Description

Write a 2 page single spaced paper with 11 font and could include graphs about the safety of vehicles. General prompt and the sources to be used will be included. The paper is due by tonight midnight. The paper should talk about what makes vehicles unsafe and what the solutions to that could be. Focus on how cars are flammable, airbags, brakes. Could use other references if needed.

ORIGINAL ARTICLE

Airbag Burns: An Unfortunate Consequence of Motor

Vehicle Safety

Thousands of people are injured in motor vehicle collisions daily and the mandated installation of airbags protects

passengers but can also cause injuries from deployment including cutaneous burns. We sought to characterize the patterns

and outcomes of burns resulting from airbag deployment by performing a retrospective review of all patients evaluated by

the burn service from May 1, 2015 to April 30, 2019. Inclusion criteria were patients of all ages with burn injuries related

to airbag deployment. Demographic data, burn characteristics, and outcomes were reviewed. Seventeen patients met the

inclusion criteria: 82.4% female and 17.6% male. The average age was 40.4 years. Fifteen patients had second-degree and

two had third-degree burns. The average TBSA was 0.45%. The hands or upper extremity (88%) were most often injured,

but there were two chest, one neck, and one anterior thigh burns. Eight patients suffered multiple burns. Burn etiology

(chemical vs thermal) was often not specified. No patients required hospitalization or surgical intervention, and all

wounds healed with wound care. The average time to re-epithelialization was 11 days. Although airbags prevent mortality

and serious injury, the exothermic chemical reaction that inflates the airbag is responsible for deployment-related burns.

Since there is a chemical and thermal component, all airbag-related burns should undergo chemical decontamination

on the initial presentation. Burns related to airbag deployment tend to be small and do not require grafting; however,

patients suffer from associated pain, scarring, and burn management can be a financial and time burden to the patient.

More than 7500 Americans are injured in motor vehicle

collisions every day, with an estimated economic burden

of $240 billion annually.1,2 All vehicles manufactured since

1997 are mandated to have dual airbags installed. The

National Highway Traffic Safety Administration estimated

that 2790 lives in people aged 13 and older were saved by

frontal airbag deployment in 2017. The use of airbags in

combination with seat belts has been shown to have an even

greater effect than either used alone.3 However, the ubiquity

of airbags in automobiles has shown a surge in airbag-related

injuries including abrasions (63.6%), contusions (37.8%),

lacerations (18.2%), burns (7.8%), fractures (3.2%), and retinal detachment (1.8%).4,5

It is important to note the mechanism of an airbag deployment, as it is intrinsically responsible for airbag-related burns.

Rapid vehicle deceleration is detected by sensors which set off

a chain reaction resulting in airbag inflation on frontal collision. The reaction starts with the ignition of sodium azide,

culminating in the release of nitrogen gas, carbon dioxide,

carbon monoxide, ammonia, and alkaline aerosol.6 The alkaline aerosol is a mixture of sodium hydroxide, sodium carbonate, and metallic oxides. The chemical reaction triggers

From the *Department of Surgery, Division of Plastic Surgery, University

of Rochester Medical Center, New York; Ã¢â‚¬Â Jacobs School of Medicine and

Biomedical Sciences at the University of Buffalo, New York

Conflict of interest statement. None.

Disclosure of funding received: None.

Address correspondence to Kathryn E. H. Skibba, MD, Department of Surgery,

Division of Plastic Surgery, University of Rochester Medical Center, 601

Elmwood Ave, Box SURG, Rochester, NY 14642. Email: Kathryn_skibba@

urmc.rochester.edu

Ã‚Â© The Author(s) 2020. Published by Oxford University Press on behalf of the

American Burn Association. All rights reserved. For permissions, please e-mail:

journals.permissions@oup.com.

doi:10.1093/jbcr/iraa117

the rapid inflation of the airbag. As an exothermic reaction,

significant heat up to 500Ã‚Â°C is generated.7 There are vents at

the base of the airbag which prevent airbag explosion during

rapid inflation as well as allowing for cushioning of the passenger during the collision. The existence of the airbag vents

allows the heat and alkaline gases produced in the exothermic

deployment reaction to be released into the vehicle.8,9

The release of hot gas and alkaline substance into the cabin

puts patients at risk for both thermal and chemical burns.

The corrosive nature of the alkaline aerosol, particularly, the

sodium hydroxide, has been implicated in alkaline chemical

keratitis and cutaneous burns.10 The proximity of the ventilation system to the driverÃ¢â‚¬â„¢s arms and hands makes this a likely

location for direct thermal burns caused by contact with the

stream of gas. Indirect thermal burns may occur by melting

or ignition of passenger clothing from contact with hot gases

released from the airbag.

There are numerous case reports of airbag-related burn

injuries but there is a paucity of literature that analyzes a cohort of these patients. The literature describes burns to the

hands or face and the etiology is split between chemical alkali

and thermal causes.6,10Ã¢â‚¬â€œ13 At our institution, we have seen numerous burn injuries related to airbag deployment. This study

aims to further characterize the size, location, severity, and

consequences of burns from airbag deployment.

METHODS

A retrospective review of all patients evaluated by the burn

service was performed from May 1, 2015 to April 30, 2019.

Inclusion criteria include patients of all ages with cutaneous

burn injuries resulting from motor vehicle airbag deployment.

Demographic data and burn characteristics including TBSA,

burn severity, anatomic areas involved, and surgical treatment

71

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Kathryn E. H. Skibba, MD,* Chelsea N. Cleveland, BS,Ã¢â‚¬Â and Derek E. Bell, MD*

Journal of Burn Care & Research

January/February 2021

72Ã¢â‚¬â€šÃ¢â‚¬â€šSkibba et al

were reviewed. The determination of burn etiology was based

on burn characteristic and patient report. Diffuse and even

depth burns over exposed skin were deemed to be chemical

burns. Patients recalling heat exposure at the site of injury

were categorized as thermal burns.

RESULTS

Table 1. Burn wound characteristics

Characteristics

Average TBSA

Etiology

Chemical

Thermal

Unspecified

Burn severity

Second degree only

Third degree only

Second and third degree

Burn location

Hands/wrist

Forearm/upper arm

Chest

Neck

Thigh

0.45%

n (%)

6 (35.3)

3 (17.6)

8 (47.1)

15 (88.2)

1 (5.9)

1 (5.9)

10 (58.8)

6 (35.3)

2 (10.0)

1 (5.0)

1 (5.0)

DISCUSSION

While airbags are an effective method to prevent serious injury and death from motor vehicle accidents, the literature

recognizes that airbag deployment can cause cutaneous burns.

The burns are a result of either contact with alkali chemicals

and/or thermal injury created by the exothermic reaction of

deployment. The clinical manifestation of the burn may not

distinguish whether it was a chemical or thermal etiology, as

seen in 47% of our patients. We recommend that all burns related to airbag deployment should be considered as partially

chemical etiology and standard decontamination with irrigation of the wound should be performed at initial evaluation.

Interestingly, 82.4% of the patients are female. This is an

unusual finding among burn cohorts, as most are either split

equally between men and women or have a male dominant

cohort. There is no obvious explanation for this finding.

Possibilities are that women may be more likely to seek

treatment, have more exposed skin vulnerable for injury, or

that they may be more likely to be involved in a motor vehicle accident.

Notably, the average wound size was small at 0.45% TBSA.

Most wounds were determined to be second degree; only

12% of patients had full-thickness burns. This is important to

consider because all patients healed their wounds without the

need for skin grafting or other surgical intervention.

The anatomic locations of burns were consistent with current literature, mostly (88%) occurring on the hands or upper

extremity. There were no patients with facial burns, but one

patient did suffer from a burn to the neck. Interestingly, two

patients had burns to the chest and one patient had an anterior thigh burn. This indicates that airbag-related burns can

occur throughout the body. Patients presenting after airbag

deployment should prompt a thorough examination for cutaneous injury on initial evaluation.

