A noise-resistant Wigner-Vile spectrum analysis method based on cyclostationarity and its application in fault diagnosis of rotating

Rolling element bearing and gear are the most common used rotating parts in rotating machinery and they are also the fragile mechanical part. Studying the effective method of timely diagnosis of them is very necessary. The Wigner-Vile spectrum (WVS) is an effective time-frequency analysis and common used method for diagnosis of rotating machinery. However, it would not work effectively when the impulsion characteristic fault signal of rotating machinery is buried by strong background noise. To solve the above problem, the property of cyclostationarity of the rotating machinery signal is used, and the cyclic spectral density basing on second order cyclostationarity statistic is combined with the WVS, and the cyclic spectral density Wigner Vile spectrum (CSDWVS) time-frequency method is proposed in the paper. Through the analysis results of simulation and experiment, the CSDWVS method has the advantages of much more noise-resistant than traditional WVS method, and it could extract the fault feature of the vibration signal of rotating machinery buried in strong background noise. Besides, it also has better time frequency aggregation effect

Fault detection and diagnosis of a multistage helical gearbox using magnitude and phase information from vibration signals

Vibration generated by a gearbox carries a great deal of information regarding its health condition. This research aims primarily on the detection and diagnosis of tooth defects in a multistage gearbox based on advanced vibration analysis. Time synchronised averaging (TSA) analysis is effective at removing noise but it is inefficient in implementation and in diagnosing different types of faults such as bearing defects other than gears. Conventional bispectrum (CB) can eliminate Gaussian noise while it preserves the signal’s phase information, however its overpopulated contents can still provide inaccurate information regarding to different types of gear faults. Recently developed modulation signal bispectrum (MSB) has the high potential to lead to the high accuracy of diagnostics of gearboxes as it more effectively characterises modulation signals such as gearbox vibrations. Therefore, the research takes MSB as the fundamental tool for analysing gearbox vibration signals and developing accurate diagnostic techniques. Firstly, it has realised that conventional techniques often ignore the effect of phase information in gearbox diagnostics. This thesis then focuses on developing CB and MSB based techniques for detecting and diagnosing of gearbox faults. Secondly, it has found that vibration responses from a multiple stage gearbox have high interferences between amplitude modulation (AM) and phase modulation (PM) which can be formalised from both gear faults and inherent manufacturing errors. However, the faults can induce wider bandwidth vibrations. Correspondingly, optimal component based schemes are also developed based on the use of MSB coherence results. Then the proposed MSB method allows an effective gearbox diagnosis using the signals in a narrower frequency band that is below twice the rotational frequency plus the highest meshing frequency amongst different gear transmission stages, being more suitable for wireless network condition monitoring systems. It has also found that the signals at resonance frequencies has a higher signal-to-noise ratio and more effective for obtaining accurate diagnosis. Also software encoder based TSA was found to be not robust and accurate due to the influences of noise and referencing components on obtaining a reliable phase signal for implementing TSA. Finally, the diagnostics carried out upon different fault cases using both CB and MSB have verified the proposed approaches can provide accurate diagnostic results, and with the new MSB based detector and estimator being more effective in differentiating between diffident fault locations for two local and one non-uniformly distributed tooth damages in a two stage helical gearbox

Discerning non-autonomous dynamics

Structure and function go hand in hand. However, while a complex structure can be relatively safely broken down into the minutest parts, and technology is now delving into nanoscales, the function of complex systems requires a completely different approach. Here the complexity clearly arises from nonlinear interactions, which prevents us from obtaining a realistic description of a system by dissecting it into its structural component parts. At best, the result of such investigations does not substantially add to our understanding or at worst it can even be misleading. Not surprisingly, the dynamics of complex systems, facilitated by increasing computational efficiency, is now readily tackled in the case of measured time series. Moreover, time series can now be collected in practically every branch of science and in any structural scale—from protein dynamics in a living cell to data collected in astrophysics or even via social networks. In searching for deterministic patterns in such data we are limited by the fact that no complex system in the real world is autonomous. Hence, as an alternative to the stochastic approach that is predominantly applied to data from inherently non-autonomous complex systems, theory and methods specifically tailored to non-autonomous systems are needed. Indeed, in the last decade we have faced a huge advance in mathematical methods, including the introduction of pullback attractors, as well as time series methods that cope with the most important characteristic of non-autonomous systems—their time-dependent behaviour. Here we review current methods for the analysis of non-autonomous dynamics including those for extracting properties of interactions and the direction of couplings. We illustrate each method by applying it to three sets of systems typical for chaotic, stochastic and non-autonomous behaviour. For the chaotic class we select the Lorenz system, for the stochastic the noiseforced Duffing system and for the non-autonomous the Poincaré oscillator with quasiperiodic forcing. In this way we not only discuss and review each method, but also present properties which help to clearly distinguish the three classes of systems when analysed in an inverse approach—from measured, or numerically generated data. In particular, this review provides a framework to tackle inverse problems in these areas and clearly distinguish non-autonomous dynamics from chaos or stochasticity

