Case Study of an Octave Band Control Method for Structural Response Notching

Figure 2 – Neutron Device – Front and Side Views

To expand on point A, this new device was different from typical loudspeakers because it was full range, meaning it covered the minimum and maximum frequencies required by a typical launch vehicle. As a result, there was no need to adjust the timing of separate band passes when changing the size (Elevation and Diameter) of the test area. This, coupled with the fact that each Neutron could deliver sound from an incoherent and completely stochastic source, contributed to a more flexible and scalable field.

Addressing point B, the field produced by this type of system was found to be more spatially uniform when used with DUT’s that are (or contain) large flexural absorbers. [5] This was partly because the stacks of Neutrons were not required to be coherent vertically and therefore did not produce large wavefronts [6] that rely on joint acceptance for excitation.

Lastly, to point C, the modular design of the Neutron device was such that any sized system could be deployed with the same level of complexity as a smaller one. Since a single Neutron connects with a single cable to one amplifier in a standardized rack, the deployment of stacks even twenty or forty feet tall are all wired the same way. Additionally, the control loops are simplified for this arrangement, as they treat each Neutron like a small acoustic field, so no advanced mixing is required.

3. LAUNCH QUALIFICATION

For both RFAN and DFAN tests, launch vehicle manufacturers provide their customers an acoustic environment, typically specified in 1/1 or 1/3 Octave band format, as part of a design qualification manual. These octave-based requirements are then simulated by one of the methods to create an acoustic field which is applied to a DUT.

Sometimes multiple launch vehicle spectra are combined if specifics about the launch are unknown at the time of testing. This is done simply by taking the maximum level at each octave or third-octave band and applying it to the overall test level, a practice known as enveloping. When using an enveloped environment, it is then determined by the spacecraft and launch vehicle manufacturers which type of test is most suited to the DUT.

In DFAN testing for spacecraft, different test levels – Flight, Protoflight, Protoqualification (Protoqual), and Qualification – are applied depending on the needs of the DUT. For routine tests, Flight testing can be performed at the exact levels expected during the mission to validate the flight hardware, with no added margin. More typically for routine products, Protoflight testing is used, which combines elements of Qualification and Flight testing, adding a small margin (typically +3 dB) to ensure the hardware’s robustness while still being conservative with respect to the flight hardware.

For first-production DUT’s, Protoqualification testing can serve as an intermediate step, testing at levels between flight and qualification or for longer durations than Protoflight to validate new designs or manufacturing changes. Qualification test levels are the most rigorous, exposing non-flight units to levels significantly above what is expected during the mission (often +6 dB) to uncover potential weaknesses. This ensures that the design is robust enough to handle worst-case scenarios, though the hardware used in these tests is usually not always intended for actual flight.

3.1 DFAN Notching

Many DUT’s, especially fully assembled spacecraft, are best served when testing as they are meant to fly, wherein little modification is made to the acoustic environment. Sometimes, however, portions of the spectrum are modified to attenuate specific frequencies in a practice known as “notching.”

One such case of notching would have been considered when utilizing legacy DFAN testing systems. In this case, a spacecraft manufacturer may have considered notching when there is a risk that standing waves could induce structural resonances that might damage sensitive components of the spacecraft. Particularly when using speakers which follow the design of a typical concert line array source, which rely on coherence to achieve the 140 to 150 dB OASPL environments, interference patterns can develop. These interference patterns appear as spectrally dependent high/low spots in the field which can overexcite structural modes, causing excessive vibrations that could compromise the integrity of the spacecraft or its subsystems. Notching has been employed as a protective measure to attenuate these frequencies on critical components, thereby preventing over-stressing of the spacecraft structure.

Modern DFAN testing methods, such as the one used for this experiment, are designed to attain launch levels with minimal summation. In this type of environment, the spatial uniformity is such that the need to notch would only be necessary if conditions of the DUT are compromised.

For example, a spacecraft assembled with all components intended for flight will benefit from testing exactly to the envelope (Plus the desired qualification level, if required) without any component notches, because this is most likely to represent the actual launch environment.

Sometimes in the manufacturing process, a DUT may have one or more components which are not flight-like, such as mass mock-ups or development units. These development units may be used for convenience or some other production constraint. Either way, the structural response from a standard environment may induce damage that would not occur in-flight because the coupled load between the mock-up and DUT are different than that of the flight units.

