Fatigue Damage Prognosis Research Articles

An aircraft structural risk assessment method considering fatigue crack propagation based on fatigue damage diagnosis and prognosis

An aircraft structural risk assessment method based on fatigue damage diagnosis and prognosis has been developed, considering fatigue crack propagation. The process is divided into three stages: initial crack diagnosis, crack diagnosis, and prediction, utilizing Monte Carlo simulation. Using 2024 aluminum alloy specimens with central holes, the study indicates that in the initial crack diagnosis stage, an inspection standard with a Single Flight Probability of Failure (SFPOF) less than 10-7 and a threshold method enhances structural fatigue crack diagnosis. In the crack diagnosis and prediction stages, iterative updates using Gaussian Process Regression (GPR) within a Dynamic Bayesian Network (DBN) improve crack propagation prediction and risk assessment accuracy. The diagnostic interval significantly impacts SFPOF, with an optimized interval balancing accuracy and computation time. Simplified and precise K value calculation methods enhance efficiency and accuracy. The method reduces costs and improves risk assessment accuracy, providing new insights for SPHM-based aircraft structural risk assessment.

Particle filter-based fatigue damage prognosis by fusing multiple degradation models

Fatigue damage prognosis always requires a degradation model describing the damage evolution with time; thus, the prognostic performance highly depends on the selection of such a model. The best model should probably be case specific, calling for the fusion of multiple degradation models for a robust prognosis. In this context, this paper proposes a scheme of online fusing multiple models in a particle filter (PF)-based damage prognosis framework. First, each prognostic model has its process equation built through a physics-based or data-driven degradation model and has its measurement equation linking the damage state and the measurement. Second, each model is independently processed through one PF to provide one group of particles. Then, the particles from all models are adopted for remaining useful life prediction. Finally, the particles from each PF are fused with those from all the other PFs to improve their particle diversity, and consequently, to provide better estimation and prognostic performance. The feasibility and robustness of the proposed method are validated by an experimental study, where an aluminum lug structure subject to fatigue crack growth is monitored by a guided wave measurement system.

Moment quadrature method for uncertainty quantification of fatigue damage prognosis

The study proposes a new method for uncertainty quantification of fatigue damage prognosis using very few, typically 4, model evaluations, while achieving an accuracy comparable to the Monte Carlo method normally requires 106 model evaluations. Higher order statistics such as skewness and kurtosis can reliably be obtained using the method with 9 to 16 model evaluations. The proposed method provides a viable solution to problems where the computational demand is prohibitively high for conventional methods and/or real time computation is needed. Validations are made using several fatigue examples with realistic testing data, and results are compared with Monte Carlo simulations.

Fatigue damage diagnosis and prognosis for 2024 aluminum plates with center holes: A strain monitoring approach

A fatigue damage diagnosis and prognosis approach has been developed based on strain monitoring. The fatigue experiment is conducted on 2024 aluminum specimens with center holes to obtain the strain/crack information. The occurrence of cracks is detected by a thresholding method. A data-driven Gaussian process regression (GPR) algorithm is used to establish the relationship between the crack length and the strain characteristic parameters. A dynamic Bayesian network (DBN) is assembled by combining the GPR algorithm and Paris formula for real-time crack propagation predictions. An experiment has been carried out to illustrate the accuracy of the approach. The results indicate that the threshold method can detect fatigue cracks effectively. The GPR algorithm can accurately identify fatigue crack length and has higher recognition accuracy than other algorithms. The crack propagation prediction error and time consumption of DBN are much smaller than mechanics-based crack growth analysis.