"Analysis of dynamic responses and instabilities in rotating machinery\u201d

The first task of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., micro Gas Turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed, and the performance of its bearings were investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial Rotor Kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for ThermoElasto-HydroDynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this work, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RK, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results. The second main task of the present work is the development and the implementation of a suitable analytical model to correctly capture rolling bearing radial stiffness, particularly nearby the critical speeds of the investigated rotor-bearings system. In this work, such bearing non-linear stiffness lumped parameter model is firstly validated on the commercial RK and then it is applied to both air bladeless turbines (or Tesla turbines) and to an innovative microturbine, in order to assess their global rotodynamic behavior when they are mounted on ball bearings. In order to properly investigate all the issues related to critical speeds and stiffness, an adequate number of experimental tests was performed by exploiting an experimental air Tesla turbine prototype located at TPG experimental facility of the University of Genoa. The correlation between measured flexural critical speeds and their numerical predictions is markedly conditioned by the correct identification of ball bearings dynamic characteristics; in particular, bearings stiffness effect may play a significant role in terms of rotor-bearings system natural frequencies and therefore it must be properly assessed. Indeed, Tesla turbine rotor FE model previously employed for numerical modal analysis relies on rigid bearings assumption and therefore it does not account for bearings stiffness overall contribution, which may become crucial in case of \u201chard mounting\u201d of rotor-bearings systems. Subsequently, high-speed air Tesla rotor is investigated by means of an enhanced FE model for numerical modal analysis within Ansys\uae environment, where ball bearings are modelled as non-linear springs whose stiffness is expressed according to the analytic model implemented in Matlab\uae. Two different numerical FE models are devised for microturbine rotor modelling which respectively rely on beam elements and on three-dimensional solid elements for mechanical system spatial discretization. The obtained results in terms of rotor-bearings system modal analysis exhibit an improvement in experimental-numerical results correlation by relying on such ball bearing stiffness model; moreover, beam-based FE model critical speeds predictions are coherent with experimental evidence and with respect to solid elements model it is characterized by lower computational time and it is more easily interpretable. Thus, such experimentally validated numerical model represents a reliable and easily adaptable tool for highspeed rotating machinery critical speeds prediction in practical industrial application cases. Finally In this work, several signal processing techniques performed on vibro-acoustic signals acquired from a T100 Turbec microturbine (which is furnished with a centrifugal compressor) are illustrated. Research activity goal focuses on the investigation different kinds of system response starting from non-intrusive probes signals like accelerometers and microphones; this is made by means of techniques such as HOSA and Wavelet Transform, developed in Matlab\uae environment, for early detection of the onset of unstable phenomena in centrifugal compressors. These new and different methods have been applied to the same set of data to get sufficiently independent information useful to synergistically improve knowledge in the diagnostic system. Data were acquired by means of an experimental facility based on a T100 turbine developed by the Thermochemical Power Group (TPG) at the University of Genoa. Sampling rate and sensor placement were carefully taken into account, basing both on the physical phenomena to be observed and on the sensor dynamic characteristics. In this context, it is meant to study microphones and accelerometers signals not from an isolated centrifugal turbomachine installed in a dedicated line, but from a whole compressor placed in a mGT system for energy generation. Indeed, the investigated machine is not operating in standalone mode, but its working point and angular velocity depend on the coupling with several elements. In particular, compressor working point and then its vibro-acoustic signals are expected to convey vibration and sound contributions coming from all the plant components; thus, they are more representative of machine realistic behavior in the energy system

