# Rodney M. Goodman
B.Sc., Ph.D., C.Eng., SMIEEE, FIEE.
## The Silicon Active Skin Research
The
active skin is also a multi-disciplinary project, involving researchers
in the fields of MEMS, Fluid Dynamics, Control Theory, and Electronics.
The objective of the project is to integrate MEMS sensors and actuators,
neural network sensory processing, and control circuits all on the
same silicon substrate to form a “smart skin”, capable
of reducing drag on an aircraft wing. In nature, such a system of
actuators controlled by biological neural networks is believed to
exist in the shark. The drag reduction implemented by this “smart
skin” contributes to the high speed of the shark, which is
the fastest creature in the ocean.
**Title: Active Drag Reduction using Neural Networks **
**Authors: **Vincent Koosh, Dave
Babcock, Rodney Goodman, Tom Tsao, Fukang Jiang, X.Q. Wang, Y.C.
Tai, J.
Kim ,C.M. Ho
**Abstract: **In turbulent boundary layers, the near-wall
high-speed streaks are responsible for producing high skin-friction.
Controlling the skin friction of a wall bounded layer is one of
the grand challenges in fluid mechanics research because the near-wall
structures have length scales of hundreds of microns and are randomly
distributed in the flow. Emerging MEMS technology is capable of
producing transducers and actuators matching the length scales of
the streaks and modern analog VLSI techniques are able to match
the time scales. This makes drag reduction by actively controlling
the near-wall structures feasible. Since the best control laws for
such drag reduction are unknown, neural networks are used to find
control laws. The entire system including sensors, control circuits
and actuators is to be integrated onto a single die to achieve the
desired reduction.
**Motivation and Aims:**
Techniques for reducing the surface drag on modern
transportation devices such as planes or high speed trains are highly
sought after. Even drag reduction on the order of 5% could lead
to enormous savings in fuel costs. Until recently, only passive
techniques, such as riblets, were available for such purpose. Recent
technological advances in circuit and MEMS techniques and greater
understanding of the problem allows active techniques which monitor
the flow and actively deform the skin based on flow conditions to
be pursued. We seek to build a fully integrated neural-networked
MEMS system to distributedly sense the shear stress, to design neural
controller with feedback mechanism, and to efficiently actuate robust
micro actuators for surface stress reduction.
**Research:**
Micro Surface Shear Stress
Sensor: A device capable of detecting fluctuating surface
shear stress is essential for the control of wall shear stress experiment.
However, the heat transfer to the substrate has always been a handicap
of the conventional hot-film type surface shear stress sensors for
several decades. For measurements in air, the sensitivity is close
to zero because of the low heat capacity of air. By using surface
micromachining technology, a vacuum chamber is placed under the
heating element. This cavity significantly decreases the heat loss
to the substrate (Liu et al., 1994, Huang et al 1995 & 1996).
The typical sensitivity of the sensor with a cavity underneath is
15 mV/Pa, which is about one order of magnitude higher than that
without a cavity.
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(a)
a single micro shear-stress sensor
In a turbulent boundary layer, the high speed streaks
are distributed in a two-dimensional domain. A sensor array containing
a large number of sensors is needed for mapping the skin-friction
distribution. A surface shear-stress imaging chip was developed
for this purpose (Jiang et al 1996). Each imaging chip consists
of 85 micro sensors. On the chip, the sensors are arranged into
multiple arrays, and the spacing between consecutive sensors is
designed to provide adequate spatial resolution in measuring the
near-wall streamwise streaks.
(b)
a sensor array
Micro Actuator: In flow
control problems, we need actuators which are able to provide about
one mm off-plane motion and about milli-Newton force per mm 2 for
sustaining the wind loading. These requirements were several orders
of magnitude higher than that available from existing micro actuators.
In order to accomplish these stringent performances, a flap type
actuator was chosen for the design (Liu et al 1995). electromagnetic
force was chosen to drive the actuator. Both surface micromachined
and bulk micromachined actuators have been developed.
