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Unscented importance sampling for parameter calibration of carbon sequestration systems

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Abstract

A Bayesian importance sampling method is developed to efficiently and accurately calibrate the parameters of non-linear and non-Gaussian system models. The unscented importance sampling (UIS) consists of two stages. The first stage uses the latest monitoring data to generate a Gaussian approximation of the true posterior distribution of the uncertain parameters and utilizes the measurement update stage of the unscented Kalman filter (UKF) to approximate the posterior. The second stage of UIS uses a mixture of approximate posterior computed in the first stage and a heavy tailed distribution as the proposal distribution for Bayesian importance sampling. UIS is repeated whenever new monitoring data becomes available. Two case studies were developed to study the UIS method and to compare it UKF and importance sampling (IS) methods: a non-linear analytical system model and synthesized CO2 injection model using a numerical multi-phase flow simulator. In analytical case study, it is shown that UIS is more accurate than both UKF and traditional IS with static proposal and the relative accuracy of the UIS over traditional IS increases with dimensionality of the parameter space. The higher accuracy of UIS compared to UKF and traditional IS with static proposal is also shown in the CO2 injection case study. It is also shown that increasing number of samples and a defensive mixture distribution with a mixture ratio between 0.1 and 0.25 enhances the performance of UIS.

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Notes

  1. For a discrete parameter space, all integrals will be replaced by summation.

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Acknowledgments

The authors acknowledge funding from the Natural Science and Engineering Research Council of Canada (NSERC) through Carbon Management Canada (CMC) and from NSERC’s Discovery Grant program. Lastly, we would like to thank our colleagues Drs. James Craig and Maurice Dusseault for their moral support and academic insights.

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  1. Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Mirhamed Sarkarfarshi & Robert Gracie

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  1. Mirhamed Sarkarfarshi
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  2. Robert Gracie
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Correspondence to Robert Gracie.

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Sarkarfarshi, M., Gracie, R. Unscented importance sampling for parameter calibration of carbon sequestration systems. Stoch Environ Res Risk Assess 29, 975–993 (2015). https://doi.org/10.1007/s00477-014-0963-7

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