Sandu, A., Sandu, C., and Ahmadian, M., 2006, “Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects,” "*Multibody System Dynamics*", Springer, The Netherlands, pp. 1–23.

Sandu, C., Sandu, A., and Ahmadian, M., 2006, “Modeling Multibody Dynamic Systems With Uncertainties. Part II: Numerical Applications,” "*Multibody System Dynamics*", Springer, The Netherlands, Vol. 15 , pp. 241–262.

Tarantola, A., 2004, "*Inverse Problem Theory and Methods for Model Parameter Estimation*", Society for Industrial and Applied Mathematics, Philadelphia, PA.

Bishwal, J. P. N., 2008, "*Parameter Estimation in Stochastic Differential Equations*", Springer, Berlin, Germany.

Aster, R. C., Borchers, B., and Thurber, C. H., 2005, "*Parameter Estimation and Inverse Problems*", Elsevier, Amsterdam, The Netherlands/Academic, Boston, MA.

Liu, C. S., 2008, “Identifying Time-Dependent Damping and Stiffness Functions by a Simple and Yet Accurate Method,” J. Sound Vib., 318 , pp. 148–165.

[CrossRef]Araújo, A. L., Mota Soares, C. M., Herskovits, J., and Pedersen, P., 2009, “Estimation of Piezoelastic and Viscoelastic Properties in Laminated Structures,” Compos. Struct., 87 (2), pp. 168–174.

[CrossRef]Pradlwarter, H. J., Pellissetti, M. F., Schenk, C. A., Schuëller, G. I., Kreis, A., Fransen, S., Calvi, A., and Klein, M., 2005, “Realistic and Efficient Reliability Estimation for Aerospace Structures,” Comput. Methods Appl. Mech. Eng., 194 (12–16), pp. 1597–1617, special issue on computational methods in stochastic mechanics and reliability analysis.

[CrossRef]Catania, F., and Paladino, O., 2009, “Optimal Sampling for the Estimation of Dispersion Parameters in Soil Columns Using an Iterative Genetic Algorithm,” Environ. Modell. Software, 24 (1), pp. 115–123.

[CrossRef]Varziri, M. S., Poyton, A. A., McAuley, K. B., McLellan, P. J., and Ramsay, J. O., 2008, “Selecting Optimal Weighting Factors in iPDA for Parameter Estimation in Continuous-Time Dynamic Models,” Comput. Chem. Eng., 32 (12), pp. 3011–3022.

[CrossRef]Fathy, H. K., Kang, D., and Stein, J. L., 2008, “Online Vehicle Mass Estimation Using Recursive Least Squares and Supervisory Data Extraction,” Proceedings of the 2008 American Control Conference , pp. 1842–1848.

Liang, J. W., 2007, “Damping Estimation via Energy-Dissipation Method,” J. Sound Vib., 307 , pp. 349–364.

[CrossRef]Oliveto, N. D., Scalia, G., and Oliveto, G., 2008, “Dynamic Identification of Structural Systems With Viscous and Friction Damping,” J. Sound Vib., 318 , pp. 911–926.

[CrossRef]Raïssi, T., Ramdani, N., and Candau, Y., 2004, “Set Membership State and Parameter Estimation for Systems Described by Nonlinear Differential Equations,” Automatica, 40 , pp. 1771–1777.

[CrossRef]Mockus, J., Eddy, W., Mockus, A., Mockus, L., and Reklaitis, G., 1997, "*Bayesian Heuristic Approach to Discrete and Global Optimization: Algorithms, Vizualization, Software and Applications*", Kluwer Academic, Dordrecht, The Netherlands.

Thompson, B., and Vladimirov, I., 2005, “Bayesian Parameter Estimation and Prediction in Mean Reverting Stochastic Diffusion Models,” Nonlinear Anal., 63 , pp. e2367–e2375.

