A better Hilbert-Huang transform and how to use it for vibration analysis

A better Hilbert-Huang transform and how to use it for vibration analysis

Nonlinear and non-stationary signals are always present in the vibration that industrial machinery produces. Recently, several novel techniques for analyzing these signals have been put forth. The Hilbert-Huang Transform is one of the more promising techniques (HHT). The Hilbert Transform and empirical mode decomposition (EMD) principles are the foundation of the HHT. Prior to applying the HHT, the acquired signal will be broken down by the EMD into a group of intrinsic mode functions (IMF). For the signal under analysis, the IMF is a form of full, adaptable, and nearly orthogonal representation. The IMF can extract all of the instantaneous frequencies from the nonlinear or non-stationary signal since it is nearly monocomponent.Secondly, the Hilbert Transform can be utilized to obtain the local energy of any instantaneous frequency. The signal's energy, frequency, and temporal distribution are the outcome. The application of HHT is not computationally demanding, making it a viable technique for extracting nonlinear and non-stationary signal features. But following a comprehensive experiment, the HHT's output was found to have some shortcomings. Initially, the low-frequency portion of the EMD will produce unwanted IMFs that could lead to a misinterpretation of the outcome. Second, depending on the signal analysis, the first obtained IMF can encompass a frequency range that is too broad to achieve the monocomponent feature. Third, signals containing low-energy components cannot be separated by the EMD process. New methods have been used in this investigation to enhance the HHT outcome. The wavelet packet transform (WPT) is used as preprocessing in the upgraded version of HHT to split the signal into a group of narrow band signals before applying EMD. Each IMF formed from the EMD can actually become a monocomponent with the assistance of WPT. Subsequently, an unrelated IMF is eliminated from the outcome using a screening procedure. It has been established by both simulated and experimental vibration signals of a rotary system with a rubbing problem that the improved HHT does, in fact, indicate the rubbing symptoms more precisely and clearly than the original HHT. As a result, the enhanced HHT is an accurate technique for non-stationary and nonlinear signal analysis. Secondly, the Hilbert Transform can be utilized to obtain the local energy of any instantaneous frequency. The signal's energy, frequency, and temporal distribution are the outcome. The application of HHT is not computationally demanding, making it a viable technique for extracting nonlinear and non-stationary signal features. But following a comprehensive experiment, the HHT's output was found to have some shortcomings. Initially, the low-frequency portion of the EMD will produce unwanted IMFs that could lead to a misinterpretation of the outcome. Second, depending on the signal analysis, the first obtained IMF can encompass a frequency range that is too broad to achieve the monocomponent feature. 

Introduction

Signal analysis has long been a crucial and essential component of many other real-world applications, including vibration-based machine failure diagnostics. When vibration-based machine fault detection is used, signal analysis is generally used for two purposes: first, it looks into the dynamic characteristics of the machine under various problem types; second, if a fault occurs, it extracts fault features and helps pinpoint its source. Due to its effectiveness and simplicity, the Fourier Transform technique has up until now dominated the field of signal analysis. Nonetheless, there are a few significant limitations on the application of the Fourier transform. The inspected machine's signal needs to be linear and temporally stationary in order for the ensuing Fourier spectrum to make any sense at all. Regrettably, non-stationary and nonlinear data are frequently to be analyzed in vibration-based machine failure diagnosis. Given how frequently the patterns of the recorded signals change over time, the resulting frequency components are not always constant. As a result, Fourier Transform is unable to meet fault diagnosis requirements, especially in practical applications.

Wavelet transform has emerged as one of the rapidly developing technologies in signal processing and mathematics within the last ten years. The wavelet transform is local, adaptive, full, and orthogonal. Each of them is essential for creating a foundation for nonlinear and non-stationary signal analysis. Dilation and translation are the fundamental operations of the wavelet transform, resulting in a multiscale signal analysis. As a result, it may successfully extract the inspected signal's frequency and time properties. Wavelet transform has been found to have numerous drawbacks, despite its ability to analyze nonlinear and non-stationary data and its suitability for vibration-based machine defect diagnostics. The interference terms, border distortion, and energy leakage are among the unavoidable flaws. These flaws could cause a great deal of unwanted little spikes across the frequency scales, which would be confusing and challenging to interpret in the findings. Wavelet transformations can be broadly divided into two categories: discrete and continuous. Continuous wavelet transform requires a lot of processing power. Analyzing a large amount of obtained data takes a lot of time. Conversely, the discrete wavelet transform exhibits high computational efficiency. At a high frequency range, the resolution in frequency is subpar. As a result, it might be useful for a variety of tasks, like noise reduction and data compression, but not high-frequency frequency analysis.

