Identification of two cracks in a rod by minimal resonant and antiresonant frequency data

In this paper we consider the identification of two cracks of equal severity in a uniform free-free rod under longitudinal vibration. Each crack is simulated by a translational spring connecting the two adjacent segments of the rod and the cracks are considered to be small. We show that the inverse problem can be formulated and solved in terms of three frequency data only, corresponding to a suitable set of low resonant and antiresonant frequencies. Closed-form expressions of the damage parameters in terms of the measured frequency shifts are obtained. The paper improves existing results available in the literature, since the use of antiresonant frequencies allows to exclude all the symmetrical crack locations occurring when only natural frequency are used as data. The analysis also explains why the use of high frequency data introduces spurious damage locations in the inverse problem solution. Numerical simulations show that if accurate input data are available then damage identification leads to satisfactory results

Crack breathing mechanism in a cracked shaft subject to nontrivial mass unbalance

Rotating machinery is widely used in many industrial fields and is often damaged owing to the breathing of the fatigue crack. The fatigue crack opens and closes once per revolution during shaft rotation. The breathing of the fatigue crack reduces the stiffness of the shaft and hence alters its dynamic response. It changes the vibration characteristics of the shaft. Fatigue cracks are a common occurrence in large rotor systems and can cause catastrophic failure. Detecting faults in rotating machinery before failure is the best way to avoid damage. However, a generalised method of positively identifying a fatigue crack as the cause of anomalous vibrations is not yet available. Vibration diagnostics deliver insights into the mechanical ‘health’ of rotating machinery in real-time when the machine is running. However, studying the vibrations of naturally occurring fatigue cracks is difficult because shafts will often either fail before, or be taken out of service once, the crack is identified. Artificially introduced cracks do not exhibit behaviour identical to that of natural ones owing to the difficulty in cutting into a shaft and leaving a slot with close to zero radius at the crack tip. Therefore, considerable efforts have been devoted to numerically modelling cracked rotors and simulating their operating conditions so that the vibrations can be studied. Numerical modelling techniques are many and varied. In the present thesis, the literature on cracked rotor dynamics is reviewed. Of the crack modelling techniques reviewed, the second area moment method is identified as having potential for improvement. The second area moment method accounts for reduction in bending stiffness of a cracked rotor. Breathing of the fatigue crack is directly related to the second area moment at the crack location. It leads to changes in one of the shaft mechanical properties, stiffness. In a shaft with a crack, the shaft stiffness will change periodically at different rotational angles. Modelling the breathing of the fatigue crack is the key step to analyse the vibration response of a cracked shaft. This breathing phenomenon must be modelled accurately to detect the crack in a rotor. However, it is not yet fully understood how partial crack closure interacts with changes in shaft stiffness, and further, with key variables of the crack detection problem. Unfortunately, almost all existing models are not applicable near the shaft critical speed, because equations of motion developed under the assumption of rotor weight dominance are no longer suitable for analysis near the critical speed. Moreover, localised reduction in stiffness is directly related to crack depth, whereas global reduction in stiffness is directly related to the crack depth and crack location along the shaft. However, researchers opt to either ignore crack location or mitigate its effects. From the literature review, it is evident that accurate modelling, which considers the influence of the crack location and the effect of the unbalance force on the crack breathing behaviour of the fatigue crack to calculate the second area moment of inertia of a cracked shaft to form the stiffness matrix, is still absent. The first topic in this research work is developing a new unbalance model—effectual bending angle—to evaluate the crack breathing response and calculate the second area moment of inertia at any crack location along the shaft length. It is developed considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. It governs the opening and closing of a shaft crack that describes the proximity of the shaft bending direction (or shaft deformation direction) relative to the crack direction. The crack breathing behaviours have been studied for every possible crack location and shaft rotation angle. The presented model identifies unique crack breathing behaviours under the influence of unbalance force and rotor physical and dimensional properties, showing the strong dependence of the breathing mechanism on the crack location. Further, the newly developed model is used to obtain the second area moment of inertia of crack cross-section closed area at any crack location along the shaft length under the unbalance force effect about the centroid. The newly developed unbalance model results are validated through 3D FEM results. This thesis finds that this analytical unbalance model captures the main features of crack breathing and is in good agreement with the 3D FEM. However, the approach adopted in this study of using the existing balance model to identify the crack breathing behaviour and the second area moment of inertia needs to be improved. In this research work, a new method is developed to determine crack breathing, which is an improvement in terms of accuracy on adopted methods. The improvement is owing to the removal of two simplifying assumptions used by previous authors, namely, that the cracked shafts will only experience symmetrical bending and the neutral axis would lie perpendicular to the bending direction, that is, always be horizontal. Both assumptions are shown to be invalid on comparison with results from a three-dimensional finite element model. The newly developed method is then used to evaluate nonlinear crack breathing behaviour under different weight–unbalance force ratios at different crack locations by examining the percentage of opening of a crack. The breathing response predicted by the developed method is validated using the three-dimensional finite element model. The results of the algorithm show a significant improvement in accuracy when compared with data from the three-dimensional finite element model of cracked rotors. The mathematical modelling of calculating the cross-section properties, namely, the second area moment and centroid location, is also improved in this research work by considering neutral axis inclination, removing the assumption of collinearity between the bending moment and neutral axis at the crack location. The newly developed equations are used to evaluate the second area moment of inertia as a function of the crack locations and shaft’s angle of rotation about centroid axes. It is found to be highly dependent on crack location, similar to crack breathing behaviours. The work presented in this thesis demonstrates that a common assumption in the literature—that the effects of axial position of a crack can be neglected—is incorrect. The second topic of this research work is analysis of the crack breathing behaviour of an unbalance shaft with a more realistic transverse slant crack and elliptical crack at different crack locations along the shaft length. A three-dimensional finite element model consisting of a two-disk rotor with a crack is simulated with unbalance mass. The finite element model is simulated using Abaqus/standard. It is simulated considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. Crack breathing behaviours are visualised by the variation of the crack closed area and represented quantitatively by the percentage of the closing of the crack. Crack breathing behaviour is found to strongly depend on its axial position, angular position and depth ratios as well as unbalance force ratios and angular position of unbalance force. Compared with the balance shaft crack breathing behaviour, two different crack breathing regions along the shaft length are identified, where shaft stiffness is larger or smaller, depending on the unbalance force orientation, magnitude and crack location. However, four specific crack locations along the shaft length are identified where the crack remains fully closed or open or the same as in balance shaft crack breathing during shaft rotation under different loading conditions. The presented research results suggest that a more accurate prediction of the dynamic response of cracked rotors can be expected on considering the effects of unbalance force and individual rotor physical properties on crack breathing. The presented method and results of this research can be used to obtain the stiffness matrix of a cracked shaft element and then to study the vibration response of a cracked rotor where the rotor-weight-dominant assumption on crack breathing no longer holds