It is precisely this condition that may require a field with diffuse acoustic properties to attenuate, or notch, at certain frequencies based on a structural response.

4. CONTROL METHODS

4.1 Narrowband Control

Legacy control strategies for Direct Field Acoustic Noise testing employ a modified random-vibration control method. This type of control strategy utilizes weighted exponential averaging of field measurements which must undergo Fast Fourier Transformations (FFT’s) and conversion to Power Spectral Density (PSD) before the averaging functions are applied. This process, as well as the exponential averaging, slows the controller’s ability to react to changes in the acoustic field significantly. For notching, however, the process provides a simple basis of control already designed to notch acceleration signals for a mechanically coupled vibration test.

This method of control makes it possible to easily apply notches to the field, but controllability suffers, as it is reliant on a slower exponential averaging technique and phase targeting that severely limit the number of available outputs. This works well for smaller tests that only need twelve Neutron devices but does not scale well for tests which require many more devices, such as one hundred to two-hundred devices.

4.2 Octave Control

A second version of acoustic control is based on one-third octave processing and has been used to some success in RFAN environments for decades. This method uses multiple overlapping Finite Impulse Response (FIR) filters to quickly determine the ultimate pressure at each octave or third-octave band. This process can happen in one second or less, controlling rapid changes to the field, potentially from power fluctuations or structural response, immediately.

Figure 3 – Example – Octave Control Method

This method has been shown to be more scalable as, currently, forty-eight or more outputs can be combined to produce a field which is closer to the ideal diffuse acoustic field. This is more easily done because there is no need to control the phase or cross power between loops, as doing so exponentially increases the required processing power to complete a test

Within this octave-band control method, however, did not exist a method for notching the acoustic field from acceleration responses on a DUT. It was posited by the authors that some combination of the above two methods would provide more accurate and stable technique by controlling octaves but notching in the narrowband, with both occurring in the same control system. This method could even prioritize the spectral response of the one third octave band requirements by boosting un-notched frequencies within each band where notching is present. In this way, the test could maintain not just the overall sound pressure level, but also each individual octave band as required by the launch manual. The following test aims to examine this method of notching.

5. TEST METHODOLOGY

Though very little is published on the subject, notching acoustic fields for DFAN is not a novel concept. There have been tests where attenuation was applied to flight DUT’s with some success. For these cases, however, a narrowband vibration control strategy was used to control the field as well as apply the notch. Due to the advantages of controlling in the one-third octave, this study focused on using an octave band control method for the control algorithm but also used a narrowband process to apply the attenuation. In short, this test was designed to determine whether it’s possible to use an octave-band control method to maintain the test requirements while attenuating the field in the narrowband.

5.1 Test Configuration

The authors originally planned to perform two separate tests to determine whether the objective of the study could be achieved. Due to the results of the second configuration, as will be evident later in this report, a third was added. Ultimately, three configurations were used and will be referred to as the following when presenting results:

01: No Notching Applied
02: Notching Applied
03: Adjusted (deeper) Notching Applied

5.2 Test Article

Typically, the test article is a complex structure to which notching will be applied. For this study, however, a simple aluminum honeycomb panel with epoxy edge treatment was used to simplify the analysis. This also provided a worst-case scenario where the test article is nearly undamped at several critical frequencies. Physically, the panel was 96” x 48” x .5” and had four mounting points for which to affix to a frame made of extruded aluminum. To measure the response of the panel, five Kistler triaxial accelerometers (3.6 gram) were used and mounted as shown in Figure 4.

A test level of 143.2 dB overall sound-pressure level at a duration of one minute was used for all test configurations and is detailed in Table 1.

Table 1- Test Levels

To conduct each test case, numerous equipment and instrumentation were used. Firstly, to control each of the twenty-four loops, a pre-polarized microphone assembly (PCB 378A12) consisting of a capsule and an amplification unit were used. These microphones were calibrated just prior to testing using a National Institute of Standards and Technology (NIST) calibrated acoustic source (Larson Davis CAL200,) which compensated for local altitude, temperature, and humidity.

To acquire the test panel response, five Kistler 8763 series accelerometers were used due to their low mass (3.6 grams) and flexible mounting options.

