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A heuristic procedure based on novel recursive formulation of sinusoid (RFS) and on regression with predictive least-squares (LS) enables to decompose both uniformly and nonuniformly sampled 1-d signals into a sparse set of sinusoids (SSS). An optimal SSS is found by Levenberg–Marquardt (LM) optimization of RFS parameters of near-optimal sinusoids combined with common criteria for the estimation of the number of sinusoids embedded in noise. The procedure estimates both the cardinality and the parameters of SSS. The proposed algorithm enables to identify the RFS parameters of a sinusoid from a data sequence containing only a fraction of its cycle. In extreme cases when the frequency of a sinusoid approaches zero the algorithm is able to detect a linear trend in data. Also, an irregular sampling pattern enables the algorithm to correctly reconstruct the under-sampled sinusoid. Parsimonious nature of the obtaining models opens the possibilities of using the proposed method in machine learning and in expert and intelligent systems needing analysis and simple representation of 1-d signals. The properties of the proposed algorithm are evaluated on examples of irregularly sampled artificial signals in noise and are compared with high accuracy frequency estimation algorithms based on linear prediction (LP) approach, particularly with respect to Cramer–Rao Bound (CRB). [ABSTRACT FROM AUTHOR]

Abstract: The main disadvantage of self-organizing polynomial neural networks (SOPNN) automatically structured and trained by the group method of data handling (GMDH) algorithm is a partial optimization of model weights as the GMDH algorithm optimizes only the weights of the topmost (output) node. In order to estimate to what extent the approximation accuracy of the obtained model can be improved the particle swarm optimization (PSO) has been used for the optimization of weights of all node-polynomials. Since the PSO is generally computationally expensive and time consuming a more efficient Levenberg–Marquardt (LM) algorithm is adapted for the optimization of the SOPNN. After it has been optimized by the LM algorithm the SOPNN outperformed the corresponding models based on artificial neural networks (ANN) and support vector method (SVM). The research is based on the meta-modeling of the thermodynamic effects in fluid flow measurements with time-constraints. The outstanding characteristics of the optimized SOPNN models are also demonstrated in learning the recurrence relations of multiple superimposed oscillations (MSO). [Copyright &y& Elsevier]

A metamodeling of complex calculation procedures (static systems) is investigated with the aim to create low-complexity surrogate models that are applicable in low-computing-power real-time (RT) measurement systems. Unlike the single-parameter error criteria and minimum description length measure, the proposed compound-squared-relative-error measure forces the group method of data handling (GMDH) algorithm to prefer the models having the smallest compound deviation of accuracy and execution time from the given thresholds and thus generally leads to more favorable models with respect to both conditions. Approximation errors, execution speed, and the applicability of the derived GMDH models in RT flow-rate measurements of natural gas are discussed and compared with the corresponding models derived by artificial neural network and support vector regression. [ABSTRACT FROM AUTHOR]

Abstract: The international standard for flowrate measurements ISO-5167 recommends the temperature sensor to be located downstream of the differential device what may cause a significant error in the measurement of the flowrate of natural gas, especially at high differential pressure, low temperature and low diameter ratio. The flowrate generally needs to be compensated for the temperature change due to the Joule–Thomson effect caused by the constriction of the metering device. The accurate compensation involves double calculation of both the natural gas properties and the flowrate. To decrease the computational load, an automatic correction of the flowrate by the GMDH polynomial surrogate is proposed. By using the compound measure of the approximation error and the execution time for model selection, the modified GMDH algorithm searches for the satisfactory model fulfilling the constraints of real-time application. The automatic correction of the flowrate measurements of a natural gas is simulated and the corresponding results are discussed. The derived model can be equally used for a natural gas specified by composition or by physical properties. [Copyright &y& Elsevier]

Describes an indirect tracking of the measurement system characteristic by using a periodic multiple-point autocalibration. Unsteady, nonlinear function that depends upon time and ambient conditions; Application of a tangent method to the ideal characteristic; Verification of the efficiency of the algorithm for direct current generation; Measurement of internal references.