BIL PUBLISHER JOURNAL TITLE

YEAR SUMMARY

Monte Carlo Method1 (Schuëller et

al., 2009)Uncertainty Analysis of a Large-Scale Satellite Finite Element Model

2009 Objective-investigated the effect of uncertainty parameters on structural performance by combining MCS with FEM

2 (Mares et al., 2006)

Stochastic model updating: Part 1—theory and simulated example

2006 Objective-proposed a Monte Carlo inverse propagation procedure by using gradient and regression method

3 (Mottershead et al., 2006)

Stochastic model updating: Part 2—application to a set of physical structures

2006 Objective-proposed a Monte Carlo inverse propagation procedure by using gradient and regression method

4 (Fang et al., 2012)

A stochastic model updating method for parameter variability quantification based on response surface models and MonteCarlo simulation(mathematical model to substitute FE model)

2012 Objective:-presented a stochastic model updating process(a series of deterministic model updating process divide the stochastic and the inverse problem solved within a deterministic framework by using 2nd order RSM and multiobjective optimization)-propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation.-RS model acted as a replacement of FE model in the interest of programming simplification, fast response computation and easy inverse optimization.-RS model used in the inverse optimization stage for parameter prediction.- Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses (response sample generation).-proposed method validated by using a numerical beam and a set of tested plate.-For plate structure- basic principle of vibration (for torsional modes-the contribution of E had no effect & G as major contributor)-For flexural mode/vibration, thickness & E dominate plate vibration (E more significant than t)-G has no contribution for flexural vibration-If t, G & E had same variability level, the significance of t would increase a lot with significance reduction of E & G-comparison with ref no 13 (Husain, Khodaparast, & Ouyang, 2010)-combination of geometrical and material properties may improve variability predictions

5 (Rui et al., 2013)

An efficient statistically equivalent reduced method on stochastic model updating

2013 Objective-used Hermite polynomial chaos expansion stochastic response surface method together with MCS for stochastic model updating based on the gradient method

6 (Bao & Wang, 2015)

A Monte Carlo simulation based inverse propagation methodfor stochastic model updating

2015 Objective:-proposed an efficient method for SMU based on statistical theory.-construct an incomplete 4th order polynomial response surface model(RSM) by implementing the F-test evaluation and DOE, and has been developed-Combination of integrates RSM and Monte Carlo simulation, reduce the calculation amount & rapid random sampling become possible.-The mean and covariance of parameters are estimated - to improve correlation btween result of exp & theory by by minimizing the weighted obj function through hybrid of particle swarm & Nelder-Mead simple optimization method-Verification of updating result using coincidence ratio criterion by employing GARTEUR assembly structure.

Conclusion:-Sensitivity of model parameter being filtered out using F-test evaluation and DOE-Nonlinear r/ship btween input & outputs being described out by the incomplete 4th order polynomial RSM-The statistical properties of parameters are synchronously estimated by minimizing the weighted sum of mean and covariance matrix objective functions-an implementation process for the stochastic model updating method based on RSM and MCS, in which the amount of calculation is greatly reduced.-Results from a multi-case three degrees-of-freedom mass-spring system and a GARTEUR assembly model validate the proposed method

PERTUBATION METHOD1 (Khodaparast et

al., 2008)Perturbation methods for the estimation of parameter variability in stochastic model updating

2008 Objective-presented an effiecent perturbation method using 1st order sensitivities neglecting the updating parameters and the measured response correlations.-discuss about the problem of model updating in the presence of test structure variability-Sensitivity method being used to develop model updating equation-Develop 2 pertubation method for estimation of the 1 st & 2nd

statistical moments of randomised updating parameters from measured variability in modal responses (natural f & mode shapes)-This study also proved that when the correlation between updating parameters & measurement is omitted, then the requirement to calc 2nd order sensitivities is no longer necessary

2 (Husain, Khodaparast, & Ouyang, 2010)

Parameter Selections For Stochastic Uncertainty InDynamic Models Of Simple And Complicated

2010 Objective:-study on how parameter selections can be sufficiently made for stochastic problem- the perturbation method used to estimate parameter variability in the exp modal data-Monte Carlo method is employed to propagate the

Structures sources of variability through a deterministic FE model.-From the study, selecting some of the material properties as the updating parameters provides better convergence than those updated by using only the thickness parameters.- The selection of parameters should also be chosen so that the mean outputs are closer to the measured outputs, and convergence between the scatter plots of the predicted and measured outputs can be obtained by using both geometrical and material properties in the updating procedure, rather than choosing a number of the geometrical properties alone, as has been demonstrated in this paper.-relies on Taylor series expansion-Method taken into account the calculation eff & retains the 1st and 2nd order Taylor expansion that contains 1st order and 2nd order sensitivity matrix however-this method only depends on initial value and distribution range of parameters

3 (Husain, Khodaparast, Mottershead, et al., 2010)

Application of the Perturbation Method With Parameter Weighting Matrix Assignments for Estimating Variability in a Set of Nominally Identical Welded Structures

2010 Objective:-the perturbation method used by Haddad Khodaparast et al. [4, 7] is employed-to investigate the variability that exists between a set of nominally identical test structures-The perturbation equations are used for estimation of means and covariance of updating parameters and two approaches of parameter weighting matrix assignments are explained.

