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Design of Discrete Wavelet by Using Transient Model for Exact Measurement of Manufacturing Faults of Tapered Roller Bearings
Abstract
This paper considers a comparison of six wavelets for bearing fault diagnosis. Five wavelets Symlet_05, Symlet_08, Daubechies_04, Daubechies_06, Daubechies_08 are typical ones which are used for fault diagnosis due to several researches. The purpose is to design a new discrete wavelet which has higher efficiency to reveal minor defects on the bearing rings. Defects derive from either manufacturing or operational problems. Detecting of tiny manufacturing defects, especially manufacturing grinding marks is quite difficult due to their special geometrical shapes, however they can cause serious problems in machines during operation. Therefore, it is an important task to diagnose these marks with the most adequate methods. The transient vibration signal model of the defect is established for signals generated by tapered roller bearing on the outer race. The wavelet creation used the sub-optimal algorithm devised by Chapa and Rao. The applicability of the matched wavelet is tested for identifying this kind of bearing failure. The new wavelet analysis and synthesis filter coefficients are determined which define the designed wavelet. To determine the efficiency of the designed wavelet and to establish comparison with the other wavelets, a test-rig was constructed with high-precision measuring sensors and devices. By using the Maximum Energy-to-Shannon Entropy criteria the efficiency of the wavelets is determined. The designed wavelet is found to be the most effective to detect the manufacturing fault compared to the others in this article. The final purpose is not only to detect the faults but to determine their sizes. By analyzing the entry points of the rollers into the defects, the de-stressing point and the exit points of the rollers from the defects the width of the grinding marks is calculated. It is proved that the new-designed wavelet obtains the most precise way for fault width measurement. Finally, the size of the failure is measured by a contact type Mahr Perthometer to compare the results to the calculated parameters and validate them. The width deviation is only 1.18 % in the case of the new-designed wavelet which is remarkable precision level for bearing fault analysis.
The paper focuses on Patch Microstrip Antennas for Radar Sensors Systems (RSS) in the Cyber-Physical Systems (CPS) environment. The CPS and subfield Internet of Things (IoT) present a diagram of existing investigation on RSS using Microstrip Patch Antenna (MPA). The subject primary concern is to draw attention to the PCB MPA opportunities and their fabrication challenges. To do these three different types of PCB antenna design characteristics are investigated.
This paper focuses on the hydrodynamic behavior of liquid pipelines in the presence of air valves. The aim of installing such valves on pipeline systems is twofold: on one hand, they release the accumulated air content and on the other hand, they allow the outer air to entrain the system when the internal pressure falls beneath ambient pressure (i.e. vacuum formation). We study the hydraulic transients in the presence of such air valve by means of experimental and numerical methods. The experiments were performed using a special test section where the pipeline close to the air valve was built from plexiglas allowing visual access. Furthermore, pressure signals were recorded at several locations of the pipeline. Numerical analysis was also performed using the commercially available CFD software (ANSYS CFX). It was revealed that the entrained air separates well from the primary liquid and the mixture behaves as two distinct phases.
The present study has used an ANN to predict shell molding performances – permeability number and transverse strength-of sand moulds employed in hot metal casting. A back propagation ANN is used. This study utilized actual experimental data in which input conditions – CaCo3%, MnO3%, Dwell time and temperature – had been varied and the corresponding resulting performances were recorded. This data was used to both train and validate the ANN with the eventual objective of identifying optimum input conditions that would deliver desirable moulding performance output – the two targeted shell molding properties. The investigation used MATLAB 7.0 while the ANN's training and validation steps empirically varied learning rate, momentum rate, the number of hidden layers and the number of hidden neurons in each layer. The trained neural network was observed to be capable of predicting the output within 10% error range of their corresponding observed values.
The rubber bumpers built into the air-spring structures of buses perform a number of critical tasks. Consequently, designing their shape requires considerable effort. This paper presents a novel solution for determining the required characteristics of axi-symmetric rubber parts, which can efficiently be used in practice. The procedure is based on the finite element method (FEM) and the support vector regression (SVR) model. A finite element code developed by the authors and based on a three-field functional is used for the rapid and appropriately accurate calculation of the characteristics of rubber bumpers. A rubber shape is evaluated via the work difference and the area between the desired and the actual load-displacement curves. The objective of shape optimization is to find the geometry where the work difference is under a specified limit. The tool of optimization is the SVR method, which provides the regression function for the work difference. The minimization process of the work-difference function leads to the optimum design parameters. The efficiency of the method is verified by numerical examples.
