Suitability of Artificial Neural Network for MEMS

Transcription

sciences & technologies
Introduction
Problem Specification and CFD Model
Predicting the Flow using an Artificial Neural Network
Optimizing the Flow
Conclusion
Suitability of Artificial Neural Network for
MEMS-based Flow Control
J.-F. C OUCHOT, K. D ESCHINKEL, and M. S ALOMON
FEMTO-ST Institute
University of Franche-Comté, France
dMEMS 2012. April 2nd-3rd, Besançon, France
Neural Network for MEMS-based Flow Control
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Introduction
Optimizing the Flow
Conclusion
Outline
1
Introduction
2
3
4
Optimizing the Flow
5
Conclusion
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Introduction
Optimizing the Flow
Conclusion
Active control of turbulent flows
Objective
Improve the aerodynamic performance of moving objects
Various potential benefits
Better maneuverability
Increasing the range or payload capability
Environmental compliance
A solution for performing active fluid control: sets of distributed MEMS
MEMS actuators are adjusted to control the flow
MEMS sensors may provide information on the real evolution of the flow
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Introduction
Optimizing the Flow
Conclusion
Application of MEMS for active flow control - Vehicle
2005 Citroen C-SportLounge Concept Car
Virtual airfoil on the tail using 40 MEMS actuators producing pulsed microjets
Improve the vehicle’s drag and stability at high speeds
e
free
g
ima
N
on
fre
N
ei
on
m
ag
fre
e
ei
m
ag
e
Non
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Introduction
Optimizing the Flow
Conclusion
Application of MEMS for active flow control - Aircraft
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Introduction
Optimizing the Flow
Conclusion
MEMS-based flow control is a scientific challenge
A closed-loop flow control system requires
A model that captures the actuation effects
A controller
Fluid models are described by Navier-Stokes equations
Highly nonlinear
CFD tools cannot solve them in real-time
Prohibitive computation time
Changing inflow velocity
A nonlinear model that can predict the forced flow in real-time is needed
Our objectives
1
Study the suitability of a neural network to model the process
2
Provide a relevant strategy to control the MEMS
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Introduction
Optimizing the Flow
Conclusion
Outline
1
Introduction
2
3
4
Optimizing the Flow
5
Conclusion
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Introduction
Optimizing the Flow
Conclusion
Simplified vehicle model: a backward facing step
Simplified ground vehicle geometry
Backward facing step (FEMTO-ST simulation)
Ahmed body
k − ω model
Fluent
v = 40 m.s−1
v = 40 m.s−1
height h = 288 mm
Re = 747000
k − RNG model
height h = 288 mm
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Introduction
Optimizing the Flow
Conclusion
Computational fluid dynamics model - Geometry
H
h
y
0 x
l
Backward facing step characteristics
t
L
Flow characteristics
height h = 0.288 m
upstream section H = 0.712 m
length l = 0.5 m
downstream section L = 2.5 m
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Introduction
Optimizing the Flow
Conclusion
Computational fluid dynamics model - Setup
5 microjet actuators located on the step
near the corner, 10, 30, 50, and 70 mm away
Microjet velocity
discrete value in {0, 33, 66, 99} m.s−1
Uniform velocity profile at inlet
inflow velocity in {30, 35, 40} m.s−1
Outlet outflow boundary conditions
19.5 mm
9.5 mm
Microjet actuators
Wall functions at the bottom wall
Computation with FLUENT CFD code
150,000 cells
5 minutes on a regular Linux Workstation
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Introduction
Optimizing the Flow
Conclusion
Objectives
Focus on pressure data on the back face
244 measure points are aggregated into a singular force f
Objective 1 - Model
Predict the force f (C, v ) for
any inflow velocity v in [30, 40]
any configuration C of actuators in {0, 33, 66, 99}5
Find a nonlinear mapping between
inputs defining the current inflow and an actuation configuration
an output describing the flow evolution
Objective 2 - Control
Control the actuators to maximize the force f (C, v ) when the inflow velocity varies
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Introduction
Optimizing the Flow
Conclusion
Outline
1
Introduction
2
3
4
Optimizing the Flow
5
Conclusion
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Introduction
Optimizing the Flow
Conclusion
Overview
Why choosing a neural network?
Successful modeling of complex relationships between data inputs and outputs
Can model linear and nonlinear systems, static and dynamic ones
Universal approximator for nonlinear systems
Analogy with biological neural networks
A set of interconnected neurons processes the inputs
A training process iteratively adapts the neurons parameters to the data
Multilayer feedforward networks
Can approximate any nonlinear function to any arbitrary precision
MultiLayer Perceptron network
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Introduction
Optimizing the Flow
Conclusion
Multilayer perceptron
Hidden layer
x1
Input
vector
x1
Output
layer
Output
vector
−1
x2
w 1j
w 2j
bias
n
ϕj
...
bias
x 0 −1
w 0j
i=0
w ij x i
y
j
−1
xn
x2
w nj
y1
−1
Supervised training using FLUENT results
−1
x3
−1
y2
Mean square criterion
