Signal Processing for Machinery Diagnostic Engineers: A Practical Approach

Diagnosing rotating machinery has consistently been a vital part of the oil and gas industry and will continue to be so. With advancements in digital computers, the use of analog oscilloscopes and spectrum analyzers is now a thing of the past. Since computers operate in the digital realm, it's necessary to convert the analog vibration signals produced by rotating equipment into a digital format. In this series of articles, we’ll explore the signal processing process from the perspective of a machinery diagnostic engineer.

Sampling

The process of turning an analog signal into a digital one is known as "sampling." To understand this better, let’s walk through the entire process, starting with an analog signal and ending with a digital signal. First, the analog signal goes through a low-pass filter, called an anti-aliasing filter (AAF), which eliminates any frequency components that exceed a certain limit. Then, the signal's voltage level is "quantized" by an Analog-to-Digital Converter (ADC). Once sampling is complete, the signal can be used for direct representation or further processing. In the following sections, we’ll take a closer look at each stage of this process.

The Analogue-To-Digital Converter (ADC)

"Analogue-to-digital" converter or ADC is a device incorporated in all data acquisition instruments and is used to convert the input analog signal into a digital or discrete signal so that it can be further processed.

To keep things simple, let’s focus on one key aspect of ADCs: the number of bits. This number directly impacts the amplitude resolution, determining how precisely the ADC slices the full-scale measurement range. The more bits an ADC has, the higher the resolution. For instance, an 8-bit ADC divides the vertical full scale into 256 levels (2^8), while a 16-bit ADC provides 65,536 levels (2^16).

It's important to note that the bit count is fixed once the data acquisition instrument is chosen. For practical applications like vibration amplitude measurements, a resolution of 12 bits is generally sufficient. While some modern ADCs offer 24 or even 32 bits, higher bit counts come with increased memory requirements.

Let’s take the 12-bit example when recording a vibration signal from a typical machine: a full-scale range of 20 mils is usually adequate. In this case, using 12 bits provides a resolution of about 0.0049 mils. At this point, it’s worth asking: do we need more resolution?

The bit number is a fixed design feature of the data collector and cannot be configured.

Time Resolution - Sampling Frequency

Time resolution is primarily determined by how quickly the instrument collects data or the sampling frequency. Unlike amplitude resolution, time resolution can be configured within certain limits when setting up the data acquisition device.

In the case below, the machine is running at 1700 rpm, with the dominant frequency being synchronous (1X). The same analogue signal from the vibration transducer was sampled at two different rates 640 Hz and 25,600 Hz. Both plots use the same vertical and horizontal scales for comparison.

The signal sampled at 640 Hz appears quite smooth, with an overall amplitude of 6 mils peak-to-peak (pp). In contrast, the signal sampled at 25,600 Hz shows a less uniform waveform, with spikes that raise the amplitude from 6.6 to 8.5 mils pp. Because of the low sampling rate in the first sample, these spikes go undetected. This illustrates that a low sampling rate can result in lost information from the original signal.

Aliasing Filter - Nyquist theorem (AAF)

Aliasing occurs when a signal is sampled at a rate that is too low to accurately capture its frequency components. This can lead to higher-frequency signals being misrepresented as lower-frequency ones, resulting in distortion and loss of important information.

Imagine trying to capture a fast-rotating object with a camera that takes only a few frames per second. If the object moves too quickly, the captured images may suggest that it’s moving slower or even in the opposite direction. Similarly, in signal processing, aliasing can create confusing or misleading representations of the original signal, obscuring critical details and affecting analysis or interpretation.

Even though the Nyquist theorem ensures that we can detect frequencies of interest, unwanted higher-frequency components can still create aliased signals within our desired frequency range.

For example, if we want to analyze frequency activity between 0 and 1000 Hz, the Nyquist theorem dictates that we must sample at twice the maximum frequency, which would be 2000 Hz. This ensures that any frequency up to 1000 Hz will be accurately represented in the reconstructed signal. However, if the analog signal includes a random 1600 Hz component, it can lead to aliasing. According to signal sampling theory, any frequency component above half the sampling frequency will produce an aliased component at the sampling frequency minus the original frequency. In this case, a 1600 Hz component will create an alias at 2000 Hz - 1600 Hz = 400 Hz. This means we would mistakenly observe a 400 Hz frequency component that isn’t real, which could lead to confusion and wasted time in diagnosing issues.

To prevent this, antialiasing filters are often applied to the original signal before sampling. These filters, typically low-pass filters, remove frequency components above the specified frequency span, thus eliminating the potential for aliasing.

To conclude, once the analog signal passes through the anti-aliasing filter (AAF) to eliminate unwanted higher-frequency components, the Analog-to-Digital Converter (ADC) takes over, transforming the continuous signal into a discrete signal suitable for processing by digital computers. At this point, the time waveform of the vibration measurement is ready to be displayed. However, to obtain the spectrum, additional operations are necessary, which we will cover in the next article.

References

1- FUNDAMENTALS OF SIGNAL PROCESSING APPLIED TO ROTATING MACHINERY DIAGNOSTICS-Gaston H. Desimone

2-https://youtu.be/HRjmPe0fncA?si=mqZgfxRx7BJIQGTt

3-https://youtu.be/sRq_gM8r6pI?si=vKtXOLKJfaFIRaRY

4- https://youtu.be/Jv5FU8oUWEY?si=zGAXO78nv0K2dTE9