This paper deals with detection of local defects existing on races of deep groove ball bearing in the presence of external vibrations using envelope analysis and Duffing oscillator. Experiments have been carried out using a test rig for capturing the vibration signals of test bearing. The external vibration has been imparted to the housing of the test bearing through electromechanical shaker. In envelope analysis the centre frequency has been selected using the spectral kurtosis for the filters length of 32 and 64 for different bandwidths. Through this study, it has been revisited and confirmed that the defect detection in envelope analysis mainly depends on the selection of centre frequency and bandwidth. The spectra of selected centre frequency with several bandwidths have been studied and compared for identification of defective frequency. The system defined by the Duffing equation entered into the periodical state from the chaotic state at the critical value of disturbing periodic force in the presence of defective bearing signal. The state change has been identified using the phase plane trajectories and Lyapunov exponents of Duffing equation. It is worth to mention here that envelope spectrum reveals the information about the defect frequencies and their harmonics. However, the Duffing oscillator only confirms the presence of defect frequencies by indicating closed phase plane trajectories and negative Lyapunov exponents. Authors believe that for speedy assessment about the presence of defects on races of rolling element bearings, the use of Duffing oscillator may be preferred.
Rolling element bearing is one of the important components in rotary machines. Although a significant quantum of work has been done on bearing defect monitoring, estimation of defect size in bearing elements is still a challenge. In this paper, a technique based on decomposition using Symlet wavelet is proposed for measuring outer race defect width of taper roller bearing. Experiments were carried out on a customized test setup. Seeded defects of different size were introduced separately in the form of an axial groove on the outer race of taper roller bearings using laser engraving technique. It is not only difficult but ambiguous to detect the entry point in the groove defect by making use of the signal. The ambiguity gets reduced by using Symlet5 wavelet due to its linear phase nature which maintains sharpness in the signal even when there is a sudden change in signal. The proposed technique has been successfully implemented for measuring defect width over a range of 0.5776–1.9614 mm. The resulting measure of defect width has been also verified using image analysis. Maximum deviation in result has been found to be 4.06% for the defect width of 1.1820 mm at no load which was found further reduced to 1.02% with increase in load.
Algorithms for designing a mother wavelet ψ(x) such that it matches a signal of interest and such that the family of wavelets {2-(j2)/ψ(2-jx-k)} forms an orthonormal Riesz basis of L2(ℛ) are developed. The algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum. Many applications require wavelets that are matched to a signal of interest. Most current design techniques, however, do not design the wavelet directly. They either build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a scaling function that generates a multiresolution analysis with some desired properties. In this paper, two sets of equations are developed that allow us to design the wavelet directly from the signal of interest. Both sets impose bandlimitedness, resulting in closed form solutions. The first set derives expressions for continuous matched wavelet spectrum amplitudes. The second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum. The discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies. An interesting byproduct of this work is the result that Meyer's spectrum amplitude construction for an orthonormal bandlimited wavelet is not only sufficient but necessary. Specific examples are given which demonstrate the performance of the wavelet matching algorithms for both known orthonormal wavelets and arbitrary signals.
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox * Companion website for instructors and selected solutions and code available for students New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox Balances presentation of the mathematics with applications to signal processing.
Fault diagnosis of bearings is essential in manufacturing to increase quality. Traditionally, fault diagnosis of tapered roller element bearings is performed by signal processing methods, which handle the nonstationary behaviour of the signal. The wavelet transform is an efficient tool for analysing the vibration signal of the bearings because it can detect the sudden changes and transient impulses in the signal caused by faults in the bearing elements. In this article, manufacturing faults on the outer ring of tapered roller bearings due to the grinding process in manufacturing are investigated. Nine different real values wavelets (Symlet-2, Symlet-5, Symlet-8, db02, db06, db10, db14, Meyer, and Morlet) are compared according to the Energy-to-Shannon-Entropy ratio criteria, and which is efficient for detecting the manufacturing faults is determined. Finally, experiments are carried out on a test rig for determining the geometrical size of the manufacturing faults with all wavelets directly from the vibration signature the result of db02, Symlet-5, and Morlet wavelets are presented. When modelling the bearing structure as an under-damped second-order mass-spring-damper mechanical system, its unit impulse response function is compared to the wavelets on the basis of their Energy-to-Shannon-Entropy ratio to determine the fault size from the vibration signal. The proposed technique has been successfully implemented for measuring defect widths. The maximum deviation in result has been found to be 4.12 % for the defect width which was verified with image analysis methods using an optical microscope and contact measurement.
