APPENDIX A-5 THE CORRESPONDING FREQUENCY DOMAIN VALIDATION. APPENDIX A-5 shows plots for the corresponding time domain validation response

Transcription

1 APPENDIX A-5 THE CORRESPONDING FREQUENCY DOMAIN VALIDATION APPENDIX A-5 shows plots for the corresponding time domain validation response records illustrated in chapter 7 for further validation. The following pattern of plots is recognized: A5.1 PLOTS AND QUANTIZED VALIDATION 1. Acceleration Amplitude Frequency Response Rectangular, time Window filter applied 2. Acceleration Amplitude Frequency Response Henning, time Window filter applied 3. Amplitude, time domain and power spectrum, Frequency-Domain of the prediction and measured responses. 4. Signal phase angle for both predicted and measured responses 5. Phasors response both real and imaginary 6. Magnitude Phase and Real-Imaginary combination semi-log Plots 7. Magnitude Phase and Real-Imaginary combination Log-Log Plots. These plots are results of processed measured excitation and measured responses, as well as model calculated response into the frequency domain. Frequency range is filtered into the relevant frequency ranges that affect human responses. In some cases a wider band of frequency spectrum is shown for just future study. A5.2.1 Power Spectrum The distribution of the "power" value of a signal as s function of frequency is named 1

2 Power-Spectrum. Power is measured in a signal as the average of the squared value of a signal. That is equals the squared value of FFT magnitude in the frequency domain in a signal is considered to be the average of the signal Frequencies that contain most of the power of the signal. That can be shown in the distribution of power values as a function of frequency, where in the frequency domain; this is the square of FFT s magnitude The corresponding time domain relevant excitation records are: S1 acc_251 non-filtered S1 acc_251 filtered into a cut-off frequency of 100 Hz S3 acc_25 S3 acc_27 S4 acc_33 S3 acc_305 S4 acc_350 A5.2 MRAP TESTS: July Tests MRAP S1:[acc:251] and S2 [acc:258] S1 - July MRAP [acc_251] Low-Pass-Filtered with a 100 Hz cutoff Figure A5.1 Rectangular-Time-Window Filter Applied on S1 Bladder MRAP Test (excitation acc_251_) Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 2

3 Figure A5.2 Hanning Time-Window Filter Applied on S1 Bladder July-MRAP Test (excitation acc_251_) Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) Figure A5.3 Right-Side Subplots: Show State Equation Prediction/Measured Time History Response (Top/Bottom). (Left Subplots): Power Spectrum of both Prediction (Top) and Measured (Bottom) Response. July MRAP-S1_acc_251 Test 3

4 Figure A5.4 Signal Phase Angle as a Function of Frequency: S1 Bladder July-MRAP Test (Excitation Acc_251_) Calculated (Top Subplot), Compared To Measured Signal (Bottom Subplot) Figure A5.5 Signal Phasors Real Value (Left) and Imaginary Value (Right), as a Function of Frequency, S1 Blackhawk Test (Excitation acc_251_) Calculated (Top Subplot) Compared to Measured (Bottom) 4

5 A B Figure A5.6 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (Left Top-Bottom), Real and Imaginary (Right-Top- Bottom), for both Measured Response (A) and State Eqns. Prediction (B). All Versus Frequency up to 100Hz. Bladder Tested is S1_Onboard MRAP- July (Excitation _Acc_251). Semi-Log Scale 5

6 A B Figure A5.7 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S1_Onboard MRAP- July (Excitation _acc_251). 6

7 Table A5.1 Percentage Accuracy Measure For S1_251 All Models Prediction. (Two Iterations Of Sblt Values) Linear Hammerstein Wiener H-W yddt_ St-Eqns. % Accuracy of Model for Bladder S1 Excitation acc_251_ (%) / % Test Duration (sec) Data points Vehicle Speed (mph) Tested Mass (kg) SBlt / July Tests MRAP S1:[acc:251] and S2 [acc:258] S1 - July MRAP [acc_251] Un-Filtered (No low pass filter) Figure A5. 8 Rectangular, time Window filter applied on S1 bladder July-MRAP test (excitation acc_251). Spectrum of Calculated (Top subplot) compared to measured signal (Bottom subplot) 7

8 Figure A5. 9 Hanning time-window filter applied on S1 bladder JULY-MRAP test (excitation acc_251..). Spectrum of Calculated (Top subplot) compared to measured signal (Bottom subplot) Figure A5. 10 Power spectrum (right) and acceleration signal amplitude for S1 bladder July-MRAP test (excitation acc_251). Spectrum of Calculated (Top subplot) compared to measured signal (Bottom subplot) 8

