Elliptical Crack Identification in a Nonrotating Shaft

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses., is work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler-Bernoulli beam, with circular cross section under pinned-pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.The authors would like to thank the Spanish Ministerio de Economía y Competitividad for the support for this work through the project DPI2013-45406-P

Vibration Analysis of a Beam using Neural Network Technique

Using changes in global dynamic characteristics for detection of cracks has been a hot research topic now a days and is a source of attraction for civil, aerospace, and mechanical engineering communities in recent years. Crack in vibrating components causes a change in physical properties of a structure which in turn affects dynamic response characteristics. Therefore we have to study the dynamic response characteristics in order to avoid any catastrophic failures and to follow structural integrity and performance for which the parameters considered are crack depth and its location. In the present study, vibration analysis is carried out on a cantilever beam with two open transverse cracks, to study the response characteristics. Its natural frequency and mode shapes are determined by applying suitable boundary conditions. The results obtained numerically are compared with the results obtained from the simulation. The simulations have done with the help of ALGOR software. Then by using Feed-forward, back propagation neural network the relationship between the location and the depth of the crack as input and the structural eigenfrequencies as output are studied. At the end by performing both the simulation and computational analysis it is proved that the presence of cracks affects the natural frequency and the mode shapes of the structure. The results indicate that the current approach can identify both the location and the extent of damages in the beam

Haari lainikute meetod omavõnkumiste analüüsiks ja parameetrite määramiseks

Tala on konstruktsioonielement, mille ülesandeks on vastu pidada erinevatele koormustele. Projekteerimisel alahinnatud koormused, ebatäpsused tootmisel, söövitav keskkond, konstruktsiooni vananemine ekspluatatsiooni käigus võivad talasid kahjustada ning põhjustada kogu konstruktsiooni purunemist. Seetõttu talade dünaamilise käitumise modelleerimine ja ekspluatatsiooni jälgimine on jätkuvalt aktuaalne teema konstruktsioonide mehaanikas. Käesolev väitekiri on suunatud süstemaatilisele lähenemisele võnkumiste analüüsimiseks ja purunemise parameetrite määramiseks Euler-Bernoulli tüüpi talades. Töös pakutakse välja Haari lainikute meetod sageduste arvutamiseks ja andmete töötlemiseks. Nimelt, väitekirja esimeses osas on Haari lainikuid ja nende integreerimist rakendatud vabavõnkumise ülesannete korral, kus lahendatavaks võrrandiks on muutuvate kordajatega diferentsiaalvõrrand, millel puudub analüütiline lahend (näiteks ebaühtlase ristlõikega tala, materjali funktsionaalse gradientjaotusega tala). Arvutused kinnitasid, et pakutud lähenemisviis on kiire ja täpne vabavõnkumiste sageduste arvutamisel. Väitekirja teine osa käsitleb vabavõnkumisega seotud pöördülesandeid: pragude, delaminatsioonide, elastsete tugede jäikuse, massipunktide parameetrite määramist modaalsete omaduste kaudu. Kuna purunemise asukoha ja ulatuse arvutamine võnkumise diferentsiaalvõrrandist ei ole analüütiliselt võimalik, kasutatakse antud töös tehisnärvivõrke ja juhumetsi. Andmekogumite genereerimiseks lahendati võnkumise võrrand ning tulemusi töödeldi Haari lainikute abil. Arvutused näitasid, et Haari lainikute abil genereeritud andmekogumite arvutamiseks kuluv aeg oli üle kümne korra väiksem kui vabavõnkumiste sagedustele põhinevate andmekogumite arvutusaeg; Haari lainikute abil genereeritud andmekogumid ennustasid paremini purunemise asukohta, samas vabavõnkumiste sagedused olid tundlikumad purunemise ulatuse suhtes; enamikel juhtudel andsid tehisnärvivõrgud sama täpseid ennustusi kui juhumetsad. Töös pakutud meetodeid ja mudeleid saab kasutada teistes teoreetilistes ülesannetes vabavõnkumiste ja purunemiste uurimiseks või rakendada talade purunemise diagnostikas.A beam is a common structural element designed to resist loading. Underestimated loads during the design stage, looseness during the manufacturing stage, corrosive environment, collisions, fatigue may introduce some damage to beams. If no action is taken, the damage can turn into a fault or a breakdown of the whole system. Hereof, the entirety of beams is a crucial issue. This dissertation proposes a systematic approach to vibration analysis and damage quantification in the Euler-Bernoulli type beams. The solution is sought on the modal properties such as natural frequencies and mode shapes. The forward problem of the vibration analysis is solved using the Haar wavelets and their integration since the corresponding differential equations do not have an analytical solution. Multiple numerical examples indicate that the proposed approach is fast and accurate. Damage quantification (location and severity) of a crack, a delamination, a point mass or changes in the stiffness coefficients of elastic supports on the bases of the modal properties is an inverse problem. Since it is not analytically possible to calculate the damage parameters from the vibration differential equation, the task is solved with the aid of artificial neural networks or random forests. The datasets are generated solving the vibration equations and decomposing the mode shapes into the Haar wavelet coefficients. Multiple numerical examples indicate that the Haar wavelet based dataset is calculated more than ten times faster than the frequency based dataset; the Haar wavelets are more sensitive to the damage location, while the frequencies are more sensitive to the damage severity; in most cases, the neural networks produce as precise predictions as the random forests. The results presented in this dissertation can help in understanding the behaviour of more complex structures under similar conditions, provide apparent influence on the design concepts of structures as well as enable new possibilities for operational and maintenance concepts.https://www.ester.ee/record=b539883

