A Multi-sensor Embedded
Microcontroller System for Condition
Monitoring of RC Helicopters
Artit Jirapatnakul
B.S. Electrical Engineering, May 2005
Honors Thesis Research
System Capabilities
 Communicate with sensors
 IMU: Crossbow IMU400-CC
 GPS: Novatel Superstar II
 Compass: Honeywell HMR3100
 Data processing
 Reliable data transmission to computer
 Visualization in graphical interface
Sensors
 Crossbow IMU400CC
 Linear acceleration
along three orthogonal
axes
 Rotational rates along
three orthogonal axes
 Connected via RS232 at
38.4kbps
 Novatel Superstar II




Latitude and Longitude
Velocity
Altitude
Time and Date
 Connected via RS232 at
9.6kbps
 Honeywell HMR3100
 Measures heading
 Connected via RS232 at
9.6kbps
Sensors
Compass
IMU
GPS
Sensors mounted in plastic containment unit
Microcontrollers
 PIC18F8720
 16-bit RISC CPU
 Up to 10MIPS
 3840 bytes RAM
 dsPIC30F6014
 16-bit RISC CPU with
DSP
 Up to 30MIPS
 8192 bytes RAM
System Design
 Several processing boards are used
 Advantages
 Allows greater number of sensors to be used
 Boards can be located closer to sensors
 Distributed processing
 Disadvantages
 Slightly greater complexity
System Diagram using PIC18s
38.4kbps
IMU
57.6kbps
Slave PIC*
9.6kbps
57.6kbps
Compass
Master PIC
9.6kbps
* Can also be used with dsPIC instead
GPS
System Setup using dsPIC
Laptop for visualization
Sensor box
dsPIC development board
System setup with dsPIC and IMU connected to laptop
Results
 Sensor monitoring with PIC18
 Can PIC18 keep up with data rate of all three
sensors?
 Connected IMU, GPS, and Compass to two
PIC18 boards
 PIC18 boards decoded sensor packets and
multiplexed them
Results
Results
 Sensor monitoring with PIC18
 Communication with sensors successful
 PIC18 is able to process at data rates of sensors
 Graphical interface works correctly
Results
 dsPIC processing of IMU data
 Perform ten sample sliding window RMS
calculation in real-time
 Transmit unprocessed IMU data along with RMS
values for three linear accelerations
Results
Results
 Statistics calculations on PIC18
Ten sample sliding
window RMS
calculation by PIC18
compared to
calculations in
MATLAB
Results
 Statistics calculation on PIC18
Ten sample sliding
window skew
calculation
performed by PIC
as compared with
calculations in
MATLAB
Results
 Statistics calculation on PIC18
Ten sample sliding
window kurtosis
calculation on
PIC18 compared
to calculation in
MATLAB
Future Work
 Wireless connection between system and
computer
 Design and fabricate small PC boards for
system
 Testing with additional algorithms
 Actual flight testing
Multi-Sensor Fusion For Feature
Tracking and Prediction Using
Particle Filters
Cory Smith
M.S. Electrical Engineering, May 2005
Committee Members:
Dr. Kenneth Jenkins – Co-advisor
Dr. Amulya Garga – Co-advisor
Dr. David Hall – Committee Member
Presentation Outline
 Motivation and thesis focus
 Theory – Kalman and particle filtering, prediction,
remaining useful life (RUL) of mechanical systems
 Results – simulation data and mechanical fault data
collected by the Conditioned-Based Maintenance
department
 Decision-level fusion – theory and results
 Conclusions and further research topics
Motivation
 Tracking in real-world scenarios usually involves
systems with non-linear models and non-Gaussian
noise
 Kalman filter provides the optimal solution as long as
the system is linear with Gaussian noise
 Particle filter does not require Gaussian noise
distributions and works with both linear and nonlinear models
Focus of the Thesis
 Compare Kalman and particle filters with regard to
their ability to track and predict features using
simulated data and CBM mechanical fault data
 Estimate remaining useful life (RUL) of mechanical
systems
 Utilize decision-level data fusion techniques to
increase RUL accuracy
Kalman Filtering
Processing Steps (Gelb, 1974)
xˆ (k )  Φ k 1xˆ (k)1
Pk(  )  Φ k 1Pk(1)Φ k 1T  Q k 1
K k  Pk(  ) H k T R k  H k Pk(  ) H k T 
z k  H k xˆ (k )  v k
xˆ (k )  xˆ (k )  K k  z k  H k xˆ (k ) 
Pk( )  I  K k Hk  Pk( )
1
Predict
Forward
Compute
Kalman Gain
Receive
Measurement
Update
Prediction
Kalman Filtering
Models for Application
State Vector:
Transition Matrix:
Measurement Vector:
Process Noise Matrix:
 xk 
xˆ k   xk 
 xk 
1 

