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Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines
Abstract
Over the years, condition monitoring of rotating machines has been extensively applied for enhancing equipment reliability and maintenance cost-effectiveness, through the early detection and reliable diagnosis of incipient machine faults. Earlier studies suggest that bispectrum analysis is a good tool for detecting and distinguishing rotor-related faults in rotating machines, with a significantly reduced number of vibration sensors. Now, the trispectrum analysis is also applied to the measured vibration data, so as to explore the usefulness of this analysis in the diagnosis. It is observed that the trispectrum further improves the reliability of rotating machines' faults diagnosis. This article presents the results and observations related to the bispectrum and trispectrum analyses for fault(s) diagnosis, through an experimental rig with different faults simulation.
... The frequency domain signal analysis, based on Fourier transformation (FT), is one of the most conventionally applied VFD signal processing techniques in practice, since it provides the opportunity to easily identify frequency components of interest. 5 Some of the frequency domain vibration signal processing techniques used for fault diagnosis (FD) in rotating machines include power spectrum, 18 higher order spectra, [19][20][21][22][23][24] holospectrum, 25 cepstrum, 26 composite spectrum (CS) 27 and composite bispectrum (CB). 28 Despite the maturity of spectrum-based techniques, the quest for more profound understanding of the dynamic characteristics of vibrating systems has led to the application of model-based approaches 29 for rotating machines' FD. ...
... For instance, the appearance of a B 11 CB peak indicates that the pCCS frequency components f l and f m (plotted on both x and y orthogonal axes) shown in equation (7) are both equal to the machine speed (also known as 13). Therefore, the B 11 CB peak is a representation of the relation between f l (13), f m (13) and f l + f m (23). Similarly, each B 12 = B 21 CB peak indicates that the pCCS frequency components f l and f m shown in equation (7) are, respectively, equal to 13 machine speed and its second harmonic (23) or vice versa, while f l + f m is equivalent to their sum (33). ...
... Therefore, the B 11 CB peak is a representation of the relation between f l (13), f m (13) and f l + f m (23). Similarly, each B 12 = B 21 CB peak indicates that the pCCS frequency components f l and f m shown in equation (7) are, respectively, equal to 13 machine speed and its second harmonic (23) or vice versa, while f l + f m is equivalent to their sum (33). Hence, each B 12 = B 21 CB peak shows the relation Similarly, the CT plots (Figure 9) for the reference (scenarios 1 and 19) and fault (scenarios 10 and 28) scenarios are different. ...
Equipment standardisation as a cost-effective means of rationalising maintenance spares has significantly increased the existence of several identical (similar components and configurations) ‘as installed’ machines in most industrial sites. However, the dynamic behaviours of such identical machines usually differ due to variations in their foundation flexibilities, which is perhaps why separate analysis is often required for each machine during fault diagnosis. In practice, the fault diagnosis process is even further complicated by the fact that analysis is often conducted at individual measurement locations for different speeds, since a significant number of rotating machines operate at various speeds. Hence, through the experimental simulation of a similar practical scenario of two identically configured ‘as installed’ rotating machines with different foundation flexibilities, this study proposes a simplified vibration-based fault diagnosis technique that may be valuable for fault detection irrespective of foundation flexibilities or operating speeds. On both experimental rigs with different foundation flexibilities, several common rotor-related faults were independently simulated. Data combination method was then used for computing composite higher order spectra (composite bispectrum and composite trispectrum), after which principal component analysis is used for fault separation and diagnosis of the grouped data. Hence, this article highlights the usefulness of the proposed fault diagnosis approach for enhancing the reliability of identical ‘as installed’ rotating machines, irrespective of the rotating speeds and foundation flexibilities.
... This integration of multiple VCM approaches sometimes complicates the entire fault finding process. Efforts aimed at overcoming these deficiencies have led to the application of higher order spectra (HOS) [18][19][20][21][22], where both amplitude and phase information are retained. Other researchers have also attempted to standardise rotating machines fault diagnosis by incorporating artificial intelligence (AI) techniques such as artificial neural networks (ANN) [23][24][25] and support vector machines (SVM) [26][27][28]. ...
... For instance, Hameed et al. [38] provided a comprehensive review of CM techniques for wind turbines, where it was shown that accurate information on the overall condition of the rotor (a very important component of the wind energy converter) can be obtained by trending the relation between wind speed and active power output of the wind energy converter (WEC). The study [38] also showed that the use of higher order signal processing tools (bispectrum and bicoherence) [18][19][20][21][22] for detecting the presence or absence of phase coupling between the frequency components of the electrical power signal when classifying the WEC as faulty or healthy is very possible. ...
