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# Applied Geometry

0
225
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find the circumfence of a circle that is inscribed in a square with side 12 cm.

Guest Aug 16, 2017

#1
+333
+1

If the side of the square is 12 cm, then the radius of the circle is half of that, or 6 cm. The circumference of a circle is 2*Pi*r. Substituting r, we get

$$2\Pi6cm=12\Pi\approx37.7cm$$

Mathhemathh  Aug 16, 2017
Sort:

#1
+333
+1

If the side of the square is 12 cm, then the radius of the circle is half of that, or 6 cm. The circumference of a circle is 2*Pi*r. Substituting r, we get

$$2\Pi6cm=12\Pi\approx37.7cm$$

Mathhemathh  Aug 16, 2017
#2
+1961
0

That was a creative way of making the symbol for pi! For future reference, use /pi in Latex to get the desired symbol. It looks like this:

$$\pi$$

TheXSquaredFactor  Aug 16, 2017


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# Real analysis- Riemann Integration.

1. Feb 8, 2014

### bonfire09

1. The problem statement, all variables and given/known data

Let $P$ be a tagged partition of $[0,3]$.
Show that the union $U_1$ of all the sub intervals in $P$ with tags in $[0,1]$ satisfies $[0,1-||P||]\subseteq U_1\subseteq [0,1+||P||]$. (||P|| is the norm of partition P).

2. Relevant equations

3. The attempt at a solution
We first show that $[0,1-||P||]\subseteq U_1$ with tags in $[0,1]$. Suppose that $r\in[0,1-||P||]$. Suppose further $||P||<1$. It follows that there exists an interval $I_k =[x_{k-1},x_k]\in P$ with tag $t_k\leq 1$ that $r$ belongs to. Since $||P||<1$ then $x_k-x_{k-1}<1\implies x_k<1+x_{k-1}$. Since $r\in[0,1-||P||]\implies x_{k-1}\leq r\leq 1-||P||\leq 1\implies x_k<1+x_{k-1}\leq 1+1=2\implies x_k<2$ Hence $r$ is in the interval $I_k$ with tag $t_k\in I_k$. Thus $r\in U_1$. I think this is wrong and I'm not seeing something here. Any help would be great thanks.

Last edited: Feb 8, 2014

format: plain


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# Analysis Seminar

#### Fractional Eigenvalues

Speaker: Eric Lindgren, NTNU

Location: Warren Weaver Hall 1302

Date: Tuesday, April 10, 2012, 11 a.m.

Synopsis:

I will discuss a non-local eigenvalue problem that arises as the Euler-Lagrange equation of Rayleigh quotients in the fractional Sobolev spaces. This can be seen as a non-local or fractional version of the eigenvalue problem for the p-Laplacian. In particular, I will talk about the limiting case when p goes to infinity for which the eigenvalues exhibit some strange behaviour that can be seen even in some one-dimensional examples.


text:
# Documentation

Lean.Elab.Deriving.SizeOf

Remark: SizeOf instances are automatically generated. We add support for deriving instance for SizeOf just to be able to use them to define instances for types defined at Prelude.lean

Equations
• One or more equations did not get rendered due to their size.


text:
## Cosine distance

I came across this calculation when I was reading about Recommender systems. The last column is the rating given by a particular user for a movie. The other columns of this matrix denote whether a particular actor appeared in the movie or not.

$\begin{pmatrix} 1& 0& 1& 0& 1& 2\\ 1& 1& 0 & 0& 1& 6\\ 0& 1& 0 & 1 & 0 & 2\\ \end{pmatrix}$

 The first five attributes are Boolean, and the last is an integer "rating." Assume that the scale factor for the rating is α. Compute, as a function of α, the cosine distances between each pair of profiles. For each of α = 0, 0.5, 1, and 2, determine the cosine of the angle between each pair of vectors.

My R code to calculate is this.

# TODO: Add comment
#
###############################################################################

A = matrix(c(1,0,1,0,1,2,
1,1,0,0,1,6,
0,1,0,1,0,2),nrow=3,ncol=6,byrow=TRUE)

rownames(A) <- c("A","B","C")

scale1 <- A
scale1[,6] <- A[,6] * 0
print( paste( "A and B is ", ( sum(scale1[1,] * scale1[2,]) )/( sqrt( sum(scale1[1,]^2) ) * sqrt( sum(scale1[2,]^2) ) )) )
print( paste( "B and C is ", ( sum(scale1[2,] * scale1[3,]) )/( sqrt( sum(scale1[2,]^2) ) * sqrt( sum(scale1[3,]^2) ) )) )
print( paste( "A and C is ", ( sum(scale1[1,] * scale1[3,]) )/( sqrt( sum(scale1[1,]^2) ) * sqrt( sum(scale1[3,]^2) ) )) )

scale2 <- A
scale2[,6] <- A[,6] * 0.5
print( paste( "A and B is ", ( sum(scale2[1,] * scale2[2,]) )/( sqrt( sum(scale2[1,]^2) ) * sqrt( sum(scale2[2,]^2) ) )) )
print( paste( "B and C is ", ( sum(scale2[2,] * scale2[3,]) )/( sqrt( sum(scale2[2,]^2) ) * sqrt( sum(scale2[3,]^2) ) )) )
print( paste( "A and C is ", ( sum(scale2[1,] * scale2[3,]) )/( sqrt( sum(scale2[1,]^2) ) * sqrt( sum(scale2[3,]^2) ) )) )

scale3 <- A
scale3[,6] <- A[,6] * 1
print( paste( "A and B is ", ( sum(scale3[1,] * scale3[2,]) )/( sqrt( sum(scale3[1,]^2) ) * sqrt( sum(scale3[2,]^2) ) )) )
print( paste( "B and C is ", ( sum(scale3[2,] * scale3[3,]) )/( sqrt( sum(scale3[2,]^2) ) * sqrt( sum(scale3[3,]^2) ) )) )
print( paste( "A and C is ", ( sum(scale3[1,] * scale1[3,]) )/( sqrt( sum(scale3[1,]^2) ) * sqrt( sum(scale3[3,]^2) ) )) )

scale4 <- A
scale4[,6] <- A[,6] * 2
print( paste( "A and B is ", ( sum(scale4[1,] * scale4[2,]) )/( sqrt( sum(scale4[1,]^2) ) * sqrt( sum(scale4[2,]^2) ) )) )
print( paste( "B and C is ", ( sum(scale4[2,] * scale4[3,]) )/( sqrt( sum(scale4[2,]^2) ) * sqrt( sum(scale4[3,]^2) ) )) )
print( paste( "A and C is ", ( sum(scale4[1,] * scale4[3,]) )/( sqrt( sum(scale4[1,]^2) ) * sqrt( sum(scale4[3,]^2) ) )) )

[1] “A and B is 0.666666666666667”
[1] “B and C is 0.408248290463863”
[1] “A and C is 0”
[1] “A and B is 0.721687836487032”
[1] “B and C is 0.666666666666667”
[1] “A and C is 0.288675134594813”
[1] “A and B is 0.847318545736323”
[1] “B and C is 0.849836585598797”
[1] “A and C is 0”
[1] “A and B is 0.946094540760746”
[1] “B and C is 0.95257934441568”
[1] “A and C is 0.8651809126974”

## Gram-schmidt

 Matrix M has three rows and three columns, and the columns form an orthonormal basis. One of the columns is [2/7,3/7,6/7], and another is [6/7, 2/7, -3/7]. Let the third column be [x,y,z]. Since the length of the vector [x,y,z] must be 1, there is a constraint that x2+y2+z2 = 1. However, there are other constraints, and these other constraints can be used to deduce facts about the ratios among x, y, and z. Compute these ratios, and then identify one of them in the list below.

I viewed the Khan academy course.

But the credit for the Matlab code goes to Vladd. I didn’t follow his explanation but the Khan academy course helped.I used the Matlab online compiler to test Vladd’s code and ported it to R.

I can’t believe the for and if loops in the R code took a full day to debug.

#
###############################################################################

A =  matrix(c(2/7,3/7,6/7,6/7,2/7,-3/7,1,2,3),ncol=3,nrow=3)
r = dim( A)[[1]];
c = dim( A)[[2]];
print(A)

Q = matrix(c(0,0,0,0,0,0,0,0,0),ncol=3,nrow=3)
for (j in 1:3){

u = matrix(A[ ,j  ]);

if( j - 1 != 0 ){
for(i in 1:(j - 1)){
e = Q[,i]
a = as.matrix(A[,j])
p = (t(e) %*% a) / (t(e) %*% e) * e;
u = u - p
}
}
# normalize it to length of 1 and store it
Q[,j] = u / sqrt(u[1,1]^2 + u[2,1]^2 + u[3,1]^2);
print(Q)
}

The result is this. The last column is what I want and that satisfies all constraints.

### Orthonormality

$\begin{pmatrix} 0.2857143& 0.8571429& -0.4285714\\ 0.4285714& -0.2857143& 0.8571429\\ 0.8571429& -0.4285714& -0.2857143\\ \end{pmatrix}$

I will check-in the R code into my Git repository.


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# How to make caption bold in ctable?

If I use

\ctable[caption = \textbf{something}]{}{}{}

the text inside the caption is bold but TABLE 1. is not ... It looks like this:

TABLE 1: something

and i would like

TABLE 1: something

-
You can increase your chance for good (and quick) answers if you add a complete but minimal example to your question. – Thorsten Donig Apr 29 '12 at 9:51

You could use the caption package and set \captionsetup[table]{font=bf,position=below} to get bold label and caption text. The position=below is necessary to get the right spacing of the caption.