Modelling the degradation of vibration characteristics of reinforced concrete beams due to flexural damage

This paper presents an improved crack model incorporating non-linearity of flexural damage in concrete to reproduce changes in vibration properties of cracked reinforced concrete beams. A reinforced concrete beam model with multiple-distributed flexural cracks is developed, in which the cracked regions are modelled using the fictitious crack approach and the undamaged parts are treated in a linear-elastic manner. The model is subject to incremental static four-point bending, and its dynamic behaviour is examined using different sinusoidal excitations including swept sine and harmonic signals. From the swept sine excitations, the model simulates changes in resonant frequency with increasing damage. The harmonic excitations are utilised to investigate changes in modal stiffness extracted from the restoring force surfaces, and changes in the level of non-linearity are deduced from the appearance of super-harmonics in the frequency domain. The simulation results are compared with experimental data of reinforced concrete beams subject to incremental static four-point bending. The comparisons revealed that the proposed crack model is able to quantitatively predict changes in vibration characteristics of cracked reinforced concrete beams. Changes are sensitive to support stiffness, where the sensitivity increases with stiffer support conditions. Changes in the level of non-linearity with damage are not suitable for damage detection in reinforced concrete structures because they do not follow a monotonic trend

A Comparative Analysis of Signal Decomposition Techniques for Structural Health Monitoring on an Experimental Benchmark

Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals

Theoretical and Experimental Study of Damage Identification of Beams and Plates

Structural characteristic deflection shapes (CDS’s) such as mode shapes and operational deflection shapes which contain spatial information of structures are highly sensitive for damage detection and localisation in beam- or plate- type structures. Despite substantial advances in this kind of methods, several issues must be addressed to boost their efficiency and practical applications, including the following: (1) The estimation of CDS’s involves substantial inaccuracies and is mainly affected by operational, environmental, measurement and computational uncertainties. (2) The curvature estimation of CDS’s is much more sensitive to measurement noise. (3) The extraction of damage-caused singularities from CDS’s or their curvatures is difficult when the baseline data of healthy structures is not available. (4) Damage index for multi-damage identification is challenging due to the different damage location sensitivities of each CDS. These problems have been investigated and the objective of this study is to enhance the accuracy and noise robustness of baseline-free damage detection and localisation. The original contributions of this study have been made in several aspects. Firstly, common principal component analysis is proposed to enhance accuracy of mode shape estimation in operational modal analysis, which statistically evaluates the common subspace bases of a set of covariance or power spectral density matrices as the mode shapes. Secondly, without the baseline data of healthy structures, polynomial fitting approaches and low-rank models are investigated for damage localisation, which extract the damage-induced local shape singularities by using only mode shapes or mode shape curvatures of damaged structures. Thirdly, in order to fairly incorporate damage information of several modes, two robust damage indexes are proposed for beam-type structures and plate-type structures, respectively. The above studies focus on linear damage such as open cracks in beam or plate structures without nonsmooth mass and stiffness distribution. Apart from these, the identification of fatigue cracks in stepped beam-type structures is investigated as well. In the theoretical aspect, the relationship between damage and structural characteristic deflection shapes is explained. Then, the finite element models of beams and plates are coded in MATLAB, which are validated by comparing corresponding results with the commercial software ABAQUS. Moreover, the numerical models of beams and plates with multiple damage are used to verify the feasibility and efficiency of the proposed methods in damage identification. Here, the damage is introduced by reducing the depth of beams or thickness of plates. In the experimental aspect, beams and plates with multiple damage are tested to demonstrate the proposed damage detection and localisation methods. In order to acquire the data of a large number of measurement points, the advanced scanning laser Vibrometer is used. It is found that the proposed mode shape estimation approaches are demonstrated to be more accurate and noise robust than the traditional frequency domain decomposition and time domain decomposition methods. Additionally, the noise effects on spatial domain features such as mode shape and mode shape curvatures can be significantly reduced by the polynomial fitting or multi-scale approaches. Furthermore, the developed robust multi-damage indexes for beams and plates are validated to be effective by using numerical simulations and experimental results. Finally, the proposed breathing crack identification approaches are effective in localising the breathing cracks but insensitive to the steps of the beams

Using optimization algorithms to detect damages on free-free beam based on dynamic results

This article describes a Modal Analysis method for detecting damage in free-free beams using natural frequency data. The method involves updating a numerical model of the beam with experimental or reference natural frequencies to determine the damage location and damage index. The accuracy of the method was verified through simulations and experiments on beams with both single and double damage zones. The results demonstrate that the method is effective in detecting the damage location for single damage zone and double damage zones with the same or different damage index. However, when the two damage zones are close together, the method that updates the model through PSO optimization algorithm using the reference frequency data may produce inaccurate results. Furthermore, when using experimental frequency data for damage beams, the results indicate that the method has a damage location error of approximately 3.5% along the entire beam length, which is considered acceptable in practical applications. The natural frequency-based damage detection method described in this article offers a useful tool for the assessment of damage in free-free beams and can be effectively combined with visual inspection techniques

Detecção e controle de trincas transversais em máquinas rotativas

In this dissertation, crack detection and crack control of rotating machinery are addressed. The objectives of this study involves building and validating a numerical model capable of simulating the dynamic behavior of a real rotating machine. Numerical and experimental results for crack detection based on the shaft vibration signals are obtained. Besides, numerical and experimental results from an active control method, capable of suppressing 2X and 3X super-harmonics are obtained, excited by the crack presence. The innovation of this thesis lays on the fact of merging crack detection and crack control techniques in one single study. It is worth mentioning that the subject of crack control is quite new in the literature. The rotor is modeled by the finite element (FE) method, considering Timoshenko beam elements with circular cross section and constant radius. The Mayes model is addressed for simulating the breathing behavior of a transverse crack in a progressive way. The linear fracture mechanics theory is applied to correlate the crack depth with the corresponding additional shaft flexibility. The so-called modal state observer (MSO) technique was chosen to verify the existence of a transverse crack on a rotating machine. Moreover, the PID active control technique was addressed to perform crack control, suppressing crack signatures over the rotor frequency spectrum. Both numerical and experimental results highlight the possibility of detecting the existence of a crack and also how to decrease its effects (through active control) of an operating rotating machine. In this way, inspections requiring full stop of the machine can be performed less often while keeping the rotating machine safety.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorTese (Doutorado)Esta tese considera detecção e controle de uma trinca transversal em máquinas rotativas. Os objetivos deste estudo envolvem a obtenção e o ajuste de um modelo matemático que represente o comportamento dinâmico de uma máquina rotativa real, a aplicação numérica e experimental de um método de detecção de falhas baseado no sinal de vibração do rotor e de um método de controle ativo de trincas que reduza os níveis dos super-harmônicos 2X e 3X excitados pela presença da trinca no espectro de frequência do rotor. A novidade desta tese está no fato de se realizar detecção e controle de trinca em um único projeto de pesquisa. Além disso, o controle ativo de trincas ainda é um assunto novo nesta área. A modelagem matemática do rotor utiliza o método dos Elementos Finitos (FE) e considera elementos de viga de Timoshenko, com seção circular e raio constates. O comportamento dinâmico da trinca transversal é modelado pelo modelo de Mayes, que considera abertura e fechamento da trinca de maneira progressiva. Mecânica da fratura linear é aplicada, a fim de relacionar a profundidade da trinca com o aumento da flexibilidade do eixo. O observador de estado modal (MSO) foi utilizado nesta tese quando do estudo do problema de detecção de trincas. Já para o controle ativo da trinca, a técnica de controle PID foi aplicada. Os resultados evidenciam a possibilidade de se diagnosticar uma trinca e diminuir seus efeitos (através do controle ativo) sobre uma máquina rotativa em operação. Desta forma, manutenções que exigem a parada da máquina podem ser realizadas com menor frequência e, mesmo assim, a segurança da máquina rotativa é garantida