Fatigue damage prognosis of orthotropic steel deck based on data-driven LSTM

Orthotropic steel decks (OSDs) are widely used in steel bridges; however, they suffer from massive fatigue cracks early into their service life, which seriously affects the service security of steel bridges. Thus, it is critical to predicting the cumulative fatigue damage of OSDs accurately. In this study, the characteristics of field-monitored strain data and fatigue damage of typical connection details are investigated, which include rib-to-deck welded joints and rib butt welds. A fatigue damage prognosis method of OSDs based on data-driven long short-term memory (LSTM) was proposed. Further, the sensitive factors of the proposed method were analyzed, and the performance was validated. The characteristics analysis results show that the hourly fatigue damage series is an appropriate data form for the fatigue damage prognosis. The sensitive factors analysis results show that a data size of at least 840 and adding three feature dimensions related to the hour, day, and week, to fatigue damage series, can contribute to the performance of the LSTM model. The validation results show that the proposed method performs well on the fatigue damage prognosis. The mean absolute percentage errors were less than 10% among the two types of fatigue vulnerable details. Data-driven LSTM can significantly maintain the precision of fatigue damage prognosis with time. This study is expected to provide new insights and guidance into the fatigue damage prognosis of OSDs on long-span cable-stayed bridges.

Bayesian inference-based prognosis of fatigue damage for MPPO polymer using Zhurkov fatigue life model

In this study, the fatigue damage prognosis of a modified polyphenylene oxide (MPPO) polymer is performed using a Bayesian framework, and a Zhurkov model-based dynamic fatigue life model is employed to obtain the probabilistic stress–cycle (P-S-N) curve. Activation energy and tensile tests are performed to determine the aleatory uncertainty of the lethargy coefficient of the Zhurkov fatigue life model. This uncertainty is quantified by performing sequential statistical modeling using experimental data with embedded scattering. The P-S-N curve is estimated using these data, and the Zhurkov fatigue life model is validated via the fatigue test. Furthermore, damage data are obtained via a low-cycle fatigue analysis in conditions identical to those of the fatigue test conducted on the specimen scale. Based on computational damage data, the initial model parameters of the fatigue damage model are obtained using the least-squares method. These model parameters are estimated while considering scattering by applying the Markov Chain Monte Carlo and particle filter. Therefore, the remaining useful life (RUL) of the MPPO, which depends on the amplitude stress, is predicted under the tension–tension fatigue loading ( R = 0), and the prediction accuracy of the RUL is evaluated using prognostics metrics.

Diagnosis and Prognosis of Fatigue Damage in Adhesively Bonded Joints Using Ultrasound Non-Destructive Evaluation

Abstract Increased effort for lightweighting of automotive structures results in the replacement of traditional metals with composites. Adhesive bonding is the best joining solution for composite components owing to its superior stress distribution and lightweighting. However, adhesive and adhesive-adhered interfaces are the weakest links in the structure. During fatigue crack propagation, joints do not show any significant visual changes. Thus, fatigue damage in adhesive bond lines is one of the challenging and complex failure mechanisms that requires real-time diagnostic and prognostic techniques to avoid any catastrophic failure. This paper proposes an acoustic technique for real-time fatigue damage diagnosis and prognosis. Based on experimental guided wave modal analysis, symmetric mode at 85 kHz is found to be the most sensitive mode–frequency combination for fatigue monitoring of selected lap-joint specimens. Further, a hybrid data-driven damage propagation model is used to estimate the remaining useful life in the bond line. The developed techniques were successfully implemented and validated on a single lap joint under fatigue loading. Estimated damage levels and remaining useful life are in good agreement with reference measurements. Successful validation is an indicator of the potential application of this technology in automotive industries.

A Bayesian approach for fatigue damage diagnosis and prognosis of wind turbine blades

This paper proposes a Bayesian framework based on particle filters for online fatigue damage diagnosis and prognosis for wind turbine blades (WTBs). The framework integrates theoretical and practical aspects with the purpose of developing a robust monitoring tool. Besides, a damage indicator based on identified modal frequencies of the WTB is defined to quantify the degree of damage to the monitored blade. Furthermore, feature extraction techniques on vibration signals are considered to obtain the online observations and inputs needed by the Bayesian framework. Experimental data collected from a fatigue test performed on a WTB was used to validate the proposed methodology. The results obtained by the damage diagnosis algorithm show the great potential of the Bayesian processor for damage estimation of the monitored WTB and uncertainty quantification related to the estimated variable. According to the damage prognosis results, the proposed algorithm could generate suitable long-term predictions of the damage indicator so as to estimate the time-of-failure (ToF) probability mass function (PMF) for the monitored WTB. Consequently, the computed ToF-PMF was able to include the experimental ToF within its 95% confidence interval, demonstrating the accuracy of the Bayesian approach.