The availability of complex rotating machines is vital for the prevention of catastrophic failures in a significant number of industrial operations. Reliability engineering theories stipulate that optimising the mean-time-to-repair (MTTR) for failed machines can immensely boost availability. In practice, however, a significant amount of time is taken to accurately detect and classify rotor-related anomalies which often negate the drive to achieve a truly robust maintenance decision-making system. Earlier studies have attempted to address these limitations by classifying the poly coherent composite spectra (pCCS) features generated at different machine speeds using principal components analysis (PCA). As valuable as the observations obtained were, the PCA-based classifications applied are linear which may or may not limit their applicability to some real-life machine vibration data that are often associated with certain degrees of non-linearities due to faults. Additionally, the PCA-based faults classification approach used in earlier studies sometimes lack the capability to self-learn which implies that routine machine health classifications would be done manually. The initial parts of the current paper were presented in the form of a thorough search of the literature related to the general concept of data fusion approaches in condition monitoring (CM) of rotation machines. Based on the potentials of pCCS features, the later parts of the article are concerned with the application of the same features for the exploration of a simplified two-staged artificial neural network (ANN) classification approach that could pave the way for the automatic classification of rotating machines faults. This preliminary examination of the classification accuracies of the networks at both stages of the algorithm offered encouraging results, as well as indicates a promising potential for this enhanced approach during field-based condition monitoring of critical rotating machines.
... Two discs D1 and D2, are mounted on the long shaft Sh1 and one disc, D3, on the short shaft Sh2. The 4 bearings, B1 to B4, are mounted on the flexible pedestals P1 to P4, respectively [12]. ...
Plant availability and reliability can be improved through a robust condition monitoring and fault diagnosis model to predict the current status (healthy or faulty) of any machines and critical assets. The model can then predict the exact fault for the faulty asset so that remedial maintenance can be carried out in a planned plant outage. Nowadays, the artificial intelligence (AI)-based machine learning (ML) model seems to be current trend to meet these requirements. Hence, the paper is also proposing such vibration-based faults diagnosis ML model through an experimental rotating rig. Here, the 2-Steps approach is used with the ML model to easy the industrial operation and maintenance process. The Step-1 provides the information about the asset health status such as healthy or faulty. The Step-2 then identifies the exact nature of fault to aid the decision making for the fault rectification and maintenance activities to avoid the risk of failure and enhance the reliability.
... However, conventional amplitude spectra are often criticised for loss of phase information during the magnitude squared operation that precedes its generation of diagnostic features. This is perhaps why research efforts explored the feasibility of using approaches that possess the capabilities of retaining both amplitude and phase information, including higher order spectra (HOS) [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and higher order coherence (HOC) [8,[22][23][24][25]. While HOS and HOC components are able to retain phase and magnitude information, their predominant applications have been centred on individualised computation of features from distinct measurement locations. ...
Rotating machines are pivotal to the achievement of core operational objectives within various industries. Recent drives for developing smart systems coupled with the significant advancements in computational technologies have immensely increased the complexity of this group of critical physical industrial assets (PIAs). Vibration-based techniques have contributed significantly towards understanding the failure modes of rotating machines and their associated components. However, the very large data requirements attributable to routine vibration-based fault diagnosis at multiple measurement locations has led to the quest for alternative approaches that possess the capability to reduce faults diagnosis downtime. Initiatives aimed at rationalising vibration-based condition monitoring data in order to just retain information that offer maximum variability includes the combination of coherent composite spectrum (CCS) and principal components analysis (PCA) for rotor-related faults diagnosis. While there is no doubt about the potentials of this approach, especially that it is independent of the number of measurement locations and foundation types, its over-reliance on manual classification made it prone to human subjectivity and lack of repeatability. The current study therefore aims to further enhance existing CCS capability in two facets—(1) exploration of the possibility of automating the process by testing its compatibility with various machine learning techniques (2) incorporating spectrum energy as a novel feature. It was observed that artificial neural networks (ANN) offered the most accurate and consistent classification outcomes under all considered scenarios, which demonstrates immense opportunity for automating the process. The paper describes computational approaches, signal processing parameters and experiments used for generating the analysed vibration data.
... Among HOS, bispectrum and trispectrum, which represent Fourier transform of third-order statistics and fourth-order statistics, respectively, have found their application in analysis of vibration signals [16]. For example, References [17,18] employed a normalized bispectral measure to examine vibration signals with periodic components and noise, Reference [19] exploited trispectrum for fault diagnosis of rotating machinery, Reference [20] applied HOS to investigate amplitude and phase modulation and Reference [21] used bispectrum to explore a system response. In addition, Reference [22] demonstrated the usefulness of HOS in detecting a fatigue crack of a straight beam and in analyzing vibration signals of rolling bearings, Reference [23] displayed the potential of bispectrum and trispectrum for fault diagnosis of rotating machinery, Reference [24] made use of HOS to distinguish between cracks and misalignment in a rotating shaft and Reference [25] made a comparison between the results of HOS and higher order coherence for fault diagnosis of rotating machinery. ...
