Hello everybody welcome to the next part of
the tutorial. So in the previous class we
have learned about is delta method like aerodynamic
parameter estimation in delta method where
I have talked about the architecture of adopted
by delta method where you are speed forward
given above. And you have some got well in
how you will for work and how it will be trace
and that the like how did you use for the
method. We will quickly revise what is with
class.
.
So as I said like is with our biological neural,
neural so you can see this architecture of
usually drawn it was like this, so it had
some wires, inputs and certain bit do it right
it is wires and you can have different inputs
X1, X2, X3 and here you have some all those
and pass non-linear activation function. And
it could be your any kind of sigma in constant
and then sigma hidden log it can also be an
linear simple way.
So initially that will talks about your artificial
neural, so this is the architecture of your
single neural this one will be the single
neural. So you have the then associated rates
of W1, W2, W3 and bias let us B then you have
to sum up all the effects and then pass non-linear
activation function and then you will get
here as output right.
So what we did like all the function not depends
on the complexity of copies get the problem.
So every kind of non-linear can be captured
by in the suitable non-linear activation function.
So that is why it is also called universal
across the metal can approximate any kind
of non-linearity, the activation function
which we discussed was we will say that F(y)
and if 1-e?y/1+2-?y and here now you can see
here we can also modify this non-linear activation
function with the ? parameter which will have
the control on the function with the parameter.
Then this is called, ? is called gain parameter
of activation function. So here you have the
flexibility of selecting this activation function
that is typically tan sigma okay. And then
with that activation comes in once you got
this output from the neural and then now it
will propagate to the next neural if it had
some other layers right. So that is how we
understood and then getting the numerator
model is about assigning them appropriate
weighted of right weighted and bias.
So with that you can have a defined zero network
model right, and the learning of this model
can be done using this back proportion called
which we have discussed earlier, so it is
based on based addition method basically it
is the bad proposition algorithm which is
based on your sleepiest yours this is there
is how the operation of weight is done so
it was basically w of support one to obtained
weight like this so it is K+ 1 stand weight
was okay w(k) are here it depends on like
how your selecting your error function so
you am also write like this so ? dE/ dw right
this weigh and then suppose your error is
becoming constant for some rezone the to improve
that you can add this momentum parameter right
w(k)- w(k-1) one step back again.
This is you know that mean parameter they
decides your convergence of powerful and this
movement which improve the result momentum
parameter when it use when your error as this
in this case here it is constant so in this
case Dw/ De / dW or directly teamed with 0
so that in that case it will allow it will
not be able to update so that need additional
term of momentum parameter where you will
get the updated weight age yeah this what
we learned and once you have the rate network
with the help of your input and output.
.
Let us say this is input and output in our
example we will make it CL CM as output and
then a ?? e qC/2 v these our input these are
our output now you got this model which was
earlier back box you got this model it was
earlier black box as straight forward user
network based model you got the trained model
so this part we have done now so further ?? method
what he suggest like you know start for input
1,2 find CL a then you further a in both the
directions corresponding to that you will
see the responses in CL the for quality for
+ a make it density CL – then twice of dealt
a actually in boot the direction so you will
get CL a like this so other variables also
like CL ?E CM ?e if you ? e ? then you will
see the changes in force and movement coefficients
you can write like this and you will get that.
So now the how hard of this method is about
getting this model FFNN based model fit forward
based network model to just to make to make
it simple you can also use this group of which
is available in math lab software distracted
in a simplest way so that you can actually
model this once you have the flight data available
a ? CL and Cm then I will tell you how to
design this network mode and then you can
use this method to estimate your parameters
L a.
So I will then later I will just explain you
or I will demonstrate with the help of three
data which I said like I will be talking about
the examples to with data how to estimate
the parameter then see the result and then
you can also try with some of the different
flight data to estimate the parameter on the
after the learning met so I will start showing
you the in this section and then with example.
.
So I just can see in this screen this is a
MATLAB software of 2040 A version right and
this window is called command window most
of you may be knowing it as I said like in
this excel we will be talking about its NN
tool right NN tool box, now in and you have
the data which I have written X in uncertainly
dot MIT file mat file jet out put under certain
category this is a output data for your problem
so here now we are ready with the data input
data and putout data.
So X in input data X out output data so first
of all you can load the data once you lead
this data so you have in the work space will
see it is like XC input data this drop in
command window you can see the data is loaded
right and further information you can see
banded you can see all those information so
essentially expenditure free cost 796 jet
output if your 2 x 7 and 96 so what its say
like it means you have 3 input data of 796
sample, two output data 796 sample so it is
like as you can find a minimum and maximum
value in the row.
