Model selection through a statistical analysis of the global minimum of a weighted non-linear least squares cost function

Pintelon, Rik; Schoukens, Johan; Vandersteen, Gerd

doi:10.1109/cdc.1996.573603

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…Tracking the model quality can be achieved by using the value of the cost function in equation and/or using the correlations of the residual errors in equation evaluated for

\overset{θ}{true}

[ Pintelon and Schoukens , ]. The expected value and the variance of the cost in its minimizer

\overset{θ}{true}

can be computed in the absence of modeling errors [ Pintelon and Schoukens , ; Pintelon et al ., ]. The expected value of the ML cost function equals

N K - 3 / 2

.…”

Section: The Lpml Methodsmentioning

confidence: 99%

Determining groundwater‐surface water exchange from temperature‐time series: Combining a local polynomial method with a maximum likelihood estimator

Vandersteen

Schneidewind

Anibas

et al. 2015

Water Resources Research

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The use of temperature-time series measured in streambed sediments as input to coupled water flow and heat transport models has become standard when quantifying vertical groundwater-surface water exchange fluxes. We develop a novel methodology, called LPML, to estimate the parameters for 1-D water flow and heat transport by combining a local polynomial (LP) signal processing technique with a maximum likelihood (ML) estimator. The LP method is used to estimate the frequency response functions (FRFs) and their uncertainties between the streambed top and several locations within the streambed from measured temperature-time series data. Additionally, we obtain the analytical expression of the FRFs assuming a pure sinusoidal input. The estimated and analytical FRFs are used in an ML estimator to deduce vertical groundwater-surface water exchange flux and its uncertainty as well as information regarding model quality. The LPML method is tested and verified with the heat transport models STRIVE and VFLUX. We demonstrate that the LPML method can correctly reproduce a priori known fluxes and thermal conductivities and also show that the LPML method can estimate averaged and time-variable fluxes from periodic and nonperiodic temperature records. The LPML method allows for a fast computation of exchange fluxes as well as model and parameter uncertainties from many temperature sensors. Moreover, it can utilize a broad frequency spectrum beyond the diel signal commonly used for flux calculations.

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“…Tracking the model quality can be achieved by using the value of the cost function in equation and/or using the correlations of the residual errors in equation evaluated for

\overset{θ}{true}

[ Pintelon and Schoukens , ]. The expected value and the variance of the cost in its minimizer

\overset{θ}{true}

can be computed in the absence of modeling errors [ Pintelon and Schoukens , ; Pintelon et al ., ]. The expected value of the ML cost function equals

N K - 3 / 2

.…”

Section: The Lpml Methodsmentioning

confidence: 99%

Determining groundwater‐surface water exchange from temperature‐time series: Combining a local polynomial method with a maximum likelihood estimator

Vandersteen

Schneidewind

Anibas

et al. 2015

Water Resources Research

Self Cite

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“…In a first attempt, a separate Forsythe polynomial basis was selected for the numerator and the denominator of the rational form. Despite its optimality for this dual basis approach, the method failed to obtain optimal conditiong ( ) for the system (7). In this paper, a basis of vector orthogonal polynomials is constructed to orthogonalise the numerator and the denominator of the rational form together.…”

Section: A Least Squares Cost Functionmentioning

confidence: 99%

“…Over-simplification of the model can be detected by comparison of the model cost function with its known expected value. Combination of all these indicators criterion leads to fully automatic model order selection methods ( [7], [8]). On the dark side, frequency domain methods suffer from a poor numerical conditioning when the frequency span and/or the model order become large (more than 2 decades frequency span and orders of more than 20 in the laplace domain, narrow banded (a few %) systems of high order (>30) in the discretetime domain).…”

Section: Introductionmentioning

confidence: 99%

Robust rational approximation for identification

Bultheel

Barel

Rolain

et al.

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

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Using vector orthogonal polynomials as basis functions for the maximum-likelihood (ML) frequency domain identification of the rational form of a linear time invariant system is shown to circumvent all the well known numerical conditioning problems. For identification of very high order systems (e.g. 100/100), systems that operate over a wide frequency band, or even in the presence of over-and undermodelling, condition numbers of less than 10 are reported on real measurements and simulation.

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Model selection through a statistical analysis of the global minimum of a weighted non-linear least squares cost function

Cited by 2 publications

References 17 publications

Determining groundwater‐surface water exchange from temperature‐time series: Combining a local polynomial method with a maximum likelihood estimator

Determining groundwater‐surface water exchange from temperature‐time series: Combining a local polynomial method with a maximum likelihood estimator

Robust rational approximation for identification

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