# Fault Diagnosis of Rotating Machinery based on vibration analysis.

## Comments

## Transcription

Fault Diagnosis of Rotating Machinery based on vibration analysis.

ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 Review Article Fault Diagnosis of Rotating Machinery based on vibration analysis Dr. F. R, Gomaa Faculty of Engineering Shebin EL-Kom -production engineering and Mechanical design department. EGYPT Dr. k. M. khader Faculty of Engineering Shebin EL-Kom -production engineering and Mechanical design department. EGYPT Eng. M. A. Eissa Faculty of Engineering Shebin EL-Kom -production engineering and Mechanical design department.EGYPT Abstract -This paper aims to provide abroad review of state of arts n faults diagnosis technique mainly in rotating machine based on vibrations analysis. Vibrations response measurements give valuable information on common faults. The general classes of methods are reviewed and particular difficulties are highlighted in each method to have accurate method for each component. Keywords: fault diagnosis, Faults Description, Monitoring method, technique analysis Introduction The objective of this paper is to provide the reader with an insight into recent developments in the field of fault. Diagnosis in rotating machines. The different types of faults that are observed in these area of rotating machine and methods of their diagnosis including (single process, modal Analysis, Stochastic Subspace Identification (SSI), Order Analysis (OHS), Frequency Domain Decomposition (FDD) Method). The paper is divided into different section, each dealing with various aspects of the subjects: it begins with a summary of review of faults diagnosis, followed by general overview of faults detection methods. Faults diagnosis technique in rotating machinery is discussed in detail including technique methods. Special treatment is given of vibration analysis. One of the major areas of interest in the modern day condition monitoring of rotating machinery is that of vibration. If a fault developed and goes undetected , then, at best, the problem will not be too serious and can be remedied quickly and cheaply ; at worst, it may results in expensive damage and down- time , injury , or even loss of life. By measurement and analysis of the vibration of rotating machinery , it is possible to detect and locate important faults such as mass unbalance , gear faults, misalignment, crack) .Problem in rotating machinery may also be caused by degradation in the bearing Pervious literature reviews and surveys The aim of this section is to provide the reader with an understanding of the state of the art in fault diagnosis. Model-based fault detection is, at this time, directly employed in most areas of fault diagnosis. The model-based approach involves the establishment of a suitable process model, either mathematical or signal-based, which can estimate and predict process parameters and variables. Described the main principles involved in model-based procedures and outlined their importance for the realistic modeling of faults. He concluded that more than one method of FDI should be utilized, in order to best reach an accurate diagnosis. Fault trees and forward and backward chaining are methods of fault diagnosis addressed b A comprehensive overview of fault diagnosis methodology is first presented, 1571 based on process measurements, dynamic models and parameter estimation to generate fault symptoms. Fault trees and forward and backward chaining. Then provide the method of fault classification. Fault trees are a heuristic means of decision making, constructed partly from knowledge of physical laws and partly from experience in the field, which may not necessarily be exactly described By these laws. Forward and backward chaining mimics the human process of decision making. All possible outcomes are considered as a first step (forward chaining), the decision making process is then enhanced by the introduction of additional information and the most likely outcome due to this extra input is analyzed, involving the input of yet more data (backward chaining). The procedure continues until www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 either it is concluded or no more likely outcomes are possible. Used the definition that a fault will alter the dynamic behavior of a system, to construct a model to detect changes in this dynamic behavior and thus identify faults. Various physical parameters and model sensitivity to fault size are used to detect and locate faults.[1,2,3,4,5,6,7] Improving model robustness with respect to these uncertainties, whilst maintaining sensitivity, helps to provide the necessary means for inserting FDI models into practical applications. Begins with a survey of the methods of improving robustness in model generation and analysis. The Generalized Observer Scheme (perfect decoupling from modeling errors achieved by increasing the number of inputs), robust parity space check, unknown input observer scheme (state estimation error decoupling), decor relation. Filter and adaptive threshold selection (uncertainties causing residual and decision functions to fluctuate) are all described as means to obtain decoupling from any modeling errors which may occur. Robustness with respect to nonlinear systems is also shown to be attainable. A more general description of robustness and the observer-based FDI approach is given by Patton and where the passive robust solution (adaptive threshold method) and active robust solutions (uncertainty in residual generation) are considered. Examples are given for the FDI of a jet engine system, a pumping system and an electric train. [8,9,10,11,12] Since the analysis and design of rotating machinery is extremely critical in terms of the cost of both production and maintenance, it is not surprising that the fault diagnosis of rotating machinery is a crucial aspect of the subject, receiving ever more attention. As the design of rotating machinery becomes increasingly complex, due to rapid progress being made in technology, so must machinery condition-monitoring strategies become more advanced in order to cope with the physical burdens being placed on the individual components of a machine. Modern conditionmonitoring techniques encompass many different themes, one of the most important and informative being the vibration analysis of rotating machinery - a topic which has prompted much research to be carried out and a corresponding amount of literature to be produced. Using vibration analysis, the state of a machine can be constantly monitored and detailed analyses may be made concerning the health of the machine and any faults which may be arising or have already arisen, serious or otherwise. Common rotor-dynamic faults include self-excited vibration, due to system instability, and, more often, vibration due to some externally applied load, such as cracked or bent shafts and mass unbalance. Vibration condition monitoring as an aid to fault diagnosis has been examined by in much the same way as Smith covered the general kinds of faults listed above and described qualitatively how they may be recognized from their vibration characteristics, and included effects caused by nonlinearity. Stewart and Taylor also included information on the actual data analysis process how measured data should be processed in order for a diagnosis to be performed. performance efficiency data to dynamic and static measurements, it is possible to then control the overall performance level of the machine presented a method for assessing the severity of vibration in 1572 terms of the probability of damage by analysis of vibration signals and its related cost, using the net present value method. The question of whether or not to shut down a machine for maintenance was considered and some guidelines were formulated, comparing maintenance and down-time costs against the possible costs that would be incurred by damage.[13,14,15,16,17,18,19,20,21,23] Iwatsubo considered possible errors likely to occur in vibration analysis and how these errors may influence calculations of critical speeds, instability and unbalance. A statistical approach was used to calculate the mean values and standard deviations of errors, which in turn allows the calculation of statistical values of unbalance response, instability and critical speeds. The sensitivity of the model with respect to errors in the various model parameters was also determined. It was found that errors in bearing coefficients have a much larger effect on the variance of system instability than do errors in mass and stiffness, which have a predominant effect on the variance of critical speed. [24, 25, 26, 27, 28, 29, 30] For the diagnosis of anisotropy and asymmetry in rotating machinery, [31] Lee and Joh (1994) developed a method incorporating directional frequency response functions (dFRFs). Anisotropy and asymmetry may cause whirl, fatigue and instability, as well as influencing system characteristics such as unbalance and critical speeds. Complex modal testing was used to estimate the dFRFs. An example was presented, showing the proposed method to be very efficient in identifying anisotropy and asymmetry. The key factor of the predictive maintenance is diagnostic. A diagnosis is not an assumption; it is a conclusion reached after a logical evaluation of the observed symptoms. Then, the diagnostic is based on a systematic inspection in vibration signal to find all susceptible defects, which may affect the machine. Fault diagnosis is essentially pattern recognition. by analyzing the symptom parameters generated by the equipment, the faults of the equipment can be known and the causes of faults can thus be determined. Speed frequency of the rotor is called the fundamental frequency. When there is a fault in the rotor-bearing system, the fault will has an impact on all the frequency bands, and it will change the distribution of energy. Fault features of the rotor-bearing system will be mainly in fraction or integer multiple frequency. Therefore, to diagnose fault, analysis of signal frequency is adopted to extract features of the fault parameter and to classify the faults based on these characteristic parameters. [32, I.H. Witten and E. Frank: Data Mining2000]. Today's industry uses increasingly complex machines, some with extremely demanding performance criteria. Attempting to diagnose faults in these systems is often a difficult and daunting task for operators and plant maintainers. Failed machines can lead to economic loss and safety problems due to unexpected and sudden production stoppages. These machines need to be monitored during the production process to improve machine operation reliability and reduce unavailability. Therefore, conducting effective condition monitoring brings significant benefits to industry [33, 34], Altmann, J. (1999), Baillie, D C and Mathew, J (1996),]. