PSN-L Email List Message
Subject: Re: nature of the mesoscopic nonlinearity
From: ChrisAtUpw@.......
Date: Sun, 10 Feb 2008 23:45:35 EST
In a message dated 11/02/2008, Brett3mr@............. writes:
Randall and Chris,
Sorry to be slow in responding to your messages, but you and Chris have
given me much to think about and it's going to take a few days more of thinking
to digest it all.
One open issue that I would like to get pinned down is getting a rough idea
of how large these effects are relative to the overall spring forces. I
think that Chris had implied that they could be of the same order of magnitude,
which I am finding very hard to visualize.
Hi Brett,
You have to make a spring arrangement such that it exactly balances the
mass, but has a very slow rate of change of force with position, a few % at
most. Hence the somewhat exotic spring arrangements used in seismometers.
Also in his message today I think he was implying that the spring can
undergo steplike changes
which contain high frequency components. If too large, they could be
deadly--see centering discussion below. In particular I am mainly interested in
the effects which will occur with the spring under constant tension--not moving
significantly.
Hooke's Law is only an approximation. You get a time dependant component
and creep. The creep is noisy and also time dependant. The changes tend to
be steps in the characteristic and these decrease with time after the load is
applied. New steps may be excited by quakes. The step changes can give
problems with velocity feedback circuits - they tend to generate spikes.
I find that I need to try to separate the fundamental spring-noise issues
which will always be present from ones that can be addressed by manufacturing
and design techniques such as limiting spring stress, ageing, heat cycling,
material choice, etc. For example, I'd heard stories of leaf-spring designs
that popped and crackled when they were first assembled and which then, over
time, would quiet down to an acceptable noise level. However a noise process
that is fundamental and always present would be of greater concern.
All common / practical spring materials are like this. You have the
electronic noise, the thermal noise of the sensor itself, the hysteretic noise and
the background seismic noise.
As an engineer, creep itself does not concern me, so long as it is
acceptably slow and not too noisy. Being able to quantify what one might expect to
see would be helpful in trying to design
something.
New subject: Both you and Chris had previously written of the idea of using
feedback to help maintain instrument centering. I came up with the
following, which if correct has some interesting implications.
"The goal of maintaining centering by the use of feedback can be restated as
the goal of using feedback to make the instrument insensitive to the
unwanted 'noise' forces which would tend to push it off center.
When trying to do this, however, a problem unfortunately arises of the 'no
free lunch' class, which in fact has nothing directly to do with feedback. The
(vertical) instrument simply can't distinguish where an input force is
coming from. Is it from the spring getting weaker as the temperature rises, from
buoyancy-force changes with the barometer, from spring creep or is it the
acceleration-related force from the very low frequency geological signal you
wanted to observe? To the extent that you succeed in reducing the instrument's
sensitivity to the 'noise' forces you also reduce its sensitivity to the
signal force. This can be restated as the well accepted generalization:
'feedback does not affect the signal to noise ratio'. (assuming, of course, that the
added feedback components are noise free)
Yes you can. You can either re-zero mechanically with a small motor to
keep the system in range or use an integrated signal as force feedback. If you
integrate the output to say 500 seconds for a 50 second period instrument,
you can keep the mean position centred without significantly effecting the 50
second response. This will take out most drifts. With a velocity output, the
very long period signals are small.
I am confident that is the reason why commercial instruments aren't designed
to have large responses to acceleration / force down to very low
frequencies. Instead they are designed to establish a compromise between letting
through sufficiently low-frequency seismic signals to be useful, while at the same
time resisting the much larger, though more slowly changing, instrument
'noise' forces. That may also explain why so much effort has to go into reducing
the noise generators at their source, by using exotic alloys in leaf spring
suspensions, maintaining constant
(usually low) ambient pressure, and attempting to maintain the temperature
as constant as possible, etc."
See Wielandt's references on psn for feedback seismometer design.
Seismometers are usually designed to give a velocity law output directly using quite
complicated feedback loops - this is 'traditional'. High sensitivity
seismometers usually have periods between 60 and 120 seconds and this covers most
surface wave periods of maybe 15 to 40 seconds. A few types go to 360 seconds. To
cover all the Earth Eigenmodes, you have to go to about 2,000 seconds.
Regards,
Chris Chapman
In a message dated 11/02/2008, Brett3mr@............. writes:
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>Randall=20
and Chris,
Sorry to be slow in responding to your messages, but you=
and=20
Chris have given me much to think about and it's going to take a few days=20=
more=20
of thinking to digest it all.
