Signal Analyzer, the software support for education of signal processing and measurements

Transcription

1 VŠB Technical University of Ostrava 17. listopadu 15, Ostrava Poruba Czech Republic Signal Analyzer, the software support for education of signal processing and measurements Jiří Tůma Faculty of Mechanical Engineering Department of Control Systems and Instrumentation 1

2 Outline Signal processing branches Requirements for education software Basic principle of handing with Signal Analyzer Input signals and instruments Output plots Teaching support Research work Conclusion 2

3 Signal Processing Branches Overall data analysis (A-, B-, C-type filtration, Lin) Fourier Transform, Hilbert Transform Spectral analysis, averaging in the frequency domain Spectral maps evaluation, auto- and cross- correlation analysis Frequency responses evaluation Envelope analysis and phase demodulation Rotational speed evaluation from an impulse signal Data resampling, averaging in the time domain Order analysis based on FFT or Vold-Kalman filter Filtration in the time and frequency domain, FIR filtering, wavelets Quadrature mixing for envelope and phase analysis Kalman filter for estimating a random constant Eigenanalysis (Pisarenko s and MUSIC methods) Spectral analysis based on AR modeling Statistics (histograms, rain-flow analysis, fatigue evaluation) 3

4 Requirements for Education Software Windows based handling Data and instrument setups encapsulation enabling capture of both data and setups in project files User interface in English Simulation of professional signal analyzers (averaging process, multispectra evaluation) Replaying signals using a PC sound card Plots based on Microsoft Graph component Importing data from data files, clipboard or sound cards Exporting graphs by Copy and Paste methods into Word documents 4

5 Main Window Arranged as a Multiple Document Interface Program Icon Organisers Notepad 5

6 Main Menu & Context Menu Main Menu Submenu Input Signal Presentation Context Menus 6

7 Organizers in the Form of Tree Structures Measurement Organiser (Root) - Measurements - Individual Signals Instrument Organiser (Root) -Instruments - Input Signals 7

8 Type of Data Sources Data Source Binary Data arranged in Columns ScopeWin binary W-Files ASCII Data from Clipboard ASCII Data from Text File Waveform File Waveform Audio Input Device and IO Device BK 232 Time, BK 355, PULSE LabShop Signal Generator Description 16 bits data in binary file Binary data generated by ScopeWin ASCII data from clipboard ASCII data text file (arbitrary format, UFF) Wave files (8, 16 and 24 bits) Data recorded directly from sound cards (mono/stereo, 8/16 bits) and NI USB-69 Binary & ASCII data from BK 234/32 and PULSE signal analyzers Data generated manually or automatically 8

9 Signal Generator Sum of components consisting of up to 4 harmonic signals differing in frequency, amplitude and initial phase (amplitude and phase of 2 of them can be modulated) and/or rectangle and/or swept sine and/or white and pink noise 9

10 FIR Filter Design Ideal Filters Lowpass/Highpass FIR filter Lowpass differentiator FIR filter Lowpass Hilbert transformer FIR filter Bandpass FIR filter Filters with Kaiser window Lowpass/Highpass FIR filter Lowpass FIR differentiator Lowpass FIR Hilbert trasformer Bandpass FIR filter 1

11 Fast 1/f α Noise Generation,8,6,4,2, -,2 -,4 -,6 Flicker Noise : Signal (Alpha 1, Filter Number 8),,2,4,6,8 1, Time [s] α =, Filtered White Noise < α < 2, Filtered 1/f α Noise α = 2, Random Walk 11

12 Processing of Raw Time Histories ZOOM, Cursor Individual sample editing Inserting signal segments into Measurement Organizer 12

13 BK Signal Analyzers as a Source of Time History Data Binary files Text files & Clipboard Data Brüel & Kjær BK 234/232 ABF Files LabShop PULSE Time History ASCII Data LabShop PULSE Time Capture Instrument BK 355 Time History Files Signal Analyzer LabShop PULSE Wave Files 13

14 Direct Recording Waveform Data Sample Frequency Mono / Stereo Bits per Sample Insert into the tree MM Control Left Channel Data Right Channel Data 14

15 Multifunction I/O Devices NI USB-69: 14-Bit, 48 ks/s Low-Cost Multifunction DAQ NI DAQCard-636E (for PCMCIA): 2 ks/s, 16-Bit, 16 Analog Input Multifunction DAQ NI USB ks/s, 1 db,.8 Hz AC/DC Coupled, 5-Input Sound and Vibration Device 15