Interaction between Actuator
and Streamwise Vortices: How the motion of the streamwise
vortices affected by the actuator and eventually achieving skin-friction
reduction is a key issue for interactive wall flow control. Experiments
have been carried out to investigate the interaction between a single
high shear-stress streak and a micromachined actuator. Experiments
are performed for different combinations of actuator frequency (w)
and maximum tip height (d). As expected, the non-linear interaction
between a moving surface and a vortex is complex. On the other hand,
skin-friction reduction can be achieved if the actuation is properly
applied. The reduction is a function of the product of w and d.
Since the product of w and d is a measurement of the transverse
velocity of the actuator flap, this result indicates that the amount
of shear stress reduction is directly related to the transport of
high-speed fluid away from the surface by the vertical motion actuator.
Variation of the shear stress coefficient, C _{DN}
, with actuator frequency, w, and maximum actuator tip height, d.
The solid O markers correspond to an w*d of 80 and the solid square
markers correspond to an w*d of 100.
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**Numerical Experiments of Neural Network
Based Control**
Lee, Kim, Babcock, and Goodman (1996) developed an adaptive controller
based on a neural network. A two layer shared weight neural network
consisting of hyperbolic tangent non-linear hidden units and linear
output units to predict similar actuation using only surface measurable
quantities, i.e. surface shear stresses, was developed. Training
off-line with data from the near-wall controlled experiments, the
neural network extracted a pattern that predicts the local actuation
to be proportional to the spanwise derivative of the spanwise shear
stress in the surrounding region. The same network was then applied
at each grid point in the input (surface spanwise shear stress)
array to generate the corresponding output (actuation) array.
This neural controller was applied in an on-line
adaptive inverse model scheme, with the desired inputs being a fractional
reduction of the local surface shear stress from the previous time
step and the outputs being the necessary actuation to achieve this
reduction. We observed that the relative magnitudes of the weights
did not change (indicating the approximate derivative pattern is
preserved) but that the absolute magnitudes fluctuated during the
course of the simulation. Therefore the input weights were fixed
to compute an approximation to the derivative leaving only a gain
and bias for each layer to adapt as the simulation progresses.
Applying this control network and employing blowing
and suction at the wall based only on the wall-shear stresses in
the spanwise direction, was shown to reduce the skin friction by
as much as 20% in direct numerical simulations of a low-Reynolds
number turbulent channel flow . Also, a stable pattern was observed
in the distribution of weights associated with the neural network.
This allowed them to derive a simple control scheme that produced
the same amount of drag reduction. This simple control scheme generates
optimum wall blowing and suction proportional to a local sum of
the wall-shear stress in the spanwise direction. The distribution
of corresponding weights is simple and localized, thus making real
implementation relatively easy.
Numerical experiment of skin friction reduction
Although the work by Lee et al. (1996) is a significant
improvement over earlier approaches that require velocity information
within the flow, there are a number technical issues before such
a control scheme can be implemented in real practice. Among other
things, precise control of blowing and suction distributed over
a surface in a laboratory test is still too difficult to implement.
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**Analog VLSI Circuits **
The previous work on the application of neural
networks to turbulence control of drag reduction showed that a neural
network could be trained to reduce drag. The network that was trained
was a standard two-layer feedforward network with inputs of du/dy
and dw/dy. However, during the training it was discovered that only
the dw/dy inputs impacted network performance. The function implemented
by the network is,
where *j* and *k* denote the numerical
grid point in the streamwise and spanwise directions. During the
training of the network it was discovered that the weight values
settled and then remained constant relative to each other but with
the same scale factor applied for each. The weight pattern was found
to be given by
.
The meaning of this weight pattern was discovered
to be that the network implemented a scaled spanwise derivative
of dw/dy. Thus it was possible to implement a new network as
.
Where an input template size of 7 is chosen. Training
of this network showed that *W*_{c} and *W*_{d}
were negligible, and that *W*_{a} and *W*_{b}
varied significantly but their product remained relatively
constant. It was further discovered that a linear network produced
similar results to the nonlinear one, but the standard deviation
of the learned weights was worse than with the nonlinear network.