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 However, condition monitoring requires effective fault diagnosis, which is labor oriented exercise to this day. Without efficient diagnosis, one is unable to make reliable prediction of lead time to failure. A natural progression is the automation of this labor oriented process of diagnosis by implementing intelligent diagnosis strategies so that experts or technicians can be relieved of this relatively expensive task. Fault diagnosis is conducted typically in the following phases: data collection, feature extraction, and fault detection and identification. Fault detection and identification usually employs artificial intelligent (AI) approaches for pattern classification. Numerous attempts have been made to improve the accuracy and efficiency of fault diagnosis of rotating machinery by employing AI techniques. Few have attempted to summaries these techniques comprehensively. [35] Zhong2000 introduced new developments in the theory and application of intelligent condition monitoring and diagnostics in China. He concluded that the trends in intelligent diagnosis are NNbased fault classifiers, NN-based expert systems, NN-based prognosis, behavior-based intelligent diagnosis, remote distributed intelligent diagnosis networks and intelligent multi-agent architecture for fault diagnosis. He provided a good overview of intelligent fault diagnosis of machinery but was somewhat general. [36] Pham1999 theoretically analyses the applicability of artificial intelligence in engineering problems and predominantly looked at knowledge-based systems, fuzzy logic, inductive learning, neural networks and genetic algorithms in different branches of engineering but not in machinery fault diagnosis. [37] Tandon1999 mentioned that automatic diagnosis was a trend in the fault diagnosis of rolling elements. [38] Gao2001 provided an up-to-date review on recent progresses of soft computing methods-based motor fault diagnosis systems. He summarized several motor fault diagnosis techniques using neural networks, fuzzy logic, neural-fuzzy, and genetic algorithms (GAs) and compared them with conventional techniques such as direct inspection .also gave a brief review, which listed 14 papers from experts in the area of motor fault detection and diagnosis. He grouped those papers into five main categories: survey papers, modelbased approaches, signal processing approaches, emerging technology approaches, and experimentation.[39] Chow2000 The task of fault diagnosis consists of determining the type, size and location of the fault as well as its time of detection based on the observed analytical and heuristic symptoms. If no further knowledge on fault symptom causalities is available, classification methods can be applied which allow for a mapping of symptom vectors into fault vectors. To this end, methods like statistical and geometrical classification or neural nets and fuzzy clustering can be used. Note that geometrical analysis, whilst simple to implement, has a few drawbacks. The most serious is that, in the presence of noise, input variations and change of operating point of the monitored process, false alarms are possible. If a-priori knowledge of fault-symptom causalities is available, e.g. in the form of causal networks, diagnostic reasoning strategies can be applied. Forward and backward chaining, with Boolean algebra for binary facts and with approximate reasoning for probabilistic or possibility facts, 1573 are examples. Finally a fault decision indicates the type, size and location of the most possible fault, as well as its time of detection. [40], Nicola Orani 2010] Fault diagnosis is the determination of specific fault that has occurred in the system. A typical fault detection method consists of the following stages: a) Data Acquisition b) Parameter Extraction c) Fault Analysis d) Decision Making Vibration monitoring is one of the main tools that allow to determine the mechanical health of various components of a machine in a non-intrusive manner. The mechanical components that are the most often encountered in rotating machinery are bearings - roller bearings in particular – and gears. Furthermore, these components are generally the most loaded and consequently subject to early damages in the machine's life. [41, Christophe Thirty, Ai-Min Yan, Jean-Claude Golinval October 2004] Vibration-based damage detection for rotating machinery (RM) has been repeatedly applied with success to a variety of machinery elements such as roller bearings and gears. In the past, the greatest emphasis has been on the qualitative interpretation of vibration signatures both in the frequency and (to a lesser extent) in the time domain. Numerous summaries and reviews of this approach are available in textbook form, including detailed charts of machinery fault analysis, e.g., see [42]-[43]. The approach taken has generally been to consider the detection of damage qualitatively on a fault-by-fault basis by examining acceleration signatures for the presence and growth of peaks in spectra at certain frequencies, such as multiples of shaft speed. A primary reason for this approach has been the inherent nonlinearity associated with damage in RM and the inability to make measurements at locations other than the exterior housing of the machine. Recently, more general approaches to damage detection in RM have been developed. These approaches utilize formal statistical methods to assess both the presence and level of damage on a statistical basis, e.g., see [44] and [45]. A particularly detailed and general treatment of mechanical signature analysis is presented in [46]. The vibration signal analysis is one of the most important methods used for condition monitoring and fault diagnostics, because they always carry the dynamic information of the system. Effective utilization of the vibration signals, however, depends upon the effectiveness of the applied signal processing techniques for fault diagnostics. With the rapid development of the signal processing techniques, the analysis of stationary signals has largely been based on wellknown spectral techniques such as: Fourier Transform (FT), Fast Fourier Transform (FFT) and Short Time Fourier Transform (STFT) [47], [48]. Unfortunately, the methods based on FT are not suitable for non-stationary signal analysis [49]. In addition, they are not able to reveal the www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 inherent information of non-stationary signals. These methods provide only a limited performance for machinery diagnostics [50]. In order to solve these problems, Wavelet Transform (WT) has been developed. WT is a kind of variable window technology, which uses a time interval to analyze the high frequency and the low frequency components of the signal [51], [52]. The data using WT can be decomposed into approximation and detail coefficients in a multi scale, presenting then a more effective tool for nonstationary signal analysis than the FT. Many studies present the applications of WT to decompose signals for improving the performance of fault detection and diagnosis in rotating machinery [53]–[54,55,56,57,58,59,60,61,62,63]. 1) Faults Description in Rotating Machine Machine fault can be defined as any change in a machinery part or component which makes it unable to perform its function satisfactorily or it can be defined as the termination of availability of an item to perform its intended function. The familiar stages before the final fault are incipient fault, distress, deterioration, and damage, all of them eventually make the part or component unreliable or unsafe for continued use [64], Pratesh Jayaswal,1 A. K.Wadhwani, and K. B.Mulchandani3,2008]. Classification of failure causes are as follows: (i) Inherent weakness in material, design, and manufacturing; (ii) Misuse or applying stress in undesired direction; (iii) Gradual deterioration due to wear, tear, stress fatigue, corrosion, and so forth. A fault is an irregularity in the functioning of the equipment which results in component damage, energy losses and reduced efficiency of the machine. The common types of machine faults are: _ Unbalance _ Shaft misalignment or bent shaft _ Damaged or loose bearings _ Damaged gears _ Faulty of misaligned belt drive. _ Mechanical looseness _ Increased turbulence _ Electrical induced vibration Fault detection using vibration analysis involves analyzing the vibration signature for signs of fault. Any predominant fault occurring results in increased vibration level which has energy concentrated at certain frequency levels. The relation of the predominant vibration frequencies with the forcing frequency (input force frequency) gives us an idea about the source of the fault. The increased amplitude of the predominant frequencies indicates the severity of the fault. Standard relations between common faults and corresponding fault signatures are available. [65, 65, 66, 67, 68] 1574 1 .1) Mass unbalance Mass unbalance is one of the most common causes of vibration;. Unbalance is a condition where the centre of mass does not coincide with the centre of rotation, due to the unequal distribution of the mass about the centre of rotation. The unbalance creates a vibration frequency exactly equal to the rotational speed, with amplitude proportional to the amount of unbalance. [69, Hocine Bendjama, Salah Bouhouche, and Mohamed Seghir Boucherit, 2012] Unbalance is a result of uneven distribution of a rotor’s mass and causes vibration to be transmitted to the bearings and other parts of the machine during operation. Imperfect mass distribution can be due to material faults, design errors, manufacturing and assembly errors, and especially faults occurring during operation of the machine. By reducing these vibrations, better performance and more cost-effective operation can be achieved and deterioration of the machine and ultimately fatigue failure can be avoided. This requires the rotor to be balanced by adding and/or removing mass at certain positions in a controlled manner. Unbalance may occur due to the following reasons. _ The shape of the rotor is unsymmetrical. _ Unsymmetrical mass distribution exists due to machining or casting error. _ A deformation exists due to a distortion. _ an eccentricity exists due to a gap of fitting. _ An eccentricity exists in the inner ring of a bearing.[70, Siva Shankar Rudraraju,] 1 .2) Gear fault The vibrations of a gear are mainly produced by the shock between the teeth of the two wheels. Gear fault is simulated with filled between teeth. The vibration monitored on a faulty gear generally exhibits a significant level of vibration at the tooth meshing frequency GMF (i.e. the number of teeth on a gear multiplied by its rotational speed) and its harmonics of which the distance is equal to the rotational speed of each wheel.