The principle of spectral analysis is that any signal can be decomposed into a combination of different frequencies. To do this, one can perform the decomposition using the Fourier Transform, which converts a signal from the time domain to the frequency domain.

## Spectral Analysis:** Fast Fourier Transform (FFT)**

The Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) and its inverse (Inverse Fourier Theorem). Basically, the goal is to analyze a function in another domain. The FFT is thus useful in signal processing by allowing the decomposition of vibration signals into frequency components. This makes it possible to identify patterns and anomalies in industrial assets. Moreover, the FFT has applications in various fields, from audio engineering to image processing.

The FFT converts a signal into individual spectral components and provides frequency information for each of them. It was defined by mathematician James William Cooley and statistician John Wilder Tukey in 1965. They conceived the FFT from an algorithm that enables the discretization of principles established by Fourier in the early 19th century, thereby improving signal analysis and the understanding of oscillatory phenomena.

A valuable application of FFT is the decomposition of a spectrum into its various vibrational components, for example. It is also possible to apply this principle to the decomposition of electromagnetic waves such as light. However, concerning its use for failure detection in maintenance, the focus is on the decomposition of mechanical waves – vibrations.

Understanding the propagation of this mechanical disturbance is crucial for comprehending and applying vibration analysis, especially for spectral analysis. Thus, it is possible to visualize the different frequency components present in the signal and analyze their behavior.

**What is spectral analysis?**

Spectral analysis is a set that encompasses the statistical analysis of time series plus Fourier analysis methods. It is, therefore, a way to organize and interpret vibration. That is, each vibration has a signature, a unique characteristic, and through decomposition, it is possible to clearly perceive each one of them.

Thus, in an asset, there will be several vibrational components occurring simultaneously, which add up and generate the perception that there is only one vibration. The FFT serves precisely to separate them and thus analyze each one carefully.

When there is something different in this vibration, it may be indicative of a failure. That is, a bearing under certain conditions will present a spectral signature, and if there is a problem, there will be specific disturbances in this signature. This indicates whether it is looseness, wear, etc.

To learn how to identify failures using spectral analysis, read more about it here.

From this, there are some mathematical and statistical tools to view different information from the spectrum and then perform the analyses.

**Main Spectrum Analysis Applied to Maintenance**

The spectrum is the complete range of frequencies. That is, it encompasses waves from low to high frequency. Spectrum analysis serves, therefore, to observe a particular signal within this range. Thus, it is possible to continuously monitor the spectrum to capture transient effects, low-power signals, and other sources of interference.

Spectral analysis consists of techniques for the study and interpretation of signals and systems. The possibility of decomposing a signal provides an understanding of its characteristics and behavior. It thus offers a series of benefits, such as pattern identification, removal of unwanted noise, and performance optimization.

In practical terms, spectral analysis allows the identification of signs of failure in components of an asset. Moreover, it is possible to apply different forms of analysis (which combine variables and distinct representations) to the same asset to facilitate this visualization. This is because some failures in specific components become more evident in certain types of analysis.

Considering this, the Dynamox web platform offers various types of analysis that facilitate the analyst’s diagnosis. Find out more about each of them:

**Time Waveform Analysis**

The **waveform analysis** is basically the representation of instantaneous values as a function of time. That is, it occurs through the relationship: frequency X time. This relationship is described by f = 1/p, where 1 is the frequency (Hz) and p is the period in seconds (or the time required to complete 1 cycle). Thus, knowing this relationship makes it possible to determine the frequency components from the raw data of the waveform.

In the Dynamox platform, it can be presented in linear form (as in the image above), circular, and orbital.

An example of the application of this type of technique is the identification of faults in the outer race of bearing housings. Usually, they manifest as a succession of evenly spaced peaks in the time domain, representing the passage of rolling elements over cracks formed throughout the bearing’s lifespan.

**Circular Analysis**

The **circular waveform** has direct interaction with the Cartesian waveform graph. It illustrates the start and end regions of the user-defined rotations.

The definition of the RPM value also has direct interaction with other features that depend on this parameter, such as bearing frequency markers.