Towards a digital twin approach for vessel-specific fatigue damage monitoring and prognosis

This paper proposes a Digital Twin approach for the monitoring and prognosis of vessel-specific fatigue damage. During design, fatigue damage estimates are based on conservative assumptions regarding operational conditions and structural response. However, variability in the vessel-specific operations from those assumed during design needs to be considered when supporting engineering-based decisions for maintenance deferrals and service life extensions. The use of Digital Twins is proposed to provide this necessary vessel-specific decision support. Digital Twins typically rely on sensor-based data to update their models, however structural health sensors for fatigue monitoring can be prohibitively expensive to install and maintain in ship structures, so the proposed method addresses this by instead combining publicly available vessel-specific operational data (global vessel position data coupled with metocean hindcast data) with computational models to monitor the environmental exposure and track the vessel fatigue accumulation over time. This approach is demonstrated through a case study of a containership that has been in operation for seven years. The results of proposed approach are compared against the fatigue estimate obtained using the design reference wave conditions. The Digital Twin is then used to forecast the remaining fatigue life, in order to support inspection and maintenance scheduling and operational decision-making.

Fatigue damage prognosis of steel bridges under traffic loading using a time-based crack growth method

Traditionally, the fatigue damage assessment of steel bridges is conducted using cycle-based methods. Cycle-based methods require stress time history be transformed to cycle history first before fatigue analysis can be performed. However, well-defined cycle history does not exist for the traffic-induced stress time history of bridges as it contains numerous large and small cycles with random stress ranges embedded together. To address this inherent difficulty, a time-based fatigue crack growth (FCG) model is proposed for fatigue damage prognosis of steel bridges under traffic loading. The time-based FCG method describes the crack growth in the time domain through a crack growth kinetics function derived based on the physical mechanism of fatigue crack propagation. To demonstrate the proposed method, numerical simulations are first performed using full-scale coupled vehicle-bridge interaction framework to generate stress time histories of a typical steel bridge under traffic loading. Then, FCG analysis is performed using the time-based method and the effects of road surface roughness and vehicle weight on the FCG are studied. Finally, a case study on the I-10 Twin Span Bridge is presented to demonstrate the time-based FCG method for fatigue damage prognosis using in situ monitoring data. The results show that the proposed method can be used to directly predict the FCG of steel bridges in the time domain using stress time histories obtained either from stress analysis or in situ monitoring.

Fatigue damage diagnosis and prognosis of an aeronautical structure based on surrogate modelling and particle filter

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.

Vehicle-induced fatigue damage prognosis of orthotropic steel decks of cable-stayed bridges

Orthotropic steel deck (OSD) in a long-span cable-stayed bridge is vulnerable to fatigue damage at the deck-to-rib (DTR) joints due to excessive vehicle-induced dynamic stresses. A framework for fatigue damage prognosis of OSD in long-span cable-stayed bridges is thus presented in this paper. The main features of the framework include hourly traffic loading simulation and prediction, multi-scale finite element bridge model, coupled vehicle-bridge system, mesh-insensitive equivalent stress responses at a DTR joint, response surface models for equivalent stress responses, OSD and pavement interaction, asphalt pavement temperature effect, fatigue test-generated S-N curve, and fatigue damage prognosis. To evaluate the feasibility of the proposed framework and to manifest the effects of pavement roughness, asphalt temperature, and vehicle transverse locations on fatigue damage accumulation, a real long span cable-stayed bridge is investigated as a case study. The results indicate that the developed framework is applicable and that the fatigue damage of a DTR joint is underestimated if the time-variant temperature of asphalt pavement and road surface condition are not considered but the fatigue damage is overestimated without consideration of variable transverse locations of vehicles.

