Composites offer unique advantages for aerospace structures and are increasingly being adopted into newer designs. However, it is also acknowledged that given current understanding of damage mechanisms in composites there is a significant risk with the extensive use of composites materials in aerospace applications. On one hand the uncertainty in damage evolution along lifetime is extremely large, and on the other hand there is a lack of knowledge about the mechanics of the onset, posterior growth, and interactions between several micro-scale damage modes. All these factors lead to the adoption of high safety margins in the design and costly inspection schedules along the service to mitigate the risks. Structural health monitoring for onboard damage diagnosis and prognosis of structural failures has the potential to reduce maintenance costs and improve the safety of the structure through a condition based maintenance scheduling. In this scheme the current damage state of a specific structural element is estimated and further used as the input for a prognostic algorithm that predicts the propagation of damage through time using updated models and based on some knowledge of the future load conditions. A novel damage prognostics framework for composites FRP under fatigue loadings is proposed in this work. The proposed methodology is grounded on physics-based models for evolution of damage at (1) micro-scale, i.e. micro-cracks and delamination, and (2) macro-scale such as stiffness reduction induced by micro-scale damage modes. Through stochastic embedding, these apriori deterministic models are converted to probabilistic models by introducing a modeling error term. This error term is controlled by a probability density function whose parameters are estimated in addition to the rest of "physical" parameters. The probabilistic damage models are then incorporated in a Bayesian filtering algorithm that sequentially updates both, a damage state variable and the set of model parameters, as fresh damage data become available along the fatigue cycling process. Next, these damage models are used to simulate fault propagation with this updated state information to generate a prognostic estimate of the remaining useful life of the structure in a probabilistic sense. The proposed methodology is demonstrated using experimental NDE damage data for micro-crack density, delamination area, and stiffness reduction from an extensive post-impact tension-tension fatigue test performed over several CFRP [0,90]4s laminates.

In this work, a prognostics framework to predict the evolution of damage in fiber-reinforced composites materials under fatigue loads is proposed. The assessment of internal damage thresholds is a challenge for fatigue prognostics in composites due to inherent uncertainties, existence of multiple damage modes, and their complex interactions. Our framework, considers predicting the balance of release strain energies from competing damage modes to establish a reference threshold for prognostics. The approach is demonstrated on data collected from a run-to-failure tension-tension fatigue experiment measuring the evolution of fatigue damage in carbon-fiber-reinforced polymer (CFRP) cross-ply laminates. Results are presented for the prediction of expected degradation by micro-cracks for a given panel with the associated uncertainty estimates.

This paper presents a reliability-based prediction methodology to obtain the remaining useful life of composite materials subjected to fatigue degradation. Degradation phenomena such as stiffness reduction and increase in matrix micro cracks density are sequentially estimated through a Bayesian filtering framework that incorporates information from both multi-scale damage models and damage measurements, that are sequentially collected along the process. A set of damage states are further propagated forward in time by simulating the damage progression using the models in the absence of new damage measurements to estimate the time-dependent reliability of the composite material. As a key contribution, the estimation of the remaining useful life is obtained as a probability from the prediction of the time-dependent reliability, whose validity is formally proven using the axioms of Probability Logic. A case study is presented using multi-scale fatigue damage data from a cross-ply carbon-epoxy laminate.

In this work, a framework for the estimation of the fatigue damage propagation in CFRP composites is proposed. Macro-scale phenomena such as stiffness and strength degradation are predicted by connecting micro-scale and macro-scale damage models in a Bayesian filtering framework that also allows incorporating uncertainties in the prediction. The approach is demonstrated on data collected from a run-to-failure tension-tension fatigue experiment measuring the evolution of fatigue damage in CRFP cross-ply laminates. Results are presented for the prediction of expected end of life for a given panel with the associated uncertainty estimates.