\documentclass{article}
\usepackage{caption}
\captionsetup[table]{font=bf,position=below}
\usepackage{ctable}

\begin{document}
This is a row of text, so we can see the whitespace around the table

\ctable[
caption = Centered,pos=hbtp!
]{cc}{}{\FL Table's first row & Second column\LL}

This is a row of text, so we can see the whitespace around the table
\end{document}

-
+1 for position=below. – lockstep Apr 29 '12 at 9:56

If you don't like to use the caption package, for example in case in would interfere with ctable somehow (ctable is not mentioned in the caption documentation), you could redefine the macro which prints the caption and is usually defined by the class. A small example:

\usepackage{letltxmacro}
\makeatletter
\LetLtxMacro{\@stdmakecaption}{\@makecaption}
\renewcommand{\@makecaption}[2]{\bfseries\@stdmakecaption{#1}{#2}}

-

Use this in the Preamble

\usepackage[labelfont=bf]{caption} %% for the figure and Tables Catption%%
\usepackage[textfont=bf]{caption}   %% For the Text of the figures and Tables%%

-


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# Does lack of seasonality imply random time series?

Some techniques for time series analysis (prediction) require that the time series not have seasonality. It seems that without seasonality, a time series is essentially random, in which case predicting values is a lost cause. What am I missing?

There are different kinds of non-seasonal randomness, with different optimal forecasts. A key part of forecasting is finding out which kind we are dealing with and choosing the corresponding optimal forecast.

Here are two examples of non-seasonal randomness.

• White noise is essentially unstructured noise, where each data point is identically distributed. The (provably) best forecast is the overall mean of the historical observations.
• In a random walk, it's the increments over the previous realization that are iid. If your previous observation is 5, then the next one will be nearer to 5 than to 0. In this case the (provably) best forecast is the last observation.

And of course, there are many other kinds of non-seasonal randomness, or of drivers. Trends, moving averages, autoregression, integration, causal drivers and so forth.

R code:

set.seed(1)

white_noise <- ts(rnorm(100))
random_walk <- ts(cumsum(rnorm(100)))

par(mfrow=c(1,2))
plot(white_noise,xlab="",ylab="",main="White noise")
plot(random_walk,xlab="",ylab="",main="Random walk")

Many time series methods consider the time series to have 4 components. Seasonality and error (which should be random) you mentioned are two of those four, but also the level and the trend. So it would not be reduced to just randomness.

That being said, there are some methods that want your time series to be "stationary", which would mean it only has a level and random error. The seasonality and/or trend would be removed through transformation. That doesn't mean it does not have seasonality, it just means that the time series is to undergo a transformation before modeling (there are many types of transformations, google "Box-Cox transformations").

With exponential smoothing there are some methods that are used for series that do not have seasonality (eg, simple exponential smoothing). Exponential smoothing can handle seasonality: it just would not be that specification.

• You can have no seasonality and still include a stochastic or deterministic trend neither of which are completely random. As noted exponential smoothing has several of these including a linear trend and a damped trend. – user54285 Apr 19 at 23:37

seasonality is just 1 aspect of an arima model .... there can be short-term autoprojective structure such as an autoregressive model of order 1 where the previous value is weighted to obtain a forecast . Additionally there can be deterministic structure such as level shifts or time trends which might be useful in characterizing a series.

For more see: ARIMA model identification should follow the following paradigm https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf culminating in a useful SARiMAX Model How to predict the next number in a series while having additional series of data that might affect it? which might include latent deterministic structure ( the I's )


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# 24.7 - Creating SAS Data Sets from Procedure Output

24.7 - Creating SAS Data Sets from Procedure Output

You may recall in the first part of Stat 483 that we used an OUTPUT statement in the MEANS procedure to create a data set containing summary statistics, such as means and standard deviations. We'll see in this section that we could have alternatively used ODS to first save the summary statistics and then send it to the OUTPUT destination. In fact, we can use ODS to save just about any part of any procedure's output!

## Example 24.11

The following program uses an ODS OUTPUT statement to create a temporary SAS data set called summout from the Summary output object created by the MEANS procedure, and then prints the resulting summout data set:

PROC MEANS data = golfbypar;
by par;
var yards;
title 'Pennsylvania Golf Courses by Par';
ODS OUTPUT Summary = summout;
RUN;

PROC PRINT data = summout NOOBS;
title 'The summout data set';
RUN;

Now, something that might not be obvious from this code is that the name of the output object, Summary, was determined from first tracing the MEANS procedure. If you refer back to the information SAS displayed in the log for Example 24.7, you can see that, since we want to capture all of the output from the MEANS procedure, the desired output object is called Summary. The ODS OUTPUT statement tells SAS that we want to save the data contained in the Summary output object in a data set called summout. Of course, the PRINT procedure then tells SAS to print the summout data set. Launch and run the SAS program, and review the output to convince yourself that the summout data set does indeed contain the data summarized by the MEANS procedure.

You do need to be careful where you put ODS statements in your program. For example, if rather than putting the ODS OUTPUT statement just before the MEAN procedure's RUN statement, we had instead put it after the MEAN procedure's RUN statement and before the PRINT procedure's PROC PRINT statement, we would not have captured the Summary data set. Instead, we would get the following Warning message:

WARNING: Output 'Summary' was not created. Make sure that the output
Object name, label, or path is spelled corectly. Also
Verify that the appropriate procedute options are used to
produce the request output object. For example, verify that
the NOPRINT option is not used

You might want to move the ODS statement as described, and re-run the SAS program just to see this for yourself.

 [1] Link ↥ Has Tooltip/Popover Toggleable Visibility


text:
TheInfoList

History

The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw. He discovered the principle of mechanical advantage in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," ( el|δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω) expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to calculate their (ideal) mechanical advantage. For example, Heron of Alexandria (c. 10–75 AD) in his work ''Mechanics'' lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw, and describes their fabrication and uses. However the Greeks' understanding was limited to the statics of simple machines (the balance of forces), and did not include dynamics, the tradeoff between force and distance, or the concept of work. During the Renaissance the dynamics of the ''Mechanical Powers'', as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in ''Le Meccaniche'' (''On Mechanics''), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it. The classic rules of sliding friction in machines were discovered by Leonardo da Vinci (1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an ethereal fluid. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785).

Ideal simple machine

If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions. Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force $F_\text\,$ is applied to the device at one point, and it does work moving a load, $F_\text\,$ at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage :$\mathrm = F_\text/F_\text\,$ that can be calculated from the machine's geometry and friction. Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. A simple machine with no friction or elasticity is called an ''ideal machine''. Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time $P_\text\,$ is equal to the power input $P_\text\,$ :$P_\text = P_\text\!$ The power output equals the velocity of the load $v_\text\,$ multiplied by the load force $P_\text = F_\text v_\text\!$. Similarly the power input from the applied force is equal to the velocity of the input point $v_\text\,$ multiplied by the applied force $P_\text = F_\text v_\text\!$. Therefore, :$F_\textv_\text = F_\textv_\text\,$ So the mechanical advantage of an ideal machine $\mathrm_\text\,$ is equal to the ''velocity ratio'', the ratio of input velocity to output velocity :$\mathrm_\text = = \,$ The ''velocity ratio'' is also equal to the ratio of the distances covered in any given period of time :$= \,$ Therefore the mechanical advantage of an ideal machine is also equal to the ''distance ratio'', the ratio of input distance moved to output distance moved This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the lever is equal to the ratio of its lever arms. The mechanical advantage can be greater or less than one: * If $\mathrm > 1\,$ the output force is greater than the input, the machine acts as a force amplifier, but the distance moved by the load $d_\text\,$ is less than the distance moved by the input force $d_\text\,$. * If $\mathrm < 1\,$ the output force is less than the input, but the distance moved by the load is greater than the distance moved by the input force. In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned.

Friction and efficiency

All real machines have friction, which causes some of the input power to be dissipated as heat. If $P_\text\,$ is the power lost to friction, from conservation of energy :$P_\text = P_\text + P_\text\,$ The mechanical efficiency $\eta \,$ of a machine (where $0 < \eta \ < 1$) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses :$\eta \equiv \,$ :$P_\text = \eta P_\text \,$ As above, the power is equal to the product of force and velocity, so :$F_\text v_\text = \eta F_\text v_\text\,$ Therefore, So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency ''η''. So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force.

Compound machines

A ''compound machine'' is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series. The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is :$\mathrm_\text = \,$ Because the output force of each machine is the input of the next, $F_\text = F_\text, \; F_\text = F_\text, \ldots \; F_\text = F_\text$, this mechanical advantage is also given by :$\mathrm_\text = \ldots \,$ Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it :$\mathrm_\text = \mathrm_1 \mathrm_2 \ldots \mathrm_\text \,$ Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it :$\eta_\text = \eta_1 \eta_2 \ldots \; \eta_\text.\,$

Self-locking machines

thumb|The screw's self-locking property is the reason for its wide use in bolts_and_bolts_and_[[wood_screw">bolt_(fastener)">bolts_and_bolts_and_[[wood_screw">bolt_(fastener)">bolts_and_[[wood_screws_">wood_screw.html"_style="text-decoration:_none;"class="mw-redirect"_title="bolt_(fastener)">bolts_and_[[wood_screw">bolt_(fastener)">bolts_and_[[wood_screws_ In_many_simple_machines,_if_the_load_force_''Fout''_on_the_machine_is_high_enough_in_relation_to_the_input_force__''Fin'',_the_machine_will_move_backwards,_with_the_load_force_doing_work_on_the_input_force.
__So_these_machines_can_be_used_in_either_direction,_with_the_driving_force_applied_to_either_input_point.___For_example,_if_the_load_force_on_a_lever_is_high_enough,_the_lever_will_move_backwards,_moving_the_input_arm_backwards_against_the_input_force.__These_are_called_"''reversible''",_"''non-locking''"_or_"''overhauling''"__machines,_and_the_backward_motion_is_called_"''overhauling''".___ However,_in_some_machines,_if_the_frictional_forces_are_high_enough,_no_amount_of_load_force_can_move_it_backwards,_even_if_the_input_force_is_zero.___This_is_called_a_"''self-locking''",_"''nonreversible''",_or_"''non-overhauling''"_machine.__These_machines_can_only_be_set_in_motion_by_a_force_at_the_input,_and_when_the_input_force_is_removed_will_remain_motionless,_"locked"_by_friction_at_whatever_position_they_were_left. Self-locking_occurs_mainly_in_those_machines_with_large_areas_of_sliding_contact_between_moving_parts:_the_[[screw_(simple_machine).html" style="text-decoration: none;"class="mw-redirect" title="wood_screws_.html" style="text-decoration: none;"class="mw-redirect" title="wood_screw.html" style="text-decoration: none;"class="mw-redirect" title="bolt (fastener)">bolts and [[wood screw">bolt (fastener)">bolts and [[wood screws ">wood_screw.html" style="text-decoration: none;"class="mw-redirect" title="bolt (fastener)">bolts and [[wood screw">bolt (fastener)">bolts and [[wood screws In many simple machines, if the load force ''Fout'' on the machine is high enough in relation to the input force ''Fin'', the machine will move backwards, with the load force doing work on the input force. So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called "''reversible''", "''non-locking''" or "''overhauling''" machines, and the backward motion is called "''overhauling''". However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a "''self-locking''", "''nonreversible''", or "''non-overhauling''" machine. These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left. Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the [[screw (simple machine)">screw, [[inclined plane]], and [[wedge (mechanical device)|wedge]]: * The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards. * In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight. * A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block. A machine will be self-locking if and only if its efficiency ''η'' is below 50%: :$\eta \equiv \frac < 0.50 \,$ Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio ''din/dout'' (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.