Dynamic stress analysis for fatigue damage prognosis of long-span bridges

For fatigue damage prognosis of a long-span steel bridge, the dynamic stress analysis of critical structural components of the bridge under the future dynamic vehicle loading is essential. This paper thus presents a framework of dynamic stress analysis for fatigue damage prognosis of long-span steel bridges under the future dynamic vehicle loading. The multi-scale finite element (FE) model of the bridge is first developed using shell/plate elements to simulate the critical structural components (local models) and using beam/truss elements to simulate the rest part of the bridge (global model). With the appropriate coupling of the global and local models, the multi-scale FE model can accurately capture simultaneously not only the global behavior in terms of displacement and acceleration but also the local behavior in terms of stress and strain. A vehicle traffic load model is then developed for forecasting the future vehicle loading based on the recorded weigh-in-motion (WIM) data and using the agent-based traffic flow microsimulation. The forecasted future vehicle loading is finally applied on the multi-scale model of a real long-span cable-stayed bridge for dynamic stress analysis and fatigue damage prognosis. The obtained results show that the proposed framework is effective and accurate for dynamic stress analysis and fatigue damage prognosis.

Multi-scale fatigue damage prognosis for long-span steel bridges under vehicle loading

Fatigue damage prognosis for long-span steel bridges is of the utmost importance in bridge maintenance and management. In this study, a multi-scale fatigue damage prognosis algorithm is developed to calculate the trans-scale fatigue damage accumulation of newly-built long-span steel bridges under vehicle loading. The necessity and procedure of establishing a multi-scale finite element (FE) model of a newly-built long-span bridge for fatigue damage prognosis are first introduced. The future vehicle loading on the bridge is forecasted using the recorded weigh-in-motion (WIM) data and the agent-based traffic flow micro-simulation method. Then, the multi-scale fatigue damage prognosis algorithm is developed based on the multi-scale FE model and using the future vehicle loading. Finally, the proposed algorithm is applied to a newly-built long-span cable-stayed bridge for the time period from 2010 to 2020. The results show that the macro-scale fatigue damage accumulation and micro-scale short crack evolution of the critical components of the bridge can be simultaneously predicted and visualized. The proposed algorithm can be used as a numerical tool for fatigue damage prognosis of steel bridges where (or near where) WIM station is installed.

Fatigue damage assessment of orthotropic steel deck using dynamic Bayesian networks

Current health monitoring of orthotropic steel deck (OSD) subjected to fatigue damage mainly relies on deterministic physical models and the field measurements through inspections and monitoring. Nevertheless, various aleatory (random) and epistemic (lack of knowledge) uncertainties exist due to empirical justifications, model simplifications, inaccurate statistics of model parameter, measurement error, etc. The present study proposes a probabilistic model for fatigue damage diagnosis and prognosis of an OSD through integrating the physical model with field inspections while accounting for the associated uncertainties, using the dynamic Bayesian network (DBN). The DBN is suitable for representation and reasoning under uncertainty in various fields. The proposed framework aims to fulfill two interdependent tasks (1) diagnosis: track the time-dependent variable (i.e., the crack growth) and calibrate the time-independent variables (i.e., the geometric parameters and the multiplier for the crack shape factor); and (2) prognosis: predict the crack growth in the future. The particle filter (PF) is employed as the Bayesian inference algorithm for the established non-Gaussian DBN composed of continuous variables of various distribution types, as well as nonlinear conditional dependence between them. In addition, a Gaussian process (GP) surrogate model is established to relate the output stress response of the physical model (OSD) under the input truck load and model parameters, which is further implemented as the conditional probability distribution (CPD) in the DBN model. Finally, the proposed framework is illustrated by a numerical example of fatigue crack growth on the OSD subjected to truck load.

Buckypaper embedded self-sensing composite for real-time fatigue damage diagnosis and prognosis

In this study, buckypaper (BP) membranes have been used to introduce self-sensing capability in glass fiber reinforced polymer matrix (GFRP) laminates by embedding them in the interlaminar region of the laminates. Piezoresistive characterization studies were conducted by subjecting the self-sensing GFRP (SGFRP) specimens to cyclic loading and high sensitivity to strain was observed. A measurement model for real-time quantification of fatigue crack, developed using in-situ resistance measurements obtained under fatigue loading, was used to quantify fatigue crack length in real time. The fatigue crack growth rates and the nature of crack propagation in baseline and SGFRP specimens were compared. The results show that the introduction of BP reduced the average crack growth rate by an order of magnitude as a result of crack tip blunting during fatigue, while facilitating real time strain sensing and damage quantification. A fully probabilistic prognosis methodology was also developed by combining the in-situ measurement model with a machine learning based prognosis model to accurately predict the real-time fatigue crack propagation using sequential Bayesian techniques.

