Fatigue Damage Prognosis Research Articles

Integrated fatigue damage diagnosis and prognosis under uncertainties


 
 
 An integrated fatigue damage diagnosis and prognosis framework is proposed in this paper. The proposed methodology integrates a Lamb wave-based damage detection technique and a Bayesian updating method for remaining useful life (RUL) prediction. First, a piezoelectric sensor network is used to detect the fatigue crack size near the rivet holes in fuselage lap joints. Advanced signal processing and feature fusion is then used to quantitatively estimate the crack size. Following this, a small time scale model is introduced and used as the mechanism model to predict the crack propagation for a given future loading and an estimate of initial crack length. Next, a Bayesian updating algorithm is implemented incorporating the damage diagnostic result for the fatigue crack growth prediction. Probability distributions of model parameters and final RUL are updated considering various uncertainties in the damage prognosis process. Finally, the proposed methodology is demonstrated using data from fatigue testing of realistic fuselage lap joints and the model predictions are validated using prognostics metrics.
 
 

A reliability-based framework for fatigue damage prognosis of composite aircraft structures

The extensive use of lightweight composite materials in composite aircraft structures drastically increases the sensitivity to both fatigue- and impact-induced damage of their critical structural components during their service life. Within this scenario, an integrated hardware–software system that is capable of monitoring the composite airframe, assessing its structural integrity, identifying a condition-based maintenance, and predicting the remaining service life of its critical components is therefore needed. As a contribution to this goal, this paper presents the theoretical basis of a novel and comprehensive probabilistic methodology for predicting the remaining service life of adhesively bonded joints within the structural components of composite aircraft, with emphasis on a composite wing structure. Non-destructive evaluation techniques and recursive Bayesian inference are used to (i) assess the current state of damage of the system and (ii) update the joint probability distribution function (PDF) of the damage extents at various locations. A probabilistic model for future aerodynamic loads and a damage evolution model for the adhesive are then used to stochastically propagate damage through the joints and predict the joint PDF of the damage extents at future times. This information is subsequently used to probabilistically assess the reduced (due to damage) global aeroelastic performance of the wing by computing the PDFs of its flutter velocity and the velocities associated with the limit cycle oscillations of interest. Combined local and global failure criteria are finally used to compute lower and upper bounds for the reliability index of the composite wing structure at future times.

Integration of structural health monitoring and fatigue damage prognosis

This paper presents a Bayesian probabilistic methodology to integrate model-based fatigue damage prognosis (FDP) with online and offline structural health monitoring (SHM) data. The prognosis uses fracture mechanics-based fatigue crack growth modeling, along with quantification of various sources of uncertainty, including natural variability, data uncertainty and model errors. These uncertainty sources are connected using a Bayesian network and a probabilistic sensitivity analysis is performed to assess the uncertainty contributions from these sources. The cycle-by-cycle simulation of fatigue crack growth is expedited via the use of a surrogate modeling technique (Gaussian process model) to replace computationally expensive finite element analysis. Real-time monitoring data of external variable amplitude loading history is used to construct a Bayesian autoregressive integrated moving average (ARIMA) model to predict and update the loading. On-ground crack inspection data is used to quantify the uncertainty in the initial and current size of an existing crack, using the Bayesian approach. Three possible cases of inspection results are considered: (1) crack is not detected; (2) crack is detected but not measured; (3) crack is detected and measured. Different scenarios of data availability (load monitoring data and inspection data) are considered for the prognosis of an individual component in a fleet. A numerical example, surface cracking in a rotorcraft mast under service loading, is implemented to illustrate the proposed methodology. The results of prognosis are validated using Bayesian hypothesis testing.

New Method for Concurrent Dynamic Analysis and Fatigue Damage Prognosis of Bridges

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is on the basis of a novel small time scale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics on the basis of the geometric relationship between the crack tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single degree-of-freedom and multiple degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated using coupon testing data from open literature. Following this, the methodology is demonstrated using a steel-girder bridge. The proposed methodology shows that the concurrent structural dynamics and material fatigue crack growth analysis can be achieved. The cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels and aluminum alloy shows a satisfactory accuracy using the proposed coupled state-space model.

Model selection, updating, and averaging for probabilistic fatigue damage prognosis

This paper presents a method for fatigue damage propagation model selection, updating, and averaging using reversible jump Markov chain Monte Carlo simulations. Uncertainties from model choice, model parameter, and measurement are explicitly included using probabilistic modeling. Response measurement data are used to perform Bayesian updating to reduce the uncertainty of fatigue damage prognostics. All the variables of interest, including the Bayes factors for model selection, the posterior distributions of model parameters, and the averaged results of system responses are obtained by one reversible jump Markov chain Monte Carlo simulation. The overall procedure is demonstrated by a numerical example and a practical fatigue problem involving two fatigue crack growth models. Experimental data are used to validate the performance of the method.