[CrossRef]Wang, J., and Zabaras, N., 2005, “Using Bayesian Statistics in the Estimation of Heat Source in Radiation,” Int. J. Heat Mass Transfer, 48 , pp. 15–29.

[CrossRef]Khan, T., and Ramuhalli, P., 2008, “A Recursive Bayesian Estimation Method for Solving Electromagnetic Nondestructive Evaluation Inverse Problems,” IEEE Trans. Magn., 44 (7), pp. 1845–1855.

[CrossRef]Nocedal, J., and Wright, S. J., 2006, "*Numerical Optimization*", Springer, New York, Vol. 2 .

Horst, R., Pardalos, P. M., and Thoai, N. V., 2000, "*Introduction to Global Optimization*", 2nd ed., Kluwer Academic, Dordrecht, The Netherlands.

Floudas, C. A., 2000, "*Deterministic Global Optimization: Theory, Methods, and Applications*", Kluwer Academic, Dordrecht, The Netherlands.

1995, "*Handbook of Global Optimization*", R.Horst and P.M.Pardalos, eds., Kluwer Academic, Dordrecht, The Netherlands, Vol. 1 .

2002, "*Handbook of Global Optimization*", P.M.Pardalos and H.E.Romeijn, eds., Kluwer Academic, Dordrecht, The Netherlands, Vol. 2 .

Liberti, L., and Maculan, N., 2006, "*Global Optimization: From Theory to Implementation*", Springer, Berlin, Germany.

Davis, L., 1991, "*Handbook of Genetic Algorithms*", Van Nostrand Reinhold, New York.

Zhang, B. T., 1999, “A Bayesian Framework for Evolutionary Computation,” Proceedings of the 1999 Congress on Evolutionary Computation , Vol. 1 , pp. 722–728.

Sun, J., Zhang, Q., and Tsang, E. P. K., 2005, “DE/EDA: A New Evolutionary Algorithm for Global Optimization,” Inf. Sci. (N.Y.), 169 (3–4), pp. 249–262.

Zhang, Q., Sun, J., Tsang, E., and Ford, J., 2004, “Hybrid Estimation of Distribution Algorithm for Global Optimization,” Eng. Comput., 21 (1), pp. 91–107.

[CrossRef]Zhang, Q., Sun, J., and Tsang, E. P. K., 2005, “An Evolutionary Algorithm With Guided Mutation for the Maximum Clique Problem,” IEEE Trans. Evol. Comput., 9 (2), pp. 192–200.

[CrossRef]Kalman, R. E., 1960, “A New Approach to Linear Filtering and Prediction Problems,” ASME J. Basic Eng., 82 , pp. 35–45.

Evensen, G., 1992, “Using the Extended Kalman Filter With a Multi-Layer Quasi-Geostrophic Ocean Model,” J. Geophys. Res., 97 (C11), pp. 17905–17924.

[CrossRef]Evensen, G., 1993, “Open Boundary Conditions for the Extended Kalman Filter With a Quasi-Geostrophic Mode,” J. Geophys. Res., 98 (C19), pp. 16529–16546.

[CrossRef]Evensen, G., 1994, “Sequential Data Assimilation With a Non-Linear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics,” J. Geophys. Res., 99 (C5), pp. 10143–10162.

[CrossRef]Blanchard, E., Sandu, A., and Sandu, C., 2007, “Parameter Estimation Method Using an Extended Kalman Filter,” Proceedings of the Joint North America, Asia-Pacific ISTVS Conference and Annual Meeting of Japanese Society for Terramechanics , Fairbanks, AK.

Saad, G., Ghanem, R. G., and Masri, S., 2007, “Robust System Identification of Strongly Non-Linear Dynamics Using a Polynomial Chaos Based Sequential Data Assimilation Technique,” Collection of Technical Papers—48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference , Honolulu, HI, Vol. 6 , pp. 6005–6013.

