Document
Chan-gi Pak, Ph.D.
NASA Dryden Flight Research Center
(FY13 Progress Report)
Follow on Research
Structural Dynamics Group, Aerostructures Branch (RS)
at NASA Dryden Flight Research Center
for Multi-Utility Technology Test-bed Aircraft
Chan-gi Pak-2 Baseline Joined Wing
Follow on Research for MUTT Aircraft
Structural Dynamic Finite Element Model Tuning for Flexible Wing Configuration Unsteady Aerodynamic Model Tuning Computation of Wing Shape (deflection and slope) from Measured Strain Flutter Optimization Study for MUTT Aircraft with Flexible Wing Configuration Aeroelastically Tailored Wing Designs Adaptive/Active Flexible Motion Control with Aeroservoelastic Uncertainties Multidisciplinary Design Optimization Structural Dynamics Group Chan-gi Pak, Ph.D.
NASA Dryden Flight Research Center Structural Dynamics Group, Aerostructures Branch (RS)
Adaptive/Active Flexible Motion Controls
with Aeroservoelastic System Uncertainties
GRT Data Model Drag Actuator On-Line Induced Chan-gi Pak-4 Reduction Parameter Estimation based on Delta Delta Control Law System Parameters Tool MDAO + - Error Prediction delta Model U Ride Model Unsteady Quality Control Validated Aerodynamic Servoelastic Tool + + Model MDAO Validated Aeroservoelastic FT Data nominal U Gust Load Alleviation Validated Structural Dynamic Model Tool MDAO Dynamically linear assumption will be used for the prediction error model. On-board computer should be powerful enough to perform on-line estimation and control law updates.
Flutter Assumptions and Limitations: Model Law based on data Dynamic Shape Gain Scheduling GVT Sensor Nominal Control Data Structural Suppression Sensing On-line Adaptive Active Flexible Motion Control System
Adaptive/Active Flexible Motion Controls with Aeroservoelastic System Uncertainties
time-varying uncertain flight conditions, transient and nonlinear unsteady aerodynamics and aeroelastic dynamic environments. On-line parameter estimation will be applied to the prediction error, uncertainties in the validated aeroservoelastic model.
The increased flexibility, due to weight reduction, creates an aircraft that is more susceptible to aeroelastic phenomena such as flutter, divergence, buzz, buffet, and gust response. Uncertainties are existed in aeroservoelastic system even with the test validated aeroservoelastic model due to An adaptive “delta control” methodology is proposed. The online update for the delta control gain is determined on the basis of a test-validated aircraft model whose predicted output response is compared with the actual aircraft measurements. The delta control scheme will act in addition to a nominal control law developed solely from the test- validated model so has to help offset some of the model’s inaccuracies and uncertainties.
Problem Objective Implementation of an adaptive delta control methodology during real flight test. Approach Structural Dynamics Group
Finite Element Model
of Multi Utility Technology Test-bed Aircraft
Creating a Test Validated Structural Dynamic
Chan-gi Pak-6 MUTT Aircraft Two Center Bodies One Rigid Wing Three Flexible Wings Ground Control Station Collaboration with AFRL & LMSW
Objectives
The primary objective of this study is to reduce uncertainties in the structural dynamic finite element model of an aircraft to increase the safety of flight. This model tuning technique is applied to improve the flutter prediction of the MUTT aircraft. This work is supported by the Aeronautics Research Mission Directorate (ARMD) Aero-Science Project (ASP) under Fundamental Aeronautics (FA) program.
Structural Dynamics Group Chan-gi Pak-7 Analysis Model Tuning Perform Flutter Dynamic Model Create Unsteady Structural Dynamic Structural Dynamic Validated Structural Aerodynamic Model Finite Element Model inertia, & GVT data Weight, C.G., Moment of Structural sizing information: Thickness, cross sectional area, area moment of inertia, etc. Point properties: lumped mass, spring constant, etc. Material properties: density, Young’s modulus, etc.
• • • Design Variables Constraints Model tuning is based on optimization.
Flutter Analysis Procedure @ NASA Dryden
Uncertainties in the structural dynamic model are minimized through the use of “model tuning technique” Based on analytical modes Use MDAO (Multidisciplinary Design, Analysis, and Optimization) tool with Model Tuning Capability or Standalone Model Tuning Code Some of the discrepancies come from analytical Finite Element modeling uncertainties, noise in the test results, and/or inadequate sensor and actuator locations. Not the same orientation for each sensor.
Flutter Analysis Validate Structural Dynamic Finite Element Model using Test Data and Update if needed Everyone believes the test data except for the experimentalist, and no one believes the finite element model except for the analyst.
Structural Dynamics Group Chan-gi Pak-8 Taurus XL DVPREL Launch Vehicle & Mode Shapes C.G., Moment of Nastran_103.f06 Nastran_103.bdf Measure Weight, Nastran_temp.bdf inertia, Frequencies, Mass Update Module Module Module input deck NASTRAN NASTRAN Frequency Mode Shape MAC Module Orthogonality Weight Module Modal Analysis X-37 DCTF ) tool Design Variables Script Commands Tool Quiet Spike Boom Optimizer Optimization Indices Performance G(x) Objective Constraints Function J & i k i i k
w J
i k i
k
J J
Structural Dynamic Model Tuning using Object Oriented Optimization Tool
: Weighting factor for the : Small tolerance value for i : Performance index : Objective function : Performance index k i k J w performance index J selected for objective function J selected for constraint functions e performance index Minimize “objective functions” using object oriented optimization (O which leverages existing tools and practices, and allows the easy integration and adoption of new state-of-the-art software. Minimize Such that X-37 Drogue Chute Test Fixture Quiet Spike Boom Aerostructures Test Wing 2 Glory Mishap Investigation: Use “Topology Optimization” Approach Optimization Problem Statements Previous applications ATW 2 Structural Dynamics Group Chan-gi Pak-9 Side Side Front Flow Top s odes for the flutter analysis m ode
