Investigation of MIMO Random Control Applied to Direct Field Acoustic Testing

Transcription

1 Investigation of MIMO Random Control Applied to Direct Field Acoustic Testing Adam Johnson, Robert Lawson Quartus Engineering Inc., San Diego, CA Vince Fogt, Ken Fiorelli NASA Johnson Space Center, Houston, TX Paul Bremner AeroHydroPLUS, Del Mar CA SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 1

2 Approved for Public Release SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 2

3 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 3

4 Qualification of Direct Field Acoustic Testing for NASA Manned Space Missions Reverberant Chamber Testing Direct Field Acoustic Testing (DFAT) G pp xx, ; G pp sin k 0 k 0 x - x x - x SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 4

5 Vibration response under random acoustic loading FE / BEM G vv S x, / r g m 4 ff, r 2 g r r 1 j r Hz S S G, ; x x x x dx dx ff, r r pp r A sin 0 G x x DAF ff, r pp r r k A 0 x k x dxdx = G pp 2 j r SEA 2 A n 2 2 Gvv, G 2 2 pp, j g / Hz 2gm SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 5

6 SOUND PRESSURE DFAT vs Reverberation Chamber Testing: Qualification Metrics 1. Third octave, RMS spectrum level ±3 db 2. Spatial uniformity ±2 db 3. Spatial correlation TBD SPACECRAFT VIBRATION 4. Third octave, RMS spectrum level ±3 db SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 6

7 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 7

8 Test Results - Acoustic field DFAT SPL versus Test Spec. Typical RESPONSE Mic. SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 8

9 Test Results Spacecraft Vibration Reverb Chamber versus DFAT SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 9

10 Test Results Spatial Correlation Reverb. Chamber versus DFAT Reverberation Chamber Test 2 DAF,3D G pp 2 pp xx, ; x, G x, G sin k0 x k0 x pp 2 Direct Field Acoustic Test? SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 10

11 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 11

12 MIMO Random Control Theory Wave6 BEM solves for deterministic frequency response between input voltage (velocity) and output sound pressure (Eq. 1) p1 h11 h12 h1 m v1 p 2 h21 h22 h 2m v 2 p h h h v r r1 r 2 rm m p Hv Random drive signals result in random pressures which can only be quantified statistically - autospectrum G pp, coherence γ 2 ij and phase φ ij depends on: BOTH cross spectrum of input voltages (velocities) AND frequency response functions (Eq. 2) G E p p * T pp * T E Hv Hv vv H G H * T s G11 G12 j G1 j G21 j G22 G2s j G r1 j Gr 2 j Grs SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 12

13 MIMO Random Control for Diffuse Acoustic Field - I For DAF we can fully define the required G pp (jω) pressure cross spectrum matrix 2 2 (Eq. 3) G rs j G 2 rs r s pp 1 12 j 1s j j 1 j s 2 2 r1 j r2 j 1 sin k0 xr-xs x, x, k0 xr-xs 2 DAF Target Cross Spectrum Coh. And use inverse of the wave6 frequency response function matrix H rm (jω) to define the required cross spectrum of input voltages (velocities) (Eq. 2.1) G H G H vv 1 1 *T pp SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 13

14 MIMO Random Control for Diffuse Acoustic Field - III Furthermore, a MIMO controller can utilize a rectangular control strategy # Outputs > # Inputs, therefore there is no exact solution HG vv H T G pp 0 the result is a least squares solution G vv = H + G pp H T + Where the pseudoinverse is derived from SVD of H H = UWV T H + = V T W 1 U = H T H 1 H T G vv = H T H 1 H T G pp H H T 1 H SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 14

15 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 15

16 esta DFAT Experimental Data Experimental data shows axial cross spectra do not approach Diffuse Acoustic Field Test Data Spatial Coherence Vertical stacks have the same input along the entire height which inhibits axial decoupling DFAT Loud Speaker Configuration Axial Azimuthal SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 16

17 BEM Scattering Simulation Scattering simulations include the effects of sound reflecting off of spacecraft and speaker surfaces Frequency Response Function Evaluation p1 h11 h12 h1 m v1 p 2 h21 h22 h 2m v 2 p h h h v r r1 r 2 rm m p Hv FRFs are evaluated one speaker at a time FRFs include effects of sound bouncing off remaining geometry SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 17

18 BEM Direct Field Simulation Direct field simulations assume that effects of scattering are negligible with respect to direct speaker output Frequency Response Function Evaluation Direct Field Simulation p1 h11 h12 h1 m v1 p 2 h21 h22 h 2m v 2 p h h h v r r1 r 2 rm m p Hv FRFs are evaluated one speaker at a time FRFs neglect effects of sound bouncing off remaining geometry SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 18

19 BEM Simulation versus Test DFAT Spatial Correlation Scattering Simulation Direct Field Simulation SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 19

20 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 20

21 Split Simulation Dividing the speakers into 2 partitions (vertically) Split 2 Configuration *All 15 stacks, split vertically into halves (Up to 30 independent inputs) SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 21

22 Random Uncontrolled Input Spatial Coherence No Split Split 2 Direct Field Split 2 configuration reduced axial coherence as predicted SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 22

23 Random Uncontrolled Input Spatial Coherence No Split Split 2 Scatter Split 2 configuration reduced axial coherence as predicted SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 23

24 Split 2 Alternate Input Configuration Random Uncontrolled Input Reduce independent inputs from 30 to 15: 15 independent inputs Independent inputs are not vertically adjacent 100% Correlated Woofer / Mid Stacks 100% Correlated Sub Stacks *Reducing the number of independent inputs does not significantly affect the cross spectrum results SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 24

25 MIMO Control Simulation DAF specified as controller target cross-spectrum Control mics are used for feedback by the controller Response mics are not seen by the controller Used to asses system performance DFAT Test Set-up With Mic Locations Shown Control Mics Response Mics SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 25

26 15 X 15 Control Simulation G H G H vv 1 1 *T pp Control mics are diffuse, but response mics are not Control mics meet SPL requirement, but response mics are significantly louder SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 26

27 15 X 30 Control Simulation G vv = H T H 1 H T G pp H H T 1 H Control mics and response mics are an approximation of DAF Control mics and response mics are within 3 db of test spec SPL SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 27

28 Outline Motivation DFAT versus Reverb Test results MIMO Control Theory Numerical Simulation of DFA Test Alternative DFAT & MIMO Control Configurations What we learned SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 28

29 What we learned 1. MIMO Random Control can achieve Ideal DAF but only at control mics NOT at other locations; leading to spatial non-uniformity (up to +10 db over drive) Controller target G pp (jω) should be based on in-situ measured (scattered) cross spectrum with multiple statistically independent inputs 2. Numerical (BEM) simulation can predict non-daf spatial correlation of complex, full scale test configurations 3. Simulations indicate DFAT vertical spatial correlation can be improved by: Vertical split of loudspeaker banks AND / OR Rectangular (vs square) MIMO random control SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 29

30 Questions? SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 30

31 MIMO Random Control for Diffuse Acoustic Field - II HOWEVER for certain physical configurations of audio sources and control microphones it may be physically impossible for the frequency response functions to support the mixing of response pressures required to achieve a DAF; viz V 2 (jω) P s (jω) V 2 (jω) P s (jω) V 1 (jω) V 1 (jω) Aligned, well-conditioned H matrix P r (jω) Orthogonal, poorly conditioned H matrix P r (jω) In which case, the H matrix may be singular (not invertible) Physically, this means that some impossibly large drive voltages would be required to achieve the specified DAF SCLV Dynamic Environments Workshop, 27 June 2018 Export Control Information 31