A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method

Yan, Gang; Sun, Hao; Waisman, Haim

doi:10.1016/j.compstruc.2015.02.010

Cited by 36 publications

(25 citation statements)

References 44 publications

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“…where x j represents the j -th sensing position with j D 1; 2; : : : ; N o ; N o is the total number of observations (sensing points); O u is the predicted displacement; and u is the measured displacement. To sum up, the basic idea is that flaws close to nearby sensors would have more pronounced effect compared with those of the pristine state, leading to large weighting coefficient values in these sensor locations [32].…”

Section: The Weighted Objective Functionmentioning

confidence: 99%

“…H. SUN, H. WAISMAN AND R. BETTI Equation (32) can be minimized using the damped Gauss-Newton algorithm proposed in Section 3.3. In this case, the entries of the Jacobian matrix can be determined in a close form by OEJ e k1 D 2x 0 .x 0 x k / 2 C .y 0 y k / 2 1 2 OEJ e k2 D 2y 0 .x 0 x k / 2 C .y 0 y k / 2 1 2 (33) which yields an admissible initial guess of the flaw position…”

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confidence: 99%

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A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

Sun

Waisman

Betti

2015

Int. J. Numer. Meth. Engng

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We present a sweeping window method in elastodynamics for detection of multiple flaws embedded in a large structure. The key idea is to measure the elastic wave propagation generated by a dynamic load within a smaller substructural detecting window domain, given a sufficient number of sensors. Hence, rather than solving the full structure, one solves a set of smaller dynamic problems quickly and efficiently.To this end, an explicit dynamic extended FEM with circular/elliptical void enrichments is implemented to model the propagation of elastic waves in the detecting window domain. To avoid wave reflections, we consider the window as an unbounded domain with the option of full-infinite/semi-infinite/quarter-infinite domains and employ a simple multi-dimensional absorbing boundary layer technique.A spatially varying Rayleigh damping is proposed to eliminate spurious wave reflections at the artificial model boundaries. In the process of flaw detection, two phases are proposed: (i) pre-analysis-identification of rough damage regions through a data-driven approach, and (ii) post-analysis--identification of the true flaw parameters by a two-stage optimization technique. The 'pre-analysis' phase considers the information contained in the 'pseudo' healthy structure and the scattered wave signals, providing an admissible initial guess for the optimization process. Then a two-stage optimization approach (the simplex method and a damped Gauss-Newton algorithm) is carried out in the 'post-analysis' phase for convergence to the true flaw parameters. A weighted sum of the least squares, of the residuals between the measured and simulated waves, is used to construct the objective function for optimization. Several benchmark examples are numerically illustrated to test the performance of the proposed sweeping methodology for detection of multiple flaws in an unbounded elastic domain.A SWEEPING WINDOW METHOD FOR DETECTION OF FLAWS 1015 Such computational models consist of both forward and inverse analyses. In the forward analysis, the system response is predicted by a user-defined or user-guessed model; while in the inverse analysis, parameters representing flaw boundaries are determined by solving a minimization problem, wherein an objective function is defined to quantify the discrepancy between the measured and predicted responses. Solving such an inverse problem of flaw detection is performed iteratively where each iteration requires a forward solution with an updated flaw parameter set. The iteration proceeds until an optimal set of parameters, which 'best' describe the flaw boundaries, are obtained. This process may require many forward analyses in particular when the updating strategies (optimization technique used) are poor or when either an insufficient number of sensors are employed or the flaws to be detected are too small compared with the finite element mesh employed. Hence, an efficient forward model is needed so as to reduce computational efforts due to repeated forward analyses.Recently, a new numerical modeling a...

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Section: The Weighted Objective Functionmentioning

confidence: 99%

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confidence: 99%

A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

Sun

Waisman

Betti

2015

Int. J. Numer. Meth. Engng

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“…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 is propagating in the structure [25,26]. These favorable features have been exploited in [27,28,29,30,31] by combining XFEM and optimization algorithms for deterministic and probabilistic flaw detection in structures. In [31], the Bayesian approach [32,33,34,35] was used to quantify uncertainties from modeling errors and measurement noise, leading to the probability distributions of the flaw parameters.…”

Section: Introductionmentioning

confidence: 99%

“…These favorable features have been exploited in [27,28,29,30,31] by combining XFEM and optimization algorithms for deterministic and probabilistic flaw detection in structures. In [31], the Bayesian approach [32,33,34,35] was used to quantify uncertainties from modeling errors and measurement noise, leading to the probability distributions of the flaw parameters. Since the extracted reflection intensity spectrum relies heavily on the accuracy of the strain field, we propose to use not only the leading, but also the higher-order terms of the Williams asymptotic solution [36] as the enrichment functions.…”

Section: Introductionmentioning

confidence: 99%

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

Yang

Wang

et al. 2016

Sensors

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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.

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“…Green 15 presented a Data Annealing-based MCMC algorithm for probabilistic system identification. Yan et al 16 investigated a reverse jump MCMC method for Bayesian updating of flaw parameters. Sun and Büyüköztürk proposed a MCMC approach with adaptive random-walk steps for probabilistic model updating of buildings.…”

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confidence: 99%

Bayesian model updating using incomplete modal data without mode matching

Sun

Büyüköztürk

2016

SPIE Proceedings

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This study investigates a new probabilistic strategy for model updating using incomplete modal data. A hierarchical Bayesian inference is employed to model the updating problem. A Markov chain Monte Carlo technique with adaptive random-work steps is used to draw parameter samples for uncertainty quantification. Mode matching between measured and predicted modal quantities is not required through model reduction.We employ an iterated improved reduced system technique for model reduction. The reduced model retains the dynamic features as close as possible to those of the model before reduction. The proposed algorithm is finally validated by an experimental example.

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A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method

Cited by 36 publications

References 44 publications

A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

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

Bayesian model updating using incomplete modal data without mode matching

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