To power the twenty-four individual Neutron units, an ARS Core Rack was used for each grouping of six, totaling four. The control unit consisted of an ARS Drive, which uses six VRAI810 units from m+p International to convert the sensor voltages to digital data for both control and data acquisition, as well as six VRT4S4 units to provide twenty-four independent source outputs. These sources are then digitized for input to the DirectOut PRODIGY.MP unit, a commercial audio routing processor, to route the source signals to the Neutron devices.

All data for each test case was taken at a sample rate of 32,768 and processed with blocks of the same size, producing PSD measurements with sixty averages and at 1 Hz resolution. Octave plots were generated in the same way but using the ANSI standard for 1/3 octave processing. The charts for all octave responses include a nominal reference line (green) with upper and lower tolerances of +/- 3 dB (orange) and an upper abort tolerance of +6 dB (red) for clarity.

Table 2 – Test Equipment List

6. RESULTS

6.1 Pre-Notch Evaluation

Before applying the notch, the test profile from Table 1 was applied without attenuation to determine the overall panel response. The panel appeared to be minimally damped, with roughly sixteen lowly damped modes appearing between 25 and 2000 Hz. Three such modes were chosen specifically for notching, with a fourth designed to encompass a bandwidth, or several peaks simultaneously. This notch was intended to capture and attenuate three or more modes with a single setting. Of the five accelerometer locations, the four most reactive axes from A01, A02, A04 and A05 were chosen for the notch.

In Figure 6 below, a PSD from the z-axis response of four accelerometer locations is shown. The vertical lines indicate the center frequencies for the first, second, and third notch. For the fourth notch, the vertical lines indicate the upper and lower frequencies of the bandwidth. The red horizontal lines indicate the initial setting in g2/Hz for all notches.

Figure 6 – Panel Response – Notch Selections

The initial settings for the notches are more precisely described in Table 3. For each accelerometer channel, the notch is defined by a starting frequency (Notch Low, in the table below,) an ending frequency (Notch High) and a single value in g2/Hz (Notch 01) for flat notches or two values for sloped notches, with the starting and ending numbers appearing respectively.

Also in Table 3 are the precise values for the peaks as measured by the pretest evaluation run. For example, channel A01_Z indicated a peak value of 8.797 g2/Hz at a frequency of 98 Hz and the notch setting was set to 2g2/Hz between 93 and 105 Hz. The results of these settings will be described in the following section.

Table 3 – Notch Settings

6.2 Acoustic Notching Results 01

Similarly to the pre-notch evaluation, the acoustic profile in Table 1 was applied to the panel for a duration of sixty seconds. Prior to the full-level portion of the test, a -3 dB level was achieved for fifteen seconds. During that level, the channels began to notch allowing the field to start attenuation before jumping to the next level. This is a recommended practice to avoid over-testing the DUT.

Figure 7 – Control Average PSD – Without Notch vs. With Notch

In Figure 7 above, the blue trace depicts the average PSD of the control microphones without notching applied and the red trace is the same but with notching.

Presumably due to the undamped nature of the panel, the applied notches yielded ultimate values that were above that of the prescribed notch, as shown in Figure 8 below.

Figure 8 – A01_Z Without vs With Notch Applied

With a notch of 2 g2/Hz applied from 93 to 105 Hz, the actual value was reduced from 8.8 g2/Hz to 6.1 g2/Hz. Though a reduction of about thirty percent, the ultimate value was above the prescribed notch. It is not uncommon for narrowband notches, especially in vibration testing, to overshoot their settings and can depend on a number of factors including but not limited to a) the delta frequency of the spectral lines in control, b) the speed at which the control averages update, and c) the quality (q) factor of the peak to be notched.

Similarly to the A01_Z example, the rest of the notched channels exceeded their prescribed values, as shown in Table 4.

Table 4 – Measured Notch Values 01

Though the notching values of the control average, when viewed in PSD, exceeded their lower limits, the goal of this exercise was to determine if the individual octave bands could be achieved while simultaneously notching the test article.

When the same data in Figure 7 was processed in one third octaves, it was observed that this goal was achieved. By slightly boosting the narrowband lines within the octave-bands that had notches applied, the overall spectrum was unchanged from the pre-test run without any notching applied. In Figure 9 the blue trace with no notch is almost identical to the red trace with notching applied.

Figure 9 – Control Average 1/3 Octave – Without Notch vs.
With Notch

Though the overall goal was achieved in this experiment, it was decided by the authors to modify the notch settings to see if the initial values could be achieved at or below the prescribed levels, while still maintaining the integrity of the one-third octave band requirements.