Φ k  0 1
0 0

Estimating
position, velocity
and acceleration
1
2
2

 
1 
1 
H k  0 
0 
 201  5

Q k   18  4
 16  3

4
1 3
3
1 2
2
1
8
Based on kinematics:
xk  xk 1  xk 1  12 xk 1 2
Only measuring
position
3
2
1 2


2
 w
 
1
6
Derivation may be
found in (BarShalom, 1993)
Particle Filter
Fundamentals
 Particle filters do not rely on any assumptions
regarding noise distributions or linear models
 Utilizes Monte Carlo (MC) Integration to
approximate the true density
 Choose an initial proposal density (Ex: Gaussian)
to get started, then use the prior distribution as the
proposal
 As the number of samples approaches infinity, the
proposal density approaches the true density
 The particle filter is more computationally
intensive than the Kalman filter
Particle Filter
Processing Flow (Ristic, 2004)
x (ki )(  ) ~ p (x k | x (ki)1(  ) )
Draw Samples from
Proposal Density
(Predict Forward)
xˆ (ki )(  )  Φ k xˆ (ki)1(  )  w k
Receive
Measurement
z k  h k (x k , v k )
  z  x(i )(  ) 2 
k
k

wk(i )  exp  


2R k


xˆ k 1  x(k ) wkT
new proposal  p(x k 1 | x
i ()
k
)
Compute Particle
Weights
Update
Proposal
Particle Filter
Graphical Representation (Doucet, 2001)
Initial Proposal
Density (Ex.
Gaussian)
~
x k( i ) {i  1,..., N }
Sample from Proposal
Density and Predict
Forward
True Underlying
Posterior Density
p( xk | zk )
Take measurement,
compute likelihoods,
and weight particles
accordingly. This
becomes the new
proposal density for
k+1.
xk( i ) {i  1,..., N }
Particle Filter
Degeneracy Phenomenon
 After a few iterations, all but one particle will contain
negligible weight. Solution: Resample (Ristic, 2004)
 Refine proposal density by sampling from the
particles with high weights and discarding those
with negligible weights.
 This will focus on “important” areas of the
distribution giving it more “definition” to resemble
the true underlying distribution
Particle Filter
Resampling (Ristic, 2004)
p( xk | zk )
Resample from
“important
areas” of the
estimated
density
New
normalized
particles for
k+1
~
xk(i )1 {i  1,..., N }
Prediction
 The Kalman and particle filters may be used to
estimate the state without any measurement updates
 The prediction relies only on the prediction equations
for each filter:
xˆ k  n  Φk  n xˆ k
x(ki) n  Φ k  n x(ki )(  )
(KF)
(PF)
T
Pk  n  Φk  n Pk Φk  n  Q k  n
xˆ  x(  ) wT
k n
k n
k
 The state transition and process noise matrices
become a function of the time interval since the last
measurement:
Φk n
1 n

 0 1
0 0

1
2
(n ) 2 

n 
1 
Qk n
 201 (n )5

  18 (n ) 4
 16 (n )3

(n ) 4
3
1
(
n

)
3
2
1
(
n

)
2
1
8
( n )3 
2
2
1
(
n

)

