Mitteklassikaliste kinnitustingimuste tuvastamine tehisnärvivõrkude abil
Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Tartu Ülikool
Abstract
Käesolev magistritöö uurib mitteklassikaliste kinnitustingimustega elastsete Euler-Bernoulli talade vabavõnkumise resonantssagedusi. Eesmärgiks on vaatluse all olevate tala mudelite korral hinnata ning võrrelda tehisnärvivõrkude abil identifitseeritud jäikuse parameetreid elastsete kinnitustingimuste korral.
Vaatluse all on kahte tüüpi talad: tala elastse otsakinnitusega ning tala vahepealse elastse toega. Mõlema variandi kohta töötatakse läbi rida näiteid erinevate kinnitustingimustega.
Kuna kinnituste jäikusparameetrite arvutamine võnkumise diferentsiaalvõrrandist ei ole analüütiliselt võimalik, siis on mõistlik otsida sellele alternatiivi. Ühe variandina pakutakse käesolevas töös välja tehisnärvivõrkude rakendamine.
Tehisnärvivõrgud põhinevad bioloogilistel närvivõrkudel, nagu näiteks inimese aju. Tehisnärvivõrgu peamiseks eeliseks teiste meetodite ees on tema võime olemasolevate näidete põhjal õppida, mis tähendab, et närvivõrke on võimalik treenida sisendi abil soovitud tulemusi produtseerima. Seega, vajaliku ülesande lahendamiseks pole enam tarvis ise kõiki parameetrite koefitsiente arvutada, vaid piisab, kui meil on olemas teatud hulk näiteid oodatavate koefitsientide kohta, ning nende näidete abil treenitud tehisnärvivõrk on suuteline ülejäänud tulemusi ise identifitseerima.
Käesolevas töös antakse ülevaade võnkuvatest Euler-Bernoulli taladest ja nende võimalikest kinnitustingimustest, ning tutvustatakse tehisnärvivõrkude peamisi omadusi. Töö peamine rõhk on asetatud praktilisele osale, kus uuritakse kahte tüüpi elastseid talasid (elastsete otsakinnitustega ja elastse vahekinnitusega) ning analüüsitakse tehisnärvivõrkude abil saavutatud ennustuste tulemusi erinevatel juhtudel.
Lisaks erinevatele kinnitustingimustele võrreldakse tulemusi erineva sisendsageduste arvu (kolm, neli, viis, kuus või üheksa sagedust) korral. Saadud tulemusi analüüsitakse ja võrreldakse teatud täpsusparameetrite põhjal.
Läbiviidud arvutuste ning analüüsi põhjal selgub, et enamikel juhtudel on ennustuse teel saavutatud tulemused üpris ligilähedased oodatavatele tulemustele, seega on võnkuvate Euler-Bernoulli talade kinnitustingimuste jäikusparameetrite ennustamisel närvivõrkude rakendamine mõistlik.
In the present thesis, an overview of the Euler-Bernoulli beam theory and the basics of artificial neural networks were presented. The main emphasis was on the practical implementation of training the artificial neural networks for predicting the stiffness parameters of the support conditions of the vibrating beams. The main purpose of the current paper was to study the frequencies of vibrating Euler-Bernoulli beams with different non-classical support conditions, and to analyze the efficiency of predicting the support condition coefficients (either translational or rotational). The calculated natural frequencies of the vibrating beams were used as the input for training the neural networks. The results were computed for various cases, using different numbers of input frequencies (three, four, five, six, or nine) besides the different support conditions. The results of the predictions were analyzed in two different parts: the efficiency of prediction in case of beams with elastic support at the boundaries, and the efficiency of prediction in case of beams with intermediate elastic support. The analysis of the efficiency of prediction in case of beams with elastic support at the boundaries showed that the overall efficiency of the predictions was substantially high and the identified results were quite similar to the expected outcomes. The best average results among all conditions were received with the beam clamped or simply supported at left end and translationally and rotationally restrained at right end. But even in the worst cases, most of the results were considerably nice. The analysis of the efficiency of predicting the rotational coefficient at the intermediate support in case of beams with intermediate elastic support showed that the results greatly depend on the generation of the training and test sets. If the training data contains noise, then the efficiency of the prediction is rather low, but it could be improved by modifying the training and test data sets. Also, alternative methods should be elaborated to extract features for parameter identification of vibrating systems.
In the present thesis, an overview of the Euler-Bernoulli beam theory and the basics of artificial neural networks were presented. The main emphasis was on the practical implementation of training the artificial neural networks for predicting the stiffness parameters of the support conditions of the vibrating beams. The main purpose of the current paper was to study the frequencies of vibrating Euler-Bernoulli beams with different non-classical support conditions, and to analyze the efficiency of predicting the support condition coefficients (either translational or rotational). The calculated natural frequencies of the vibrating beams were used as the input for training the neural networks. The results were computed for various cases, using different numbers of input frequencies (three, four, five, six, or nine) besides the different support conditions. The results of the predictions were analyzed in two different parts: the efficiency of prediction in case of beams with elastic support at the boundaries, and the efficiency of prediction in case of beams with intermediate elastic support. The analysis of the efficiency of prediction in case of beams with elastic support at the boundaries showed that the overall efficiency of the predictions was substantially high and the identified results were quite similar to the expected outcomes. The best average results among all conditions were received with the beam clamped or simply supported at left end and translationally and rotationally restrained at right end. But even in the worst cases, most of the results were considerably nice. The analysis of the efficiency of predicting the rotational coefficient at the intermediate support in case of beams with intermediate elastic support showed that the results greatly depend on the generation of the training and test sets. If the training data contains noise, then the efficiency of the prediction is rather low, but it could be improved by modifying the training and test data sets. Also, alternative methods should be elaborated to extract features for parameter identification of vibrating systems.