Although the wounds may be considered minor, burn

injuries should not be an expected complication of airbag

deployment. Patients who experience injuries secondary to

airbag deployment are inconvenienced by burn management

including the emergency department and clinic visits, as well

as wound care. Hand burns are especially burdensome as open

wounds may prevent patients from returning to work until

re-epithelialization. Patients may suffer permanent scars from

the burns which primarily occur in cosmetically sensitive areas

such as the hands, neck, and face. Therefore, airbag-related

burns can burden patients with pain, scars, need for wound

care, cost of healthcare, and missed wages.

CONCLUSIONS

There is no question about the efficacy of airbags in preventing

death and serious injury. However, the current mechanism of

an airbag deployment is intrinsically hazardous to passengers

as it releases hot gases and alkaline substances into the cabin.

Thermal and chemical burns may be avoided with alteration in airbag deployment location or mechanism design.

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A total of 17 patients met the inclusion criteria: 82.4% female and 17.6% male. The average age at the time of burn

evaluation was 40.4 Ã‚Â± 23.7 years (range 20Ã¢â‚¬â€œ82 years). Most

patients self-identified as Caucasian (82.4%). Comorbidities

were found in seven patients, which included obesity (35.3%),

psychiatric illness (23.5%), smoking (11.8%), hypertension

requiring medication (11.8%), and diabetes mellitus (6.5%).

The characteristics of the burns are summarized in Table 1.

There were 15 patients with exclusively second-degree burns

with an average TBSA of 0.47% Ã‚Â± 0.40%; one patient suffered

an exclusively third-degree burn with a TBSA of 0.16%; and

one patient had both second- and third-degree burns with a

total TBSA of 0.51%. The average TBSA for all patients was

0.45%. Ten patients (58.8%) had burns on the hand or wrist, six

(35.3%) had forearm or upper arm burns, two had chest burns,

one had a neck burn, and one had an anterior thigh burn.

In eight patients (47%), the burn etiology (thermal or

chemical) could not be clinically distinguished. Six patients

(35%) had chemical burns and three patients (18%) recalled

heat exposure and were categorized as thermal injury. One of

the three thermal patients had ignition of his clothing, causing

a flame burn injury.

Three patients required hospitalization for concurrent

injuries sustained in the motor vehicle collision. The burn

service monitored and treated the burn injuries while inpatient, but no patients required admission solely to receive

burn care. The average length of stay was 12.7 days. No

patients required intensive care or intubation. No patients

died on admission.

No patients received antibiotic therapy and there were no

burn wound infections. All patients were able to heal their

burns with daily wound care; therefore, no patients required

surgical intervention. The average number of wound care days

performed before burn wound re-epithelialization was 11 Ã‚Â± 5.

Journal of Burn Care & Research

Volume 42, Number 1

Skibba et alÃ¢â‚¬â€šÃ¢â‚¬â€š73

Airbag-related burns should not be minimized as they cause

pain, scarring, and a financial and time burden to the patient.

4.

5.

ACKNOWLEDGEMENTS

6.

None.

7.

8.

1. National Center for Statistics and Analysis. People injured per day.

2017 Quick facts. Washington (DC): National Highway Traffic Safety

Administration; 2019. Report No.: DOT HS 812 747.

2. National Center for Statistics and Analysis. The economic and societal

impact of motor vehicle crashes, 2010. Traffic Safety Facts Crash Stats.

Washington (DC): National Highway Traffic Safety Administration;

2015. Report No.: DOT HS 812 013.

3. National Center for Statistics and Analysis. Lives saved in 2017 by restraint use and minimum-drinking-age laws. Traffic Safety Facts Crash

9.

10.

11.

12.

13.

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REFERENCES

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Baruchin AM, Jakim I, Rosenberg L, Nahlieli O. On burn injuries related

to airbag deployment. Burns 1999;25:49Ã¢â‚¬â€œ52.

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Cundill DJ. Airbag venting mechanism. United States Patent 5725244;

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Yamada I. Airbag with vent hole. United States Patent 7240918; 2004.

Ulrich D, Noah EM, Fuchs P, Pallua N. Burn injuries caused by air bag

deployment. Burns 2001;27:196Ã¢â‚¬â€œ9.

Hendrickx I, Mancini LL, Guizzardi M, Monti M. Burn injury secondary

to air bag deployment. J Am Acad Dermatol 2002;46(2 Suppl Case

Reports):S25Ã¢â‚¬â€œ6.

Suhr M, Kreusch T. Burn injuries resulting from (accidental) airbag inflation. J Craniomaxillofac Surg 2004;32:35Ã¢â‚¬â€œ7.

Wallis LA, Greaves I. Injuries associated with airbag deployment. Emerg

Med J 2002;19:490Ã¢â‚¬â€œ3.

Simulation-Based Assessment of Vehicle Safety Behavior

under Hazardous Driving Conditions

Suren Chen, P.E., M.ASCE1; and Feng Chen, S.M.ASCE2

Abstract: Future sustained economic growth of the nation very much depends on the reliability and efficiency of its highway infrastructure system. Some vehicles, such as trucks, emergency vehicles, and sport utility vehicles, often experience increasing risks of singlevehicle accidents under hazardous driving conditions, such as inclement weather and/or complicated topographical conditions. An

advanced simulation-based single-vehicle accident assessment model is developed considering the coupling effects between vehicles and

hazardous driving conditions, including wind gust, snow-covered or icy road surface, and/or curving. Compared to existing simulation

models, the new model focuses on characterizing the transient process of accidents, introducing new critical variables on assessing the

accident risks under more comprehensive hazardous driving conditions and establishing more realistic accident criteria. As a holistic

deterministic model, it can be used to provide useful assessment and prevention information for traffic and emergency management. For

example, it can be used to define appropriate safe driving speed limits for vulnerable vehicles under normal and extreme conditions and

predict potential crash and injury risk of vulnerable drivers. Moreover, the new deterministic vehicle safety behavior simulation model

lays a critical basis for future reliability-based studies of single-vehicle accident risks of vulnerable vehicles under hazardous conditions.

After the model is introduced, numerical analyses on a typical truck under several representative hazardous scenarios will be conducted

for demonstration purposes.

DOI: 10.1061/Ã¥â€¦Â±ASCEÃ¥â€¦Â²TE.1943-5436.0000093

CE Database subject headings: Traffic accidents; Hazards; Vehicles; Simulation.

Author keywords: Accident; Hazardous; Traffic; Conditions; Simulation.

Introduction

In the United States as well as other developed countries, road

accidents are causing more injuries and casualties than any other

natural or man-made hazard. Large commercial trucks, high-sided

sport utility vehicles Ã¥â€¦Â±SUVsÃ¥â€¦Â², and emergency vehicles Ã¥â€¦Â±e.g., fire

trucks and emergency medical service Ã¥â€¦Â±EMSÃ¥â€¦Â² vehiclesÃ¥â€¦Â² are especially vulnerable to single-vehicle crashes Ã¥â€¦Â±e.g., rollover, sideslipÃ¥â€¦Â²

under hazardous driving environments on rural highways. The

hazardous driving environments may include inclement weather

Ã¥â€¦Â±e.g., strong crosswind gusts, snow, rain, or iceÃ¥â€¦Â² and/or complicated terrain Ã¥â€¦Â±e.g., steep slopes or sharp curvesÃ¥â€¦Â² Ã¥â€¦Â±The National

Academies 2006; USDOT 2005Ã¥â€¦Â². In 2005, single-vehicle accidents were responsible for 57.8% of accident fatalities Ã¥â€¦Â±USDOT

2005Ã¥â€¦Â². Each year in the United States, adverse weather alone is

associated with more than 1.5 million vehicular crashes, which

result in 800,000 injuries and 7,000 fatalities Ã¥â€¦Â±The National Academies 2006Ã¥â€¦Â². Among various causes of crashes in rural areas, it

has been found that the dominant causes are excessive speeds and

adverse environments Ã¥â€¦Â±The Road Information Program 2005Ã¥â€¦Â². In

1

Assistant Professor, Dept. of Civil and Environmental Engineering,

Colorado State Univ., Fort Collins, CO 80523 Ã¥â€¦Â±corresponding authorÃ¥â€¦Â².