2
 v
 
1
6
Remaining Useful Life (RUL)
Feature Value
Predicted Track with
Confidence Intervals
Failure Threshold
Detection Threshold
Failure
Threshold
Crossing
Feature Track
RUL
Time
• RUL is the amount of time left before a
system reaches mechanical failure
Third-Order Simulation
Third-order simulation data
2
3
was generated using the model: f (t )  1  2t  5t  5t  
where  is zero-mean Gaussian noise ~ N(0,0.2)
Feature Plot
Tracking Error
3rd Order Simulation Data
3rd Order Simulation Tracking Results
Particle Filter, Proc. Noise = 0.9
Particle Filter, Proc. Noise = 0.09
Particle Filter, Proc. Noise = 0.009
Kalman Filter, Proc. Noise = 0.9
Kalman Filter, Proc. Noise = 0.09
Kalman Filter, Proc. Noise = 0.009
0.7
Absolute Error (Feature Value)
14
12
Feature Value
10
8
6
4
2
0
0
20
40
60
Time (Hrs.)
80
100
0.6
0.5
0.4
0.3
0.2
0.1
0
100
200
300
400 500 600 700
Number of Particles (N)
800
900
1000
Third-Order Simulation
Tracking Results
14
12
14
10
Feature Value
10
Feature Value
Actual Data
Kalman Filter Track, Proc. Noise = 0.009
12 Particle Filter Track (N=1000), Proc. Noise = 0.9
Actual trajectory
Kalman filter track, Proc. Noise = 0.009
Particle filter track (N=100) , Proc. Noise = 0.9
8
6
6
4
4
2
2
0
0
8
0
20
40
60
80
100
0
20
14
Actual Data
Kalman Filter Track, Proc. Noise = 0.009
Particle Filter Track (N=100), Proc. Noise = 0.009
12
14Actual
10
10
8
6
6
4
2
2
0
20
40
60
Time (Hrs.)
80
100
100
8
4
0
80
Data
Kalman Filter Track, Proc. Noise = 0.009
12Particle Filter Track (N=1000), Proc. Noise = 0.009
Feature Value
Feature Value
Time (Hrs.)
40
60
Time (Hrs.)
0
0
20
40
60
Time (Hrs.)
80
100
Particle Paths
Proc.
Noise
= 0.009
Particle
Paths,
Proc. Noise
= 0.009
12
12
10
10
8
8
6
6
Feature Value
Feature Value
Proc.
Noise
= 0.9
Particle
Paths,
Proc. Noise
= 0.9
4
2
0
4
2
0
-2
-2
-4
-4
-6
44
46
48
50
52
Time (Hrs.)
54
56
• With the high process
noise many particles
are discarded during
resampling
-6
44
46
48
50
52
Time (Hrs.)
54
• By lowering the
process noise, more
particles have
sufficient weight
56
Computational Comparison
• Kalman filter is O(2d3) dominated by the covariance update
• The computation time
for both filters was
computed using
cputime in Matlab
• Plot shows that
increasing the
number of particles
increases the
computational costs
as expected
Average Computation Time (seconds)
• Particle filter is O(Nd2) from individual particle propagation
(Gustafsson, 2002)
5
Particle Filter, Proc. Noise = 0.009
Kalman Filter, Proc. Noise = 0.009
4
3
2
1
0
100
200
300
400 500 600 700
Number of Particles (N)
800
900
1000
Simulation
Prediction Results
Time = 26
Time = 50
10
9
8
8
6
7
4
4
2
5
0
20
40
60
Time (Hrs.)
80
0
100
4
2
10
1
2
3
4
5
2
2
100
6
7
8
9
10
6
4
80
100
8
4
40
60
Time (Hrs.)
80
10
1
6
20
40
60
Time (Hrs.)
12
8
0
20
Time = 90
Feature Value
12
0
0
3
Time = 75
Feature Value
Measurements
10
Feature track
8
Feature prediction
95% Confidence
bounds
6
Failure threshold
6
2
0
12
Feature Value
10
Feature Value
12
0
0
20
40
60
Time (Hrs.)
80
100
H-60 Intermediate Gearbox (IGB)
3 Separate Seeded Fault Run to Failure Tests
EDM Notch Initiated at Input Pinion Tooth Root
(EDM: Electrical Discharge Machine)
2 Accelerometers (100kHz sampling)
Source: NAVAIR 4.4.2 Patuxent
River Naval Air Station
NAWCAD Helicopter Data
FM0
Feat.Avg.All.FM0
4.5
80
Raw Data
Smoothed Data
4
Actual RUL
Particle Filter Estimate (N=1000)
Particle Filter Lower 95% Conf. Interv.
Kalman Filter Estimate
Kalman Filter Lower 95% Conf. Interv.
70
3.5
50
RUL
Feature Value
60
3
40
30
2.5
20
2
10
1.5
0
10
20
30
40
50
Time
60
70
80
90
0
10
20
30
40
50
Time
60
70
80
NAWCAD Helicopter Data
SBlvl
Feat.Avg.All.SBlvl
0.35
70
Raw Data
Smoothed Data
0.3
60
50
0.2
RUL
Feature Value
0.25
40
0.15
30
0.1
20
0.05
10
0
0
10
20
30
40
50
Time
60
70
80
90
Actual RUL
Particle Filter Estimate (N=1000)
Particle Filter Lower 95% Conf. Interv.
Kalman Filter Estimate
Kalman Filter Lower 95% Conf. Interv.
0
10
20
30
40
50
Time
60
70
80
References








