Leveraging Long-Duration, Low-Level Acoustic Excitation for Modal Testing: From the NASA VIPER Acoustic Modal Experiment

With excerpts published at the 34^th Aerospace Testing Seminar, March 31^st, 2025, Los Angeles, CA, USA.

Author: Dale Schick with information from ATA Engineering and NASA Johnson Spaceflight Center.

Introduction

The launch vehicle Direct Field Acoustic Noise (DFAN) test for the NASA Volatiles Investigating Polar Exploration Rover (VIPER) required an acoustic test level of 138.2 dB OASPL, which was delivered by 24 Neutron™ acoustic devices configured in six stacks of four devices per stack. The shape, amplitude, and duration of this spectrum is conducive to simulating and qualifying for launches, but sometimes the goal of the test is to characterize the test article. To move beyond simple Operating Deflection Shapes (ODS) testing, ARS and ATA Engineering collaborated with NASA on VIPER to explore what modes can be extracted during DFAN testing.

The VIPER spacecraft program limited exposure pertaining to sound levels in terms of duration and amplitude, so it was important to operate the modal test at a level significantly lower than that of the DFAN test. The program agreed to a flat spectrum of 110 dB OASPL, ranging from 20 to 10,000 Hz, for a duration of ten minutes. To characterize any nonlinearities, a −6 dB run and a −3 dB run were also performed in succession prior to the 0 dB run. The subsequent data processing is from the 0 dB (110 dB OASPL) portion, as no significant nonlinearities were noted.

Extracting Modes from Long-Duration Acoustic Excitation

The Neutron™ acoustic devices do not rely on constructive interference to create the noise field, so they were ideal to operate as acoustic modal exciters, as each device, or group of devices, can act as incoherent sources. Multiple incoherent sources controlled simultaneously can help to extract closely spaced modes when processed using multiple references.

Being a test of opportunity, schedule demands during the test campaign dictated that there was no time to experiment with excitation levels (or methods) to determine what most adequately excited the structure. As such, the data was processed in several ways to produce the best possible results within the various frequency bands.

For frequencies where the acoustic devices are most active (typically from 20 to 10,080 Hz), FRF was processed using the microphones as a reference. Doing so leads to cleaner data processing, but there is a risk at higher frequencies of “zeros” in the microphone auto-spectrum matrix due to destructive interference between the Neutrons, which would result in fictitious structural modes. These fictitious modes can be identified by observing the singular values of the microphone cross-spectrum matrix. A fictitious mode would have a near-zero singular value.

FRF-synthesized cross-spectrum data was generated to account for the phase lag. This was done by assuming that the input cross-spectrum matrix, [Sxx], is equal to the identity matrix, which is a typical assumption in operational modal analysis. Operational modal analysis tools were then used to extract modes from the FRF-synthesized output cross-spectrum matrix, [Syy].

It was observed during the acoustically excited modal test that frequencies below the active output of the acoustic devices were present in the test-measured cross-spectrum matrix. Therefore, at these lower frequencies, the test-measured cross-spectrum matrix operational modal analysis was used to extract shapes, even though they were somewhat noisy. To validate this method, ATA Engineering processed the combined FRF-synthesized and test-measured cross-spectrum data using the ATA Engineering developed IMAT™ modal analysis software packages, particularly the OPoly modal estimation software. When using cross-spectrum data, OPoly calculates all four poles for each extracted mode, even though only two are commonly used in traditional modal parameter estimation of FRFs. The additional two poles, shown in Figure 1, with negative damping, are needed to account for the Hermitian part of the FRF matrix, [Hyx]ᴴ, associated with cross-spectrum matrices.

Figure 1: Four-pole solution for cross spectrum referenced modes

What the Data Revealed

The resulting auto spectra from processing the acoustic modal run produced the cleanest data of all the instrumentation, due to their ability to range well above the noise floor. This force data also revealed modes well below the lower excitation frequency of twenty hertz. In Figure 2, the low-frequency modes are clear and were used in further processing of the acceleration data, where possible.

Figure 2: Auto spectrum data from force sensors

Since the acoustic excitation generated ranged, generally, from the 20 Hz octave band to the 10,000 Hz octave band, it was of special interest to attempt to characterize the modes discovered below this frequency range. The predicted true fixed-base natural frequencies for the first two modes were below 20 Hz, and it was expected that compliance in the test stand would reduce the frequencies even further.

The FRF-synthesized and test-measured cross spectra were partitioned into rows associated with the accelerometers and load cells, and columns associated with the force sensors.

The top of Figure 3 compares PSD responses from those measured during the test (i.e., processed from directly measured test data) with the PSD responses synthesized from a single mode. These plots show good agreement in the PSD responses. The bottom of Figure 3 shows the extracted mode shapes, natural frequencies, and damping.

Figure 3: Modes obtained from cross-spectra

Excitation Type, and Time Matters

It was found that longer test runs, even at a lower test level, can allow for cleaner data, smaller frequency spacing, and better definition of peaks for modal extraction. Additionally, the same features of the acoustic devices that allow them to achieve high test levels without constructive interference, as systems that use separate bandpass boxes do, also made them well-suited to assume the use of the identity matrix for the input cross-spectrum [Sxx], which is a necessary assumption for operational modal analysis.In further Application Notes, we will explore how ARS and ATA Engineering were able to extend modal measurements into infrasound territory to characterize modes that are traditionally only excited with shakers.