2nd meeting on ”Analysis of dynamic measurements”,
NPL London 18/11, 2008
Analysis and synthesis of speed limiting
Road Humps
Jan Peter Hessling
SP Technical Research Institute of Sweden,
Measurement Technology
P.Y. Zhu, Hunan Provincial Key Lab. of Health Maintenance for Mechanical
Equipment, Hunan Univ. of Science and Techn., Xiangtan, China
Mrigank Gupta, Indian Institute of Technology, Kanpur, India
1
Road bumps/humps for speed reduction
Patent:
(Engwall, Bertil. Device to prevent vehicles from passing a
temporarily speed-reduced part of a road with high speed.
United States Patent 4135839, 1979.)
’Solution’ used worldwide !!!
(Sweden, Great Britain, USA, China, India…)
Positive
• Speed reduction / efficiency
– Feel in stomach?
– Visual impact / disorientation?
– Risk of car damage?
Negative
• Risk of injury
– Spinal cord
• Reduced comfort at allowed speed
• Low efficiency
– Poor threshold effect
– ’Negative’ threshold
(Increased comfort at high speed!!!)
2
Often poor design of road humps!
”…the bus driver was exposed to some 1.6 MPa over the flat top
bumps at X, which is about 170% more than the 0.6 MPa achieved
over the flat tops at Y. …indicates that
the status of current speed humps is so poorly standardized
(design, construction,… tear and wear…), that each bump
should be regarded as an individual…*”
”…the maximum acceleration at the driver’s seat in the city bus
running at allowed speed was up to 1g when some humps were
passed…**”
Complaints common => public interest of our method
(JPH Sweden: two newspapers, one radio and one TV-station)
* Granlund J., Brandt A., “Bus Drivers’ Exposure To Mechanical Shocks Due To Speed Bumps”,
26th International Modal Analysis Conference (IMAC XXVI), Orlando, Florida, USA, Feb. 2008.
** Measurements in the city of Borås, Sweden 2008 by the health consultant Grönesjö L.
for the local bus company.
3
Design of road humps
Profile of hump matters!
ƒ Height (~5-10 cm) only scales the (dis-)comfort!
(linear response)
Changing the height is not a solution for poor design!
ƒ Variation of comfort with speed set by profile.
Profile Ù operating principle / efficiency / threshold effect
Established methods of evaluation – new and existing humps
ƒ Widely accepted quantitative analysis: None
ƒ Measurements, difficulties
¾ Many many combinations of vehicles, speed and humps
¾ Not practical method for optimizing profile
4
Design of road humps
Properties
• Efficiency / threshold
- Change in comfort with speed
• Risk of injury
Existing road hump
Analysis
Synthesis
Optimal road hump
0.1
0.09
Optima l roa d profile (m)
Less precise!
• Broad spectrum of vehicles
(Cars, buses, new/old etc.)
• Optimal hump for just one typical vehicle
• Uncertainty ‘irrelevant’
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
5
10
15
20
Dis ta nce (m)
25
30
5
35
Model of vehicle (car / bus)
Output 1:
Translation
car body
Output 2:
Rotation
car body
’Measurement system’
Input 1:
Front wheel
coordinate
Input 2:
Rear wheel
coordinate
Tools of dynamic [measurement]
systems
LTI (linear time-invariant)
MIMO (multiple input multiple output):
•
•
•
•
•
•
•
•
•
•
Dynamic Calibration /
Characterization
System Identification
Differential / difference equation
Transfer function / Frequency
response function
Impulse response
Auto- / cross- correlation
Signal processing
Digital filtering
Poles / zeros
Etc.
Road Hump
• Variable velocity
• Designed geometric profile
⇒ Transient pulse signal of variable
bandwidth and regularity
(different shapes)
6
Dynamic equations of motion – Vibration analysis
Newton’s force-law
∑
f kn = mk ∂ t2 xk ,
n
∑
n
µ kn
Λ
= ρ 2 mB ∂ t2 (Λθ )
al1F −a l1R
 −l1F −l1R
For convenience

2
2
 al1F −a l1R −a l1F +a l1R
T
• Topology
L = L = {K , C} = 
(a = 1 − a )
•
State-space variables
Dynamic matrix equation



( y1
yk +d
− al1F
a l1R
l1F
l1R
y2
y3
y4 ) ≡
(w
Λθ
l1F
− al1F
−l1F −l 2 F
0
x1F
x1R )
≡ ∂ t yk , k = 1,2,3,4
x 
1 0 
 0 1