Proof

When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work $W_\text \,$ is equal to the sum of the work done on the load force $W_\text \,$ and the work lost to friction $W_\text \,$ If the efficiency is below 50% $\eta = W_\text/W_\text < 1/2 \,$ :$2W_\text < W_\text \,$ From :$2W_\text < W_\text + W_\text \,$ :$W_\text < W_\text \,$ When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction $W_\text \,$ is the same :$W_\text = W_\text + W_\text \,$ So the output work is :$W_\text = W_\text - W_\text < 0 \,$ Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force

Modern machine theory

Machines are studied as mechanical systems consisting of actuators and mechanisms that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains.

Kinematic chains

Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint. Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a six-bar linkage or in series to form a robot.

Classification of machines

The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines. However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.Hartenberg, R.S. & J. Denavit (1964
New York: McGraw-Hill, online link from Cornell University.
This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.

Kinematic synthesis

The design of mechanisms to perform required movement and force transmission is known as kinematic synthesis. This is a collection of geometric techniques for the mechanical design of linkages, cam and follower mechanisms and gears and gear trains.


text:
40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
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ID Date Author Type Category Subject
14136   Mon Aug 6 00:26:21 2018 gautamUpdateCDSMore CDS woes

I spent most of today fighting various CDS errors.

• I rebooted c1lsc around 3pm, my goal was to try and do some vertex locking and figure out what the implications were of having only ~30% power we used to have at the AS port.
• Shortly afterwards (~4pm), c1lsc crashed.
• Using the reboot script, I was able to bring everything back up. But the DC lights on c1sus models were all red, and a 0x4000 error was being reported.
• This error is indicative of some timing issue, but all the usual tricks (reboot vertex FEs in various order, restart the mx_streams etc) didn't clear this error.
• I checked the Tempus GPS unit, that didn't report any obvious problems (i.e. front display was showing the correct UTC time).
• Finally, I decided to shut down all watchdogs, soft reboot all the FEs, soft reboot FB, power cycle all expansion chassis.
• This seems to have done the trick - I'm leaving c1oaf disabled for now.
• The remaining red indicators are due to c1dnn and c1oaf being disabled.

Let's see how stable this configuration is. Onto some locking now...

Attachment 1: CDSoverview.png
14135   Sun Aug 5 15:43:50 2018 gautamUpdateSUSAnother low noise bias path idea

• Attachment #1 shows the proposed schematic.
• It consists of a second order section with Gain x10 to map the +/-10V DC range of the DAC to +/- 100V DC such that we preserve roughly the same amount of DC actuation range.
• Corner frequency of the SOS is set to ~0.7 Hz. In hindsight, maybe this is more aggressive than necessary, we can tune this.
• DC gain is 20 dB (typo in the text where I say the DC gain is x15, though we could go with this option as well I think if we want a larger series resistance).
• A first order passive low-pass stage is added to filter out the voltage noise of the PA91, which dominates the output voltage noise (next bullet).
• Attachment #2 shows the transfer function from input to output
• The two traces compare having just a single SOS filtering stage vs the current topology of having two SOS stages.
• The passive output RC network is necessary in either case to filter the voltage noise of the PA91 OpAmp.
• For the DAC noise, I just assumed a flat noise level of $5 \mu V / \sqrt{\mathrm{Hz}}$, I don't actually know what this is for the Acromag DACs.
• Attachments #3 shows a breakdown of the top 5 noise contributions.
• The PA91 datasheet doesn't give current noise information so I just assumed $1 fA / \sqrt{\mathrm{Hz}}$, which was what was used for the PA85 in the existing opamp.lib file.
• The voltage noise is modelled as $4.5 \sqrt{1+\frac{80}{f}} nV / \sqrt{\mathrm{Hz}}$, which seems to line up okay with the plot on Pg4 of the datasheet.
• So the model suggests we will be dominated by the voltage noise of the PA91.
• Attachment #4 translates the noise into current noise seen by the actuator.
• I add the Johnson noise contribution of the series resistance for this path, which is assumed to be $10 k \Omega$.
• For comparison, I add the filtered DAC noise contribution, and Johnson noise of the proposed series resistance in the fast path.
• For the bias path, we are dominated by the Johnson noise of the series resistor from ~60 Hz upwards.
• It's not quite fair to say that the Johnson noise of the resistance in the fast path dominates, the quadrature sum of fast and bais paths will be ~1.2 times of the former alone.
• Bottom line: we will be in the regime of total current noise of ~2.2 pA/rtHz, where I think Kevin's modeling suggests we can see some squeezing.

The question still remains of how to combine the fast and bias paths in this proposed scheme. I think the following approach works for prototyping at least:

• Remove the series resistance on the existing coil driver boards' bias path, hence isolating this from the coil.
• Route the DB15 output connector from the coil driver board (which is now just the fast actuation signals) into a sub-sattelite box housing the bias path electronics.
• Sum the two signals as it is done now, by simply having a conductor (PCB trace) merge the two paths after their respective series resistances.

In the longer term, perhaps the Satellite Box revamp can accommodate a bias voltage summation connector.

 Quote: Bah! Too complex.

I have neglected many practical concerns. Some things that come to mind:

1. Is it necessary to protect the upstream DAC from some potential failure of the PA91 in which the high voltage appears at the input?
2. What is the correct OpAmp for this purpose? This chart on Apex's page suggests that PA15, PA85, PA91 and PA98 are all comparable in terms of drive capability, and the spec sheets don't suggest any dramatic differences. Some LIGO circuits use PA85, some use PA90, but I can't find any that use PA91. Perhaps Rana/Koji can comment about this.
3. What kind of protection is necessary for the PA91 power?
4. What is the correct way to do heat management? Presumably we need heatsinks, and in fact, there is a variant of the packaging style that has "formed" legs, which from what I can figure out, allow the heat sink plane on the PA91 to be parallel to the PCB surface. But I think the heat-sink wisdom suggests vertical fins are the most efficient (not sure if this holds if the PCB is inside a box though). What about the PCB itself? Are some kind of special traces needed?
5. Can we use the current-limiting resistor feature on the PA91? The datasheet seems to advice against it for G>10 configurations, which is what we need, although our requirement is only at DC so I don't know if that table is applicable to this circuit.
6. Are 3W resistors sufficient? I think we require only 10mA maximum current to preserve the current actuation range, so 100 V * 10mA = 1W, so 3W leaves some safety margin.
7. All capacitors should be rated for 500 V per the datasheet.
Attachment 1: HV_Bias_schematic.pdf
Attachment 2: TF.pdf
Attachment 3: bias.pdf
Attachment 4: HVbias_currentNoise.pdf
14134   Sun Aug 5 13:45:00 2018 gautamUpdateSUSETMX tripped

Independent from the problems the vertex machine has been having (I think, unless it's something happening over the shared memory network), I noticed on Friday that the ETMX watchdog was tripped. Today, once again, the ETMX watchdog was tripped. There is no evidence of any abnormal seismic activity around that time, and anyways, none of the other watchdogs tripped. Attachment #1 shows that this happened ~838am PT today morning. Attachment #2 shows the 2k sensor data around the time of the trip. If the latter is to be believed, there was a big impulse in the UL shadow sensor signal which may have triggered the trip. I'll squish cables and see if that helps - Steve and I did work at the EX electronics rack (1X9) on Friday but this problem precedes our working there...

Attachment 1: ETMX_tripped.png
Attachment 2: ETMX_tripped_zoom.png
14133   Sun Aug 5 13:28:43 2018 gautamUpdateCDSc1lsc flaky

Since the lab-wide computer shutdown last Wednesday, all the realtime models running on c1lsc have been flaky. The error is always the same:

[58477.149254] c1cal: ADC TIMEOUT 0 10963 19 11027 [58477.149254] c1daf: ADC TIMEOUT 0 10963 19 11027 [58477.149254] c1ass: ADC TIMEOUT 0 10963 19 11027 [58477.149254] c1oaf: ADC TIMEOUT 0 10963 19 11027 [58477.149254] c1lsc: ADC TIMEOUT 0 10963 19 11027 [58478.148001] c1x04: timeout 0 1000000  [58479.148017] c1x04: timeout 1 1000000  [58479.148017] c1x04: exiting from fe_code()

This has happened at least 4 times since Wednesday. The reboot script makes recovery easier, but doing it once in 2 days is getting annoying, especially since we are running many things (e.g. ASS) in custom configurations which have to be reloaded each time. I wonder why the problem persists even though I've power-cycled the expansion chassis? I want to try and do some IFO characterization today so I'm going to run the reboot script again but I'll get in touch with J Hanks to see if he has any insight (I don't think there are any logfiles on the FEs anyways that I'll wipe out by doing a reboot). I wonder if this problem is connected to DuoTone? But if so, why is c1lsc the only FE with this problem? c1sus also does not have the DuoTone system set up correctly...

