It was concluded that the post processing digital filter is quite effective for removing unwanted high frequency and noise without distorting the signal. In addition, digital filtering is effective for smoothing low-level low resolution digital data where the digital stairstep phenomena are pronounced. Integrating the acceleration data to obtain velocity traces is quite useful. The velocity change provides a check on the validity of the acceleration trace. (Zero offsets in acceleration must be removed before integrating.) Average accelerations can be obtained from the velocity trace by dividing the change in velocity for an acceleration pulse by the pulse duration. One can obtain the peak of an equivalent triangular pulse by doubling the average acceleration

Pasanella, E. L.

English

NASA Technical Reports Server

DIGITAL FILTERING
AhD ACCELERATION PULSE INTERPRETATION
E. L. Fasanella
PRC Kentron, Inc.
Aerospace Technologies Division
Hampton, Virginia
NASA/FAAGovernment/IndustryCID _brkshop
NASA Langley Research Center
April i0, 1985
103
https://ntrs.nasa.gov/search.jsp?R=19860012470 2020-03-20T14:57:07+00:00Z
TOPICS
This presentation will address digital filtering of the CID data and a
technique to analyze the acceleration data (fig. I). Analog filtering was
performed by electronic hardware (low pass analog filters) on board the
aircraft to remove undesired high frequencies and to prevent errors due to
sampling. Digital filtering is a computerized post-processing filtering
technique that can be applied to the digitized time history data. Low pass,
high pass, and notch filters can be mathematically simulated with this ,
technique.
In order to validate acceleration traces, the integrated crash pulse
velocity change was computed. Traces with velocity change outside the
expected envelope were either rejected or set aside for additional study.
Average accelerations were computed by dividing the primary impact velocity
change by the pulse duration. An equivalent triangular pulse acceleration
was computed by doubling the average acceleration and this value was
compared to peak acceleration values. Selected traces were chosen that
illustrate the effects of digital filtering for structure and dummy
occupants. Other traces were chosen to illustrate the method used to obtain
the average pulse acceleration and to triangularize the acceleration pulse.
• Digital filtering
• Digital versus analogfiltering
• Data interpretation
• Peakand averageaccelerations
• Velocity
• Triangularizing the accelerationpulse
• Discussionof selecteddatatraces
Figure 1
104
SAE CLASS 60 FILTER
A low pass filter with frequency response that lies within the inner
and outer limits sh_n by the solid straight lines is defined by SAE J211a
(ref. I) to be a class 60 filter. The digital filter chosen to smooth CID
accelerometer data is shown on figure 2 by a dashed line. The digital
filter is flat with no attenuation (0 decibels) to the cutoff frequency fc
and then rolls off until it attenuates all frequencies above the terminal
frequency ft" This digital filter with fc = I0 Hz and ft = 188 Hz will be
designated henceforth as the CID 100-Hz digital filter.
2 - ClD 100Hzdigital filter Outer limit
0-- ---_ "_/-
-4- x\ Digitalfilter
-6 - Inner limit fc 10Hz
,o- /', \Decibels ft = 188Hz
-15 - I _
-20 -
-25 I I I I
•1 1.0 10 100 1000
Logfrequency, Hz
Figure 2
I05
DIGITAL FILTERING EXAMPLE
The upper trace in figure 3 illustrates the "raw" acceleration time
history for channel 276 without any digital filtering. At the bottom left
corner of the lower plot, the number 33731.000 is the starting time of the
plot in seconds and corresponds to 9 hours 22 minutes and ii seconds. The
lower plot is a magnification of the 0.02 second period from 33731.60 to
33731.62 seconds. The circles are the original raw data points that were
sampled at every 1000th of a second, and these raw data points are connected
by straight line segments. (In the top plot the circles are left out and
only the line segments are present.) The data points represented by circles
were input into the 100-Hz digital filter program. For each circle or raw
data point, a corresponding square digitally filtered point is shown in the
bottom plot. In actual practice, the filtering program uses N raw data
points before time tnand N data points after time tn to calculate one
filtered value at tn.