 ∂ t y = 
 y + E  2 F 
ˆ
0 M 
K C
 x2 R 
Mˆ
= diag(M ρΛ m F m R ) ,
T
E
Solution (La-place transf.)
Y (s )
~
E (s )
D
l1R 

a l1R 
0 

−l1R −l 2 R 
0 
 0 L 0 ϕ2F

= 
L
ϕ
0
0
0
2R 

 1 
−1 ~
= [s − D ] E (s )  − sΛ   X 2 F (s )
 e v  


T
0

 0 L Φ 2 F (s ) m F

= 
(
)
0
L
0
Φ
s
m
2R
R

1 
 0

=  ˆ −1
ˆ −1C 
M
K
M


(Φ n ≡ k n + scn )
7
Transfer function vehicle (measurement system)
’Direct’ transfer function,
road profile to car body translation and rotation
1


 HW 
−1 ~

(s ) = P[s − D ] E (s ) exp − sΛ  



 Hθ 
 v 

P
1 0 0 L 0

= 
0 1 0 L 0
Propagation:
• Input road profile – time delay front/rear
• Road profile => force, state space
• Through vehicle – dynamic matrix
• Projection to output
(x1F
x1R )
(" F = k + sc" ,
x1F = y3,
D(M , K , C )
(w = y1, Λθ = y2 )
x1R = y4 )
8
Time domain propagators – digital filtering
∏ (1 − s ~
z Fk ) ∏ (1 − s ~
p Fk ) +

