Test standards often include a random vibration test to validate aerospace reliability. The test generates a power spectral density (PSD) graph that identifies resonances across a frequency range and shows if they are within a defined tolerance.
Does the PSD graph show what is really happening on the shaker table? When it comes to short-duration random tests that are common for expensive launch systems and complex payloads, the answer is not always yes.
Short-duration Random Tests
The underlying issue with short-duration aerospace vibration testing is the process of PSD estimation.
Control software generates a PSD graph by separating time-domain data into a series of frames, calculating the fast Fourier transform (FFT) for each frame, and then averaging the power values of the FFTs. The inherent nature of randomness leads to significant variations in the PSD called estimation errors. The error resolves after the software captures sufficient data frames to contribute to the calculation. This process takes time, which engineers do not have during a short-duration test.
Aerospace test engineers want a random test that starts at a low level but ramps up quickly, highlights resonances, and ends before the device under test (DUT) is overly stressed. Visually, these necessities translate to a smooth line on the PSD graph that has some resonance peaks and stays within an established tolerance range.
Low-Level Data Multiplication
When the standard method of PSD estimation does not fulfill an aerospace engineer’s time constraints, they may seek an alternative. While some PSD estimation methods produce a visually appealing PSD, the data can be misleading.
A popular approach to achieving an appealing PSD graph is data multiplication. This method starts the test at a low level; as the test ramps up, it multiplies the low-level data by a scaling factor and presents it as full-level data. Data multiplication assumes that a DUT’s mechanical behavior at the high level mimics the low-level behavior, which is untrue.
PSD graph with low-level data multiplication | PSD graph of real behavior
Multiplying low-level data is not only inaccurate but potentially dangerous. Resonances typically shift in frequency and amplitude when signal levels change. Data multiplication masks the changes at the product resonances, making the test engineer unaware of potentially damaging vibration energy levels.
iDOF®: A Statistically Valid Approach
Fortunately, there is a statistically valid approach to quickly creating an accurate PSD graph. The variance in a random test is based on Chi-squared distribution. It can be calculated and removed from the PSD plot, thereby “removing” the estimation error. This approach delivers a smooth but accurate PSD graph.
The Instant Degrees of Freedom® (iDOF) software is an optional module in the VibrationVIEW software suite. It uses an advanced algorithm to deliver accurate, low-variance PSD estimates that are calculated more quickly than traditional averaging. iDOF removes the estimation error while displaying the control error, which is the true difference between the PSD of the signal and the demand PSD.
With iDOF, aerospace test engineers can verify that the control PSD is maintained within tolerance throughout the test and make informed conclusions on how a test affects the DUT. Most importantly, the engineer can stop the test before a resonance inflicts damage.
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