79 resultados para Fuzzy optimization

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


Relevância:

20.00% 20.00%

Publicador:

Resumo:

Selostus: Ó-lactalbumiinin ja ¿̐ư-lactoglobuliinin sentrifugointierotuksen optimointi

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Due to the large number of characteristics, there is a need to extract the most relevant characteristicsfrom the input data, so that the amount of information lost in this way is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the principal components analysis (PCA) may be used. This thesis describes an extension of principal components analysis (PCA) allowing the extraction ofa finite number of relevant features from high-dimensional fuzzy data and noisy data. PCA finds linear combinations of the original measurement variables that describe the significant variation in the data. The comparisonof the two proposed methods was produced by using postoperative patient data. Experiment results demonstrate the ability of using the proposed two methods in complex data. Fuzzy PCA was used in the classificationproblem. The classification was applied by using the similarity classifier algorithm where total similarity measures weights are optimized with differential evolution algorithm. This thesis presents the comparison of the classification results based on the obtained data from the fuzzy PCA.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Diplomityön tarkoituksena oli parantaa Stora Enso Sachsenin siistausprosessissa tuotetun uusiomassan vaaleuden kehitystä ja tutkia siihen vaikuttavia tekijöitä. Työn kirjallisessa osassa käsiteltiin uusiomassan kuidutusta ja vaahdotussiistausprosessia, sekä keräyspaperin ominaisuuksia ja käyttöä paperiteollisuuden raaka-aineena. Kokeellisessa osassa keskityttiin modifioidun natriumsilikaatin annostuksenoptimointiin ja vaikutuksiin laboratorio- ja prosessioloissa, sekä kesäefektin vaikutuksen tutkimiseen kuidutuksessa ja flotaation eri vaiheissa. Natriumsilikaatin laboratoriotutkimuksessa havaittiin, että korkein vaaleus suhteellisesti pienimmällä laboratorioflotaation häviöllä saavutettiin korkeimmalla tutkitulla natriumsilikaatin annostuksella, joka oli 1,1 %. Korkea natriumsilikaattiannostus yhdistettyinä korkeisiin vetyperoksidiannostukseen, 0,5 %, sekä korkeaan kokonaisalkaliteettiin, 0.33 %, johti korkeimpaan massan vaaleuteen ja pienimpiin häviöihin. Laboratoriotutkimuksen pohjalta modifioidulla natriumsilikaatilla suoritettiin koeajoja prosessissa. Noin 1 % natriumsilikaatin annostuksella havaittiin parempi pH:n bufferointikyky, pienempi kalsiumkarbonaatin määrä flotaation primäärivaiheissa, sekä lievästi parempi massan vaaleus verrattuna prosessissa aiemmin käytettyyn standardinatriumsilikaattiin. Kesäefektitutkimuksessa havaittiin, että kesäefektillä on suurin vaikutus esiflotaation primäärivaiheeseen, sillä primäärivaiheessa kuitujen osuus on huomattavasti suurempi kuin sekundäärivaiheissa. Esiflotaation primäärivaiheen uusiomassojen laboratorioflotaatioiden avulla saavutettujen maksimivaaleuksien ero kesän ja talven välillä oli noin 1,5 %ISO. Kesäefektin ei havaittu suuresti vaikuttavan flotaation sekundäärivaiheisiin.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Pumppauksessa arvioidaan olevan niin teknisesti kuin taloudellisestikin huomattavia mahdollisuuksia säästää energiaa. Maailmanlaajuisesti pumppaus kuluttaa lähes 22 % sähkö-moottorien energiantarpeesta. Tietyillä teollisuudenaloilla jopa yli 50 % moottorien käyttämästä sähköenergiasta voi kulua pumppaukseen. Jäteveden pumppauksessa pumppujen toiminta perustuu tyypillisesti on-off käyntiin, jolloin pumpun ollessa päällä se käy täydellä teholla. Monissa tapauksissa pumput ovat myös ylimitoitettuja. Yhdessä nämä seikat johtavat kasvaneeseen energian kulutukseen. Työn teoriaosassa esitellään perusteet jätevesihuollosta ja jäteveden käsittelystä sekä pumppaussysteemin pääkomponentit: pumppu, putkisto, moottori ja taajuusmuuttaja. Työn empiirisessä osassa esitellään työn aikana kehitetty laskuri, jonka avulla voidaan arvioida energiansäästöpotentiaalia jäteveden pumppaussysteemeissä. Laskurilla on mandollista laskea energiansäästöpotentiaali käytettäessä pumpun tuoton ohjaustapana pyörimisnopeuden säätöä taajuusmuuttajalla on-off säädön sijasta. Laskuri ilmoittaa optimaalisimmanpumpun pyörimisnopeuden sekä ominaisenergiankulutuksen. Perustuen laskuriin, kolme kunnallista jätevedenpumppaamoa tutkittiin. Myös laboratorio-testitsuoritettiin laskurin simuloimiseksi sekä energiansäästöpotentiaalin arvioimiseksi. Tutkimukset osoittavat, että jätevedenpumppauksessa on huomattavia mandollisuuksia säästää energiaa pumpun pyörimisnopeutta pienentämällä. Geodeettisen nostokorkeuden ollessa pieni, voidaan energiaa säästää jopa 50 % ja pitkällä aikavälillä säästö voi olla merkittävä. Tulokset vahvistavat myös tarpeen jätevedenpumppaussysteemien toiminnan optimoimiseksi.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