The last time this happened, the problem apparently fixed itself so I still don't have any insight as to what is causing the problem in the first place . Maybe I'll try disabling c1oaf since that's the configuration we've been running in for a few weeks.

14132   Fri Aug 3 19:02:11 2018 gautamUpdateASSX arm ASS recovery

[koji, gautam]

After I effected the series resistance change for ETMX, the X arm ASS didn't work (i.e. IR transmission would degrade if the servo was run). Today, we succeeded in recovering a functional ASS servo .

So both arms have working dither alignment servos now. But remember that the Y arm ASS gains have been set for locking the Y arm with MC2 as the actuator, not ETMY.

Details:

• Koji pointed out that the demodulated signals from the ETM dither are only used to center the spot on the ETM, and that we should first run the servo with existing settings with the ETM pitch and yaw spot centering loops disabled.
• This improved TRX level from ~0.8 to 1.1
• Next, we tried increasing the LO amplitudes by x5 to account for the reduced actuation of the dither on ETMX
• We then re-enabled the two loops that were earlier disabled.
• This resulted in TRX degrading very quickly.
• So we decided to try going back to the nominal LO gains, and reducing the gain of the two ETM spot centering loops.
• This did the trick, TRX went from 1.1 --> ~1.23, which is the nominal maximum pre-vent value.
• The snap file used to recover the correct settings to run the dither alignment servos have been updated, the old one has been backed up with today's datestamp.

We then tried to maximize GTRX using the PZT mirrors, but were only successful in reaching a maximum of 0.41. The value I remember from before the vent was 0.5, and indeed, with the IR alignment not quite optimized before we began this work, I saw GTRX of 0.48. But the IR dither servo signals indicate that the cavity axis may have shifted (spot position on the ITM, which is uncontrolled, seems to have drifred significantly, the Pitch signal doesn't stay on the StripTool scale anymore). So we may have to double check that the transmitted beam isn't falling off the GTRX DC PD.

14131   Fri Aug 3 18:54:58 2018 gautamUpdateSUSGlitchy MC1

The wall StripTool indicated that the IMC wasn't too happy when I came in today. Specifically:

• MC1 watchdog was tripped.
• Even in the tripped state, MC REFL spot on the camera showed spot motion that was too large to be explained as normal seismic driven motion (i.e. with local damping supposedly disabled).
• Strange excursions were observed in the MC1 shadow sensor signal levels as well, see Attachment #1 - negative values don't make any sense for this readout.

The last time this happened, it was due to the Sorensens not spitting out the correct voltages. This time, there were no indications on the Sorensens that anything was funky. So I just disabled the MCautolocker and figured I'd debug later in the evening.

However, around 5pm, the shadow sensor values looked nominal again, and when I re-enabled the local damping, the MC REFL spot suggested that the local damping was working just fine. I re-enabled the MCautolocker, MC re-locked almost immediately. To re-iterate, I did nothing to the electronics inside the VEA. Anyways, this enabled us to work on the X arm ASS (next elog).

Attachment 1: MC1_sensorAnomaly.png
14130   Fri Aug 3 16:27:40 2018 ranaUpdateSUSLow noise bias path idea

Bah! Too complex.

14129   Fri Aug 3 15:53:25 2018 gautamUpdateSUSLow noise bias path idea

Summary:

The idea we are going with to push the coil driver noise contribution down is to simply increase the series resistance between the coil driver board output and the OSEM coil. But there are two paths, one for fast actuation and one that provides a DC current for global alignment. I think the simplest way to reduce the noise contribution of the latter, while preserving reasonable actuation range, is to implement a precision DC high-voltage source. A candidate that I pulled off an LT application note is shown in Attachment #1.

Requirements:

• The series resistance in the bias path should be $10 k\Omega$, such that the noise from this stage is dominated by the Johnson noise of said resistor, and hence, the current noise contribution is negligible compared to the series resistance in the fast actuation path ($4.5 k\Omega$).
• Since we only really need this for the test masses, what actuation range do we want?
• Currently, ETMY has a series resistance of $400\Omega$ and has a pitch DC bias voltage of -4 V.
• This corresponds to 10 mA of DC current.
• To drive this current through $10 k\Omega$, we need 100 V.
• I'm assuming we can manually correct for yaw misalignments such that 10mA of DC current will be sufficient for any sort of corrective alignment.
• So +/- 120 V DC should be sufficient.
• The current noise of this stage should be negligible at 100 Hz.
• The noise of the transistors and the HV supply should be suppressed by the feedback loop and so shouldn't be a significant contribution (I'll model to confirm).
• The input noise of the LT1055 is ~20nV/rtHz at 100 Hz, while the Johnson noise of $10 k\Omega$ is ~13nV/rtHz so maybe the low-passing needs to be tuned, but I think if it comes to it, we can implement a passive RC network at the output to achieve additional filtering.
• To implement this circuit, we need +/- 125V DC.
• At EX and EY, we have a KEPCO HV supply meant to be used for the Green Steering PZTs.
• I'm not sure if these can do bipolar outputs, if not, for temporary testing, we can transport the unit at EY to EX.

If all this seems reasonable, I'd like to prototype this circuit and test it with ETMX, which already has the high series resistance for the fast path. So I will ask Steve to order the OpAmp and transistors.

Attachment 1: LT1055_precOpAmp.pdf
14128   Fri Aug 3 14:35:56 2018 gautamSummaryElectronicsEX AUX electronics power restored

Steve and I restored the power to the EX AUX electronics rack. The power strip on the lowest shelf of the AUX rack now goes to another power strip laid out vertically along the NW corner of 1X9. The EX green locks to the arm just fine now.

14127   Thu Aug 2 23:09:25 2018 ranaSummaryComputersX Green "Mystery" solved

I'm going to guess that this was me: I was disconnecting some octopus power strip nonsense down there (in particular illuminators and cameras), so I might have turned off the AUX rack by mistake.

Quote:

I walked down to the X end and found that the entire AUX laser electronics rack isn't getting any power. There was no elog about this.

I couldn't find any free points in the power strip where I think all this stuff was plugged in so I'm going to hold off on resurrecting this until tomorrow when I'll work with Steve.

 Quote: The X arm green does not stay locked to the cavity - the alignment looks fine, and the green flashes are strong, but the lock does not hold. This shouldn't be directly connected to anything we did today since the Green PDH servo is entirely analog.
14126   Thu Aug 2 20:54:18 2018 gautamSummaryComputersc1omc model looks stable

Actually, c1lsc had crashed again sometime last night so I had to reboot everything this morning. I used the reboot script again, but I increased the sleep time between trying to start up the models again so that I could walk into the VEA and power cycle the c1lsc expansion chassis, as this kind of frequent model crash has been fixed by doing so in the past. Sure enough, there have been no issues since I rebooted everything at ~1030 in the morning.

The c1omc model itself has been stable as well, though of course, there is nothing in there at the moment. I may do a check of the newly installed DAC tomorrow just to see that we can put out a sine wave.

Steve has ordered the D-sub cabling that will allow us to route signals between AA/AI boards in 1X1/1X2 to the HV PZT electronics in the OMC rack. Things look setup for a measurement next week. Aaron will post a block diagram + photoz of what box goes where in the electronics racks.

14125   Thu Aug 2 20:47:29 2018 gautamSummaryElectronicsX Green "Mystery" solved

I walked down to the X end and found that the entire AUX laser electronics rack isn't getting any power. There was no elog about this.

I couldn't find any free points in the power strip where I think all this stuff was plugged in so I'm going to hold off on resurrecting this until tomorrow when I'll work with Steve.

 Quote: The X arm green does not stay locked to the cavity - the alignment looks fine, and the green flashes are strong, but the lock does not hold. This shouldn't be directly connected to anything we did today since the Green PDH servo is entirely analog.
14124   Thu Aug 2 16:30:08 2018 SteveUpdateTreasuretime capsule location

I 've just found this time capsule note from Nov. 26, 2000 by Kip Thorne:  LIGO will discover gravitational waves by Dec.31, 2007

 Quote: Beautifully Done Atm 3, Ron Drever could not celebrate with us because of health issues.

Attachment 1: time_capsule.JPG
14123   Wed Aug 1 20:44:57 2018 gautamSummaryComputersc1omc model (re?)created

The main motivation behind adding a DAC card in c1ioo was to setup an RTCDS model for the OMC. Attachment #1 shows the new look CDS overview screen. Here is what I did.

Mostly, I followed instructions from when I setup the model for the EX green PZTs.

The model is just a toy for now (CDS parameters, ADC block and 2 CDS filter modules). I leave it to Aaron to actually populate it, check functionality etc. The path to the model is /opt/rtcds/caltech/c1/userapps/release/isc/c1/models/c1omc.mdl. I am listing the parameters set on the CDS_PARAMETERS block:

• host = c1ioo
• site = c1
• rate = 16k
• dcuid = 27 (which I chose after making sure that this dcuid was not used on this list which I also updated by adding c1omc and moving c1imc to "old")
• specific_cpu = 6 (again chosen after checking the available CPUs in the above list and confirming using the cset utility).
• shmem_daq = 1
• no_rfm_dma = 1

Building and installing model:

Once the model was installed, I logged into c1ioo, and built and installed the models using the usual rtcds make and rtcds install instructions. Before starting the model, I edited /diskless/root.jessie/etc/rtsystab to allow c1omc to be run on c1ioo. Using sudo cset set, I verified that CPU #6 is no longer listed (if I understand correctly, the RTCDS system takes over the core).

MEDM:

To reflect all this on the MEDM CDS OVERVIEW screen, I just edited the screen.

• Moved the orange explanation of bits over to the c1iscey panel to make space in the c1ioo panel.
• Edited the macros to reflect the c1omc parameters.

