analysis and synthesis of speed limiting road humps

8/12/2019 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!

[email protected]

[email protected]

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analysis and synthesis of speed limiting road humps

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