In this thesis, cleaning of ceramic filter media was studied. Mechanisms of fouling and dissolution of iron compounds, as well as methods for cleaning ceramic membranes fouled by iron deposits were studied in the literature part. Cleaning agents and different methods were closer examined in the experimental part of the thesis. Pyrite is found in the geologic strata. It is oxidized to form ferrous ions Fe(II) and ferric ions Fe(III). Fe(III) is further oxidized in the hydrolysis to form ferric hydroxide. Hematite and goethite, for instance, are naturally occurring iron oxidesand hydroxides. In contact with filter media, they can cause severe fouling, which common cleaning techniques competent enough to remove. Mechanisms for the dissolution of iron oxides include the ligand-promoted pathway and the proton-promoted pathway. The dissolution can also be reductive or non-reductive. The most efficient mechanism is the ligand-promoted reductive mechanism that comprises two stages: the induction period and the autocatalytic dissolution.Reducing agents(such as hydroquinone and hydroxylamine hydrochloride), chelating agents (such as EDTA) and organic acids are used for the removal of iron compounds. Oxalic acid is the most effective known cleaning agent for iron deposits. Since formulations are often more effective than organic acids, reducing agents or chelating agents alone, the citrate¿bicarbonate¿dithionite system among others is well studied in the literature. The cleaning is also enhanced with ultrasound and backpulsing.In the experimental part, oxalic acid and nitric acid were studied alone andin combinations. Also citric acid and ascorbic acid among other chemicals were tested. Soaking experiments, experiments with ultrasound and experiments for alternative methods to apply the cleaning solution on the filter samples were carried out. Permeability and ISO Brightness measurements were performed to examine the influence of the cleaning methods on the samples. Inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis of the solutions was carried out to determine the dissolved metals.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

