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.