Structural Dynamic Finite Element Model
Assembled configuration 8249 nodes Use 40 modes for the flutter analysis Based on MSC/NASTRAN code Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 Chan-gi Pak-10 5~10 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Target error (%) (%) 2.1 0.0 1.7 2.3 6.3 0.6 3.0 2.0 1.1 0.8 4.2 0.8 3.3 -0.2 -2.0 -5.3 -0.9 -0.2 -0.9 -1.2 -4.8 -0.1 -3.3 -15.9 Error 1.090 1.540 3.159 3.607 3.636 4.514 4.567 4.961 5.223 5.294 5.349 6.061 6.189 7.283 7.381 8.574 8.085 9.205 9.416 11.048 11.462 10.035 11.835 12.811 Baseline Frequency 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode Number NASTRAN Results 3.8 2.3 4.8 -3.0 -0.5 -8.3 -7.1 -4.6 -4.3 -4.4 -7.2 -4.1 -6.7 -8.1 -7.2 -3.4 N/A N/A -13.7 -14.9 -14.1 -13.9 -10.3 -10.4 Error (%) Final Design N/A N/A 1.035 1.534 2.781 3.068 3.522 4.127 4.262 4.467 4.530 4.569 5.159 5.404 5.815 8.133 8.812 9.433 9.798 9.889 10.186 10.969 11.355 11.986 Frequency 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 10.598 11.370 11.930 12.235 12.405 Frequency SWL AWL Mode Shape SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AW3B AW2T AEngL AWFA GVT data BoomH BoomV NLGFA SMLGL AMLGL SMLGFA AMLGFA
Frequencies of MUTT Aircraft: EFEW case
Table 1. The first 24 flexible modes of the MUTT aircraft with empty fuel empty water before model tuning 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode Number Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 Chan-gi Pak-11 5~10 5~10 5~10 5~10 5~10 Target error (%) 0.1 0.9 7.4 0.0 1.9 0.2 0.2 0.6 0.9 1.4 -0.9 -0.9 -3.5 -5.4 -1.4 -1.1 -1.0 -1.7 -2.0 -4.8 -4.9 -2.0 -3.4 -10.84 Error (%) 1.001 1.398 2.912 3.445 3.454 4.285 4.446 4.944 5.067 5.217 5.336 5.694 6.018 7.220 7.283 7.848 8.071 8.673 9.186 9.766 11.148 11.704 10.576 11.566 Baseline Frequency 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30 27 29 Mode Number NASTRAN Results 7.5 -6.3 -1.3 -5.5 -9.6 -5.7 -8.6 -2.5 -7.1 N/A N/A 22.4 15.3 -11.2 -19.7 -10.3 -14.3 -15.2 -15.5 -13.5 -14.5 -10.8 -12.1 -12.7 Error (%) Final Design N/A N/A 0.937 1.392 2.608 3.374 2.932 3.898 5.393 4.159 4.339 4.476 4.555 5.015 5.251 7.350 9.788 8.161 9.816 9.112 9.714 10.076 11.562 11.130 Frequency 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.540 11.862 11.977 Frequency SWL AWL Mode Shape SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AW3B AW2T AEngL AWFA GVT data BoomH BoomV SMLGL NLGFA AMLGL SMLGFA AMLGFA
Frequencies of MUTT Aircraft: FFFW Case
Table 2. The first 24 flexible modes of the MUTT aircraft with full fuel full water before model tuning 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode Number Structural Dynamics Group Chan-gi Pak-12 Front Side Sid Side Top Top Flow Fl Flow
Unsteady Aerodynamic Model
416 elements Select 16 reduced frequencies between 0 & 1 Mach = .130, .195, and .284 Linear Theory Use Matched Flutter Analysis Based on ZAERO code Structural Dynamics Group 3rd 0.0 0.0 0.0 2.5 0.0 0.0 0.0 0.5 0.1 0.0 0.4 0.0 0.0 1.0 40.2 28.1 33.6 28.1 98.9 8.6 0.0 2.2 0.0 0.0 7.5 0.1 1.7 0.0 0.0 0.0 0.0 0.6 0.3 2.7 2nd 39.0 39.7 76.4 97.0 M=0.284 Chan-gi Pak-13 1st 0.0 1.7 0.0 0.0 1.2 0.0 0.6 0.0 0.0 0.0 0.0 2.5 1.7 4.8 24.6 13.0 53.7 84.7 94.2 3rd 0.0 0.0 0.0 4.2 0.0 0.0 0.0 0.4 0.7 0.0 0.4 0.0 0.0 1.5 40.5 12.5 35.7 40.9 98.1 9.2 0.0 2.5 0.0 0.0 7.6 0.1 1.7 0.0 0.0 0.0 0.0 0.8 0.4 3.0 2nd 35.7 41.5 76.3 96.5 M=0.195 Baseline Model 1st 0.0 1.8 0.0 0.0 1.7 0.0 0.7 0.0 0.0 0.0 0.0 2.5 1.7 4.9 27.9 14.9 47.8 85.7 94.1 0.0 8.3 0.0 0.0 4.5 0.0 0.0 0.0 0.5 1.0 0.0 0.4 0.0 0.0 1.9 3rd 42.8 36.9 42.1 97.7 0.0 2.8 0.0 0.0 7.1 0.1 1.6 0.0 0.0 0.0 0.0 1.0 0.5 3.2 2nd 33.3 10.0 43.0 77.5 96.2 M=0.130 1st 0.0 1.9 0.0 0.0 2.6 0.0 0.7 0.0 0.0 0.0 0.0 2.6 1.8 5.1 33.7 17.0 38.6 87.4 93.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 1.7 0.0 1.9 4.1 3rd 25.2 35.1 35.1 95.4 95.4 8.1 0.0 0.0 0.0 0.7 0.6 1.0 0.0 0.0 0.1 0.3 0.0 0.8 0.0 2.2 2nd 34.3 54.1 96.5 97.8 M=0.284 1st 9.7 0.0 0.0 0.0 1.2 1.2 1.2 0.0 0.0 1.1 1.3 0.0 3.2 0.0 6.8 25.0 56.1 90.8 93.2 3rd 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.0 0.0 1.6 0.0 1.9 4.2 33.0 31.1 31.1 95.2 95.2 8.8 0.0 0.0 0.0 0.9 0.6 1.2 0.0 0.0 0.2 0.4 0.0 0.9 0.0 2.7 2nd 32.6 54.4 95.8 97.3 M=0.195 Final Design 1st 0.0 0.0 0.0 1.3 1.2 1.2 0.0 0.0 1.0 1.2 0.0 3.1 0.0 6.5 27.5 12.1 51.1 90.7 93.2 0.0 0.0 0.1 0.0 0.0 0.0 0.1 1.0 0.0 0.0 1.6 0.0 1.6 4.3 3rd 40.3 27.3 27.3 94.9 95.0 9.5 0.0 0.0 0.0 1.3 0.7 1.5 0.0 0.0 0.3 0.5 0.0 1.1 0.0 3.4 2nd 30.7 54.6 94.8 96.8 M=0.130 1st 0.0 0.0 0.0 1.5 1.3 1.2 0.0 0.0 1.0 1.1 0.0 2.9 0.0 6.2 31.6 15.0 44.3 90.9 93.7
Modal Participation Factor for EFEW Case
SWL Rigid Mode Shape SW1B SW1T AW1T SW2B SW3B SW2T AW2T AW1B SWFA AW2B BoomH SMLGL AMLGL AMLGFA Total Total 7 8 9 11 Sum of first five 12 13 14 10 15 18 19 25 26 28 30 1-6 : Second Flutter Mode : Third Flutter Mode : First Flutter Mode GVT Mode Primary Modes Secondary Modes st nd rd Structural Dynamics Group Number Table 9. Modal participation factors (%) of the MUTT aircraft with empty fuel empty water (EFEW) 1 2 3 0.0 1.2 0.0 0.0 0.0 9.5 2.1 2.4 0.0 0.0 0.0 4.5 3rd 32.4 68.3 50.7 93.8 8.9 0.0 0.7 0.0 0.0 0.0 0.0 0.0 0.8 0.2 1.0 2nd 36.0 30.8 89.5 22.2 98.6 M=0.284 Chan-gi Pak-14 1st 0.0 0.8 0.0 8.6 0.0 0.0 0.0 0.0 4.3 1.2 5.5 32.6 10.7 40.6 93.0 93.3 0.0 1.3 0.0 0.0 0.0 8.4 1.9 2.3 0.0 0.0 0.0 4.2 3rd 34.4 53.0 50.1 94.2 9.5 0.0 0.7 0.0 0.0 0.0 0.0 0.0 0.9 0.2 1.1 2nd 32.0 34.1 88.9 21.9 98.2 M=0.195 Baseline Model 1st 0.0 0.7 0.0 8.2 0.0 0.0 0.0 0.0 3.8 1.1 4.9 36.8 12.8 35.4 92.4 93.9 0.0 1.6 0.0 0.0 0.0 7.3 1.8 2.3 0.0 0.0 0.0 4.1 3rd 35.3 51.1 50.2 94.4 0.0 0.8 0.0 0.0 0.0 0.0 0.0 1.2 0.2 1.4 2nd 29.2 10.4 37.1 89.1 20.3 97.8 M=0.130 1st 0.0 0.7 0.0 7.6 0.0 0.0 0.0 0.0 3.1 0.9 4.0 42.1 14.9 29.7 91.2 95.0 3rd 0.0 0.0 0.0 1.4 0.0 1.4 0.0 0.0 0.0 5.6 7.0 39.0 25.0 25.0 89.0 90.4 0.0 0.0 0.1 0.0 7.5 0.0 0.5 0.5 0.6 0.0 1.6 2nd 40.5 10.3 39.5 90.3 97.9 M=0.284 1st 0.0 0.0 0.1 0.0 1.3 0.0 0.8 1.9 2.9 0.0 5.6 34.8 11.1 45.9 91.8 93.2 3rd 0.0 0.0 0.0 1.3 0.0 1.2 0.0 0.0 0.0 3.0 4.2 38.4 27.2 27.2 92.8 94.1 0.0 0.0 0.1 0.0 7.4 0.0 0.6 0.5 0.7 0.0 1.8 2nd 36.2 10.9 42.9 90.0 97.5 M=0.195 Final Design 1st 0.0 0.0 0.1 0.0 1.6 0.0 0.7 1.6 2.5 0.0 4.8 38.5 11.8 42.0 92.3 94.0 0.0 5.2 0.0 0.0 2.5 0.0 1.1 0.0 0.0 0.0 1.1 2.2 3rd 44.7 44.0 93.9 96.4 0.0 0.0 0.1 0.0 6.8 0.0 0.7 0.5 0.9 0.0 2.1 2nd 32.3 11.5 46.3 90.1 97.0 M=0.130 1st 0.0 0.0 0.1 0.0 1.9 0.0 0.5 1.3 2.0 0.0 3.8 42.4 12.9 38.0 93.3 95.3