An alternative relation to Pareto-dominance relation is proposed. The new relation is based on ranking a set of solutions according to each separate objective and an aggregation function to calculate a scalar fitness value for each solution. The relation is called as ranking-dominance and it tries to tackle the curse of dimensionality commonly observedin evolutionary multi-objective optimization. Ranking-dominance can beused to sort a set of solutions even for a large number of objectives when Pareto-dominance relation cannot distinguish solutions from one another anymore. This permits search to advance even with a large number of objectives. It is also shown that ranking-dominance does not violate Pareto-dominance. Results indicate that selection based on ranking-dominance is able to advance search towards the Pareto-front in some cases, where selection based on Pareto-dominance stagnates. However, in some cases it is also possible that search does not proceed into direction of Pareto-front because the ranking-dominance relation permits deterioration of individual objectives. Results also show that when the number of objectives increases, selection based on just Pareto-dominance without diversity maintenance is able to advance search better than with diversity maintenance. Therefore, diversity maintenance is connive at the curse of dimensionality.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Small centrifugal compressors are more and more widely used in many industrialsystems because of their higher efficiency and better off-design performance comparing to piston and scroll compressors as while as higher work coefficient perstage than in axial compressors. Higher efficiency is always the aim of the designer of compressors. In the present work, the influence of four partsof a small centrifugal compressor that compresses heavy molecular weight real gas has been investigated in order to achieve higher efficiency. Two parts concern the impeller: tip clearance and the circumferential position of the splitter blade. The other two parts concern the diffuser: the pinch shape and vane shape. Computational fluid dynamics is applied in this study. The Reynolds averaged Navier-Stokes flow solver Finflo is used. The quasi-steady approach is utilized. Chien's k-e turbulence model is used to model the turbulence. A new practical real gas model is presented in this study. The real gas model is easily generated, accuracy controllable and fairly fast. The numerical results and measurements show good agreement. The influence of tip clearance on the performance of a small compressor is obvious. The pressure ratio and efficiency are decreased as the size of tip clearance is increased, while the total enthalpy rise keeps almost constant. The decrement of the pressure ratio and efficiency is larger at higher mass flow rates and smaller at lower mass flow rates. The flow angles at the inlet and outlet of the impeller are increased as the size of tip clearance is increased. The results of the detailed flow field show that leakingflow is the main reason for the performance drop. The secondary flow region becomes larger as the size of tip clearance is increased and the area of the main flow is compressed. The flow uniformity is then decreased. A detailed study shows that the leaking flow rate is higher near the exit of the impeller than that near the inlet of the impeller. Based on this phenomenon, a new partiallyshrouded impeller is used. The impeller is shrouded near the exit of the impeller. The results show that the flow field near the exit of the impeller is greatly changed by the partially shrouded impeller, and better performance is achievedthan with the unshrouded impeller. The loading distribution on the impeller blade and the flow fields in the impeller is changed by moving the splitter of the impeller in circumferential direction. Moving the splitter slightly to the suction side of the long blade can improve the performance of the compressor. The total enthalpy rise is reduced if only the leading edge of the splitter ismoved to the suction side of the long blade. The performance of the compressor is decreased if the blade is bended from the radius direction at the leading edge of the splitter. The total pressure rise and the enthalpy