Vibration data from rotating machinery working in different conditions display different properties in spatial and temporal scales. As a result, insights into spatial- and temporal-scale structures of vibration data of rotating machinery are fundamental for describing running conditions of rotating machinery. However, common temporal statistics and typical nonlinear measures have difficulties in describing spatial and temporal scales of data. Recently, statistical linguistic analysis (SLA) has been pioneered in analyzing complex vibration data from rotating machinery. Nonetheless, SLA can examine data in spatial scales but not in temporal scales. To improve SLA, this paper develops symbolic-dynamics entropy for quantifying word-frequency series obtained by SLA. By introducing multiscale analysis to SLA, this paper proposes adaptive multiscale symbolic-dynamics entropy (AMSDE). By AMSDE, spatial and temporal properties of data can be characterized by a set of symbolic-dynamics entropy, each of which corresponds to a specific temporal scale. Afterward, AMSDE is employed to deal with vibration data from defective gears and rolling bearings. Moreover, the performance of AMSDE is benchmarked against five common temporal statistics (mean, standard deviation, root mean square, skewness and kurtosis) and three typical nonlinear measures (approximate entropy, sample entropy and permutation entropy). The results suggest that AMSDE performs better than these benchmark methods in characterizing running conditions of rotating machinery.
... Different types of nondestructive techniques are available to detect the bearing defects such as ultrasonic testing, wear analysis, thermal analysis, acoustic signal analysis and vibration signal analysis, which are patronage in designing the maintenance strategies. Acoustic and vibration signal based techniques are developing at higher pace over other techniques because of their high reactivity to incipient fault and non-invasive nature [1,2]. When bearing is installed in the complex mechanical system, the signal acquired in such cases is often clouded with the background noises caused by other machine element [3]. ...
Statistical parameters are having great significance in bearing condition monitoring where characteristic signature localization is not possible in time, frequency or time-frequency domain. In this paper, the presence of local defect is analyzed by carrying out statistical analysis on Acoustic and Vibration signal. The variation of statistical parameters for the defective bearing in comparison to healthy bearing at particular loading condition is presented for the purpose of analysis. Among all the parameters Shannon entropy (SE) is exhibiting better variations for defective bearing compared to the healthy bearing for both the signals. It has also been observed that with increase in loading only standard deviation (s ) and SE have shown downward trend. This might be because of change in characteristics of signature with loading, the main reason is still underlying. To check the sensitive parameter for loading among the responded parameters simple sensitivity index (SSI) is calculated. From the results it has been observed that SE is having better sensitivity for the loading than s because of its calculation capability in logarithmic scale.
... However, bispectrum analysis generally requires the signal to be steady-state; for unsteady or cyclostationary signals, the analysis results are not accurate enough. So many scholars had proposed some improved algorithms based on the bispectrum analysis for different research objects and specific questions, like wavelet domain bispectrum analysis [2][3][4], order bispectrum analysis [5], vector bispectrum analysis [6], cyclic bispectrum analysis [7,8], and so on [9][10][11]. In 2004, a new AM detector and its normalized form are proposed and defined [12]; Gu et al. named this method as the modulation signal bispectrum (MSB) analysis and achieved fault diagnosis of downstream mechanical equipment using electrical motor current signal based on MSB in 2011 [13]. ...
Modulation signal bispectrum (MSB) analysis is an effective method to obtain the fault frequency for rolling bearing, but harmonics make fault frequency dense and even frequency aliasing. Carrier frequency of bearing is generally determined by its structure and inherent characteristics and changes with the increase of the damage degree, so it is hard to be accurately found. To solve these problems, this paper proposes a sparse modulation signal bispectrum analysis method. Firstly the vibration signal is demodulated by MSB analysis and its bispectrum is obtained. After the frequency domain filtering, the carrier frequency is computed based on the characteristics of energy concentration at the carrier frequency on MSB. By shift-frequency MSB (SF-MSB), the carrier frequency is moved to the coordinate origin, the entire MSB is shifted for the same distance, and SF-MSB is obtained. At last, the bispectrum is shifted to the frequency zero point and diagonal slices are performed to obtain a sparse representation of MSB. Experimental results show that sparse MSB (S-MSB) method can not only eliminate the interference of harmonic frequency, but also make the extracted characteristic frequency of fault more obvious.
... Analyses of rotating machinery conducted in the last few years also took into account the variation of external forces acting on the system [14,28] and various types of defects as well [29]. The article [30] presents the research on the operational stability of the rotor which was subjected to stochastic axial loads. ...
The article presents how the system equipped with a rotor supported by slide bearings loses stability, operating under random load conditions. The computer simulations were applied for the analysis of the rotating machinery (using in-house developed codes). The MESWIR software is presented herein that can be used to assess dynamic performance of machines of this type. A special algorithm for the randomisation of loads was implemented and discussed in detail on the basis of a representative example. The rotor model was subjected to randomly-generated transverse forces during its operation. It exhibited unstable behaviour manifesting itself in the form of oil whirl or oil whip. The system operation was analysed both under constant and random load.
