Understanding how kurtosis is transferred from input acceleration to stress response and it's influence on fatigue life

High cycle fatigue of metals typically occurs through long term exposure to time varying loads which, although modest in amplitude, give rise to microscopic cracks that can ultimately propagate to failure. The fatigue life of a component is primarily dependent on the stress amplitude response at critical failure locations. For most vibration tests, it is common to assume a Gaussian distribution of both the input acceleration and stress response. In real life, however, it is common to experience non-Gaussian acceleration input, and this can cause the response to be non-Gaussian. Examples of non-Gaussian loads include road irregularities such as potholes in the automotive world or turbulent boundary layer pressure fluctuations for the aerospace sector or more generally wind, wave or high amplitude acoustic loads. The paper first reviews some of the methods used to generate non-Gaussian excitation signals with a given power spectral density and kurtosis. The kurtosis of the response is examined once the signal is passed through a linear time invariant system. Finally an algorithm is presented that determines the output kurtosis based upon the input kurtosis, the input power spectral density and the frequency response function of the system. The algorithm is validated using numerical simulations. Direct applications of these results include improved fatigue life estimations and a method to accelerate shaker tests by generating high kurtosis, non-Gaussian drive signals

Vibration-based Fault Diagnostics in Wind Turbine Gearboxes Using Machine Learning

A significantly increased production of wind energy offers a path to achieve the goals of green energy policies in the United States and other countries. However, failures in wind turbines and specifically their gearboxes are higher due to their operation in unpredictable wind conditions that result in downtime and losses. Early detection of faults in wind turbines will greatly increase their reliability and commercial feasibility. Recently, data-driven fault diagnosis techniques based on deep learning have gained significant attention due to their powerful feature learning capabilities. Nonetheless, diagnosing faults in wind turbines operating under varying conditions poses a major challenge. Signal components unrelated to faults and high levels of noise obscure the signature generated by early-stage damage. To address this issue, we propose an innovative fault diagnosis framework that utilizes deep learning and leverages cyclostationary analysis of sensor data. By generating cyclic spectral coherence maps from the sensor data, we can emphasize fault-related signatures. These 2D color map representations are then used to train convolutional neural networks capable of detecting even minor faults and early-stage damages. The proposed method is evaluated using test data obtained from multibody dynamic simulations conducted under various operating conditions. The benchmark test cases, inspired by an NREL study, are successfully detected using our approach. To further enhance the accuracy of the model, subsequent studies employ Convolutional Neural Networks with Local Interpretable Model-Agnostic Explanations (LIME). This approach aids in interpreting classifier predictions and developing an interpretable classifier by focusing on a subset range of cyclic spectral coherence maps that carry the unique fault signatures. This improvement contributes to better accuracy, especially in scenarios involving multiple faults in the gearbox that need to be identified. Moreover, to address the challenge of applying this framework in practical settings, where standard deep learning techniques tend to provide inaccurate predictions for unseen faults or unusual operating conditions, we investigate fault diagnostics using a Bayesian convolutional neural network. This approach incorporates uncertainty bounds into prediction results, reducing overconfident misclassifications. The results demonstrate the effectiveness of the Bayesian approach in fault diagnosis, offering valuable implications for condition monitoring in other rotating machinery applications

Fault Detection in Rotating Machinery: Vibration analysis and numerical modeling

This thesis investigates vibration based machine condition monitoring and consists of two parts: bearing fault diagnosis and planetary gearbox modeling. In the first part, a new rolling element bearing diagnosis technique is introduced. Envelope analysis is one of the most advantageous methods for rolling element bearing diagnostics but finding the suitable frequency band for demodulation has been a substantial challenge for a long time. Introduction of the Spectral Kurtosis (SK) and Kurtogram mostly solved this problem but in situations where signal to noise ratio is very low or in presence of non-Gaussian noise these methods will fail. This major drawback may noticeably decrease their effectiveness and goal of this thesis is to overcome this problem. Vibration signals from rolling element bearings exhibit high levels of 2nd order cyclostationarity, especially in the presence of localized faults. A second-order cyclostationary signal is one whose autocovariance function is a periodic function of time: the proposed method, named Autogram by the authors, takes advantage of this property to enhance the conventional Kurtogram. The method computes the kurtosis of the unbiased autocorrelation (AC) of the squared envelope of the demodulated and undecimated signal, rather than the kurtosis of the filtered time signal. Moreover, to take advantage of unique features of the lower and upper portions of the AC, two modified forms of kurtosis are introduced and the resulting colormaps are called Upper and Lower Autogram. In addition, a new thresholding method is also proposed to enhance the quality of the frequency spectrum analysis. Finally, the proposed method is tested on experimental data and compared with literature results so to assess its performances in rolling element bearing diagnostics. Moreover, a second novel method for diagnosis of rolling element bearings is developed. This approach is a generalized version of the cepstrum pre-whitening (CPW) which is a simple and effective technique for bearing diagnosis. The superior performance of the proposed method has been shown on two real case data. For the first case, the method successfully extracts bearing characteristic frequencies related to two defected bearings from the acquired signal. Moreover, the defect frequency was highlighted in case two, even in presence of strong electromagnetic interference (EMI). The second part presents a newly developed lumped parameter model (LPM) of a planetary gear. Planets bearings of planetary gear sets exhibit high rate of failure; detection of these faults which may result in catastrophic breakdowns have always been challenging. Another objective of this thesis is to investigate the planetary gears vibration properties in healthy and faulty conditions. To seek this goal a previously proposed lumped parameter model (LPM) of planetary gear trains is integrated with a more comprehensive bearing model. This modified LPM includes time varying gear mesh and bearing stiffness and also nonlinear bearing stiffness due to the assumption of Hertzian contact between the rollers/balls and races. The proposed model is completely general and accepts any inner/outer race bearing defect location and profile in addition to its original capacity of modelling cracks and spalls of gears; therefore, various combinations of gears and bearing defects are also applicable. The model is exploited to attain the dynamic response of the system in order to identify and analyze localized faults signatures for inner and outer races as well as rolling elements of planets bearings. Moreover, bearing defect frequencies of inner/outer race and ball/roller and also their sidebands are discussed thoroughly. Finally, frequency response of the system for different sizes of planets bearing faults are compared and statistical diagnostic algorithms are tested to investigate faults presence and growth

