On the calibration problem

The classical calibration problem is primarily concerned with comparing an approximate measurement method with a very precise one. Frequently, both measurement methods are very noisy, so we cannot regard either method as giving the true value of the quantity being measured. Sometimes, it is desired to replace a destructive or slow measurement method, by a noninvasive, faster or less expensive one. The simplest solution is to cross calibrate one measurement method in terms of the other. The common practice is to use regression models, as cross calibration formulas. However, such models do not attempt to discriminate between the clutter and the true functional relationship between the cross calibrated measurement methods. A new approach is proposed, based on minimizing the sum of squares of the differences between the absolute values of the Fast Fourier Transform (FFT) series, derived from the readings of the cross calibrated measurement methods. The line taken is illustrated by cross calibration examples of simulated linear and nonlinear measurement systems, with various levels of additive noise, wherein the new method is compared to the classical regression techniques. It is shown, that the new method can discover better the true functional relationship between two measurement systems, which is occluded by the noise.

Download Full-text

A complete characterization and solution to the microphone position self-calibration problem

2013 IEEE International Conference on Acoustics, Speech and Signal Processing ◽

10.1109/icassp.2013.6638384 ◽

2013 ◽

Cited By ~ 34

Author(s):

Yubin Kuang ◽

Simon Burgess ◽

Anna Torstensson ◽

Kalle Astrom

Keyword(s):

Complete Characterization ◽

Self Calibration ◽

Calibration Problem

Download Full-text

Calibration and Uncertainty Quantification of Gas Turbine Performance Models

Volume 7A: Structures and Dynamics ◽

10.1115/gt2015-42392 ◽

2015 ◽

Author(s):

Manuel Arias Chao ◽

Darrel S. Lilley ◽

Peter Mathé ◽

Volker Schloßhauer

Keyword(s):

Uncertainty Quantification ◽

Gas Turbine ◽

Bayesian Approach ◽

Least Squares Method ◽

Measurement Data ◽

Operating Conditions ◽

Performance Models ◽

Regression Problem ◽

Calibration Problem ◽

Calibration Parameters

Calibration and uncertainty quantification for gas turbine (GT) performance models is a key activity for GT manufacturers. The adjustment between the numerical model and measured GT data is obtained with a calibration technique. Since both, the calibration parameters and the measurement data are uncertain the calibration process is intrinsically stochastic. Traditional approaches for calibration of a numerical GT model are deterministic. Therefore, quantification of the remaining uncertainty of the calibrated GT model is not clearly derived. However, there is the business need to provide the probability of the GT performance predictions at tested or untested conditions. Furthermore, a GT performance prediction might be required for a new GT model when no test data for this model are available yet. In this case, quantification of the uncertainty of the baseline GT, upon which the new development is based on, and propagation of the design uncertainty for the new GT is required for risk assessment and decision making reasons. By using as a benchmark a GT model, the calibration problem is discussed and several possible model calibration methodologies are presented. Uncertainty quantification based on both a conventional least squares method and a Bayesian approach will be presented and discussed. For the general nonlinear model a fully Bayesian approach is conducted, and the posterior of the calibration problem is computed based on a Markov Chain Monte Carlo simulation using a Metropolis-Hastings sampling scheme. When considering the calibration parameters dependent on operating conditions, a novel formulation of the GT calibration problem is presented in terms of a Gaussian process regression problem.

Download Full-text

A global optimization algorithm for laboratory star sensors calibration problem

Measurement ◽

10.1016/j.measurement.2018.10.060 ◽

2019 ◽

Vol 134 ◽

pp. 253-265

Author(s):

Tao Ye ◽

Xi Zhang ◽

Ping Song ◽

Fei Yang

Keyword(s):

Global Optimization ◽

Optimization Algorithm ◽

Global Optimization Algorithm ◽

Calibration Problem

Download Full-text

Decision-theoretical formulation of the calibration problem

Journal of Automatic Chemistry ◽

10.1155/s1463924689000143 ◽

1989 ◽

Vol 11 (2) ◽

pp. 70-75

Author(s):

Miroslav Kárný ◽

Katalin M. Hangos

Keyword(s):

Analytical Chemistry ◽

Uncertain Data ◽

Conditional Distributions ◽

Theoretical Formulation ◽

Calibration Experiment ◽

Calibration Problem ◽

Estimation And Filtering ◽

Relationship Of ◽

The Relationship ◽

Abstract Formulation

The choice of calibration policy is of basic importance in analytical chemistry. A prototype of the practical calibration problem is formulated as a mathematical task and a Bayesian solution of the resulting decision problem is presented. The optimum feedback calibration policy can then be found by dynamic programming. The underlying parameter estimation and filtering are solved by updating relevant conditional distributions. In this way: the necessary information is specified (for instance, the need for knowledge of the probability distribution of unknown samples is clearly recognized as the conceptually unavoidable informational source); the relationship of the information gained from a calibration experiment to the ultimate goal of calibration, i.e., to the estimation of unknown samples, is explained; an ideal solution is given which can serve for comparing various ways of calibration; and a consistent and conceptually simple guideline is given for using decision theory when solving problems of analytical chemistry containing uncertain data. The abstract formulation is systematically illustrated by an example taken from gas chromatography.

Download Full-text