Modal Participation Factor for FFFW Case
SWL Mode Rigid Shape SW1B SW1T SW2B SW3B AW1B AW1T AW2T BoomH NLGFA SMLGL AMLGL Total Total 7 8 9 11 12 13 14 16 19 24 25 30 1-6 Sum of first five Modes GVT : Second Flutter Mode Mode Primary Modes : Third Flutter Mode : First Flutter Mode Number Secondary st nd rd Structural Dynamics Group Table 10. Modal participation factors (%) of the MUTT aircraft with full fuel full water (FFFW) 1 2 3 Chan-gi Pak-15 L 1.8 1.15 V 1.6 L V 1.4 Model Tuning 30%~70% 1.2 35% 10% 0.8 Non-dimensional Speed 0.6 Flight Envelope 0.4 0.2 : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter Final Design Baseline 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 Non-dimensional Altitude
Flutter Boundaries
Structural Dynamics Group Chan-gi Pak-16 Sectional properties of the main Landing Gear Beams Young’s Modulus E Shear Modulus G Design Variable Linking: Right = Left Lumped mass properties of accelerometer cables
Optimization Run #1, #2, #3, & #4
Design Variables Design Variables Optimizer: DOT Run #1, #2, & #3: Improve Frequency Correlations Run #4: Improve Orthonomalized Mass Matrix Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 (%) 15.9 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-17 2.9 0.8 0.3 0.8 0.2 3.0 0.8 1.3 3.0 2.1 1.7 1.5 4.6 1.5 4.9 -2.4 -1.1 -1.3 -0.9 -0.7 -5.0 -0.1 -2.8 Error -15.9 Freq DOT1 1.098 1.555 3.233 3.637 4.451 4.600 5.236 5.350 7.283 7.392 8.625 8.068 9.206 3.747 4.703 5.215 6.105 6.218 9.487 11.086 11.537 10.034 11.897 13.008 Constraints 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 2.1 0.0 1.7 2.3 6.3 0.6 3.0 2.0 1.1 0.8 4.2 0.8 3.3 -0.2 -2.0 -5.3 -0.2 -0.9 -1.2 -4.8 -0.1 -3.3 -0.9 Error -15.9 Freq 1.090 1.540 3.159 3.607 3.636 4.514 4.567 4.961 5.223 5.294 5.349 6.061 6.189 7.283 7.381 8.574 8.085 9.205 9.416 Nastran Results 11.048 11.462 10.035 11.835 12.811 Baseline 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 3.8 2.3 4.8 -3.0 -0.5 -8.3 -7.1 -4.6 -4.3 -4.4 -7.2 -4.1 -6.7 -8.1 -7.2 -3.4 N/A N/A Error -13.7 -14.9 -14.1 -13.9 -10.3 -10.4 Objective Function Final Design Freq N/A N/A 1.035 1.534 2.781 3.068 3.522 4.127 4.262 4.467 4.530 4.569 5.159 5.404 5.815 8.133 8.812 9.433 9.798 9.889 10.186 10.969 11.355 11.986 Freq 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 11.370 11.930 10.598 12.235 12.405 Mode Shape SWL AWL
Optimization Run #1: EFEW Case
SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-18 0.8 0.1 1.1 0.9 1.7 2.2 0.2 1.1 0.6 1.5 2.7 -2.7 -2.7 -0.4 -2.2 -1.1 -1.0 -1.0 -1.6 -4.4 -4.8 -1.7 -3.0 Error -10.6 Freq DOT1 1.008 1.412 2.972 3.474 4.387 4.952 5.336 5.738 7.238 7.283 7.875 8.081 9.791 3.553 4.390 4.679 5.219 6.042 8.750 9.187 11.215 11.854 10.610 11.618 Constraints 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30 27 29 Mode # 0.1 0.9 7.4 0.0 1.9 0.2 0.2 0.6 0.9 1.4 -0.9 -0.9 -3.5 -5.4 -1.4 -1.1 -1.0 -1.7 -2.0 -4.8 -4.9 -2.0 -3.4 Error -10.84 Freq 1.001 1.398 2.912 3.445 3.454 4.285 4.446 4.944 5.067 5.217 5.336 5.694 6.018 7.220 7.283 7.848 8.071 8.673 9.186 9.766 Nastran Results 11.148 11.704 10.576 11.566 Baseline 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30 27 29 Mode # 7.5 -6.3 -1.3 -5.5 -9.6 -5.7 -8.6 -2.5 -7.1 N/A N/A Error 22.4 15.3 -11.2 -19.7 -10.3 -14.3 -15.2 -15.5 -13.5 -14.5 -10.8 -12.1 -12.7 Objective Function Final Design Freq N/A N/A 0.937 1.392 2.608 3.374 2.932 3.898 5.393 4.159 4.339 4.476 4.555 5.015 5.251 7.350 9.788 8.161 9.816 9.112 9.714 10.076 11.562 11.130 Freq 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.540 11.862 11.977 Mode Shape SWL AWL
Optimization Run #1: FFFW Case
SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-19 3.0 0.8 0.2 0.8 3.6 0.7 2.0 1.3 3.0 2.1 1.7 0.0 1.5 5.6 1.4 1.3 4.9 -2.4 -1.0 -1.2 -0.9 -0.8 -5.0 Error -13.3 Freq Constraints 1.099 1.554 3.229 3.634 3.747 4.600 4.498 4.758 5.219 5.240 5.351 6.104 6.216 7.283 7.391 8.627 8.068 9.214 9.483 DOT2 11.195 11.532 10.345 12.395 13.014 7 8 9 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 2.9 0.8 0.3 0.8 0.2 3.0 0.8 1.3 3.0 2.1 1.7 1.5 4.6 1.5 4.9 -2.4 -1.1 -1.3 -0.9 -0.7 -5.0 -0.1 -2.8 Nastran Results Error -15.9 Freq 3.233 5.236 7.283 8.068 9.206 1.098 1.555 3.637 3.747 4.451 4.600 4.703 5.215 5.350 6.105 6.218 7.392 8.625 9.487 DOT1 11.086 11.537 10.034 11.897 13.008 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # Objective Function Freq 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 10.598 11.370 11.930 12.235 12.405 SWL AWL Mode Shape SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #2: EFEW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-20 0.9 0.0 1.0 0.9 0.4 3.0 2.1 0.2 1.0 0.7 1.5 2.8 1.2 -2.7 -2.7 -1.8 -1.0 -1.0 -4.5 -4.8 -0.2 -8.2 -1.1 -1.7 Error Freq 1.009 1.411 2.968 3.471 3.552 4.385 4.425 4.739 4.972 5.218 5.336 5.736 6.040 7.236 7.283 7.874 8.081 8.743 9.192 9.943 Constraints DOT2 11.213 11.860 10.885 12.117 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 29 27 30 Mode # 0.8 0.1 1.1 0.9 1.7 2.2 0.2 1.1 0.6 1.5 2.7 -4.8 -2.7 -2.7 -0.4 -2.2 -1.1 -1.0 -1.0 -1.6 -4.4 -1.7 -3.0 Nastran Results Error -10.6 Freq 1.008 1.412 2.972 3.474 3.553 4.387 4.390 4.679 4.952 5.219 5.336 5.738 6.042 7.238 7.283 7.875 8.081 8.750 9.187 9.791 DOT1 11.215 11.854 10.610 11.618 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 30 27 29 Mode # Objective Function Freq 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.862 11.977 11.540 SWL AWL Mode Shape SW1B SW1T SWFA AW1T SW2B NLGL SW3B SW2T AW2T AW1B AW2B SEngL AWFA AW3B AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #2: FFFW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 (%) 3~5 13.3 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-21 2.7 0.5 