9 Figure A5.11 Phase Angle as a Function of Frequency. S1 Bladder July-MRAP Test (Excitation acc_251_) Calculated (Top Subplot), Compared To Measured Signal (Bottom Subplot) Figure A5.12 Signal Phasors Real Value (Left) and Imaginary Value (Right), as a Function of Frequency, S1 Blackhawk Test (Excitation acc_251_) Calculated (Top Subplot) Compared to Measured (Bottom) 9

10 A B Figure A5.13 Both Figures (A) and (B) Shows Signal Magnitude and Phase angle (Left Top-Bottom ), and Real and Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) all versus Frequency up to 100 Hz. Bladder Tested is S1_Onboard Blackhawk,(Excitation _acc_251). S-log Scale 10

11 A B Figure A5.14 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S1_Onboard MRAP- July (Excitation _acc_251). 11

12 Figure A5.15 Atypical screen shot, after a Matlab code run. Here is an actual last work-space view of end screen for S4-bladder of November MRAP on excitation (acc_30) SBlt values: Linear Hammerstein Wiener Hammerstein-Wiener Notice the effect of non-filtering and non-optimum SBlt values on accuracy and agreement between the Equation model prediction and measured responses Percentage = Linear yddt SBlt Lowest band is of fs - resampling to Hz for bands up to 4.0 Hz center freq... 12

13 S2 - July MRAP [acc_258] filtered into a 100 Hz cutoff Figure A5.16 Hanning Time-Window Filter Applied on S2 Bladder July-MRAP Test (Excitation acc_258). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) Figure A5.17 Hanning Time-Window Filter Applied on S2 Bladder July-MRAP Test (Excitation acc_258). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 13

14 Figure A5.18 State Equation Prediction Time History and Measured Response (Left Subplots). Right Side: is the Power Spectrum of both Prediction and Measurement Response. (St. Eqnns: Up, Measured: Down). S2 Bladder July-MRAP Test (Excitation acc_258). Figure A5.19 Phase Angle as a Function of Frequency. S2 Bladder July-MRAP Test (Excitation acc_258_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) 14

15 Figure A5.20 Signal Phasors Real Value (Left) and Imaginary Value (Right), as a Function of Frequency. S2 Blackhawk Test (Excitation acc_258_) Calculated (Top Subplot) Compared to Measured Signal- (Bottom) A B Figure A5.21 Both Figures (A) and (B) Shows Signal Magnitude and Phase angle (Left Top-Bottom ), and Real and Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) all versus Frequency up to 100 Hz. Bladder Tested is S2_Onboard Blackhawk,(Excitation _acc_258). S.log Scale 15

16 A B Figure A5.22 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S2_Onboard MRAP- July (Excitation _acc_258). 16

17 S2 AAA Distinct_Plots_Sound_Match_S2_258 S2 S2_258 Model : [test Foam D M SBlt ] = [ ] test = test; Foam = 2.0; D = 3/8; M = M; SBlt = SBlt; Model = [test Foam D M SBlt ] Linear-S2-258 Hammerstein Wiener Hammerstein-Wiener Linear Hammerstein Wiener Hammerstein-Wiener A t t e n c i o n " ATTENTION For SOUND-PLEASE Linear State_Eqn_yddt Linear-S2-258 State_Eqn_yddt Lowest band is of fs - resampling to Hz for bands up to 4.0 Hz center freq... 17

18 Nov. Tests MRAP S3:[acc:25] and S4 [acc:33] S3 - November MRAP [acc_25] filtered into a 100 Hz cutoff Figure A5.23 Hanning Time-Window Filter Applied On S3 Bladder Nov-MRAP Test (Excitation acc_25). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) Figure A5.24 Hanning Time-Window Filter Applied on S3 Bladder Nov-MRAP Test (Excitation Acc_25_). Spectrum of Calculated (Top Subplot) Compared To Measured Signal (Bottom Subplot) 18

19 Figure A5.25 State Equation prediction time history and measured response (left subplots). Right side: power spectrum of both prediction and measurement response. Plots show large disparities in both cases. But not at the frequency location of the peaks Figure A5.26 Shows Signal Phase Angle vs. Frequency. S3 Bladder Nov-MRAP Test (Excitation acc_25_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) 19

20 Figure A5.27 Signal Phasors Real Value (Left) and Imaginary Value (Right), vs Frequency. S3 Blackhawk Test (Excitation Acc_25) Calculated (Top Subplot) Compared to Measured Signal-(Bottom) 20

