The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Realisation of an effective dual-parameter sensor employing a single fibre Bragg grating structure

A novel technology for simultaneous and independent measurement of dual parameters is proposed and experimented. The length of a single fibre Bragg grating (FBG) is divided into two parts. The temperature variation and another measurand can be measured independently and simultaneously, and the thermal effect can be erased with great ease. © 2005 Elsevier Ltd. All rights reserved.

Metallocene ethylene-1-octene copolymers:influence of comonomer content on thermo-mechanical, rheological, and thermo-oxidative behaviours before and after melt processing in an internal mixer

The influence of the comonomer content in a series of metallocene-based ethylene-1-octene copolymers (m-LLDPE) on thermo-mechanical, rheological, and thermo-oxidative behaviours during melt processing were examined using a range of characterisation techniques. The amount of branching was calculated from 13C NMR and studies using differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) were employed to determine the effect of short chain branching (SCB, comonomer content) on thermal and mechanical characteristics of the polymer. The effect of melt processing at different temperatures on the thermo-oxidative behaviour of the polymers was investigated by examining the changes in rheological properties, using both melt flow and capillary rheometry, and the evolution of oxidation products during processing using infrared spectroscopy. The results show that the comonomer content and catalyst type greatly affect thermal, mechanical and oxidative behaviour of the polymers. For the metallocene polymer series, it was shown from both DSC and DMA that (i) crystallinity and melting temperatures decreased linearly with comonomer content, (ii) the intensity of the ß-transition increased, and (iii) the position of the tan δmax peak corresponding to the a-transition shifted to lower temperatures, with higher comonomer content. In contrast, a corresponding Ziegler polymer containing the same level of SCB as in one of the m-LLDPE polymers, showed different characteristics due to its more heterogeneous nature: higher elongational viscosity, and a double melting peak with broader intensity that occurred at higher temperature (from DSC endotherm) indicating a much broader short chain branch distribution. The thermo-oxidative behaviour of the polymers after melt processing was similarly influenced by the comonomer content. Rheological characteristics and changes in concentrations of carbonyl and the different unsaturated groups, particularly vinyl, vinylidene and trans-vinylene, during processing of m-LLDPE polymers, showed that polymers with lower levels of SCB gave rise to predominantly crosslinking reactions at all processing temperatures. By contrast, chain scission reactions at higher processing temperatures became more favoured in the higher comonomer-containing polymers. Compared to its metallocene analogue, the Ziegler polymer showed a much higher degree of crosslinking at all temperatures because of the high levels of vinyl unsaturation initially present.

Microfiber-based inline Mach-Zehnder interferometer for dual-parameter measurement

An approach to realizing simultaneous measurement of refractive index (RI) and temperature based on a microfiber-based dual inline Mach-Zehnder interferometer (MZI) is proposed and demonstrated. Due to different interference mechanisms, as one interference between the core mode and the lower order cladding mode in the sensing single-mode fiber and the other interference between the fundamental mode and the high-order mode in the multimode microfiber, the former interferometer achieves RI sensitivity of -23.67 nm/RIU and temperature sensitivity of 81.2 pm/oC, whereas those of the latter are 3820.23 nm/RIU, and -465.7 pm/oC, respectively. The large sensitivity differences can provide a more accurate demodulation of RI and temperature. The sensor is featured with multiparameters measurement, compact structure, high sensitivity, low cost, and easy fabrication.

Nonlinear Variational Inequalities Depending on a Parameter

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Parameter Identification of a Fed-Batch Cultivation of S. Cerevisiae using Genetic Algorithms

Fermentation processes as objects of modelling and high-quality control are characterized with interdependence and time-varying of process variables that lead to non-linear models with a very complex structure. This is why the conventional optimization methods cannot lead to a satisfied solution. As an alternative, genetic algorithms, like the stochastic global optimization method, can be applied to overcome these limitations. The application of genetic algorithms is a precondition for robustness and reaching of a global minimum that makes them eligible and more workable for parameter identification of fermentation models. Different types of genetic algorithms, namely simple, modified and multi-population ones, have been applied and compared for estimation of nonlinear dynamic model parameters of fed-batch cultivation of S. cerevisiae.

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.

A lumped parameter model for the analysis of the motion of the muscles of the lower limbs under whole-body vibration

Through a lumped parameter modelling approach, a dynamical model, which can reproduce the motion of the muscles of a human body standing in different postures during Whole Body Vibrations (WBVs) treatment, has been developed. The key parameters, associated to the dynamics of the motion of the muscles of the lower limbs, have been identified starting from accelerometer measurements. The developed model can be usefully applied to the optimization of WBVs treatments which can effectively enhance muscle activation. © 2013 IEEE.

