analysis and synthesis of speed limiting road humps
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2ndmeeting 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 MechanicalEquipment, Hunan Univ. of Science and Techn., Xiangtan, China
Mrigank Gupta, Indian Institute of Technology, Kanpur, India
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Road bumps/humps for speed reduction
Patent:
(Engwall, Bertil. Device to prevent vehicles from passing atemporarily 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!!!)
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Often poor design of road humps!
the bus driver was exposed to some 1.6 MPa over the flat topbumps 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 bumpshould be regarded as an individual*
the maximum acceleration at the drivers seat in the city bus
running at allowed speed was up to 1gwhen 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 Bors, Sweden 2008 by the health consultant Grnesj L.
for the local bus company.
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Design of road humps
Profile of hump matters! Height (~5-10 cm) only scales the (dis-)comfort!
(linear response)
Changing the height is not a solution for poor design! Variation of comfort with speed set byprofile.
Profile operating principle / efficiency / threshold effect
Established methods of evaluation new and existing humps Widely accepted quantitative analysis: None
Measurements, difficulties
Many many combinations of vehicles, speed and humps
Not practical method for optimizing profile
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Design of road humps
Analysis
5 10 15 20 25 30 350
0.01
0.020.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Distance (m)
Optimalroadprofile(m)
Optimalroad hump
Synthesis
Less precise!
Broad spectrum of vehicles
(Cars, buses, new/old etc.)
Optimal hump for just one typical vehicle
Uncertainty irrelevant
Properties Efficiency / threshold
- Change in comfort with speed
Risk of injuryExisting road hump
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Model of vehicle (car / bus)Tools of dynamic [measurement]
systemsLTI (linear time-invariant)
MIMO (multiple input multiple output):
Dynamic Calibration /Characterization
System Identification
Differential / difference equation
Transfer function / Frequencyresponse function
Impulse response
Auto- / cross- correlation
Signal processing
Digital filtering Poles / zeros
Etc.
Road Hump Variable velocity
Designed geometric profile
Transient pulse signal of variablebandwidth and regularity
(different shapes)
Measurement system
Input 1:Front wheel
coordinate
Input 2:Rear wheel
coordinate
Output 1:Translation
car body
Output 2:Rotation
car body
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Dynamic equations of motion Vibration analysis
Newtons force-law
For convenience
Topology
State-space variables
Dynamic matrix equation
Solution (La-place transf.)
{ }
+
===
RRRR
FFFF
RFRFRF
RFRFRF
T
lllal
llall
laallalalaal
lllaalll
CKLL
2111
2111
1112
12
11
111111
0
0,
( )
=
=
222
, tBn
kn
ktkn
kn mxmf
( )aa =1
( ) ( )4,3,2,1,
114321
=
+ kyy
xxwyyyy
ktdk
RF
( ) ( )nnnT
R
F
RF
R
Ft
sck
E
mmMM
x
xEy
CKy
M
+
=
=
+
=
,
000
000
100
01
2
2
2
2
L
L
diag
( ) [ ] ( ) ( )
( ) ( )
( )
=
=
=
CMKMD
ms
mssE
sXe
sEDssY
T
RR
FF
Fv
s
11
2
2
2
1
1000
00~
1~
L
L
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Transfer function vehicle (measurement system)
Direct transfer function,road profile to car body translation and rotation
( ) [ ] ( )
=
=
0010
0001
exp
1~1
L
L
P
v
ssEDsPs
H
HW
Propagation:
Input road profile time delay front/rear
Road profile => force, state space Through vehicle dynamic matrix
Projection to output
( )
( )( )
( )2,1
41,31
11
,,
,""
yyw
CKMD
yxyxsckF
xx
RF
RF
==
==+=
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Time domain propagators digital filtering
The transfer function:
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 )
( )( ) ( )
( ) ( )
+
= RkRk
FkFk
pszsv
s
pszs
sH ~1~1exp
~1~1
( )
( ) ( )( )
( )( )
( )( )
( )( )
( )
+=
+
=
==
kk
k
kvT
kk
k
k
k
k
k
kvT
k
k
k
k
kkkSkk
za
zb
zza
zb
zG
pzp
zzzz
pzp
zzzzG
pzqTqq
S
S
1
11
1
,,~exp
ST
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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!
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Part 0. Public interest
1. Newspaper articles: 2 Bors Tidning (local Bors)
TTELA (Trollhttan, where SAAB is made)
2. News on radio
3. News on public television (prime time, western part of Sweden)
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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, Bors, Sweden in May-July 2008.
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Part 2. Optimal hump profile Synthesis
5 10 15 20 25 30 35
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Distance (m)
Acceleration(g)
5 10 15 20 25 30 350
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Distance (m)
Optimalroa
dprofile(m)
Desired acceleration profile Synthesized road hump
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.
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Part 3. Optimal hump length - Synthesis
Rotation particularly important for buses large separation seat and center of mass
Impulse response
(Car/Bus):
0 5 10 15 20-0.04
-0.02
0
0.02
0.04
Dis tance (m)
BUS:
0 5 10 15 20-0.04
-0.02
0
0.02
0.04
Dis tance (m)
CAR:
5 km/h
30 km/h60 km/h
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.
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0 1 2 3 4 5 6 7
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Travelled distance (m)
Front side response
Rear side res ponse (= 2m)
Part 3. Contd.
Rotation and hump length
2 axes vehicle,
2 sides of road hump
2x2=4 pulses
(2 pos., 2 neg.)
Auto-correlation of
ang. impulse response
=> optimal hump length!Min. corr. => Max. response
Max. corr. => Min. response
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-0.1
-0.05
0
0.05
0.1
Lag (m)
BU
S:Imp.resp.autocorr.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-0.1
-0.05
0
0.05
0.1
Lag (m)
CAR:Imp.
resp.autocorr.
15 km/h
30 km/h
45 km/h
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1515
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Dis tance (m)
BU
S:
t2
/g
5 km/h
10 km/h
30 km/h
Part 3. Contd.
Variation of acceleration with speed
Large variation!
Acceleration
drivers seat:
10(!) times threshold
of discomfort!
Risk of injury*!
m5.4=
hkmg 30@1~
?22 speed t
*ISO 2631-5: 2004 Evaluation of the Human Exposure to Whole-BodyVibration, Geneva: International Standard Organization, 2004
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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
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Part 4. Contd. Measured response
4 km/h 9.4 km/h
Analysis / parameter estimation remains!
Goal: Find method and general approach to determine vehicle filters.
20 21 22 23 24 25 26 27
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time (s )
Acceleration
Front
Rear
4 5 6 7 8 9-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (s)
Acceleration
Front
Rear
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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)
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Concluding Why study road hump design???
Discussion! Whats the benefit for dynamic analysis of measurement systems?
Short time (
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Thanks for your
attention!
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]