Comparison of machine learning methods for crack localization

In this paper, the Haar wavelet discrete transform, the artificial neural networks (ANNs), and the random forests (RFs) are applied to predict the location and severity of a crack in an Euler–Bernoulli cantilever subjected to the transverse free vibration. An extensive investigation into two data collection sets and machine learning methods showed that the depth of a crack is more difficult to predict than its location. The data set of eight natural frequency parameters produces more accurate predictions on the crack depth; meanwhile, the data set of eight Haar wavelet coefficients produces more precise predictions on the crack location. Furthermore, the analysis of the results showed that the ensemble of 50 ANN trained by Bayesian regularization and Levenberg–Marquardt algorithms slightly outperforms RF

Smart FRP Composite Sandwich Bridge Decks in Cold Regions

INE/AUTC 12.0

A procedure for the identification of multiple cracks on beams and frames by static measurements

In this work, a model of the Euler-Bernoulli beam in presence of multiple-concentrated open cracks, based on the adoption of a localized flexibility model, is adopted. The closed-form solution in terms of transversal displacements due to static loads and general boundary condition is exploited to propose an inverse damage identification procedure. The proposed identification procedure does not require any solution algorithm, on the contrary is formulated by means of simple explicit sequential expressions for the crack positions and intensities including the identification of the integration constants. The number of possible detected cracks depends on the couples of adopted sensors. Undamaged beam zones can also be easily detected in relation to the sensor positions. The analytical character of the explicit expressions of the identification procedure makes the inverse formulation applicable to damaged beams included in more complex frame structures. The proposed procedure is applied for the identification of the number, position, and intensity of the cracks along simple straight beams and also to more complex frame structures with the aim of showing its simplicity for engineering applications. In addition, the robustness of the methodology here described is shown through an accurate analysis of the basic assumptions on which the theory relies and by means of a study of the effect of noise on the identification results

Vibration Analysis of Cracked Beam using Intelligent Technique

Structural systems in a wide range of Aeronautical, Mechanical and Civil Engineering fields are prone to damage and deterioration during their service life. So an effective and reliable damage assessment methodology will be a valuable tool in timely determination of damage and deterioration in structural members. Interest in various damage detection methods has considerably increased over the past two decades. During this time many detection methods founded on modal analysis techniques have been developed. Non-destructive inspection techniques are generally used to investigate the critical changes in the structural parameters so that an unexpected failure can be prevented. These methods concentrate on a part of the structure and in order to perform the inspection, the structure needs to be taken out of service. Since these damage identification techniques require a large amount of human intervention, they are passive and costly methods

Fault Detection of Cracked Cantilever Beam Sing Smart Technique

Over the years damage detection in structures is being given prior attention. For this purpose different newer techniques are being used so far. In this investigation defect in cantilever beam in the form of a transverse crack is being investigated using smart Technique like Fuzzy Logic. Gaussian membership functions are used for the Fuzzy Controller. The input parameters to the Fuzzy Controller are relative divergence of first three natural frequencies and the output parameters of the Fuzzy Controller are relative crack depth and relative crack location in dimensionless forms. For deriving the fuzzy rules for the controller; theoretical expressions have been developed considering three parameters such as; natural frequencies, crack depths and crack locations. Strain energy release rate has been used for calculating the local stiffnesses of the beam. The local stiffnesses of the beam are dependent on the crack depth. Different boundary conditions are being outlined which take into account the crack location. Several fuzzy rules are derived and the Fuzzy controller has been designed accordingly. Experimental setup has been developed for verifying the robustness of the developed fuzzy controller. Finite Element Analysis is performed on the single and double cracked cantilever beam to obtain the modal natural frequencies. The proposed approach is verified by comparing the results obtained from the numerical analysis and the developed experimental set-up. And it was observed that the Fuzzy Controller can predict the location and depth of the crack in a close proximity as par with the actual results

Crack Detection Using Wavelets

This report develops an algorithm for the detection of cracks on bridge structures, based on the Wavelet Transform (WT). A review of the state of the art techniques for crack detection of beams and bridges is made, and studies for the effectiveness of Finite Element Modeling and WT characteristics, such as wavelet type and noise effects, are performed. The results are used for the development of a robust approach to detecting damage in bridge structures, introducing the concept of multiple-support-bridge crack detection. Both direct use of mode shapes and of moving load approaches to detection are made, commenting on the advantages and drawbacks of each. An overall assessment of the state of the art of WT damage detection is given in the concluding paragraphs