Application of Wavelets-based SVM Classification for Automated Fault Diagnosis and Prognosis of Mechanical Systems

Anwendung der Wavelet-basierte SVM Klassifizierung für die automatisierte Fehlerdiagnose und -prognose mechanischer Systeme In dieser Arbeit werden Techniken der Mustererkennung auf verschiedene Problemstellungen der Fehlerdiagnose und -prognose angewendet. Die untersuchten Anwendungen stellen reale industrielle Anwendungen dar, bei denen verschiedene Messeigenschaften (wie zyklische, impulsive, und periodische Signale), verschiedene Charakteristik der Erkennungsobjektiven (wie kumulativ und einmalige Ereignisse), verschiedene Betriebsbedingungen und -parameter der Maschine, und verschiedene Fehler und Erkennungssystemanforderungen (wie Verschleiß, Riss, und Objekterkennung; Systemzustand und Restlebensdauer) die modulare Mustererkennungsverfahren und -techniken erfordern. Verschiedene Ansätze werden untersucht und angewendet, wie Support Vector Machine (SVM), Continuous Wavelet-Transform (CWT),Wavelet Packet Transform (WPT) und Diskrete Wavelet-Transform (DWT), und viele Konzepte und Lösungen werden vorgeschlagen und überprüft, um ein zuverlässiges Zustandsüberwachungssystem zu erreichen, dass die Instandhaltungsplanung der Maschine unterstützt und die Produktionsqualität und Produktionskosten verbessert. In der ersten untersuchten Anwendung in dieser Arbeit wird ein Ansatz für die Entwicklung eines Fehlerdiagnose- und -prognosesystems vorgestellt. Das System wird als Vorwarnmodul verwendet, um die Notwendigkeit für das Ersetzen von Verschleißteilen von Produktionsmaschinen zu erkennen und die Restlebensdauer des überwachten Teils zu bewerten. In der zweiten untersuchten Anwendung wird ein Produktionsverfahren überwacht. Ziel ist die Erkennung eines Objektes mit einer möglichst geringen Fehlalarmrate. Die Signale beinhalten nichtstationäre, impulsartige bzw. einmalige Ereignisse. Ein weiteres Merkmal der Sensorcluster-Signale ist die nicht gleichzeitige Erzeugung von Ereignissen, die die Verwendung von geeigneten Entscheidungsfusionstechniken erfordert. In der letzten untersuchten Anwendung, werden modell- und signalbasierte Verfahren für die Risserkennung und Prognose in rotierenden Maschinen untersucht, um eine Vorwarnung für Rotor-Risse zu erreichen für Online- Überwachung in Turbomaschinen. Die angetroffenen Signale sind periodische Schwingungssignale mit kumulativen Auswirkungen der Fehlerereignisse. Offene Fragen stellen sich bei den Themen Zustandsbewertung, Fehlerschweregrad und Restlebensdauer, basierend auf spezifischen Sensordaten mit besonderen anwendungsorientierten Eigenschaften. Diese Arbeit befasst sich mit diesen offenen Fragen, um ein zuverlässiges Zustandsüberwachungssystem zu erreichen. Es kann festgestellt werden, dass Wavelets und SVM sehr nützliche Werkzeuge für die Merkmalsextraktion und Klassifikation im Bereich der Zustandsüberwachung sind. Der Merkmalsraum von SVM ist nützlich für die Bewertung der verbleibenden Lebensdauer. Allerdings zeigt sich ebenfalls, dass angesichts der Herausforderungen anwendungsorientierte Lösungen gefunden werden müssen.In this thesis, the application of pattern recognition techniques is considered for different kinds of fault diagnosis and prognosis problems and applications. The investigated applications represent real industrial applications, in which different measurement characteristics (such as cyclic, impulsive, and periodic signals), different recognition objective characteristics (such as accumulative and one-time events), different operational conditions and parameters of the machine, and different faults and detection system requirements (such as wear, crack, and object detection; System state and remaining life time) are challenging the existence of modular pattern recognition procedures and techniques. Different approaches are investigated and applied such as Support Vector Machine (SVM), Discrete Wavelet Transform (DWT), Wavelet Packet Transform (WPT), and Continuous Wavelet Transform (CWT), and many concepts and solutions are proposed and verified, in order to achieve a reliable condition monitoring system, which supports the maintenance planning of the machine and adds value to the production quality and cost. In the first investigated application in this thesis, an approach for developing a fault diagnosis and prognosis system is presented. The system is used as a prewarning module to detect the necessity for replacing wear parts of production machines and to evaluate the remaining life time of the supervised part. The sensor signals encountered for processing are nondeterministic with cyclic nature related to the operation cycle of the machine. In the second investigated application, the goal is to monitor a production process for online detection of a target object with the lowest possible false alarm rate. The signals encountered in the system of this work are characterized with nonstationary impulsive one-time events representing the goal object. Another characteristic of the sensor cluster signals is the partly simultaneous stimulation of events which requires the use of suitable decision fusion techniques. In the last investigated application, two main approaches used for crack detection and prediction in rotating machinery; model based and signal based, are investigated, in order to achieve a prewarning technique for rotor cracks to be applied for online monitoring in turbo-machinery. The signals encountered are periodic vibration signals with accumulative impact of the fault incident. Open questions arise in the issues of state evaluation, severity estimation, and remaining life time prediction, based on specific sensor data with particular applicationoriented characteristics. This work deals with these open questions, in order to achieve a reliable condition monitoring system. As a general conclusion of the work, it can be stated that Wavelets and SVM are reliable tools for feature extraction and classification in the field of condition monitoring, and the feature space of SVM is useful for remaining life prediction. However; specific application oriented Solutions and tricks are necessary, considering the diversity of fault diagnosis and prognosis problems and difficulties

