A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Levenberg-Marquardt application to two-phase nonlinear parameter estimation for finned-tube coil evaporators

A procedure for calculation of refrigerant mass flow rate is implemented in the distributed numerical model to simulate the flow in finned-tube coil dry-expansion evaporators, usually found in refrigeration and air-conditioning systems. Two-phase refrigerant flow inside the tubes is assumed to be one-dimensional, unsteady, and homogeneous. In themodel the effects of refrigerant pressure drop and the moisture condensation from the air flowing over the external surface of the tubes are considered. The results obtained are the distributions of refrigerant velocity, temperature and void fraction, tube-wall temperature, air temperature, and absolute humidity. The finite volume method is used to discretize the governing equations. Additionally, given the operation conditions and the geometric parameters, the model allows the calculation of the refrigerant mass flow rate. The value of mass flow rate is computed using the process of parameter estimation with the minimization method of Levenberg-Marquardt minimization. In order to validate the developed model, the obtained results using HFC-134a as a refrigerant are compared with available data from the literature.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

A two phase flow nonlinear parameter estimation for capillary tube-suction line heat exchanger

Here we present two-phase flow nonlinear parameter estimation for HFC's flow through capillary tube-suction line heat exchangers, commonly used as expansion devices in small refrigeration systems. The simplifying assumptions adopted are: steady state, pure refrigerant, one-dimensional flow, negligible axial heat conduction in the fluid, capillary tube and suction line walls. Additionally, it is considered that the refrigerant is free from oil and both phases are assumed to be at the same pressure, that is, surface tension effects are neglected. Metastable flow effects are also disregarded, and the vapor is assumed to be saturated at the local pressure. The so-called homogeneous model, involving three, first order, ordinary differential equations is applied to analyze the two-phase flow region. Comparison is done with experimental measurements of the mass flow rate and temperature distribution along capillary tubes working with refrigerant HFC-134a in different operating conditions.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Inversão em geofísica de poço: um estudo sobre ambiguidade

A ambiguidade na inversão de dados de geofísica de poço é estudada através da análise fatorial Q-modal. Este método é baseado na análise de um número finito de soluções aceitáveis, que são ordenadas, no espaço de soluções, segundo a direção de maior ambiguidade. A análise da variação dos parâmetros ao longo dessas soluções ordenadas permite caracterizar aqueles que são mais influentes na ambiguidade. Como a análise Q-modal é baseada na determinação de uma região de ambiguidade, obtida de modo empírico a partir de um número finito de soluções aceitáveis, é possível analisar a ambiguidade devida não só a erros nas observações, como também a pequenos erros no modelo interpretativo. Além disso, a análise pode ser aplicada mesmo quando os modelos interpretativos ou a relação entre os parâmetros não são lineares. A análise fatorial é feita utilizando-se dados sintéticos, e então comparada com a análise por decomposição em valores singulares, mostrando-se mais eficaz, uma vez que requer premissas menos restritivas, permitindo, desse modo, caracterizar a ambiguidade de modo mais realístico. A partir da determinação dos parâmetros com maior influência na ambiguidade do modelo é possível reparametrizá-lo, agrupando-os em um único parâmetro, redefinindo assim o modelo interpretativo. Apesar desta reparametrização incorrer na perda de resolução dos parâmetros agrupados, o novo modelo tem sua ambiguidade bastante reduzida.

Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

Développement de fibres optiques composites pour la génération du supercontinuum dans l’infrarouge

Les sources laser à large bande possédant les caractéristiques requises pour émettre sur la plage spectrale correspondant à la seconde fenêtre de transmission atmosphérique (3 à 5 μm) exercent un attrait considérable pour divers domaines tels que la télédétection de polluants atmosphériques et les contremesures infrarouges. Les supercontinua générés à l’intérieur de fibres optiques représentent une option intéressante pour réaliser ce type de sources laser. En effet, ils possèdent une intensité élevée, un large contenu spectral, une excellente directionnalité de faisceau, ainsi qu’un bon potentiel pour constituer des sources lumineuses compactes et robustes. Toutefois, la génération d’un tel supercontinuum implique certains défis à relever sur le plan de la conception des fibres optiques employées. En fait, ces fibres optiques doivent présenter de faibles pertes de propagation sur la plage spectrale de 3 à 5 μm, posséder un paramètre de non-linéarité élevé et permettre le pompage en régime anomal de dispersion à des longueurs d’onde pour lesquelles des sources laser compactes sont offertes commercialement. En matière de robustesse, ces fibres doivent également démontrer de bonnes propriétés mécaniques ainsi qu’une stabilité chimique appropriée vis-à-vis de la corrosion causée par l’humidité. Dans le cadre de cette thèse, un nouveau type de fibres composites à saut d’indice fortement contrasté a été développé pour atteindre ces objectifs de génération de supercontinuum. Ce type de fibres combine respectivement un verre de tellurite et un verre de germanate pour son coeur et sa gaine permettant ainsi d’atteindre une différence d’indice de réfraction d’environ 0.3 entre ces deux dernières structures. Grâce à cet important saut d’indice, ces fibres peuvent fortement confiner les modes optiques à l’intérieur de leur coeur, ce qui leur donne la possibilité d’atteindre un niveau élevé de non-linéarité et d’optimiser leurs caractéristiques de dispersion chromatique pour la génération du supercontinuum. D’autre part, leur section transversale toute solide leur confère aussi une meilleure stabilité environnementale comparativement à celle démontrée par les fibres optiques microstructurées à base de verres d’oxydes de métaux lourds, de verres de chalcogénure et de verres fluorés. Toutefois, leur fabrication nécessite l’appariement de verres dont les propriétés thermomécaniques concordent suffisamment ensemble pour permettre leur fibrage. Les travaux effectués ici démontrent la production de fibres optiques composites et leur potentiel pour la génération du supercontinuum dans l’infrarouge moyen.

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented