Robert B. Randall

Spectral kurtosis optimization for rolling element bearings

Spectral kurtosis (SK) represents a valuable tool for extracting transients buried in noise, which makes it very powerful for the diagnostics of rolling element bearings. However, SK requires the selection of a time-frequency frame for decomposition, so that the kurtosis of each frequency slot can be estimated over time. This paper proposes a technique to optimise SK for diagnostics of rolling element bearings. This technique involves two steps. First, the power spectral density of the signal is prewhitened using an autoregressive model. Second, the prewhitened signal (consisting of noise and transients) is decomposed using complex Morlet wavelets. The complex Morlet wavelet is used as a filter bank with constant proportional bandwidth (uniform resolution on a logarithmic frequency scale). Different banks are used to select the best filter for the envelope analysis - in terms of centre frequency and bandwidth - as the one that maximizes the SK.

Applications of Spectral Kurtosis in Machine Diagnostics and Prognostics

Many machine faults, such as local defects in bearings and gears, manifest themselves in vibration signals as a series of impulsive events. Kurtosis is a measure of the impulsiveness of a signal, and spectral kurtosis (SK) gives an indication of how the kurtosis (of a bandpass filtered signal) varies with frequency. This not only gives an indication of the frequency bands to be processed, but can also be used to generate a filter to extract the most impulsive part of a signal. The first step in calculating SK is to perform a time/frequency decomposition of the signal, and then calculate the kurtosis for each frequency line. The paper compares the original STFT (short time Fourier transform) with wavelet analysis for the time/frequency decomposition, and for determining the optimum combination of centre frequency and bandwidth for maximizing the SK. The paper also describes how the SK can be enhanced by “prewhitening” the signal using an autoregressive (AR) model, this sometimes revealing an incipient fault at a much earlier stage.

Damage identification based on response-only measurements using cepstrum analysis and artificial neural networks

This article presents a response-only structural health monitoring technique that utilises cepstrum analysis and artificial neural networks for the identification of damage in civil engineering structures. The method begins by applying cepstrum-based operational modal analysis, which separates source and transmission path effects to determine the structure’s frequency response functions from response measurements only. Principal component analysis is applied to the obtained frequency response functions to reduce the data size, and structural damage is then detected using a two-stage ensemble of artificial neural networks. The proposed method is verified both experimentally and numerically using a laboratory two-storey framed structure and a finite element representation, both subjected to a single excitation. The laboratory structure is tested on a large-scale shake table generating ambient loading of Gaussian distribution. In the numerical investigation, the same input is applied to the finite model, but the obtained responses are polluted with different levels of white Gaussian noise to better replicate real-life conditions. The damage is simulated in the experimental and numerical investigations by changing the condition of individual joint elements from fixed to pinned. In total, four single joint changes are investigated. The results of the investigation show that the proposed method is effective in identifying joint damage in a multi-storey structure based on response-only measurements in the presence of a single input. Because the technique does not require a precise knowledge of the excitation, it has the potential for use in online structural health monitoring. Recommendations are given as to how the method could be applied to the more general multiple-input case.

Helicopter Gearbox Bearing Blind Fault Identification Using a Range of Analysis Techniques

Vibration acceleration signals were obtained from an overload test of a Bell 206 helicopter main rotor gearbox in order to complete a blind bearing fault analysis where no knowledge of the fault was made available prior to the analysis. A range of diagnostic techniques was applied. These included power spectral density comparisons, constant percentage bandwidth (CPB) spectrum analysis, SK analysis to determine the frequency bands with maximum impulsiveness and to filter the signal to maximise that impulsiveness, and envelope analysis to determine the fault frequencies. Order tracking was used to compensate for speed fluctuations, while linear prediction using autoregressive models (AR) was used to remove the regular gear meshing contribution in the signals. As a result of applying these techniques, a fault in one of the planetary bearings was identified. A match with the cage frequency and the inner race ball pass frequency indicated deterioration associated with these components. Roller fault frequencies were not directly detected, but the fact that roller faults give a modulation at cage frequency shows that their effect was still detected. SK gave a good measure of the severity of the fault when compared to the amount of metal wear debris in the oil. Details of the test, as well as application of a statistical fault detection technique can be found in a companion paper submitted by the Defence Science and Technology Organisation (DSTO) Australia.

