Interpolated Linear Modeling of the F16 Benchmark Maarten Schoukens - PowerPoint PPT Presentation

2017 Workshop on Nonlinear System Identification Benchmarks Interpolated Linear Modeling of the F16 Benchmark Maarten Schoukens April 2017

Overview Global vs Local Nonlinear Behavior Interpolated Linear Modeling F16 Results

Best Linear Approximation

Best Linear Approximation y s (t): non-coherent nonlinear contributions n y (t): output noise source

Best Linear Approximation Only valid for a fixed input signal class Input class changes  BLA can change

BLA: Shifting Resonances Increasing Amplitude: Shifting Resonances

Global vs Local Nonlinear Behavior ‘Local’ Nonlinear Behavior Shifting BLA  ‘Global’ Nonlinear Behavior Model ‘Global’ Nonlinear Behavior using interpolated LTI models

F16 Benchmark Data Multisine Data – Force to Acceleration Payload Frequency Range: 2-15 Hz 4 Estimation Amplitudes 3 Validation Amplitudes RMS: [12 24 36 61 74 86 98] N rms

LTI Estimation

LTI Estimation s-domain (continuous time) 12 poles, 12 zeros Start with lowest amplitude, initialize all the other based on lowest amplitude estimate.

LTI Estimation

LTI Estimation

Interpolation Linear interpolation of the numerator and denominator coefficients Other choices possible: Interpolation of the pole & zero locations Interpolation of the pole-residue representation

Results Interpolated model vs Model estimated on validation data

Results: 24 N rms

Results: 61 N rms

Results: 86 N rms

Results Interpolated model vs Model estimated on estimation data: lower level

Results: 24 N rms

Results: 61 N rms

Results: 86 N rms

Results 24 N rms 61 N rms 86 N rms Estimated 0.098 N rms 0.216 N rms 0.254 N rms Interpolated 0.103 N rms 0.338 N rms 0.263 N rms Level Lower 0.352 N rms 0.823 N rms 0.307 N rms Level Higher 0.262 N rms 0.287 N rms 0.330 N rms RMS error in excited frequency range

Results 24 N rms 61 N rms 86 N rms Estimated 15,2 % 18,5 % 17,3 % Interpolated 16,0 % 29,0 % 17,9 % Level Lower 55,0 % 70,6 % 20,9 % Level Higher 40,9 % 24,6 % 22,4 % Relative error in excited frequency range

Conclusion Global Nonlinear Behavior Interpolated LTI Models Good F16-Benchmark Results

2017 Workshop on Nonlinear System Identification Benchmarks Interpolated Linear Modeling of the F16 Benchmark Maarten Schoukens April 2017