Application and comparison of performance of two filtering techniques, Kalman and H ∞ Filters, for bearing fault identification, under various types of noise are reported herein. Kalman and H ∞ Filters are optimal state estimators; Kalman is the minimum variance estimator while H ∞ minimizes the worst case estimation error. Existing state equations of a rotor bearing system has been taken and non-linearity along with a number of unmodelled effects is blended with the process noise. Experimental investigations have also been carried out to study the application of these filters for bearing signal de-noising.
This paper presents a novel solution for shape optimization of compressed rubber parts. The procedure is based on the finite element method (FEM). A special purpose FEM code written in FORTRAN has been developed for the analysis of nearly incompressible axi-symmetric rubber parts. Numerical stability of the code and sensitivity analysis of the FEM input parameters are investigated. The aim of the parameter optimization is to reduce the time consuming FEM computations for the optimization process. The objective of the optimization is to find the optimal shape of the investigated rubber parts with a specified load-displacement curve. A regression model is used to determine the connection between the input and output data calculated by the FEM.
This paper considers the creation of a transient vibration signal model
established for signals generated in deep grove ball bearings with pitting (spalling)
formulation on their inner race. The fault on the inner race was created artificially. The
derivation of the signal model is based on data acquisition, signal filtering and parametric
identification. A new filtering method is presented that is suitable to eliminate the effect of
amplitude modulation and noise that usually arises in the case of bearing vibration
measurements. We show that a three-parameter signal model is adequate to describe
unmodulated transient pulses. Our signal model can be used in developing new bearing
vibration analysis and condition monitoring methods.
Keywords: Condition monitoring; bearing vibration analysis; model identification
The sliding behaviour of polyamide-6 (PA6) treated by nitrogen plasma immersion ion implantation (N PIII) has not been studied yet, even if PIII is a promising technique for polymer surface modification. The effect of N PIII of PA6 on its sliding properties against low carbon structural steel S235 was studied. The surface changes were characterised by XPS, contact angle measurements and optical microscopy, while alterations in the sliding properties including friction coefficient, wear and temperature close to contact were studied by a pin-on-disc tribometer under dry and variously lubricated conditions. The N-content of the surface layer increased, while those of C and O decreased upon N PIII treatment. The contact angles decreased and the total surface energy and its polar and dispersive components increased significantly. Under dry sliding in the low Pv regime, the friction coefficient of the treated sample started from a value lower than that of the untreated version and the corresponding specific wear rate was also smaller. Under dry sliding, the increased surface energy caused increased adhesion of the treated PA6, associated with the formation of a transfer layer on the steel disc. Water lubrication was more efficient – in accordance with the increased polar component of surface energy – for the treated PA6 than found earlier for PETP. For the treated PA6, a decreased friction was observed upon run-out type lubrication test with gearbox oil, due to increased retention of oil on the treated surface characterised by an increased dispersive component of the surface free energy.
This paper introduces an automatic feature extraction algorithm for bearing fault diagnosis using correlation filtering-based matching pursuit. This algorithm is described and investigated in theory and practice on both simulated and real bearing vibration signals. First, the vibration model for rolling bearing with fault is derived. Then, the numerical simulation signal being taken as an example, the principle of matching pursuit is mathematically explained and its drawbacks are analyzed. Afterward, to enhance the similarity of model related to the bearing faulty impulses, the model shape parameters are optimized using spectrum kurtosis and smoothing index. After that, the model with optimum shape and period parameters is taken as a template to approximate the impulses in faulty bearing signal. Finally, based on maximizing correlation principle, the optimized cycle parameter being as impuls e repetition period is matched up. The proposed method has been successfully applied in actual vibration signals of rolling element bearing with different faults.
In order to overcome the shortcomings in the traditional envelope analysis in which manually specifying a resonant frequency band is required, a new approach based on the fusion of the wavelet transform and envelope spectrum is proposed for detecting and localizing defects in rolling element bearings. This approach is capable of completely extracting the characteristic frequencies related to the defect from the resonant frequency band. Based on the Shannon entropy of wavelet-based envelope spectra, a criterion to select optimal scale to monitor the condition of bearings is also presented. Experiment results show that the proposed approach is sensitive and reliable in detecting defects on the outer race, inner race, and rollers of bearings.