The transfer function: H θ (s ) =   − sΛ 
~
~
(
)
(
exp
1
1
s
z
s
p Rk )
−
−


∏
∏
Rk
  v 

…’propagates’ road profile to car body translation and rotation.
• …’filter’ applied to the ’road profile signal’.
• …preferably realized in the time domain for road hump passage
• …approximated in discrete time, implemented as a digital filter
• …formulated in poles/zeros allows for exponential map
(sampling time TS )
qk = exp(q~k TS ), qk = z k , pk
Λ
−
(
(
(
(
z − zk )
z − zk )
1 − pk )
1 − pk )
vT
⇒ Gθ ( z ) = ∏
+z
∏
∏ (1 − z ) ∏ (z − p )
(1 − zk ) (z − pk )
k
k
S
⇒ Gθ ( z ) =
k
b
z
∑k
∑ ak z
k
+z
−
Λ
vTS
k
b
z
∑k
k
a
z
∑ k
9
Method – repeated digital filtering
•
•
⇒
•
⇒
•
Road profile input
Application of vehicle filters
Car body response
Application of seat filter
Seat response
Application of non-linear human body filter
– ISO 2631-5
– Pulse impact – not continuous spectrum!
– Fatigue model of spinal cord
⇒ Human body response – risk of injury
‘Calibration’:
• Vehicle
• Seat
• Human body – ISO 2631-5
Analysis Synthesis
Symmetry!
10
Part 0. Public interest
1. Newspaper articles: 2
– Borås Tidning (local Borås)
– TTELA (Trollhättan, where ’SAAB’ is made)
2. News on radio
3. News on public television (’prime time’, western part of Sweden)
11
Part 1. The Road Hump Toolbox
How to analyse/synthesize road humps in practice?
• Make a user-friendly toolbox with simple in-/output!
• Matlab ‘GUIDE’ development
• Mrigank Gupta student from IIT, Kanpur, India.
Summer internship at SP, Borås, Sweden in May-July 2008.
12
Part 2. Optimal hump profile – Synthesis
Desired acceleration profile
Synthesized road hump
0.04
0.1
0.03
0.09
Optima l roa d profile (m)
Acce le ra tion (g)
0.02
0.01
0
-0.01
-0.02
0.08
0.07
0.06
0.05
0.04
0.03
0.02
-0.03
0.01
-0.04
5
10
15
20
Dis ta nce (m)
25
30
35
0
5
10
15
20
Dis ta nce (m)
25
30
35
One axle model:
P.Y. Zhu, J.P. Hessling, D.S. Liu, “Optimal road hump for comfortable speed reduction”,
4th ISPMM’ 2008, International Symposium on Precision Mechanical Measurements,
Anhui, China, Aug. 25-29, 2008.
13
Part 3. Optimal hump length - Synthesis
Rotation particularly important for buses
– large separation seat and center of mass
Impulse response
(Car/Bus):
BUS : θ Λ
0.04
0.02
0
-0.02
-0.04
0
5
10
Dis tance (m)
15
20
CAR: θ Λ
0.04
0.02
0
5 km/h
30 km/h
60 km/h
-0.02
-0.04
0
5
10
Dis tance (m)
15
20
J. P. Hessling, P. Y. Zhu, “Analysis of Vehicle Rotation during Passage over Speed Control
Road Humps ”, ICICTA’ 2008, International Conference on Intelligent Computation Technology
and Automation, Changsha, China, Oct. 20-22, 2008.
14
0.03
Part 3. Cont’d.
Rotation and hump length 0.02
0.01
Λθ
2 axes vehicle,
2 sides of road hump
Ω
Λ
0
⇒ 2x2=4 pulses
-0.01
⇒ (2 pos., 2 neg.)
-0.02
Front s ide re s pons e
Re a r s ide re s pons e (Ω= 2m)
-0.03
CAR: Imp. res p. autocorr.
Auto-correlation of
ang. impulse response
=> optimal hump length!
Min. corr. => Max. response
Max. corr. => Min. response
BUS : Imp. res p. autocorr.
0
1
2
3
4
5
Tra ve lle d dis ta nce (m)
6
7
0.1
0.05
0
-0.05
-0.1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Lag (m)
0.1
0.05
15 km/h
30 km/h
45 km/h
0
-0.05
-0.1
15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Lag (m)
Part 3. Cont’d.
Variation of acceleration with speed
Large variation!
0.8
Ω = 4.5 m
0.6
5 km/h
10 km/h
30 km/h
2
BUS : ∂t θ Λ/g
0.4
∂ t2θ ∝ speed 2 ?
Acceleration
driver’s seat:
0.2
~ 1g @ 30 km h
0
10(!) times threshold
of discomfort!
-0.2
-0.4
-0.6
0
1
2
3
4
5
6 7 8 9
Dis ta nce (m)
10 11 12 13 14 15
Risk of injury*!
*ISO 2631-5: 2004 Evaluation of the Human Exposure to Whole-Body
Vibration, Geneva: International Standard Organization, 2004
16
Part 4. Calibration of a bus…
The question: How to obtain model of vehicles?
1. ’Ask’ for it
2. Calibration (!)
The hump=Excitation
The bus=‘Measurement system’
17
Part 4. Cont’d. The pulse calibration measurement
•
Hump profile: Height vs. distance
– Easy to measure!
• Velocity
– Determined from measurement:
delay of front/rear wheel response and axle separation
=> Height vs. time= Input pulse excitation
18
Part 4. Cont’d. Measured response
4 km/h
9.4 km/h
1
Front
Re a r
0.5
0.4
0.6
0.3
0.4
Acce le ra tion
Acce le ra tion
0.2
0.1
0
-0.1
-0.2
0.2
0
-0.2
-0.4
-0.3
-0.6
-0.4
-0.8
-0.5
20
Front
Re a r
0.8
21
22
23
24
Time (s )
25
26
27
-1
4
5
6
7
8
9
Time (s )
Analysis / parameter estimation remains!
Goal: Find method and general approach to determine vehicle filters.
19
Part 4. Cont’d.
Calibration bandwidth – variation with speed…
4 km/h
4.5
Roa d Hump
De -convolution
Ca libra tion ba ndwidth
4
3.5
3.5
3
S pe ctrum
S pe ctrum
Roa d Hump
De -convolution
Ca libra tion ba ndwidth
4
3
2.5
2
2.5
2
1.5
1.5
1
1
0.5
0.5
0
9.4 km/h
4.5
0
2
4
6
Fre que ncy (Hz)
8
10
12
0
0
2
4
6
Fre que ncy (Hz)
8
10
12
Calibration bandwidth very important !!!
Bandwidth increase with velocity
- but also the mixing of front/rear wheel responses:
“Correlation time of impulse response longer than delay between
impacts!”
- Optimal speed for calibration???
20
Remaining: Road hump analysis and synthesis…
Decided (-2009):
• Road hump toolbox
– Finalize (polishing and testing)
– Report (Mrigank G)
• Joint publication method / toolbox(?)
• Apply for funding (Swedish road authority)
– Spread use of toolbox
– Preferably joint project with consultant of road authority (’Profilograf’)
• Joint presentation/article ’Calibration of a bus’ (IMEKO 2009 if possible…)
Optional:
• Export to license-free executable SW (compiler)
• Provide support/consultation
• Make display-window for dynamic analysis at SP:
’Road hump analysis’ for free (SW at SP, internet login)
• Extend toolbox to include calibration (thesis worker in control theory)
21
Concluding… Why study road hump design???
Discussion!
• What’s the benefit for dynamic analysis of measurement systems?
– Short time (<1yr)
– Long time
• Visibility
• Financial support
• ’Simplicity of question’
• ’Complexity of answer’
• Spread
– Geographic
– People
– Disciplines
• Challenges?
• High precision analysis, ’traceability’ etc.
22
Thanks for your
attention!
peter.hessling@sp.se
zhu.pingyu@gmail.com
mrigank@iitk.ac.in
23