E-mail: suren.chen@colostate.edu

2

Graduate Research Assistant, Dept. of Civil and Environmental

Engineering, Colorado State Univ., Fort Collins, CO 80523. E-mail:

feng.chen@colostate.edu

Note. This manuscript was submitted on October 14, 2008; approved

on August 13, 2009; published online on August 15, 2009. Discussion

period open until September 1, 2010; separate discussions must be submitted for individual papers. This paper is part of the Journal of Transportation Engineering, Vol. 136, No. 4, April 1, 2010. Ã‚Â©ASCE, ISSN

0733-947X/2010/4-304Ã¢â‚¬â€œ315/$25.00.

addition to direct safety threats, frequent single-vehicle accidents

will also cause serious congestions, affecting the functionality of

the whole highway network in normal situations, as well as under

emergency. Therefore, for trucking industries, transportation, and

emergency management agencies, it is critical to accurately predict the crash risk and further advise appropriate driving speeds

under complicated adverse driving environments.

Different from multivehicle crashes, single-vehicle crashes

under adverse or hazardous environments were found to be

closely related to the coupling among vehicle, infrastructure, and

environment Ã¥â€¦Â±Baker 1991; Guo and Xu 2006; Chen and Cai 2004;

Chen et al. 2009Ã¥â€¦Â². As a result of this unique coupling, observations solely from historical crash data in one place can hardly be

translated into accurate risk prediction in different places or under

driving environments which were not covered by the actual crash

data. Therefore, in addition to analyzing actual historical crash

data gathered after the crashes, investigations on single-vehicle

crashes also require a reasonable simulation model which can be

used more than for an after-the-fact reconstruction of the crash

Ã¥â€¦Â±TRB 2007Ã¥â€¦Â², but more important, to reasonably predict the potential risk of crashes under comprehensive scenarios including those

which may not be covered by historical crash data.

In automobile engineering, significant efforts have been put

forth on simulating vehicle dynamics and accidents with engineering simulation models, from the simple rigid body model, the

bicycle model, to the complicated spring-mass multiple-degreeof-freedom model Ã¥â€¦Â±Thomas 1992Ã¥â€¦Â². Despite extensive works in

these fields Ã¥â€¦Â±e.g., Winkler and Ervin 1999; Gaspar et al. 2004,

2005; Sampson 2000Ã¥â€¦Â², research on vehicle accident risks, which

considers the coupling among the vehicle dynamic model, inclement weather, and topographical condition, is still very limited. Baker Ã¥â€¦Â±1986, 1987, 1991, 1994Ã¥â€¦Â² was the first researcher who

304 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

tried to investigate the high-sided vehicle accident risks under

strong crosswind. In his studies, vehicle accident risks were assessed through solving several static equilibrium equations with

some predefined accident criteria. Based on BakerÃ¢â‚¬â„¢s work, several

reliability-based accident assessments were recently conducted

Ã¥â€¦Â±SigbjÃƒÂ¶rnsson and SnÃƒÂ¦bjÃƒÂ¶rnsson 1998; SnÃƒÂ¦bjÃƒÂ¶rnsson et al. 2007Ã¥â€¦Â².

Chen and Cai Ã¥â€¦Â±2004Ã¥â€¦Â² improved the accident risk assessment by

introducing a general dynamic interaction model, based on which

the vehicle accident assessment was conducted by considering

excitations from the supporting structure Ã¥â€¦Â±e.g., bridgeÃ¥â€¦Â². Guo and

Xu Ã¥â€¦Â±2006Ã¥â€¦Â² introduced an integrated vehicle safety assessment

model on bridges. In the model, the dynamic bridge-vehicle-wind

interaction analysis as well as the safety assessment was carried

out at the same time based on the same accident criteria by Baker

Ã¥â€¦Â±1991Ã¥â€¦Â². In most existing studies, however, only situations that

vehicles are driven on straight routes with only crosswind excitation were considered. In the present study, a general vehicle

safety behavior simulation model is introduced to consider the

coupling effects with more realistic hazardous environments, including combinations of both inclement weather and complicated

topographical conditions. Improved transient dynamic equations,

accident criteria, and new critical variables will also be incorporated into the model.

Theoretical Formulation

Fig. 1. Addition of the velocity vectors

ar = longitudinal distances from the center of sprung mass to the

front and the rear axles, respectively.

Crosswind Forces

Crosswind velocity can be obtained from actual measurements or

from numerical simulations based on existing wind velocity spectra Ã¥â€¦Â±Baker 1991; Chen and Cai 2004Ã¥â€¦Â². Typically, quasistatic assumptions are applied to simulate the wind loadings acting on

moving vehicles Ã¥â€¦Â±Baker 1987, 1994; Coleman and Baker 1994Ã¥â€¦Â².

The crosswind-induced quasistatic forces and moment acting on

the vehicle body on x-, y-, and z-directions are defined as follows

Ã¥â€¦Â±Baker 1994Ã¥â€¦Â²:

2

Fx = 0.5Ã¢ÂÂ³CFxAVre

drag force

Ã¥â€¦Â±5Ã¥â€¦Â²

2

lift force

Fy = 0.5Ã¢ÂÂ³CFyAVre

Ã¥â€¦Â±6Ã¥â€¦Â²

The general accident simulation model is introduced in this

section: after the primary forces acting on a vehicle are introduced, series dynamic models are developed to simulate the dynamic response under different stages of the transient process of

accidents.

2

Fz = 0.5Ã¢ÂÂ³CFzAVre

side force

Ã¥â€¦Â±7Ã¥â€¦Â²

2

M x = 0.5Ã¢ÂÂ³C MxAVre

hre rolling moment

Ã¥â€¦Â±8Ã¥â€¦Â²

Primary Forces Acting on Vehicles

2

M y = 0.5Ã¢ÂÂ³C MyAVre

hre yawing moment

Ã¥â€¦Â±9Ã¥â€¦Â²

2

M z = 0.5Ã¢ÂÂ³C MzAVre

hre pitching moment

Ã¥â€¦Â±10Ã¥â€¦Â²

Tire Forces

When a vehicle is cornering, the lateral tire forces perpendicular

to the direction of the driving velocity applied at the contact

patches of the wheels are approximated to be proportional to

the tire slip angle. The lateral tire forces of the front and the

rear tires are defined in Eqs. Ã¥â€¦Â±1Ã¥â€¦Â² and Ã¥â€¦Â±2Ã¥â€¦Â² as follows, respectively

Ã¥â€¦Â±Gaspar et al. 2004, 2005Ã¥â€¦Â²:

Fy,f = Ã¢ÂÂ®c f Ã¢ÂÂ£ f

Ã¥â€¦Â±1Ã¥â€¦Â²

Fy,r = Ã¢ÂÂ®crÃ¢ÂÂ£r

Ã¥â€¦Â±2Ã¥â€¦Â²

where ci Ã¥â€¦Â±i = f or rÃ¥â€¦Â² = tire cornering stiffness and Ã¢ÂÂ£i Ã¥â€¦Â±i = f or rÃ¥â€¦Â²

= tire side slip angle associated with the front and the rear axles,

respectively; Ã¢ÂÂ® = road adhesion coefficient; and subscripts y, f,

and r denote the lateral direction Ã¥â€¦Â±y-directionÃ¥â€¦Â², front and rear

wheels, respectively.