DAQD:

Finally, I followed the instructions here to get the channels into frames and make all the indicators green. Went into fb and restarted the daqd processes. All looks good . I'm going to leave the model running overnight to investigate stability. I forgot to svn commit the model tonight, will do it tomorrow.

The testing plan (at least initially) is to install the AA and AI boards from the OMC rack in 1X1/1X2. Then we will have short SCSI cables running from the ADC/DAC to these. The actual HV driving stages will remain in the OMC rack (NE corner of AS table).

@Steve, can we get 10 Male-Female D9 cables so that we can run them from 1X1/1X2 to the OMC rack?

Unrelated to this work: There were 2 crashes of the models on c1lsc, one ~6pm and one right now ~1030pm. The restart script brought everything back gracefully  ...

Attachment 1: CDS_OVERVIEW_withOMC.png
14122   Wed Aug 1 19:41:15 2018 gautamSummaryComputersRTCDS recovery, c1ioo changes

[Gautam Koji]

After this work, we recovered the nominal RTCDS state. The main points were:

1. We needed to restart the bind9 service on chiara such that the FEs knew their IP addresses upon reboot and hence, could get their root filesystems over NFS.
2. We recovered suspension local damping, IMC locking and POX/POY locking with nominal arm transmission.

Some stuff that is not working as usual:

1. The EX QPD is reporting strange transmission values - even with the PRM completely misaligned, it reports transmission of ~30. But we were able to lock the Xarm with the Thorlabs PD and revover transmission of ~1.15.
2. The X arm green does not stay locked to the cavity - the alignment looks fine, and the green flashes are strong, but the lock does not hold. This shouldn't be directly connected to anything we did today since the Green PDH servo is entirely analog.

I made a model change in c1x03 (the IOP model on c1ioo) to add a DAC part. The model compiled, installed and started correctly, and looking at dmesg on c1ioo, it recognises the DAC card as what it is. Next step is to use a core on c1ioo for a c1omc model, and actually try driving some signals.

Note that the only change made to the c1ioo expansion chassis was that a DAC card was installed into the PCIe bus. The adaptor card which allows interfacing the DAC card to an AI board was already in the expansion chassis, presumably from whenever the DAC was removed from this machine.

*I think I forgot to restart optimus after this work...

Attachment 1: CDS_overview.png
14121   Wed Aug 1 16:23:48 2018 KojiSummaryComputersTransition of the main NFS disk on chiara

[Gautam Koji]

Taking the opportunity to shutdown c1ioo for adding a DAC card, we shutdown chiara and worked on moving of the main disk to the bigger home.

We shutdown most of the martian machines including the control machines, megatron, optimus, and nodus.

- Before shutting down chiara, we ran rsync to make the 4TB disk (used to be teh backup) and /cvs/cds synced.

sudo rsync -a --progress /home/cds/ /media/40mBackup

- Modified /etc/fstab

proc            /proc           proc    nodev,noexec,nosuid 0       0 # / was on /dev/sda1 during installation UUID=972db769-4020-4b74-b943-9b868c26043a /               ext4    errors=remount-ro 0       1 # swap was on /dev/sda5 during installation UUID=a3f5d977-72d7-47c9-a059-38633d16413e none            swap    sw              0       0 UUID="90a5c98a-22fb-4685-9c17-77ed07a5e000"    /media/40mBackup       ext4      defaults,relatime,commit=60       0         0 #fb:/frames      /frames nfs     ro,bg

UUID=92dc7073-bf4d-4c58-8052-63129ff5755b   /home/cds    ext4    defaults,relatime,commit=60    0   0

- Shutdown chiara. Put the 4TB disk in the chassis. We also installed a new disk (but later it turned out that it only has 2TB...)

- Restart the mahcine. This already made the 4TB disk mounted as /cvs/cds .

- Restart bind9 with DHCP for the diskless clients (cf. https://wiki-40m.ligo.caltech.edu/CDS/How_to_join_martian)

sudo service bind9 restart
sudo service isc-dhcp-server restart

- Looks like /etc/resolv.conf is automatically overwritten by a tool or something everytime we restart the machine!? I still don't know how to avoid this. (cf.  https://www.ctrl.blog/entry/resolvconf-tutorial). But at least for today we manually wrote /etc/resolv.conf

controls@chiara|backup> cat /etc/resolv.conf # Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8) #     DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN nameserver 192.168.113.104 nameserver 131.215.125.1 nameserver 8.8.8.8

search martian

14120   Tue Jul 31 22:50:18 2018 aaronUpdateOMCOMC Expected Refl Signal

I learned a lot about lasers this week from Siegman. Here are some plots that show the expected reflectivity off of the OMC for various mode matching cases.

The main equation to know is 11.29 in Siegman, the total reflection coefficient going into the cavity:

$R=r-\frac{t^2}{r}\frac{g(\omega)}{1-g(\omega)}$

Where r is the mirror reflectivity (assumed all mirrors have the same reflectivity), t is the transmissivity, and g is the complex round-trip gain, eq 11.18

$g(\omega)=r_1r_2(r_3...)e^{-i\phi}e^{-\alpha_0p}$

The second exponential is the loss; in Siegman the \alpha_0 is some absorption coecfficient and p is the total round trip length, so the product is just the total loss in a round trip, which I take to be 4*the loss on a single optic (50ppm each). \phi is the total round trip phase accumulation, which is 2\pi*detuning(Hz)/FSR. The parameters for the cavity can be found on the wiki.

I've added the ipynb to my personal git, but I can put it elsewhere if there is somewhere more appropriate. I think this is all OK, but let me know if something is not quite right.

Attachment 1: omcRefl.pdf
14119   Tue Jul 31 08:17:55 2018 SteveUpdateSUSTrillium interface box was fixed,reinstalled & working

Attachment 1: all_OK.png
14118   Mon Jul 30 18:19:03 2018 KojiUpdateSUSTrillium interface box was fixed and reinstalled

The trillium interface box was removed from the rack.

The problem was the incorrect use of an under-spec TVS (Transient Voltage Suppression) diodes (~ semiconductor fuse) for the protection circuit.
The TVS diodes we had had the breakdown voltages lower than the supplied voltages of +/-20V. This over-voltage eventually caused the catastrophic breakdown of one of the diodes.

I don't find any particular reason to have these diodes during the laboratory use of the interface. Therefore, I've removed the TVS diodes and left them unreplaced. The circuit was tested on the bench and returned to the rack. All the cables are hooked up, and now the BRLMs look as usual.

Details

- The board version was found to be D1000749-v2

- There was an obvious sign of burning or thermal history around the components D17 and D14. The solder of the D17 was so brittle that just a finger touch was enough to remove the component.

- These D components are TVS diodes (Transient Voltage Suppression Diodes) manufactured by Littelfuse Inc. It is sort of a surge/overvoltage protector to protect rest of the circuit to be exposed to excess voltage. The specified component for D17/D14 was 5.0SMMDJ20A with reverse standoff voltage (~operating voltage) of 20V and the breakdown voltage of 22.20V(min)~24.50V(max). However, the spec sheet told that the marking of the proper component must be "5BEW" rather than "DEM," which is visible on the component. Some search revealed that the used component was SMDJ15A, which has the breakdown voltage of 16.70V~18.50V. This spec is way too low compared to the supplied voltage of +/-20V.

Attachment 1: P_20180730_173134.jpg
Attachment 2: P_20180730_180151.jpg
14117   Mon Jul 30 16:11:54 2018 gautamUpdateSUSTrillium interface box is broken

[koji, steve, gautam]

We debugged this in the following way:

1. Disconnect all fuses in the terminal blocks coming from the +/- 20 VDC Sorensens.
2. Check that they are indeed isolated using DMM.
3. Test blocks of fuses in order to identify where the problem is happening (i.e. plug fuses in, turn up Sorensen voltage knobs, look for current overload). We did things in the following order:
• MC suspensions
• BS, PRM and SRM
• ITMY
• ITMX
• Trillium interface box.
4. Turns out that the Trillium box is the culprit.
5. Confirmed that the problem is in the trillium interface box and not in the seismometer itself by unplugging all cables leading out of the interface box, and checking that the problem persists when the box is powered on.

So for now, the power cable to the box is disconnected on the back end. We have to pull it out and debug it at some point.

Apart from this, megatron was un-sshable so I had to hard reboot it, and restart the MCautolocker, FSSslowPy and nds2 processes on it. I also restarted the modbusIOC processes for the PSL channels on c1auxex (for which the physical Acromag units sit in 1X5 and hence were affected by our work), mainly so that the FSS_RMTEMP channel worked again. Now, IMC autolocker is working fine, arms are locked (we can recover TRX and TRY~1.0), and everything seems to be back to a nominal state. Phew.

14115   Mon Jul 30 11:05:44 2018 gautamUpdateSUSIFO SUS wonky

When I came in this morning:

• PMC was unlocked.
• Seis BLRMS were off scale.
• ITMX OSEM LEDs were dark on the CRT monitor even though Sat Box was plugged in.

Checking status of slow machines, it looked like c1sus, c1aux, and c1iscaux needed reboots, which I did. Still PMC would not lock. So I did a burtrestore, and then PMC was locked. But there seemed to be waaaaay to much motion of MCREFL, so I checked the suspension. The shadow sensor EPICS channels are reporting ~10,000 cts, while they used to be ~1000cts. No unusual red flags on the CDS side. Everything looked nominal when I briefly came in at 6:30pm PT yesterday, not sure if anything was done with the IFO last night.

Pending further investigation, I'm leaving all watchdogs shutdown and the PSL shutter closed.

A quick look at the Sorensens in 1X6 revealed that the +/- 20V DC power supplies were current overloaded (see Attachment #1). So I set those two units to zero until we figure out what's going on. Possibly something is shorted inside the ITMX satellite box and a fuse is blown somewhere. I'll look into it more once Steve is back.

