• How to Gather PSD Data

IST Hardware tech tip 

November, 1999 
Daniel R. Burk 
IST Applications Engineering 

mailto: Hello from IST Applications Engineering!

If you are reading this on our website, it means that DynaMax Suite version 1.2.0 may be already on-line. If you are a DynaMax Suite user, be sure to download the latest update! I have been using the code for some consulting projects, and now use it exclusively. The only thing I dont use it for is for processing Acceleration Spectral Density (ASD) analysis for whole-body vibration applications. This is a rather esoteric function that relatively few users require, so it is not high on the list of development priorities. Ah, the realities of budgeting development time.

The Tech Tips for November 1999  deal with how to choose and configure an instrumentation configuration for vibration measurements. There are several different topics that are covered, from defining the environment, choosing the correct equipment, and the configuration of this equipment.

Part of my analysis involves the use of power spectral density analysis (PSD). This particular application compares two different suspension configurations in an electric vehicle. Since the test involves the study of vibration, the recording control parameters were optimized to cover the bandwidth of interest.  Now, the information presented below goes into the specifics of how to set up the individual parameters for vibration, but you can always choose to use the "quick-start vibration" profiles found in DynaMax Suite. The quick-starts encode some of the following rules in order to make it easy to set up your test. It is, however, beneficial to know HOW the quick-start menus arrive at their particular configurations, because it allows you to fine-tune your setup for a given test scenario. 

Collecting data for Power Spectral Density analysis
Do you use your recorder for the analysis of Power Spectral Density profiles? If so, here are a few tips that will help you collect your data in a more effective manner.

Tip # 1: Define your environment

If you measure the profile of a train boxcar and compare it to that from the floor of an Indy race car, you would notice a completely different profile. There would be the obvious difference in amplitude. There would also be a considerable difference in the measure of high-frequency energy. There would also be quite a large difference in the length of the test. Each of these variables governs the proper setup of a recorder. For instance: A boxcar sees acceleration that peaks at between 10 and 20 g. An Indy car may see normal accelerations as high as 100 g. A Boxcar generally does not transmit significant energy at frequencies higher than 200 Hz. An Indy car may have significant energy up to 600 Hz. A box car might require a test period measured in days. An Indy car may finish the test in a matter of a few hours. Because of these large differences, we must optimize the recorder setup for each situation. Setup parameters such as sample rate, event length, and recorder on/off times are governed by these differences.

Here are a few questions you can use to define your environment:

What is the expected frequency distribution? 100 Hz? 500 Hz? 1 kHz?
What is the expected peak magnitude for acceleration? 10 g? 50g? 100g?
What is the length of the test? 1 Hr? 1 Day? 1 Hour?

Tip # 2: Choose your recording equipment and know the limitations

piezoresistive accelerometers 
IST recorders are generally equipped with internal Piezoresistive accelerometers. These accelerometers have a characteristic frequency response that starts at DC and ends generally between 400 Hz and 2 kHz, depending on the accelerometer range. In many instances, this response is sufficient. However, there are cases where the internal accelerometers are not the best choice.

piezoelectric accelerometers 
External Piezoelectric accelerometers are available for use with IST recorders that can measure to several Kilohertz. These accelerometers sacrifice DC response for a wide bandwidth. They are also good for a place where mass is a consideration. If, for instance, you are intent on measuring the PSD profile of a small object such as a soup can during transportation, then the mass of an entire EDR recorder is bound to influence your measurement. In this case, the use of an external accelerometer that weighs only a few grams would be a better choice.

space considerations 
External accelerometers are also useful in situations where space is at a premium. When you are measuring vibration inside a structure like a piece of electronic equipment, or in a space that is hard to access, you may wish to mount an external accelerometer. Your recorder may then be installed outside where you have ready access to it.

cabling tradeoffs 
One thing to consider with external accelerometers is the fact that they are attached to the recorder with cables. These cables are susceptible to physical damage as well as Radio Frequency interference. Route them carefully.

Anti-aliasing filters 
Anti-aliasing filters are installed in all IST recorders. Aliasing is a phenomenon where high-frequency signals appear in digitized data as a low frequency harmonic. If the frequency of a signal is greater than one-half that of the sample rate, there exists the possibility of aliasing. There is no way to determine if a recorded signal is real or alludes. Thus, the filters are used to reduce the likelihood. One consequence of these filters is that they limit your frequency response of your recorder. Thus, your PSD measurements are bandwidth limited by the sample rate, transducer response, and the anti-aliasing filter response.

Range and resolution 
The full-scale range of your recorder is very important when it comes to the measurement of PSD data. If you have a low full-scale range, you risk clipping of the waveform. Clipping will introduce high frequency and near-DC spikes on the PSD plot. Less known is problems associated with a full-scale range that is too large. A 200-g recorder is not well equipped for measuring sub-10g measurements: It leads to quantization error. Because the data is digitized, there are only several discrete numbers that can be used to "quantize" a given acceleration measurement. Quantization error will adversely influence low-amplitude PSD measurements.