The classic equations for the tire slip angles of the front Ã¥â€¦Â±Ã¢ÂÂ£ f Ã¥â€¦Â²

and the rear Ã¥â€¦Â±Ã¢ÂÂ£rÃ¥â€¦Â² wheels can be defined as Ã¥â€¦Â±Gaspar et al. 2004,

2005Ã¥â€¦Â²

Ã¢ÂÂ£ f = Ã¢Ë†â€™ Ã¢ÂÂ¤ + Ã¢ÂÂ¦ Ã¢Ë†â€™ a f Ã¢ÂÂºÃ‹â„¢ /V

Ã¥â€¦Â±3Ã¥â€¦Â²

Ã¢ÂÂ£r = Ã¢Ë†â€™ Ã¢ÂÂ¤ Ã¢Ë†â€™ arÃ¢ÂÂºÃ‹â„¢ /V

Ã¥â€¦Â±4Ã¥â€¦Â²

where Ã¢ÂÂ¤, Ã¢ÂÂ¦, and Ã¢ÂÂºÃ‹â„¢ = sideslip angle, steer angle, and yaw

rate, respectively; V = driving speed of the vehicle; and a f and

where Ã¢ÂÂ³ = density of air; A = reference area; hre = reference arm;

CFx, CFx, and CFz = wind force coefficients; and C Mx, C My, and

C Mz = wind moment coefficients in Ã¥â€¦Â±aboutÃ¥â€¦Â² x-, y-, and z-directions,

respectively. These wind coefficients, which are typically obtained from wind tunnel testing Ã¥â€¦Â±Baker 1994Ã¥â€¦Â², are related to the

profile of a specific vehicle and are functions of attack angle Ã¢ÂÂ½.

Due to the lack of wind tunnel testing results of vehicles during

the process of accident-related motions, it is assumed in the

present study that the wind loadings acting on the vehicle remain

the same during the process of rollover or sideslip. Vre is the wind

velocity relative to the vehicle, which is defined as Ã¥â€¦Â±Fig. 1Ã¥â€¦Â²

Vre = Ã¥â€ â€˜V2 + Ã¥â€¦Â³U + uÃ¥â€¦Â±tÃ¥â€¦Â²Ã¥â€¦Â´2 + 2VÃ¥â€¦Â³U + uÃ¥â€¦Â±tÃ¥â€¦Â²Ã¥â€¦Â´ Ã‚Â· cos Ã¢ÂÂ¸

Ã¥â€¦Â±11Ã¥â€¦Â²

where U = mean wind velocity and uÃ¥â€¦Â±tÃ¥â€¦Â² = turbulent component of

wind velocity in the alongwind direction. Wind turbulent velocity

can be obtained from actual wind measurements or from simulations based on wind velocity spectrums Ã¥â€¦Â±Chen and Cai 2004Ã¥â€¦Â². Ã¢ÂÂ¸ is

the wind direction Ã¥â€¦Â±Fig. 1Ã¥â€¦Â².

Forces due to Topology

In typical highway designs, there will be an appropriate roadway

superelevation on any curved path to provide centripetal acceleration which acts toward the center of the curvature Ã¥â€¦Â±AASHTO

2004Ã¥â€¦Â². So it is necessary to consider the corresponding superelevation Ã¢ÂÂª in the model to replicate the real situation when a vehicle moves through a curved path. In the following numerical

JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010 / 305

Fig. 2. Single-body vehicle model: Ã¥â€¦Â±aÃ¥â€¦Â² elevation view; Ã¥â€¦Â±bÃ¥â€¦Â² top view

results, Ã¢ÂÂª is defined based on typical design values suggested by

AASHTO Ã¥â€¦Â±2004Ã¥â€¦Â², which are dependent on the road design speed

and radius of curvature.

Basic Vehicle Dynamic ModelÃ¢â‚¬â€Wheels Are Not Lifted

up or Sideslip

rFy,r = Ã¢Ë†â€™ mu,rVÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² + mu,rgÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂ¾t,r

+ mu,rgÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂª Ã¢Ë†â€™ arollIxÃ¢Â¬ËœxÃ¢Â¬Ëœmr/m Ã¢Ë†â€™ mu,rayÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²

Ã‹â„¢ Ã¢Ë†â€™Ã¢ÂÂ¾

Ã‹â„¢ t,rÃ¥â€¦Â² + ur

+ kt,rÃ¢ÂÂ¾t,r Ã¢Ë†â€™ krÃ¥â€¦Â±Ã¢ÂÂ¾ Ã¢Ë†â€™ Ã¢ÂÂ¾t,rÃ¥â€¦Â² Ã¢Ë†â€™ lrÃ¥â€¦Â±Ã¢ÂÂ¾

Ã¥â€¦Â±16Ã¥â€¦Â²

The vehicle model is shown with the coordinate system fixed on

the vehicle in Fig. 2. In the following model, pitching and bouncing motions are not considered because they typically have insignificant impacts on the rolling and lateral movements of the

vehicle Ã¥â€¦Â±Sampson 2000Ã¥â€¦Â². The sprung mass rotates about the roll

center which is dependent on the kinematical properties of the

suspensions. The unsprung masses can also rotate, combined with

the effect of the vertical compliance of the tires. The vehicle

motion equations are developed according to the change of the

momentum and the sum of external forces based on the model

introduced by Sampson Ã¥â€¦Â±2000Ã¥â€¦Â². The suspension parameters such

as damping coefficients are assumed to be constant.

As a general model which considers wind load, road superelevation, curvature, and excitations from supporting structures

Ã¥â€¦Â±e.g., vibration induced by pavement roughness or bridge/vehicle

interactionsÃ¥â€¦Â², five force and moment equilibrium equations of

vehicle motions of sprung mass and suspensions in y- and zdirections are defined in Eqs. Ã¥â€¦Â±12Ã¥â€¦Â²Ã¢â‚¬â€œÃ¥â€¦Â±16Ã¥â€¦Â², respectively

where Fw,y, M x, and M z = lateral wind force, wind-induced roll

moment, and wind-induced yaw moment, respectively; Ã¢ÂÂª = road

superelevation; ay and aroll = accelerations in y-direction and rolling direction of the supporting infrastructures Ã¥â€¦Â±e.g., pavement or

bridgeÃ¥â€¦Â², respectively; m, ms, and mu = total mass, sprung mass,

and unsprung mass, respectively; h = height of the center of

sprung mass, measured upwards from the roll center; r and

hu = heights of rolling center and unsprung mass center, measured

upwards from ground, respectively; Fy,f and Fy,r = lateral forces of

front and rear tires, respectively; IxÃ¢Â¬ËœxÃ¢Â¬Ëœ, IxÃ¢Â¬ËœzÃ¢Â¬Ëœ, and IzÃ¢Â¬ËœzÃ¢Â¬Ëœ = roll

moment, yaw-roll product, and yaw moment of inertia of sprung

mass, respectively; k, kt, and l = suspension roll stiffness, tire roll

stiffness, and suspension roll damping rate, respectively; Ã¢ÂÂ¾

and Ã¢ÂÂ¾t = absolute roll angle of sprung mass and unsprung mass,

respectively; Ã¢ÂÂ¤ and Ã¢ÂÂº = sideslip angle and heading angle; and

u = active roll torque. A full list of all variables can be found in the

nomenclature.

The above equations can be expressed using a state-space representation, which is suitable for numerical integrations

Ã‚Â¨ = mVÃ¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² Ã¢Ë†â€™ Fy,f Ã¢Ë†â€™ Fy,r + Fw,y Ã¢Ë†â€™ mgÃ¢ÂÂª + may

mshÃ¢ÂÂ¾

Ã¥â€¦Â±12Ã¥â€¦Â²

xÃŒâ€¡ = Ax + B0u + B1Ã¢ÂÂ¦ + C

Ã¥â€¦Â±17Ã¥â€¦Â²

Ã¢Ë†â€™ IxÃ¢Â¬ËœzÃ¢Â¬ËœÃ¢ÂÂ¾Ã‚Â¨ + IzÃ¢Â¬ËœzÃ¢Â¬ËœÃ¢ÂÂºÃ‚Â¨ = Fy,f a f + Fy,rar + M z

