Extended Kalman Filter and Markov Chain Monte Carlo Methods forUncertainty Estimation. Application to X-Ray Fluorescence MachineCalibration and Metal Testing
2017
This paper is concerned with a method for uncertainty evaluation of steel sample content using X-Ray
Fluorescence method. The considered method of analysis is a comparative technique based on the X-Ray
Fluorescence; the calibration step assumes the adequate chemical composition of metallic analyzed sample.
It is proposed in this work a new combined approach using the Kalman Filter and Markov Chain Monte Carlo
(MCMC) for uncertainty estimation of steel content analysis. The Kalman filter algorithm is extended to the model
identification of the chemical analysis process using the main factors affecting the analysis results; in this case the
estimated states are reduced to the model parameters. The MCMC is a stochastic method that computes the statistical
properties of the considered states such as the probability distribution function (PDF) according to the initial state
and the target distribution using Monte Carlo simulation algorithm. Conventional approach is based on the linear
correlation, the uncertainty budget is established for steel Mn(wt%), Cr(wt%), Ni(wt%) and Mo(wt%) content
respectively. A comparative study between the conventional procedure and the proposed method is given. This kind
of approaches is applied for constructing an accurate computing procedure of uncertainty measurement
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