Fatigue in rolling element bearings, resulting in spalling of the races and/or rolling elements, is the most common cause of bearing failure. The useful life of the bearing may extend considerably beyond the appearance of the first spall and a premature removal of the bearing from service can be very expensive, but on the other hand chances cannot be taken with safety of machines or personnel. Previous studies indicated that there might be two parts to the defect vibration signal of a spalled bearing, the first part being originating from the entry of the rolling element into the fault (de-stress) and the second part being due to the departure of the rolling element from the fault (re-stress). This is investigated in this paper using vibration signatures of seeded faults at different speeds. The acceleration signals resulting from the entry of the rolling element into the spall and exit from it were found to be of different natures. The entry into the fault can be described as a step response, with mainly low frequency content, while the impact excites a much broader frequency impulse response. The latter is the most noticeable and prominent event, especially when examining the high pass filtered response or the enveloped signal. In order to enable a clear separation of the two events, and produce an averaged estimate of the size of the fault, two approaches are proposed to enhance the entry event while keeping the impulse response. The first approach (joint treatment) utilizes pre-whitening to balance the low and high frequency energy, then octave band wavelet analysis to allow selection of the best band (or scale) to balance the two pulses with similar frequency content. In the second approach, a separate treatment is applied to the step and the impulse responses, so that they can be equally represented in the signal. Cepstrum analysis can be used to give an average estimate of the spacing between the entry and impact events, but the latter can also be assessed by an arithmetic estimation of the mean and standard deviation of the event separation for a number of realizations, in particular for the second approach. In order to determine the effects of various simulations and signal processing parameters on the estimated delay times, the entry and exit events were simulated as modified step and impulse responses with precisely known starting times. The simulation was also found useful in pointing to artefacts associated with the cepstrum calculation, which affect even the simulated signals, and have thus prompted modifications of the processing of real signals. The results presented for the two approaches give a reasonable approximation of the measured fault widths (double the spacing between the entry and impact events) under different speed conditions, but the method of separate treatment is somewhat better and is thus recommended.
To target the characteristic of roller bearing fault vibration signals, the impulse response wavelet is constructed by using continuous wavelet transform to extract the feature of fault vibration signals, based on which two methods namely scale-wavelet power spectrum comparison and auto-correlation analysis of time-wavelet power spectrum are proposed. The analysis results from roller bearing vibration signals with out-race or inner-race fault show that the two proposed methods can detect the faults of roller bearing and identify fault patterns successfully.
Rolling element bearings are the most common cause of rotating machinery failure. Over the past 20years, Acoustic Emission (AE) technology has evolved as a significant opportunity to monitor and diagnose the mechanical integrity of rolling element bearings. This paper presents results of an investigation to assess the potential of the Acoustic Emission (AE) technology for detecting and locating natural defects in rolling element bearings. To undertake this task a special purpose test-rig was built that allowed for accelerated natural degradation of a bearing race. It is concluded that sub-surface initiation and subsequent crack propagation can be detected using a range of data analysis techniques on AE’s generated from natural degrading bearings. The paper also investigates the source characterisation of AE signals associated with a defective bearing whilst in operation. This study also attempted to identify the size of a natural defect on bearings using AE technology. In conclusion, the results from this investigation show that whilst measurements on operational bearings cannot be achieved as described in this paper, the method of identifying the onset of crack propagation can be employed as a quality control tool for bearing manufacturers particularly for testing bearing material homogeneity.
Vibration signals resulting from rolling element bearing defects, present a rich content of physical information, the appropriate analysis of which can lead to the clear identification of the nature of the fault. The envelope detection or demodulation methods have been established as the dominant analysis methods for this purpose, since they can separate the useful part of the signal from its redundant contents. This paper proposes an effective demodulation method, based on the use of a complex shifted Morlet wavelet family. The method is designed in a way that can fully exploit the underlying physical concepts of the modulation mechanism, present in the vibration response of faulty bearings, using a time–frequency representation of the signal. A key element of the proposed method is the systematic introduction of selection criteria for the automated choice of the critical parameters that characterise the Morlet wavelet family used. Experimental results and industrial measurements for two different types of bearing faults confirm the validity of the overall approach.
In this paper, the Morlet wavelet is studied to apply in the envelope analysis for the bearing vibration and, in practice, would be easier to apply in the real-time vibration analyses. The parameter designation of Morlet wavelet is proposed to filter out and demodulate one of the resonance modes of a bearing vibration, but the designation of the filtering passband would not be required. Therefore, the mode vibration and its corresponding envelope could be derived from the real part and the absolute value of the wavelet transform, respectively. In addition, the Morlet wavelet with properly designating the parameters possesses a very excellent property of fast waveform convergence and could effectively reduce the computing burden. From theoretical and experimental studies, it is shown that the designation of Morlet wavelet could be effectively applied in the envelope detection for the vibration signals and could be useful in the defect diagnosis of bearing vibrations.