... Until now, studies on VFD of rotating machines have been significantly based on the premise that vibration data from all sensors are intact and available, irrespective of whether the measured vibration data will be separately analysed for individual measurement locations with known techniques such as spectrum analysis, 2-7 wavelet analysis [8][9][10][11][12][13][14][15] and higher order statistical analysis [16][17][18][19][20][21][22][23] or fused together for all measurement locations to generate a single but representative polycoherent composite spectrum (pCCS). 1 In practise, the amount of data available for faults diagnosis of some rotating machines may be limited at certain instances, due to faults/damages associated with the sensors or connecting cables during auxiliary activities in the plant such as machine cleaning and general maintenance, especially when dealing with critical industrial rotating machines that are installed in highly remote and/or restricted plant locations (e.g. river gallery pumps in water generation plants or drilling machines in mines). ...
In an earlier study, the poly-coherent composite higher order spectra (i.e. poly-coherent composite bispectrum and trispectrum) frequency domain data fusion technique was proposed to detect different rotor-related faults. All earlier vibration-based faults detection involving the application of poly-coherent composite bispectrum and trispectrum have been solely based on the notion that the measured vibration data from all measurement locations on a rotating machine are always available and intact. In reality, industrial scenarios sometimes deviate from this notion, due to faults and/or damages associated with vibration sensors or their accessories (e.g. connecting cables). Sensitivity analysis of the method to various scenarios of measured vibration data availability (i.e. complete data from all measurement locations and missing/erroneous data from certain measurement locations) is also examined through experimental and industrial cases, so as to bring out the robustness of the method.
Recently, the technique of nonlinear Lamb wave mixing has been developed for the detection of fatigue crack in engineering structures. In this technique, two or three Lamb waves with distinct frequencies are applied to a structure. The cross-mixing between these waves results in nonlinear mixed components depending on the sum and difference of the incident frequencies. However, the amplitude of the mixed components generated by the fatigue crack becomes weak in a noisy environment. Thus, noise elimination is critical for reliable crack detection. To address this gap, a novel hybrid method that incorporates a deep learning (DL) model with higher-order spectral analysis is proposed in this study. First, a nonlinear Lamb wave mixing technique is developed to capture ultrasonic data from the aluminum plates during fatigue testing. Subsequently, the DL model based on long short-term memory (LSTM) accepts an original ultrasonic time signal as input and yields an output of a reconstructed ultrasonic signal after noise reduction. Finally, the random noise in the reconstructed signal is eliminated and the mixed components are extracted by trispectrum (TS)-based higher-order spectral analysis. Furthermore, the proposed and existing methods (e.g., power spectrum) are applied to the ultrasonic data collected from fatigue experiments. The results validated the improved performance of the proposed LSTM-TS method for reliable fatigue crack detection in noisy environments.
Mechanical unbalance is a phenomenon that concerns rotating elements, including rotors in electrical machines. An unbalanced rotor generates vibration, which is transferred to the machine body. The vibration contributes to reducing drive system reliability and, as a consequence, leads to frequent downtime. Therefore, from an economic point of view, monitoring the unbalance of rotating elements is justified. In this paper, the rotor unbalance of a drive system with a permanent magnet synchronous motor (PMSM) was physically modelled using a specially developed shield, with five test masses fixed at the motor shaft. The analysed diagnostic signal was mechanical vibration. Unbalance was detected using selected signal analysis methods, such as frequency-domain methods (classical spectrum analysis FFT and a higher-order bispectrum method) and two methods applied in technical diagnostics (order analysis and orbit method). The efficiency of unbalance symptom detection using these four methods was compared for the frequency controlled PMSM. The properties of the analysed diagnostic methods were assessed and compared in terms of their usefulness in rotor unbalance diagnosis, and the basic features characterizing the usefulness of these methods were determined depending on the operating conditions of the drive. This work could have a significant impact on the process of designing diagnostic systems for PMSM drives.
Earlier studies have successfully demonstrated the use of the poly-coherent composite bispectrum (pCCB) in the faults identification in rotating machines. However, only amplitudes of the pCCB components were used in the earlier studies. Since the pCCB components are complex numbers (both amplitudes and phases). Hence, the real and imaginary features of the pCCB components are also explored in the fault identification of rotating machines in the current study. The observations from the present study through the experimental rig are presented and compared with the earlier observations using the amplitudes of the pCCB components. It shows that the real and imaginary of the pCCB components shows improvements in fault identification and classification along with a good representation of machine behavior, compared with the magnitude only of pCCB components.
It is fair to assume that the main challenge in maintenance decision-making is the existence of gaps between theory and sustainable practice which is attributable to complexity, too much emphasis on development of new models that only serve to criticize earlier ones, underrepresentation of case study-based researches and lack of adequate incorporation of industry-based knowledge into most theoretical studies. In this paper, we revisited the application of decision making grids (DMG) for maintenance optimization but the main novelty here is harmonizing the strengths of the two most popular DMG approaches as opposed to the previous trends of advocating one over the other. The current initiative limits assumptions associated with the process, since both approaches depend on the main objective and nature of data involved. The data required for implementation are breakdown frequency and downtime for each event, which is readily available within most in-house maintenance management systems.