Attachment 1: IMG_7102.JPG
14114   Sun Jul 29 23:15:34 2018 poojaUpdateCamerasDeveloping CNN

## Aim: To develop a convolutional neural network that resolves mirror motion from video.

Input : Previous simulated video of beam spot motion in pitch by applying 4 sine  waves of frquencies 0.2, 0.4, 0.1, 0.3 Hz  and amplitude ratios to frame size to be 0.1, 0.04, 0.05, 0.08 where random uniform noise ranging 0.05 has been added to amplitudes and frequencies. This is divided into train (0.4), validation (0.1) and test (0.5).

Model topology:

• Number of filters = 2
• Kernel size = 2
• Size of pooling windows = 2
•                                        ----->         Dense layer of 4 nodes  ---->    Output layer of 1 node

Activation:                      selu                                                  linear

Batch size = 32, Number of epochs = 128, loss function = mean squared error

Optimizer: Nadam ( learning rate = 0.00001, beta_1 = 0.8, beta_2 = 0.85)

Plots of CNN output & applied signal given in Attachment 1. The variation in loss value with epochs given in Attachment 2.

This needs to be further analysed with increasing random uniform noise over the pixels and by training CNN on simulated data of varying ampltides and frequencies for sine waves.

Attachment 1: conv_nn_varying_freq_amp_1.pdf
Attachment 2: conv_nn_varying_freq_amp_2.pdf
14113   Sun Jul 29 20:03:02 2018 ranaUpdatePEMSeismometer temp control

While Shruti is re-building Kira's heater circuit, I looked up how to do one of these (i.e. what does a real EE say about how to build a current source?):

It turns out that there is an Analog Devices application note (AN-968) about this (as there usually is once we get tired of playing around and try to look up the right answer).

I've linked to the note and attached the recommended schematic for high current applications. We'll go ahead as is, but we'll make a PCB according to this App Note for the v3 circuit.

Attachment 1: Screen_Shot_2018-07-29_at_8.00.27_PM.png
14112   Sun Jul 29 00:59:54 2018 KojiUpdateElectronicsCharacterization of Transimpedance Amplifier

You have this measurement problem when the IF bandwidth is larger than the measurement frequency. I suspect the IF bandwidth is 30kHz.

14111   Sat Jul 28 22:16:49 2018 John MartynUpdate Characterization of Transimpedance Amplifier

Kevin and I meaured the transfer function of the photodiode circuit using the Jenne laser and agilent in the 40m lab. The attached figures depict our measured transfer function over the modulation frequency ranges of 30kHz-30MHz and 1kHz-30MHz when the power of the laser was set to 69 and 95 μW. These plots indicate a clear roll off frequency around 300 kHz. In addition, the plots beginning at 1kHz display unstable behavior at frequencies below 30kHz. I am not sure why there is such a sharp change in the transfer function around 30kHz, but I suspect this to be due to an issue with the agilent or photodiode.

Attachment 1: PD_TF1.pdf
Attachment 2: PD_TF2.pdf
Attachment 3: PD_and_TIA_Transfer_Function_Measurements.zip
14110   Sat Jul 28 00:45:11 2018 terra, sandrineSummaryThermal CompensationHeater measurements overview

[Sandrine, Koji, Terra]

Summary: We completed multiple scans at different heating powers for the reflector set up, observing unique HOM peak shifts of tens of kHz. We also observed HOM5 shifts with the cylinder set up. Initial Lorentzian fittings of the magnitude give tens of Hz resolution. I summarize the main week's work below.

Set-up

Heater set-up is described in several previous elogs, but attachments #1 and #2 show the full heater set-up and wiring/pinouts in and out of vacuum, since we're all intimately aware of how confusing in-vacuum pinouts can be. We are not using the Sorenson power supply (as described in 14071); we just have the BKPrecision power supply 1735 sitting next to the ETMY rack and are manually going out to turn on/off.

We've continued to use the scan setup described in elog 14086, which is run using /users/annalisa/postVent/AGfast.py. Step by step notes for setting up the scan, running the scans, and processing the scans are attached in notes.txt.

Inducing/witnessing HOMs

The aux input beam was already clipped and on wednesday (after Trans was centered, 14093) we also clipped the output aux beam with razor blade (angled vertically and horizontally, elog 14103) before PDA255; we clipped ~1/3 of the output beam. Attachment #3 shows before and after clipping output, where orange 'cold' == unclipped, black 'mean' == clipped (all in cold state). Up to HOM5 is visible.

Measurements

Below is a summary of the available scan data. We also have cold (0A) scans CAR-HOM5 and full FSR scans for most configurations.

Elliptic Reflector
current[A] voltage[V] power[W] scans
0.4 2 0.8 CAR-HOM3(x1)
0.5 3.4 1.7 CAR-HOM3(x1)
0.6 5 3.0 CAR-HOM3(x1)
0.8 9.4(9.7) 7.5(7.8) CAR-HOM5(>x5)
0.9 12 10.8 CAR-HOM5(x4)
1.09 17 18.5 CAR-HOM3

Cylinder + Lenses
current[A] voltage[V] power[W] scans
0.9 15 13.5 CAR-HOM5(odds x4)

We tried the cylinder set-up again tonight for the first time since inital try and can see shifts of HOM5 - see attachment #5; we haven't looked in detail yet, but it looks like odd modes are more effected, suggesting the ring heat pattern is off centered from the beam axis.

Scan data is saved in the following format: users/annalisa/postVent/scandata/{reflector,cylinder}/{parsed,unparsed}/{CAR,HOM1,HOM2,HOM3,HOM4,HOM5}{_datetime}{_parsed,_unparsed}.{txt,pdf}

Minimum heating

On 7/26 we increased the power to the elliptical reflector heater in steps to find the minimum heater power required to see frequency shifts with our measurement setup. Lowest we can resolve is a shift in HOM3 with 1.7W (0.5A/3.4V). According to Annalisa's measurements in elog 14050, this would be something like 30-60 mW radiated power hitting the test mass. We only looked at CAR - HOM3 for this investigation; data for scans at 0.4A, 0.5A, 0.6A is available as indicated above.

Lorentizian Fitting

The Lorentzian fitting was done using the equation a + b / sqrt(1+((x-c)/d*2), where a = constant background, b = peak height above background, c = peak frequency, d = full width at half max.

The fitting is still being edited and optimized. We will crop the data to zoom in around the peak more.

The Lorentzian fit of the magnitude shows ~10Hz of resolution. (See attachment 6 for the carrier at 8A and attachment 7 for HOM 1 at 9A)

We're working on fitting the full complex data.

Attachment 1: heater_setup.jpg
Attachment 2: heater_wiring.jpg
Attachment 3: notes.txt
Notes for running scans:
1. when first turning on Agilent, set initial stuff
> cd /users/annalisa/postVent/20180718
> AGmeasure TFAG4395Atemplate.yml
2. tweak arm alignment and offset PLL
> sitemap (then IFO --> ALIGN and also PSL --> AUX)
> to increase
3. make sure X-arm is misagligned (hit '! Misalign' button for ITMX, ETMX)
3. run scan
> python AGfast.py startfreq stopfreq points

... 36 more lines ...
Attachment 4: FSR_clipped.pdf
Attachment 5: cylinderHOM5.pdf
Attachment 6: pt8A_CAR.pdf
Attachment 7: pt9A_HOM1.pdf
14109   Fri Jul 27 17:16:14 2018 SandrineUpdateThermal CompensationCopied working scripts for mode spectroscopy into new directory (modeSpec)

The scripts: AGfast.py, make HDF5.py, plotSpec_marconi.py, and SandrineFitv3.py were copied into the new directory modeSpec.

The path is: /opt/rtcds/caltech/c1/scripts/modeSpec

These scripts can still be found under Annalisa's directory under postVent.

14108   Fri Jul 27 10:48:57 2018 SteveUpdateSUSBS oplev window

Yesterday I inspected this BS oplev viewport. The heavy connector tube was shorting to table so It was moved back towards the chamber. The connection is air tight with kapton tape temporarly.

The beam paths are well centered. The viewport is dusty on the inside.

The motivation was to improve the oplev noise.

Attachment 1: BSOw_.jpg
Attachment 2: dustInsideBSO.jpg
14107   Fri Jul 27 02:30:51 2018 gautamUpdateGeneralGlitchy MC

Kevin and I saw some weird IMC / PEM BLRMS behaviour today - see Attached screenshot. Not sure what was happening with the IMC, but MCtrans was oscillating at ~3Hz for a good 20 minutes or so. I just killed the lock, and restarted MCautolocker on megatron. There was a strange feature in the 3-10Hz BLRMS around that time as well. All seems back to normal now...

Attachment 1: 38.png
14106   Thu Jul 26 15:11:18 2018 SteveUpdateGeneral Viewports & coating of 2001

New optical quality BK-7 windows in 2001 [4 substrates ] AR coated R<0.75 % for 630-1064nm " Azury BLue" broadband : TRX, TRY, ITMY-Oplev &  ITMX-Oplev viewports.

The BS-Oplev and PRM-Oplev 10" CF with 5.38" diameter view was coated the same way. The window here is Corning 7056 Borosilicate

5 more BK-7 substrates were coated R <0.1% of 1064 nm "Golden Orange" Their location: IMC-IN, IFO-REF and OMC   The next vent we have to confirm optical quality window locations.

All other conflat flange viewports are 7056 Kovar sealed .

Technical notes of 2001 40m upgrade can be seen at LIGO-T010115- 00- R  ....page 14

Attachment 1: BK7window_Coatings.PDF
14105   Thu Jul 26 01:52:01 2018 terraUpdateThermal Compensationheater work update

Just a quick update: over the past few days we've taken (at least) 5 scans around each peak [carrier - HOM3] at 9.4V/0.8A, 4 scans around [carrier - HOM5] at 12V/0.9A hot state with the reflector setup. We also have (at least) 5 scans of carrier - HOM5 in cold state. I attach a rough overview of the peak magnitude shifts in the first attachment. Analysis ongoing. All data stored in annalisa/postVent/{date}

Initial shifts just based on rought peak placement in the meantime:

[9.4V/0.8A]   [12V/0.9A]

HOM1    10 kHz         20 kHz

HOM2    18 kHz         28 kHz

HOM3     30 kHz        40 kHz

HOM4     N/A             26 kHz

HOM5     N/A             35 kHz

I also attach the heating thermal transient from today (12V/0.9A) as seen by the opLevs. We see a shorter time constant for pitch, longer for yaw, preceeded by a dip in yaw. Similar behavior yesterday for slightly less heating, though less pronounced pre-dip. The heater is offcentered on the optic horizontally; likely this is part of the induced yaw. The spikey stuff i removed is from people walking around inside during the transient.