[69, Hocine Bendjama, Salah Bouhouche, and Mohamed Seghir Boucherit,2012] Gear faults can be generally classified into two major categories: distributed faults and local faults. Distributed faults are those faults that results from poor gear mounting, or manufacturing inaccuracies such as eccentricities, varying gear tooth spacing, etc. Meanwhile, local faults are those resulting from localizing defects that may occur in gear teeth such as tooth surface wear, cracks in gear teeth, and loss of part of the tooth due to breakage or loss of the whole teeth. [71, A.AIbrahim, S. M.Abdel Rahman,M.Z.Zahran,H.H.ELMongey] 1. 3) Misalignment Misalignment in rotating machinery is one of the most common faults causing other faults and machine failure. It causes over 70% of rotating machinery vibration problems [72, Bognatz, S. R., 1995]. A misaligned rotor generates bearing forces and excessive vibrations making diagnostic process more difficult. A perfect alignment can never be www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 achieved practically and misalignment is always present. [73, Mohsen Nakhaeinejad, Suri Ganeriwala, Sep. 2009] There are two types of misalignment: parallel and angular misalignment. With parallel misalignment, the center lines of both shafts are parallel but they are offset. With angular misalignment, the shafts are at an angle to each other. The parallel misalignment can be further divided up in horizontal and vertical misalignment. Horizontal misalignment is misalignment of the shafts in the horizontal plane and vertical misalignment is misalignment of the shafts in the vertical plane Parallel horizontal misalignment is where the motor shaft is moved horizontally away from the pump shaft, but both shafts are still in the same horizontal plane and parallel. Parallel vertical misalignment is where the motor shaft is moved vertically away from the pump shaft, but both shafts are still in the same vertical plane and parallel.Similar, angular misalignment can be divided up in horizontal and vertical misalignment: Angular horizontal misalignment is where the motor shaft is under an angle with the pump shaft but both shafts are still in the same horizontal plane. Angular vertical misalignment is where the motor shaft is under an angle with the pump shaft but both shafts are still in the same vertical plane. Errors of alignment can be caused by parallel misalignment, angular misalignment or a combination of the two. 1 .4) bearing failure Antifriction bearings failure is a major factor in failure of rotating machinery. Antifriction bearing defects may be categorized as localized and distributed. The localized defects include cracks, pits, and spalls caused by fatigue on rolling surfaces. The distributed defect includes surface roughness, waviness, misaligned races, and off-size rolling elements. These defects may result from manufacturing and abrasive wear. [74, M. Amarnath, R. Shrinidhi, A. Ramachandra, and S. B. Kandagal, 2004]. Fatigue: The change in the structure that is caused by the repeated stresses developed in the contacts between the rolling elements and the raceways. Fatigue is manifested visibly as flaking of particles. Fatigue can be divided into: *Subsurface Initiated Fatigue *Surface Initiated Fatigue Wear: Wear is the progressive removal of material resulting from the interaction of the asperities of two sliding or rolling/sliding contacting surfaces during service. Wear can be divided into: *Abrasive Wear * Adhesive Wear 1575 Corrosion: Corrosion is a chemical reaction on metal surfaces. Corrosion can be divided into: * Moisture Corrosion: When steel used for rolling bearing components is in contact with moisture (e.g., water or acid), oxidation of surfaces takes place. Subsequently, the formation of corrosion pits occurs and finally flaking of the surface . *Frictional Corrosion: Frictional corrosion is a chemical reaction activated by relative micro movements between mating surfaces under certain friction conditions. These micro movements lead to oxidation of the surfaces and material, becoming visible as powdery rust and/or loss of material from one or both mating surfaces. [75, SKF 2008, Chapter 5 – ISO Classification] 1 .5) crack Cracked rotors are not only important from a practical and economic viewpoint, they also exhibit interesting dynamics. Cracks in rotor machine is greatest danger and research in crack detection has been ongoing for the past 30 years. A crack in rotor will change the dynamic behaviour of the system but in practice it has been found that small or medium size cracks make such a small change to the dynamics of the machine system that they are undetectable by this means. Only if the crack grows a potentially dangerous size it can be readily detected. So we use high resolution frequency and filter. Crack detection methods fall into two groups, model updating and pattern recognition (see, for example, [76, and 77]). In the former method, the dynamic behavior of the rotor is used to update a model of the rotor and in the process determine both the severity and location of any crack. Clearly the crack model used must be adequate for the task. If the pattern recognition approach is used, then whilst a crack model is not directly required, it is desirable to have some idea of the dynamic behavior that will result from a cracked rotor in order that it can be recognized in the pattern of behavior. There are a number of approaches to the modeling of cracks in beam structures reported in the literature, that fall into three main categories; local stiffness reduction, discrete spring models, and complex models in two or three dimensions. [78] Dimarogonas and [79] Ostachowicz and Krawczuk gave comprehensive surveys of crack modeling approaches. [80] Friswell and Penny considered the performance of various crack models in structural health monitoring. If the vibration due to any out-of-balance forces acting on a rotor is greater than the static deflection of the rotor due to gravity, then the crack will remain either opened or closed depending on the size and location of the unbalance masses. In the case of the permanently opened crack, the rotor is then asymmetric and this condition can lead to stability problems. If the vibration due to any out-of-balance forces acting on a rotor is less than the static deflection of the rotor due to gravity the crack will open and close (or breathe) as the rotor turns. [81,Jerzy T. Sawiciki , Michael I. Friswell, ,Zbingniew Kulesza, Adam Wroblewski , John D. Lekki, 2011] www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 2) Technique of Monitoring For Fault Detection Based On Vibration Machine monitoring, or early detection of incipient faults, aims to survey the machine health, or condition, at critical locations, e g, gears and bearings, and possibly predict a future failure. At a certain stage of defect progress or severity, a scheduled stop for maintenance can be made, the damaged element replaced, and production can then continue without unnecessary delays. [82, a Barkov, N Barkova and a Azovtsev] Actually developments still deal with minimization of measurement equipment and analysis techniques implementing worldwide standards for data processing and acquisition, with the possibility of central data acquisition. The supply of more cost-effective monitoring tools has been made possible by technical advances such as: * reduced costs of instrumentation, * increased capability of instrumentation such as data preacquisition, data storage, radio transmission direct by the sensors with integrated electronically circuits, * improved data storage media in combination with low cost computation, * faster and more effective data analysis using specialist software tools.[83, Wilfried Reimche, Ulrich Südmersen, Oliver Pietsch, Christian Scheer, Fiedrich-Wilhelm Bach, 2003] 3) Monitoring Methods The defect signature energy is usually distributed over a wide frequency interval and is therefore easily masked by energy from other sources. Several time domain as well as frequency domain methods have been developed over the years to cope with this problem and provide an accurate defect detection method. Time domain methods dealing with localized defects involve indicators sensitive to impulsive oscillations. Well-known examples are the peak value, root mean square (r.m.s) value, crest factor and Kurtosis. Intelligent signal filtering is crucial for the success of all these methods. Early methods, developed before FFT analyzers appeared, used peak and r.m.s detecting instruments in combination with various filters. After birth of the FFT analyzer, methods focused on frequency domain properties like harmonic sequences of the characteristic defect frequencies. Finally, during the last two decades of the 20th century, methods such as high frequency envelope detection, relying on advanced signal processing and stochastic signal analysis have emerged.[84,85,86,87] 3.1) Early Time Domain Methods The classical machine monitoring method, used by machine operators since the 1920’s, is to press a screw driver tip to the machine casing and the handle to the skull bone and listen to the machine vibrations, taking advantage of bone conduction. This is basically an instrument which uses the screw driver as vibration sensor and the operator's auditory system as the signal analyzer. In the 1950´s, efforts were made to summaries these experiences in automatic 1576 measurement systems. At that time the available instruments were simple accelerometers, analog filters, root mean square indicating voltmeters and oscilloscopes indicating peak values. So the early machine monitoring methods used various combinations of vibration r.m.s and peak values. Several methods used either the peak or the r.m.s -value; others used their ratio, the crest factor. Unfortunately indicators based on the r.m.s -value are insensitive to incipient defects. Crest factor indicators, on the other hand, are sensitive for early defects when the peak value is high and the r.m.s-value is low. At later stages of defect life the overall r.m.s value increases significantly and the crest factor is reduced. This fact has led to the common misconception that defect severity decreases after the early stage when it in reality is progressing towards the final failure. The early methods suffer from some severe disadvantages: - early defect detection is difficult in a noisy environment, - defect localization and - defect identification are in practice impossible. A solution to these problems requires intelligent filtering and signal processing. 