1. 3 parameters- Eweld &Epatch & weld diameter-demonstrate good correlation between the predicted mean natural frequencies and their measured data, but poor correlation is obtained between the predicted and measured covariances of the outputs-regularisation parameter λ = 40

2. 8 parameters - five from the components and three from the welds-Latter approaches are in very good agreement with the experimental data and excellent correlation between the predicted and measured covariance of the outputs is achieved.-(diff parameter weighting matrices are assigned to the means and covariance updating parameters because the low level of variability in parameters from component compare to weld parameter)

-FE modelling -3500QUAD4 & 20 CWELD element-main uncertainties : weld parameters(e.g Eweld &Epatch & weld diameter-advantage using perturbation method over Hua - only the first-order sensitivitymatrix is needed in Eq. 12, hence big reduction in terms of computationalEffort is achieved.

4 (Govers & Link, 2010)

Stochastic model updating—Covariance matrix adjustment from uncertain experimental modal data

2010 Objective-defined an objective function to identify parameters covariance;the updating process was divided into 2 independent steps by which parameter means and covariances matrices were adjusted in sequence based on gradient iteration method

5 (Chen & Maung, 2014)

Regularised finite element model updating using measured incomplete data

2014 Objective:-To present new based modal updating method that adopt measured incomplete modal data for evaluating the chosen structural updating parameters of the initial FE model at local level.-based on dynamic perturbation method, exact relationship between the structural parameter modifications and the incomplete measured modal data of the tested structure is generated- do not require the sensitivity analysis and the construction of an objective function.

-using an iterative soln procedure and simplified to estimate chosen structural updating parameters in the least square sense w/out requiring an optimization tech.-employed the Thikonov regularization algorithm incorporating L-curve criterion method for determining the regularisation parameter to reduce the instability of solutions with respect to modal measurement uncertainty & produce reliable solutions for the structural updating parameters.- demonstrated by the numerical simulation investigations and experimental studies of the space steel frame structure tested in the laboratory, where limited incomplete modal data

Two efficient methods in stochastic model updating,1) a perturbation method, and 2) a method based upon the minimisationof an objective function

Bao, N., & Wang, C. (2015). A Monte Carlo simulation based inverse propagation method for stochastic model updating. Mechanical Systems and Signal Processing.

Chen, H.-P., & Maung, T. S. (2014). Regularised finite element model updating using measured incomplete modal data. Journal of sound and vibration, 333(21), 5566-5582.

Fang, S.-E., Ren, W.-X., & Perera, R. (2012). A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation. Mechanical Systems and Signal Processing, 33(0), 83-96. doi: http://dx.doi.org/10.1016/j.ymssp.2012.06.028

Govers, Y., & Link, M. (2010). Stochastic model updating—Covariance matrix adjustment from uncertain experimental modal data. Mechanical Systems and Signal Processing, 24(3), 696-706. doi: http://dx.doi.org/10.1016/j.ymssp.2009.10.006

Husain, N. A., Khodaparast, H. H., Mottershead, J. E., & Ouyang, H. (2010). Application of the Perturbation Method With Parameter Weighting Matrix Assignments for Estimating Variability in a Set of Nominally Identical Welded Structures. Paper presented at the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis.

Husain, N. A., Khodaparast, H. H., & Ouyang, H. (2010). Parameter selections for stochastic uncertainty in dynamic models of simple and complicated structures. Paper presented at the Proceedings of the 10th International Conference on Recent Advances in Structural Dynamics, University of Southampton, Southampton.

Khodaparast, H. H., Mottershead, J. E., & Friswell, M. I. (2008). Perturbation methods for the estimation of parameter variability in stochastic model updating. Mechanical Systems and Signal Processing, 22(8), 1751-1773.

Mares, C., Mottershead, J., & Friswell, M. (2006). Stochastic model updating: part 1—theory and simulated

example. Mechanical Systems and Signal Processing, 20(7), 1674-1695. Mottershead, J., Mares, C., James, S., & Friswell, M. (2006). Stochastic model updating: part 2—application to

a set of physical structures. Mechanical Systems and Signal Processing, 20(8), 2171-2185. Rui, Q., Ouyang, H., & Wang, H. Y. (2013). An efficient statistically equivalent reduced method on stochastic

model updating. Applied Mathematical Modelling, 37(8), 6079-6096. doi: http://dx.doi.org/10.1016/j.apm.2012.11.026

Schuëller, G. I., Calvi, A., Pellissetti, M. F., Pradlwarter, H. J., Fransen, S. H. J. A., & Kreis, A. (2009). Uncertainty Analysis of a Large-Scale Satellite Finite Element Model. Journal of Spacecraft and Rockets, 46(1), 191-202. doi: 10.2514/1.32205