Detection of Spatial and Temporal Interactions in Renal Autoregulation Dynamics

Renal autoregulation stabilizes renal blood flow to protect the glomerular capillaries and maintain glomerular filtration rates through two mechanisms: tubuloglomerular feedback (TGF) and the myogenic response (MR). It is considered that the feedback mechanisms operate independently in each nephron (the functional unit of the kidney) within a kidney, but renal autoregulation dynamics can be coupled between vascular connected nephrons. It has also been shown that the mechanisms are time-varying and interact with each other. Understanding of the significance of such complex behavior has been limited by absence of techniques capable of monitoring renal flow signals among more than 2 or 3 nephrons simultaneously. The purpose of this thesis was to develop approaches to allow the identification and characterization of spatial and temporal properties of renal autoregulation dynamics. We present evidence that laser speckle perfusion imaging (LSPI) effectively captures renal autoregulation dynamics in perfusion signals across the renal cortex of anaesthetized rats and that spatial heterogeneity of the dynamics is present and can be investigated using LSPI. Next, we present a novel approach to segment LSPI of the renal surface into phase synchronized clusters representing areas with coupled renal autoregulation dynamics. Results are shown for the MR and demonstrate that when a signal is present phase synchronized regions can be identified. We then describe an approach to identify quadratic phase coupling between the TGF and MR mechanisms in time and space. Using this approach we can identify locations across the renal surface where both mechanisms are operating cooperatively. Finally, we show how synchronization between nephrons can be investigated in relation to renal autoregulation effectiveness by comparing phase synchronization estimates from LSPI with renal autoregulation system properties estimated from renal blood flow and blood pressure measurements. Overall, we have developed approaches to 1) capture renal autoregulation dynamics across the renal surface, 2) identify regions with phase synchronized renal autoregulation dynamics, 3) quantify the presence of the TGF-MR interaction across the renal surface, and 4) determine how the above vary over time. The described tools allow for investigations of the significance and mechanisms behind the complex spatial interactions and time-varying properties of renal autoregulation dynamics

Specialized data analysis of SSME and advanced propulsion system vibration measurements

The basic objectives of this contract were to perform detailed analysis and evaluation of dynamic data obtained during Space Shuttle Main Engine (SSME) test and flight operations, including analytical/statistical assessment of component dynamic performance, and to continue the development and implementation of analytical/statistical models to effectively define nominal component dynamic characteristics, detect anomalous behavior, and assess machinery operational conditions. This study was to provide timely assessment of engine component operational status, identify probable causes of malfunction, and define feasible engineering solutions. The work was performed under three broad tasks: (1) Analysis, Evaluation, and Documentation of SSME Dynamic Test Results; (2) Data Base and Analytical Model Development and Application; and (3) Development and Application of Vibration Signature Analysis Techniques

Enhanced information extraction from noisy vibration data for machinery fault detection and diagnosis

As key mechanical components, bearings and gearboxes are employed in most machines. To maintain efficient and safe operations in modern industries, their condition monitoring has received massive attention in recent years. This thesis focuses on the improvement of signal processing approaches to enhance the performance of vibration based monitoring techniques taking into account various data mechanisms and their associated periodic, impulsive, modulating, nonlinear coupling characteristics along with noise contamination. Through in-depth modelling, extensive simulations and experimental verifications upon different and combined faults that often occur in the bearings and gears of representative industrial gearbox systems, the thesis has made following main conclusions in acquiring accurate diagnostic information based on improved signal processing techniques: 1) Among a wide range of advanced approaches investigated, such as adaptive line enhancer (ALE), wavelet transforms, time synchronous averaging (TSA), Kurtogram analysis, and bispectrum representations, the modulation signal bispectrum based sideband estimator (MSB-SE) is regarded as the most powerful tool to enhance the periodic fault signatures as it has the unique property of simultaneous demodulation and noise reduction along with ease of implementation. 2) The proposed MSB-SE based robust detector can achieve optimal band selection and envelope spectrum analysis simultaneously and show more reliable results for bearing fault detection and diagnosis, compared with the popular Kurtogram analysis which highlights too much on localised impulses. 3) The proposed residual sideband analysis yields accurate and consistent diagnostic results of planetary gearboxes across wide operating conditions. This is because that the residual sidebands are much less influenced by inherent gear errors and can be enhanced by MSB analysis. 4) Combined faults in bearings and gears can be detected and separated by MSB analysis. To make the results more reliable, multiple slices of MSB-SE can be averaged to minimise redundant interferences and improve the diagnostic performance

Application of Higher-Order Statistics and Subspace-Based Techniques to the Analysis and Diagnosis of Electrocardiogram Signals