18- CH276
8
Accel, ml _V VV_ V_v',_
12 ' VV-'" ",
- I " \
.. \
-22 I _.1" I I I I \_ I I
3 - o" Timeslice showing "i"/\ ' CH2761 /\ digital filter smoothing "t \
1..." /
Accel, _ - _.D-_'_- o \\ FCH276
G /-3 - \o/ o,,,,_Rawdata Dtgltal filter
-5 I ,I , I , I , I , I
.600 .604 .608 .612 .616 ,620
33731.000 Time,sec
Figure 3
106
DIGITAL FILTERING BACKGROUhD MA_EMATICS
Figure 4 illustrates the low pass filter gain ratio H (w) in the
frequency domain. The gain is one (no attenuation) for frequencies from 0
to the cutoff frequency wc and then starts rolling off as defined by an
arbitrary decreasing function g (w) with boundary conditions g(Wc) = 1 and
g(wt) = 0. To transform the gain function to the time domain, the inverse
Fourier transform h(t) must be evaluated.
Lowpassfilter characteristics
• Frequencydomain
1.0 g (w) = arbitrary decreasingfunction
Hlw) w) glw )= I
Boundaryconditions c
-_ g(wt) = 0
wc wt
wherew = 2 7rf
• Time domain
CX3
l / e iwt H (w)dwh(t) = 2 _
Figure 4
107
DIGITAL FILTERING BACKGROUqq3MATHEMATICS
For simplicity, let us assume the function g(w), which defines the
rolloff of the filter in the frequency domain, is a cosine function (ref.
2). Then the inverse Fourier transform h(t) can be evaluated in closed form
as given in figure 5. Next assume the data points to be filtered are
equally spaced with interval delta t. For this fixed delta t, let us
evaluate an arbitrary 2N + 1 values of h(n delta t). The n th normalized
value of h(n delta t) is denoted by hn bar.
EvaluateInverse Fourier Transform
oO
1 / iwth (t) = 2--_ e H(w) dw with rolloff g(w ) a cosinefunction
--<X)
_, [sin wtt + sin wet
then hit)=2-{- [_.2_(wt_wcl2t2
assume m equally spaceddatapoints (dl, tl) , (d2, t2) ...(dm, tin)
where t = nat
n
Evaluateh (t)to obtain2N+ t coefficientsfor a given fixed At
Denoteh the nth normalizedcoefficient
_n
h =h
n n
N
T:.h
-N
Figure 5
108
DIGITAL FILTERING BACKGROUSD MATHEMATICS
The N+I filtered data point is denoted in figure 6 as d'N+1 and is
given by a summation which is a Fourier convolution. Note from the formula
(figure 6) that to calculate the first filtered data point N data points
are used before the first filtered value and N data points are used after
the first filtered value. In the simple example where N = 3, there are
seven (2N+I) terms in the formula to calculate each filtered data value.
The first filtered value d'4 is generated by using points dI to d7 in the
formula. To calculate the second filtered value d'5 the same process is
used by taking the seven points d2 through d8 each multiplied by the proper
h bar.
The integer N needed for 1 percent accuracy can be computed from the
last formula where ft - fc is the rolloff frequency region.
N _ _
d'N = ]C hndN = h_NdI + +hodN + hNd2N+1 -N +n+l " " " +1" " " +1;
whereh = h.
-i I
-  od4  3d7for exampleif N= 3 d'4= h_3dl + ...... + + +
d4 /--1st filtered point d'4d2
,_d3_ d6 d_ d8/
t l t2 t3 t4 t5 t6 t7 t8 t9 tm
For l%accuracy we require NAt (ft-fc)-> 2
Figure 6
109
ERROR ANALYSIS OF CID 100-Hz DIGITAL FILTER
To evaluate the accuracy of the 2N+I terms used to represent the gain
function, one can expand H(f) as a Fourier series using the formula given in
figure 7. For the CID digital filter, FI, the cutoff frequency, was chosen to
be i0 Hz, F2,the termination frequency, was chosen to be 188 Hz, and N was
arbitrarily chosen to be 150. The gain function H(f) plotted on the left
can be seen to accurately represent the intended filter. Using the .accuracy
check formula at the bottom of figure 7, N(delta t)*rolloff is equal to 53.7
for a sample rate of 500. Since this value is greater than two, the error
of the filter is less than one percent. For a sample rate of i000 a
digital filter of 100-Hzcanalsobegeneratedwith error less than one
percent. Since CIDdatawere sampled at both 500 and 1000 samples per
second, two 100-Hz digital filters had to be programmed, one for each sample
rate.