Theorem for Series in Three-Parameter Mittag-Leffler Function

Mathematics Subject Classification 2010: 26A33, 33E12.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Microfiber Fabry-Perot interferometer for dual-parameter sensing

We propose and demonstrate a microfiber Fabry-Perot interferometer (MFPI) fabricated by taper-drawing microfiber at the center of a uniform fiber Bragg grating (FBG). The MFPI employing the two separated sections of FBG as reflectors and a length of microfiber as its cavity is derived. Theoretic study shows that the reflection spectrum of such MFPI is consisted of two parts-interference fringes induced by multi-beam interference and reflection spectrum envelope induced by FBGs. Temperature affects both interference fringes and reflection wavelength of FBGs while ambient refractive index (RI) only influences the interference fringes, i.e., MFPI has different response to temperature and RI. Therefore, MFPI for simultaneous sensing of RI and temperature is experimentally demonstrated by tracking a reflection peak of interference fringes and the Bragg wavelength of the FBGs, which are respectively assisted by frequency domain processing and Gaussian fitting of the optical spectrum. Consequently, wavelength measurement resolution of 0.5 pm is realized. © 1983-2012 IEEE.

Type space on a purely measurable parameter space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure.

A diszkrét kiválasztási modell becslése Cox-regresszióval (Parameter estimation for multinomial discrete choice model using Cox-regression)

Considering the so-called "multinomial discrete choice" model the focus of this paper is on the estimation problem of the parameters. Especially, the basic question arises how to carry out the point and interval estimation of the parameters when the model is mixed i.e. includes both individual and choice-specific explanatory variables while a standard MDC computer program is not available for use. The basic idea behind the solution is the use of the Cox-proportional hazards method of survival analysis which is available in any standard statistical package and provided a data structure satisfying certain special requirements it yields the MDC solutions desired. The paper describes the features of the data set to be analysed.

Környezeti kockázatok felmérése. Paraméterek bizonytalanságának hatása a kockázatkezelési döntéshozatalra = Assessment of environmental risks – effects of parameter uncertainty to the risk management decisions

A környezeti kockázatok megfelelő felmérése és kezelése napjaink egyik legfontosabb kérdése, nemcsak a szakmai, hanem a széles értelemben vett közvélemény számára. A szerző cikkében azt vizsgálja, hogy a környezeti kockázatok felmérésének milyen megközelítései vannak. Kulcskérdésként pedig arra koncentrál, hogy a kockázatkezelési döntéseket hogyan befolyásolja a becslések bizonytalansága. Először a környezeti kockázat definícióját adja meg, majd azt mutatja be, hogy a környezeti kockázatok kezelésére vonatkozó megközelítések milyen párhuzamban állnak a pénzügyi rendszerrel, mint komplex rendszerre vonatkozó megközelítésekkel. Végül a jelenleg legnagyobb kockázatoknak tartott környezeti kockázatokat ismerteti röviden. A cikk második részében kockázatkezelési alternatívákat mutat be, és azt, hogy a kockázatkezelési lépések kiválasztását befolyásolja a bizonytalanság. Ezt illusztrálandó Brouwer-Blois (2008) modelljét használva a soklépéses szimulációt és alternatív döntési kritériumot – a kritikus (extrém) költség-hatás mutatót – alkalmazza. _____________ Adequate assessment and management of environmental risks is a key question nowadays also for professional experts and also for the overall public. In this article the author examines the different approaches concerning environmental risks. He concentrates as a key question the influence on risk management decisions of uncertainties raised by our estimations. First he analyses the definition of environmental risks, and he shows the similarities and differences between approaches concerning environmental risks and risks threatening financial system, and finally he gives short overview on the most current environmental risks. In the second part of the paper he presents risk management alternatives and analyses the influential power of uncertainty on risk management decisions. In order to illustrate this phenomenon the author applies the model of Brouwer-Blois (2008) with multistep simulation and an alternative decisive criterion, the ranking based on critical (extreme) cost to effect measure.

Magyarország hét régiójának új gazdaságföldrajzi modellje – paraméterbecslés (The new economic-geography model of Hungary's seven regions - a parameter estimate)

Az új gazdaságföldrajz – amely napjaink egy igen népszerű közgazdaságtani tudományága – modelljének majdnem minden paramétere előállítható közvetlenül külső adatok segítségével. A helyettesítési rugalmassághoz azonban más módszerre van szükség. Puga [1999] által felvázolt új gazdaságföldrajzi modellt követve, egy regressziós egyenlettel megbecsülhetővé válik a kívánt paraméter, amit Magyarország hét régiójára vonatkozó béregyenlet becsléséből nyertünk. A helyettesítési rugalmasság értéke eltér a szakirodalomhoz képest, aminek magyarázata Magyarország fejlettségi szintjével állhat összefüggésben. ____ The model of the new economic geography - very popular material for economic study these days - allows almost every parameter to be presented directly with the aid of outside data. However, another method is required for substitution flexibility. With the new economic-geography model devised by Puga [1999], a regression equation allows an estimate to be made for the desired parameter, which yielded the wage equation for the six regions of Hungary. The value for substitution flexibility differs from that of the literature, the explanation for which may lie in Hungary's level of development.