0.6 3.4 0.6 2.0 1.1 3.0 2.1 1.5 0.0 1.3 5.6 1.3 1.4 4.7 -0.1 -2.7 -1.1 -1.3 -0.9 -0.8 -5.0 Error -13.3 Freq Constraints 1.097 1.550 3.220 3.627 3.735 4.590 4.495 4.758 5.217 5.237 5.351 6.093 6.211 7.283 7.388 8.614 8.067 9.214 9.466 DOT3 11.192 11.522 10.344 12.407 12.989 7 8 9 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 3.0 0.8 0.2 0.8 3.6 0.7 2.0 1.3 3.0 2.1 1.7 0.0 1.5 5.6 1.4 1.3 4.9 -2.4 -1.0 -1.2 -0.9 -0.8 -5.0 Nastran Results Error -13.3 Freq 3.229 5.240 7.283 8.068 9.214 1.099 1.554 3.634 3.747 4.600 4.498 4.758 5.219 5.351 6.104 6.216 7.391 8.627 9.483 DOT2 11.195 11.532 10.345 12.395 13.014 7 8 9 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # Objective Function Freq 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 10.598 11.370 11.930 12.235 12.405 SWL AWL Mode Shape SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #3: EFEW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-22 0.6 0.7 0.6 0.3 3.0 2.1 0.2 0.8 0.7 1.4 2.6 1.3 -0.3 -2.9 -3.0 -1.9 -1.0 -1.2 -4.5 -4.8 -0.3 -8.2 -1.1 -1.8 Error Freq 1.006 1.407 2.960 3.464 3.541 4.372 4.420 4.739 4.967 5.218 5.336 5.727 6.036 7.232 7.283 7.867 8.078 8.725 9.192 9.932 Constraints DOT3 11.205 11.843 10.888 12.128 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 29 27 30 Mode # 0.9 0.0 1.0 0.9 0.4 3.0 2.1 0.2 1.0 0.7 1.5 2.8 1.2 -4.8 -2.7 -2.7 -1.8 -1.1 -1.0 -1.0 -1.7 -4.5 -0.2 -8.2 Nastran Results Error Freq 1.009 1.411 2.968 3.471 3.552 4.385 4.425 4.739 4.972 5.218 5.336 5.736 6.040 7.236 7.283 7.874 8.081 8.743 9.192 9.943 DOT2 11.213 11.860 10.885 12.117 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 29 27 30 Mode # Freq 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.862 11.977 11.540 SWL AWL Mode Shape SW1B SW1T SWFA AW1T SW2B NLGL SW3B SW2T AW2T AW1B AW2B SEngL AWFA AW3B AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #3: FFFW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 30 0.02 0.01 0.16 0.04 0.04 0.02 0.00 0.00 0.17 1.00 -0.02 -0.02 -0.09 -0.09 -0.01 0.00 0.07 0.10 0.02 0.00 0.00 1.00 -0.04 -0.01 -0.01 -0.03 -0.05 28 0.01 0.01 0.02 0.02 0.04 0.00 0.06 1.00 0.17 -0.03 -0.02 -0.01 -0.08 -0.02 -0.01 Chan-gi Pak-23 0.00 0.02 0.01 0.01 0.01 0.00 0.01 1.00 -0.01 -0.05 -0.01 -0.05 27 0.02 0.02 0.02 0.00 0.03 0.06 1.00 0.00 -0.02 -0.10 -0.07 -0.03 -0.01 -0.01 -0.01 0.03 0.01 0.00 0.02 0.00 0.02 0.00 1.00 0.01 0.00 -0.05 -0.04 25 0.03 0.00 0.07 0.01 0.00 0.00 1.00 0.06 0.06 -0.02 -0.02 -0.05 -0.01 -0.05 -0.01 19 0.00 0.05 0.07 0.04 1.00 0.03 0.00 0.00 0.00 0.05 0.01 0.02 1.00 0.00 -0.02 -0.01 -0.02 -0.02 -0.04 -0.01 -0.01 -0.01 -0.03 -0.04 -0.03 -0.05 -0.05 Constraints 18 0.02 0.04 0.05 0.03 0.01 0.08 1.00 0.00 0.04 0.02 -0.02 -0.03 -0.11 -0.05 -0.01 0.00 0.00 0.00 0.01 1.00 0.00 0.00 0.02 -0.01 -0.01 -0.01 -0.02 15 0.01 0.01 0.00 0.01 0.01 1.00 0.08 0.00 0.04 -0.02 -0.01 -0.04 -0.03 -0.01 -0.02 0.02 0.18 1.00 0.01 0.02 0.01 -0.07 -0.01 -0.03 -0.08 -0.02 -0.03 14 0.00 0.00 0.18 0.01 1.00 0.01 0.01 0.00 0.02 0.04 -0.03 -0.02 -0.08 -0.04 -0.01 0.01 0.10 0.01 1.00 0.02 0.00 0.10 -0.06 -0.01 -0.08 -0.01 -0.05 13 0.02 0.05 1.00 0.01 0.04 0.01 0.16 -0.01 -0.08 -0.10 -0.14 -0.04 -0.11 -0.03 -0.08 0.03 0.00 0.03 0.02 1.00 0.18 0.01 0.03 0.02 0.00 0.01 1.00 0.01 0.18 0.00 0.01 -0.06 -0.14 -0.03 -0.05 -0.07 -0.01 -0.09 -0.03 -0.01 -0.05 -0.01 11 0.00 0.00 0.05 1.00 0.02 0.00 0.05 0.02 0.02 -0.01 -0.10 -0.01 -0.01 -0.02 -0.09 0.01 0.01 1.00 0.10 0.02 0.01 0.02 0.01 0.07 -0.02 -0.03 -0.01 10 0.03 1.00 0.05 0.00 0.04 0.07 0.07 -0.04 -0.07 -0.06 -0.08 -0.08 -0.10 -0.02 -0.02 1.00 0.01 0.00 0.05 0.00 -0.05 -0.01 -0.02 -0.01 -0.03 -0.01 -0.01 0.01 1.00 0.00 0.03 0.01 0.02 0.05 0.02 0.01 -0.05 -0.07 -0.01 -0.02 -0.02 -0.02 0.01 1.00 0.01 0.00 0.00 0.00 0.01 0.02 Objective Function -0.01 -0.06 -0.01 -0.04 1.00 0.01 0.03 0.00 0.00 0.05 0.00 0.01 0.00 0.00 0.02 0.01 -0.02 -0.03 -0.03 1.00 0.03 0.02 0.03 0.01 0.02 -0.02 -0.05 -0.04 -0.01 -0.03 -0.02 -0.02 -0.01 -0.02 1.00 0.01 0.01 0.02 0.01 0.03 0.00 0.00 -0.05 -0.07 -0.01 -0.02 7 8 9 10 11 12 13 14 15 18 19 25 27 28 30 7 8 9 11 12 13 14 16 19 24 25 28
Orthonormalized Mass Matrices After #3
Number Number GVT Mode GVT Mode SWL Mode Shape SW1B SW1T SW2B SW3B SW2T SWL AW1B SWFA AW1T AW2B AW2T Mode Shape BoomH SW1B SW1T SW2B SW3B AW1B AW1T AW2T SMLGL BoomH Structural Dynamics Group AMLGL NLGFA AMLGFA SMLGL AMLGL Table 15. Orthonormalized mass matrix of the MUTT aircraft after the third model tuning procedure (with empty fuel empty water; Auto Correlation) Table 16. Orthonormalized mass matrix of the MUTT after the third model tuning procedure (with full fuel full water; Auto Correlation) 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 3.4 (%) 13.3 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-24 2.2 0.7 0.6 3.4 0.6 2.0 1.0 3.0 2.1 1.5 0.0 1.4 5.7 1.4 1.3 4.7 -0.1 -2.5 -1.0 -1.2 -0.9 -0.7 -5.0 Error -13.3 Freq Constraints 1.091 1.553 3.220 3.628 3.742 4.591 4.492 4.757 5.218 5.240 5.350 6.089 6.222 7.283 7.392 8.615 8.068 9.214 9.477 DOT4 11.198 11.533 10.344 12.393 12.993 7 8 9 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 2.7 0.5 0.6 3.4 0.6 2.0 1.1 3.0 2.1 1.5 0.0 1.3 5.6 1.3 1.4 4.7 -0.1 -2.7 -1.1 -1.3 -0.9 -0.8 -5.0 Nastran Results Error -13.3 Freq 3.220 5.237 6.211 7.283 8.067 9.214 1.097 1.550 3.627 3.735 4.590 4.495 4.758 5.217 5.351 6.093 7.388 8.614 9.466 DOT3 11.192 11.522 10.344 12.407 12.989 7 8 9 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # Freq 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 10.598 11.370 11.930 12.235 12.405 SWL AWL Mode Shape SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #4: EFEW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-25 0.3 0.8 0.4 0.5 3.0 2.1 0.2 0.9 0.7 1.4 2.7 1.2 -0.1 -2.9 -2.9 -1.9 -1.0 -1.2 -4.5 -4.8 -0.3 -8.2 -1.1 -1.6 Error Freq 1.003 1.409 2.961 3.465 3.547 4.365 4.429 4.739 4.970 5.218 5.336 5.723 6.045 7.237 7.283 7.867 8.080 8.736 9.191 9.933 Constraints DOT4 11.212 11.847 10.892 12.122 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 29 27 30 Mode # 0.6 0.7 0.6 0.3 3.0 2.1 0.2 0.8 0.7 1.4 2.6 1.3 -4.8 -0.3 -2.9 -3.0 -1.9 -1.1 -1.0 -1.2 -1.8 -4.5 -0.3 -8.2 Nastran Results Error Freq 1.006 1.407 2.960 3.464 3.541 4.372 4.420 4.739 4.967 5.218 5.336 5.727 6.036 7.232 7.283 7.867 8.078 8.725 9.192 9.932 DOT3 11.205 11.843 10.888 12.128 7 8 9 11 23 10 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 29 27 30 Mode # Freq 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.540 11.862 11.977 SWL AWL Mode Shape SW1B SW1T SWFA AW1T SW2B NLGL SW3B SW2T AW2T AW1B AW2B SEngL AWFA AW3B AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data