21 A B Figure A5.28 Both Figures (A) and (B) Shows Signal Magnitude and Phase angle (Left Top-Bottom ), and Real and Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) all versus Frequency up to 100 Hz. Bladder Tested is S3_Onboard Blackhawk,(Excitation _acc_25). S.log Scale 21

22 A B Figure A5.29 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S3_Onboard MRAP- July (Excitation _acc_25). 22

23 S3 - November MRAP [acc_27] filtered into a 100 Hz cutoff Figure A5.30 Hanning Time-Window Filter Applied on S3 Bladder Nov-MRAP Test (Excitation acc_27_). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) Figure A5.31 Hanning Time-Window Filter Applied on S3 Bladder Nov-MRAP Test (Excitation Acc_27_). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 23

24 Figure A5.32 State Equation Prediction Time History And Measured Response (Left Subplots). Right Side: Power Spectrum of both Prediction and Measurement Response. S3_ Acc_27 S3_27 Model : S3 S3_27 Model = [test Foam D M SBlt ] = [ ] Linear Hammerstein Wiener Hammerstein-Wiener Linear Hammerstein Wiener Hammerstein-Wiener A t t e n c i o n " ATTENTION For SOUND-PLEASE Linear State_Eqn_yddt Linear State_Eqn_yddt

25 November Tests MRAP S3:[acc:27] and S4 [acc:33] S4 - November MRAP [acc_33] filtered into a 100 Hz cutoff Figure A5.33: Signal Phase Angle as a Function of Frequency. S3 Bladder Nov-MRAP Test (Excitation acc_27_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) Figure A5.34 Signal Phasors Real Value (Left) and Imaginary Value (Right), vs. Frequency. S3 Nov. MRAP Test (Excitation acc_27_) Calculated (Top Subplot) Compared to Measured Signal-(Bottom) 25

26 A B Figure A5.35 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (Left Top-Bottom ), Real And Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) vs. Frequency up to 100 Hz. Bladder Tested Is S3_Onboard Blackhawk,(Excitation _acc_27). S-Log Scale 26

27 A B Figure A5.36 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S3_Onboard MRAP-July (Excitation _acc_27). 27

28 Figure A5.37 Hanning Time-Window Filter Applied on S4 Bladder Nov-MRAP Test (Excitation acc_33_). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) Figure A5.38 Hanning Time-Window Filter Applied on S4 Bladder Nov-MRAP Test (Excitation acc_33_). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 28

29 Figure A5.39 State Equation Prediction Time History and Measured Response (Left Subplots). Right Side: Power Spectrum of both Prediction and Measurement Response. S4_acc_33 Nov. MRAP Figure A5.40: Signal Phase Angle vs Frequency. S4 Bladder Nov-MRAP Test (Excitation acc_33_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) 29

30 Figure A5.41 Signal Phasors Real Value (Left) and Imaginary Value (Right), vs. Frequency. S4 Blackhawk Test (Excitation Acc_33_) Calculated (Top Subplot) Compared to Measured Signal-(Bottom) 30

31 A B Figure A5.42 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (Left Top-Bottom ), and Real and Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) all versus Frequency up to 100 Hz. Bladder Tested is S4_Onboard Blackhawk,(Excitation _acc_33). S.log Scale 31

32 A B Figure A5.43 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff Hz. Bladder Tested is S4_Onboard Nov-MRAP (Excitation _acc_33). 32

33 S4 S4_33 Model = [test Foam D M SBlt ] AAA_l_accel100_Distinct_Plots_Sound_Match_S4_33_ sym S4 test = test; Foam = 2.0; D = 3/8; M = M; SBlt; Model = [test Foam D M SBlt ] S4 S4_33 Model: [test Foam D M SBlt ] = [ ] Linear Hammerstein Wiener Hammerstein-Wiener Linear Hammerstein Wiener Hammerstein-Wiener Linear State_Eqn_yddt Linear State_Eqn_yddt Lowest band is of fs - resampling to Hz for bands up to 4.0 Hz center freq... 33

34 A5.2.2 BLACKHAWK HELICOPTER TESTS Blackhawk S3:[acc:305] and S4 [acc:330] S3 - Blackhawk [acc_305] filtered into a 100 Hz cutoff Figure A5.44 Rectangular Time-Window Filter Applied on S3 Bladder Blackhawk Test (Excitation acc_305). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom) Figure A5.45 Hanning Time-Window Filter Applied on S3 Bladder Blackhawk Test (Excitation acc_305). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 34

35 Figure A5.46 State Equation Prediction Time History and Measured Response (Left Subplots). Right Side: Power Spectrum of Both Prediction and Measurement Response. (Blackhawk-S3_acc_305) Figure A5.47 Signal Phase Angle vs. Frequency. S3 Bladder Blackhawk Test (Excitation Acc_305_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) 35