Snyder, C., Bengtsson, T., Bickel, P., and Anderson, J., 2008, “Obstacles to High-Dimensional Particle Filtering,” Mon. Weather Rev., 136 (12), pp. 4629–4640.

[CrossRef]Sohns, B., Allison, J., Fathy, H. K., and Stein, J. L., 2006, “Efficient Parameterization of Large-Scale Dynamic Models Through the Use of Activity Analysis,” Proceedings of the ASME IMECE 2006 , Chicago, IL.

Zhang, D., and Lu, Z., 2004, “An Efficient, High-Order Perturbation Approach for Flow in Random Porous Media via Karhunen–Loeve and Polynomial Expansions,” J. Comput. Phys., 194 (2), pp. 773–794.

[CrossRef]Ghanem, R. G., and Spanos, P. D., 2003, "*Stochastic Finite Elements*", Dover, Mineola, NY.

Ghanem, R. G., and Spanos, P. D., 1990, “Polynomial Chaos in Stochastic Finite Element,” ASME J. Appl. Mech., 57 , pp. 197–202.

[CrossRef]Ghanem, R. G., and Spanos, P. D., 1991, “Spectral Stochastic Finite-Element Formulation for Reliability Analysis,” J. Eng. Mech., 117 (10), pp. 2351–2372.

[CrossRef]Ghanem, R. G., and Spanos, P. D., 1993, “A Stochastic Galerkin Expansion for Nonlinear Random Vibration Analysis,” Probab. Eng. Mech., 8 (3–4), pp. 255–264.

[CrossRef]Xiu, D., and Karniadakis, G. E., 2002, “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations,” J. Sci. Comput., 24 (2), pp. 619–644.

Xiu, D., Lucor, D., Su, C. H., and Karniadakis, G. E., 2002, “Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos,” ASME J. Fluids Eng., 124 , pp. 51–59.

[CrossRef]Xiu, D., and Karniadakis, G. E., 2002, “Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos,” Comput. Methods Appl. Mech. Eng., 191 , pp. 4927–4948.

[CrossRef]Xiu, D., and Karniadakis, G. E., 2003, “Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos,” J. Comput. Phys., 187 , pp. 137–167.

[CrossRef]Sandu, C., Sandu, A., Chan, B. J., and Ahmadian, M., 2004, “Treating Uncertainties in Multibody Dynamic Systems Using a Polynomial Chaos Spectral Decomposition,” Proceedings of the ASME IMECE 2004, Sixth Annual Symposium on Advanced Vehicle Technology , Anaheim, CA, Paper No. IMECE2004-60482.

Sandu, C., Sandu, A., Chan, B. J., and Ahmadian, M., 2005, “Treatment of Constrained Multibody Dynamic Systems With Uncertainties,” Proceedings of the SAE Congress 2005 , Detroit, MI, Paper No. 2005-01-0936.

Li, L., Sandu, C., and Sandu, A., 2005, “Modeling and Simulation of a Full Vehicle With Parametric and External Uncertainties,” Proceedings of the 2005 ASME International Mechanical Engineering Congress and Exposition, Seventh VDC Annual Symposium on ‘Advanced Vehicle Technologies,’ Session 4: Advances in Vehicle Systems Modeling and Simulation , Orlando, FL, Paper No. IMECE2005-82101.

Sandu, C., Sandu, A., and Li, L., 2006, “Stochastic Modeling of Terrain Profiles and Soil Parameters,” SAE 2005 Transactions Journal of Commercial Vehicles, 114 (2), pp. 211–220.

Blanchard, E., Sandu, C., and Sandu, A., 2007, “A Polynomial-Chaos-Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems,” Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2007, Ninth International Conference on Advanced Vehicle and Tire Technologies (AVTT) , Las Vegas, NV.

Soize, C., and Ghanem, R., 2004, “Physical Systems With Random Uncertainties: Chaos Representations With Arbitrary Probability Measure,” SIAM J. Sci. Comput. (USA), 26 (2), pp. 395–410.