And this entire output now as we showing you
about NN tool box so just you write NN tool
here and pervious enters into series tool
box here okay, so here what you can see here
you have the box four input data and this
input and this data we keep it out output
data and here you can see these are network
so I will just tell you how to design a network
fit forward neural network in input data and
output data.
So let us start loading the data so you can
load the data remain this input so basically
you are trying to import the data so input
data is our FG so we select XC here input
so here it is coming like variable X in has
been default imported as input data into the
network or data managing that mean we have
imported the data now target data is our output
data set it output data now you can import
the output data, yes.
So now enclose it so now you are able to see
input data box you have input data target
data box we have output data next thing is
now you design a network right so you select
a new network that you can keep name of your
work so I will write network under score answer
three like simple way to answer this so we
are getting a design of this particular network
or example is about longitudinal you can write
LON, so now we are trying to create a network
for uncertainly longitudinal data right now
you see the network time already we have discussed
about free forward network.
Training done by math preparation so this
is the structure default structure so you
can select that you can also try with some
of the deferent method which is prior interest
like it want to showed further you can go
for the next but juts forward backward days
in network time input data already you have
so we make it extreme other data get down
so 20 algorithm I am leaving the default you
just for a starting time from beginning.
You can more emotion the command motion of
the data which we already is a time here default
data and as I said this number of layers talk
about hidden layers number of hidden layer,
so you can take one without one it generate
to 10 of to capture the complicity in times
of a problem so we see that the layer, layer
number one now in this number of neurons so
you have a command over or control over number
o9f neuron in hidden layer as I said number
of neuron in input layer in number of input.
So whatever you have because you have two
input so default we have 3 neuron in input
layer and we have two output in LNCM so we
can two output actually neuron in output layer
but this number of neuron is about your number
of neuron incident layer. So default we are
coming then so if you want to change it you
can change you can take ever number you want
whether third like go to target that you call
value that we would happen and then this is
your transition that diffusion function.
So I just activation function can be of different
type we call with ten signal function right,
take this tan ? function and now you can with
your network with values so this is enable
greater network by clicking on wait, okay.
So now your new network call hands network
that is why enter t that should long as I
told data manger if you were able to create
your network right, okay. If you want to leave
your network you can see from data when you
see what is your network look like right so
here you have three inputs so number of you
know that way input layer, number of you know
if you done this you have selected 10 so it
is 10 output layer you have two errors, okay
so now you can close this.
So you have your network structure right,
so if you want to take click on it so this
is your network be forward me the model. Now
you want to train your network right, so you
go to training and train here so this air
about the filling data so we have to fill
input this about xn and target data is our
data output so that because you do not have
to manage it here you can see different taps
are there you can explore more if you want
let us do it with default data so the data
is going network looking to data.
So now you will see your network you are trained
and it can converge it see two iteration number
of iteration you can see here because then
permission relate to performance time and
if you want to check your performance you
can say it from here right, let us see so
this y axis here talked about mean squared
error a twinned data validation data and test
data and this dotted line taught you about
that the result where your valuation error
came minimum for the first time right here,
so ideally you are network will stop here
and training should be done till this but
it has taken it is more value so obvious augmentation
of this feature here.
So blue line is about your training error
in training data, green is about error in
your validation data and red is about error
in your test data and dotted line is about
their performance. So bits number of iteration
it call the if box your error is terrifically
changing with it is results into a very low
value even lower than your 10-4 and first
time you are valuation error come minimum
at this number may be around 56 this value
before this into and here is your network
is trained very well.
Here what, how it works like you itself 70%
of the data for that training rest of the
among with data 15% for validation and 15%
for the testing of your results, so at that
time makes your that you have not under over
grating to that 15% of the data which we were
not included in the training where used to
check it is not over 15. Now you can see the
regression value it confident in your result
like this, so here you can see four different
boxes first is your training validation test
and this is about inputting very I think all
the results, okay.
Now you see this how well they are fitting
and the imposition of this fit you get from
this parameter r, so basically you understand
like this r, when r is 1 it means all the
data samples are fitting on hidden line the
basic line right. So r traps your work the
relationship between the spit data and from
the observe data so this profiles at data
and it further then it affect so if it is
r values quite high all most close to one
so that is the reason we can see all your
data sample are able to spit on this blue
line that is for the training vibration also
you got very good result when 9997 almost
all the data samples like you know you have
it total 796 samples so all the samples almost
all, the samples including few may be five
6 or all those likely although in line.
But this we have include so that is why you
did not get r = 1 but evaluation r value evaluate
in such it has got the good training and then
you have tested with different data and then
this also saying about confident in your train
model with the very high equation of 0.9997
that is could all the until you get this then
rather then.
.