DYNAMIC STRAIN MAPPING AND REAL-TIME DAMAGE STATE ESTIMATION UNDER BIAXIAL RANDOM FATIGUE LOADING SUBHASISH MOHANTY*, ADITI CHATTOPADHYAY*, JOHN N. RAJADAS**, AND CLYDE COELHO* Abstract. Fatigue damage and its prediction is one of the foremost concerns of structural integrity research community. The current research in structural health monitoring (SHM) is to provide continuous (or on demand) information about the state of a structure. The SHM system can be based on either active or passive sensor measurements. Though the current research on ultrasonic wave propagation based active sensing approach has the potential to estimate very small damage, it has severe drawbacks in terms of low sensing radius and external power requirements. To alleviate these disadvantages passive sensing based SHM techniques can be used. Currently, few efforts have been made towards, time-series fatigue damage state estimation over the entire fatigue life (stage-I, II & III). A majority of the available literature on passive sensing SHM techniques demonstrates the clear trend in damage growth during the final failure regime (stage-III regime) or during when the damage is comparatively large enough. The present paper proposes a passive sensing technique that demonstrates a clear trend in damage growth almost over the entire stage-II and III damage growth regime. A strain gauge measurement based passive SHM frameworks that can estimate the time-series fatigue damage state under random loading is proposed. For this purpose, a Bayesian Gaussian process nonlinear dynamic model is developed to map the reference condition dynamic strain at a given instant of time. The predicted strains are compared with the actual sensor measurements to estimate the corresponding error signals. The error signals estimated at two different locations are correlated to estimate the corresponding fatigue damage state. The approach is demonstrated for an Al-2434 complex cruciform structure applied with biaxial random loading.

Model-based prognostics approaches employ do- main knowledge about a system, its components, and how they fail through the use of physics-based models. Compo- nent wear is driven by several different degradation phenom- ena, each resulting in their own damage progression path, overlapping to contribute to the overall degradation of the component. We develop a model-based prognostics method- ology using particle filters, in which the problem of charac- terizing multiple damage progression paths is cast as a joint state-parameter estimation problem. The estimate is repre- sented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control mechanism that maintains an uncertainty bound around the hidden parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump, to which we apply our model- based prognostics algorithms. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the chosen approach when multiple damage mechanisms are active.

Multiple fault diagnosis is a difficult problem for dynamic systems. Due to fault masking, compensation, and relative time of fault occurrence, multiple faults can manifest in many different ways as observable fault signature sequences. This decreases diagnosability of multiple faults, and therefore leads to a loss in effectiveness of the fault isolation step. We develop a qualitative, event-based, multiple fault isolation framework, and derive several notions of multiple fault diagnosability. We show that using Possible Conflicts, a model decomposition technique that decouples faults from residuals, we can significantly improve the diagnosability of multiple faults compared to an approach using a single global model. We demonstrate these concepts and provide results using a multi-tank system as a case study.

Structural damage to ball grid array interconnects incurred during vibration testing has been monitored in the prefailure space using resistance spectroscopy-based state space vectors, rate of change of the state variable, and acceleration of the state variable. The technique is intended for condition monitoring in high reliability applications where the knowledge of impending failure is critical and the risks in terms of loss of functionality are too high to bear. Future state of the system has been estimated based on a second-order Kalman Filter model and a Bayesian Framework. The measured state variable has been related to the underlying interconnect damage in the form of inelastic strain energy density. Performance of the prognostic health management algorithm during the vibration test has been quantified using performance evaluation metrics. The method- ology has been demonstrated on leadfree area-array electronic assemblies subjected to vibration. Model predictions have been correlated with experimental data. The presented approach is applicable to functional systems where corner interconnects in area-array packages may be often redundant. Prognostic metrics including α − λ precision, β accuracy, and relative accuracy have been used to assess the performance of the damage proxies. The presented approach enables the estimation of residual life based on level of risk averseness.

In this paper, a probabilistic delamination location and size detection framework is proposed. The delamination probability image using Lamb wave-based damage detection is constructed using the Bayesian updating technique. First, the algorithm for the probabilistic delamination detection framework using Bayesian updating (Bayesian Imaging Method - BIM) is proposed. Following this, the composite coupon fatigue testing setup is introduced and the corresponding lamb wave diagnosis signal is collected and interpreted. Next, the obtained signal features are incorporated in the Bayesian Imaging Method to detect delamination size and location, as well as their confidence bounds. The damage detection results using the proposed methodology are compared with X-ray images for verification and validation. Finally, some conclusions and future works are drawn based on the proposed study.