Modelling and diagnosis of big-end bearing knock fault in internal combustion engines

Big-end bearing knock is considered to be one of the common mechanical faults in internal combustion engines (IC engines). In this paper, a model has been built to simulate the effects of oversized clearance in the big-end bearing of an engine. In order to find a relationship between the acceleration response signal and the oversized clearance, the kinematic/kinetic and lubrication characteristics of the big ending bearing were studied. By adjusting the clearance, the impact forces with different levels of bearing knock fault can be simulated. The acceleration on the surface of the engine block was calculated by multiplying the simulated force spectrum by an experimentally measured frequency response function (FRF) in the frequency domain (and then inverse transforming to the time domain). As for experimentally measured vibration signals from bearing knock faults, the signal processing approach used involved calculating the squared envelopes of the simulated acceleration signals. The comparison to the experimental results demonstrated that the simulation model can correctly simulate vibration signals with different stages of bearing knock faults.

Gearbox bearing fault simulation using a finite element model reduction technique

The dynamics of a mechanical system such as a gearbox assembly comprising shafts, gears and bearings can be simulated using Lumped Parameter Models (LPMs). Finite Element Method (FEM) reduction techniques based on the Craig-Bampton method of Component Mode Synthesis (CMS) are useful in creating more accurate dynamic models. These models, despite having more degrees-of-freedom for the individual components than the LPM, make very much larger FE models computationally tractable. In this paper both these approaches, namely LPM and reduced FEM, are compared to create a dynamic model of a gearbox. Earlier simulation models (both LPM and combined LPM and reduced FEM) are further improved to better match the geometry of the bearing faults used in the experimental measurements, and the experimental results from a gearbox test rig. The dynamic model is used to simulate the vibration signals in the presence of localised inner and outer race faults. The new results show better correspondence with the measured signals, in particular with respect to the detailed response to entry and exit from the fault, which can be used to determine fault size. The paper highlights the plausibility of fault simulation in Machine Condition Monitoring (MCM) where a large amount of data can be gathered without experiencing large numbers of actual failures or carrying out costly and time consuming experiments until failure with seeded faults. The simulation data can be used to train neural networks to automate the diagnostic and prognostic processes.

Signal Processing Tools for Tracking the Size of a Spall in a Rolling Element Bearing

There is considerable interest in diagnostics and prognostics of operating machines based on vibration analysis and signal processing, because the major economic benefit from condition-based monitoring comes from being able to predict with reasonable certainty the likely lead time before breakdown. In the case of rolling element bearings, a number of powerful techniques have been developed in recent years to separate the rather weak signals coming from faulty bearings from strong background vibrations, and to diagnose the type of fault. The MED (minimum entropy deconvolution) technique was initially applied to bearings to reduce the overlap of adjacent impulse responses in high speed bearings and thus allow their diagnosis by envelope analysis. It was then suspected that the technique also might have the potential to separate the impulses from entry into, and exit from an individual fault, and thus give information on the fault size. This paper gives the results of an initial study into the application of MED, and other techniques, to obtain the best measure of the length of a developing spall, to use in prognostic algorithms to estimate safe remaining life, based on current size and rate of evolution with time. It was found that the response to the entry and exit events was markedly different, so considerable pre-processing was required before the MED could be applied. The paper also discusses a number of methods to reduce noise and obtain an averaged estimate of the spall length.

Use of the cepstrum to remove selected discrete frequency components from a time signal

