composite materials under fatigue loading. Non-Homogenous Hidden Semi Markov model (NHHSMM) is a suitable candidate with a rich mathematical structure capable of describing the composite’s multi-state damage evolution in time. The proposed model uses as input SHM data in the form of strain measurements obtained from the Digital Image Correlation (DIC) technique to a coupon-level constant amplitude fatigue test campaign. The obtained from the stochastic model RUL estimations are compared with the actual RUL and the effectiveness of the prognosis is discussed. @en