How to Read Centile Statistical Vibration Data

I recently wrote about timescales and temporal variability in vibration environments. 

In that post, and in a related talk I gave at ESTECH, I presented a set of data broken down statistically. That is to say, I took long-term monitoring data and calculated centile statistics for the period. This plot illustrates how often various vibration levels might be expected. Here's an example:

The above data illustrate the likelihood of encountering different vibration levels in a laboratory. Each underlying data point is a 30-second linear average. In this case, the statistics are based on 960 observations over the course of 480 minutes between 9AM and 5PM. 

Like spatial statistics, temporal statistics are based on multiple observations. Unlike spatial statistics, however, far more data points may be collected. Considerably greater detail is available, and you can generate representations far more finely-grained than "min-max" ranges or averages.

For field or building-wide surveys, our practice is to supplement the spatial data gathered across the site with data from (at least) one location gathered over time. This really helps illustrate how much of the observed variability in the spatial data might actually be due to temporal variability. If vibrations from mechanical systems are present, and if they cycle on and off (like an air compressor), then it also helps you see those impacts.

But interpreting these data isn't intuitive for some people. So, I figured it would be helpful to explain a little bit about how to look at centile statistical vibration data. Returning to the example above: Each Ln curve illustrates the vibration level exceeded n% of the time. This is calculated for each frequency point in the spectrum. In other words, the L10 spectrum isn't the spectrum that was exceeded 10% of the time. Instead, the L10 spectrum shows the level that was exceeded at each individual frequency 10% of the time.

One of the most striking features of centile statistical data is the presence of "bulges" and "pinches". The large bulge between 8 and 10Hz is indicative of a very wide range of vibration levels at this frequency – the distribution is skewed, such that higher vibration levels are more likely than at other frequencies. The pinch at 63Hz indicates that the range of vibration levels has collapsed, perhaps due to the dominance of near-constant vibrations emitted by a continuously-operating nearby machine.

The figure may be read to say that, for a typical work day on the 30-sec timescale, this particular environment meets VC-D/E 99.7% of the time; VC-E 99% of the time; and VC-E/F 95% of the time. There are other interpretations, but this is the most straightforward way to think about it.

Of course, your input data (the monitoring period) has to be representative. If you do a 24-hour measurement, then the statistics won't make perfect sense in a lab that operates 9~5. And if you are looking for rare events, then you'd better collect enough data to be able to make credible statements about those rare events.