[1] Kalman, R.E., A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 82(1), 1960, 35–45, doi: 10.1115/1.3662552.
[2] Schmidt, S.F., The Kalman filter - Its recognition and development for aerospace applications, Journal of Guidance and Control, 4(1), 1981, 4–7, doi: 10.2514/3.19713.
[3] Sorenson, H.W., Kalman filtering techniques, Advances in Control Systems, 3, 1966, 219–292, doi: 10.1016/b978-1-4831-6716-9.50010-2.
[4] Julier, S.J., Uhlmann, J.K., Durrant-Whyte, H.F., A new approach for filtering nonlinear systems, Proceedings of American Control Conference, 1995, 3, 1628–1632, doi: 10.1109/ACC.1995.529783.
[5] Wan, E.A., Van Der Merwe, R., The unscented Kalman filter for nonlinear estimation, IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, 2000, 153–158.
[6] Zhou, L., Wu, S., Yang, J.N., Experimental study of an adaptive extended Kalman filter for structural damage identification, Journal of Infrastructure Systems, 14(1), 2008, 42–51.
[7] Chatzi, E.N., Smyth, A.W., Masri, S.F., Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty, Structural Safety, 32, 2010, 326–337, doi: 10.1016/j.strusafe.2010.03.008.
[8] Song, W., Dyke, S.J., Real-time dynamic model updating of a hysteretic structural system, Journal of Structural Engineering, 140(3), 2014, 1–14, doi: 10.1061/(ASCE)ST.1943-541X.0000857.
[9] Sarkka, S., Bayesian filtering and smoothing, 1st ed. Cambridge University Press, Cambridge, United Kingdom, 2013.
[10] Olivier, A., Smyth, A.W., On the performance of online parameter estimation algorithms in systems with various identifiability properties, Frontiers in Built Environment, 3(14), 2017, 1–18, doi: 10.3389/fbuil.2017.00014.
[11] Wan, E., van der Merwe, R., Nelson, A.T., Dual estimation and the unscented transformation, Advances in Neural Information Processing Systems, 2000, 666–672.
[12] Lund, A., Dyke, S.J., Song, W., Bilionis, I., Identification of an experimental nonlinear energy sink device using the unscented Kalman filter, Mechanical Systems and Signal Processing, 136, 2020, doi: https://doi.org/10.1016/j.ymssp.2019.106512.
[13] Dertimanis, V.K., Chatzi, E.N., Eftekhar Azam, S., Papadimitriou, C., Input-state-parameter estimation of structural systems from limited output information, Mechanical Systems and Signal Processing, 126, 2019, 711–746, doi: 10.1016/j.ymssp.2019.02.040.
[14] Yuen, K.V., Kuok, S.C., Online updating and uncertainty quantification using nonstationary output-only measurement, Mechanical Systems and Signal Processing, 66, 2016, 62–77, doi: 10.1016/j.ymssp.2015.05.019.
[15] Lei, Y., Xia, D., Erazo, K., Nagarajaiah, S., A novel unscented Kalman filter for recursive state-input-system identification of nonlinear systems, Mechanical Systems and Signal Processing, 127, 2019, 120–135, doi: 10.1016/j.ymssp.2019.03.013.
[16] Solonen, A., Hakkarainen, J., Ilin, A., Abbas, M., Bibov, A., Estimating model error covariance matrix parameters in extended Kalman filtering, Nonlinear Processes in Geophysics, 21(5), 2014, 919–927, doi: 10.5194/npg-21-919-2014.
[17] Erazo, K., Sen, D., Nagarajaiah, S., Sun, L., Vibration-based structural health monitoring under changing environmental conditions using Kalman filtering, Mechanical Systems and Signal Processing, 117, 2019, 1–15, doi: 10.1016/j.ymssp.2018.07.041.
[18] Song, M., Astroza, R., Ebrahimian, H., Moaveni, B., Papadimitriou, C., Adaptive Kalman filters for nonlinear finite element model updating, Mechanical Systems and Signal Processing, 143, 2020, 106837, doi: 10.1016/j.ymssp.2020.106837.
[19] Gordon, N.J., Salmond, D.J., Smith, A.F.M., Novel approach to nonlinear / non-Gaussian Bayesian state estimation, IEE Proceedings (Radar and Signal Processing), 140(2), 1993, 107–113.
[20] Doucet, A., Godsill, S., Andrieu, C., On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, 10(3), 2000, 197–208.
[21] Chatzi, E.N., Smyth, A., The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing, Structural Control and Health Monitoring, 16, 2009, 99–123, doi: 10.1002/stc.
[22] Snyder, C., Bengtsson, T., Bickel, P., Anderson, J., Obstacles to high-dimensional particle filtering, Monthly Weather Review, 136(12), 2008, 4629–4640, doi: 10.1175/2008MWR2529.1.
[23] Chatzi, E., Smyth, A., Particle filter scheme with mutation for the estimation of time-invariant parameters in structural health monitoring applications, Structural Control and Health Monitoring, 20, 2013, 1081–1095, doi: 10.1002/stc.
[24] Olivier, A., Smyth, A.W., Particle filtering and marginalization for parameter identification in structural systems, Structural Control and Health Monitoring, 24, 2017, 1–25, doi: 10.1002/stc.1874.
[25] Azam, S.E., Mariani, S., Dual estimation of partially observed nonlinear structural systems: A particle filter approach, Mechanics Research Communications, 46, 2012, 54–61, doi: 10.1016/j.mechrescom.2012.08.006.
[26] Haug, A.J., Bayesian Estimation and Tracking: A Practical Guide, 1st ed. John Wiley & Sons, Hoboken, New Jersey, 2012.