36 Figure A5.48 Signal Phasors Real Value (Left) and Imaginary Value (Right), vs Of Frequency. S3 Blackhawk Test (Excitation acc_305_) Calculated (Top Subplot) Compared To Measured Signal-(Bottom) 36

37 A B Figure A5.49 Both Figures (A) and (B) Shows Signal Magnitude And Phase Angle (Left Top-), And Real and Imaginary (Right-Top, for Both Measured Response (A) and State Eqns. Prediction (B) all vs Frequency up to 100Hz. Bladder Tested Is S3_Onboard Blackhawk,(Excitn.. _Acc_305). S-Log Scale 37

38 A B Figure A5.50 Both Figures (A) and (B) Shows Signal Magnitude and Phase Angle (A): Semi-Log-Scale (Top Eqns, Bottom- Measured), (B): Log-Log Scale (Left-Magnitude, Right, and Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S3_Blackhawk (Excitation _acc_305). 38

39 S3 S3_305 Model: [test Foam D M SBlt ] = [ ] Linear Hammerstein Wiener Hammerstein-Wiener A t t e n c i o n " ATTENTION For SOUND-PLEASE Linear State_Eqn_yddt Linear State_Eqn_yddt Lowest band is of fs - resampling to Hz for bands up to 4.0 Hz center freq... S4 BLACKHAWK [acc_350] filtered into a 100 Hz cutoff 39

40 Figure A5.51 Rectangular-Time-Window Filter Applied on S4 Bladder Blackhawk Test (Excitation acc_350) of Calculated (Top Subplot) Compared to Measured Response (Bottom Subplot) Figure A5.52 Hanning Time-Window Filter Applied on S4 Bladder Blackhawk Test (Excitation Acc_350_). Spectrum of Calculated (Top Subplot) Compared to Measured Signal (Bottom Subplot) 40

41 Figure A5.53 State Equation Prediction Time History and Measured Response (Left Subplots). Right Side: Power Spectrum of Both Prediction and Measurement Response. (Blackhawk-S4_acc_350) Figure A5.54: Signal Phase Angle vs Frequency. S4 Bladder Blackhawk Test (Excitation acc_350_) Calculated (Top Subplot), Compared to Measured Signal (Bottom Subplot) 41

42 Figure A5.55: Signal Phasors Real value (left) and Imaginary value (right), vs. S4 Blackhawk Test (excitation acc_330_) Calculated (Top subplot) Compared to Measured Signal-(Bottom) 42

43 A B Figure A5.56 Both Figures (A) and (B) Shows Signal Magnitude and Phase angle (Left Top-Bottom ), and Real and Imaginary (Right-Top- Bottom), for Both Measured Response (A) and State Eqns. Prediction (B) versus Frequency up to 100 Hz. Bladder Tested is S4_Onboard Blackhawk,(Excitation _acc_350). S-log Scale 43

44 Figure A5.57 Shows Signal Magnitude and Phase Angle (Top Eqns, Bottom- Measured), (Left-Magnitude, Right, Phase), Both Measured Response (Bottom) and State Eqns. Prediction (Top). Low-Pass-Frequency cutoff is to 100 Hz. Bladder Tested is S4_Onboard MRAP-July (Excitation _acc_350). Semi-Log-Scale A5. 3 DISCUSSION Validation for viability of our Model prediction requires comparing measured actual and calculated results. We will show in this chapter both acquired measured acceleration and model calculated acceleration results both for the same input acceleration values acquired directly from input accelerometers. Results will be analyzed in next chapters. Frequency and time domain responses will be listed here than later discussed. Both System Identification and Model calculated through the system of developed equations are compared to the respective measured values in terms of acceleration responses and response criteria. Model calculated results used for comparisons and measured values averages are obtained in the same manner, as both tabulated and the operated on to obtain, the required response criteria such as, transmissibility or RMS, VDV, and even test averages, are all made in the same way and on both sets tabulated together in the same matrix. Results presented in this chapter will be discussed in the following 44

45 chapters along with and co moments and conclusion. Test environment and tested items will be identified, followed by results of each test. There are four bladders. Input accelerometer is placed under the bladder, in each test and output or measured response accelerometer is placed above the bladder, and underneath the seat occupant. No accelerometer is placed on the seat back portion.... " T h e I m p o r t a n t T h i n g i s N o t t o S t o p Q u e s t i o n i n g. C u r i o s i t y h a s i t s O w n R e a s o n f o r E x i s t i n g ; Albert Einstein. 45