Optimization Run #4: FFFW Case
7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 0.02 0.01 0.16 0.04 0.05 0.02 0.16 1.00 -0.02 -0.02 -0.09 -0.08 -0.01 -0.02 -0.01 0.00 0.07 0.10 0.02 0.00 1.00 -0.01 -0.04 -0.01 -0.03 -0.01 -0.05 0.00 0.01 0.03 0.02 0.04 0.01 0.06 1.00 0.16 -0.03 -0.02 -0.01 -0.08 -0.02 -0.01 Chan-gi Pak-26 0.00 0.02 0.01 0.01 0.01 0.00 0.01 1.00 -0.01 -0.05 -0.01 -0.05 0.02 0.02 0.02 0.00 0.03 0.06 1.00 -0.01 -0.10 -0.07 -0.04 -0.01 -0.01 -0.01 -0.01 0.03 0.00 0.00 0.01 0.00 0.02 0.00 1.00 0.01 0.00 -0.04 -0.04 0.03 0.00 0.07 0.01 0.00 0.00 1.00 0.06 0.06 -0.02 -0.01 -0.05 -0.01 -0.04 -0.02 19 0.01 0.05 0.01 0.01 1.00 -0.02 -0.01 -0.02 -0.02 -0.04 -0.01 -0.01 0.05 0.07 0.03 1.00 0.03 0.01 -0.01 -0.01 -0.01 -0.03 -0.04 -0.02 -0.04 -0.04 -0.01 0.02 0.05 0.05 0.02 0.00 0.08 1.00 0.00 0.04 0.02 -0.02 -0.03 -0.11 -0.04 -0.01 16 0.00 0.00 0.00 0.01 1.00 0.00 0.00 0.02 -0.01 -0.01 -0.01 -0.02 0.01 0.01 0.00 0.01 0.00 1.00 0.08 0.00 0.05 -0.02 -0.01 -0.04 -0.02 -0.01 -0.02 0.02 0.18 1.00 0.01 0.02 0.01 -0.07 -0.01 -0.03 -0.07 -0.02 -0.03 0.00 0.00 0.17 0.02 1.00 0.00 0.00 0.00 0.02 0.04 -0.04 -0.03 -0.08 -0.04 -0.01 0.01 0.10 0.02 1.00 0.01 0.00 0.10 -0.06 -0.01 -0.07 -0.01 -0.05 0.02 0.04 0.00 1.00 0.02 0.03 0.01 0.16 -0.09 -0.10 -0.13 -0.04 -0.11 -0.04 -0.08 0.02 0.00 0.01 1.00 0.02 0.18 0.00 0.01 -0.02 -0.01 -0.04 -0.01 0.03 0.00 0.03 0.01 1.00 0.17 0.01 0.02 -0.06 -0.13 -0.03 -0.05 -0.07 -0.01 -0.08 0.00 0.00 0.06 1.00 0.01 0.00 0.05 0.02 0.03 -0.01 -0.10 -0.01 -0.01 -0.01 -0.09 0.01 0.01 1.00 0.10 0.02 0.01 0.01 0.01 0.07 -0.01 -0.02 -0.01 0.03 1.00 0.06 0.00 0.05 0.07 0.07 -0.03 -0.08 -0.06 -0.09 -0.08 -0.10 -0.02 -0.02 0.00 1.00 0.01 0.00 0.05 0.00 0.00 -0.05 -0.01 -0.01 -0.03 -0.01 0.00 1.00 0.03 0.00 0.01 0.02 0.05 0.02 0.01 -0.05 -0.08 -0.01 -0.03 -0.02 -0.02 0.01 1.00 0.00 0.01 0.00 0.00 0.01 0.00 0.02 -0.06 -0.01 -0.04 1.00 0.00 0.03 0.00 0.00 0.04 0.00 0.01 0.00 0.02 0.01 -0.01 -0.03 -0.01 -0.03 1.00 0.01 0.01 0.02 0.01 0.03 0.00 1.00 0.00 0.03 0.02 0.03 0.00 0.02 -0.05 -0.07 -0.01 -0.02 -0.01 -0.01 -0.05 -0.03 -0.04 -0.02 -0.02 -0.01 -0.01 7 8 9 10 11 12 13 14 15 18 19 25 27 28 30 7 8 9 11 12 13 14 16 19 24 25 28
Orthonormalized Mass Matrices After #4
Number Number GVT Mode GVT Mode SWL Mode Shape SW1B SW1T SW2B SW3B SW2T SWL AW1B SWFA AW1T AW2B AW2T Mode Shape BoomH SW1B SW1T SW2B SW3B AW2T AW1B AW1T Structural Dynamics Group SMLGL BoomH AMLGL NLGFA AMLGFA SMLGL AMLGL Table 17. Orthonormalized mass matrix of the MUTT aircraft after the fourth model tuning procedure (with empty fuel empty water; Auto Correlation) Table 18. Orthonormalized mass matrix of the MUTT after the fourth model tuning procedure (with full fuel full water; Auto Correlation) 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 3.4 (%) 13.3 5~10 5~10 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-27 2.2 0.7 0.6 3.4 0.6 2.0 1.0 3.0 2.1 1.5 0.0 1.4 5.7 1.4 1.3 4.7 -0.1 -2.5 -1.0 -1.2 -0.9 -0.7 -5.0 Error -13.3 Freq 1.091 1.553 3.628 5.240 5.350 7.283 7.392 8.615 8.068 9.214 3.220 3.742 4.591 4.492 4.757 5.218 6.089 6.222 9.477 DOT4 11.198 11.533 10.344 12.393 12.993 7 8 10 11 13 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 2.1 0.0 1.7 2.3 6.3 0.6 3.0 2.0 1.1 0.8 4.2 0.8 3.3 -0.2 -2.0 -5.3 -0.2 -0.9 -1.2 -4.8 -0.1 -3.3 -0.9 Error -15.9 Freq 1.090 1.540 3.159 3.607 3.636 4.514 4.567 4.961 5.223 5.294 5.349 6.061 6.189 7.283 7.381 8.574 8.085 9.205 9.416 Nastran Results 11.048 11.462 10.035 11.835 12.811 Baseline 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 26 29 30 Mode # 3.8 2.3 4.8 -3.0 -0.5 -8.3 -7.1 -4.6 -4.3 -4.4 -7.2 -4.1 -6.7 -8.1 -7.2 -3.4 N/A N/A Error -13.7 -14.9 -14.1 -13.9 -10.3 -10.4 Final Design Freq N/A N/A 1.035 1.534 2.781 3.068 3.522 4.127 4.262 4.467 4.530 4.569 5.159 5.404 5.815 8.133 8.812 9.433 9.798 9.889 10.186 10.969 11.355 11.986 Freq 1.067 1.543 3.223 3.607 3.839 4.440 4.466 4.666 5.273 5.305 5.399 6.026 6.264 7.067 7.238 8.484 8.490 9.217 9.346 11.370 11.930 10.598 12.235 12.405 Mode Shape SWL AWL
Summary: EFEW Case
SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 (%) 5~10 5~10 5~10 5~10 5~10 Error Target Chan-gi Pak-28 0.3 0.8 0.4 0.5 3.0 2.1 0.2 0.9 0.7 1.4 2.7 1.2 -0.1 -2.9 -2.9 -1.9 -1.1 -1.0 -1.2 -1.6 -4.5 -4.8 -0.3 -8.2 Error Freq 3.465 4.970 5.336 5.723 7.237 7.283 7.867 8.080 9.933 1.003 1.409 2.961 3.547 4.365 4.429 4.739 5.218 6.045 8.736 9.191 DOT4 11.212 11.847 10.892 12.122 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 27 30 Mode # 0.1 0.9 7.4 0.0 1.9 0.2 0.2 0.6 0.9 1.4 -0.9 -0.9 -3.5 -5.4 -1.4 -1.1 -1.0 -1.7 -2.0 -4.8 -4.9 -2.0 -3.4 Error -10.84 Freq 1.001 1.398 2.912 3.445 3.454 4.285 4.446 4.944 5.067 5.217 5.336 5.694 6.018 7.220 7.283 7.848 8.071 8.673 9.186 9.766 Nastran Results 11.148 11.704 10.576 11.566 Baseline 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30 27 29 Mode # 7.5 -6.3 -1.3 -5.5 -9.6 -5.7 -8.6 -2.5 -7.1 N/A N/A Error 22.4 15.3 -11.2 -19.7 -10.3 -14.3 -15.2 -15.5 -13.5 -14.5 -10.8 -12.1 -12.7 Final Design Freq N/A N/A 0.937 1.392 2.608 3.374 2.932 3.898 5.393 4.159 4.339 4.476 4.555 5.015 5.251 7.350 9.788 8.161 9.816 9.112 9.714 10.076 11.562 11.130 Freq 1.000 1.411 2.938 3.569 3.651 4.346 4.408 4.601 5.065 5.276 5.390 5.795 6.144 7.085 7.270 8.240 8.490 8.657 9.129 9.965 11.053 11.540 11.862 11.977 Mode Shape SWL AWL
Summary: FFFW Case
SW1B SW1T SW2B NLGL SW3B SW2T AW1B SWFA AW1T AW2B SEngL AWFA AW3B AW2T AEngL SMLGL BoomH BoomV SMLGFA AMLGL NLGFA AMLGFA GVT data 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mode # Structural Dynamics Group Chan-gi Pak-29 = 0.
