Sähkökoneiden etädiagnostiikan kenttätason tiedonsiirtotarpeen arviointi ja instrumentoinnin kehittäminen

Tässä diplomityössä tarkastellaan sähkökoneiden tyypillisiä vikoja ja joitain näiden havaitsemiseen käytettäviä mittauksia ja analyysejä; mittausten tuottamaa tietomäärää arvioidaan. Muutamia teollisuuslaitoksissa käytettyjä väyliä ja tiedonsiirtoprotokollia esitellään, ja analysoidaan kunnonvalvonnan mittauksien siirtämisen näillä väylillä vaatimaa väylän datansiirtonopeutta. Valvottavien sähkökoneiden määrän ylärajaa arvioidaan kunkin väylän/protokollan tapauksessa. Työssä esitellään ratkaisuja sähkökoneiden etädiagnostiikan tiedonsiirron toteuttamiseksi ja arvioidaan valvottavien sähkökoneiden määrän ylärajaa kussakin tapauksessa. Lisäksi työssä suunnitellaan ja toteutetaan kunnonvalvonnan mitta-antureiden kanssa käytettävä mittaustiedon keräily-yksikkö. Keräily-yksikön sisältävä kunnonvalvonnan ja etädiagnostiikan tiedonkeruu- ja tiedonsiirtojärjestelmä asennetaan kahteen pilot-kohteeseen: sellutehtaalle ja pienvesivoimalaan.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.