16 Signal Analyzer Instruments 1 Instruments based on the Fast Fourier Transform Fourier Hilbert Instrument Time FFT CPB Autospectrum Cross-Spectrum FRF` Description Hilbert transform, filtration in the frequency domain, amplitude and phase demodulation (full spectrum) FFT, filtration in the frequency domain (full spectrum) Averaged 1/1-octave and 1/3-octave frequency spectrum Averaged autospectrum (full spectrum) Averaged cross-spectrum Averaged frequency response 16

17 Signal Analyzer Instruments 2 Instrument Overall Tachometer Resampling 2nd Resampling Correlation FIR Filters FIR Filter FRF Description Overall level of the high passed signal in RMS or PWR RPM evaluated from an impulse tachosignal Resampling of signal 2nd Resampling of signal and time delay Auto and cross correlation Two FIR Filters, Hilbert transform, quadrature mixing FIR filter FRF including filter zeros 17

18 Signal Analyser Instruments 3 Instrument Vold-Kalman Kalman Filter Statistics AR Model AR Spectrum Description Vold-Kalman order tracking filter Kalman Filter for Estimating a Random Constant Histogram, Cumulative Histogram, Empirical distribution function, Expected values of normally distributed data Autoregressive model coefficients evaluation Frequency spectrum based on autoregressive model including filter poles 18

19 Signal Analyzer Instruments 4 Instrument Linear Combiner Eigenanalysis Difference Detrend Test Unit Script Description Linear combiner, Prediction, AR Process Eigenanalysis of correlation matrix, Pisarenko s method, Music pseudospectrum Weighted difference of two signals Detrend of a signal Unit is only for testing response of the 2-order system Programming language for signals 19

20 Saving Output Data Format of output data files ASCII Files Waveform Files (16 bits) ME scope spreadsheet files for Operational Deflection Shapes & Modal Analysis Binary files for INOVA loading stands Files containing projects including signals and instrument setting ASCII Files (extension *.sga) Binary Files (extension *.sgb) Export charts in the graphic format *.gif files *.jpeg files 2

21 Inserting Signals into Instrument Input Signal Group Main Menu Drag & Drop Context Menu 21

22 Plot & Data Editing Data Sheet Microsoft Graph Environment 22

23 [-] Output Plot Time History : DRIVEBY : Signal,,2,4,6,8 1, Scatter with Line Plot Microsoft Graph Microsoft Graph Environment Time [s] 3-D Surface Plot 23

24 Output Plot 2 3-D Clustered Bar Plot Surface (Top View) Plot Microsoft Graph Environment 24

25 Plot Export into a Word Document Click Copy button Click Paste button Here doubleclick to edit Select this form 25

26 Setup 1 for Data Processing 26

27 Setup 2 for Data Processing 27

28 Signal Processing and Machine Diagnostics Teaching Support Demo-projects based on both simulated signals and real signals from a research work for industry ( Help file and e-book support (76 pages in Czech) Textbook on signals and signal processing methods (126 pages in Czech) Student s homework support 28

29 Running Autospectra RMS [U] Noise excited by run-up of a 8-cylinder and 4-stoke Diesel engine Autospectrum 1 : VPM11A : Misto 1 hluk db(a) RPM Color: Noise RMS,35-,4,3-,35,25-,3,2-,25,15-,2,1-,15,5-,1 -,5 Frequency [Hz] Frequency 29

30 Full Multispectrum of Signal x(t) + j y(t) Two-side spectrum for journal bearing diagnostics x(t) y(t) Autospectrum : X + jy.475 ord 1. ord 2. ord RPM RMS μm Frequency [Hz] 3

31 FRF [db] Test Unit Frequency Response Function with Resonance & Anti-resonance Input Frequency [Hz] Output Time : Generator 4 : Col ,,2,4,6,8 1, Time [s] Test Unit : Generator 4 : Col ,,2,4,6,8 Time [s] 31

32 CPB, Autospectra and Frequency Response Functions Ride comfort, truck seat frequency response functions 32

33 Frequency Weighting Sound Lin (no weighting), A-Type, B-Type, and C-Type Vibrations ISO, SAE J149 Characteristics Frequency range Mezinárodní norma Total vibration Vertical direction (V-ISO ),5 až 8 Hz ISO : 1997 Horizontal direction (H-ISO ),5 až 8 Hz ISO : 1997 Building, all directions (Bu-ISO ) 1 až 8 Hz ISO : 1989 Vertical direction, motion sickness,1 až,5 Hz ISO : 1997 (TV-ISO ) Z-SAE J149 SAE J149 X-SAE J149 SAE J149 Hands All directions 8 až 1 Hz ISO 5349 :