[27] Blei, D.M., Kucukelbir, A., Mcauliffe, J.D., Variational inference: A review for statisticians, Journal of the American Statistical Association, 112(518), 2017, 859–877, doi: 10.1080/01621459.2017.1285773.
[28] Bishop, C.M., Pattern recognition and machine learning, 1st ed. Springer, Cambridge, UK, 2006.
[29] Saul, L.K., Jaakkola, T., Jordan, M.I., Mean field theory for sigmoid belief networks, Journal of Artificial Intelligence Research, 4, 1996, 61–76.
[30] Saul, L.K., Jordan, M.I., Exploiting Tractable Substructures in Intractable Networks, Advances in Neural Information Processing Systems, 1996, 486–492.
[31] Jaakkola, T.S., Jordan, M.I., A variational approach to Bayesian logistic regression models and their extensions, 6th International Workshop on Artificial Intelligence and Statistics, 1996, 4–15.
[32] Hinton, G.E., Van Camp, D., Keeping Neural Networks Simple by Minimizing the Description Length of the Weights, 6th Annual Conference on Computational Learning Theory, 1993.
[33] Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K., An introduction to variational methods for graphical models, Machine Learning, 37(2), 1999, 183–233, doi: 10.1007/978-94-011-5014-9_5.
[34] Blei, D.M., Ng, A.Y., Jordan, M.I., Latent Dirichlet allocation, Journal of Machine Learning Research, 3, 2003, 993–1022.
[35] Barber, D., Wiegernick, W., Tractable Variational Structures for Approximating Graphical Models, Advances in Neural Information Processing Systems, 1999, 183–199.
[36] Beal, M.J., Variational Algorithms for Approximate Bayesian Inference, Ph. D. Thesis, University College, London, 2003.
[37] Hoffman, M.D., Blei, D.M., Wang, C., Paisley, J., Stochastic variational inference, Journal of Machine Learning Research, 14(1), 2013, 1303–1347.
[38] Ranganath, R., Gerrish, S., Blei, D.M., Black box variational inference, Artificial Intelligence and Statistics, 2014, 814–822.
[39] Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., Blei, D.M., Automatic differentiation variational inference, Journal of Machine Learning Research, 18(1), 2017, 430–474.
[40] Gardner, P., Lord, C., Barthorpe, R.J., A unifying framework for probabilistic validation metrics, Journal of Verification, Validation, and Unvertainty Quantification, 2019, doi: 10.1115/1.4045296.
[41] Bamler, R., Zhang, C., Opper, M., Mandt, S., Tightening Bounds for Variational Inference by Revisiting Perturbation Theory, Journal of Statistical Mechanics: Theory and Experiment, (12), 2019, doi: https://doi.org/10.1088/1742-5468/ab43d3.
[42] McInerney, J., Ranganath, R., Blei, D., The population posterior and Bayesian modeling on streams, Advances in Neural Information Processing Systems, 2015, 1153–1161.
[43] Jihan, N., Jayasinghe, M., Perera, S., Streaming stochastic variational Bayes; An improved approach for Bayesian inference with data streams, PeerJ Preprints, 2019, doi: 10.7287/peerj.preprints.27790v2.
[44] Blei, D.M., Lafferty, J.D., A Correlated Topic Model of Science, The Annals of Applied Statistics, 1(1), 2007, 17–35, doi: 10.1214/07-AOAS114.
[45] Cohen, S.B., Smith, N.A., Covariance in unsupervised learning of probabilistic grammars, Journal of Machine Learning Research, 11, 2010, 3017–3051.
[46] Likas, A., Galatsanos, N.P., A variational method for Bayesian blind image deconvolution, International Conference on Image Processing, 2004, 52(8), 2222–2233, doi: 10.1109/ICIP.2003.1246846.
[47] Logsdon, B.A., Hoffman, G.E., Mezey, J.G., A variational Bayes algorithm for fast and accurate multiple locus genome-wide association analysis, BMC Bioninformatics, 11(1), 2010, 58–70.
[48] Raj, A., Stephens, M., Pritchard, J.K., fastSTRUCTURE: variational inference of population structure in large SNP data sets, Genetics, 197(2), 2014, 573–589, doi: 10.1534/genetics.114.164350.
[49] Lund, A., Bilionis, I., Dyke, S.J., Approximate Bayesian approach to rapid structural identification, Proceedings of the 17th World Conference on Earthquake Engineering, 2020.
[50] Wu, M., Smyth, A.W., Application of the unscented Kalman filter for real-time nonlinear structural system identification, Structural Control and Health Monitoring, 14, 2007, 971–990, doi: 10.1002/stc.
[51] Kingma, D.P., Ba, J., Adam: A Method for Stochastic Optimization, International Conference on Learning Representations, 2014, 1–15.
[52] Paszke, A. et al., PyTorch: An Imperative Style, High-Performance Deep Learning Library, Advances in Neural Information Processing Systems, 2019, 8024–8035.
[53] Lund, A., Dyke, S.J., Song, W., Bilionis, I., Global sensitivity analysis for the design of nonlinear identification experiments, Nonlinear Dynamics, 98(1), 2019, 375–394, doi: 10.1007/s11071-019-05199-9.
[54] Saltelli, A. et al., Global Sensitivity Analysis. The Primer, 1st ed. John Wiley & Sons, West Sussex, England, 2008.
[55] Herman, J., Usher, W., SaLib: An open-source Python library for sensitivity analysis, Journal of Open Source Software, 2(9), 2017, doi: doi:10.21105/joss.00097.
[56] Øksendal, B., Stochastic Differential Equations, 5th ed. Springer, Heidelberg, Germany, 2003.
[57] Murphy, K.P., Machine Learning: A Probabilistic Perspective. MIT Press, Cambridge, Massachusetts, 2012.