In machine diagnostics there are a number of tools for separating discrete frequency components from random and cyclostationary components. This is the basis of separating gear (deterministic) from bearing (second order cyclostationary) signals for example. Time synchronous averaging (TSA) requires a separate operation, including resampling, to be carried out for each periodic frequency, and the method cannot be used for discrete frequency sidebands, or partial bandwidth spectra. Self adaptive noise cancellation (SANC) and discrete/random separation (DRS) remove all discrete frequencies, whether harmonics or sidebands, and it is not possible to decide if some should be left. The method proposed here uses the cepstrum to localise discrete frequency components, which manifest themselves as harmonic or sideband families. Selected families can be removed in the cepstrum, leaving any it might be desirable to retain, and generating a notch filter that is flexible enough to allow for small speed fluctuations, or even narrow band noise peaks that sometimes result from slight random modulation of periodic signals. Normally, to edit the cepstrum and return to the time domain, it is necessary to use the complex cepstrum, but the latter requires the phase signal to be unwrapped. This is not possible for response signals containing discrete frequencies and noise, where the phase is not continuous. The procedure proposed here uses the real cepstrum to localise and edit the log amplitude of the original signal, removing the unwanted discrete frequency components, and then combines the edited amplitude with the original phase spectrum to return to the time domain. The paper shows how this technique can be used to remove discrete frequency components from signals measured on two machines with a faulty bearing, and then perform envelope analysis on the residual signal to diagnose the bearing fault. One is a gear test rig for which the discrete frequencies are harmonics of the shaft speed and gearmesh frequency, and the other a bladed disc test rig for which the discrete frequencies are harmonics of the shaft speed and bladepass frequency. Envelope analysis can be done on both full bandwidth and partial (zoom) bandwidth signals, the latter to save on computation, and restrict the amount of discrete frequency components to be removed, since the signal envelope is independent of frequency shifts.

Artificial Neural Network Based Fault Diagnosis of IC Engines

Fault diagnosis is important to avoid unforeseen failures of IC engines, but normally requires an expert to interpret analysis results. Artificial Neural Networks are potential tools for the automated fault diagnosis of IC engines, as they can learn the patterns corresponding to various faults. Most engine faults can be classified into two categories: combustion faults and mechanical faults. Misfire is a typical combustion fault; piston slap and big end bearing knock are common mechanical faults. The automated diagnostic system proposed in this paper has three main stages, each stage including three neural networks. The first stage is the fault detection stage, where the neural networks detect whether there are faults in the engine and if so which kind. In the second stage, based on the detection results, the severity of the faults was identified. In the third stage, the neural networks localize which cylinder has a fault. The critical thing for a neural network is its input feature vector, and a previous study had indicated a number of features that should differentiate between the different faults and their location, based on advanced signal processing of the vibration signals measured for different normal and fault conditions. In this study, an advanced feature selection technology was employed to select the significant features as the inputs to networks. The input vectors were separated into two groups, one for training the network, and the other for its validation. Finally it has been demonstrated that the neural network based system can automatically differentiate and diagnose a number of engine faults, including location and severity.

Automated misfire diagnosis in engines using torsional vibration and block rotation

Even though a lot of research has gone into diagnosing misfire in IC engines, most approaches use torsional vibration of the crankshaft, and only a few use the rocking motion (roll) of the engine block. Additionally, misfire diagnosis normally requires an expert to interpret the analysis results from measured vibration signals. Artificial Neural Networks (ANNs) are potential tools for the automated misfire diagnosis of IC engines, as they can learn the patterns corresponding to various faults. This paper proposes an ANN-based automated diagnostic system which combines torsional vibration and rotation of the block for more robust misfire diagnosis. A critical issue with ANN applications is the network training, and it is improbable and/or uneconomical to expect to experience a sufficient number of different faults, or generate them in seeded tests, to obtain sufficient experimental results for the network training. Therefore, new simulation models, which can simulate combustion faults in engines, were developed. The simulation models are based on the thermodynamic and mechanical principles of IC engines and therefore the proposed misfire diagnostic system can in principle be adapted for any engine. During the building process of the models, based on a particular engine, some mechanical and physical parameters, for example the inertial properties of the engine parts and parameters of engine mounts, were first measured and calculated. A series of experiments were then carried out to capture the vibration signals for both normal condition and with a range of faults. The simulation models were updated and evaluated by the experimental results. Following the signal processing of the experimental and simulation signals, the best features were selected as the inputs to ANN networks. The automated diagnostic system comprises three stages: misfire detection, misfire localization and severity identification. Multi-layer Perceptron (MLP) and Probabilistic Neural Networks were applied in the different stages. The final results have shown that the diagnostic system can efficiently diagnose different misfire conditions, including location and severity.