34 db/ref 1 V V db/ref 1E-6 Filtration in the Frequency Domain Band Pass Band Stop Comb Band Pass Comb Band Stop H(f) H(f) H(f) H(f),,5 1, 1,5 2, 2,5 3, Frequency,,5 1, 1,5 2, 2,5 3, Frequency Conversion the frequency modulated impulse signal to a harmonic signal, 1,5 3, 4,5 6, 7,5 9, Frequency, 1,5 3, 4,5 6, 7,5 9, Frequency Time 3 : Expanded Time(Encoder1) ; Expanded Time(Encoder2),,5,1,15,2,25,3, Time [s] Timer : Time: Real (Expanded Time(Encoder1)) ; Time 2: Real (Expanded Time(Encoder2)),,5,1,15,2,25,3,35 Time [s] Autospectrum 1 2 Frequency [Hz] Autospectrum 1 2 Frequency [Hz] 34

35 FFT Convolution Segments FFT Filter IFFT Rev Ord Low Pass Rev Rev Ord Low Pass Rev = = 2-2 Rev (FFT Convolution for smoothing discontinuities of consecutive records) 2-2 Rev

36 RMS m/s2 RMS m/s2 m/s2 m/s2 Averaging in the Time or Frequency Domain ,2,18,16,14,12,1,8,6,4,2, Resampled signal Time : Acc (Resampled),,2,4,6,8 1, Revolution [-] Autospectrum : Acc (Resampled) Order [-],8,6,4,2, -,2 -,4 -,6 -,8,2,18,16,14,12,1,8,6,4,2, Synchronously averaged signal Time History : Acc (Averaged),,2,4,6,8 1, Revolution [-] Autospectrum : Acc (Averaged) Order [-] 36

37 Magnitude U U Magnitude U Wavelets Denoising 3 Time History : Clipboard : s Time [s] FRF of Quadrature mirror filters LP filter HP filter FIR Filter : QMF - db 2, Lp 1,5 1,,5,,,3,5,8 1, Normalised Frequency [-] FIR Filter : QMF - db 2, Hp 1,5 1,,5,,,3,5,8 1, Normalised Frequency [-] Approximation FIR Filters : Clipboard : s Details Time [s] FIR Filters : Clipboard : s Time [s] 37

38 m m/s2 Structure Vibration Analysis Signal Analyser Input acceleration data Time History : Ram za kab. pravy Time [s] Double integration ME scope ODS (Operational Deflection Shape) software,1,5, -,5 -,1 Time History : Ram za kab. pravy Time [s] Export 38

39 Expected Values of Normally Distributed Data Expected Values of Normally Distributed Data [m/s^2] Number [m/s^2] Number Histograms Cab floor acceleration Time History : PODLAHA Histogram Time [s] Normal distribution Straight line Statistics : PODLAHA [m/s^2] Statistics : PODLAHA [m/s^2] Seat pan acceleration Time History : SEDACKA Histogram Time [s] Non-linearity effect Statistics : SEDACKA [m/s^2] Statistics : SEDACKA [m/s^2] 39

40 ,84 5,88 1,92 15,96 21, 26,4 31,8 36,12 Number of cycles Number of cycles Extremes for Rainflow Rain-flow Counting Method Time History : Signal Time [s] Statistics : Sequence of local extremes Index 3D Rain-flow Balda s algorithm 5 2D Rain-flow ,28 4,2-5,88 Mean 2 1,84 4,2 7,56 1,92 14,28 17,64 Amplitude 21, 24,36 27,72 31,8 34,44-15, 96 Analysis of fatigue data Amplitude 4

41 Fatigue Damage, Palmgren-Miner's Rule (Sm=) Fatigue Damage, Palmgren-Miner's Rule (Sm<>) Rainflow - Mean Values vs. Amplitudes Stress amplitude Stress-Life Fatigue Analysis Amplitude vs. Mid Value of Cycles 3 2 Statistics : Test : x Endurance Limit Stress-Number Curve 1 S-N Curve Amplitude Number of cycles,35,3,25,2,15,1,5, Statistics : Test : x Cumulative Damage Index Zero Mid Value of Cycles,35,3,25,2,15,1,5, Statistics : Test : x Cumulative Damage Index Non-Zero Mid Value of Cycles 41

