Wybrane problemy bezpieczenstwa w ruchu drogowym

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Wybrane problemy bezpieczenstwa w ruchu drogowym

• Prof. dr hab. inz. Jerzy Kisilowski
• mgr inz. Jaroslaw Zalewski

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Contents

• Introduction
• Chosen theoretical and practical aspects of
  safety problems
• 2.1. Problems of stable motion (definition of
  the stochastic technical stability (STS) by
  prof. W. Bogusz, STS aspects in mathematical
  model of railway car, possible STS aspects in
  mathematical model of road car)
• 2.2. Problems connected with road accidents
• Chosen statistical data
• Conclusions
• Bibliography

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1. Introduction

• This lecture is to give an overview on the
  possibilities of the use of stochastic technical
  stability (STS) in analysis concerning behaviour
  of mathematical models in different conditions.
  Some chosen statistical data are presented as
  well.

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2. Chosen theoretical and practical aspects of
safety problems
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2.1. Problems of stable motion
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Definition of STS - assumptions

• the set of stochastic equations ,
• for the stochastic process and t?0 there
  is ,
• fulfills the Lipschitz condition for another
  process ,
• as a result there is only one solution tt0,
  x(t0)x0, which is a stochastic process.

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Definition of STS

• there are two areas in En ? finite and open, O
  finite and closed, where ? ? O,
• there is a positive number e, 0ltelt1,
• if every solution of , having the initiative
  conditions within ?, lies within O with
  probability 1-e then the structure is technically
  stochastically stable respectfully of ?, O and
  ?(t) with the probability of 1- e (fig. 2.1).

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Fig. 2.1. Graphic illustration of stochastic
technical stability 2.
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STS aspects in mathematical model of railway car

• STS was used as a base on which a model of
  railway track was considered (lateral stability),
• it was presented by E. Kardas-Cinal, PhD, while
  the basic assumptions are taken from Bogusz
  definition,
• the areas of O adapted to this analysis are
  presented in fig. 2.2 and 2.3.

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Fig. 2.2. Illustration of O for the lateral
translation of railway car 2.
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Fig. 2.3. Technical conditions defining maximal
size L of O 2.
wL the space between the wheel and the track
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STS aspects in mathematical model of road car

• it is believed that car mathematical model can be
  analysed with the use of technical stochastic
  stability,
• the area of the allowed solutions O is defined
  within the width of the road (fig. 2.4),
• the car model will have its geometry disturbed to
  examine the stability with both correct and
  disturbed parameters.

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Fig. 2.4. The maximal (approval) L of O between
the center of mass in car and the side of the
road. Source own research.
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3. Chosen statistical data
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Fig. 3.1. Number of Volvo and Fiat 126 cars that
took part in accidents in the period of 1995
2000. Source own research.
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Fig. 3.2. Number of accidents with the
participation of Volvo and Fiat 126 cars in
relation to 100 vehicles of the given
make. Source own research.
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Fig. 3.3. Number of trucks, killed in injured
accidents with trucks in Poland and Germany in
2000. Source own research.
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Fig. 3.4. Killed and injured per 100 trucks in
Poland and Germany in 2000 Source own research.
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4. Conclusions

• According to the presented results, the classic
  methods of solving road safety problems basing on
  the elimination of consequences may not give the
  possitive effect.
• It is important to take the reasons why road
  accidents occur into account. There are three
  areas of consideration.

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The areas of consideration

• Implementation of a selective system to evaluate
  road accidents considering such elements as type
  of vehicle and type of crash.
• Connecting accidents with the condition of
  infrastructure.
• Elimination of collisions and accidents results
  on the basis of road car stability and following
  research with the use of the existing tools.

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Fig 4.1. The results of ISO Lane change with the
disturbed center of mass. Source own research.
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5. Bibliography

• Bogusz W. Statecznosc techniczna, Polish Academy
  of Sciences IPPT, Warsaw 1972.
• Kardas-Cinal E. Badanie statecznosci
  stochastycznej modelu matematycznego pojazdu
  szynowego, Doctoral Thesis, Warsaw University of
  Technology, Warsaw 1994.
• Kisilowski J., Kardas-Cinal E. On a Certain
  Method of Examining Stability of Mathematical
  Models of Railway Vehicles with Disturbances
  Occurring in Real Objects, Vehicle System
  Dynamics, Vol.3, 1994.
• Kisilowski J., Choromanski W., Lopata H.
  Investigation of Technical Stochastic Stability
  of Lateral Vibrations of Mathematical Model of
  Rail Vehicle, Engineering Transactions, Polish
  Academy of Sciences IPPT, Vol.33, Warsaw 1985.

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Thank you