This chapter presents signal processing in the frequency domain, which has the ability to divulge information based on frequency characteristics that are not easy to observe in the time domain. It describes Fourier analysis, including Fourier series, discrete Fourier transform, and fast Fourier transform (FFT), which are the most commonly used signal transformation techniques and allow one to transform time domain signals to the frequency domain. With the invention of FFT and digital computers, the efficient computation of the signal's power spectrum became feasible. The spectrum of the frequency components generated from the time domain waveforms makes it easier to see each source of vibration. The chapter provides an explanation of different techniques that can be used to extract various frequency spectrum features that can more efficiently represent a machine's health. These include: envelope analysis, also called high‐frequency resonance analysis or resonance demodulation; and frequency domain features.
In CI engines, injector spraying into the combustion chamber has extreme importance in fuel atomization and knocking control in the CI engines. Knocking and malfunction of engines due to faulty injectors can lead to efficiency reduction, damages, and acoustic noise. Much research is developing methods of engine knock detection. Hence, injector fault detection has not been addressed specifically, this research is focused on the subject and corresponding vibration amplitudes and frequencies, likely to cause the knock phenomenon. Welch test, Short-Term Fourier Transform (STFT), Wigner-Ville Distribution (WVD), and Choi-Williams Distribution (CWD) were employed for detailed scrutiny of vibrations generated by an under-load engine. For an ideal combustion, the acceleration peak values should be placed in the range of 0–10 kHz in time-frequency (TFR) diagram. While a faulty injection unit can cause components at higher frequency, between 10 and 25 kHz, in TFR diagram for each cylinder, and this can effects on the engine performance. Regarding the results which are presented in this research it infers that, in real- time performance monitoring of an engine, the STFT technique is more efficient for fault diagnosis of fuel injection nozzles and knock detection. By comparing vibration response of healthy and faulty injectors, the RMS and kurtosis of the faulty injectors showed an increase of 12.9% and 20.6% respectively.
Purpose
The purpose of this paper is mainly to highlight how a simplified and streamlined approach to the condition monitoring of industrial rotating machines through the application of frequency domain data combination can effectively enhance the eMaintenance framework.
Design/methodology/approach
The paper commences by providing an overview to the relevance of maintenance excellence within manufacturing industries, with particular emphasis on the roles that rotating machines condition monitoring of rotating machines plays. It then proceeds to provide details of the eMaintenance as well as its possible alignment with the introduced concept of effective vibration-based condition monitoring (eVCM) of rotating machines. The subsequent sections of the paper respectively deal with explanations of data combination approaches, experimental setups used to generate vibration data and the theory of eVCM.
Findings
This paper investigates how a simplified vibration-based rotating machinery faults classification method based on frequency domain data combination can increase the feasibility and practicality of eMaintenance.
Research limitations/implications
The eVCM approach is based on classifying data acquired under several experimentally simulated conditions on two different machines using combined higher order signal processing parameters so as to reduce condition monitoring data requirements. Although the current study was solely based on the application of vibration data acquired from rotating machines, the knowledge exchange platform that currently dominates present day scientific research makes it very likely that the lessons learned from the development of eVCM concept can be easily transferred to other scientific domains that involve continuous condition monitoring such as medicine.
Practical implications
The concept of eMaintenance as a cost-effective and smart means of increasing the autonomy of maintenance activities within industries is rapidly growly in maintenance related literatures. As viable as the concept appears, the achievement of its optimum objectives and full deployment to the industry is still subjective due to the complexity and data intensiveness of conventional condition monitoring practices. In this paper, an effective vibration-based condition monitoring (eVCM) approach is proposed so that rotating machine faults can be effectively detected and classified without the need for repetitive analysis of measured data.
Originality/value
Although the currently existing body of literature already contains studies that have attempted to show how the combination of measured vibration data from several industrial machines can be used to establish a universal vibration-based faults diagnosis benchmark for incorporation into eMaintenance framework. However, these studies are limited in the scope of faults, severity and rotational speeds considered. In the current study, the concept of multi-faults, multi-sensor, multi-speed and multi-rotating machine data combination approach using frequency domain data fusion and principal components analysis is presented so that faults diagnosis features for identical rotating machines with different foundations can be shared between industrial plants. Hence, the value of the current study particularly lies in the fact that it significantly highlights a new dimension through which the practical implementation and operation of eMaintenance can be realized using big data management and data combination approaches.
Literatures have shown that there is a significant rise in the use of measured vibro-acoustic signals for faults diagnosis in rotating machines. This is particularly based on the premise that affluent information about a rotating machine’s operating conditions is usually conveyed by the sounds of the machine. Several earlier studies have already shown the usefulness and capabilities of amplitude spectra for faults diagnosis. However, very limited analyses of rotating machine’s vibro-acoustic signals are available in literatures. Hence, the current study compares the fused amplitude spectra of measured vibration signals from a flexibly supported rotating machine with different faults, using accelerometers and microphones. The experiments, spectra computations and observations are presented here.
This paper discusses the significance of state monitoring and fault diagnosis of rotating machinery. A framework is put forward to support each other in four aspects of state monitoring and fault diagnosis: theories and methods, key technologies, systems diagnosis, and applications. An example of the research on the system of state monitoring and fault diagnosis for the ultra-supercritical steam turbine generator is given. Progress in the previously mentioned four aspects is reviewed. Finally, thoughts and suggestions about state monitoring and diagnostic studies of rotating machinery are given. ©, 2015, Nanjing University of Aeronautics an Astronautics. All right reserved.