42 Programming language Operators +, -, *, /, ^, ==, ~=, <, >, <=, >= Signals, variables x1, x2[n], a[n1][n2], c, del, Instructions for, while, exit, if - else, { } Functions iif, sin, cos, tan, atn, abs, sqr, mag, angle, unwrap, ones, exp, log, avg, sum, cumsum, length, max, min, filter, Text box for inserting a script 42

43 VB Code versus Scripts Example: Computation of the matrix product Visual Basic code For i = To m - 1 For j = To n - 1 S = For k = To p - 1 S = S + a(i, k) * b(k, j) Next k c(i, j) = S Next j Next i VB Code - Predefined algorithms Matlab script >> c=a*b; Script statements Script interpreter VB Code - Predefined algorithms Scripts facilitate programming 43

44 Features of Scripts Easy to understand and to use Based on C++ an Matlab, handling with signals as vectors and matrixes Set of built-in functions for signal processing (FFT, IFFT, Hilbert, ) Repeating instructions (for, while) Saving results as a part of projects Graphic output (MS Graphs) Code debugging (TraceOn, TraceOff, TraceIn, TraceOut) 44

45 Creating the Library of Subroutines List of subroutines Parameters Statements of Script Build-in statements and functions can be extended by subroutines, which are designed by a software user. A subroutine An example: _norm(x, a); 45

46 Example of a Script Code 'Pocet vzorku: ; n = 124; n; FS = get(x1,'freq'); M = 2; index = [;cumsum(ones(n-1))]; hanning = 1- cos(2*pi*index/n); d = [ ]; for(i=1;i<=m;i=i+1) { status(i); rem('poznámka'); a = extract(x1,round(n*(i-1)/3),n); if(i==1) variables; a = a * hanning; column b = (mag(fft(a,'real'),fft(a,'imag'))/n*2/sqr(2))^2; column c = [sqr(2)*b[]/2, extract(b,1,n/2-1)]; d = [d, c] column }; e = transpose(d); pwr = avg(e,m); rms = sqr(pwr); 'CrLf ; 'CrLf ; 'Autospektrum: ; 'CrLf ; set(rms,n/fs,'freq'); set(rms,'hz,'unit'); format(rms,.') Weighted and averaged frequency spectrum signal a b c matrix a b c a b c transposition 46

47 [m/s2] Additional Functionality in Gear Diagnostics Resulting from Scripts Rem( Script for polar plots ); a=input1; fi=input2/27; r=.3+a; x=r*cos(fi); y=r*sin(fi); save(x); save(y),4,2 Polar Plot [(m/s2)^2],3,2,1, 27-tooth wheel tooth wheel 37 4, -,2 -,4 -,4 -,2,,2,4 [m/s2] Rem( Averaging synchronized with hunting frequency ); x=extract(input1,, 18*27*4*6); x=set(x,6,'columns'); y=transpose(x); y=avg(y,6); y=set(y,486/27,'freq'); y=set(y,4,'columns'); matrix(y^2) 47

48 Evaluation of the ARX Model using a Script x=input1;y=input2; z=[y(-1),y(-2),x,x(-1),x(-2)]; c=z\y; a=[c[];c[1]]; b=[c[2];c[3];c[4]]; 'Model '; 'y = a1*y(-1) + a2*y(-2) + b*x + b1*x(-1) + b2*x(-2)';'crlf';'crlf'; 'Coefficients';'CrLf';'a = ';a;'crlf';'b = ';b;'crlf';' sy=get(c,'param1')/len(y); 'Model error standard deviation ';sqr(sy);'crlf'; zz=diag(invs(prod(tr(z),z))); 'Coefficient error standard deviations';'crlf';sqr(sy*zz);'crlf'; freqz(b,a,1,'mag'); Results Model y = a1*y(-1) + a2*y(-2) + b*x + b1*x(-1) + b2*x(-2) Coefficients a = [1,9175 -,9816] b = [,2436 -,413,2421] Model error standard deviation,123 Coefficient error standard deviations [5,523E-3 5,521E-3 3,231E-3 3,483E-3 3,427E-3] ,1,1,1 Input - Output Signals,,2,4,6,8 1, Time [s] Frequency Response,,1,2,3,4,5 Frequency Relative to Nyquist Frequency 48

49 Linear Algebra and Signal Processing in Scripts of the Signal Analyzer Software MATLAB Matrix & vector product Array multiplication as the element by element product Matrix left division of a column vector Matrix inversion and pseudoinversion Svd, chol (Cholesky factorization) Roots, poly, trace, eig, det, cond Filter, conv, deconv, fft, ifft, angel, abs, unwrap, ar, arx,... Sparse matrices Signal Analyzer yes yes yes yes yes yes yes not implemented yet 49