Filter F1= 10, F2= 188 ChooseN= 150(arbitrary)
1.0 Coefficients= 2N+ 1= 301
Theapproximationto the idealH(f)
is given by:
150
H(f)=h0+2 _ h cos(2 ;rnfAt)Gain 1 n
ratio, . 5 \k 1H(f) At= "" 0o 002
- \ samplerate
\ Accuracy check
Error < 1%
I I I I i i J'_ _
0 100 200
Frequency,Hz
Figure 7
110
EXAMPLE OF DIGITAL FILTER WITH ERROR EXCEEDING 1 PERCENT
Figure 8 illustrates an example of a digital filter with N = 150 that
demonstrates undesirable overshoot and undershoot from the ideal gain
function. In this example if one calculates N(delta t)*(rolloff) using the
accuracy check formula, a value of only 0.375 is obtained. Since this value
is less than 2, the error would exceed 1 percent. To obtain the desired
accuracy, either N or the rolloff region would need to be increased.
Error > 1%
N= 150
1.8- SR= 4000
fc = 57.9 Hzr shoot
ft = 67.9HzI. 0
Gain
ratio,
H(f)
o ;n0erh 's oot
-I.0 I I
0 I00 200
Frequency,Hz
Figure 8
111
PILOT FLOOR ACCELERATION NORMAL DIRECTION
The pilot floor acceleration data (normal to the floor) were sampled at
500 samples per second and were taken from an accelerometer attached to the
floor at body station 228. The two plots shown in figure 9 are from channel
1 for the first second after engine number one on the left wing contacted
the ground. The top plot is the raw data as recorded with no post-crash
digital filtering. The second plot shows the data after passing through the
100-Hz digital filter discussed previously. The filter attenuates the high
frequencies and smoothes the digital data.
BS 228 SR= 5005-
No post filter FCH1
Acce,, 0 uU_L_J __, , _j_ul_ ,LL__bI__ ,_
G -5-
-10 -
-15 t t t _ t I t i I
5- 100Hz digital filter
CHI
-15 i i I I t [ I t t I
0 .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec(9 hr 22 min II sec)
Figure 9
112
FLOOR TRACK ACCELERATION NORMAL DIRECTION
The two plots in figure i0 show the floor track acceleration for the
first instrumented frame at body station 400. For this example, the sample
rate is 1000. Again the top plot is the data with no post filter and the
bottom plot is for the data passed post test through the 100-Hz digital
filter with F1 = 10 Hz and F2 = 188 Hz. These data were taken from CID
channel 276.
BS 400 ( Frame1) SR= 1000
18 F Nopost filter CH276
8 IJ
Accel, | ...... I_ll_A.J_lX,l,l... ,.._.__.o
18 [- 100Hzdigital filter
8 _- FCH276
Accel, - I __^ ._^^. _ F 10/188
G -2- _ _'-_-_"-_'_-_I_I_Vl/w_'_V_'_-_-_°
-12-
-22 i i I i [ _ _ r l i
0 .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure I0
113
FLOOR ACCELERATION NORMAL FOR FRAME 2
These two acceleration traces (CID channel 120) were taken at body
station 540. As we move back in the airplane, the acceleration levels
become lower and lower and the digital nature of the data is more
pronounced. In figure ii the smoothing effect of the 100-Hz digital filter
can clearly be seen. In the top plot, the acceleration data are quite
"stairstep looking" due to the resolution of the 8-bit digital data over the
+/- 150 G range required for the normal (vertical) direction. The lower
plot, which is the same data filtered with the 100-Hz digital filter, has
all the low-frequency characteristics of the raw data without the digital
"stairsteps."
BS 540 (Frame2) SR=IO00
2- / Nopost filter
o n |1 II111IoCH120
Accel, _JlllI]II[_Ill_l_ I_ I
G -2- ?
-4 --
-6 I I I I I I I I I
2 - I00Hzdigitalfilter
0 IJU V ll/ v ^ FCH120
Accel, -2 - F 10/188G
-4 -
-6 I I I I I I I I I I
0 .i .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure ii
114
DUMMY 14B PELVIS ACCELERATION NORMAL
The pelvis acceleration along the spineward direction for the center
dumny in the left seat in row 14 is shown in the two traces in figure 12.
The sample rate is 1000 per second. Again the 100-Hz filter removes the
high-frequency noise and cleans up the trace quite well.