The application of the wavelet transform for machine fault diagnostics has been developed for last 10 years at a very rapid rate. A review on all of the literature is certainly not possible. The purpose of this review is to present a summary about the application of the wavelet in machine fault diagnostics, including the following main aspects: the time–frequency analysis of signals, the fault feature extraction, the singularity detection for signals, the denoising and extraction of the weak signals, the compression of vibration signals and the system identification. Some other applications are introduced briefly as well, such as the wavelet networks, the wavelet-based frequency response function, etc. In addition, some problems in using the wavelet for machine fault diagnostics are analysed. The prospects of the wavelet analysis in solving non-linear problems are discussed.
Bearing race faults have been detected by using discrete wavelet transform (DWT). Vibration signals from ball bearings having single and multiple point defects on inner race, outer race and the combination faults have been considered for analysis. The impulses in vibration signals due to bearing faults are prominent in wavelet decompositions. It is found that the impulses appear periodically with a time period corresponding to characteristic defect frequencies. It has been shown that DWT can be used as an effective tool for detecting single and multiple faults in the ball bearings.
Vibration monitoring of rolling element bearings is probably the most established diagnostic technique for rotating machinery. The application of acoustic emission (AE) for bearing diagnosis is gaining ground as a complementary diagnostic tool, however, limitations in the successful application of the AE technique have been partly due to the difficulty in processing, interpreting and classifying the acquired data. Furthermore, the extent of bearing damage has eluded the diagnostician. The experimental investigation reported in this paper was centred on the application of the AE technique for identifying the presence and size of a defect on a radially loaded bearing. An experimental test rig was designed such that defects of varying sizes could be seeded onto the outer race of a test bearing. Comparisons between AE and vibration analysis over a range of speed and load conditions are presented. In addition, the primary source of AE activity from seeded defects is investigated. It is concluded that AE offers earlier fault detection and improved identification capabilities than vibration analysis. Furthermore, the AE technique also provided an indication of the defect size, allowing the user to monitor the rate of degradation on the bearing; unachievable with vibration analysis.
This paper is focused on fault diagnosis of ball bearings having localized defects (spalls) on the various bearing components using wavelet-based feature extraction. The statistical features required for the training and testing of artificial intelligence techniques are calculated by the implementation of a wavelet based methodology developed using Minimum Shannon Entropy Criterion. Seven different base wavelets are considered for the study and Complex Morlet wavelet is selected based on minimum Shannon Entropy Criterion to extract statistical features from wavelet coefficients of raw vibration signals. In the methodology, firstly a wavelet theory based feature extraction methodology is developed that demonstrates the information of fault from the raw signals and then the potential of various artificial intelligence techniques to predict the type of defect in bearings is investigated. Three artificial intelligence techniques are used for faults classifications, out of which two are supervised machine learning techniques i.e. support vector machine, learning vector quantization and other one is an unsupervised machine learning technique i.e. self-organizing maps. The fault classification results show that the support vector machine identified the fault categories of rolling element bearing more accurately and has a better diagnosis performance as compared to the learning vector quantization and self-organizing maps.
Two techniques for finding the discrete orthogonal wavelet of
support less than or equal to some given integer that leads to the best
approximation to a given finite support signal up to a desired scale are
presented. The techniques are based on optimizing certain cost
functions. The first technique consists of minimizing an upper bound
that is derived on the L2 norm of error in approximating the
signal up to the desired scale. It is shown that a solution to the
problem of minimizing that bound does exist and it is explained how the
constrained minimization over the parameters that define discrete finite
support orthogonal wavelets can be turned into an unconstrained one. The
second technique is based on maximizing an approximation to the norm of
the projection of the signal on the space spanned by translates and
dilates of the analyzing discrete orthogonal wavelet up to the desired
scale. Both techniques can be implemented much faster than the
optimization of the L2 norm of either the approximation to
the given signal up to the desired scale or that of the error in that
approximation
On Finding Better Wavelet Basis for Bearing Fault Detection
- L Tóth
- T Tóth
Tóth, L., Tóth T. "On Finding Better Wavelet Basis for Bearing Fault
Detection", Acta Polytechnica Hungarica, 10(3), pp. 17-35, 2013.
https://doi.org/10.12700/APH.10.03.2013.3.3.
Nemlineáris osztályozásra vezető műszaki probléma megoldása SVC módszerrel" (Nonlinear Classification by
- A Vámosi
Vámosi, A. "Nemlineáris osztályozásra vezető műszaki probléma megoldása SVC módszerrel" (Nonlinear Classification by
SVC Method in Applied Engineering), In: Műszaki Tudomány az
Észak-Kelet Magyarországi régióban 2014 Konferencia, Szolnok,
Hungary, 2014, pp. 40-47. (in Hungarian)