50 Research Work Vold-Kalman order tracking Sound quality Kalman filter for estimating a random constant Angular vibration Quadrature mixing Spectral analysis based on autoregressive (AR) modeling Pisarenko s method Music pseudospectrum 5

51 RMS db / ref,77 Hz Vold-Kalman Order Tracking Filter First generation filter Second generation filter 1 Filter frequency response Abs(H) r = Time History : Clipboard : Col Time [s] Swept sine frequency V-K Filter centre frequency Vold-Kalman One-Pole Filter : Generator : SweptSine f /f s Time [s] 1-pole filter 2-ple filter 3-pole filter 4-pole filter 51

52 RPM c/(c-v) RMS db(a)/ref 2E-5 [Pa] [Pa] Pass-By Noise Analysis Enabling De-Dopplerisation 1,5 1,,5, -,5-1, -1,5 Sound pressure time history Time History : 3r : Left Time [s] RPM profile 3r : Inst Speed Time [s] Doppler factor c/(c-v) Vold-Kalman : 3r : Left 1,2 1,1 1,,99,98, Position [m] Noise level of RPM orders Vold-Kalman : 3r : Left Position [m] 27 ord 54 ord 81 ord 52

53 [-] Sound Quality Analysis Filtered signal synthesis Vold-Kalman : vyfuk_l_mono.wav 2 : Signal Time [s] 2 ord 4 ord 6 ord 8 ord 53

54 Hilbert Transform & Phase Demodulation Transmission Error Measurements 54

55 rad U Quadrature Mixing s(t) - j sin(ω c t) cos(ω c t) Modulated harmonic signal Modulation signal , -,5-1, -1,5-2, -2,5 LPF LPF Real part x Real (t) Complex signal x Imag (t) Imag part Phase demodulation of amplitude and phase modulated harmonic signals Time History : Generator 1 : Sine1/PM - 1,,2,4,6,8 1, Time [s] FIR Filters : Generator 1 : Sine1/PM - 1,,2,4,6,8 Time [s] 55

56 U U U Number Kalman Filter for Estimating a Random Constant ADC wideband noise due to the thermal effect Time History : data1 : Col Filter output Time [s] Time History : data1 : Kalman Filter (Col 1) Time [s] y i s i Grounded-input histogram Statistics : data1 : Col Cumulative difference U Difference 1 : data1 : Kalman Filter (Col 1) Time [s] i s k y k k 56

57 RMS V RMS V V Coefficients AR Modeling in Spectral Analysis AR y a y a y... a : t 1 t 1 2 t 2 M y t M e t PSD f M 2 2 T a exp j2 mft 1 m 1 m Decaying signal 5-order AR model coefficients,6,4,2, -,2 -,4 -,6 -,8,15,12,9,6,3, Time History : MA5_8 : Signal,,1,2,3,4 Time [s] FFT Autospectrum FFT Autospectrum : MA5_8 : Signal Frequency [Hz] 3, 2, 1,, -1, -2, -3,,15,12,9,6,3, AR Model 6 : MA5_8 : Signal AR Spectrum Index AR Spectrum : MA5_8 : AR Model Frequency [Hz] 57

58 RMS Music Pseudospectru m db 4,5 Hz 2,15 Hz U RMS 4,1 Hz 2,4 Hz Pisarenko s and MUSIC Methods 1-sample record of a signal Pisarenko s method 2, 1,5 1,,5, -,5-1, -1,5 Time History : Sine1+Sine2+Noise,,2,4,6,8 1,,8,6,4,2, Eigenanalysis : Sine1+Sine2+Noise Background noise level Time [s] Frequency [Hz] FFT Autospectrum Autospectrum : Sine1+Sine2+Noise,7,6,5,4,3,2,1, Frequency [Hz] MUSIC method Eigenanalysis : Sine1+Sine2+Noise Frequency [Hz] Sine1: 4 Hz, Amplitude 1 Sine2: 2 Hz, Amplitude.5 58

59 Conclusion The paper describes software that supports signal processing education at the Faculty of Mechanical engineering of the VŠB Technical University of Ostrava. The signal processing lectures are extended by a set of exercises based on measurements performed as a result of the research work for industry. Students that are working with Signal Analyzer can analyze imported measurement data or make their own noise measurements using a sound card as the first step to become experts. 59