rise of thecompressor are increased if pinch is used at the diffuser inlet. Among the fivedifferent pinch shape configurations, at design and lower mass flow rates the efficiency of a straight line pinch is the highest, while at higher mass flow rate, the efficiency of a concave pinch is the highest. The sharp corner of the pinch is the main reason for the decrease of efficiency and should be avoided. The variation of the flow angles entering the diffuser in spanwise direction is decreased if pinch is applied. A three-dimensional low solidity twisted vaned diffuser is designed to match the flow angles entering the diffuser. The numerical results show that the pressure recovery in the twisted diffuser is higher than in a conventional low solidity vaned diffuser, which also leads to higher efficiency of the twisted diffuser. Investigation of the detailed flow fields shows that the separation at lower mass flow rate in the twisted diffuser is later than in the conventional low solidity vaned diffuser, which leads to a possible wider flow range of the twisted diffuser.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Tämän diplomityön tavoitteena oli sekundäärisen esiflotaation optimointi Stora Enso Sachsen GmbH:n tehtaalla. Optimoinnin muuttujana käytettiin vaahdon määrää ja optimointiparametreinä ISO-vaaleutta, saantoja sekä tuhkapitoisuutta. Lisäksi tutkittiin flotaatiosakeuden vaikutusta myös muihin tehtaan flotaatioprosesseihin. Kirjallisuusosassa tarkasteltiin flotaatiotapahtumaa, poistettavien partikkeleiden ja ilmakuplien kontaktia, vaahdon muodostumista sekä tärkeimpiä käytössä olevia siistausflotaattoreiden laiteratkaisuja. Kokeellisessa osassa tutkittiin flotaatiosakeuden pienetämisen vaikutuksia tehtaan flotaatioprosesseihin tuhkapitoisuuden, ISO-vaaleuden, valon sironta- ja valon absorpiokerrointen kannalta. Sekundäärisen esiflotaation optimonti suoritettiin muuttamalla vaahdon määrää kolmella erilaisella injektorin koolla, (8 mm, 10 mm ja 13 mm), joista keskimmäinen kasvattaa 30 % massan tilavuusvirtaa ilmapitoisuuden muodossa. Optimonnin tarkoituksena oli kasvattaa hyväksytyn massajakeen ISO-vaaleutta, sekä kasvattaa kuitu- ja kokonaissaantoa sekundäärisessä esiflotaatiossa. Flotaatiosakeuden pienentämisellä oli edullisia vaikutuksia ISO-vaaleuteen ja valon sirontakertoimeen kussakin flotaatiossa. Tuhkapitoisuus pieneni sekundäärisissä flotaatioissa enemmän sakeuden ollessa pienempi, kun taas primäärisissä flotaatiossa vaikutus oli päinvastainen. Valon absorptiokerroin parani jälkiflotaatioissa alhaisemmalla sakeudella, kun taas esiflotaatioissa vaikutus oli päinvastainen. Sekundäärisen esiflotaation optimoinnin tuloksena oli lähes 5 % parempi ISO-vaaleus hyväksytyssä massajakeessa. Kokonaissaanto parani optimoinnin myötä 5 % ja kuitusaanto 2 %. Saantojen nousu tuottaa vuosittaisia säästöjä siistauslaitoksen tuotantokapasiteetin noustessa 0,5 %. Tämän lisäksi sekundäärisessä esiflotaatiossa rejektoituvan massavirran pienentyminen tuottaa lisäsäästöjä tehtaan voimalaitoksella.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Tässä työssä optimoidaan keskinopean Wärtsilä 32 -dieselmoottorin jäähdytysjärjestelmää ja tutkitaan taajuusmuuttajien käyttömahdollisuutta kiertopumppujen yhteydessä niin, että järjestelmässä saataisiin kiertämään vain kulloinkin tarvittava määrä vettä. Tutkimuksen mallinnus on toteutettu laatimalla aiemmin käytössä olleista yksinkertaisista simulointimalleista yksi malli, johon on sisällytetty sekä virtauksen että lämmönsiirron laskenta, jotka on aiemmin mallinnettu erillisillä ohjelmilla. Diplomityö on osa projektia, joka on tehty Sähkötekniikan osaston tutkijan Mikko Pääkkösen kanssa yhteistyössä. Tämän diplomityö keskittyy lähinnä virtausteknisiin ja lämmönsiirtoon liittyviin asioihin, kun taas sähkötekniikan osuus on esitetty Mikko Pääkkösen raportissa. Tulosten perustella voidaan sanoa, että taajuusmuuttajakäyttö kannattaa kiertopumppujen yhteydessä. Käyttämällä pumppujen virtaussäätöä voidaan jäähdytysjärjestelmästä jättää monia komponentteja, kuten termostaattiventtiilejä pois. Mallinnetut yksinkertaiset piiriratkaisut näyttävät toimivan ainakin yleisellä tasolla. Tutkimusta pumppujen säädöstä ja tässä projektissa luoduista jäähdytysjärjestelmäkonfiguraatioista kannattaa jatkaa.