Simultaneous Model Parameter Estimation Research Articles

In Situ Estimation of Erosion Model Parameters Using an Advection‐Diffusion Model and Bayesian Inversion

AbstractWe describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Markov Chain Monte Carlo sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters.

Simultaneous Estimation of Model Parameters and Deceleration Intent by Unscented Kalman Filter Integrated with Dual Filter

Simultaneous Estimation of Model Parameters and Deceleration Intent by Unscented Kalman Filter Integrated with Dual Filter

Combined parameter and state estimation in the radio frequency hyperthermia treatment of cancer

ABSTRACTParticle filters are general methods for the solution of state estimation problems, which can be applied to nonlinear models with non-Gaussian uncertainties. In this paper, an algorithm of the particle filter is used for the simultaneous estimation of model parameters and state variables in a bioheat transfer problem associated with the radio frequency (RF) hyperthermia treatment of cancer. Results obtained with simulated measurements indicate an excellent agreement between the estimated and the exact quantities, even for cases with large uncertainties in the measurements, as well as in the evolution and measurement models.

Uncertainty based modeling of rainfall-runoff: Combined differential evolution adaptive Metropolis (DREAM) and K-means clustering

Simulation of rainfall-runoff process in urban areas is of great importance considering the consequences and damages of extreme runoff events and floods. The first issue in flood hazard analysis is rainfall simulation. Large scale climate signals have been proved to be effective in rainfall simulation and prediction. In this study, an integrated scheme is developed for rainfall-runoff modeling considering different sources of uncertainty. This scheme includes three main steps of rainfall forecasting, rainfall-runoff simulation and future runoff prediction. In the first step, data driven models are developed and used to forecast rainfall using large scale climate signals as rainfall predictors. Due to high effect of different sources of uncertainty on the output of hydrologic models, in the second step uncertainty associated with input data, model parameters and model structure is incorporated in rainfall-runoff modeling and simulation. Three rainfall-runoff simulation models are developed for consideration of model conceptual (structural) uncertainty in real time runoff forecasting. To analyze the uncertainty of the model structure, streamflows generated by alternative rainfall-runoff models are combined, through developing a weighting method based on K-means clustering. Model parameters and input uncertainty are investigated using an adaptive Markov Chain Monte Carlo method. Finally, calibrated rainfall-runoff models are driven using the forecasted rainfall to predict future runoff for the watershed. The proposed scheme is employed in the case study of the Bronx River watershed, New York City. Results of uncertainty analysis of rainfall-runoff modeling reveal that simultaneous estimation of model parameters and input uncertainty significantly changes the probability distribution of the model parameters. It is also observed that by combining the outputs of the hydrological models using the proposed clustering scheme, the accuracy of runoff simulation in the watershed is remarkably improved up to 50% in comparison to the simulations by the individual models. Results indicate that the developed methodology not only provides reliable tools for rainfall and runoff modeling, but also adequate time for incorporating required mitigation measures in dealing with potentially extreme runoff events and flood hazard. Results of this study can be used in identification of the main factors affecting flood hazard analysis.

An Approximate Expectation Maximization Algorithm for Estimating Parameters, Noise Variances, and Stochastic Disturbance Intensities in Nonlinear Dynamic Models

An algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities, and measurement noise variances for nonlinear dynamic systems that are described by stochastic differential equations. The proposed fully-Laplace approximation expectation maximization (FLAEM) algorithm uses an iterative approach wherein, in the first step, the model parameters are estimated using the approximate maximum likelihood estimation objective function developed by Varziri et al.,1 assuming that disturbance intensities and noise variances are known. In the second step, process disturbance intensities and measurement noise variance estimates are updated using expressions that rely on the fully-Laplace approximation in the expectation maximization algorithm. The proposed FLAEM method is illustrated using a nonlinear two-state continuous stirred tank reactor (CSTR) example. The effectiveness of the FLAEM algorithm is compared with a maximum-likelihood based method proposed by Kristensen et al.2...

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

SummaryThe variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.

Nonlinear dynamic data reconciliation and parameter estimation through particle swarm optimization: Application for an industrial polypropylene reactor

Abstract This work presents a procedure to solve nonlinear dynamic data reconciliation (NDDR) problems with simultaneous parameter estimation based on particle swarm optimization (PSO). The performance of the proposed procedure is compared to the performance of a standard Gauss–Newton (GN) scheme in a real industrial problem, as presented previously by Prata et al. [2006. Simultaneous data reconciliation and parameter estimation in bulk polypropylene polymerizations in real time. Macromolecular Symposia 243, 91–103; 2008. In-line monitoring of bulk polypropylene reactors based on data reconciliation procedures. Macromolecular Symposia 271, 26–37]. Both methods are used to solve the NDDR problem in an industrial bulk propylene polymerization process, using real data in real time for the simultaneous estimation of model parameters and process states. A phenomenological model of the real process, based on the detailed mass and energy balances and constituted by a set of algebraic–differential equations, was implemented and used for interpretation of the actual plant behavior in real time. The resulting nonlinear dynamic optimization problem was solved iteratively on a moving time window, in order to capture the current process behavior and allow for dynamic adaptation of model parameters. Obtained results indicate that the proposed PSO procedure can be implemented in real time, allowing for estimation of more reliable process states and model parameters and leading to much more robust and reproducible numerical performance.

Simultaneous estimation of model parameters and diffuse pollution sources for river water quality modeling

Diffuse pollution sources along a stream reach are very difficult to both monitor and estimate. In this paper, a systematic method using an optimal estimation algorithm is presented for simultaneous estimation of diffuse pollution and model parameters in a stream water quality model. It was applied with the QUAL2E model to the South Han River in South Korea for optimal estimation of kinetic constants and diffuse loads along the river. Initial calibration results for kinetic constants selected from a sensitivity analysis reveal that diffuse source inputs for nitrogen and phosphorus are essential to satisfy the system mass balance. Diffuse loads for total nitrogen and total phosphorus were estimated by solving the expanded inverse problem. Comparison of kinetic constants estimated simultaneously with diffuse sources to those estimated without diffuse loads, suggests that diffuse sources must be included in the optimization not only for its own estimation but also for adequate estimation of the model parameters. Application of the optimization method to river water quality modeling is discussed in terms of the sensitivity coefficient matrix structure.

MODELLING OF AN INTEGRATED SUPERHEATER BASED ON A WIENER APPROACH

This paper considers identification of a multiple-input single-output Wiener model of a new type of superheater integrated to a CFB boiler. The static part is based on energy- and mass balances. Simultaneous estimation of model parameters in both static and dynamic parts was based on the industrial data from an 80 MW CFB boiler. The results indicate that the approach can be satisfactorily used to capture and describe the steam temperature in a wide range of variation in the input variables.