Jingjing He

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.

A multi-feature integration method for fatigue crack detection and crack length estimation in riveted lap joints using Lamb waves

This paper presents an experimental study of damage detection and quantification in riveted lap joints. Embedded lead zirconate titanate piezoelectric (PZT) ceramic wafer-type sensors are employed to perform in situ non-destructive evaluation (NDE) during fatigue cyclical loading. PZT wafers are used to monitor the wave reflection from the boundaries of the fatigue crack at the edge of bolt joints. The group velocity of the guided wave is calculated to select a proper time window in which the received signal contains the damage information. It is found that the fatigue crack lengths are correlated with three main features of the signal, i.e., correlation coefficient, amplitude change, and phase change. It was also observed that a single feature cannot be used to quantify the damage among different specimens since a considerable variability was observed in the response from different specimens. A multi-feature integration method based on a second-order multivariate regression analysis is proposed for the prediction of fatigue crack lengths using sensor measurements. The model parameters are obtained using training datasets from five specimens. The effectiveness of the proposed methodology is demonstrated using several lap joint specimens from different manufactures and under different loading conditions. (Some figures may appear in colour only in the online journal)

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.

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.

Principle component feature detector for motor cortical control

Principle component analysis (PCA) was performed on recorded neuronal action potentials from neural ensembles in rats motor cortex when the rat was involved in a closed-loop real-time brain machine interface (BCI). The implanted rat was placed in a conditioning chamber, but freely moving, to decide which one of the two paddles should be activated to shift the light to the center. It is found that the principle component feature vectors revealed the importance of individual neurons and their temporal dynamics in relation to the intention of activating either left or right paddle. In addition, the first principle component feature has much higher discriminative capability than others although it represents only a few percentage of the total variance. Using the first principle component with the Bayes classifier achieved 90% classification accuracy, which is comparable with the accuracy obtained by a more sophisticated high performance support vector classifiers.

A Probabilistic Damage Identification Method for Shear Structure Components Based on Cross-Entropy Optimizations

A probabilistic damage identification method for shear structure components is presented. The method uses the extracted modal frequencies from the measured dynamical responses in conjunction with a representative finite element model. The damage of each component is modeled using a stiffness multiplier in the finite element model. By coupling the extracted features and the probabilistic structural model, the damage identification problem is recast to an equivalent optimization problem, which is iteratively solved using the cross-entropy optimization technique. An application example is used to demonstrate the proposed method and validate its effectiveness. Influencing factors such as the location of damaged components, measurement location, measurement noise level, and damage severity are studied. The detection reliability under different measurement noise levels is also discussed in detail.

An Integrated Health Monitoring Method for Structural Fatigue Life Evaluation Using Limited Sensor Data

A general framework for structural fatigue life evaluation under fatigue cyclic loading using limited sensor data is proposed in this paper. First, limited sensor data are measured from various sensors which are preset on the complex structure. Then the strain data at remote spots are used to obtain the strain responses at critical spots by the strain/stress reconstruction method based on empirical mode decomposition (REMD method). All the computations in this paper are directly performed in the time domain. After the local stress responses at critical spots are determined, fatigue life evaluation can be performed for structural health management and risk assessment. Fatigue life evaluation using the reconstructed stresses from remote strain gauge measurement data is also demonstrated with detailed error analysis. Following this, the proposed methodology is demonstrated using a three-dimensional frame structure and a simplified airfoil structure. Finally, several conclusions and future work are drawn based on the proposed study.

A model assessment method for predicting structural fatigue life using Lamb waves

HighlightsModel assessment method for predicting structural fatigue life is proposed.POD models for Lamb wave‐based NDE are investigated.The influence of model choice on fatigue life prediction is studied. ABSTRACT This paper presents a study on model assessment for predicting structural fatigue life using Lamb waves. Lamb wave coupon testing is performed for model development. Three damage sensitive features, namely normalized energy, phase change, and correlation coefficient are extracted from Lamb wave data and are used to quantify the crack size. Four data‐driven models are proposed. The average relative error and the probability of detection (POD) are proposed as two measures to evaluate the performance of the four models. To study the influence of model choice on the probabilistic fatigue life prediction, probability density functions of the actual crack size are obtained from the POD models given the Lamb wave data. Crack growth model parameters are statistically identified using Bayesian parameter estimation with Markov chain Monte Carlo simulations. The model assessment and the influence of model choice on fatigue life prediction are made using both coupon testing data with artificial cracks and realistic lap joint testing data with naturally developed cracks.

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data

This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions.

Fatigue damage diagnosis and prognosis using Bayesian updating

In this paper, a methodology integrating a Lamb wave-based damage detection technique and a Bayesian updating method for remaining useful life (RUL) prediction is proposed. 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. Second, a small time scale model is used as the physics 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 and the small time scale model for RUL prediction. Probability distributions of model parameters 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.