[CrossRef]Desceliers, C., Ghanem, R., and Soize, C., 2006, “Maximum Likelihood Estimation of Stochastic Chaos Representations From Experimental Data,” Int. J. Numer. Methods Eng., 66 (6), pp. 978–1001.

[CrossRef]Desceliers, C., Soize, C., and Ghanem, R., 2007, “Identification of Chaos Representations of Elastic Properties of Random Media Using Experimental Vibration Tests,” Comput. Mech., 39 (6), pp. 831–838.

[CrossRef]Li, J., and Xiu, D., 2009, “A Generalized Polynomial Chaos Based Ensemble Kalman Filter With High Accuracy,” J. Comput. Phys., 228 , pp. 5454–5694.

[CrossRef]Evensen, G., 2003, “The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,” Ocean Dyn., 53 , pp. 343–367.

[CrossRef]Lenartz, F., Raick, C., Soetaert, K., and Grégoire, M., 2007, “Application of an Ensemble Kalman Filter to a 1-D Coupled Hydrodynamic-Ecosystem Model of the Ligurian Sea,” J. Mar. Syst., 68 , pp. 327–348.

[CrossRef]Smith, A. H. C., Monti, A., and Ponci, F., 2007, “Indirect Measurements via a Polynomial Chaos Observer,” IEEE Trans. Instrum. Meas., 56 (3), pp. 743–752.

[CrossRef]Wan, X., and Karniadakis, G. E., 2006, “Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures,” SIAM J. Sci. Comput. (USA), 28 (3), pp. 901–928.

[CrossRef]Cheng, H., and Sandu, A., 2009, “Uncertainty Quantification and Apportionment in Air Quality Models,” Environ. Modell. Software, 24 , pp. 917–925.

[CrossRef]Cheng, H., and Sandu, A., 2009, “Efficient Uncertainty Quantification With the Polynomial Chaos Method for Stiff Systems,” Math. Comput. Simul., 79 (11), pp. 3278–3295.

[CrossRef]Wiener, N., 1938, “The Homogeneous Chaos,” Am. J. Math., 60 , pp. 897–936.

[CrossRef]Askey, R., and Wilson, J., 1985, “Some Basic Hypergeometric Polynomials that Generalize Jacobi Polynomials,” Mem. Am. Math. Soc., 319 , pp. 1–55.

Cohn, S. E., 1997, “An Introduction to Estimation Theory,” J. Meteorol. Soc. Jpn., 75 , pp. 257–288

Fisher, M., 2002, “Assimilation Techniques (5): Approximate Kalman Filters and Singular Vectors.”

Simon, D. E., 2001, “An Investigation of the Effectiveness of Skyhook Suspensions for Controlling Roll Dynamics of Sport Utility Vehicles Using Magneto-Rheological Dampers,” Ph.D. thesis, Virginia Tech, Blacksburg, VA.

Halton, J. H., and Smith, G. B., 1964, “Radical-Inverse Quasi-Random Point Sequence,” Commun. ACM, 7 (12), pp. 701–702.

[CrossRef]Hammersley, J. M., 1960, “Monte Carlo Methods for Solving Multivariables Problems,” Ann. N.Y. Acad. Sci., 86 , pp. 844–874.

[CrossRef]Blanchard, E., Sandu, A., and Sandu, C., 2008, “Parameter Estimation for Mechanical Systems Using an Extended Kalman Filter,” Computer Science Department, Virginia Tech, Technical Report No. CS-TR-08-18.

Blanchard, E., Sandu, A., and Sandu, C., 2007, “A Polynomial Chaos Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems—Part I: Theoretical Approach,” Computer Science Department, Virginia Tech, Technical Report No. TR-07-38.

Blanchard, E., Sandu, A., and Sandu, C., 2007, “A Polynomial Chaos Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems—Part II: Applications to Vehicle Systems,” Computer Science Department, Virginia Tech, Technical Report No. TR-07-39.