I've left the heater and LSC off for the night. Heater off at 2:07 am local time.

Please don't touch the oplevs; we're taking a cool down measurement.

Attachment 1: OpLev_thermal_drift.pdf
Attachment 2: hotColdAll.pdf
14104   Wed Jul 25 22:46:15 2018 gautamConfigurationComputersNDS access from outside

After this work, I've been having some trouble getting data with Python NDS. Eventually, I figured out that the nds connection request has to be pointed at '131.215.115.200' (the address of the NAT router which faces the outside world), port 31200 (it used to work with 'nds40.ligo.caltech.edu' or '131.215.115.189'). So the following snippet in python allows a connection to be opened. Offline access of frame data via NDS2 now seems possible.

import nds2
conn = nds2.connection('131.215.115.200',31200)
 Quote: So far, ssh (22), web services (30889), and elog (8081, 8080) were tested. We also need to test megatron NDS port forwarding and rsync for nodus, too.Finally I turned off the firewall rules of shorewall on nodus as it is no longer necessary.
14103   Wed Jul 25 14:45:59 2018 SandrineSummaryThermal CompensationETM Y Table AUX read out

Attached is a photo of the set up of the ETM Y table showing the AUX read out set up.

Currently, the flip mount sends the AUX to the PDA255. Terra inserted a razor blade so the PDA255 will witness more HOMs. The laser is also sent to the regular PD and the CCD.

Attachment 1: EY_table_.JPG
14101   Tue Jul 24 09:47:51 2018 gautamUpdateCamerasDeveloping neural networks on simulated video

I was thinking a little more about the way we are training the network for the current topology - because the network has no recurrent layers, I guess it has no memory of past samples, and so it doesn't have any sense of the temporal axis. In fact, Keras by default shuffles the training data you give it randomly so the time ordering is lost. So the training amounts to requiring the network to identify the center of the Gaussian beam and output that. So in the training dataset, all we need is good (spatial) coverage of the area in which the spot is most likely to move? Or is the idea to develop some tools to generate video with spot motion close to that on the ETM in lock, so that we can use it with a network topology that has memory?

 Quote: This looks like good progress. Instead of fixed sines or random noise, you should generate now a time series for the motion which is random noise but with a power spectrum similar to what we see for the ETM pitch motion in lock. You can use inverse FFT to get the time series from the open loop OL spectra (being careful about edge effects)
14100   Tue Jul 24 06:11:50 2018 ranaUpdateCamerasDeveloping neural networks on simulated video

This looks like good progress. Instead of fixed sines or random noise, you should generate now a time series for the motion which is random noise but with a power spectrum similar to what we see for the ETM pitch motion in lock. You can use inverse FFT to get the time series from the open loop OL spectra (being careful about edge effects).

Quote:

## Aim: To develop a neural network that resolves mirror motion from video.

14098   Mon Jul 23 09:58:52 2018 SteveSummaryVACRGA scan at day 6

Attachment 1: pd81-560Hz-d6.png
14097   Sun Jul 22 14:01:07 2018 poojaUpdateCamerasDeveloping neural networks on simulated video

## Aim: To develop a neural network that resolves mirror motion from video.

Since error was high for the same input as in my previous elog http://nodus.ligo.caltech.edu:8080/40m/14089

I modified the network topology by tuning the number of nodes, layers and learning rate so that the model fitted the sum of 4 sine waves efficiently, saved weights of the final epoch and then in a different program, loaded saved weights & tested on simulated video that's produced by moving beam spot from the centre of image by sum of 4 sine waves whose frequencies and amplitudes change with time.

Input : Simulated video of beam spot motion in pitch by applying 4 sine  waves of frquencies 0.2, 0.4, 0.1, 0.3 Hz  and amplitude ratios to frame size to be 0.1, 0.04, 0.05, 0.08. This is divided into train (0.4), validation (0.1) and test (0.5).

Model topology:

Input               -->                  Hidden layer               -->                    Output layer

8 nodes                                              1 node

Activation function:                                  selu                                             linear

Batch size = 32, Number of epochs = 128, loss function = mean squared error

Optimizer: Nadam ( learning rate = 0.00001, beta_1 = 0.8, beta_2 = 0.85)

Normalized the target sine signal of NN by dividing by its maximum value.

Plot of predicted output by neural network, applied input signal & residual error given in 1st attachment. These weights of the model in the final epoch have been saved to h5 file and then loaded & tested with simulated data of 4 sine waves with amplitudes and frequencies changing with time from their initial values by random uniform noise ranging from 0 to 0.05. Plot of predicted output by neural network, target signal of sine waves & residual error given in 2nd attachment. The actual signal can be got from predicted output of NN by multiplication with normalization constant used before. However, even though network fits training  & validation sets efficiently, it gives a comparatively large error on test data of varying amplitude & frequency.

Gautam suggested to try training on this noisy data of varying amplitudes and frequencies. The results using the same model of NN is given in Attachment 3. It was found that tuning the number of nodes, layers or learning rate didn't improve fitting much in this case.

Attachment 1: nn_simulation_2_normalized_mult_sin_nodes8_128epochs_lr0p00001_beta1_0p8_beta2_0p85_0p4train_0p1valid_marked.pdf
Attachment 3: nn_simulation_2_normalized_varying_mult_sin_nodes8_128epochs_lr0p00001_beta1_0p8_beta2_0p85_0p4train_0p1valid_marked.pdf
14096   Sat Jul 21 14:03:19 2018 KojiSummaryThermal CompensationY arm locking

Ah. With MC2 feedback, we have about 3 times smaller "optical gain" for the ASS A2L. We have same dither, same actuator, but we need only 1/3 actuation of the MC2 compared to the ETMY case.
We had to reduce the ASS spot servo from 1 to 0.3 to make is stable, so this means that the ASS is really merginally stable.

14095   Sat Jul 21 01:14:02 2018 gautamUpdateOMCPZT Jena driver board check

[Aaron, gautam]

We did a quick check of this board today. Main takeaways:

• There are two voltages (HV pos and HV neg) that are output from this unit.
• Presumably, these goto different piezoelectric elements, referenced to ground. Are there any spec sheets for these describing the geometry/threshold voltages?
• The outputs are:
• $\mathrm{HV_{+}} = 10(V_{\mathrm{DAC}}+V_{\mathrm{offset}}), \mathrm{HV_{-}} = 10(-V_{\mathrm{DAC}}+V_{\mathrm{offset}})$
• So with $V_{\mathrm{offset}} = 7.5 \mathrm{V}$, we expect to be able to use +/- 7.5 V of DAC range.
• The trim pot had to be adjusted to realize $V_{\mathrm{offset}} = 7.5 \mathrm{V}$.
• I assume 150V is some kind of damage threshold of the PZT, so there is no benefit to using 10V offset voltage (as this would result in 200 V at full range DAC voltages).

With the correct $V_{\mathrm{offset}} = 7.5 \mathrm{V}$, we expect 0V from the DAC to result in 0 actuation on the mirror, assuming that an equal 75V goes to 2 PZTs mounted diametrically opposite on the optic. Hopefully, this means we have sufficient range to scan the input pointing into the OMC and get some sort of signal in the REFL signal (while length PZT is being scanned) which indicates a resonance.

We plan to carve out some IFO time for this work next week.

14094   Sat Jul 21 01:06:49 2018 gautamSummaryThermal CompensationY arm locking

I implemented this today. For now, the LSC output matrix is set to actuate on MC2 for Y arm locking. As expected, the transmission was much more stable, and the PLL control signal RMS was also reduced by factor of ~3. MC2 control signal does pick up a large (~2000 cts) DC component over a few hours, so we need to relieve this periodically.

Now that we have a workable ASS for the Y arm as well, we should be able to have more confidence in returning to the same beam spot position on the ETM and staying there during a scan using this technique.

The main improvement to be trialled next in the scanning is to improve the speed of scanning. As things stand, my script takes ~2.5 seconds per datapoint. If we can cut this in half, that'd be huge. On Wednesday night, we were extraordinarily lucky to avoid MC3 glitching, EPICS/slow machine failures, and GPIB freezes. Today, the latter reared its head. Fortunately, since I'm dumping data to file for each datapoint, this means we at least have data till the GPIB freeze.

 Quote: For future measurements, we should consider locking the IMC length to the arm cavity - this would eliminate such alignment drifts, and maybe also make the PLL control signal RMS smaller.

Not related to this work: Terra, Sandrine, Keerthana and I cleaned up the lab a bit today, and made better cable labels. Aaron and I have to clean up the OMC area a bit. Huge thanks to Steve for taking care of our mess elsewhere in the lab!

14093   Fri Jul 20 22:53:15 2018 KojiUpdateASSAttempt to resurrect Yarm ASS

[Koji Gautam]

We managed to realize stable ASS configuration for Yarm. The transmission of 1.06~1.07 was recovered by introducing intentional beam spot offset in the horizontal direction towards the opposite side of the elliptic reflector. The end table optics were adjusted to have the spots about the center of the mirrors, lenses, and PDs/QPDs.

Preparation

- The Y arm was manually aligned with a given input axis. The transmission was ~0.8.
- Then, TT2 was moved in yaw such that it introduced the horizontal beam shift at the end. By moving the spot to the opposite side of the reflector. The transmission ~0.95 was obtained after patient alignment work.

- Went to the end table and checked the spots. The beam was not at the center of the last 1" lens for the Trans PDs. The beam steering was adjusted to have the spot nicely going through the lens and the mirrors. This made the transmission level to be ~1.05.