3.2) Spectral methods The character of the vibration signature is most prominent in the frequency domain. For this reason many monitoring techniques are based on frequency domain characteristics, the spectrum, of the vibration signature. Spectral methods are most successfully applied to the low and intermediate part of the frequency range. The strategy is to extract the signature from a single gear or bearing from the total vibration measured on the machine casing and to monitor the characteristic defect frequency amplitudes. The basic assumption is, of course, that a growing defect implies increasing amplitudes at the defect frequencies. Some defect indicators, like the defect severity index, focus on the difference in amplitude at the defect frequency and the amplitude of the background. Other alternative methods focus on the side bands and seek to construct indicators measuring the relative amplitudes of the side bands. The main problem of spectral methods is, as always, to suppress the contributions from other vibration sources to such an extent that they do not interfere with the investigated signature. In some cases the signature dominates the measured vibrations whereas in other cases the signature may be hidden in other contributions. In such cases some signal processing is needed to extract the signature and suppress contributions from other sources. One useful signal processing tool is time domain averaging or synchronised time domain averaging, Synchonised averaging means that the signal is ensemble averaged in the time domain with each time record synchronised with a tachometer signal tracking the shaft rotation period. This averaging will, if properly performed, cancel out all frequency components except the ones synchronous with the shaft, i e the ones periodic in the time window. It is common practice to normalize the frequency axis with a characteristic frequency, e g the shaft rotation frequency, to get an order spectrum. The use of order spectra has several advantages as compared to standard frequency spectra. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 3.3) Cepstral methods The signal cepstrum is useful for detecting repetitive patterns in a signal. In principle, the signal cepstrum is defined as the Fourier transform of the magnitude of the signal spectrum, Hence, vibration signatures including harmonic side bands are relatively easy to detect in a signal cepstrum. On the other hand several experimental investigations have shown that monitoring the cepstrum may give ambiguous results, especially regarding the defect progress. detect, identify and diagnose the defect. Several indicators exist. In the time-domain, abrupt changes in the envelope can be detected and quantified using r.m.s-value, peakvalue, crest factor or statistical measures like Kurtosis, in the frequency domain peaks in the envelope spectrum coinciding with characteristic defect frequencies can identify and localize a defect. A damaged gear tooth can be localized using phase information. Experience shows that phase is more sensitive than amplitude in detecting and localizing gear tooth cracks. A frequently used indicator is for instance. [89, 90, 91, 92] 3.4) Envelope methods 4) Technique Analysis The main difficulty with spectral and cepstral methods is that they focus on low and mid frequencies where the influence from other sources is usually large. Thus, it may be very difficult to extract the correct signature from the large number of frequency lines found at low frequencies. Envelope methods aims to avoid this problem by focusing on high frequencies, e.g. for bearings from 20 kHz to 30 kHz. The fundamental idea of high frequency envelope methods is to use the high frequency part of the defect modulated vibration signal and demodulate it to obtain the vibration signature. To ensure that the vibration signal is dominated by contributions from the correct element, the accelerometer is placed as closes possible to the monitored element. Contributions from other distant sources will then be attenuated before they reach the accelerometer. Obviously, high frequency envelope methods require the excitation to have a substantial amount of energy at high frequencies. This is true for localized defects, such as cracks and spalls, but also for surface wear in fluid film bearings. When a ball in a ball bearing rolls over a spall on the bearing inner race an abruptly changing contact force is experienced. This contact force has impact character and excites vibrations from low frequencies up to ultrasound frequencies. One of the crucial elements of envelope methods is to select a suitable high frequency region and band-pass filter the accelerometer signal. Some methods suggest that the filter should be centered on a structural resonance frequency. Others recommend regions free from strong tones due to resonances or harmonic components. A second important element is to demodulate or calculate the vibration signature from the band-pass filtered vibration signal. High frequency resonance techniques use the large amplitude vibration in the neighborhood of a structural high frequency resonance. After band-pass filtering the vibration signal its time history consists of a series of exponentially decaying impulse responses. Each impulse response consists of a narrowband resonant vibration signal acting as carrier modulated with a series of impacts produced by the defect. This implies that information on the defect, its periodicity etc., is available in the signal modulation. The defect signature is obtained by removing the carrier wave, that is, by extracting the envelope, from the band-passed signal. Below describes the defect signature extraction procedure schematically. When the residual error signature has been extracted by demodulating the band-pass filtered vibration signal it can be processed in various ways to 1577 Basically, machine vibration monitoring uses so called signature analysis, i.e. the characteristic vibration signature of the monitored machine element is investigated. In practice, machine monitoring requires some physically measureable signal to monitor. It might be vibration, sound pressure or a temperature signal. Vibrations are the most commonly used monitoring signals. Vibrations are not subject to background disturbances to the same extent as acoustic noise. Vibration sensors, accelerometers, can be placed closer to the source than microphones. [84, 85, 86, 87] 4.1) single process The vibration signal analysis is one of the most important methods used for condition monitoring and fault diagnostics because they always carry the dynamic information of the system. Effective utilization of the vibration signals, however, depends upon the effectiveness of the applied signal processing techniques for fault diagnostics. With the rapid development of the signal processing techniques, the analysis of stationary signals has largely been based on wellknown spectral techniques such as: Fourier Transform (FT), Fast Fourier Transform (FFT) and Short Time Fourier Transform STFT) [87, K. Shibata, A. Takahashi, T. Shirai,2000], 88, S. Seker, E. Ayaz,2000] Unfortunately, the methods based on FT are not suitable for non-stationary signal analysis [89, C. Cexus, “Analyse des signaux non-stationnaires par Transformation de Huang, Opérateur de Teager-Kaiser, et Transformation de HuangTeager (THT, 2005]. In addition, they are not able to reveal the inherent information of non-stationary signals. These methods provide only a limited performance for machinery diagnostics [90, J. D. Wu, C.-H. Liu, 2008]. In order to solve these problems, Wavelet Transform (WT) has been developed. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 Wavelet Transform A wavelet means a small wave (the sinusoids used in Fourier analysis are big waves) and in brief, a wavelet is an oscillation that decays quickly. The wavelet analysis is done similar to the STFT analysis. The signal to be analyzed is multiplied with a wavelet function just as it is multiplied with a window function in STFT, and then the transform is computed for each segment generated. However, unlike STFT, in Wavelet Transform, the width of the wavelet function changes with each spectral component. The Wavelet Transform, at high frequencies, gives good time resolution and poor frequency resolution, while at low frequencies, the Wavelet Transform gives good frequency resolution and poor time resolution. In comparison to the Fourier transform, the analyzing function of the wavelet transform can be chosen with more freedom, without the need of using sine-forms. A wavelet function (t) is a small wave, which must be oscillatory in some way to discriminate between different frequencies. The wavelet contains both the analyzing shape and the window. Shows an Figure (4.1) example of a possible wavelet, known as the Morlet wavelet has been extensively used for impulse isolation and mechanical fault diagnosis [71, A.A Ibrahim, S.M.Abdel-Rahman,M.Z.Zahran,H.H.EL-Mongey] use in Adaptive wavelet analysis. For the CWT several kind of wavelet functions are developed which all have specific properties. Wavelets is much larger than that of the Fourier transform. In fact, the mathematics of wavelets encompasses the Fourier transform. The size of wavelet theory is matched by the size of the application area. Initial wavelet applications involved signal processing and filtering. However, wavelets have been applied in many other areas including nonlinear regression and compression. An offshoot of wavelet compression allows the amount of determinism in a time series to be estimated. The main difference is that wavelets are well localized in both time and frequency domain whereas the standard Fourier transform is only localized in frequency domain. The Short-time Fourier transform (STFT) is also time and frequency localized but there are issues with the frequency time resolution and wavelets often give a better signal representation using Multi resolution analysis[91, M. Sifuzzaman1, M.R. Islam1 and M.Z. Ali,2009] Wavelet decomposes a signal in both time and frequency in terms of a wavelet, called mother wavelet. The WT includes Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). Let s (t) is the signal; the CWT of s(t) is defined as.[92,Hocine Bendjama, Salah Bouhouche, and Mohamed Seghir Boucherit,2012] ∞ CWT (a,b) = 1/ ( √|𝒂| )∫−∞ 𝒔( 𝒕 ) 𝝍∗ ((t - b)/ a )d t (4.1.1) Where ψ*(t) is the conjugate function of the mother wavelet ψ (t) (1.2), a and b are the dilation (scaling) and translation (shift) parameters, respectively. The factor 1/√|𝑎| is used to ensure energy preservation. Ψ (t) = 1/ (√𝒂 ) ψ ((t −b) / a) (4.1.2) The mother wavelet must be compactly supported and satisfied with the admissibility condition +∞ ∫−∞ |𝝓(𝒘)|𝟐 /|𝒘| 𝒅𝒘 < ∞ Where (w)=∫ 𝝍 (t)exp(-jwt)dt Figure (4.1): Morlet wavelet (4.1.3) (4.1.4) 𝜙 (w): mother wavelet function Comparison Transform Wavelet Transform with Fourier The Fourier transform is less useful in analyzing nonstationary signal (a non-stationary signal is a signal where there is change in the properties of signal). Wavelet transforms allow the components of a non-stationary signal to be analyzed. Wavelets also allow filters to be constructed for stationary and non-stationary signal. The Fourier transform shows up in a remarkable number of areas outside of classic signal processing. Even taking this into account, we think that it is safe to say that the mathematics of 1578 The DWT is derived from the discretization of CWT. The most common discretization is dyadic. The DWT is given by ∞ DWT (j,k ) =1/( √𝟐𝒋 )∫−∞ 𝒔( 𝒕 ) ψ ((t - 𝟐𝒋 k ) /𝟐𝒋 )d t (4.1.5) Where a and b are replaced by 2j and 2jk, j is an integer. A very useful implementation of DWT, called multi resolution analysis [93, S.G.Mallat, 1989], is demonstrated DWT analyzes the signal at different scales. It employs two sets of functions, called scaling functions and wavelet functions [93, S. G. Mallat, 1989], [94, N.Lu,F. Wang, F. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 Gao,2003], which are associated with low pass and high pass filters, respectively. In engineering application , the square of the modulus of the CWT is often called scalogram which is a time - scale distribution , and is defined : SGX (a,b) = |WX(a,b)|2 (4.1.6) Compared to SHFT, whose time - frequency resolution is fixed, the time -frequency resolution of the wavelet transform depends on the frequency of the signal. At high frequencies, the wavelet uses narrow time windows yielding high time resolution but a low frequency resolution. Whereas, at low frequencies, wide time windows are used so the frequency resolution is high while the time resolution is low. Thus, Wavelet transform is very suitable for the analysis of the analysis of the transient and non-stationary signals. [71,A.AIbrahim,S.M.AbdelRahman,M.Z.Zahran,H.H.ELMongey] Some Application of Wavelets Wavelets are a powerful statistical tool which can be used for a wide range of applications, namely • Signal processing • Data compression • Smoothing and image denoising • Fingerprint verification • Biology for cell membrane recognition, to distinguish the normal from the pathological membranes • DNA analysis, protein analysis • Blood-pressure, heart-rate and ECG analyses • Finance (which is more surprising), for detecting the properties of quick variation of value • In Internet traffic description, for designing the services size • Industrial supervision of gear-wheel • Speech recognition • Computer graphics and multiracial analysis • Many areas of physics have seen this paradigm shift, including molecular dynamics, astrophysics, optics, turbulence and quantum mechanics. Wavelets have been used successfully in other areas of geophysical study [91, M. Sifuzzaman1, M.R. Islam1 and M.Z. Ali, 2009] d) A wavelet transform can be used to decompose a signal into component wavelets e) In wavelet theory, it is often possible to obtain a good approximation of the given function f by using only a few coefficients which is the great achievement in compare to Fourier transform. f) Most of the wavelet coefficients { j k }j k N d , , ≥ vanish for large N. g) Wavelet theory is capable of revealing aspects of data that other signal analysis techniques miss the aspects like trends, breakdown points, and discontinuities in higher derivatives and self-similarity. h) It can often compress or de-noise a signal without appreciable degradation. [91, M. Sifuzzaman1, M.R. Islam1 and M.Z. Ali, 2009] Wavelets are an incredibly powerful tool, but if you can’t understand them, you can’t use them. Up till now, wavelets have been generally presented as a form of Applied Mathematics. Most of the literature still uses equations to introduce the subject. [95, preview of wavelets, wavelet filters, and wavelets transform space and signal's Technology, 2009] 4.2) Modal Analysis Modal analysis has been widely applied in vibration trouble shooting, structural dynamics modification, analytical model updating, optimal dynamic design, vibration control, as well as vibration-based structural health monitoring in aerospace, mechanical and civil engineering. Traditional experimental modal analysis (EMA) makes use of input (excitation) and output (response) measurements to estimate modal parameters, consisting of modal frequencies, damping ratios, mode shapes and modal participation factors. EMA has obtained substantial progress in the last three decades. Numerous modal identification algorithms, from SingleInput/Single-Output (SISO), Single-Input/Multi-Output (SIMO) to Multi-Input/Multi-Output (MIMO) techniques in Time Domain (TD), Frequency Domain (FD) and Spatial Domain (SD), have been developed . Some Advantages of Wavelet Theory: Traditional experimental modal analysis a) One of the main advantages of wavelets is that they offer a simultaneous localization in time and frequency domain. b) The second main advantage of wavelets is that, using fast wavelet transform, it is computationally very fast. (EMA), however, suffers from several limitations, as described below. 1– It requires artificial excitation to evaluate frequency response functions (FRF) or impulse response functions (IRF). In some cases, such as civil structures, providing adequate excitation is difficult if not impossible. 2– Operational conditions are often different from those adopted in tests because traditional EMA is conducted in a laboratory environment. c) Wavelets have the great advantage of being able to separate the fine details in a signal. Very small wavelets can be used to isolate very fine details in a signal, while very large wavelets can identify coarse details. 1579 www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 3– The boundary conditions are simulated because tests are usually conducted in a laboratory environment on components instead of with complete systems. 4– Structural modification and sensitivity analysis to evaluate the effect of changes on the dynamics of a structure without actual modifications; 5– Structural health monitoring and damage detection by comparing modal parameters from the current state of a structure with those at a reference state to obtain information about the presence, location and severity of damage; 6– Performance evaluation, if modal parameters and mode shapes are used to evaluate the dynamic performance of a system. 7– Force identification starting with only structural response measurements. Operational modal analysis Although most operational modal analysis techniques are derived from traditional EMA procedures, the main difference is related to the basic assumptions about the inputs. In fact, EMA procedures are developed in a deterministic framework, while OMA methods are based on random responses and, therefore, a stochastic approach. Thus, many OMA techniques can be seen as the stochastic counterparts of the deterministic methods used in classical EMA, despite the availability of new hybrid deterministic-stochastic techniques. [96, Carlo Rainieri and Giovanni Fabbrocino, 2011] This technique has been successfully used in civil engineering structures (buildings, bridges, platforms, towers) where the natural excitation of the wind is used to extract modal parameters. It is now being applied to mechanical and aerospace engineering applications (rotating machinery, on-road testing, and in-flight testing). The advantage of this technique is that a modal model can be generated while the structure is under operating conditions. That is, a model within true boundary conditions and actual force and vibration levels. Another advantage of the technique is the ability to perform modal testing in-situ, i.e., without removing parts under test.[97, Mehdi Batel, Brüel & Kjær, Norcross, Georgia,2002] Operational modal analysis techniques are based on the following assumptions: 1– Linearity: the response of a system to a certain combination of inputs is equal to the same combination of corresponding outputs; 2– stationary: the dynamic characteristics of a structure do not change over time, and the coefficients of the differential equations are constant with respect to time; and 3– observability: the test setup must be defined to enable measurements of the dynamic characteristics of interest; for instance, nodal points must be avoided to detect a certain mode.[96, Carlo Rainieri and Giovanni Fabbrocino.2011] The technique of modal analysis can't be used in rotating element because modal analysis techniques are based on assumptions (linearity, stationary) so 1580 vibration analysis is the best in case of rotating machine element. 4.3) Stochastic Subspace Identification (SSI) Stochastic Subspace Identification (SSI) modal estimation algorithms have been around for more than a decade by now. The real break-through of the SSI algorithms happened in 1996 with the publishing of the book by van Overschee and De Moor [98, Peter van Overschee and Bart De Moor, 1996]. A set of MATLAB files were distributed along with this book and the readers could easily convince themselves that the SSI algorithms really were a strong and efficient tool for natural input modal analysis. Because of the immediate acceptance of the effectiveness of the algorithms the mathematical framework described in the book where accepted as a de facto standard for SSI algorithms. However, the mathematical framework is not going well together with normal engineering understanding. The reason is that the framework is covering both deterministic as well as stochastic estimation algorithms. To establish this kind of general framework more general mathematical concepts has to be introduced. Many mechanical engineers have not been trained to address problems with unknown loads enabling them to get used to concepts of stochastic theory, while many civil engineers have been trained to do so to be able to deal with natural loads like wind, waves and traffic, but on the other hand, civil engineers are not used to deterministic thinking. The book of van Overschee and De Moor [98, Peter van Overschee and Bart De Moor, 1996] embraces both engineering worlds and as a result the general formulation presents a mathematics that is difficult to digest for both engineering traditions. take a another ride with the SSI train to discover that most of what you will see you can recognize as generalized procedures well established in classical modal analysis. [99, Rune Brincker, Palle Andersen] The discrete time formulation We consider the stochastic response from a system as a function of time 𝒚𝟏 (𝒕) 𝒚𝟐 (𝒕) . 𝒚(𝒕) = (4.3.1) . . { 𝒚𝒎 } The system can be considered in classical formulation as a multi degree of freedom structural system M y..(t)+D y. (t) +k y (t) =f (t) (4.3.2) Where Κ, D, Μ, is the mass, damping and stiffness matrix, and where f (t) is the loading vector. In order to take this classical continuous time formulation to the discrete time domain the easiest way is to introduce the State Space formulation. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 𝒚(𝒕) X (t) = { . } 𝒚 (𝒕) (4.3.3) Here we are using the rather confusing terminology from systems engineering where the states are denoted x (t) (so please don’t confuse this with the system input, the system input is still f (t)). Introducing the State Space formulation, the original 2nd order system equation given by eq. (3.2) simplifies to a first order equation X∙ (t)=ACX(t)+Bf(t) (4.3.4) y (t)=CX(t) (4.3.4) Where the system matrix AC in continuous time and the load matrix B is given by 𝟎 𝐈 AC=[ ] (4.3.5) −𝐌 −𝟏 𝐊 −𝐌 −𝟏 𝐃 B=[ 𝟎 ] 𝑴−𝟏 (4.3.5) The advantage of this formulation is that the general solution is directly available, 𝒕 X (t) =exp (ACt) X (0∫𝟎 𝒆𝒙𝒑(𝑨𝑪 (𝒕 − 𝛕))𝐁𝐟(𝛕)𝒅𝒕 (4.3.6) Where the first term is the solution to the homogenous equation and the last term is the particular solution. To take this solution to discrete time, we sample all variables like yk=y (k∆t) and thus the solution to the homogenous equation becomes (ACK∆t)X0 -AdkX0 X (t) =exp Ad=exp(AC∆t) yk=CAdkX0 (4.3.7) (4.3.7) (4.3.7) The Block Henkel Matrix In discrete time, the system response is normally represented by the data matrix 𝒀 = [ 𝒚𝟏 𝒚𝟐 … … . . 𝒚𝑵 ] (4.3.8) Where N is the number of data points. To understand the meaning of the Block Henkel matrix, it is useful to consider a more simple case where we perform the product between two matrices that are modifications of the N data matrix given by eq. (2.5.3.7). Let Y (1: N-K) be the data matrix where we have removed the last K data points, and similarly, let Y (K: N) be the data matrix where we have removed the first K data points, then 𝟏 RK= Y (1: N-K) Y (K: N) (4.3.9) SSI is simply a gathering of a family of matrices that are created by shifting the data matrix 𝐘(𝟏:𝐍−𝟐𝐬) 𝐘(𝟐:𝐍−𝟐𝐬+𝟏) 𝒀𝒉𝒑 . Yh= =[ 𝒚 ] (4.3.10) . 𝒉𝒇 . [ 𝐘(𝟐𝐬:𝐍) ] The upper half part of this matrix is called “the past” 𝒀𝒉𝒑 and denoted and the lower half part of the matrix is called “the future” and is denoted 𝒚𝒉𝒇 . The total data shift 2sis and is denoted “the number of block rows” (of the upper or lower part of the Block Hankel matrix). The number of rows in the Block Hankel matrix is 2sM, the number of columns is N-2S. [99, Rune Brincker, Palle Andersen] 4.4) Order Analysis (OHS) One of the most popular analysis methods for engineers/scientists has been harmonic analysis. Here, the term harmonic refers to frequencies that are integer (or fractional) multiples of a fundamental frequency. In the automobile industry, such harmonics are traditionally referred to as orders. Accordingly, the harmonic analysis is called as order analysis. [100, Shie Qian,] .Order tracking (OT) is one of the most important vibration analysis techniques for diagnosing faults in rotating machinery. The main advantage of OT over other vibration analysis techniques lies in the analysis of non-stationary noise and vibration, [101, K. S. Wang and P. S. Heyns] Bispectral Analysis The statistical properties of a stationary random process are completely described by its mean value m (first order moment) and variance s2 (second order central moment) if and only if its probability density function has a Gaussian distribution. HOS measures, such as higher order moments, are extensions of second-order measures to higher orders and cannot provide additional information about a signal if it is Gaussian. However, many signals found in the industrial field are non-Gaussian, e.g. vibration signals of rotating machines. Therefore, HOS may be used to extract information about signals and systems which cannot be obtained from conventional statistics. The most used traditional signal processing measure is the power spectrum that is the decomposition over frequency of the signal power and is therefore related to the signal variance s2. The bispectrum (third order spectrum) can be viewed as a decomposition of the third moment (skewness) of a signal over frequency and as such can detect non-symmetric nonlinearity. For a stationary random process, the discrete bispectrum B (k,l) can be defined in terms of the signal's Discrete Fourier Transform X(k) as: 𝐍−𝐊 B (k,l) =E[X(k ) X(l ) X * (k +l )] Is an unbiased estimate of the correlation matrix at time lag K. This follows directly from the definition of the correlation estimate, The Block Henkel Yh matrix defined in 1581 (4.4.1) Where E [] denotes the expectation operator. It should be noted that the bispectrum is complex-valued (it contains phase information) and that it is a function of two www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 independent frequencies, k and l. Furthermore, it is not necessary to compute B (k, l) for all (k, l) pairs, due to several symmetries existing in the (k, l) plane. In particular there exists a non-redundant region called the Principal Domain which is defined as: {K, l}: 0 ≤ k ≤ 𝒇𝒔 𝟐 , l ≤ k, 2k + l ≤ fs (4.4.2) Where fs is the sampling frequency the bispectrum is able to detect the non-linear interactions between spectral components and to measure the extent of their dependencies. Second-order measures contain no phase information and, consequently, cannot be used to identify phase coupling, which are often associated with system non-linearity. This is in contrast to third order methods which are sensitive to certain types of phase Moreover, since the signals encountered in practice are often contaminated by Gaussian measurement noise, to which HOS measure are theoretically insensitive, they are potentially powerful tools for analyzing real-life signals. Bicoherence Bispectral analysis often does not deal with the bispectrum, as given by equation (4.4.1), but with a normalized form of bispectrum, e.g. the bicoherence, b2 (k, l), which is defined by: b2(k,l) = |𝐄[𝐗(𝐊)𝐗(𝐋)𝐗 ∗ (𝐊+𝐋)]|𝟐 𝑬[| 𝑿(𝑲)𝑿(𝑳)|𝟐 𝑬[|𝑿(𝑲+𝑳)|𝟐 ] (4.4.3) The reason for normalizing the bispectrum is due to the fact that this estimator has a variance which is proportional to the triple product of the power spectra, which can result in the second order properties of the signal dominating the estimate. The advantage of normalization is to make the variance approximately flat across all frequencies. For stochastic (random) signals the bicoherence is a measure of the signal skewness (the third order moment). An important feature of the bicoherence is that it is always restricted to vary between 0 and 1 .The bicoherence, as well as the bispectrum, can be computed from a signal by dividing it into K segments, applying an appropriate window to each segment to reduce leakage, computing the quantities in Equations (4.4.1) and (4.4.3) for each segment by using the Discrete Fourier Transform and then obtaining the statistical estimate by averaging over all segments. Segment averaging is used in order to achieve a consistent estimate. Accordingly, the bicoherence can be calculated using the following estimator: B^2 (k,l)= ∑𝒌 ∗ 𝟐 | ∑𝒌 𝒊=𝟏 𝒙𝒊 (𝒌)𝒙𝒊 (𝒍)𝒙𝒊 (𝒌+𝒍)| 𝟐 𝒌 𝟐 𝒊=𝟏 |𝒙𝒊 (𝒌)𝒙𝒊 (𝒍)| ∑𝒊=𝟏 |𝒙𝒊 (𝒌+𝒍)| (4.4.4) It is important to observe that the bicoherence is only a normalization of the bispectrum and it should not be confused with the second order coherence function; moreover, its computation requires a single signal measurement, whilst the ordinary coherence function needs two measures. [102, A. RIVOLA] 1582 4.5) Frequency Domain Decomposition (FDD) Method The FDD method [103 Brincker R, Zhang LM, Andersen200] can be viewed as an extension of the traditional basic frequency domain method. It is performed using the output power spectral density (PSD), and based on the assumption that the excitation is pure Gaussian white noise and that all natural modes are lightly damped [53]. A singular value decomposition (SVD) is carried out for each PSD matrix and all modes contributing to the vibratory signature of a structure at a given frequency are separated into principal values and orthogonal vectors. When a single mode identified by peak picking at a Given frequency prevails in the spectrum, the first vector obtained by the SVD will constitute an estimate of the mode shape. The first singular value corresponding to this mode should be approximately equal to the sum of the terms on the diagonal of the PSD matrix, which means that most of the power of the measured signals at this frequency can be attributed to the vibratory signature of this particular mode. Other singular values that are not associated with any mode will consist of decomposed noise initially contained in the signals before the SVD was performed. Once natural frequencies have been roughly identified by peak picking and mode shapes have been estimated using the singular vector matrices, equivalent single degree of freedom ‘spectral bells’ are identified for each mode. This step is achieved by comparing the estimated mode shape of interest with all vectors previously estimated throughout the spectrum by SVD of all the PSD matrices. A comparison of the mode shapes is then carried out by computing the modal assurance criterion (MAC). All singular values corresponding to a MAC value superior to a user specified parameter (which is called the MAC rejection level) are kept, thus forming an equivalent single degree of freedom spectral bell. Then, by inverse fast Fourier transform (IFFT) of that spectral bell, the resulting autocorrelation function can be used to reevaluate the frequency by counting the number of zero crossings in a finite time interval. Damping ratios are also estimated using the logarithmic decrement of the auto-correlation function. More details on the theory and implementation of the FDD method can be found in Reference [103]. The Frequency Domain Decomposition (FDD) is an extension of the Basic Frequency Domain (BFD) technique, or more often called the Peak-Picking technique. This approach uses the fact that modes can be estimated from the spectral densities calculated, in the condition of a white noise input, and a lightly damped structure. It is a nonparametric technique that estimates the modal parameters directly from signal processing calculations, Refs. [103,104]. The FDD technique estimates the modes using a Singular Value Decomposition (SVD) of each of the data sets. This decomposition corresponds to a Single Degree of www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 Freedom (SDOF) identification of the system for each singular value. The relationship between the input x(t), and the output y(t) can be written in the following form, Refs. [105,106] The Enhanced Frequency Domain Decomposition (EFDD) technique is an extension to the Frequency Domain Decomposition (FDD) technique. FDD is a basic technique that is extremely easy to use. You simply pick the modes by locating the picks in SVD plots calculated from the spectral density spectra of the responses. Animation is performed immediately. As the FDD technique is based on using a single frequency line from the FFT analysis, the accuracy of the estimated natural frequency depends on the FFT resolution and no modal damping is calculated. Compared to FDD, the EFDD gives an improved estimate of both the natural frequencies and the mode shapes and also includes damping. In EFDD, the SDOF Power Spectral Density function, identified around a peak of resonance, is