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

SMART STRUCTURAL CONDITION ASSESSMENT METHODS FOR CIVIL INFRASTRUCTURES USING DEEP LEARNING ALGORITHM

Smart Structural Health Monitoring (SHM) technique capable of automated and accurate structural health condition assessment is appealing since civil infrastructural resilience can be enhanced by reducing the uncertainty involved in the process of assessing the condition state of civil infrastructures and carrying out subsequent retrofit work. Over the last decade, deep learning has seen impressive success in traditional pattern recognition applications historically faced with long-time challenges, which motivates the current research in integrating the advancement of deep learning into SHM applications. This dissertation research aims to accomplish the overall goal of establishing a smart SHM technique based on deep learning algorithm, which will achieve automated structural health condition assessment and condition rating prediction for civil infrastructures. A literate review on structural health condition assessment technologies commonly used for civil infrastructures was first conducted to identify the special need of the proposed method. Deep learning algorithms were also reviewed, with a focus on pattern recognition application, especially in the computer vision field in which deep learning algorithms have reported great success in traditionally challenging tasks. Subsequently, a technical procedure is established to incorporate a particular type of deep learning algorithm, termed Convolutional Neural Network which was found behind the many success seen in computer vision applications, into smart SHM technologies. The proposed method was first demonstrated and validated on an SHM application problem that uses image data for structural steel condition assessment. Further study was performed on time series data including vibration data and guided Lamb wave signals for two types of SHM applications - brace damage detection in concentrically braced frame structures or nondestructive evaluation (NDE) of thin plate structures. Additionally, discrete data (neither images nor time series data), such as the bridge condition rating data from National Bridge Inventory (NBI) data repository, was also investigated for the application of bridge condition forecasting. The study results indicated that the proposed method is very promising as a data-driven structural health condition assessment technique for civil infrastructures, based on research findings in the four distinct SHM case studies in this dissertation