ߠ = 0 ߠ near DOT is inefficient 0 Slope at Ply Angles and Thicknesses
Optimization Run #5 ~
PCOMP elements for Wings Off-diagonal Terms of Orthonormalized Mass Matrices, Mode Shape Matrices (cross-correlation Matrices), and MAC Matrices Frequency errors Off-diagonal Terms of Orthonormalized Mass Matrices, Mode Shape Matrices (cross-correlation Matrices), and MAC Matrices not selected as objective functions 0 1 -1 0.5 -0.5 Design Variables Optimizer: Big-Bang Big-Crunch + DOT Objective Functions Constraints Structural Dynamics Group
Development of unsteady
aerodynamic model tuning tool
File ZAERO ~.f06 file NASTRAN Frequency & Data Flow Mode Shapes Template Input Chan-gi Pak-31 Script commands File V-g & V-f Flight Test Input Data Ua-tune.dat Frequencies Ua-temp.dat ZAERO Input Measured from Pre- Analysis Update2 Compute Difference Processor Frequency Aeroelastic AutoZAERO DVPREL2.dat ZAERO Flutter Frequency and In-direct Method Difference Frequency Design Variables Script Commands Tool Optimizer Optimization Indices Performance G(x) Objective Constraints Function J &
Unsteady aerodynamic model tuning tool using MDAO and test data
Scaling factor for each element of AIC matrices Aerodynamic mesh geometries Faster than in-direct method Update AIC matrices Design Variables Physics based approach Update AIC matrices through the change of aerodynamic panel geometry Design Variables To use the 15% flutter margin requirement in Mil Spec, unsteady aerodynamic model might be validated with respect to flight test data. If needed, then model should be tuned. Direct Method (already developed) In-direct Method (current development) Structural Dynamics Group Problem Objective Minimize uncertainty in an aerodynamic model. Approach
from measured strain
Computation of wing deflection and slope
Chan-gi Pak-33 Slope (angle) Deflection ௫ ௬ ௭ ௫ ௬ ௭ ߜ ߜ ߜ ߠ ߠ ߠ ൌ Complete degrees of freedom ࢚ ሻ࢚ሺǡ ࢎࢉࢇࡹ ࢇ ࡲ ൌ ࢚۹ : Inertia Force : Damping Force : Elastic Force : Aerodynamic Force ࢚ሶ۵ ࢇ
What the technology does ሻ࢚ሷሺۻ ࢚ሶ۵ ࢚۹ ࡲ
ǣ External Load: using unsteady aerodynamic model ࢚ሷۻ Loads can be computed from the following governing equations of motion. Wing deflection and slope (complete degrees of freedom) are essential quantities for load computations during flight. Real-time measurement of deflection and slope in flight is a valuable tool. Several methods predict deflection and slope at discrete locations, but few predict deflection or slope of “entire structures”. Wing slope is not easy to measure during flight.
Structural Dynamics Group Problem Statement Chan-gi Pak-34 Loads Compute Black Box #2 Wing & Slope Compute Deflection Wing Compute Deflection Black Box #1 Strain Measure
Technical features of new technology
Wing deflection will be computed along the fiber optic sensor line. This is a finite element model independent method. Slope computation will be based on a model dependent technique. Wing deflection and slope will be computed at all the finite element grid points.
First Step: Compute wing deflection along fibers using measure strain data (Black Box #1) Second Step: Compute wing slope and deflection of entire structures (Black Box #2) The new method for obtaining the deflection over a flexible full 3D aircraft structure is based on the following two steps.
Structural Dynamics Group Proposed solutions: Chan-gi Pak-35 ௫ ௬ ߠ ߠ Deflection
Sample Results: Cantilevered Swept Back Wing
Strain: use as if measured values Deflection: use as an exact solutions (target deflections) Strain and deflection at sensor point are computed using MSC/NASTRAN code. A total of 22 sensor configurations were tested Deflections are computed from the strain values and compared with target deflections.
Computational Validation Structural Dynamics Group L M Chan-gi Pak-36 T Error starts Trailing- edge fiber Deflection and angle are available everywhere fiber Middle Current Method
Sample Results: Cantilevered Swept Back Wing (continued)
Leading- edge fiber Experimental results were compared to photogrammetry data and to deflection results computed by Bakalyar and Jutte for the same test data Strain at the root of each fiber was extrapolated using a fifth-order polynomial Curvature measurements from each pair of upper and lower fibers were averaged to eliminate the effect of any axial load Experimental Testing Structural Dynamics Group GRT Data Model Drag Actuator On-Line Induced Reduction Parameter Estimation Chan-gi Pak-37 based on Delta Delta Control Law System Parameters Tool MDAO + - Error Prediction delta Model U Ride Model Unsteady Quality Control Validated Aerodynamic Servoelastic Tool + + Model MDAO Validated Aeroservoelastic FT Data nominal U Gust Load Alleviation Validated Structural Dynamic Model Dissertation Topic Advisor: Prof. Maruthi R. Akella Tool MDAO Ph.D. Candidate at University of Texas, Austin Kelley Hutchins (Fellowship Student) Flutter Model Law based on data Dynamic Shape Gain Scheduling GVT Sensor Nominal Control Data Structural Suppression Sensing On-line Adaptive Active Flexible Motion Control System
Future Work
Use CFD code (CFL3D and/or CAPTSDv) Create Validated Aeroservoelastic model Testing Shape Sensing codes Work with Internship Students Nominal Control Law Design On-line Parameter Estimator for a MIMO System Delta Control Law Design Subsonic Regime: use MUTT Subsonic, Transonic, and Supersonic Regimes: use N+2 Low Boom Supersonic Aircraft Chan-gi Pak: PI Samson Truong Ashante Jordan Alex Chin & Marty Brenner: Supported by Fixed Wing Project Nominal Control Law Design using Validated Aeroservoelastic Model On-line Parameter Estimator for a MIMO System Delta Control Law Design Flexible Motion Control in Subsonic, Transonic, and Supersonic Flight Regimes Team Members Structural Dynamics Group
Questions ?
