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1

Bayesian multidimensional-matrix polynomial empirical regression

Mukha Vladimir S.

Control and Cybernetics

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2020

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Vol. 49, No. 3

291--314

EN

The problem of parameter estimation for the polynomial in the input variables regression function is formulated and solved. The input and output variables of the regression function are multidimensional matrices. The parameters of the regression function are assumed to be random independent multidimensional matrices with Gaussian distribution and known mean value and variance matrices. The solution to this problem is a multidimensional-matrix system of the linear algebraic equations in multidimensional-matrix unknown regression function parameters. We consider the particular cases of constant, affine and quadratic regression function, for which we have obtained formulas for parameter calculation. Computer simulation of the quadratic regression function is performed for the two-dimensional matrix input and output variables.

2

System identification and tuning of wireless power transfer systems with multiple magnetically coupled resonators

Winges J., Rylander T., Petersson C., Ekman C., Johansson L.-Å., McKelvey T.

Transactions on Environment and Electrical Engineering

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2017

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Vol. 2, No. 2

86--92

EN

We present a procedure for system identification and tuning of a wireless power transfer (WPT) system with four magnetically coupled resonators, where each resonator consists of a coil and a capacitor bank. The system-identification procedure involves three main steps: 1) individual measurement of the capacitor banks in the system; 2) measurement of the frequency-dependent two-port impedance matrix of the magnetically coupled resonators; and 3) determining the inductance of all coils and their corresponding coupling coefficients using a Bayesian approach. The Bayesian approach involves solving an optimization problem where we minimize the mismatch between the measured and simulated impedance matrix together with a penalization term that incorporates information from a direct measurement procedure of the inductance and losses of the coils. This identification procedure yields an accurate system model which we use to tune the four capacitance values to recover high system-performance and account for, e.g., manufacturing tolerances and coil displacement. For a prototype WPT system, we achieve 3.3 kW power transfer with 91% system efficiency over an air-gap distance of approximately 20 cm.

3

Application of a Bayesian estimator for identification of edible oils on the basis of spectrophotometric data

Morawski R. Z., Niedziński C.

Metrology and Measurement Systems

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2008

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Vol. 15, nr 3

247-266

EN

Spectrophotometric analysis of oil mixtures, containing olive oil, is the subject of this paper. Its objective is to compare a new Bayesian estimator with the constrained least-squares estimator, when applied for estimation of concentrations of components of edible oil mixtures, and to assess its applicability for solving problems of industrial monitoring. The comparison is based on the use of semi-synthetic NIR spectrophotometric data and criteria related to measurement uncertainty.