Ã¥â€¦Â±13Ã¥â€¦Â²

Ã‹â„¢ Ã¢ÂÂ¾t,f Ã¢ÂÂ¾t,r Ã¥â€¦Â´T

x = Ã¥â€¦Â³Ã¢ÂÂ¤ Ã¢ÂÂºÃ‹â„¢ Ã¢ÂÂ¾ Ã¢ÂÂ¾

Ã¥â€¦Â±18Ã¥â€¦Â²

u = Ã¥â€¦Â³u f ur Ã¥â€¦Â´T

Ã¥â€¦Â±19Ã¥â€¦Â²

where

IxÃ¢Â¬ËœxÃ¢Â¬ËœÃ¢ÂÂ¾Ã‚Â¨ Ã¢Ë†â€™ IxÃ¢Â¬ËœzÃ¢Â¬ËœÃ¢ÂÂºÃ‚Â¨ = msghÃ¢ÂÂ¾ + msVhÃ¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² + M x Ã¢Ë†â€™ msghÃ¢ÂÂª + msgay

Ã‹â„¢ t,f Ã¥â€¦Â²

+ Fw,yhw Ã¢Ë†â€™ k f Ã¥â€¦Â±Ã¢ÂÂ¾ Ã¢Ë†â€™ Ã¢ÂÂ¾t,f Ã¥â€¦Â² Ã¢Ë†â€™ l f Ã¥â€¦Â±Ã¢ÂÂ¾Ã‹â„¢ Ã¢Ë†â€™ Ã¢ÂÂ¾

+ u f Ã¢Ë†â€™ krÃ¥â€¦Â±Ã¢ÂÂ¾ Ã¢Ë†â€™ Ã¢ÂÂ¾t,rÃ¥â€¦Â² Ã¢Ë†â€™ lrÃ¥â€¦Â±Ã¢ÂÂ¾Ã‹â„¢ Ã¢Ë†â€™ Ã¢ÂÂ¾Ã‹â„¢ t,rÃ¥â€¦Â² + ur

Ã¥â€¦Â±14Ã¥â€¦Â²

rFy,f = Ã¢Ë†â€™ mu,f VÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² + mu,f gÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂ¾t,f

B0 = EÃ¢Ë†â€™1

+ mu,f gÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂª Ã¢Ë†â€™ arollIxÃ¢Â¬ËœxÃ¢Â¬Ëœm f /m Ã¢Ë†â€™ mu,f ayÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²

Ã‹â„¢ t,f Ã¥â€¦Â² + u f

+ kt,f Ã¢ÂÂ¾t,f Ã¢Ë†â€™ k f Ã¥â€¦Â±Ã¢ÂÂ¾ Ã¢Ë†â€™ Ã¢ÂÂ¾t,f Ã¥â€¦Â² Ã¢Ë†â€™ l f Ã¥â€¦Â±Ã¢ÂÂ¾Ã‹â„¢ Ã¢Ë†â€™ Ã¢ÂÂ¾

Ã¥â€¦Â±15Ã¥â€¦Â²

306 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

Ã¥â€ â€¹

0 0 1 1 0 0

0 0 1 0 1 0

Ã¥â€ Å’

B1 = EÃ¢Ë†â€™1Ã¥â€¦Â³Ã¢ÂÂ®Y Ã¢ÂÂ¦ Ã¢Ë†â€™ Ã¢ÂÂ®NÃ¢ÂÂ¦ 0 rÃ¢ÂÂ®Y Ã¢ÂÂ¦,f 0 0 Ã¥â€¦Â´T

Ã¥â€¦Â±20Ã¥â€¦Â²

Ã¥â€¦Â±21Ã¥â€¦Â²

A = EÃ¢Ë†â€™1

Ã¥â€ Â¤

Ã¢ÂÂ®Y Ã¢ÂÂ¤

Ã¢ÂÂ®Y Ã¢ÂÂºÃ‹â„¢ + mV

0

0

0

Ã¢Ë†â€™ Ã¢ÂÂ®NÃ¢ÂÂ¤

Ã¢Ë†â€™ Ã¢ÂÂ®NÃ¢ÂÂºÃ‹â„¢

0

0

0

0

rÃ¢ÂÂ®Y Ã¢ÂÂ¤,f

0

0

msgh Ã¢Ë†â€™ k f Ã¢Ë†â€™ kr Ã¢Ë†â€™ l f Ã¢Ë†â€™ lr

kf

msVh

rÃ¢ÂÂ®Y Ã¢ÂÂºÃ‹â„¢ ,f Ã¢Ë†â€™ mu,f VÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²

Ã¢Ë†â€™ lf

k f + kt,f + mu,f gÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²

Ã¢Ë†â€™ kf

rÃ¢ÂÂ®Y Ã¢ÂÂ¤,r rÃ¢ÂÂ®Y Ã¢ÂÂºÃ‹â„¢ ,r Ã¢Ë†â€™ mu,rVÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²

0

C = EÃ¢Ë†â€™1

0

Ã¢Ë†â€™ kr

Ã¢Ë†â€™ lr

0

k f + kt,r + mu,rgÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²

0

1

0

0

0

Ã¥â€ â€¹

kr

Fw,y Ã¢Ë†â€™ mgÃ¢ÂÂª + may,M z,M x Ã¢Ë†â€™ msghÃ¢ÂÂª + msayh + Fw,yhw,mu,f gÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂª Ã¢Ë†â€™ mu,f ayÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²,

mu,rgÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²Ã¢ÂÂª Ã¢Ë†â€™ mu,rayÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²,0

E=

Ã¥â€ Â¤

Ã¢Ë†â€™ mV

0

0

I zÃ¢Â¬ËœzÃ¢Â¬Ëœ

m sh

0 Ã¢Ë†â€™ I xÃ¢Â¬ËœzÃ¢Â¬Ëœ

Ã¢Ë†â€™ I xÃ¢Â¬ËœzÃ¢Â¬Ëœ 0

Ã¢Ë†â€™ msVh

mu,f VÃ¥â€¦Â±hu,f Ã¢Ë†â€™ rÃ¥â€¦Â²

mu,rVÃ¥â€¦Â±hu,r Ã¢Ë†â€™ rÃ¥â€¦Â²

0

N and Y terms in Ã¥â€¦Â³Eqs. Ã¥â€¦Â±21Ã¥â€¦Â² and Ã¥â€¦Â±22Ã¥â€¦Â²Ã¥â€¦Â´ are partial derivatives of net

tire yaw moment or lateral force, and the detailed definitions can

be found in the nomenclature. The Runge-Kutta method will be

used to solve dynamic equations in time domain with a time step

of dt = 0.001 s.

Criteria of Wheel Being Lifted up or Sideslip

Taking the summation of moment about the point on the ground

plane at the midtrack position, one can get the weight transfer

ratio between the left and right wheels

Wtrans = Ã¥â€¦ÂµÃ¥â€¦Â³mVÃ¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² + may + mgÃ¥â€¦Â±Ã¢ÂÂ¾ Ã¢Ë†â€™ Ã¢ÂÂªÃ¥â€¦Â²Ã¥â€¦Â´ Ã¢Â«Â» hcm + Fw,yÃ¥â€¦Â±hw + rÃ¥â€¦Â²

+ M x + arollIxÃ¢Â¬ËœxÃ¢Â¬ËœÃ¥â€¦Â¶/d

0

Ã¥â€¦Â±25Ã¥â€¦Â²

Wheel Being Lifted up

When the weight transferred between the left and right wheels is

larger than a half of the vehicle weight minus a half of the vertical

wind force Ã¥â€¦Â±lift forceÃ¥â€¦Â², there is no reaction force existing on one

side of wheels. In addition, the roll angle between the sprung

mass and the suspension system typically cannot exceed 6 or 7Ã‚Â°

due to the mechanical restraints of the suspension movements

Ã¥â€¦Â±Sampson 2000Ã¥â€¦Â². Thus if either of the following two criteria is

satisfied, the wheel is believed to be lifted up

Wtrans Ã¢Â¬Å½ mg/2 Ã¢Ë†â€™ Fw,z/2

Ã¥â€¦Â±26Ã¥â€¦Â²

i

i

Ã¨â€°Å’ Ã¢ÂÂ¾cri or Ã¢ÂÂ¾i Ã¢Ë†â€™ Ã¢ÂÂ¾t,r

Ã¨â€°Å’ Ã¢ÂÂ¾cri

Ã¢ÂÂ¾i Ã¢Ë†â€™ Ã¢ÂÂ¾t,f

Ã¥â€¦Â±27Ã¥â€¦Â²

or

where Ã¢ÂÂ¾cri = maximum allowable relative roll-over angle due to

the mechanical restraints Ã¥â€¦Â±e.g., 7Ã‚Â°Ã¥â€¦Â².