Similarly, there is the reflection in the circular waveform of different metrics, filter parameters, and other signal transformations applied to the Cartesian visualization.

An example of the application of this type of technique is the identification of failures in the outer race of bearing housings. They usually manifest as a succession of evenly spaced peaks in the time domain, representing the passage of rolling elements over cracks formed throughout the bearing’s lifespan.

Autocorrelation is another technique that can be used in conjunction with circular waveform. Especially when applied to the signal and visualized in the polar system, it helps make patterns of interest more evident during the analysis.

Read more about : Circular Waveform: Interactive graph to asset failure (dynamox.net)

**Autocorrelation of the waveform**

**Waveform autocorrelation** is a tool for identifying failures in machinery that, through analysis in the time domain, correlates waveforms with themselves to calculate a correlation factor at each moment in time. Thus, it highlights what is repetitive and what is random.

Read more about : Autocorrelation: identifying machine vibration signals (dynamox.net) (available in Portuguese)

**Orbit Analysis**

**Orbit Analysis** allows for identifying vibration issues where other techniques cannot provide sufficient information for analysis. An example is machines equipped with plain bearings or struts (turbines, pumps, generators, compressors, etc.). This is because observation occurs based on the frequency, amplitude, and phase of the component, through the transducer and the stability state of the operation. Therefore, it is necessary to collect triaxial data (as done by Dynamox sensors) for the analysis to work.

Hence, the tool is ideal for examining rotor movements and evaluating any movement restrictions that cause vibration. It also helps determine lubrication status and bearing conditions.

**Spectral Waterfall**

The **waterfall spectrum** graph (also known as a spectral waterfall) allows for the visualization of a series of spectra from the same monitoring point collected at different times in a single graph.

This tool is essential for observing variations in spectra over time. Thus, it is possible to highlight the emergence of premature failures or changes in equipment operating conditions in terms of frequency ranges. One possible application is identifying the evolution of a bearing defect in a conveyor belt’s pulley.

Read more about Pioneering solution waterfall spectrum for maintenance (dynamox.net)

**Cepstrum**

Frequency spectra have many vibrational components, making interpretation difficult. Therefore, the Cepstrum is useful for identifying families of harmonics and sidebands in complex and consistent signals. In this way, the periodicities of the spectrum are analyzed as if it were a waveform. In this way, the focus of the analysis is on the characteristics of the sidebands rather than the machine’s normal engagement frequency.

Consequently, one indication for using the Cepstrum is to identify failures in gear systems. This is because, through this analysis, it is possible to perceive the frequency of the sidebands. After all, it is these sidebands that define the severity of the defect. The more sidebands and the more energy, the more severe the defect.

**Acceleration Envelope**

**Spectral envelope analysis** allows determining the repetition rates of impacts that generate stress waves, identifying defective components. This analysis method enables the visualization of micro impacts at high frequencies by attenuating the low frequencies and highlighting the high ones. This characteristic allows for the visualization of a smaller range but with high resolution.

The tool is recommended for detecting faults in bearings, mechanical problems that can generate shocks, such as gears in bad condition, backlash, loosening, etc.

**Dynamox Platform: Supplementary Spectral Analysis**

**Prediction**

Prediction is a feature that allows for forecasting the worsening of a fault. That is, by correctly configuring the asset’s characteristics and having a history available, the tool can provide a predictability cone for the worsening of the problem. This projection is based on the most critical scenario of activity and enables maintenance scheduling.

If all parameters are well configured, it is possible to predict faults many days in advance. **Prediction can be applied to all monitored assets**, becoming extremely valuable information for efficient maintenance planning.

**Comparison of Spectral Analyses**

Another highly useful functionality for understanding asset performance is the comparison between spectral analyses. In the Dynamox platform, it is possible to compare analyses from different periods, as well as from different spots. This allows for observing the evolution of a problem or noticing differences between identical assets.

The comparison works for spectra from different samples of the same asset, as well as for comparisons between spots of the same machine. In this case, it’s possible to analyze the left side versus the right side, for example. This functionality is available for all types of analysis on the platform.

Interested in bringing the Dynamox solution to your industry? Contact us to find out more!