taken back to the time domain using the Inverse Discrete Fourier Transform (IDFT). The natural frequency is obtained by determining the number of zero-crossing as a function of time, and the damping by the logarithmic decrement of the corresponding SDOF normalized auto correlation function. The SDOF function is estimated using the shape determined by the previous FDD peak picking - the latter being used as a reference vector in a correlation analysis based on the Modal Assurance Criterion (MAC). A MAC value is computed between the reference FDD vector and a singular vector for each particular frequency line. If the MAC value of this vector is above a user-specified MAC Rejection Level, the corresponding singular value is included in the description of the SDOF function. The lower this MAC Rejection Level is, the larger the number of singular values included in the identification of the SDOF function will be. [106] N-J. Jacobsen, P. Andersen, R. Brincker] The advantages of the FDD are that the technique is easy and fast to use. There is a “snap to peak” feature that can be applied on the Averaged Normalized Singular Value function. The corresponding singular vector, which is an approximation to the mode shape, is extracted from all dataset at the selected frequency. In fact, the singular vectors can be extracted from any singular value at any frequency, which may lead to better understanding of the structural behavior. The disadvantages are that no damping is estimated and the frequency resolution is no better than the FFT line spacing. The main advantages of the EFDD technique are that both Frequency and Damping are estimated. The “snap to peak” is applied to the maximum Singular Values for each dataset. Then the averaged frequency and damping values are estimated as well as their standard deviations from all data sets. Major disadvantage is that the algorithm does not work properly if no distinguished peak is found in some of the data sets. It is also required to fine tune the three modal estimation parameters, MAC Rejection Level, maximum and minimum correlation (i.e. correlation interval) for each resonance frequency in each dataset, which may be a very 1583 time consuming procedure, when there are many data sets and/or many modal frequencies present. Conclusion This paper presents a fault diagnosis method. Many methods have been developed to monitor machine condition. and describe the main types defect which occur in rotating element and in this paper has present technique of monitoring for fault diagnosis and compare with this method and choose the best way for monitoring .we also talk about technique of analysis (signal processing , modal analysis) the technique of modal analysis can't be use in rotating element because modal analysis techniques are based on assumptions(linearity, stationary) so vibration analysis is the best in case of rotating machine element, (SSI) Many mechanical engineers have not been trained to address problems with unknown loads enabling them to get used to concepts of stochastic theory, while many civil engineers have been trained to do so to be able to deal with natural loads like wind, waves and traffic and ( HOS) It is important to observe that the bicoherence is only a normalization of the bispectrum and it should not be confused with the second order coherence function; moreover, its computation requires a single signal measurement, whilst the ordinary coherence function needs two measures) ,paper shows that The disadvantages of (FDD) Method are that no damping is estimated and the frequency resolution is no better than the FFT line spacing and Major disadvantage of (EFDD) is that the algorithm does not work properly if no distinguished peak is found in some of the data sets. It is also required to fine tune the three modal estimation parameters, MAC Rejection Level, maximum and minimum correlation (i.e. correlation interval) for each resonance frequency in each dataset, which may be a very time consuming procedure, when there are many data sets and/or many modal frequencies present. We will notice from comparison that the best way for analysis is signal process use in the most application. The vibration signal analysis is one of the most important methods used for condition monitoring and fault diagnostics. Unfortunately, the methods of vibration analysis based on FT are not suitable for non-stationary signal analysis so we use the wavelet transform for non-stationary signal as shown in the paper the technique of wavelet .Short Time Fourier Transform (SHFT) has fixed resolution that depends upon the selection of the window half-width . Continuous Wavelet transform (CWT) is very efficient in localizing impulses and detecting periodic events as well due to its multi-resolution property. Complex CWT is very sensitive to any abrupt changes in time signal so it can detect impulses. Adaptive Wavelet (DWT) is efficient in locating impulses but it is difficult to specify frequencies of periodic events. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 Reference [1] Baschmid, N., Diana, G., and Pizzigoni, B., 1984, "The Influence of Unbalance on Cracked Rotors," Proceedings of the Ins titution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 193-198. [2] Cempel, C., 1991, "Condition Evolution of Machinery and its Assessement from Passive Diagnostic Experiment," Mechanical Systems and Signal Processing, Vol. 5(4), pp. 317-326. [3] Childs, D.W., and Jordan, L.T., 1997, "Clearance Effects on Spiral Vibrations due to Rubbing," Proceedings of the ASME Design Engineering Technical Conference, DETC97/VIB-4058. [4] Den Hartog, J.P., 1934, "Mechanical Vibrations," New York, McGraw-Hill. [5] Ding, J., and Krodkiewski, J.M., 1993, "Inclusion of Static Indetermination in the Mathematical-Model for Nonlinear Dynamic Analyses of Multi-Bearing Rotor System," Journal of Sound and Vibration, Vol. 164(2), pp. 267-280. [6] Doebling, S.W., Farrar, C.R., Prime, M.B., and Shevitz, D.W., 1996, "Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics - A Literature Review," Los Alomos National Laboratory Report, No. LA-13070-MS. [7] Downham, E., 1976, "Vibration in Rotating Machinery: Malfunction Diagnosis - Art & Science," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 1-6. [8] Eshleman, R.L., 1984, "Some Recent Advances in Rotor Dynamics", Proceedings Of The Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. xi-xx. [9] Flack, R.D., Rooke, J.H., Bielk, J.R., and Gunter, E.J., 1982, "Comparison of the Unbalance Responses of Jeffcott Rotors with Shaft Bow and Shaft Runout," Journal of Mechanical Design Transactions of the ASME, Vol. 104, pp. 318-328. [10] Frank, P.M., 1994, "Enhancement of Robustness in ObserverBased Fault-Detection," International Journal of Control, Vol. 59(4), pp. 955-981. [11] Frank, P.M., and Köppen-Seliger, B., 1997, "New Developments Using Artificial Intelligence in Fault Diagnosis", Engineering Applications of Artificial Intelligence, Vol. 10(1), pp. 3-14. [12] Garcia, E.A., and Frank, P.M., 1997, "Deterministic Nonlinear Observer-Based Approaches to Fault Diagnosis: A Survey," Control Engineering Practice, Vol. 5(5), pp. 663-670. [13] Gasch, R., 1976, "Dynamic Behaviour of a Simple Rotor with a Cross-Secional Crack," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 123-128. [14] Gasch, R., 1993, "A Survey of the Dynamic Behavior of a Simple Rotating Shaft with a Transverse Crack," Journal of Sound and Vibration, Vol. 160(2), pp. 313-332. [15] Genta, G., 1993, "Vibration of Structures and Machines: Practical Aspects," New York, Springer-Verlag. [16] Ghauri, M. K. K., Fox, C.H.J., and Williams, E.J., 1996, "Transient Response and Contact due to Sudden Imbalance in a Flexible Rotor-Casing System with Support Asymmetry," Proceedings of the Institution of Mechanical Engineers Vibrations in Rotating Machinery, pp. 383-394. [17] Gnielka, P., 1983, "Modal Balancing of Flexible Rotors without Test Runs - An Experimental Investigation," Journal of Sound and Vibration, Vol. 90(2), pp. 157-172. [18] Göttlich, E.H., 1988, "A Method for Overall Condition Monitoring by Controlling the Efficiency and Vibration Level of Rotating Machinery," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 445-447. 1584 [19] Halliwell, N.A., 1996, "The Laser Torsional Vibrometer - A Step Forward in Rotating Machinery Diagnostics," Journal of Sound and Vibration, Vol. 190(3), pp. 399-418. [20] He, Z.J., Sheng, Y.D., and Qu, L.S., 1990, "Rub Failure Signature Analysis for Large Rotating Machinery," Mechanical Systems and Signal Processing, Vol. 4(5), pp. 417-424. [21] Hill, J.W., and Baines, N.C., 1988, "Application of an Expert System to Rotating Machinery Health Monitoring," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 449-454. [22] Howell, J., 1994, "Model-Based Fault-Detection in Information Poor Plants," Automatica, Vol. 30(6), pp. 929-943. [23] Huang, S.C., Huang, Y.M., and Shieh, S.M., 1993, "Vibration and Stability of a Rotating Shaft Containing a Transverse Crack," Journal of Sound and Vibration, Vol. 162(3), pp. 387-401. [24] Isermann, R., 1984, "Process Fault Detection Based on Modeling and Estimation Methods - A Survey," Automatica, Vol. 20, pp. 387-404. [25] Isermann, R., 1993, "Fault Diagnosis of Machines via Parameter Estimation and Knowledge Processing - Tutorial Paper," Automatica, Vol. 29(4), pp. 815-835. [26] Isermann, R., 1994, "On the Applicability of Model-Based Fault-Detection for Technical Processes," Control Engineering Practice, Vol. 2(3), pp. 439-450. [27] Isermann, R., 1997, "Supervision, Fault Detection and FaultDiagnosis Methods - An Introduction," Control Engineering Practice, Vol. 5(5), pp. 639-652. [28] Isermann, R., and Ballé, P., 1997, "Trends in the Application of Model-Based Fault Detection and Diagnosis of Technical Processes," Control Engineering Practice, Vol. 5(5), pp. 709-719. [29] Iwatsubo, T., 1976, "Error Analysis of Vibration of Rotor/Bearing System," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 8792. [30] Jun, O.S., Eun, H.J., Earmme, Y.Y., and Lee, C.W., 1992, "Modeling and Vibration Analysis of a Simple Rotor with a Breathing Crack," Journal of Sound and Vibration, Vol. 155(2), pp. 273-290. [31] Kirk, R.G., 1984, "Insights from Applied Field Balancing of Turbomachinery," Proceedings of the Institution of Mechanical Engineers - Vibrations in Rotating Machinery, pp. 397-407. [32] I.H. Witten and E. Frank: Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations (Academic Press. USA, 2000). [33] Altmann, J. (1999) Application of Discrete Wavelet Packet Analysis for the Detection and Diagnosis of Low Speed RollingElement Bearing Faults. PhD Thesis, Monash University: Melbourne. [34] Baillie, D C and Mathew, J (1996), A comparison of autoregressive modeling techniques for fault diagnosis of rolling element bearings, Journal of Mechanical Systems and Signal Processing, Vol 10(1), pp. 1-17. [35] Zhong, B. (2000) Developments in intelligent condition monitoring and diagnostics. in System Integrity and Maintenance , the 2nd Asia-Pacific Conference(ACSIM2000), pp 1-6, Brisbane, Australia. [36] Pham, D.T. and P.T.N. Pham. (1999) Artificial intelligence in engineering. International Journal of Machine Tools & Manufacture, 39, 937-949. [37] Tandon, N. and A. Choudhury. (1999) A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribology International, 32(8), 469-480. [38] Gao, X.Z. and S.J. Ovaska. (2001) Soft computing methods in motor fault diagnosis. Applied Soft Computing, 1(1), 73-81. [39] Chow, M.