Filtering of Vibration Data for SBR A Measurements

This is part 2 in the series "How does the Frogwatch Vibration Sensor work?". In this article, we discuss the signal processing applied in the Frogwatch Vibration Sensor when configured for the Dutch SBR A measurement method.

Signal processing flow chart

This flow chart schematically shows what happens to the measured sensor values for each of the axes (X, Y, and Z). Throughout the rest of the article, we refer to the P labels of the blocks in the flow chart. The S branches represent the real-time data that is, for example, available via Triggered Traces.

P1. Scaling to acceleration

The Frogwatch Vibration Sensor uses MEMS accelerometers to measure acceleration. The acceleration signal is sampled at 1000 samples per second. The first step in the chain is scaling the raw sensor output to acceleration in mm/s2. For this scaling, we multiply the raw sensor data by a coefficient that is determined separately for each axis (X, Y, Z) through calibration against gravity.

After this, we have an unfiltered acceleration signal that still contains gravity. This means there is a 0 Hz component of about 9810 mm/s2 on one (or distributed over) of the axes. This is a very large signal compared to the typical SBR values we monitor for. For example, SBR Category 2 has threshold values between 5 and 20 mm/s2.

P2. Highpass filter

The highpass filter allows higher frequencies to pass and blocks low frequencies. In the Frogwatch Sensor, this filter serves two purposes:

1. Removing the gravity component. Since this is a 0 Hz signal, it is attenuated to the point of being negligible.
2. The low-frequency part of the prescribed SBR filter.

The gray area is prescribed by the SBR A guideline. The filter magnitude response must stay within this area to comply with the guidelines. This means there is some leeway. We have designed this filter so that it is suitable for both SBR A and SBR B.

P3. Lowpass filter

SBR guidelines specify that we are only interested in frequencies between 1 and 100 Hz for SBR A. Therefore, we use a lowpass filter to filter out frequencies above 100 Hz. This effectively makes the signal 'cleaner' because all high-frequency noise is filtered out.

In this figure, the transfer function of the lowpass filter is combined with that of the highpass filter. So, we are actually looking at the bandpass filter that meets the SBR A guidelines.

P4. Integrator

SBR standards are defined in the velocity domain and use mm/s as the unit. This originated because earlier generations of vibration sensors were based on geophone technology. A geophone measures velocity.

To be able to assess against the SBR standards and to allow the devices to be calibrated according to SBR guidelines, we integrate the acceleration data to velocity. Mathematically, an integrator is nothing more than a first-order lowpass filter. In the Laplace domain, we write this filter as

with $s=j\omega ,\omega =2\pi f$

The problem with an ideal integrator is that for frequencies $s<1$ the magnitude is amplified, e.g. $\frac{1}{s}=\frac{1}{0.01}=100$. So signals at frequency s=0.01 are amplified by a factor of 100, which would have very strange consequences.

To prevent this, we use a so-called leaky integrator. This ensures that the gain never exceeds 1.0.

In this figure, the blue line shows the transfer function of an ideal integrator. Both the green line and the dashed dark line are suitable leaky integrators. Within the spectrum of interest for SBR, they closely follow the ideal integrator. Below 1 Hz, they provide attenuation to keep the signal stable. The green line adds an extra 3dB of attenuation, which results in slightly less noise in the final result.

Calibration

This was, in broad terms, the data processing pipeline as implemented in the Frogwatch Vibration Sensor. The entire data processing pipeline as described here is ultimately tested during calibration. The calibration is performed in the velocity domain, and the measured values are read from the Frogwatch Dashboard. This way, we test the entire chain: sensors, filters, integrator, communication, database, and visualization.

In the figure above, you can see the result of a Frogwatch V2 Vibration Sensor on the shaker table at SONOR Calibration. The shaker table provides a constant acceleration at varying frequencies. In the graph below, you can clearly see the effect of filtering outside the range of 1-100Hz. There, a difference arises compared to the shaker table because our filters (as expected) attenuate the signal. The curves clearly show the attenuating effect of $\frac{1}{2\pi f}$ of the integrator.