It is commonly observed in practise that rotating machines installed at different plant locations often exhibit different dynamic behaviours, due to variations in the flexibilities of their supports. This often makes the faults diagnosis complex from one machine to another machine. In the current study, a similar scenario has been experimentally simulated on a rotating rig with different foundation flexibilities. Also, different faults were experimentally simulated at different machine speeds so as to develop a reliable diagnosis technique that will be suitable for different machine foundations. Recently developed data fusion methods for constructing composite spectrum (CS) and composite bispectrum (CB) for a machine are again applied for faults diagnosis here. In addition, the present study introduces the composite trispectrum (CT) as a new feature for diagnosis. The paper hereby presents the computational concepts of all composite spectra, rig details, data analysis and diagnosis.
The composite spectrum (CS) data fusion technique has been shown to simplify rotating machines faults diagnosis by earlier studies. Faults diagnosis with the earlier CS relied solely on the amplitudes of several harmonics of the machine speed, owing to the loss of phase information leading to its computation. The proposed improved CS applies the concept of cross power spectrum density for computing a poly-Coherent Composite Spectrum (pCCS) of a machine, which retains amplitude and phase information at all measurement locations. The present study compares the proposed pCCS method with the earlier CS method for faults diagnosis in rotating machines, using experimental data from a rotating rig. Results and observations show that the proposed pCCS offered a much better representation of the machines dynamics when compared to the earlier CS method and hence better fault diagnosis.
In the field of machine condition monitoring one can observe that a link exists between machine vibrations and its health condition, that is, there is a change in the machine vibration signature when machine faults occur. Damages occurring in machine elements are often related to non-linear effects, which may lead to non-linearities in the machine vibration. This paper concerns the study of some systems by means of techniques based on Higher Order Spectra (HOS). These techniques are particularly useful in the situation where only a single measurement sensor is available. If a process is Gaussian then HOS provide no information that cannot be obtained from the second order statistics. On the contrary, HOS give information about a signal's non-Gaussianity. Since a Gaussian input passing through a linear system leads to a Gaussian output, assuming the signal as an output of a system with a Gaussian input, then HOS make it possible to analyse the structure of the output signal and to provide information related to the non-linearity within the system. A simple model is presented with the aim of showing the effectiveness of the normalised version of polyspectra in detecting different kinds of system non-linearities. HOS are used to interpret the signal structure and the system's physical characteristics. Moreover, two experimental cases are presented. The HOS are applied to detect the presence of a fatigue crack in a straight beam and to analyse the vibration signal measured on a test bench for rolling element bearings. Both third and fourth order spectra seem to provide a possibility of using HOS as a condition monitoring tool.
Higher order spectra (HOS) are the tools in signal processing for the identification of the presence of higher harmonics in a signal which is a typical case of a non-linear dynamic behavior in mechanical systems. The breathing of a crack during shaft rotation also exhibits a non-linear behavior. The crack is known to generate 2X (twice the machine RPM) and higher harmonics in addition to 1X component in the shaft response during its rotation. Misaligned shaft also shows such feature as a crack in a shaft. The HOS have now been applied on a small rotating rig to observe its features. Results are found to be encouraging to distinguish these two faults based on a few experiments conducted on a small rig, which are presented here. The presented results though limited suggest the potential of the use of the HOS in the condition monitoring of rotating machinery.
A marine propulsion system is a very complicated system composed of many mechanical components. As a result, the vibration
signal of a gearbox in the system is strongly coupled with the vibration signatures of other components including a diesel
engine and main shaft. It is therefore imperative to assess the coupling effect on diagnostic reliability in the process of
gear fault diagnosis. For this reason, a fault detection and diagnosis method based on bispectrum analysis and artificial
neural networks (ANNs) was proposed for the gearbox with consideration given to the impact of the other components in marine
propulsion systems. To monitor the gear conditions, the bispectrum analysis was first employed to detect gear faults. The
amplitude-frequency plots containing gear characteristic signals were then attained based on the bispectrum technique, which
could be regarded as an index actualizing forepart gear faults diagnosis. Both the back propagation neural network (BPNN)
and the radial-basis function neural network (RBFNN) were applied to identify the states of the gearbox. The numeric and experimental
test results show the bispectral patterns of varying gear fault severities are different so that distinct fault features of
the vibrant signal of a marine gearbox can be extracted effectively using the bispectrum, and the ANN classification method
has achieved high detection accuracy. Hence, the proposed diagnostic techniques have the capability of diagnosing marine gear
faults in the earlier phases, and thus have application importance.