Tip # 3: Choose the optimum RCPs

There are three areas of concern that are specific to the collection of PSD data. They are:

Maximum Frequency of Interest: This parameter determines your sample rate. The sample rate equals twice the highest frequency of interest. Thus, if you want to record a maximum of 1 kHz frequency for your data, your sample rate must be 2 kHz. One note: Does your recorder allow you to record the maximum frequency of interest? Internal accelerometers have a lower frequency response: 400 Hz for a 10g system, up to 2 kHz for a 200g system. In addition, the anti-aliasing filters may dampen the higher frequencies. Typically, most 10g systems are equipped with anti-aliasing filters of 200 Hz and below. One note: You may wish to oversample your data anyway. There will be frequencies that are resolved over and above the anti-aliasing filter frequency, but the lower frequencies will have a bit more accurate measurement of amplitude. Just be sure to note that the instrument damps the higher frequencies (above the response frequency of your recorder).
Frequency Resolution: This is determined by the overall event length. An event is a continuous record of samples. The longer the event, the more frequency resolution from a given PSD. There is more to it than that though: Most PSD profiles are calculated from the data by using a Fast Fourier Transform (FFT). The FFT requires that your event length be an integer power of two in length. This limits our choices for the record length to 128, 256, 512, 1024, 4096, or 8192 samples.
If we use event lengths that are different than these numbers, some form of adding or subtracting from the event must be accomplished. If we pad the event with data points of zero value (The zero padding technique), we introduce distortions to the PSD profile. We, in effect, attempt to resolve to a finer resolution than the data allows. If we subtract samples (Truncate each event), we resolve to a more coarse resolution than allowed by the data. Thus, it is good practice to simply designate a sample size equal to an integer power of two. IST Recorders refer to this as the "maximum event length", or "total event length". DynaMax DOS also requires that the system use equal-length windows via the overwrite mode.

Frequency resolution is the maximum measured frequency divided by the number of available frequency bands. A quick formula to determine your resolution is Frequency resolution= Sample Rate/ Number of samples per event.

Tip # 4: Triggering Criteria: Choose your acceleration measurement thresholds:

I participated on a project a few years ago that involved the measurement of forklift vibrations at the floor/human foot interface. To that end, we placed EDR3 recorders as close as possible to the human foot, and gathered the data over the course of a week. The systems were set up in overwrite mode, with a very low trigger threshold so that the system would trigger whenever there was movement in the forklift.

In the end, we ended up with 500 events that were scattered throughout about eight shifts. The system triggered between 2,000 and 12,000 times during the shift. At the time, this did not seem to be a problem, as we were event averaging these plots. An averaged composite of the PSD profile across all 500 events yielded a PSD Profile that indicated the worst amplitude over the course of the test period with respect to frequency.

Unfortunately, this skewed the results of the test towards a "worst-case" measurement rather than a true characterization of the factory floor.

A better method for gathering PSD data might have been to shorten up the test to ensure that the overwrite ratio stayed low. Another method would be to set up overwrite to gather more events than can possibly fit in memory, and simply let the system expire when memory runs out.

An excellent method is to use the time-triggered events (slow track data) as a trigger source for acceleration measurements. Turn off the amplitude triggering, let the system periodically sample acceleration, and remove the system from the test when the memory fills up. Let the chips fall where they may, and remove those events with no obvious acceleration measurements from the summation. This provides a statistically random sampling of the acceleration environment, independent of the vibration. One variation of this method is to move the periodic trigger off-board, and use the external trigger input in conjunction with a smart box.. You can now control WHEN the system stores a vibration measurement, and trigger periodically only when there is the potential of movement. This is handy when the vehicle that you are testing spends a lot of time in a stationary position. 

In conclusion, when preparing your recorder for the collection of vibration data for PSD analysis, you must:

Define your operating Environment. Although it is hard to know the exact system response, you will have to estimate the high-frequency content of your system. You should also estimate the peak amplitude of acceleration of the system, and the length of the test.
Choose your recording equipment: Based on your assumptions of the environment, you should choose equipment that has the correct full-scale measurement range, as well as frequency band width. Internal piezoresistive accelerometers generally have better DC response, but less high-frequency response than piezoelectric accelerometers. The total response of the recording equipment will be a function of sample rate, accelerometer response, and anti-aliasing filter frequency response.
Choose your RCPs. The highest possible frequency of measurement is half the sample rate. Oversampling improves amplitude measurement accuracy. Event size should be an even power of two. The frequency resolution of your PSD is dependent on sample rate and event length. If you oversample, part of your PSD profile may exceed the frequency response of your recorder and thus should be noted.
Avoid excessive overwriting if you want an average amplitude measurement of the overall test. Consider using threshold triggering without overwrite, or use a periodic function to randomly trigger the recorder without regard to acceleration level.

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