Bar-Shalom, Y., Li, X.-R., Estimation and Tracking: Principles, Techniques, and
Software, Boston, MA, Artech House, 1993.
Cleveland, W. S., “Robust Locally Weighted Regression and Smoothing
Scatterplots,” Journal of the American Statistical Association, Vol. 74, No. 368,Dec.
1979, pp. 829-836.
Doucet, A., Freitas, N., Gordon, N., Sequential Monte Carlo Methods in Practice,New
York, NY, Springer-Verlag, 2001.
Erdley, J., “Data Fusion for Improved Machinery Fault Classification,” M.S. Thesis in
Electrical Engineering, The Pennsylvania State University, University Park, PA, May.,
1997
Gelb, A., and technical staff of The Analytic Sciences Corportation, Applied Optimal
Estimation, The M.I.T. Press, Cambridge, Massachusetts, and London,
England,1974.
Gustafsson, F., Gunnarsson, F., Bergman, N., Forssell, U., Jansson, J., Karlsson, R.,
and Nordlund, P.-J., “Particle Filters for Position, Navigation, and Tracking,” IEEE
Transactions on Signal Processing, Vol. 50, No. 2, Feb. 2002, pp. 425-237.
McClintic, K. T., “Feature Prediction and Tracking for Monitoring the Condition of
Complex Mechanical Systems,” M.S. Thesis in Acoustics, The Pennsylvania State
University, University Park, PA, Dec., 1998
Ristic, B., Arulampalam, S., Gordon, N., Beyond the Kalman Filter, Boston, MA,
Artech House, 2004.
Third-Order Simulation
Particle Distributions
Time =at50
Particle Distributions
TimeHrs.
= 50
0.05
= 0.009
N=100,
Proc.
Noise
= 0.9 0.015N=100,
N = 100,
Proc. Noise
= 0.9
N = 100,Proc.
Proc. Noise Noise
= 0.009
Weight
Weight
0.04
0.03
0.02
0.01
0.005
0.01
0
2
4
6
0
8
N = 500,
Proc. NoiseNoise
= 0.9
N=500,
Proc.
= 0.9
0.01
0.005
0
0
0
2
4
6
8
-3
1
0
2
4
6
8
2
4
6
8
Proc. Noise = 0.009
N=1000,
Proc. Noise = 0.9 N=1000,
x 10
N = 1000, Proc. Noise = 0.009
N = 1000, Proc. Noise = 0.9
-3
x 10
1.5
1
Weight
Weight
6
x 10
N=500,
Proc.
Noise
= 0.009
N = 500,
Proc. Noise
= 0.009
0
8
4
2
0
4
3
-3
6
2
2
Weight
Weight
0.015
0
0
2
4
Feature Value
6
8
0.5
0
0
Feature Value