Where to we go from here?
To summarize, we have at our disposal a simple method allowing to isolate the instrumental noise of any setup, provided that we have 3 independent sensors (not necessarily identical). The convergence rate will be dependent on the Signal to Noise Ratio, but ultimately this estimator is unbiased, it will converge to the true value.
The ultimate objective, of course in not to perform a beauty contest among sensors. What we want to do is performing actual measurements in the field, where signal levels can not be controlled (in particular, OMA tasks, or even more specifically, the directly useful motion transmissibility functions ).
Knowing one’s sensor noise allows of course to wisely choose among vendor’s (and trust me, you can’t trust them. Well, not all of them).
But what are we to do with the numbers. Say, we have this PSD amplitude of 10-3mm/s²/Hz1/2 around 1Hz. How small or big is that number, anyway?
Perhaps the simplest way to decide on this is to compare with the natural earth background noise. After all, if the instrumental noise is comparable to the earth background noise or even below, this means, at least in principle that we will never need artificial excitation to characterize an actual structure. The trouble being that, background noise it is heavily dependent on the actual location being considered, even letting aside cultural (human induced) contribution.
To illustrate this, let’s turn to another classic, the paper by Peterson [2].
It appears that, at least for the most seismically active regions, the background noise expressed using acceleration has PSD amplitude around 1Hz about 10-12 (m/s²)^2/Hz, that is an Amplitude Spectral Density of about 10-6 (m/s²)^2/Hz1/2. Now, here comes the good news: that’s about the same level than that of our instrument setup. And for frequencies above 1Hz, the signal-noise-ratio would become largely positive.
In real life, the micro-seismic noise will generally exhibit a significant -if not dominant- contribution from the cultural noise above 2Hz. The natural environment will also play a role. For example nearby buildings or trees act as “transducers”, converting the wind power into ground vibrations. Rail or road traffic, obviously, will tend to contribute, with an efficiency drastically dependent on track or road condition.
Conclusion
As it appears, there are indeed lots of situations where a conventional vibration measurement setup, with suitable configuration and adequate shielding from external influences, can be used to characterize large structures and components, only by taking advantage of background vibrations.
Now, there will always be some need for de-noising of some sort, but we will save those aspects for an upcoming article. In the meantime, happy holidays to you all and see you in 2025.
References
- J. Bendat and A. Piersol – Random Data – Analysis and measurement procedures – 4th edition – Wiley.
- J. Peterson – Observation and modeling of seismic background noise – USGS – Open File report 93-322