A.G. Polak

Publications (2)1.21 Total impact

• Article: An Error-Minimizing Approach to Regularization in Indirect Measurements

  A.G. Polak
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  ABSTRACT: Indirect measurements often amount to the estimation of the parameters of a mathematical model that describes the object under investigation, and this process may numerically be ill conditioned. Various regularization techniques are used to solve the problem. This paper shows that popular regularization methods can be depicted as special cases of a generalized approach based on a penalty term in the minimized criterion function and how different kinds of a priori knowledge can be engaged into each of them. A new function, which depends on the estimate bias and variance, is proposed to find a regularization parameter that minimizes the error of estimation, as well as a novel approach for nonlinear estimation that results in the iterative minimization (IM) method. The superiority of IM with respect to the conventional Marquardt procedure is demonstrated. Based on analysis, it also follows that the regularization technique can be used even in the case of numerically well-conditioned indirect measurements, decreasing the total error of estimation.
  IEEE Transactions on Instrumentation and Measurement 03/2010; · 1.21 Impact Factor
• Conference Proceeding: Toward a metrological model of maximal expiration

  A.G. Polak
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  ABSTRACT: The purpose of this investigation is to derive a metrological model of maximal expiration characterized by a small amount of independent parameters that can be estimated from experimental data. Elaboration of the model was based on a forward-inverse method. The carried out regression analysis showed good approximation of airway properties by exponential functions with correlation coefficients lower then -0.95. The cross-sectional areas, airway lengths and compliances were replaced by the exponential functions with two parameters. The complex and simplified models for maximal expiration were implemented on a PC and compared. The sensitivity index expressing the effect of parameter reduction was 0.64%. The study showed possibility to reduce the parameters number of the maximal expiration model at least to 18
  Engineering in Medicine and Biology Society, 1996. Bridging Disciplines for Biomedicine. Proceedings of the 18th Annual International Conference of the IEEE; 12/1996