A proposal of a technique for correlating defect dimensions to vibration amplitude in bearing monitoring

The capability of early stage detection of a defect is gaining more and more importance because it can help the maintenance process, the cost reduction and the reliability of the systems. The increment of vibration amplitude is a well-known method for evaluating the damage of a component, but it is sometimes difficult to understand the exact level of damage. In other words, the amplitude of vibration cannot be directly connected to the dimension of the defect. In the present paper, based on a non-Hertzian contact algorithm, the spectrum of the pressure distribution in the contact surface between the race and the rolling element is evaluated. Such spectrum is then compared with the acquired spectrum of a vibration response of a defected bearing. The bearing vibration pattern was previously analyzed with monitoring techniques to extract all the damage information. The correlation between the spectrum of the pressure distribution in the defected contact surface and the analyzed spectrum of the damaged bearing highlights a strict relationship. By using that analysis, a precise correlation between defect aspect and dimension and vibration level can be addressed to estimate the level of damaging

Characterising the friction and wear between the piston ring and cylinder liner based on acoustic emission analysis

In this paper, an experimental investigation was carried out to evaluate the friction and wear between the cylinder liner and piston ring using acoustic emission (AE) technology. Based on a typical compression ignition (CI) diesel engine, four types of alternative fuels (Fischer-Tropsch fuel, methanol-diesel, emulsified diesel and standard diesel) were tested under dif-ferent operating conditions. AE signals collected from the cylinder block of the testing en-gine. In the meantime, the AE signals in one engine cycle are further segregated into small segments to eliminate the effects of valve events on friction events of cylinder liner. In this way, the resulted AE signals are consistent with the prediction of hydrodynamic lubrication processes. Test results show that there are clear evidences of high AE deviations between dif-ferent fuels. In particular, the methanol-diesel blended fuel produces higher AE energy, which indicates there are more wear between the piston ring and cylinder liner than using standard diesel. On the other hand, the other two alternative fuels have been found little dif-ferences in AE signal from the normal diesel. This paper has shown that AE analysis is an ef-fective technique for on-line assessment of engine friction and wear, which provides a novel approach to support the development of new engine fuels and new lubricants

A simple condition monitoring method for gearboxes operating in impulsive environments

Reliable condition indicators are necessary to perform effective diagnosis and prognosis. However, the vibration signals are often corrupted with non-Gaussian noise and rotating machines may operate under time-varying operating conditions. This impedes the application of conventional condition indicators. The synchronous average of the squared envelope is a relatively simple yet effective method to perform fault detection, fault identification and fault trending under constant and time-varying operating conditions. However, its performance is impeded by the presence of impulsive signal components attributed to impulsive noise or the presence of other damage modes in the machine. In this work, it is proposed that the synchronous median of the squared envelope should be used instead of the synchronous average of the squared envelope for gearbox fault diagnosis. It is shown on numerical and experimental datasets that the synchronous median is more robust to the presence of impulsive signal components and is therefore more reliable for estimating the condition of specific machine components.http://www.mdpi.com/journal/sensorsam2021Mechanical and Aeronautical Engineerin

Understanding How Kurtosis Is Transferred from Input Acceleration to Stress Response and Its Influence on Fatigue Llife

High cycle fatigue of metals typically occurs through long term exposure to time varying loads which, although modest in amplitude, give rise to microscopic cracks that can ultimately propagate to failure. The fatigue life of a component is primarily dependent on the stress amplitude response at critical failure locations. For most vibration tests, it is common to assume a Gaussian distribution of both the input acceleration and stress response. In real life, however, it is common to experience non-Gaussian acceleration input, and this can cause the response to be non-Gaussian. Examples of non-Gaussian loads include road irregularities such as potholes in the automotive world or turbulent boundary layer pressure fluctuations for the aerospace sector or more generally wind, wave or high amplitude acoustic loads. The paper first reviews some of the methods used to generate non-Gaussian excitation signals with a given power spectral density and kurtosis. The kurtosis of the response is examined once the signal is passed through a linear time invariant system. Finally an algorithm is presented that determines the output kurtosis based upon the input kurtosis, the input power spectral density and the frequency response function of the system. The algorithm is validated using numerical simulations. Direct applications of these results include improved fatigue life estimations and a method to accelerate shaker tests by generating high kurtosis, non-Gaussian drive signals

A study of two bispectral features from envelope signals for bearing fault diagnosis

: To accurately detect and diagnose bearing faults, bispectral analysis has received more attention recently because of its unique property of noise reduction and nonlinearity extraction. Particularly this study investigates two typical bispectra: conventional bispectrum (CB) and modulation signal bispectrum (MSB) for suppressing noise influences in envelope signals and hence obtaining more accurate diagnostic features. The first component from the diagonal slice of CB results and that of the subdiagonal slices of MSB results are taken as the diagnostic features considering effective inclusion of information and easy of computations. Simulative and experimental studies show that both MSB and CB features result in good diagnostic performances but MSB may outperform CB slightly in that it shows smaller variance in attaining the feature and more sensitive to weak fault signatures. This merit of MSB may be due to that the MSB feature has more diagnostic information as it is the combination of first three harmonics, whereas the CB feature is combined from just the first two harmonics