The first and main contribution of this research work is the higher-order statistics (HOS)-based non-linear analysis and subsequent diagnosis of abnormal electrocardiogram (ECG) signals, particularly myocardial ischaemia. In the time domain; the second-, third-, and the fourth-order cumulants have been used in the analysis. In the frequency domain; up to the tenth-order polyspectra have been exploited. This HOS-based analysis of normal and ischaemic electrocardiogram signals has led to the identification of certain key discriminant features for the two physiological states of the heart. These features are then fed to different backpropagation-based multiple layer perceptrons for classification. The second contribution is a proposed new methodology to discriminate patients with angina pectoris or with old myocardial infarction (MI) during the first 60 seconds of stress test (or in some cases using rest ECG). It is based on the pseudo-spectral Multiple Signal Classification (MUSIC) and has the potential of being highly sensitive diagnostic signal processing tool. The third contribution is the development of a novel higher-order statistics, high-resolution estimator for quadratically coupled frequencies based on subspace spectral estimation. Extensive studies of cumulants, bispectra and bicoherence-squared of normal and ischaemic ECG signals collected from MIT and ST-T European databases has enabled us to see key discriminant features in both the third- and fourth-order cumulant domains. In the frequency domain, the polyspectral study has been extended to the lOth-order poly spectra. By calculating one-dimensional polyspectrum slices using an algorithm developed by Zhou and Giannakis (1995) a considerable reduction in the CPU time has been achieved. Furthermore, Zhou’s algorithm has been further extended to estimate the polycoherency slices which are used to characterise non-linearities in normal and ischaemic ECG signals. An important finding in this thesis is the decrease of the order of non-linearity representing the electrocardiogram signals of ischaemic patients. This thesis also includes the results of a pilot study involving eighteen healthy subjects (MIT database) and confirmed that the ECG signal is non-Gaussian, cyclostationary and quasi periodic. Combined spectral and bispectral analysis of the signal revealed that there are unique harmonic characteristics for the P-wave, QRS complex and T-wave and other frequencies due to harmonic interactions. In this work three linear and one non-linear adaptive filtering/predictions techniques have been applied to noisy ECG signals and their respective performances appraised. It is shown that the Kalman filter gives the best mean-square error MSE error but its comparatively long execution time and problems arising from ill-conditioning of the state-error covariance matrix render it of limited use in ECG applications. It is also shown that the LMS-based quadratic and cubic Volterra filters are the most superior for the ECG signal prediction. For ECG classifications; three multi-layer perceptrons employing back-propagation and modified back-propagation algorithms, and using two sets from the higher-order most discriminant features as their inputs, have yielded fairly high classification rates

The Optimization of Vibration Data Analysis for the Detection and Diagnosis of Incipient Faults in Roller Bearings

The rolling element bearing is a key component of many machines. Accurate and timely diagnosis of its faults is critical for proactive predictive maintenance. The research described in this thesis focuses on the development of techniques for detecting and diagnosing incipient bearing faults. These techniques are based on improved dynamic models and enhanced signal processing algorithms. Various common fault detection techniques for rolling element bearings are reviewed in this work and a detailed experimental investigation is described for several selected methods. Envelope analysis is widely used to obtain the bearing defect harmonics from the spectrum of the envelope of a vibration signal. This enables the detection and diagnosis of faults, and has shown good results in identifying incipient faults occurring on the different parts of a bearing. However, a critical step in implementing envelope analysis is to determine the frequency band that contains the signal component corresponding to the bearing fault (the one with highest signal to noise ratio). The choice of filter band is conventionally made via manual inspection of the spectrum to identify the resonant frequency where the largest change has occurred. In this work, a spectral kurtosis (SK) method is enhanced to enable determination of the optimum envelope analysis parameters, including the filter band and centre frequency, through a short time Fourier transform (STFT). The results show that the maximum amplitude of the kurtogram indicates the optimal parameters of band pass filter that allows both outer race and inner race faults to be determined from the optimised envelope spectrum. A performance evaluation is carried out on the kurtogram and the fast kurtogram, based on a simulated impact signal masked by different noise levels. This shows that as the signal to noise ratio (SNR) reaches as low as -5dB the STFT-based kurtogram is more effective at identifying periodic components due to bearing faults, and is less influenced by irregular noise pulses than the wavelet based fast kurtogram. A study of the accuracy of rolling-bearing diagnostic features in detecting bearing wear processes and monitoring fault sizes is presented for a range of radial clearances. Subsequently, a nonlinear dynamic model of a deep groove ball bearing with five degrees of freedom is developed. The model incorporates local defects and clearance increments in order to gain the insight into the bearing dynamics. Simulation results indicate that the vibrations at fault characteristic frequencies exhibit significant variability for increasing clearances. An increased vibration level is detected at the bearing characteristic frequency for an outer race fault, whereas a decreased vibration level is found for an inner race fault. Outcomes of laboratory experiments on several bearing clearance grades, with different local defects, are used herein for model validation purposes. The experimental validation indicates that the envelope spectrum is not accurate enough to quantify the rolling element bearing fault severity adequately. To improve the results, a new method has been developed by combining a conventional bispectrum (CB) and modulation signal bispectrum (MSB) with envelope analysis. This suppresses the inevitable noise in the envelope signal, and hence provides more accurate diagnostic features. Both the simulation and the experimental results show that MSB extracts small changes from a faulty bearing more reliably, enabling more accurate and reliable fault severity diagnosis. Moreover, the vibration amplitudes at the fault characteristic frequencies exhibit significant changes with increasing clearance. However, the vibration amplitude tends to increase with the severity of an outer race fault and decrease with the severity of an inner race fault. It is therefore necessary to take these effects into account when diagnosing the size of a defect