A new kind of time-frequency analysis known as the Hilbert-Huang transform has been introduced for the study of nonlinear and non-stationary signals in response to the shortcomings of the wavelet transform. The Hilbert Transform and empirical mode decomposition principles are the foundation of the HHT. Prior to applying the HHT, the acquired signal will be broken down by the EMD into a group of intrinsic mode functions. For the signal under analysis, the IMF is a form of full, adaptable, and nearly orthogonal representation. The IMF can extract all of the instantaneous frequencies from the nonlinear or non-stationary signal since it is nearly monocomponent. Secondly, the Hilbert Transform can be utilized to obtain the local energy of any instantaneous frequency. The end product is an HHT spectrum with the signal's energy, frequency, and time distribution. Any event can be localized on its instantaneous frequency and time of occurrence using the HHT spectrum. The EMD, the most computationally demanding step in the HHT, does not require convolution in contrast to the wavelet transform. Because of this, EMD's computing time is comparatively short, making it appropriate for analyzing large amounts of data or signals. Numerous applications have made use of the HHT approach for vibration signal analysis. Yang and Sun interpreted the nonlinear response of a crack-induced rotor using the HHT. An HHT-based damage identification method was presented by Yang and Lei, who then used it on the ASCE structural health monitoring benchmark structure.

While the HHT has several advantages over other signal studies, it also has certain drawbacks that prevent it from being a reliable method for obtaining the characteristics of nonlinear and non-stationary signals. Initially, the low-frequency portion of the EMD will produce unwanted IMFs that could lead to a misinterpretation of the outcome. Second, the first obtained IMF may cover a frequency range that is too wide to achieve the property of a monocomponent, depending on the signal that was examined.Third, signals containing low-energy components cannot be separated by the EMD process. An enhanced HHT is provided here to address these issues. To divide the inspected signal into a collection of narrow band signals, the enhanced HHT preprocesses the signal using the wavelet packet transform (WPT). Low energy frequency components can therefore be more easily distinguished at various narrow bands. Then, just like with the original EMD, the EMD method will be used to break down these narrow band signals. The resulting IMFs will be in narrower bands and will be more easily satisfied with the monocomponent requirement. The second and third aforementioned flaws can be avoided by utilizing both WPT and the EMD.

After that, a screening procedure will be used to separate the important IMFs from the unimportant IMFs. This can be done by using the examined raw signal to calculate the correlation coefficients of the IMFs. Unrelated IMFs that could skew the results, especially in the low-frequency range as indicated in the first insufficiency, can be reduced based on the coefficient values. The efficacy of the enhanced HHT has been confirmed using both genuine signals produced by a rotary machine with the rubbing defect and simulated signals of rubbing between a rotor and a stator. In Section 2, the instantaneous frequency definition, the Hilbert transform deficiency, and the HHT principle—which consists of the Hilbert transform and the EMD—are presented. The development of the upgraded HHT, its theory, and its formation were covered in Section 3. Section 4 presents the design of the simulated data, the experimental setup for producing defective vibration from a real rotary machine exhibiting rubbing, and a comparison of the upgraded HHT's and the original IT's rubbing detection capabilities. Section 5 presents the conclusion and the potential of the enhanced HHT.

Definition of the instantaneous frequency and Hilbert transform capacity

While there is always debate regarding the precise definition of instantaneous frequency, it is reasonable to say that a signal is monocomponent if it contains only one frequency value throughout the whole length of the signal. The Hilbert transform can be used to determine a monocomponent signal's instantaneous frequency.

The enhanced Hilbert-Huang transform's fundamental idea

A comparison study between the improved HHT and wavelet transform in roller bearing fault diagnosis has been published in an authors publication , which also offers the basic theory of the improved HHT. However, this part explains the specific theory and construction of the enhanced HHT. The HHT is a potentially useful tool for analyzing non-stationary and nonlinear signals, as was indicated in Section 2. 

The analysis of rubbing vibration signals using enhanced HHT

The rotor and stator surfaces of any rotating machine frequently scrape against one another. If there is too little space between a stator and rotor, it might cause the rubbing symptom. Rubbly conditions will worsen and ultimately cause the rotary machine to break down catastrophically if the machine operator ignores the issue. For instance, a motor may fatally malfunction due to constant rubbing between the rotor and stator.

Conclusion

This study provides a detailed introduction to a revolutionary time-frequency analysis technique known as HHT. There are three main issues with the HHT that have been raised. These include the possibility that the first obtained IMF covers an excessively wide frequency range, which could lead to the HHT failing to produce an accurate frequency pattern for the inspected signal; the creation of undesired pseudo components in the result, which could lead to incorrect interpretation of the result; and the loss of low-energy frequency components.