Stochastic prediction of fatigue loading using real-time monitoring data

Accurate characterization and prediction of loading, while properly accounting for uncertainty, are essential for probabilistic fatigue damage prognosis. Three different techniques – rainflow counting, the Markov chain method, and autoregressive moving average (ARMA) modeling – are investigated for stochastic characterization and reconstruction of the fatigue load history. The ARMA method is extended in this paper by introducing random coefficients and probabilistic weights, to account for the uncertainty in the selection of the model, inherent variability in loading, and uncertainty due to sparse data. A continuous model updating approach based on real-time monitoring data is developed and applied to all the three techniques mentioned above. The relation between prediction accuracy and updating interval is evaluated quantitatively. A quantitative model validation approach using Bayesian hypothesis testing is proposed to assess the confidence in load prediction from all the three methods.

Structural fatigue prognosis using limited sensor data

In this paper, a general framework for concurrent structural fatigue prognosis using limited sensor data is developed. The Empirical Mode Decomposition method is employed to reconstruct the structural dynamical response for the critical spot susceptible to fatigue damage. The sensor data available at limited locations measured from the usage monitor system are decoupled into several Intrinsic Mode Functions using the Empirical Mode Decomposition method. Those IMFs are applied to extrapolate the dynamic response for the critical spot where the direct response measurements are unavailable. The extrapolated dynamic response time series for the critical spot is then integrated with a physical fatigue crack growth model for fatigue damage prognosis. The proposed procedure is demonstrated using a multi degree-of-freedom (MDOF) cantilever beam example. The proposed method has great potential for the real-time decision making in the vehicle health management framework due to its ability for the concurrent damage prognosis.

Stochastic Characterization and Update of Fatigue Loading for Mechanical Damage Prognosis

Accurate characterization and prediction of loading, while properly accounting for uncertainty, are essential for probabilistic fatigue damage prognosis. Three different techniques, including rainflow counting, the Markov chain method, and autoregressive moving average (ARMA) method, are reviewed for stochastic characterization and reconstruction of the fatigue load spectrum for prognosis. The ARMA method is extended by introducing random coefficients and probabilistic weights, to account for the uncertainty in the selection of models, inherent variability of loading, and uncertainty due to sparse data. A continuous model updating framework based on usage monitoring data is developed and applied to all the three techniques mentioned above. The relation between prediction accuracy and updating period is evaluated quantitatively. A quantitative model validation metric is proposed for assessing the accuracy of load prediction.*

Efficient probabilistic methods for real-time fatigue damage prognosis


 
 
 A general probabilistic fatigue crack growth prediction methodology for accurate and efficient damage prognosis is proposed in this paper. This methodology consists two major parts. First, the realistic random loading is transformed to an equivalent constant amplitude loading process based on a recently developed mechanism model. This transformation avoids the cycle-by-cycle calculation of fatigue crack growth under variable amplitude loading. Following this, an inverse first-order reliability method (IFORM) is used to evaluate the fatigue crack growth at an arbitrary reliability level. Inverse FORM method does not require a large number of function evaluations compared to the direct Monte Carlo simulation. Computational cost is significantly reduced and the proposed method is very suitable for real-time damage prognosis. Numerical examples are used to demonstrate the proposed method. Various experimental data under variable amplitude loading are collected and model predictions are compared with experimental data for model validation.
 
 

Probabilistic fatigue damage prognosis using maximum entropy approach

A general framework for probabilistic fatigue damage prognosis using maximum entropy concept is proposed and developed in this paper. The fatigue damage is calculated using a physics-based crack growth model. Due to the stochastic nature of fatigue crack propagation process, uncertainties arising from the underlying physical model, parameters of the model and the response variable measurement noise are considered and integrated into this framework. Incorporating all those uncertainties, a maximum relative entropy (MRE) approach is proposed to update the statistical description of model parameters and narrow down the prognosis deviations. A Markov Chain Monte Carlo (MCMC) simulation is then employed to generate samples from updated posterior probability distributions and provide statistical information for the maximum relative entropy updating procedure. A numerical toy problem is given to demonstrate the proposed MRE prognosis methodology. Experimental data for aluminum alloys are used to validate model predictions under uncertainty. Following this, a detailed comparison between the proposed MRE approach and the classical Bayesian updating method is performed to illustrate advantages of the proposed prognosis framework.

Developing impact and fatigue damage prognosis solutions for composites

An approach to developing a damage prognosis solution that integrates advanced sensing technology, data interrogation procedures for damage detection, novel model validation and uncertainty quantification techniques, and reliability-based decision-making algorithms is summarized in this article. In parallel, experimental efforts are underway to deliver a proof-of-principle technology demonstration by assessing impact damage and predicting the subsequent fatigue damage accumulation in a composite plate. This article provides an overview of the various technologies that are being integrated to address this damage prognosis problem.