2.0 F Nopostfilter CH264
.5
Accel, f o
G -I.0
-2.5
-4.0 I i I i I , I i l l
2.0-
100Hzdigital filter FCH264
Accel, / / _/ °
G -I.0 -
-2.5
-4.0 t i l J i t i i l i
0 .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure 12
115
DUMMY 3E PELVIS ACCELERATION LONGI_I]DINALDIRECTION
All longitudinal accelerations measured on the aircraft and dummies
were relatively low. Since the resolution of the 8-bit system was
approximately 1 G per count for this particular channel (an 8-bit system can
have frem 0 to 255 counts), the actual acceleration trace is only bounded by
the data. The digital filter does a reasonable job; however, it cannot make
up for the loss of resolution in this case (fig. 13).
1 F Nopost filter
0 CH194
Accel,
(3 -1
-2
-3 t I t J t I i t
1 _- 100Hzdigital filter FCH1940 F 10/188
AcceI,G-1 /_-_W %-/ _ I°
-2
-3 I I I I I I I I I I
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure 13
116
VERTICAL FLOOR ACCELERATION AhD INTEGRATED VELOCITY
The top plot in figure 14 is of the normal acceleration of the floor at
body station 540. The bottom plot shows the velocity curve obtained by
integrating the top acceleration plot. The dominant acceleration pulse from
0.48 to 0.62 seconds in time occurs when the fuselage impacts the ground.
The acceleration from 0 to 0.48 seconds is from the left wing impact.
Notice that the total vertical velocity change is approximately 18 ft/s, but
that the velocity change is composed of almost 4 ft/s taken out by the wing
and about 14 ft/s taken out by the fuselage. The average acceleration for
the fuselage impact can be computed from delta V of 14 ft/s divided by delta
T of 0.14 seconds which when expressed in G-units is 3.1 G's. If the
acceleration from 0.48 to 0.62 seconds were a triangular pulse, then the
peak would be twice the average or 6.2 G's. For this example, twice the
average acceleration and the peak acceleration directly from the plot are
nearly the same. The average acceleration and twice the average
acceleration are useful indicators in data interpretation of crash impact
severity.
BS 540 (Frame2) Normaldirection
2- _ CIDfloorNBS _40
o m I!1 |11 IoCH120
Accel, LII 11LII_1111 i/UllI
G - - -. _A-_ .I- Averageaccel= 3.1G'sI
-4 --
-6 t i r I If J i I I
,, ; AT= 0.14
0 _-__, VCH 120
-5- T
-T
Velocity, /
ft/sec-I0- AV=14.0
-15_-
-20 --C i i i _ -J°
0 .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure 14
I17
PILOT FLOOR ACCELERATION AND INTEGRATED VELOCITY (LONGI_JDINAL)
Using the same technique as in figure 14, the longitudinal acceleration
of the pilot floor is analyzed for the 0.13 second pulse shown in figure 15.
Note that the average acceleration is only 0.84 G in this case. Twice the
average acceleration, which would correspond to a 0.13 second triangular
pulse, would only have a peak of 1.68 G's. The peak G taken from the top
trace is about 6 G's, but it is of very short duration. The average
acceleration or peak triangularized acceleration has more meaning in this
case and can be compared with other locations in the aircraft with better
results.
6 Longitudinaldirection
I CH 2
3 I
 cce,,f !Vllij l,,,
G 0 r_uu_u" AverageUU-tfr'lV_,x'_' , u °
-3 accel=. 84G's
-6 i i i i ;Vj ]l i I I i
2 , ,AT= 0.13
' ' VCH 2
- I I
-I _--_
---_
Velocity, -4 - AV= 3.5
ft/sec __ j_ _
-7 - \__
-10 i J j i i l l l J j
0 .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
33731.00 Time, sec
Figure 15
i18
S_C_CHANNELS-P_MARYI_A_
The primary impact is defined to be the impact from the time the left
wing contacted the ground (9 hrs 22 min ii sec or 33731.0 sec) until the
rear of the fuselage made contact (about one second). The wing cutter
impact which occurred later will not be analyzed in this discussion. A
cross section of data from 51 representative CID channels was analyzed and
distributed at this conference. Figure 16 shows the format of the 34
fuselage accelerometer channels that were analyzed. For each channel the
location of the accelerometer, the direction, the body station, the peak
acceleration value, time the peak occurred, the velocity change of the main
pulse, the average acceleration of the main pulse, twice the average
acceleration, the sample rate, and the analog filter on board the aircraft
are all given. In addition, one-second traces from the time of left wing
contact are shown.