One open issue that I would like to g=
et=20
pinned down is getting a rough idea of how large these effects are relativ=
e to=20
the overall spring forces. I think that Chris had implied that they=20
could be of the same order of magnitude, which I am finding very hard to=20
visualize.
Hi Brett,
You have to make a spring arrangement such that=
it=20
exactly balances the mass, but has a very slow rate of change of force with=20
position, a few % at most. Hence the somewhat exotic spring arrangements use=
d in=20
seismometers.
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>Also in=20
his message today I think he was implying that the spring can undergo step=
like=20
changes
which contain high frequency components. If too large, t=
hey=20
could be deadly--see centering discussion below. In particular I am=20
mainly interested in the effects which will occur with the spring under=20
constant tension--not moving significantly.
Hooke's Law is only an approximation. You get a=
=20
time dependant component and creep. The creep is noisy and also time dependa=
nt.=20
The changes tend to be steps in the characteristic and these decrease with t=
ime=20
after the load is applied. New steps may be excited by quakes. The step chan=
ges=20
can give problems with velocity feedback circuits - they tend to generate=20
spikes.
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>I find=20
that I need to try to separate the fundamental spring-noise issues which w=
ill=20
always be present from ones that can be addressed by manufacturing and des=
ign=20
techniques such as limiting spring stress, ageing, heat cycling, material=20
choice, etc. For example, I'd heard stories of leaf-spring designs t=
hat=20
popped and crackled when they were first assembled and which then, over ti=
me,=20
would quiet down to an acceptable noise level. However a noise proce=
ss=20
that is fundamental and always present would be of greater concern. =20
All common / practical spring materials are lik=
e=20
this. You have the electronic noise, the thermal noise of the sensor itself,=
the=20
hysteretic noise and the background seismic noise.
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>As an=20
engineer, creep itself does not concern me, so long as it is acceptably sl=
ow=20
and not too noisy. Being able to quantify what one might expect to s=
ee=20
would be helpful in trying to design
something.
New subject: Bo=
th=20
you and Chris had previously written of the idea of using feedback to help=
=20
maintain instrument centering. I came up with the following, which i=
f=20
correct has some interesting implications.
"The goal of maintaining=
=20
centering by the use of feedback can be restated as the goal of using feed=
back=20
to make the instrument insensitive to the unwanted 'noise' forces which wo=
uld=20
tend to push it off center.
When trying to do this, however, a prob=
lem=20
unfortunately arises of the 'no free lunch' class, which in fact has nothi=
ng=20
directly to do with feedback. The (vertical) instrument simply can't=20
distinguish where an input force is coming from. Is it from the spri=
ng=20
getting weaker as the temperature rises, from buoyancy-force changes with=20=
the=20
barometer, from spring creep or is it the acceleration-related force from=20=
the=20
very low frequency geological signal you wanted to observe? To the=20
extent that you succeed in reducing the instrument's sensitivity to the=20
'noise' forces you also reduce its sensitivity to the signal force. =20=
This=20
can be restated as the well accepted generalization: 'feedback does=20=
not=20
affect the signal to noise ratio'. (assuming, of course, that the added=20
feedback components are noise free)
Yes you can. You can either re-zero mechanicall=
y=20
with a small motor to keep the system in range or use an integrated signal a=
s=20
force feedback. If you integrate the output to say 500 seconds for a 50 seco=
nd=20
period instrument, you can keep the mean position centred without significan=
tly=20
effecting the 50 second response. This will take out most drifts.=20=
With=20
a velocity output, the very long period signals are small.
<=
FONT=20
style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>I am=20
confident that is the reason why commercial instruments aren't designed to=
=20
have large responses to acceleration / force down to very low=20
frequencies. Instead they are designed to establish a compromise bet=
ween=20
letting through sufficiently low-frequency seismic signals to be useful, w=
hile=20
at the same time resisting the much larger, though more slowly changing,=20
instrument 'noise' forces. That may also explain why so much effort=20=
has=20
to go into reducing the noise generators at their source, by using exotic=20
alloys in leaf spring suspensions, maintaining constant
(usually low)=20
ambient pressure, and attempting to maintain the temperature as constant a=
s=20
possible, etc."
See Wielandt's references on psn for=20
feedback seismometer design. Seismometers are usually designed to give=20=
a=20
velocity law output directly using quite complicated feedback loops - this i=
s=20
'traditional'. High sensitivity seismometers usually have periods between 60=
and=20
120 seconds and this covers most surface wave periods of maybe 15 to 40 seco=
nds.=20
A few types go to 360 seconds. To cover all the Earth Eigenmodes, you have t=
o go=20
to about 2,000 seconds.
Regards,
Chris Chapman
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