Keywordsmarine propulsion system–fault diagnosis–vibration analysis–bispectrum–artificial neural networks
Vibration-based condition monitoring (VCM) has gained tremendous successes in the detection and differentiation of faults associated with rotating machines, through the installation of various numbers of vibration transducers at individual bearing pedestals of the monitored machine. This chapter however exposes the future potentials of the use of the higher order spectra (HOS) i.e., the bispectrum and the trispectrum for rotating machines faults diagnosis (FD). The aim of this is to achieve a significant reduction in the number of vibration transducers required at each bearing pedestal, without necessarily compromising valuable information required for the diagnosis. Four cases (healthy, shaft misalignment, cracked shaft and shaft rub) were simulated on an experimental rig with two rigidly coupled shafts supported by four ball bearings. Only four accelerometers (one at each bearing pedestal) were used for this study. The HOS results were compared for the different conditions of the rig. The observations and findings are presented in the chapter.
Vibration-based condition monitoring (VCM) requires vibration measurement on each bearing pedestal using a number of vibration transducers and then signals processing for all the measured vibration data to identify fault(s), if any, in a rotating machine. Such a large vibration data set makes the diagnosis process complex generally for a large rotating machine supported through a number of bearing pedestals. Hence a new method is used to construct a single composite spectrum using all the measured vibration data set. This composite spectrum is expected to represent the dynamics of the complete machine assembly and can make fault diagnosis process relatively easier and more straightforward. The paper presents the concept of the proposed composite spectrum which was applied to a laboratory test rig with different simulated faults; healthy and three faulty cases named misalignment, crack shaft, and shaft rub. A comparison between the composite spectrum with and without the coherence has been investigated for the simulated faults in the rig. It has been observed that the coherent composite spectrum provides much better diagnosis compared to the non-coherent composite spectrum.
In Part 1 of this paper, a theoretical model to determine the dynamic behaviour of misaligned shaft rotors connected by a flexible coupling was developed. In this Part 2, experimental tests are performed to validate the model and simulation results obtained in Part 1. Vibratory characteristics, such as the frequency spectrum, waveform and phase shifts of the spectral components across the coupling are presented for different magnitudes of misalignment and types of coupling. Traditional vibration analysis rules used in practical predictive maintenance to diagnose shaft misalignment are evaluated. The influence of the frequency response functions on the amplitude of the spectral components and on the phase shifts of the spectral components across a coupling were studied. Finally, some practical conclusions for more reliable shaft misalignment identification using vibration analysis are suggested.
Damage detection by means of non-destructive testing plays an important role in ensuring the integrity of machine elements and structures. Vibration testing is an effective means of detecting crack development in structures. In this paper the effect of crack closure on the dynamic behaviour of cantilever beams is studied. Since the crack opens or closes depending on the direction of the vibration, the beam exhibits bilinear characteristics. The aim of the paper is to analyze the system response by using bispectral analysis which forms a subset of higher order statistical analysis. The study has been conducted both on simulated and experimental vibration signals. Firstly, a simplified model is employed to simulate the bilinear behaviour of a beam with a closing crack. The model is an oscillator with a bilinear restoring forcing function. The analysis of the forced vibrations of the model is performed by means of the harmonic balance method showing the occurrence of harmonics in the response spectrum which are strictly related to the bilinear nature of the model. Moreover, an experimental test carried out on a straight beam with a fatigue crack is presented. The beam is excited with white noise by means of a vibration shaker. The bispectral analysis performed both on the model and the actual structure shows high sensitivity of the non-linear behaviour of the system: that is to say, to the presence of the fatigue crack in the structure. In particular, the interactions between the frequency components contained in the signal response are analyzed. The results provide a possibility of using the bispectral analysis technique to detect damages in structures.
The vibration signals measured from rotating machinery can be very complex and a number of machine malfunctions can create complicated modulation patterns which are sometimes difficult to detect and to understand. Conventional linear spectral analysis will be of limited use in particular instances when frequency components interact together to form new spectral components due to some non-linear process. Under these circumstances, various signal processing tools are available for performing sophisticated analysis of the measured vibration to detect the non-linear interaction of frequency components and hence changes in machine performance and condition. This paper presents two higher-order spectral analysis techniques, the bispectrum and the trispectrum, and demonstrates how they can be used to detect phase coherence between various frequency components. The theoretical relationship of the higher-order spectral techniques to the power spectrum is given along with the derivation of the normalized bispectrum and trispectrum using the Fourier series of phase-related signals to show that the higher-order spectral analysis techniques can detect various forms of phase coupling between frequency components as well as the strength of the phase coupling. The particular case of modulation is investigated to show the applicability of the higher-order spectral techniques to detect amplitude and phase modulation.
This paper is concerned with the development of techniques to detect and analyse non-linearities. The methods developed are based on the concepts of higher-order spectra (HOS), in particular the bispectrum and trispectrum. The study of HOS has been dominated by work on the bispectrum. The bispectrum can be viewed as a decomposition of the third moment (skewness) of a signal over frequency and proves useful for analysing systems with asymmetric non-linearities. In studying symmetric non-linearities, the trispectrum is a more powerful tool, as it represents a decomposition of kurtosis over frequency. Techniques are presented that enable the estimation and display of bispectra and trispectra. HOS are studied in detail with particular attention being paid to normalisation methods. Two traditional methods, the bicoherence and skewness function, are studied and these are extended to their fourth-order equivalents, the tricoherence and kurtosis functions. Under certain conditions, notably narrowband signals, the above normalisation methods are shown to fail, and so a new technique based on pre-whitening the signal in the time domain is developed. Examples of these functions are given both for an amplitude modulated process and the Duffing oscillator.
