Data analysis of full scale measurements with a hybrid computer

Report no. 352

r

March 1972

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

DATA ANALYSIS OF FULL SCALE MEASUREMEWPS

WITH A HYBRID COMPUTER

by

Ir. F.J. Pasveer

Ir. C.C. Glansdorp

M. Buiterihek

L

I

Scientific Officer Computation Center, Deift University of Technology

Members of the Staff of the Shipbuilding Laboratory

Summary

A short description of data reduction and analysis of full scale

w,

Introduction.

Planned full scale motion measurements with a containership lead to a careful

re-examination of the method of data reduction in view of the new hybrid

computer facilities available at the Computation Center of the Deift University of Technology.

The method of data reduction used so far was very time consuming due to

separate real time tape punching of all time histories of the measured

signals. Furthermore punching errors could not be entirely avoided because

of the large amount of numbers to be punched.

In 1969 a hybrid computer ADl/IBM18OO was installed and now a vast software

package is available or in development for the users of this facility.

It was found that existing progranis for the calculation of power spectra

together with data supply by a taperecorder could be applied with a number

of modifications as to meet the requirements of full scale motion measurements.

After some trialruns with old measurements it was decided to adopt this new method for data reduction and analysis of the measurements.

It appeared that when a suitable division in analog and digital calculation

work was made a substantial decrease in total analyzing time could be

realised. Furthermore, comparing to the old method which made use of punch tapes the hybrid method causes no unallowable losses due to transmission

errors.

2-The old method.

During motion measurements various signals are measured.

The measured signals and a reference signal were simultaneously recorded

on magnetic tape of an instrumentation tape recorder. The internal modulator

transforms an- analog signal in a frequency modulated signal. Generally

speaking, when reproducing the signal is internally demodulated and an analog

signal is produced.

Because of the sometimes very severe motions during the measurements the

recording speed of the tape recorder is not constant. This fact leads to

decreasing accuracy when demodulating in the usual way with the internal

frequency demodulator. The reason is that the carrier frequency on tape is no more sufficiently constant.

To overcome this difficulty a digitizer was made controlled by the reference

signal put on the tape during the measurements.

Generahly speaking the digitizing of each signal was successively done

on a reãl time base; at the same time the speach channel gave the particulars

of the specific run. In fig. i a sketch of the set up is given.

The punch tapes were fed into a digital computer in which autocovariance

functions and power spectra were calculated according to the formula's

given in appendix 1.

The new method

The same recording principle will be used in this case.

Deviations of the uniform recording speed are expressed in frequency changes

of both frequency modulated measured signal and reference signal. These speed

deviations can be compensated when the demodulator is controlled by the

reference signal of the tape.

In fig. 2 the principle pf' this demodulator is given, while fig. 3 presents the time chart of relevant signals and commands.

The measured signal can be written as fcn ± Af in which is the

carrier-frequency and is the modulating frequency.

In the timing- and controlcircuit both the sampling time and the counting

time are determined from the reference signal

_r

During the counting time the leading edges of (r ±

f) and

into two pulsers with constant pulse width T. These pulsers control the

electronic switches Sn and Sr

During the pulsertime T the voltages and _Ur are fed into integrator I,

which is in the "operate mode" during the counting time.

Becaus of the opposite signs of and Ur the output voltage (Vn - Vref)

of I is proportional to the modulating frequency if the ratio fr/fc

equals the coefficient setting 1cc (see appendix II).

The sc.ling of integrator I is controlled by coefficient setting Kr. The

value of Kr is chosen in such a way that the integrator output is at a maximun

when tfn is maxima]. (see appendix II). The values V - Vref of all integrators

of all measured signals are read into the digital computer on a command

at the end of the counting time. During the time between two conunandpulses

the digital partner calculates the contributions of the autocovariance function for each signal.

As the ratio between digital calculation time and sampling time is rery small, it is possible to increase the reproducing speed.

With the present analog hardware it is expected that at least an increase in tape spetd by a factor 8 can be reached when 6 signals are simultaneously processed. The total time consumption of data reduction and analysis is

Prelimenary results.

From old motion measurements a pitch spectrum has been calculated according

to the new method. This spectrum is compared with the spectrum calculated

according to the old method. The differences between the two spectra _are

marginal and they are mainly caused bythe fact that the sampling time

was not equal in both cases. Fig. 4 gives an impression of the spectra.

In fig. 5 and fig. 6 _{a photograph of the autocovariance function and the}

power spectrum are given, taken from the oscilloscope, immediately after

calculation in order to have a visual check. 5

Appendix I

Formula's for the digital computation of the autocövariance function

and the power spectrum.

The autocovariance function of a signal x(t) is given by

T/2

I f

= hm

Jx(t).x(t+T)dt

T- -TI2

The power spectrum is calculated according to:

Sxx(e)

(Rxx(t)

cos eT

o

These formal expressions (i) and (2) are approximated by

n=N-p x(tn).x(tn+p)

(3)

K.ca?

with K is the integration constant of the trapezoidrule,

=

_{if p0 arid pm}

K

It is to be noted that

= and t

t -t

e _p P-1

The raw spectrum is now smoothed by the window of Henning giving the

following modified coordinates of the power spectrum:

G0 O..5L0 + 0.5L1

(5)

Gb = O.25Lh...1 + O.5Lh + O.2SLh.,..

During the processing of the tapes the digital computer calculates the

values according to (3).

At the end of a run the digital computer calculates the power spectra according

to

(4)

=

N-p

Appendix II

IÍ the counting time is x sea then the integrator I gives an output

voltage V Vref as follows:

- = x(f ± Af)T Kc Kr K -

T X

where: _f ± Af is the mod1ating signal

T 15 the pulsertime

K1., K are coefficient settings

K is the integration speed of all integrators I

If one requires that

V- - Vref = O when _n O

fr

then (i) gives K

= - with K1. + O and

C fc

Eq. (i) can be written as:

V

_{- Vref = xf Kc}

When (Af) is at the maximum (Af) the output voltage reaches the

umax maximum Vmax.

The value of the coefficientsetting Kr is now given by:

Vmax

Kr _{(Af)max Kc X T}

A digital service program calculates and controiB the coefficient settings

s

_Ô

_.

_.

figure 1 Block Diagran Old Method.

Counter

Memory

Punchdrivers

p

Punch Tape Digital

- signal

f c± ofc

Channel 2

_Reference

_{Signal fr}

Gate

Pulser

timing - contro

Coef.

Switch

Kc

Coef.J Kr

Integra t or

Vref

1

figure 3 Time Chart.

from tape reference

FM-signal fc±f

and PuLser t

Integrator VoLtage

without

fr

Reference SignaL fr

Integrator Voltage

'wìthout fc

±&f

Integrator VoLtage

Vref

Command PuLse to

DigitaL Computer

___p

1

sampUnq time

counting

time

4

4

vcn

/

/

/

_/

/

ri

ri

Vref

VcnVref

V

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A

/

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t

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PITCH

)

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old method

new method

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