6.3 Acoustic Notching Results 02

To achieve the initial notch values, each was adjusted to below the intended target. In Figure 10, the initial notch values are darkened to blue with the adjusted values appearing in red. Note that Notch Four’s beginning and ending values were flattened, so some overshoot was still expected within that region.

Figure 10 – Panel Response – Adjusted Notch Settings

With the test applied exactly as before but with the adjusted settings, as shown in Figure 11, the resulting acoustic field was much more attenuated within the ranges which were notched. It was also noted that the regions around the notches were boosted by the control algorithm more than in the previous run to maintain the one-third octave requirements. This is especially true in the notch with the lowest frequency (centered around 42 Hz) as there are less lines of resolution to resolve.

Figure 11 – Control Average PSD – Without Notch vs. With Adjusted Notch

Overall, the results of the adjusted notch were much more favorable in terms of not exceeding the prescribed notch. For example, the A01_Z measurement, which originally targeted 2 g2/Hz now achieved a peak value of 1.7 g2/Hz with a notch setting of 0.5 g2/Hz as shown in Figure 12.

Figure 12 – A01_Z With Adjusted Notch Applied

This trend was consistent with the rest of the notches save the very last value, as shown in Table 5, but this was expected due to the flattened nature of the fourth notch.

Table 5 – Measured Notch Values 02

Similarly to the original notch test, the adjusted notch values produced 1/3 octave results that were nearly unchanged from the requirement as shown in Figure 13. Only the one octave band centered at 31.5 Hz measured at slightly higher than the three-decibel upper tolerance, though it is common for tests which are performed in reverb chambers to allow for a six-decibel tolerance in this band, so this is a somewhat typical deviation. This slight deviation was likely due to the lack of spectral lines available for which to both a) notch the response channel in the narrowband, and b) boost the remaining frequencies within the one-third octave band to maintain the test requirements. This can easily be remedied by increasing the delta frequency in the narrowband processing, which is a proposed improvement because of this study.

Figure 13 – Control Average 1/3 Octave – Without Notch vs. With Adjusted Notch

The following figures show the additional plots of notches two through four in more detail.

In Figure 14 the original target of 0.8 g2/Hz was attenuated to 0.33 g2/Hz at 42 Hz. Note the slightly increased response at 30 Hz, which is an artifact of the algorithm attempting to maintain specification in the octave band.

Figure 14 – A02_Z – PSD – Adjusted Notch

In Figure 15 the original target of 2 g2/Hz was attenuated to 1.4 g2/Hz at 216 Hz.

Figure 15 – A03_Z – PSD – Adjusted Notch

In Figure 16 the original target from 0.2 g2/Hz at 346 Hz to 0.1 g2/Hz at 450 Hz, three separate peaks were reduced to 0.2, 0.18, and 0.17 g2/Hz at 360, 390, and 428 Hz, respectively.

Figure 16 – A05_Z – PSD – Adjusted Notch

CONCLUSION & FORWARD WORK

Notching in acoustic fields is not new and has been used in several testing situations. It is somewhat new, however, to notch in narrowband while controlling the output levels in one-third octaves to match the original specifications. In this study, both were achieved using the same control system and some observations were made.

Firstly, it is indeed possible to maintain the one-third octave specification for a DFAN test while still applying relatively deep structural attenuation in the narrowband. By boosting the frequencies within the one-third octave band that remain after a notch is applied, the specification can be maintained.

Secondly, similarly to a random vibration test with lowly- damped articles, the ultimate setting of the notch value needs to be considered in terms of the amount of damping on the test article. Since this test was performed with a highly reactive panel, the typical damping of a more structurally complex DUT did not exist. There exist some post processing techniques to invert the overshoot of the notch, as in the m+p VibControl software for Random Vibration Testing, which are effective at preventing overshoot and this can be done with basic analysis to create a more well-defined notch.

Looking back to the original progressive-wave test performed on the Apollo Lunar Module, which was made at great expense to simulate only a single environment, it seems pragmatic to continue evolving testing to more expansive and reusable means. This extends, even, to test articles from one iteration to another, as described in this paper, where notching may be required for attenuation.

The authors would like to thank the following for their invaluable contributions: Eric Friedlander, Jeremiah Leiter, Cassandra Dutt, Geoff Eckert, Nathan Kiefer, Zachary Crawford, Steve Nichols, and Gleb Kleyman.

Reference

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