So at least now you have able to train your
model with this train as it is suppose it
is present conversing first time you can try
this multiple time and then you can also ask
the permission of about the weight and by
as dropping of the critical dimension part
you see that associated with that earth and
including by it and if you want to change
the weight and bios we want to prove your
all weights you can do it independently get
to so her ideas can be excluded that different
futures of this goal part and then accordingly
it will be modified as the part.
Now again you are able to create this network
model you can export this to the met lap fine
so this network under so that is why we are
knowing about training of the network you
can export or you can also say that your,
you know your option let us say that whether
tin permission also that is important all
the error we cannot check and see okay.
.
So now you got this network model so how will
you test like the code if you have different
data so for that we can try to dictate the
data or good okay how good it was like that
we can write the command then you can do it
by your own simulation of since the network
name is unsetting this from you have to write
it just you can go for this okay, here write
this name and here you can keep your different
locoed okay.
So here I split this network using this input
output data that will show you as option for
input output data so I will just show you
that input output data they could not be got
data from different flight not different flight
different set of flight data yeah so maybe
two or something along if you do it you can
write that if you do not have data is available
it is not sure so if we are extreme the name
that I extreme so we going to this.
So her I have suppose you want first see the
result for the same data you can write yes
so it will give you about the next time will
give you the result for predictor also, so
now itself you got again 7986 samples of data
for both the outputs then if we end here so
future if it is won predictor so once you
have designed your network like this then
you will able to predict the output for any
inputs which is suitable models.
And then once you got this predictor output
like this so what essentially you want to
do now you want to part of the inputs x data
let us x in it can tells your input information
about a d nqc / 2v so you can give different
input so you can add first time maybe difference
in a you note down the value like it set it
somewhere as it in part of the network connection
maybe x – d a you feed some design where
name in different variables store it and then
finally form the d method if you want to find
in all further a and then it will become your
predictor out for those projective observation
– predictive output for the negative observation
divide by probe of for the term input will
give you the result.
So this is what actually we have done it and
I am shoeing you the method so this was the
part of process and domination of entering
code bond I hope you will be always appreciate
and then you can also do it by as it.
.
So let us see Aerodynamic parameter estimation
will be delta method we have taken the same
data or we have use for this estimation. So
basically we have taken the same data what
we have used for this illustration this is
the aircraft we have already been earlier
introduced that so this the parameter and
for the data which you are familiar now if
you see the will not be equal to a beta.
.
What we assume is that is the rate of input
data, data connective data and this is the
model actually the n coffins of 3 where you
no more worried about the aircraft. Now we
are treating the black box we have gathered
the data from flight in terms of input data
and output data and we are trying to model
e. In the last year of the network ready coffin
method it has said it can approximate any
knowing aircraft.
.
And once train this model we have it know
our same model of that will be your longitudinal
data in theatrically proved about the training
data. The data which is for the training red
line to show the power. Ann symmetric what
we did like we have trained it's from the
first flight data different flight datas and
we have moved different flight datas to estimate
the coefficient at the end movement coefficient
so there is a well the match with each other
and then once you apply your ??.
.
Once you applied the data all the parameters
so all the parameter are seen here cl a Cl
?? e cml a cmq ?? e so this is the prime information
what it says you had a multiple data sample
like many example so this is this gives you
the information about the maximum occurrence
of the critical value from all the sample
data example if you see a plot if you see
that the cl a is estimated one it is close
to between 5 and 6. So let us say 5 and 5.
Occurrence of right value happened more than
around 50 times and the value also require
let us see the estimate of all the estimated
parameter values so how many times it occurs
it we can also get the added value the maxi
mum level of the value the which represents
at a point cl aerodynamic parameter are about
cl and cm wherever you see all the results
are here and now you should compare this with
your results which you have got earlier.
.
These are the test results they are getting
?? method estimation for longitude parameters
hansa3 aircraft like it okay. you see here
you have cl a clq cl ?? cmq and cl ?? e estimated
parameter and using this methods if you see
they are in the cl a 5172 a this aircraft
5.411 these kinds of methods so here you are
strong parameter are a cl a cm ?? and cl ?? e
so those two parameter are in 5 with shape
and you have done it from flight data.
Further this thing can be proved applied for
the testable data accuracy is ?? with performance
and I said there are two derivatives cl and
clq where not very much variable the nature
of the data may be you can design a better
input you have applied on the 3211 if you
want to get those dynamic then you should
capture the mode dynamic model and then you
eill be seeing manages in this derivative
and from there you can get better estimation.
So this was the idea of the to introduce with
the ?? method flight data and there are different
set of data you can do this algorithm and
you can look for the what has been prevented
here I think it should be good enough to understand
to that for a new flight data I talked about
the proceeds I have talked about how to design
this network and then from the network ?? method
estimate the parameter I can switch all for
this session you can practice more come up
with your ideas and methods comparing with
the results thank you so much.