Bispectral analysis is emerging as a new powerful technique in signal processing, offering insight into non-linear coupling between frequencies and having potential applications in many areas where traditional linear (i.e. power spectral) analysis provides insufficient information. However, it is more difficult to interpret bispectral features than power spectral features, and this has hindered the applications of the theory. In this paper a normalised bispectral measure is used in the analysis of vibration signals containing periodic components and noise. Part I of the paper presented bispectral features associated with various signal types, and discussed practical matters regarding the choice of sampling rate. In Part II these theoretical results are used to interpret the bispectra of data collected from a variety of vibration sources, showing that there is potential for using these measures for machine condition monitoring.
Horizontal rotors are always imposed to periodic stresses and, therefore, a crack due to a fatigue is unavoidable. The proper diagnosis of machinery is necessary to prevent tragic accidents and the vibration monitoring is the most important tool for such a diagnosis system. In order to develop a monitoring system that can detect a crack in an early stage of propagation, it is important to know the vibration characteristics of a cracked rotor. A crack opens or closes due to the direction of the lateral deflection. Therefore, a cracked rotor has nonlinear spring characteristics of a piecewise linear type. In order to diagnose the vibration characteristics properly, it is essential to understand the behavior caused by the nonlinearity. These piecewise linear characteristics make a directional difference in stiffness and this difference rotates with the rotor. As the result, the coefficients of linear and nonlinear terms in restoring forces become time dependent. According to the physical characteristics, cracked rotors can be classified into a class of nonlinear parametrically excited system. At first, this article introduces case histories of cracks found in industrial machines. Secondly, it explains the vibration characteristics of various kinds of resonances due to cracks using simple Jeffcott rotor with nonlinear spring characteristics. The utilization of the nonstationary vibrations for monitoring system is also explained.
Bispectral analysis is emerging as a new powerful technique in signal processing, offering insight into non-linear coupling between frequencies and having potential applications in many areas where traditional linear (i.e. power spectral) analysis provides insufficient information. However, it is more difficult to interpret bispectral features than power spectral features, and this has hindered the applications of the theory. In this paper a normalised bispectral measure is used in the analysis of vibration signals containing periodic components and noise. In Part I the bispectral features associated with various signal types are derived, and practical considerations regarding the choice of sampling rate are considered. Part II describes the application of this theory to experimental data from a variety of vibration sources, and discusses the possible applications of bispectral analysis in machine condition monitoring.
The application of bispectral and trispectral analysis in
condition monitoring is discussed. Higher-order spectral analysis of
machine vibrations for the provision of diagnostic features is
investigated. Experimental work is based on vibration data collected
from a small test rig subjected to bearing faults. The direct use of the
entire bispectrum or trispectrum to provide diagnostic features is
investigated using a variety of classification algorithms including
neural networks, and this is compared with simpler power spectral and
statistical feature extraction algorithms. A more detailed investigation
of the higher-order spectral structure of the signals is then
undertaken. This provides features which can be estimated more easily in
practice and could provide diagnostic information about the machines
The strengths and limitations of correlation-based signal processing methods are discussed. The definitions, properties, and computation of higher-order statistics and spectra, with emphasis on the bispectrum and trispectrum are presented. Parametric and nonparametric expressions for polyspectra of linear and nonlinear processes are described. The applications of higher-order spectra in signal processing are discussed.< >
Condition monitor-ing: a simple and practical approach (Dissertation con-verted into a book)
- Yunusa
- Sinha
Yunusa-Kaltungo A and Sinha JK. Condition monitor-ing: a simple and practical approach (Dissertation con-verted into a book). Saarbru¨ : Lambert Academic Publishing (LAP) GmbH & Co. KG, 2012.
Bispectrum for faults diagnosis in rotating machines In: Proceedings of the 17th interna-tional congress on sound and vibration
- Elbhbah
- Sinha
Elbhbah K and Sinha JK. Bispectrum for faults diagnosis in rotating machines. In: Proceedings of the 17th interna-tional congress on sound and vibration, Cairo, Egypt, 18– 22 July 2010, sponsored by international institute of acoustics and vibration (IIAV), Curran Associates, Inc., Red Hook NY 12571.
Bispectrum: a tool for distin-guishing faults in rotating machine In: Proceedings of ASME turbo expo 2012: turbine technical conference and exposition
- Elbhbah
- Sinha
Elbhbah k and Sinha JK. Bispectrum: a tool for distin-guishing faults in rotating machine. In: Proceedings of ASME turbo expo 2012: turbine technical conference and exposition, Copenhagen, Denmark, 11–15 June 2012, vol-ume 7: structures and dynamics, parts A and B, paper no. GT2012-68010, 477–483.