Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Jet Engine Health Signal Denoising Using Optimally Weighted Recursive Median Filters

The removal of noise and outliers from health signals is an important problem in jet engine health monitoring. Typically, health signals are time series of damage indicators, which can be sensor measurements or features derived from such measurements. Sharp or sudden changes in health signals can represent abrupt faults and long term deterioration in the system is typical of gradual faults. Simple linear filters tend to smooth out the sharp trend shifts in jet engine signals and are also not good for outlier removal. We propose new optimally designed nonlinear weighted recursive median filters for noise removal from typical health signals of jet engines. Signals for abrupt and gradual faults and with transient data are considered. Numerical results are obtained for a jet engine and show that preprocessing of health signals using the proposed filter significantly removes Gaussian noise and outliers and could therefore greatly improve the accuracy of diagnostic systems. [DOI: 10.1115/1.3200907].

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

An optimal weighted-average congestion based pricing scheme for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes under a single service class and multiple queues, and present a multi-layered pricing scheme. We propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. The pricing policy used depends on a weighted average queue length at each node. This helps in reducing frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks. We observe in our numerical results a considerable improvement in performance using our scheme over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our approach exhibits a throughput improvement in the range of 34 to 69 percent in all cases studied (over all routes) over the above scheme.

Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Elimination of cross-talk in diffuse optical tomographic reconstructions through a weighted update procedure: results of simulation study - art. no. 61640S

Reconstructions in optical tomography involve obtaining the images of absorption and reduced scattering coefficients. The integrated intensity data has greater sensitivity to absorption coefficient variations than scattering coefficient. However, the sensitivity of intensity data to scattering coefficient is not zero. We considered an object with two inhomogeneities (one in absorption and the other in scattering coefficient). The standard iterative reconstruction techniques produced results, which were plagued by cross talk, i.e., the absorption coefficient reconstruction has a false positive corresponding to the location of scattering inhomogeneity, and vice-versa. We present a method to remove cross talk in the reconstruction, by generating a weight matrix and weighting the update vector during the iteration. The weight matrix is created by the following method: we first perform a simple backprojection of the difference between the experimental and corresponding homogeneous intensity data. The built up image has greater weightage towards absorption inhomogeneity than the scattering inhomogeneity and its appropriate inverse is weighted towards the scattering inhomogeneity. These two weight matrices are used as multiplication factors in the update vectors, normalized backprojected image of difference intensity for absorption inhomogeneity and the inverse of the above for the scattering inhomogeneity, during the image reconstruction procedure. We demonstrate through numerical simulations, that cross-talk is fully eliminated through this modified reconstruction procedure.

Optimal Weighted Antenna Selection For Imperfect Channel Knowledge From Training

Receive antenna selection (AS) reduces the hardware complexity of multi-antenna receivers by dynamically connecting an instantaneously best antenna element to the available radio frequency (RF) chain. Due to the hardware constraints, the channels at various antenna elements have to be sounded sequentially to obtain estimates that are required for selecting the ``best'' antenna and for coherently demodulating data. Consequently, the channel state information at different antennas is outdated by different amounts. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, the channel estimates of different antennas should be weighted differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then derive an explicit formula for the optimal selection weights that minimize the SEP. We find that when selection weights are not used, the SEP need not improve as the number of antenna elements increases, which is in contrast to the ideal channel estimation case. However, the optimal selection weights remedy this situation and significantly improve performance.

Luotettavaa tietoa ja merkityksellisiä valintoja – Kuluttajien ympäristövastuullista järkeilyä ilmastonmuutoksesta ja ohjausjärjestelmien hyväksyttävyydestä

Tutkielmassa tarkastellaan kuluttajien näkemyksiä ilmastonmuutoksesta ja ilmastovaikutusten seuranta- ja palautejärjestelmän hyväksyttävyydestä kulutuksen ohjauskeinona. 15 kuluttajaa kokeili kuukauden ajan kulutuksen ilmastovaikutusten seuranta- ja palautejärjestelmän demonstraatioversiota ja he osallistuivat kokeilun pohjalta aihepiiriä käsitelleeseen verkkokeskusteluun. Analysoin verkkokeskustelun aineistoa arkisen järkeilyn näkökulmasta tutkien kuluttajien ilmastonmuutokseen ja ympäristövastuullisuuteen liittyvää arkitietoa sekä palvelun hyväksyttävyyteen liittyviä heuristiikkoja. Ilmastonmuutoksen todettiin yleisesti olevan vielä melko abstrakti ja monitulkintainen ilmiö, minkä vuoksi kuluttajilla on vaikeuksia ymmärtää omien valintojensa konkreettista merkitystä ilmastonmuutoksen kannalta. Vaikka tietoa kulutuksen ilmastovaikutuksista on saatavilla paljon, niin erityisesti yritysten tuottama tieto koettiin ristiriitaiseksi ja osin epäluotettavaksi. Kuluttajat myös kritisoivat ilmastonmuutoskeskustelun tarjoamaa kapeaa näkemystä kulutuksen ympäristövaikutuksista. Hiilidioksidipäästöihin keskittymisen sijaan ympäristövaikutuksia tulisi kuluttajien mielestä tarkastella kokonaisuutena, josta ilmastovaikutukset muodostavat vain yhden osan. Tutkimukseen osallistuneiden kuluttajien kulutustottumuksiin ilmastonmuutos vaikutti eriasteisesti. Toisille ilmastonmuutoksesta oli muodostunut keskeinen omaa kulutusta ohjaava normi, kun taas toiset kertoivat pohtivansa ilmastovaikutuksia pääasiassa suurimpien hankintojen kohdalla. Ympäristövastuullisuudessa merkitykselliseksi koettiin tasapainon löytäminen ja henkilökohtainen tunne siitä, että kokee toimivansa oikein. Ilmasto- tai ympäristökysymyksiä punnitaan valinnoissa joustavasti yhdessä muiden tekijöiden kanssa. Vaikka kuluttajilla toisaalta olisi tietoa ja halua ottaa ilmasto- ja ympäristövaikutukset huomioon valinnoissaan, toimintaympäristö rajaa keskeisesti kuluttajien mahdollisuuksia toimia ympäristövastuullisesti. Tutkimus toi esille neljä kuluttajien käyttämää heuristiikkaa heidän pohtiessaan ilmastovaikutusten seuranta- ja palautejärjestelmän hyväksyttävyyden ehtoja ja toimivuutta ohjauskeinona. Ensinnäkin palvelun tulee olla käytettävyydeltään nopea ja vaivaton sekä tarjota tietoa havainnollisessa ja helposti ymmärrettävässä muodossa. Toiseksi palvelun tarjoaman tiedon tulee olla ehdottoman luotettavaa ja kuluttajien valintojen kannalta merkityksellistä siten, että palvelu ottaa huomioon erilaiset kuluttajat ja tiedontarpeet. Kolmanneksi palvelu tulee toteuttaa kokonaisvaltaisesti ja läpinäkyvästi useampien kaupparyhmittymien ja julkisten toimijoiden yhteistyönä. Neljänneksi toteutuksessa tulee huomioda palvelun kannustavuus ja kytkeytyminen muihin ohjauskeinoihin.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.