Margins Flutter & Divergence Gain/Phase Sparibs Curvilinear Mode Shape Frequency & Control Adaptive Buckling Flexible Motion Design Variables Script CFD Based Flutter Deflection, Commands Stress, & Strain tool … O Central Module … Executive Optimizer Weight Trim Indices Performance G(x) Objective Constraints Function J & Model Tuning Structural Taxiing Landing &
Chan-gi Pak, Ph.D. & Wesley Li
Aerodynamic Lift & Drag Model Tuning NPSS NASA Dryden Flight Research Center Sonic Boom ??
Structural Dynamics Group, Aerostructures Branch (RS)
for AeroScience, Fixed Wing, and High Speed Projects
Design of an Aeroservoelastically Tailored Wings and Aircraft
L 1.0 Chan-gi Pak-40 1.15 V B777 L V Mach Number omax V 0.5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) HWB supersonic aircraft Use Tailoring Aeroservoelastic Use Flutter Boundary p pa bs Tailoring Aeroelastic Optimization of an unconventional aircraft: Use N3-X HWB aircraft with turbo-electric distributed propulsion system lications (continue) e Equivalent Speed V Support AeroScience Project Applications (continue) App MUTT Curvilinear sparibs and ntrol and tailoring near ax co (CRM): use omax line Structure and control systems are simultaneously improved.
omax L Design of an Aeroservoelastically Tailored Wings and Aircraft for AeroScience, Fixed Wing, and High Speed Projects Optimization of a low-boom supersonic aircraft: Use LM’s concept aircraft Perform topology optimization with curvilinear sparibs Use aeroelastic tailoring up to V Use aeroservoelastic tailoring between V 1.15 V Optimization of MUTT aircraft: Aeroelastic tailoring and mass balancing studies Optimization of Common Research Model (CRM): use B-777 type of wing Use aeroelastic tailoring theory and active flexible motion control technique to satisfy the overall strain, aeroelastic, and aeroservoelastic instability requirements within given flight envelopes Use curvilinear sparib concept as well as composite ply angles for aeroelastic tailoring Simultaneously update structural as well as control design variables during early design phase Support Fixed Wing Project Support High Speed Project Structural Dynamics Group Problem Design innovations are needed to further down the weight of an aircraft which current design technologies can take care of. Objective Approach Applications 2.5 Chan-gi Pak-41 2.0 1.5 Flutter Primary p Mach Mach Flight 1.0 Envelope 0.5 Flutter Boundaries at Mach 0.9 & 1.8 N+2 Low Boom Supersonic Aircraft 0.0 0 0 0 0 0 Use 10000 20000 30000 40000 50000 60000 70000 Grids Altitude (ft) existing Remove Engines Structure and control systems are simultaneously improved.
HWB-TeDP Motors Put Electric Curvilinear sparibs Curvilinear sparibs C generator Put Turbo Design of an Aeroservoelastically Tailored Wings and Aircraft for AeroScience, Fixed Wing, and High Speed Projects (continued) CRM (B-777) l Keep working on a critical optimization study with MUTT aircraft. Through the use of lumped masses together with our MDAO tool, flutter speeds will be tuned within the flight envelope. Creating wing skins using laminated composites is underway.
Preparing for optimization using baseline configuration Create unsteady aerodynamic model and perform modal & flutter analyses Keep working on for creating a finite element model Flutter speeds of the current MUTT aircraft is too high for the active flutter suppression study. (some flutter speeds are outside the flight envelope where aircraft can’t reach with current propulsion systems.) Generated a finite element model (FEM) of full-scale CRM for aeroelastic tailoring optimization.
Support High Speed Project Support Fixed Wing Project Support AeroScience Project Structural Dynamics Group RESULTS
with Flexible Wing Configuration
Flutter Optimization Study for MUTT Aircraft
1.76 2.35 3.52 Upper Chan-gi Pak-43 Bounds 1.76 2.35 3.52 0.53 2.25 2.43 Upper Bounds FFFW Frequency Frequency (Hz) 0.68 2.34 1.52 EFEW 0.53 1.17 1.50 Lower Bounds 0.53 1.17 1.50 Lower Bounds Flutter Constraints* 0.98 1.18 1.30 Upper 0.98 1.18 1.30 Bounds Upper Bounds Baseline flutter points at Mach = 0.16 1.16 1.48 1.68 Speed FFFW 0.79 0.98 0.98 Speed (Keas) 1.48 1.68 1.13* EFEW non-dimensional) Lower Bounds flutter: ~0.98 to 1.18 rd 0.79 0.98 0.98 Lower Bounds st rd nd and 3 1 flutter (body freedom): ~0.78 to 0.93
Flutter Speed and Frequency Constraints
st nd Based on GVT correlated flexible wing model from Lockheed Martin Two weight configuration was used: EFEW and FFFW 1 2 st rd nd Flutter mode 1 3 Design requirement ( Baseline flutter model mode Flutter *Note: optimization constraints for Aft Wing Tip Boom Optimization *Note: Baseline flutter speeds violate flutter speed constraints Structural Dynamics Group Chan-gi Pak-44 L 1.8 1.15 V 1.6 L V 1.4 Model Tuning 30%~70% 1.2 35% 10% 0.8 Non-dimensional Speed 0.6 Flight Envelope 0.4 0.2 : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter Final Design Baseline 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 Non-dimensional Altitude
Flutter Boundaries
Structural Dynamics Group Chan-gi Pak-45 optimization run.
single ݆ൌ ͳǡ ʹǡ Ƭ͵ ݆ൌ ͳǡ ʹǡ Ƭ͵ ݂ ܸ ܆ ܆ ிிிௐ ிிிௐ ݂ ܸ ݂ ܸ & & ଵ ଶ ே ڭ ݔ ݔ ݔ ݀݁݁ݏݎ݁ݐݐݑ݈݂ݎ ݐ݄݃݅݁ݓ݈ܽݎݑݐܿݑݎݐݏ݈ܽݐݐ ൌ ܆ ܸ ݂ ܆ ܆ : Side constraints ாிாௐ ாிாௐ ܸ ݂ ݔ Flutter speed constraints ܸ Flutter frequency constraints ݂ such that: ݆ܾܿ݁ ݂݊݅ݐܿ݊ݑ݂݁ݒ݅ݐ Optimization Problem Statement Two different weight configurations will be taken into account in a O Ͳ ݔ When j-th flutter speed is selected for an objective function, then j-th flutter speed is not included as a constraint function.
܆ ൌ Flutter speed and frequency constraints will be computed using two different weight configurations, i.e. empty fuel empty water (EFEW) and full fuel full water (FFFW) configurations Structural Dynamics Group Chan-gi Pak-46 27223 27723 27285 Aft wing tip boom j 27781 27200 27768 27184 27755 Lumped Masses M 27172 27670 27165 27665 10022 27513 27013 27518 27020 Nose ballast Nose ballast 27602 27107 27615 27048 27628 Use design variable linking for wing symmetric masses Wing leading and trailing edge (12 design variables) 25” long aft wing tip boom (5 design variables) Primarily to reduce body freedom flutter speed
Summary of Optimization Approach
27061 27571 Based on DOT, a gradient-based optimization Lumped mass design variables (0 to 5 lbs. each = side constraints) Nose ballast (up to 20.0 lbs.)
27071 Structural Dynamics Group 27223 27219 Chan-gi Pak-47 27723 27285 27200 j 27184 Lumped Masses M 27107 27048 27061 6 design variables Wing lumped masses (0 to 5 lbs.) Use design variable linking for these symmetric masses. Optimization results: two 5 lbs. masses were added at aft wing tip location, node 27723 and 27571.
Optimization Run #1
27571 Make masses install symmetrically 27139 27071 Structural Dynamics Group Chan-gi Pak-48 27223 27723 27285 j 27781 27200 27768 27184 27755 Lumped Masses M 27172 27670 27165 27665 10022 27513 27013 27518 27020 27602 27107 27615 27048 27628 27061 12 wing and 1 nose design variables Wing lumped mass (0 to 5 lbs.) Nose ballast (0 to 20 lbs.) Use design variable linking for wing symmetric masses. Optimization results: two 5 lbs. masses were added at aft wing tip location, node 27723 and 27571. Also a 20 lbs. mass at the nose, node 10022.