Sideslip

The front or the rear wheel will start to sideslip when the actual

lateral tire forces Fy,f or Fy,r quantified with Ã¥â€¦Â³Eqs. Ã¥â€¦Â±1Ã¥â€¦Â² and Ã¥â€¦Â±2Ã¥â€¦Â²Ã¥â€¦Â´

exceeds the corresponding sideslip critical friction forces, respectively

0

0

0

0

0

1

0

0

0

0

I xÃ¢Â¬ËœxÃ¢Â¬Ëœ

Ã¢Ë†â€™ l f Ã¢Ë†â€™ lr

0

0

0

Ã¢Ë†â€™ lf 0

0 Ã¢Ë†â€™ lr

0

0

Ã¥â€ Â¥

Ã¥â€ Å’

Ã¥â€ Â¥

Ã¥â€¦Â±22Ã¥â€¦Â²

T

Ã¥â€¦Â±23Ã¥â€¦Â²

Ã¥â€¦Â±24Ã¥â€¦Â²

max

Fy,f Ã¢Â¬Å½ Fla,f

= Ã¢ÂÂ®Fz,f

Ã¥â€¦Â±28Ã¥â€¦Â²

max

= Ã¢ÂÂ®Fz,r

Fy,r Ã¢Â¬Å½ Fla,r

Ã¥â€¦Â±29Ã¥â€¦Â²

or

where Fz,f and Fz,r = vertical reaction forces on the front and rear

max

max

axles, respectively; Fla,f

and Fla,r

= sideslip critical friction forces

of the front and the rear wheels, respectively; and Ã¢ÂÂ® = static lateral

friction coefficient. The longitudinal rolling resistance of the tires

in the driving direction, which is related to vehicle driving speed

and tire condition Ã¥â€¦Â±temperature, inflation pressure, and so onÃ¥â€¦Â², is

relatively insignificant to the vehicle stability compared to the

side friction force. Therefore, the longitudinal rolling resistance is

not considered in this model.

Two sets of criteria, as shown in Ã¥â€¦Â³Eqs. Ã¥â€¦Â±26Ã¥â€¦Â²Ã¢â‚¬â€œÃ¥â€¦Â±29Ã¥â€¦Â²Ã¥â€¦Â´, will be

checked at each time step to identify whether any wheel will be

lifted up or will start to sideslip, under either of which, the corresponding new dynamic equations as introduced below will be

used to continue the simulation.

Updated Vehicle Dynamic Model

After Wheels Being Lifted up

After wheels on one side of the vehicle are lifted up, the suspension system of a vehicle cannot generate resistant moment anymore and the roll center moves toward the wheels which are not

yet lifted up. Accordingly, in Ã¥â€¦Â³Eqs. Ã¥â€¦Â±12Ã¥â€¦Â²Ã¢â‚¬â€œÃ¥â€¦Â±16Ã¥â€¦Â²Ã¥â€¦Â´, IxÃ¢Â¬ËœxÃ¢Â¬Ëœ, IzÃ¢Â¬ËœzÃ¢Â¬Ëœ, and IxÃ¢Â¬ËœzÃ¢Â¬Ëœ

will be changed to IÃ¢Â¬Ëœx x , IzÃ¢Â¬Ëœ z , and IxÃ¢Â¬Ëœ z , which are moments of

Ã¢Â¬ËœÃ¢Â¬Ëœ Ã¢Â¬ËœÃ¢Â¬Ëœ

Ã¢Â¬ËœÃ¢Â¬Ëœ

inertia about the wheels remaining on the ground in three directions, respectively. kt,iÃ¢ÂÂ¾t,i in Eqs. Ã¥â€¦Â±12Ã¥â€¦Â²Ã¢â‚¬â€œÃ¥â€¦Â±16Ã¥â€¦Â² will be changed to

kt,iÃ¢ÂÂ¾Ã¢Â´Â±t,i, where Ã¢ÂÂ¾Ã¢Â´Â±t,i is the value of Ã¢ÂÂ¾t,i when the wheels are just

lifted up. In addition, in Eqs. Ã¥â€¦Â±12Ã¥â€¦Â²Ã¢â‚¬â€œÃ¥â€¦Â±16Ã¥â€¦Â², all the moment reference

arms are changed to the distances to the wheels remaining on the

ground from, originally, to the suspension roll center of the vehicle due to the fact that the vehicle starts to rotate about the

contact points of the wheels remaining on the ground once the

wheels on one side are lifted up.

JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010 / 307

After Starting to Sideslip

When a wheel starts to sideslip, the lateral slipping friction forces

can be assumed approximately equal to the sideslip critical fricmax

max

tion forces Fla,f

and Fla,r

that the road can generate for the left

and right wheels, respectively. Before the vehicle hits roadside or

another object, Fy,f and Fy,r in Eqs. Ã¥â€¦Â±12Ã¥â€¦Â², Ã¥â€¦Â±15Ã¥â€¦Â², and Ã¥â€¦Â±16Ã¥â€¦Â² will be

max

max

changed to Fla,f

and Fla,r

, respectively. As a result, the vehicle

will laterally slip with the slipping acceleration aslip which can be

derived as

max

Ã‚Â¨

aslip = Ã¥â€¦Â³mVÃ¥â€¦Â±Ã¢ÂÂ¤Ã‹â„¢ + Ã¢ÂÂºÃ‹â„¢ Ã¥â€¦Â² Ã¢Ë†â€™ Fmax

f,f Ã¢Ë†â€™ F f,r + Fw,y Ã¢Ë†â€™ mgÃ¢ÂÂª + ma y Ã¢Ë†â€™ mshÃ¢ÂÂ¾Ã¥â€¦Â´/m

Ã¥â€¦Â±30Ã¥â€¦Â²

Vehicle Accident Assessment Criteria

Vehicle Rollover

A vehicle ultimately rolls over only when the y value of the center

of gravity exceeds the y-coordinate of the wheel. Therefore, the

corresponding roll angle at the moment when the vehicle ultimately rolls over is set as the criterion to identify the occurrence

of rollover accidents

Ã¢ÂÂ¾ Ã¢Â¬Å½ arc sinÃ¥â€¦Â±d/2Ã¥â€ â€˜d2/4 + h2cmÃ¥â€¦Â² + Ã¢ÂÂª

only take 2 s to go through a ramp at one specific driving speed.

If the CST for this vehicle under the specific combination of the

adverse environmental and driving conditions is larger than 2 s,

the accident may not really happen as the environmental conditions will change right after 2 s. One common situation is when

the truck suddenly experiences a change of strong wind gust load

on the vehicle Ã¥â€¦Â±i.e., both imposing and removingÃ¥â€¦Â² due to special

topographical conditions, such as getting into a valley from open

areas or passing a bridge tower or mountain and getting to open

areas.

According to the Green book Ã¥â€¦Â±AASHTO 2004Ã¥â€¦Â², the median

reaction time of drivers is 0.66 s based on the data from 321

drivers. The design reaction time is 2.5 s which exceeds 90th

percentile of reaction time for all drivers Ã¥â€¦Â±AASHTO 2004Ã¥â€¦Â². In the

present study, both Ã¢â‚¬Å“median reaction timeÃ¢â‚¬Â Ã¥â€¦Â±0.66 sÃ¥â€¦Â² and Ã¢â‚¬Å“design

reaction timeÃ¢â‚¬Â Ã¥â€¦Â±2.5 sÃ¥â€¦Â² will be checked. If the CST is larger than

the reaction time of the driver, the driver may have sufficient

time to take appropriate actions Ã¥â€¦Â±e.g., reduce speedsÃ¥â€¦Â² to possibly

prevent the occurrence of accidents. Obviously, CDS suggests

the appropriate driving speed assuming the driver has sufficient

time to react while CST discloses the information about whether

the driver has enough time to react under a particular driving

condition.