- The beam centering on the Trans PD was checked and adjusted.
- The beam centering on the RF BBPD for the arm scan was checked. The spot was too big for that PD. The lens was slightly moved away from the PD to make the spot on the BBPD small. Now the PD saw the plateu when the steering was scanned (i.e. the spot is small enough).

- With the Y arm locked with MC2, the servo gain needs to be 0.012 instead of nominal 0.015 with ETMY to prevent from servo oscilating.

ASS tuning

- First of all, only the bottom 4 loops out of total 8 loops were tuned. They are the servos for the beam alignment with regard to the caivty. The linearity and the zero crossings were checked with regard to the reference alignment. All of these 4 showed offsets that causes the servo running away. Don't know the reason of this offset, but it is freq dependent. Therefore the dither freqs were tuned to make the offset zeroed, and tuned the demod phases there. This kept the transmission as high as the reference (~1.05)

- This allowed us to play with the spot position a bit by tuning the caivty alignment. In the end, the transmission of ~1.08 was obtained. Using this alignment, A2L offset for ETMY Yaw was determined to be +17 (to make the error signal -17). This offset produces almost a beam radius (5mm) shifted on the end mirror towards the opposite direction of the reflector.

- The nominal servo setting made the spot servo running away. Gautam pointed out that this could be a gain hierarchy problem (i.e. the spot servos are too fast). We ended up reducing the gain of the servo from 1.0 to 0.3 to make the spot servo stable.

- All the ASS setting was stored in a new snap file "script/ASS/ASS-DITEHR_ON.snap". The previous snap was saved to "script/ASS/ASS_DITHER_ON_preVent201807.snap". This did not save the exc gains of the oscillators. Therefore "DITHER_ASS_ON.py" was modified to have the new exc gains (CLKGAIN). The old values are stored in the comments in this script.

Overall this is not an ideal situation as we don't know what is the actually cause of the offsets in the dither error signals. We expect to correct the beam clipping and the suspension sooner or later. Therefore, we will come back to the ASS again once the other issues are corrected.

Attachment 1: 02.png
14092   Fri Jul 20 22:51:28 2018 KojiUpdateIOOIMC WFS path alignment

IMC WFS tuning

- IMC was aligned manually to have maximum output and also spot at the center of the end QPD.
- The IMC WFS spots were aligned to be the center of the WFS QPDs.
- With the good alignment, WFS RF offset and MC2 QPD offsets were tuned via the scripts.

14091   Fri Jul 20 18:30:47 2018 JonConfigurationAUXRecommend to install AUX PZT driver

I recently realized that the PLL is only using about 20% of the available actuation range of the AUX PZT. The +/-10 V control signal from the LB1005 is being directly inputted into the fast AUX PZT channel, which has an input range of +/-50 V.

I recommend to install a PZT driver (amplifier) between the controller and laser to use the full available actuator range. For cavity scans, this will increase the available sweep range from +/-50 MHz to +/-250MHz. This has a unique advantage even if slow temperature feedback is also implemented. To sample faster than the timescale of most of the angular noise,  scans generally need to be made with a total sweep time <1 sec. This is faster than the PLL offset can be offloaded via the slow temperature control, so the only way to scan more than 100 MHz in one measurement is with a larger dynamic range.

14090   Fri Jul 20 07:43:54 2018 SteveSummarySUSETMY

Attachment 1: ETMY_leveling.png
Attachment 2: ETMY.png
14089   Thu Jul 19 18:09:17 2018 poojaUpdateCamerasUpdate in developing neural networks

## Aim: To develop a neural network that resolves mirror motion from video.

Case 1:

Input : Simulated video of beam spot motion in pitch by applying 4 sine  waves of frquencies 0.2, 0.4, 0.1, 0.3 Hz  and amplitude ratios to frame size to be 0.1, 0.04, 0.05, 0.08

The data has been split into train, validation and test datasets and I tried training on neural network with the same model topology & parameters as in my previous elog (https://nodus.ligo.caltech.edu:8081/40m/14070)

The output of NN and residual error have been shown in Attachment 1. This NN model gives a large error for this. So I think we have to increase the number of nodes and learning rate so that we get a lower error value with a single sine wave simulated video ( but not overfitting) and then try training on linear combination of sine waves.

Case 2 :

Normalized the target sine signal of NN so that it ranges from -1 to 1 and then trained on the same neural network as in my previous elog with simulated video created using single sine wave. This gave comparatively lower error (shown in Attachment 2). But if we train using this network, we can get only the frequency of test mass motion but we can't resolve the amount by which test mass moves. So I'm unclear about whether we can use this.

Attachment 1: nn_simulation_mlt_sine_nodes4_lr0p00001_beta1_0p8_beta2_0p85_marked.pdf
Attachment 2: nn_simulation_2_nodes4_target-1to1_marked.pdf
14088   Thu Jul 19 13:35:30 2018 SteveSummaryVACannuloses pumped

Roughing down the annuloses required closing V1 for 13 minutes

IFO is 2.2e-5 Torr

Attachment 1: AnsPumped.png
14087   Thu Jul 19 11:01:03 2018 SteveSummaryVACpd81 @ 2e-5 Torr

Cold cathode gauge just turned on.

Attachment 1: pd81@2days.png
14086   Thu Jul 19 04:44:09 2018 Annalisa, TerraSummaryThermal Compensationfrequency shift observed with heating!

Annalisa, Gautum, Koji, Terra

Summary: with the reflector setup, we measured a frequency shift of the first and second order modes! First looks of shifts show 1st HOM shift ~-10 kHz, 2nd HOM shift ~-18 kHz (carrier ~4 kHz). We saw no shift with the cylinder/lenses set up.

- - - - -

Tonight we modified the cavity scan setup: the LO is provided by the Marconi which, at the same time, is also used to scan the AUX laser frequency instead of the Agilent. In order to get rid of the free running noise between Marconi and Agilent, the Marconi frequency was scanned and, point by point, the Agilent center frequency was changed accordingly. In order to speed up the process, the whole procedure was automated. The script is called AGfast.py and can be found in /users/annalisa/postVent.

One thing that helped in improving the data quality of the phase information was to set the Agilent IF bandwidth @1kHz. Not yet clear why, but it was better than having a lower bandwidth. To be further investigated.

With this setup, we made some coarse scan of the full FSR and then we "zoomed" around the main peaks in order to increase the resolution and get a more precise information about the peak frequency.

Here are the frequency ranges that we scanned:

• carrier - central frequency: 31.73MHz; range: [31.68MHz - 31.78MHz]
• HOM1 - central frequency: 32.88MHz; range: [32.84MHz - 32.93MHz]
• HOM2 - central frequency: 34.03MHz; range: [33.95MHz - 34.06MHz]
• HOM3 - central frequency: 35.18MHz; range: [35.09MHz - 35.25MHz]

We powered the heater of the lenses setup @4:55 am at 14.4V and 0.9A. Then we slightly increased the power @5:05am and the final "hot state" configuration is with heater powered at 16V and 0.9A.

With this setup we couldn't see any frequency shift

Then, at around 6:30 am we turned on the reflector setup and we measured a frequency shift of the first and second order modes. First scans show 1st HOM shift ~10 kHz, 2nd HOM shift ~18 kHz. First attachment shows carrier hot/cold, second attachment shows HOM2 hot/cold. We started to get plauged by high seismic noise. Heaters turned off at 7:45 am. Lots of scans and actual analysis to go.

gautam: about the questionable plotting -

• 10 faint (alpha~0.3) lines are individual measurements with the reflector doing its heating. (AG4395A, 0 span, single frequency measurements plotted together).
• charcoal line, labelled mean, is the mean of the 10 above lines.
• bright green ("Reference") is the mean of a coarse scan (cold ETM) overlaid for comparison.
• "cold" - self explanatory.

My personal favourite plot is Attachment #3, which is a 5 MHz scan (cold) to identify positions of the various peaks. The power of including phase information in the analysis is clear. The second FSR on the right edge of the plot is not as prominent as the first is because the arm transmission was degrading throughout the measurement. For future measurements, we should consider locking the IMC length to the arm cavity - this would eliminate such alignment drifts, and maybe also make the PLL control signal RMS smaller.

Attachment 1: scanning_fine_2018-07-19-07-32-08_parsed.pdf
Attachment 2: scanning_fine_2018-07-19-06-57-47_parsed.pdf
Attachment 3: Yscan_scanning_parsed_2am.txt.pdf
14085   Thu Jul 19 01:56:25 2018 gautamSummaryVACAUX pump shutdown

[koji, gautam]

Per Steve's instructions, we did the following:

• TP3fl pressure reading was 65 torr.
• TP3 controller reported pumping current of ~0.18A, temperature of 24C.
• We throttled the manual valve which was connecting the "AUX" pump to the TP3fl.
• The TP3fl pressure went up to 330 torr.
• TP3fl controller reported current of 0.22A, temperature of 24C.
• After ~5mins, we shut the AUX pump off.
• We have monitored it over the last 1hour, no red flags.
• (Before stopping AUX RP)
0:56AM TP3 I=0.18A, P=6W, 23degC, TP3FL: 66
• 0:59AM TP3 I=0.22A, P=7W, 23degC, TP3FL: 336
• 1:15AM TP3 I=0.21A, P=7W, 23degC, TP3FL: 320
• 1:31AM TP3 I=0.21A, P=7W, 23degC, TP3FL: 310
• 2:06AM TP3 I=0.21A, P=7W, 23degC, TP3FL: 301
• 5:06AM TP3 I=0.21A, P=7W, 23degC, TP3FL: 275
14084   Wed Jul 18 23:43:50 2018 KojiUpdateGeneralVent 80 recovery

Is the reflector too close to the beam and causing clipping?

 Quote: For unknown reasons, the Y arm ASS does not maximize TRY. So we are in the unfortunate situation of neither arm having a working ASS servo. To be worked on later.
Attachment 1: IMG_5868.JPG
Attachment 2: IMG_5382.JPG
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