27571
Optimization Run #2
27071 Make masses install symmetrically Structural Dynamics Group Chan-gi Pak-49 Aft wing tip boom 27223 p 27723 g 27285 j j 27781 M M M M M 27200 27768 27184 27755 Lumped Masses M 27172 27670 Comments Comments 27165 27665 No lump mass 0.5 lbs. at each nodes 1.0 lbs. at each nodes 5.0 lbs. at tip - 10022 7.3 5.4 17.3 17.3 dimensional) dimensional) Frequency (non- Frequency (non 27513 27013 lbs.
antilever Wing Tip Boom Modal Analysis 27518 , Cantilever Wing Tip Boom Modal Analysis C 1.25 3.75 6.25 6.25 27020 Weight, lbs. Weight, 27602 27107 27615 27048
Optimization Run #3
27628 27061 Nose ballast (0 to 20 lbs.) Add a 25” long aft wing tip boom with lumped masses (0 to 5 lbs.) Optimization results: two 5 lbs. masses were added to the tip of the aft wing tip boom. Also a 20 lbs. mass at the nose, node 10022.
27571 27071 Structural Dynamics Group 20.0 0.00 0.04 0.04 2.44 5.00 215.0 221.0 226.0 231.0 236.0 Case 203 Chan-gi Pak-50 20.0 0.00 0.00 0.00 0.34 4.74 212.0 221.0 226.0 231.0 236.0 Case 202 20.0 0.00 0.00 0.00 0.00 5.00 216.0 221.0 226.0 231.0 236.0 Nose Lumped Mass Case 201 Final Design Variables Wing Tip Boom Lumped Mass Wing Tip Mass Grid X Location 1 2 3 4 5 6 7 8 9 Case 201 is the best design 10 11 DESVAR Symmetric flutter first and then BBF Too Low !!
0.53 2.25 2.43 1.03 1.55 1.03 1.55 0.95 1.42 0.58 0.58 0.57 Flutter Frequency <1.18, FFFW <1.18) 1.16 1.48 1.68 1.18 1.26 1.18 1.26 1.10 1.26 1.14 1.14 1.14 Speed Flutter 0.68 2.34 1.52 1.07 1.57 1.07 1.57 0.99 1.44 0.72 0.72 0.71 Flutter flutter speed (0.98<f Baseline flutter speed are reduced mainly.
Frequency rd rd EFEW flutter speed (0.79<f st and 3 and 3 1.13 1.48 1.68 1.11 1.29 1.12 1.29 1.06 1.30 1.13 1.13 1.14 nd Speed nd Flutter With Wing Tip Boom Optimization st rd st rd st rd st rd <1.3) nd nd nd nd 3 1 3 1 3 1 3 2 2 2 2
Optimization Run #3 (continued) Flutter
Objective: Min 1 Constraints: 2 0.98<f Several optimization runs with different initial condition were performed Results: the 2 Not the body freedom flutter. Nose ballasts change the Body freedom flutter speed.
201 202 203 Case Structural Dynamics Group 1.76 2.35 3.52 0.98 1.18 1.30 Upper Upper Chan-gi Pak-51 Bounds Bounds 1.18 1.26 0.58 1.03 1.55 1.14 FFFW FFFW Run #3 Run #3 1.13 1.11 1.29 0.72 1.07 1.57 EFEW EFEW 1.12 1.49 1.56 0.71 1.28 2.07 FFFW FFFW Run #1 & #2 Run #1 & #2 Flutter Speeds 1.12 1.55 1.67 0.58 2.01 1.25 Flutter Frequency flutter speed EFEW EFEW ) rd rd and 3 , or 3 nd nd 1.16 1.48 1.68 0.53 2.25 2.43 FFFW FFFW , 2 st Baseline Baseline 1.13 1.48 1.68 0.68 2.34 1.52 EFEW EFEW flutter speed can be reduced by adding aft wing tip boom mass.
rd 0.79 0.98 0.98 0.53 1.17 1.50 Lower Lower Bounds Bounds and 3 nd With or without constraints: 2
Optimization Results
st st rd rd nd nd 1 1 3 3 2 2 Several optimization runs with different initial condition were performed. Objective: Min flutter speeds (1 The 2 The Body freedom flutter speed can be reduced by Nose ballast. mode mode Flutter Flutter Structural Dynamics Group Chan-gi Pak-52 L 1.8 1.15 V MUTT MUTT 1.6 L V Mass Balancing using MDO 1.4 Model Tuning 1.2 0.8 Non-dimensional Speed 0.6 Flight Envelope 0.4 0.2 : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter : Body Freedom Flutter : Symmetric Wing Flutter : Anti-symmetric Wing Flutter Final Design Baseline After Mass Balancing 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 Non-dimensional Altitude
Flutter Boundaries
Structural Dynamics Group 2.43 1.96 1.82 1.72 1.62 1.55 1.56 Freq.
FFFW rd Chan-gi Pak-53 1.68 1.37 1.32 1.29 1.28 1.26 1.28 Speed 2.25 1.29 1.19 1.12 1.07 1.03 1.03 Freq.
FFFW nd 1.48 1.60 1.43 1.32 1.24 1.18 1.18 Speed 0.53 0.59 0.59 0.58 0.58 0.58 0.51 Freq.
FFFW st 1.16 1.12 1.13 1.13 1.13 1.14 1.20 Speed 1.52 2.02 1.87 1.75 1.65 1.57 0.65 Freq.
EFEW rd 1.68 1.38 1.34 1.31 1.30 1.29 1.32 Speed 2.34 1.30 1.23 1.17 1.11 1.07 1.07 Freq.
Too low EFEW nd 1.48 1.39 1.28 1.21 1.16 1.11 1.11 Speed 0.68 0.73 0.73 0.72 0.72 0.72 0.65 Freq.
EFEW st flutter can be reduced by adding ballasts at aft wing tip.
1.13 1.11 1.12 1.12 1.12 1.13 1.17 Speed At least 0.04 (non-dimensional) speed separation for the first and second flutter modes rd
Optimization Observation
But not that much Aft wing tip boom is added. 20 lb & 4 lb configuration looks the best choice ** and 3 & 1 nd * Body freedom flutter can be reduced by adding nose ballasts. 2 Recommendation 0 & 5 20 & 2 20 & 3 20 & 4 20 & 5 : Nose Mass (lb) Baseline 20 Configuration * ** : Wing tip mass (lb) Structural Dynamics Group Chan-gi Pak-54 CRM (B-777) s s Tails Tails or - or - to V s r o t Remove V-Tails o M c i r t c Put Turbo generator e l E t Doc Position if possible Model and Unsteady Aerodynamic Model u - t t Put Electric Motors P es Curvilinear sparibs Remove Engines Create Structural Finite Element Model and Unsteady Aerodynamic Model Perform Optimization
Future Work
Designing N+2 Low Boom Supersonic Aircraft Designing Common Research Model (B-777 Type of Wing) Incorporating Curvilinear Mesh Generation code Designing Hybrid Wing Body Aircraft with Turboelectric Distributed Propulsion Chan-gi Pak: PI Wesley Li Roger Truax Create One Fellowship Student or Post-Doc Position if possible Use Team Members Grids existing Structural Dynamics Group Margins Flutter & Divergence Gain/Phase Sparibs Curvilinear Mode Shape Frequency & Control Adaptive Buckling Flexible Motion Design Variables CFD Script Based Flutter Deflection, Commands Stress, & Strain tool … O Central Module … Executive Optimizer Weight Trim Indices Performance G(x) Objective Constraints Function J & Model Tuning Structural Taxiing Landing & Aerodynamic Lift & Drag Model Tuning NPSS Sonic Boom ??
Questions ?
1 1 1 X X X Chan-gi Pak-56 2 2 2 X X X i X .
X is the number of current big bang NBB i i i i J J XL ) X N N i i i NBB (XU CG r X .
GO GO X )X i ( XU is the standard normal random number; α is the parameter r CG i X X i n i
Big Bang Big Crunch Algorithm
XL where, limiting the size of the design space; iteration; and β is the parameter controlling the influence of the global optimum solution Parameters α and β for the best performance was α=1 and β=0.2 for the truss design problems and α=1 and β=0.7 for the parameter estimation problems. X Selection of the N (number of population) random design variable vectors (i=2, 3,…, N) using uniform random number generator such that Current design configuration is saved in the design variable vector Shrink design variable vectors to a single representative design point via a center of gravity (CG) Compute new candidate design variable vectors around the CG location using the standard normal random number generator First step: Big Bang step Second step: Big Crunch step Third step: Big Bang step Go to the second step until converge A global optimizer Structural Dynamics Group