-Y. (2000) Guest editorial special section on motor fault detection and diagnosis. Industrial Electronics, IEEE Transactions on, 47(5), 982-983. www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 [40] Nicola Orani," HIGHER-ORDER SLIDING MODE TECHNIQUES FOR FAULT DIAGNOSIS",XXII Cycle March 2010. .[41] Christophe Thiry, Ai-Min Yan, Jean-Claude Golinval ,'' Damage Detection in Rotating Machinery Using Statistical Methods : PCA Analysis and Autocorrelation Matrix '',surveillance5 cetim senils 11-13 October 2004 [42] J. S. Mitchell, introduction to Machinery Analysis and Monitoring, PenWel Books, Tulsa (1993). [43] J. I.Taylor, Back to the Basics of Rotating Machinery Vibration Analysis, Vibration Consultants, Inc., Tampa Bay, FL ( 1994). [44] J. T. Roth and S. M. Pandit, “’Condition Monitoring and Failure Prediction for Various Rotating Equipment Components”, Proceedings of the 17th International Modal Analysis Conference, Kissimmee, FL ( 1999), pp. 1674-1680 [45] C. J. Li, J. lMa, B. Flwang, and G.W. Nickerson, “Pattern Recognition Based Bicoherence Analysis of Vibrations for Bearing Condition Monitoring”, in Sensors, Controls, and Quality Issues in Manufacturing, American Society of Mechanical Engineers ( 199 1), pp. 1-11. [46] S. Braun (1986), Mechanical Signature Analysis - Theory and Applications, Academic Press, Inc., London.. [47] K. Shibata, A. Takahashi, T. Shirai, “Fault diagnosis of rotating machinery through visualisation of sound signal,” Journal of Mechanical Systems and Signal Processing, vol. 14, pp. 229241, 2000. [48] S. Seker, E. Ayaz, “A study on condition monitoring for induction motors under the accelerated aging processes,” IEEE Power Engineering, vol. 22, no. 7, pp. 35-37, 2002. [49] J. C. Cexus, “Analyse des signaux non-stationnaires par Transformation de Huang, Opérateur de Teager-Kaiser, et Transformation de Huang-Teager (THT),” Thèse de Doctorat, Université de Rennes-France, 2005. [50] J. D. Wu, C.-H. Liu, “Investigation of engine fault diagnosis using discrete wavelet transform and neural network,” Expert Systems with Applications, vol. 35, pp. 1200-1213, 2008. [51] S. H. Cao, J. C. Cao, “Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis,” Applied ThermalEngineering, vol. 25, no. 2-3, pp. 161-172, 2005. [52] G. Strang, “Wavelet transforms versus Fourier transforms,” Bulletin of the American Mathematical Society, vol. 28, pp. 288305, 1993. [53] Z. K. Peng, F. L. Chu, “Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography,” Mechanical Systems and Signal Processing, vol. 18, pp. 199-221, 2004. [54] A. Djebala, N. Ouelaa, N. Hamzaoui, “Detection of rolling bearing defects using discrete wavelet analysis,” Meccanica, vol. 43, no. 2, pp. 339-348, 2008. [55] I.H. Witten and E. Frank: Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations (Academic Press. USA, 2000). [56] Altmann, J. (1999) Application of Discrete Wavelet Packet Analysis for the Detection and Diagnosis of Low Speed RollingElement Bearing Faults. PhD Thesis, Monash University: Melbourne. [57] Baillie, D C and Mathew, J (1996), A comparison of autoregressive modeling techniques for fault diagnosis of rolling element bearings, Journal of Mechanical Systems and Signal Processing, Vol 10(1), pp. 1-17. [58] Zhong, B. (2000) Developments in intelligent condition monitoring and diagnostics. in System Integrity and Maintenance , the 2nd Asia-Pacific Conference(ACSIM2000), pp 1-6, Brisbane, Australia. [59] Pham, D.T. and P.T.N. Pham. (1999) Artificial intelligence in engineering. International Journal of Machine Tools & Manufacture, 39, 937-949. [60] Tandon, N. and A. Choudhury. (1999) A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribology International, 32(8), 469-480. [61] Gao, X.Z. and S.J. Ovaska. (2001) Soft computing methods in motor fault diagnosis. Applied Soft Computing, 1(1), 73-81. [62] Chow, M.-Y. (2000) Guest editorial special section on motor fault detection and diagnosis. Industrial Electronics, IEEE Transactions on, 47(5), 982-983. [63] Nicola Orani," HIGHER-ORDER SLIDING MODE TECHNIQUES FOR FAULT DIAGNOSIS",XXII Cycle March 2010. [64]. Steve Goldman, “Vibration Spectrum Analysis – A Practical Approach”, Second Edition, Industrial Press Inc. [65]. Keith Mobley, “Vibration Fundamentals”, Newnes. [66] Thompson, W.T., “Theory of Vibration with Applications”, Prentice Hall, New Jersey, 1972. [67]. Madhujit Mukhopadhyay, “Vibrations, Dynamics and Structural Systems”, Oxford & IBH Publishing Company Pvt. Ltd., New Delhi, 2000. [68]. Alan V.Oppenheim & Ronald W.Schafer, “Discrete-Time Signal Processing”, Pearson Education Signal Processing Series, 2002. [69] Hocine Bendjama, Salah Bouhouche, and Mohamed Seghir Boucherit," Application of Wavelet Transform for Fault Diagnosis in Rotating Machinery", International Journal of Machine Learning and Computing, Vol. 2, No. 1, February 2012. [70] Siva Shankar Rudraraju,'' Vibration analysis based machine unbalance fault detection and correction.” INDIAN SCHOOL OF MINES DHANBAD, INDIA January-May 2005 [71] A.A Ibrahim , S.M.Abdel-Rahman,M.Z.Zahran,H.H.ELMongey,'' An Investagation for Machinery Fault Diagnosis Using Adaptive Wavelet'', [72] Bognatz, S. R., 1995, “Alignment of Critical and Non Critical Machines,” Orbit, pp. 23 25. [73] Mohsen Nakhaeinejad ,Suri Ganeriwala,'' OBSERVATIONS ON DYNAMIC RESPONSES OF MISALIGNMENTS', Observations on Dynamic Response of Misalignments Tech Note, SpectraQuest Inc. (Sep. 2009) ' [74] M. Amarnath, R. Shrinidhi, A. Ramachandra, and S. B. Kandagal,“Prediction of defects in antifriction bearings using vibration signal analysis,” Journal of the Institution of Engineers India Part MC Mechanical Engineering Division, vol. 85, no. 2, pp. 88–92, 2004. [75], SKF 2008, Chapter 5 – ISO Classification [76] N. Bachschmid, P. Pennacchi, P., E. Tanzi, A. Vania, Identification of transverse crack position and depth in rotor systems, Meccanica, Vol. 35 (2000), pp. 563-582. [77] R. Markert, R. Platz, M. Seidler, Model based fault identification in rotor systems by least squares fitting, International Journal of Rotating Machinery, Vol. 7, No. 5 (2001), pp. 311-321. [78] A.D. Dimarogonas, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics, Vol. 55 (1996), pp. 831–857. [79] W. Ostachowicz, M. Krawczuk, On modeling of structural stiffness loss due to damage, Proceedings of DAMAS, Cardiff, UK (2001), pp. 185–199. [80] M.I. Friswell, J.E.T. Penny, Crack modelling for structural health monitoring, Structural Health Monitoring: An International Journal, Vol. 1 (2002), pp. 139-148. [81],Jerzy T. Sawiciki , Michael I. Friswell, ,Zbingniew Kulesza, Adam Wroblewski , John D. Lekki, Detecting cracked rotors using 1585 www.ijaegt.com ISSN No: 2309-4893 International Journal of Advanced Engineering and Global Technology I Vol-04, Issue-01, January 2016 auxiliary harmonic excitation, Journal Of Sound and Vibration 2011] [82] A Barkov, N Barkova and A Azovtsev Peculiarities of SlowRotating ElementBearingsConditionDiagnostics.. [83] Wilfried Reimche, Ulrich Südmersen, Oliver Pietsch, Christian Scheer, Fiedrich-Wilhelm Bach,'' BASICS OF VIBRATION MONITORING FOR FAULT DETECTION AND PROCESS CONTROL'',2003 [84] P D McFadden 1987 Mechanical Systems and Signal Processing 1 (2), p 173-183, Examination of a Technique for the Early Detection of Failure in Gears by Signal Processing of the Time Domain Average of the Meshing Vibration. [85]"FAULT DENTIFICATION AND MONITORING", Indian institute of technology delhi [86] A Barkov and N Barkova Condition Assessmentand Life Prediction of RollingElement Bearings – Part 1. [87] K. Shibata, A. Takahashi, T. Shirai, “Fault diagnosis of rotating machinery through visualisation of sound signal,” Journal of Mechanical Systems and Signal Processing, vol. 14, pp. 229241, 2000. [88] S. Seker, E. Ayaz, “A study on condition monitoring for induction motors under the accelerated aging processes,” IEEE Power Engineering, vol. 22, no. 7, pp. 35-37, 2002. [89] J. C. Cexus, “Analyse des signaux non-stationnaires par Transformation de Huang, Opérateur de Teager-Kaiser, et Transformation de Huang-Teager (THT),” Thèse de Doctorat, Université de Rennes-France, 2005. [90] J. D. Wu, C.-H. Liu, “Investigation of engine fault diagnosis using discrete wavelet transform and neural network,” Expert Systems with Applications, vol. 35, pp. 1200-1213, 2008, [91] M. Sifuzzaman1, M.R. Islam1 and M.Z. Ali, Application of Wavelet Transform and its Advantages Compared to Fourier Transform, Journal of Physical Sciences, Vol. 13, 2009, 121-134 [92],Hocine Bendjama, Salah Bouhouche, and Mohamed Seghir Boucherit,2012] 1586 [93] S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans Pattern Anal Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989 [94] ,N.Lu,F. Wang, F. Gao,2003] [95] preview of wavelets , wavelet filters, and wavelets transform space and signal's technology,2009] [96] Carlo Rainieri and Giovanni Fabbrocino,'' Operational modal analysis for the characterization of heritage structures'', GEOFIZIKA VOL. 28 2011 [97] Mehdi Batel, Brüel & Kjær, Norcross, Georgia, ''Operational Modal Analysis –Another Way of Doing Modal Testing'', SOUND AND VIBRATION/AUGUST 2002 [98] Peter van Overschee and Bart De Moor: Subspace Identification for Linear Systems. Kluwer Academic Publishers, 1996 [99] Rune Brincker, Palle Andersen,'' Understanding Stochastic Subspace Identification'', [100] Shie Qian," Application of Gabor expansion for Order Analysis'', [101] K. S. Wang and P. S. Heyns," The combined use of order tracking techniques for enhanced Fourier analysis of order components" [102] A. RIVOLA," CRACK DETECTION BY BISPECTRAL ANALYSIS [103]. Brincker R, Zhang LM, Andersen P. Modal identification of output-only systems using frequency domain decomposition. Smart Materials and Structures 2000; 10:441–445. [104] Bendat, Julius S. and Allan G. Piersol: “Random Data, Analysis and Measurement Procedures”, John Wiley and Sons, 1986 [105] Brincker, R. and Andersen, P.: “ARMA (Auto Regressive Moving Average) Models in Modal Space”, Proc. Of the 17th International Modal Analysis Conference, Kissimmee, Florida, 1999 [106] N-J. Jacobsen, P. Andersen, R. Brincker '' Using Enhanced Frequency Domain Decomposition as a Robust Technique to Harmonic Excitation in Operational Modal Analysis''2006 www.ijaegt.com