⇒ reflects the prediction mismatch
Training algorithm
⇒ minimizes the criterion
x4
−1
How many hidden neurons
and which training algorithm ?
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Introduction
Optimizing the Flow
Conclusion
Network topology and implementation
Network features
3rd order HPU network ⇒ better approximation of functions with sharp variations
Single hidden layer
Number of neurons found by trial and error process
Sigmoidal activation
Output layer
Number of neurons specified by the problem
Linear activation
Training process
L-BFGS quasi-Newton algorithm with Wolfe linear search
Holdout validation to avoid overfitting
⇒ dataset split in training, validation and test subsets
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Introduction
Optimizing the Flow
Conclusion
Training setup
Global dataset of 3072 samples obtained with FLUENT simulations
3 inflow and 4 microjet velocities → 3 × 45 = 3072 samples
Dataset randomly partitionned in
training subset ≈ 65% of the samples
validation subset ≈ 10% of the samples
test subset ≈ 25% of the samples
Network topology
6 initial inputs = (C, v ) → 83 ones with HPU
1 output = f (C, v )
Hidden layer of 15, 20, 25, and 30 neurons
Control of the training process
500, 750, and 1000 training epochs
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Introduction
Optimizing the Flow
Conclusion
Prediction results
Performances of the different networks - Test subset of 769 data samples
Average on 20 trainings
Random subsets and initial network parameters
Topology
Hidden neurons
15
20
25
30
6 initial/83 HPU inputs and 1 output
Epochs
% CVRMSE
R2
500
10.26
0.9475
750
10.21
0.9480
1000
10.23
0.9477
500
10.20
0.9481
750
10.14
0.9487
1000
10.15
0.9486
500
10.31
0.9469
750
10.28
0.9473
1000
10.26
0.9475
500
10.25
0.9476
750
10.20
0.9480
1000
10.20
0.9481
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Introduction
Optimizing the Flow
Conclusion
Prediction results
Observation
Prediction
20
Resulting force f
0
-20
-40
-60
-80
0
100
200
300
400
500
Test data samples indexes
600
700
800
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Introduction
Optimizing the Flow
Conclusion
Prediction results
Observation
Prediction
20
Resulting force f
0
-20
-40
-60
-80
500
550
600
Test data samples indexes
650
700
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Introduction
Optimizing the Flow
Conclusion
Outline
1
Introduction
2
3
4
Optimizing the Flow
5
Conclusion
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Introduction
Optimizing the Flow
Conclusion
Controller - Objective
Hypotheses
Continuously varying inflow velocity v
Changing configuration C is time consuming
Objective
Real-time maximization of the back face step force f (C, v )
by modification of the actuators
Definition (Optimal configuration)
The optimal configuration C ∗ (v ) maximizes the force f (_, v ):
C ∗ (v ) =
f ((c0 , . . . , c4 ), v )
argmax
(c0 ,...,c4 )∈{0,33,66,99}5
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Introduction
Optimizing the Flow
Conclusion
Controller - Local optimal configuration
Global optimization is not suited
Ideally, instantaneously change the current configuration to C ∗ (v ).
Takes time δt practically
Inflow velocity at time t + δt: v 0 6= v → C ∗ (v 0 ) 6= C ∗ (v )
Optimization using a neighborhood structure
Search the “best” configuration in the neighborhood of C
Neighborhood set N(C) = {C 0 = (c00 , . . . , c40 ) | |cj0 − cj | ≤ 33 and 0 ≤ j ≤ 4}
For each pair (C, v ) the local optimal configuration is C̃(v ) = argmax f (C 0 , v )
C 0 ∈N(C)
Greedy algorithm to find C̃(v )
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Introduction
Optimizing the Flow
Conclusion
Validating the approach - Protocol
Scenario
Random initial configuration C0
Random sequence of inflow velocities vi [30, 40] s.t. −kd < vi+1 − vi < ka
Comparison
cumulative optimized force
σ=
i=n−1
X
f (C̃(vi−1 ), vi )
i=1
cumulative force obtained with the static configuration C0
σ̄ =
i=n−1
X
f (C0 , vi )
i=1
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Introduction
Optimizing the Flow
Conclusion
Validating the approach - Experiments
Setup
ka = 2.5m.s−1 and kd = 5m.s−1
20 random scenarios with each time a sequence of 10 velocities
Experimental observations
Optimized forces ⇒ always positive
σ = 118 N in average
Without optimization ⇒ always negative
σ̄ = −475 N in average
Average improvement of almost 125%
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Introduction
Optimizing the Flow
Conclusion
Outline
1
Introduction
2
3
4
Optimizing the Flow
5
Conclusion
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Introduction
Optimizing the Flow
Conclusion
Conclusion
Summary
A neural network can provide suitable predictions in a simplified case
Only 5 actuators
Relevance of active flow control
The proposed control strategy improves the aerodynamic performances
Future works
Neural network design
Incremental training
Online training using information from sensors
Control strategy
Scalability of the method
Distributed approach
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Introduction
Optimizing the Flow
Conclusion
Thank you for your attention
Questions?
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Suitability of Artificial Neural Network for MEMS

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