Fuselageaccelerometer data:
Peakvai Peaktime AV AT
Cha Location DIR BSTA G S ft/s S
2 Pilot floor L 228 6.10 0.48 3..51 0.13
1 Pilot floor N 228 14.30 0.48 17.60 0.08
3 Pilot floor T 228 4.00 0.14 10.00 0.12
276 FR#1 floor N 400 14o50 0.47 14.00 0.12
rt track
286 Frame1 top N 400 16.20 0.48 15.20 0.12
AVEACC 2xAVE Samplerate Analogfilter
Cha Location G G Hz Hz
2 Pilot floor 0.84 1.68 500 100
1 Pilot floor 7.29 14.58 500 100
3 Pilot floor 2.59 5.18 1000 100
276 Fr# 1 floor 3.62 7.25 1000 100
ft track
286 Frame 1 top 3.93 7.87 1000 180
Figure 16
119
SELECTED CID CHANNELS - PRIMARY IMPACT
Figure 17 illustrates the format of the 14 selected channels of wing
and pylon accelerometer data. Some of the velocity changes and other
analysis are not given because of accelerometer overranging that occurred
for some channels. All of the 14 selected channels were sampled at 500
samples per second and were filtered on board with 100-Hz analog filters.
Wing and pylon accelerometer data:
Sample rate: 500per second
Analog filter: 100Hz Peak val Peak time AV AT AVEACC 2xAVE
Cha Location DIR BSTA G S ft/sec S G G
332 L Engine front pylon N XXXX 80.00 0.15
339 R Engine front pylon N XXXX 5.10 0.62 14.40 0.19 2.35 4.71
336 L Engine rear pylon N XXXX 162.70 0.12
342 R Engine rear pylon N XXXX 28.70 0.62
184 L Wing F spar in L 806 19.10 0.11
Figure 17
120
LAP BELT LOAD CELL DATA
Figure 18 presents the lap belt load cell data for three selected
channels. Since load cells have lower frequency response than
accelerometers, a 50-Hz digital filter was chosen to filter the lap belt
load cell data. The digital filter for load cell data attenuates more of
the high frequencies with F1 = 6 Hz, F2 = 94 Hz, and - 3 dB attenuation for
50 Hz. The loads measured in the lap belts were very low because of the low
longitudinal accelerations in the crash.
Loadcells digitally filtered postcrash (fl = 6 Hz, f2= 94 Hz, -3dbat 50 Hz)
Sampleanalog
Peakval Peaktime Rate Filter
Cha Location BSTA LB S 1/S Hz
267 Dummy14Bleft belt 1220 80.00 0°98 500 60
103 Dummy14Eleft belt 1220 43.00 0.54 500 100
104 Dummy14Ert belt 1220 60.00 0.54 500 100
Figure 18
121
SUMMARY
In s_m_ary, the post processing digital filter is quite effective for
removing unwanted high frequency and noise without distorting the signal.
In addition, digital filtering is effective for smoothing low-level low
resolution digital data where the digital "stairstep" phenomena are
pronounced.
Integrating the acceleration data to obtain velocity traces is quite
useful. The velocity change provides a check on the validity of the
acceleration trace. (Zero offsets in acceleration must be removed before
integrating.) Average accelerations can be obtained from the velocity trace
by dividing the change in velocity for an acceleration pulse by the pulse
duration. One can obtain the peak of an equivalent triangular pulse by
doubling the average acceleration (fig.19).
• Digital filter effectivefor
1. Removingunwantedhigh-frequency vibrations
and noise
2. Smoothingdigital data
• Integratedacceleration(velocity) useful for
1. Obtainingvelocity changes
2. Establishingvalidity of accelerationtraces
3. Obtainingaverageaccelerations
4. Triangularizing the accelerationpulse
Figure 19
122
REFERENCES
I. Society of Automotive Engineers: Instrumentation for Impact Tests. SAE
J211a, revised 1971.
2. Graham, Ronald J. : Determination and Analysis of Numerical Smoothing
Weights. NASA TR R-179, 1963.
123


Digital filtering and acceleration pulse interpretation

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