Ã¥â€¦Â±31Ã¥â€¦Â²

where d = track width of the truck; hcm = height of the mass center

of the truck; and Ã¢ÂÂª = road superelevation.

Sideslip

Once a vehicle starts to sideslip, driver operations such as applying steering or brakes usually have little effect on stopping the

motion before the vehicle hits an object Ã¥â€¦Â±e.g., road side curbs,

other vehiclesÃ¥â€¦Â², which may or may not cause tripped rollover.

With the purpose of introducing the general model in this study,

the travel distance after sideslip starts will be the critical variable

to be investigated without dealing with different site-specific road

conditions Ã¥â€¦Â±e.g., different distances from the center of the driving

lane to the curbÃ¥â€¦Â². It is noted that any particular tripped rollover

scenario can be simulated with the proposed model as long as the

specific descriptions of the obstacle Ã¥â€¦Â±e.g., locations, size, and materialÃ¥â€¦Â² are available. Due to the limited scope of the present study,

different particular tripped rollover scenarios will not be discussed in this paper.

CDS and CST

For any given hazardous condition and any specific vehicle, the

occurrence of single-vehicle accidents is significantly related

to excessive driving speeds. To maintain an appropriate driving

speed to balance the safety and efficiency is obviously critical.

Therefore, for the proposed deterministic model, the Ã¢â‚¬Å“critical

driving speed Ã¥â€¦Â±CDSÃ¥â€¦Â²Ã¢â‚¬Â is the highest allowable driving speed without causing any type of accidents under a specific combination of

environmental and vehicular conditions. In the future reliabilitybased model, it will become the highest allowable driving speed

which results in the crash risk at the desired level.

In addition to the CDS which has been studied in some existing studies Ã¥â€¦Â±e.g., Baker 1991; Chen and Cai 2004; Guo and Xu

2006; SigbjÃƒÂ¶rnsson and SnaebjÃƒÂ¶rnsson 1998; SnÃƒÂ¦bjÃƒÂ¶rnsson et al.

2007Ã¥â€¦Â² another critical variable which has been rarely discussed is

the Ã¢â‚¬Å“critical sustained time Ã¥â€¦Â±CSTÃ¥â€¦Â².Ã¢â‚¬Â CST is the minimum time

period required to sustain the specific combination of the adverse

environments Ã¥â€¦Â±e.g., wind speed, curvatureÃ¥â€¦Â² and the driving conditions Ã¥â€¦Â±e.g., specific driving speedÃ¥â€¦Â². For example, a vehicle may

Parametric Study

A numerical example will be conducted for demonstration purposes. Although the simulation process as introduced above can

be applied to any type of single-body vehicle, a truck model is

adopted in the parametric study because of its relatively larger

safety risks under hazardous driving conditions. Comparative

studies among different types of vehicles are beyond the scope of

the present study.

Truck Model

A singe-body truck model will be used in the numerical studies

and the same parameters from Winkler and Ervin Ã¥â€¦Â±1999Ã¥â€¦Â² are

adopted Ã¥â€¦Â±Table 1Ã¥â€¦Â². In automobile engineering, the steering angle Ã¢ÂÂ¦

is typically expressed as Ã¢ÂÂ¦ = L / R Ã¥â€¦Â±neutral steerÃ¥â€¦Â², where L is the

wheelbase of the vehicle, R is the turning radius of the curved

path, and the steering angle can be determined for each different

R. The corresponding superelevation is considered for different R

and typical speed limits according to AASHTO Ã¥â€¦Â±2004Ã¥â€¦Â². Although

there are some limited studies on quantifying the steering angle

due to driver behavior Ã¥â€¦Â±Baker 1991; Chen and Cai 2004Ã¥â€¦Â², to the

writersÃ¢â‚¬â„¢ knowledge, there is not yet a well-accepted model which

can accurately relate the steering angle and the motion of vehicles

from existing literature. Besides, existing studies also showed

limited impact of driver behavior of steering on single-vehicle

accidents Ã¥â€¦Â±Chen and Cai 2004Ã¥â€¦Â². Therefore, in the present study,

impacts of driving behavior on steering angles will not be considered. However, it is noted that the present model can easily incorporate the driver behavior model on steering angles when a

reliable one becomes available in the future.

Adverse/Hazardous Driving Environments

It is well known that the same vehicle experiences different accident risks under different driving environments. For large trucks,

some driving environments can be hazardous which often cause

rollover or sideslip accidents. These adverse driving environments

308 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

Table 1. Parameters of the Single-Body Truck Model

Parameters

ms

mu,f , mu,r

a f , ar

h

hcm

hw Ã¥â€¦Â±hreÃ¥â€¦Â²

r

d

Ã¢ÂÂ®

u f , ur

Value

Parameters

Value

23,000 lb

1,202 lb, 4603 lb

14.8 ft, Ã¢Â«Âº5.22 ft

2.12 ft

3.98 ft

5.46 ft

2.42 ft

6 ft

1

0 in. lb, 0 in. lb

C f , Cr

k f , kr

l f , lr

kt,f , kt,r

hu,f , hu,r

Ixx

Ixz

Izz

A

Ã¢ÂÂ½

714.6 lb/deg, 2,544 lb/deg

24,119 in. lb/deg, 245,826 in. lb/deg

393 lb/deg, 938 lb/deg

31,8491 in. lb/deg, 274,583 in. lb/deg

1.67 ft, 1.67 ft

66,132 in. lb s s

31,799 in. lb s s

465,180 in. lb s s

107.6 ft2

90Ã‚Â°

typically include strong crosswind gust, slippery road surface

which is covered by snow or ice, a curved path, or with dynamic

excitations from the supporting structures Ã¥â€¦Â±e.g., roughness of

pavement and/or bridge structureÃ¥â€¦Â². These adverse driving environments may work individually or integrally to significantly increase the crash risk of trucks. In the present study, three different

road surface conditions Ã¥â€¦Â±dry, snow-covered, and icyÃ¥â€¦Â² and the situation with excitations from supporting structures will be considered along with different wind gust conditions, on both straight

and curved paths. To capture the most critical scenarios, wind is

assumed to be perpendicular to the driving direction of the vehicle all the time, including on both straight and curved paths.

Given the randomness of actual wind directions in nature, this

assumption will lead to slightly more conservative results than the

reality, which is usually preferred in engineering fields. However,

the present model can easily consider varying wind directions

during curving when one specific initial wind direction is given.

In the following sections, CST, CDS, and transient accidentrelated response in time domain will be investigated for various

conditions.

Critical Sustained Time of Accidents

Straight Road

When the truck is driven on a straight road with dry road surface,

rollover accidents are found to occur first. Fig. 3 shows the relationship between CST of rollover, the wind speed U, and the

driving speed V. The lowest V of each curve also suggests the

CDS under which the accident may happen. There are two hori-

Fig. 3. CST of rollover on a straight and dry road

zontal lines shown in the figure which suggest the median Ã¥â€¦Â±0.66 sÃ¥â€¦Â²

and design reaction time Ã¥â€¦Â±2.5 sÃ¥â€¦Â², respectively. It can be found

from Fig. 3 that the CST of rollover decreases when U or V

increases. When the wind speed is relatively low Ã¥â€¦Â±lower than 45

mphÃ¥â€¦Â², the required CST to roll over a truck quickly drops when

the vehicle driving speed increases. For instance, when the truck

moves in a speed of 70 mph and the wind speed is 35 mph, it

requires about 1.7 s to roll over the truck. Depending on the

driving experience and how fast an individual driver senses and

reacts to the danger, a rollover accident may or may not actually

happen. When the wind speed is more than 50 mph, it only takes

around 0.6 s to roll over the truck with about 25-mph driving

speed and there is no significant difference for the CST of rollover when the wind speed keeps increasing. As compared to the

median reaction time Ã¥â€¦Â±0.66 sÃ¥â€¦Â², 0.6 s is usually too short for most

drivers to react and a rollover accident is very likely to happen in

this scenario. An accurate accident risk assessment based on the

CST relies on a reliability-based risk assessment model considering the uncertainties of reaction times among different drivers. It

will be the future task for the writers based on the proposed

deterministic model. It is also noted that none of the scenarios in

Fig. 3 can satisfy the design reaction time requirement Ã¥â€¦Â±2.5 sÃ¥â€¦Â² as

specified in AASHTO, which is known to be very conservative.

