Apresentação - Cilamce 2020

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PRESENTATION OF CILAMCE - 2020
		 Venicio Silva Araujo 
Slide 1 -
Good morning, my name is Venicio, I am graduating student of mechanical engineering from the federal university of Mato Grosso, and in this work, I’m going to present Shunt Control On Cantilever Beam By Neural Network, an objective function approach. The central idea of this work is using a neural network to define parameters of Resistance and Inductance for an electronic circuit, associated to a Piezoelectric ceramic, has intention to provide damping for a fixed beam structure. In the end, we’ll present a comparison between this technique, and an evolutionary one, focusing on time’s executions and the usage of the objective function.
Slide 2 -
The presentation proceedings these are. I’m going by the first talk over the adopted structure, where we have the structure used, the dimensions, the material, and all, following to the transference functions of the structure and system as one. The concept of Shunt Control, follows, where I’ll explain the way we do the damping in this work, and in the end we have the usage of Neural Techniques to get our parameters of Resistance and Inductance, and their respective results in a computational demand comparison, as was said, and the damping efficiency.
Slide 3 - 4 
The structure dimension these are, to this work we use a cantilever beam, made of aluminum, coupled to a Piezoelectric Layer in a piezo-beam configuration. The Piezo-layer it’s a PZT-5H material that when its get deformed changes its internal structure, producing electricity, that can be used for structural damping.
 Associated with the piezo-layer, we have an R-L electronic circuit, whose parameters establish control over this damping. This work looks for define these parameters.
Slide 5 - 6
The beam was modeled by a software with finite element technique implemented, were used 50 elements at all to produce the beam, and the associated circuit has parameters set off to adapt its energy dissipation only for the first natural mode of the beam.
Slide 7 – 9
Following to the equations, we have, at first the movement equation. For the study of the structure was adopted the classic beam model, in this case was considered only presence of deflection, discarding shear, thus we can use the Bernoulli theory to develop the equation of movement for the structure. In first line on this equation, we have the mechanical parameters and in the second the Electrical, the bound between them is made on the stiffness matrix.
The second equation is the transference equation of the system, used to evaluate the mobility frequency response of the structure, and for this work we have two particular cases for analysis. The open and short circuit, with resistance equals infinity and zero respectively.
For these particular cases we have the equations 3 and 4.
The last equation is the objective function of this work. It was developed using the Standard Optimal LQR to a single input and output case, used to minimize vibration at one specific location on the beam, so the objective of the function is be minimized.
Slide 10 - 
Let’s now follow to the concept of shunt control that is the way we do damping in this work. The main idea of this concept, comes from the principle of energy conservation that establish that the total quantity of energy in an isolated system remains the same, so in a circumstance of external excitation, if the piezo layer has its parameters adapted to convert this received energy to an electrical form, there’s nothing last to be convert on movement.
So this is what we’re doing. The first image is the natural frequency response for the beam, with the piezo with resistance equals zero and infinite, for the two green and blue line, that is the same of assume the system doesn’t work at all, in the red line we have the frequency response with the piezo configured with an R and L provided by an analytical calculus, whose equations I’ll show a little later. These images shows the dependency of R and L parameters for the vibration response of the system, the technique used in this work search for get a better damping than the provided by the analytical calculation. 
Slide 11 -
This way, to provide the correct R and L, we use a neural network technique, so now let’s follow to Artificial Neural Network
Slide 12 - 13
The artificial neural network is a computational technique based on the principal of animal thinking that is learning by experience. Exemplifying, let’s think, if a throw something to you, in a certain way you will, probably, be able to catch in less than a second, but you could even take minutes to calculate the right position of your hand and its angle necessary to catch anything, but even though you caught that, cause you learned years before caught, not by calculus, but by practice. The artificial neural network tries to reproduce that.
In this Image, we have a general view of how an artificial Neural Network works; we have an input layer, that’s the layer responsible for translate the proposed problem for the algorithm. The first and second hidden layer, responsible for seeking connections between the received information, and the output layer, that’s the layer that present the results for the proposed problem. 
Slide 14 – 
To produce the individuals for training we use the equations that comes from the analytical method we talked previously, and these equations these are. It comes from the deduction of Dynamic Damping for Den Hartog to a system of two degrees of freedom, assuming mechanical inertia, such as Resistance, and Mechanical damping as Inductance. With these values, we used a normal distribution to randomize this data and creates a population of resistance and inductance parameters, our training set, that produces different FRFs once coupled to the system. In the training step, we search for combination that provides minor amplitude response for the structure. 
Slide 15 – 
So that’s what we do. At first, we get these optimal values, from the analytical calculation and randomize these, with a normal distribution, to produce our training set, setting the parameters of resistance and inductance as target data. We produce the FRF for the systems, with theses values, and give to the code, these answers associated with the respective RL configuration that produced each one. In training step, the algorithm seeks for the connections between these parameters. Once it understands the dependency of system and the resistance and inductance parameters and the FRF, we asked for the configuration of R and L that provides the minor amplitude answer for the structure. 
Slide 16 – 
So we have, the normal distribution to data random. R and L parameters set as target data, and the FRF as input data.
Slide 17 – 
Here’s a look of our histograms for our training set, such for resistance and inductance, produced by the normal distribution.
Slide 18 – 
And here’s the parameters used on our normal distribution. Having such mean as standard deviation based on optimal values of the analytical calculation, having a hundred percent of variation over these values. Producing a thousand individuals for training.
Slide 19 - 
And finally, the responses for neural network are here. We’ve got in first image 10 example answers plotted on that of frequency responses with configuration of R and L suggested by the neural network, both for the same structural parameters of the beam, where we see a great damping comparing to the open and short states in black line. We also see, in the second image where we have two vibrations mode for the beam plotted, that the configurations for resistance and inductance parameters only effects the first vibration of the beam as we arbitrate.
Slide 20 - 
Here’s a better look for the answers of the neural network, showing us a damping superior than 20dB for the answers.
Slide 21 – 
In order to do some comparisons, we set up a genetic algorithm, centered on the same optimal values were used to train our neural network, alsoworking in the same population of a thousand individuals. We set this algorithm to solve the same optimization problem for the beam structure and these are the FRF produced by the configuration of R and L parameters suggested by the genetic algorithm.
Slide 22 –
Here’s a better look to the behave of ten experimental tests of the configurations provided by the genetic algorithm
Slide 23 – 
Here’s the general behavior for the experimental tests of the Neural Network
Slide 24 –
And here’s the behavior for the Genetic Algorithm’s answers.
Slide 25 –
Plotting that together we can see that both provides damping superior than 20dB, very close behave and zero interactions with another vibration modes. 
Slide 26 – 
Although close in behave, these techniques demonstrate large difference in computational demands. It is seen when we compare the time for the execution for the genetic algorithm, that takes almost 2 thousand seconds to provide an answers while artificial neural network barely takes a minute.
The same discrepancy it’s seen to the number of usages of the objective function of the system, or the number of interactions demanded. Where genetic algorithm demands 61 thousand of interactions, while ANN takes only a thousand.
Slide 27 – 
Here’s a better look for the range of interactions for ten experimental tests.
Slide 28 – 
Here’s a look for the range of time.
Slide 29 – 
So for conclusion… Ler o slide
Slide 30 – 
As future works, we think… Ler o slide
Slide 31 – 
Thank u