Probabilistic fatigue damage prognosis using surrogate models trained via three-dimensional finite element analysis

Utilizing inverse uncertainty quantification techniques, structural health monitoring (SHM) can be integrated with damage progression models to form a probabilistic prediction of a structure’s remaining useful life (RUL). However, damage evolution in realistic structures is physically complex. Accurately representing this behavior requires high-fidelity models which are typically computationally prohibitive. In this paper, high-fidelity fatigue crack growth simulation times are reduced by three orders of magnitude using a model based on a set of surrogate models trained via three-dimensional finite element analysis. The developed crack growth modeling approach is experimentally validated using SHM-based damage diagnosis data. A probabilistic prediction of RUL is formed for a metallic, single-edge notch tension specimen with a fatigue crack growing under mixed-mode conditions.

Probabilistic fatigue damage prognosis of lap joint using Bayesian updating

A general framework for probabilistic prognosis and uncertainty management under fatigue cyclic loading is proposed in this article. First, the general idea using the Bayesian updating in prognosis is introduced. Several sources of uncertainties are discussed and included in the Bayesian updating framework. An equivalent stress level model is discussed for the mechanism-based fatigue crack growth analysis, which serves as the deterministic model for the lap joint fatigue life prognosis. Next, an in situ lap joint fatigue test with pre-installed piezoelectric sensors is designed and performed to collect experimental data. Signal processing techniques are used to extract damage features for crack length estimation. Following this, the proposed methodology is demonstrated using the experimental data under both constant and variable amplitude loadings. Finally, detailed discussion on validation metrics of the proposed prognosis algorithm is given. Several conclusions and future work are drawn based on the proposed study.

A recursive Bayesian approach for fatigue damage prognosis: An experimental validation at the reliability component level

Fatigue-induced damage is one of the most uncertain and highly unpredictable failure mechanisms for a large variety of mechanical and structural systems subjected to cyclic and random loads during their service life. A health monitoring system capable of (i) monitoring the critical components of these systems through non-destructive evaluation (NDE) techniques, (ii) assessing their structural integrity, (iii) recursively predicting their remaining fatigue life (RFL), and (iv) providing a cost-efficient reliability-based inspection and maintenance plan (RBIM) is therefore ultimately needed. In contribution to these objectives, the first part of the paper provides an overview and extension of a comprehensive reliability-based fatigue damage prognosis methodology — previously developed by the authors — for recursively predicting and updating the RFL of critical structural components and/or sub-components in aerospace structures. In the second part of the paper, a set of experimental fatigue test data, available in the literature, is used to provide a numerical verification and an experimental validation of the proposed framework at the reliability component level (i.e., single damage mechanism evolving at a single damage location). The results obtained from this study demonstrate (i) the importance and the benefits of a nearly continuous NDE monitoring system, (ii) the efficiency of the recursive Bayesian updating scheme, and (iii) the robustness of the proposed framework in recursively updating and improving the RFL estimations. This study also demonstrates that the proposed methodology can lead to either an extent of the RFL (with a consequent economical gain without compromising the minimum safety requirements) or an increase of safety by detecting a premature fault and therefore avoiding a very costly catastrophic failure.

A Stochastic Collocation Method for Uncertainty Analysis of Fatigue Damage Prognosis

This article proposes a stochastic collocation method to investigate the uncertainty quantification in fatigue damage prognosis where experimental data are limited and only interval bounds on uncertain parameters are given. The method derived from tensor-products or sparse grids consists in a Galerkin approximation in random space, requires the use of structured collocation point sets and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. The distribution of remaining useful life can be acquired by dividing each interval into several small parts and assuming the corresponding random variable obeys uniform distribution in the small range. Compared with Monte Carlo method and interval arithmetic, this approach is much more efficient, time-saving and gets more accurate predictions. An experimental investigation of fatigue life prediction of a metallic plate with a central crack is presented to demonstrate the efficiency and effectiveness of the proposed method.