For the linear network it was seen that the same
weight pattern could be used, and that the constant scale factor
could be chosen such that the root-mean-squared value of the actuation
was kept at 0.15 *u*_{t} . Thus,
for a single row of actuators, and K is determined
by the parameters of the flow.
In hardware, we will implement a single row of
dw/dy sensors that trigger a single row of actuators. Thus the circuits
used to control the actuations must be able to perform the aforementioned
computations.
The dw/dy sensors come from constant temperature
circuits that place them in a Wheatstone bridge configuration. The
output is a voltage related to dw/dy. The first thing that must
be accomplished is the summing and weighting of these voltages.
The following circuit is used for this purpose.
The output of this circuit is given by
, and
Thus, the weight pattern can be implemented by
choosing the capacitor ratios to match the equation for *W*_{j}
given above. Furthermore, the constant k/U_{t} can be varied
from a value of about 20 to about 40. This serves to act as the
variable gain stage that implements the gain *W*_{b}
within the tanh function.
One benefit of the weight pattern is that for
an input template of size 7, only 4 sensors are actually needed
since the even weights are zero and nullify those sensors.
To implement the linear function instead of the
tanh, we can simply increase *C*_{T} to reduce the
inputs until we are in the linear portion of the tanh, then we can
provide gain afterwards.
The rest of the signal processing is done in current
mode since the previous stage, which does weight multiplication
and summing, outputs a current. Both the nonlinear network and the
linear one require the output of the weighting and summing network
to be scaled and normalized by the rms value of the other sensor
arrays.
The building blocks of the rms circuit are shown
below.
These building blocks are placed together to provide
the rms normalization and scaling circuit given below.
The above circuit performs the necessary normalization.
We can also actively control the *I*_{C} input to
act as the external gain *W*_{a} which is required
by our functions.
These circuits form the core of the signal processing
circuitry necessary to implement the neural networks that have only
previously been implemented in software.
Other circuits which are not shown are required
for impedance matching between the stages, but they do not contribute
to the mathematical function implementation.
The final stage of processing is a current amplification
stage which amplifies the currents from the small levels which are
used for the analog signal processing to the larger current levels
necessary to drive the actuators. This is a fixed gain stage for
all signal currents to the actuators.
These circuits are all analog and perform the
computations required in real-time. The nonlinear network requires
actively controlling two inputs, while the linear network only requires
setting *I*_{C} for the flow conditions, and the
normalization circuitry provides the rest of the signal gain adjustment.
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**Achievements:**
M^{3} System for
Shear Stress Reduction:To integrate microsensors, microelectronics
and microactuators on a chip is possible, yet is not a trivial task.
We have fabricated an *M*^{3} system for shear stress
reduction. On this 1 cm by 1 cm die, 18 micro shear stress sensors,
3 micro flap actuators as well as circuits for logic, sensor driver
and actuator drivers are monolithically integrated. It is not fully
functional yet, but experience gained through this exercise is extremely
valuable for us to proceed toward a working system.
An *M*^{3} System for Shear Stress
Reduction
**Publications**:
Gupta, B., Goodman, R., Jiang, F., Tai, Y.C., Tung, S., Ho, C.M.,"Analog
VLSI For Active Drag Reduction", IEEE Micro, Vol. 16, No..
5, pp 53-59, 1996.
D. Babcock, C. Lee, B. Gupta, J. Kim, R. Goodman. "Active Drag
Reduction Using Neural Networks," In the Proceedings of International
Workshop on Neural Networks for Identification, Control, Robotics,
and Signal/Image Processing, Venice, Italy, August 1996.
Jiang, F., Tai, Y.C., Gupta, B., Goodman, R., Tung, S., Huang J.,
and Ho, C.M., "A Surface-Micromachined Shear-stress Imager,*
" Proceedings, IEEE Micro Electro mechanical Systems Meeting*
, pp. 110- 115, San Diego, California, Feb. 1996.
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