When road surface is covered by snow or ice, sideslip accidents usually happen first. Fig. 4 shows the relationship between

the CST of sideslip and the driving speed V when the truck moves

straight on a snow-covered and ice-covered road surfaces, along

with different wind speeds. For any higher driving speeds beyond

the x-coordinate of each curve in Fig. 4, rollover accidents will

Fig. 4. CST of sideslip accident on a straight road

JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010 / 309

Fig. 5. CST of rollover accident on a dry curved road

Fig. 7. CST of sideslip accident on ice-covered curved roads

happen first, as marked in the figure with the text Ã¢â‚¬Å“rollover.Ã¢â‚¬Â

Under the same wind condition, driving faster Ã¥â€¦Â±e.g., higher VÃ¥â€¦Â² will

require a shorter duration of the sustained hazardous condition

Ã¥â€¦Â±i.e., smaller CSTÃ¥â€¦Â² to finally make the accident happen.

When the truck is on icy road surface, the CST remains relatively constant when the driving speed is above 20 mph Ã¥â€¦Â±Fig. 4Ã¥â€¦Â².

The CST values are all smaller than the median reaction time

when the wind speed is more than 40 mph, which suggest sideslip

accidents are very difficult to be avoided by majority of drivers.

When the truck is on icy road surface with 40-mph wind speed, it

is also found that the CST actually slightly increases with the

driving speed and this trend continues until the driving speed

reaches 30 mph when the CST becomes nearly constant despite

further increase of the driving speed. This is different from the

observation under the snow-covered situation, and it is probably

related to the unique vehicle movement manner on ice when the

lateral friction is very small. As shown in Fig. 4, when wind is

strong Ã¥â€¦Â±U = 40 mphÃ¥â€¦Â², the truck will experience rollover accidents

first when the driving speed is over 57.5 mph on both snowcovered and icy road surfaces.

can be found that the respective CST considerably decreases

under the same curving situation when the wind speed increases.

For example, when the curving radius R is 130 ft Ã¥â€¦Â±a typical value

of many highway rampsÃ¥â€¦Â², the driving speed of 42.5 mph and

higher may cause rollover accidents with the CST about 3 s when

there is no wind. When the wind speed is 20 mph, the driving

speed of 37.5 mph or higher will cause rollover accidents with the

CST of about 2 s on the same path. When the wind speed is

further increased to 40 mph, the truck will roll over with the

driving speed of 30 mph and the CST is about 0.6 s. In reality,

wind gust with 20Ã¢â‚¬â€œ40 mph wind speed is pretty common on

highways and 0.6 s is typically not enough for most drivers to

react. As we often observe on highways, curving operations of

large trucks in windy weather, especially under a sharp curve

Ã¥â€¦Â±e.g., ramp or in mountain areasÃ¥â€¦Â², are much more vulnerable than

the situation without strong wind. By comparing the differences

of results for R = 130 and 260 ft under various wind speeds, it is

found that the different radiuses affect the CST significantly when

wind is not strong. While wind is strong Ã¥â€¦Â±e.g., U = 40 mphÃ¥â€¦Â², different radiuses only affect the CST slightly, which suggests that

the dominant impact shifts from the geometric condition Ã¥â€¦Â±curvatureÃ¥â€¦Â² to environmental condition Ã¥â€¦Â±windÃ¥â€¦Â².

Fig. 6 gives the results of the CST of sideslip under different

combinations of driving speeds and curvature radiuses when the

wind speed is 0 or 20 mph while the road surface is covered by

snow. It is found that when the radius R is about 130 ft, 60-mph

driving speed without existence of wind, or 50-mph driving speed

with 20-mph wind will all cause the CST to be lower than the

median reaction time.

Fig. 7 shows the CDS under different radiuses when the road

surface is covered by ice. Similar to the results for the snowcovered road on curves and icy surface on a straight road, sideslip

accidents will dominate and the truck may experience sideslip

accidents when it is driven in a speed of 45 mph on a curve with

a radius of 260 ft or the driving speed of 25 mph on a curve with

a radius of 130 ft when there is no wind. When wind speed

increases to 20 mph, the CDS will be changed to 17.5 mph on a

curve with a radius of 260 ft or 15 mph on a curve with a radius

of 130 ft. For all these cases, the CST is generally between the

median and design reaction time.

Curved Roads

Fig. 5 shows the relationship between the CST of rollover and the

driving speed V under different radiuses of curvature R and wind

conditions. Two representative curve radiuses Ã¥â€¦Â±130 and 260 ftÃ¥â€¦Â²

and three wind conditions Ã¥â€¦Â±U = 0, 20, and 40 mphÃ¥â€¦Â² are studied. It

Fig. 6. CST of sideslip accident on snow-covered curved roads

Excitations from Supporting Infrastructures

When a vehicle moves on roadways, vehicles will be excited to

vibrate in several directions by the surface roughness on the roadway Ã¥â€¦Â±Xu and Guo 2003; Chen and Cai 2004Ã¥â€¦Â². When a vehicle

310 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

Fig. 8. CST of rollover on a supporting structure

moves on a bridge, dynamic interactions between the bridge and

the vehicle will cause the vehicle to vibrate more significantly

Ã¥â€¦Â±Cai and Chen 2004Ã¥â€¦Â². In either case Ã¥â€¦Â±i.e., on pavement or on

bridgesÃ¥â€¦Â², the vehicle will experience additional accelerations as a

type of base excitations. In the present vehicle accident assessment model, safety behavior of the truck will be evaluated

through a general consideration of excitations from supporting

infrastructures by defining accelerations in the lateral direction

ay and that in rolling direction aroll as base excitations. The relationship between rollover critical time and ay as well as aroll

Ã¥â€¦Â±U = 40 mph, V = 40 mphÃ¥â€¦Â² is demonstrated in Fig. 8. When aroll

Ã¢Â¬Å½ 0.4 rad/ s2, rollover accidents will occur even when the wind

speed and vehicle velocity are both not very high. It is found that

the rolling acceleration caused by interaction with supporting

structures is pretty critical to the truck safety and will increase

the chance of having accidents when all other conditions are the

same. Since considerable rolling excitations may exist on some

bridges, it suggests that vehicles are more vulnerable to rollover

accidents on a vibrating bridge, which has also been observed in

existing studies Ã¥â€¦Â±Guo and Xu 2006; Chen and Cai 2004Ã¥â€¦Â².

Critical Driving Speeds of Accidents

Straight Roads

Assuming that the CST of the specific environmental conditions

is satisfied Ã¥â€¦Â±i.e., the actual time duration of a specific set of conditions is longer than the required CSTÃ¥â€¦Â², Fig. 9 shows the CDS of

the truck under different wind conditions on dry Ã¥â€¦Â³Fig. 9Ã¥â€¦Â±aÃ¥â€¦Â²Ã¥â€¦Â´, snowcovered Ã¥â€¦Â³Fig. 9Ã¥â€¦Â±bÃ¥â€¦Â²Ã¥â€¦Â´, and icy road surfaces Ã¥â€¦Â³Fig. 9Ã¥â€¦Â±cÃ¥â€¦Â²Ã¥â€¦Â´.

With the increase of the wind speed, the CDS generally decreases. It can be found from Fig. 9Ã¥â€¦Â±aÃ¥â€¦Â² that a sideslip accident will

not occur before a rollover accident does first when the truck

moves on a dry straight path. Generally speaking, depending on

the driving speed of the truck, it is found that there exist various

levels of rollover risk when the wind speed exceeds 35 mph.

When the wind speed is more than 55 mph, even the truck in still

Ã¥â€¦Â±V = 0 mphÃ¥â€¦Â² will have the risk of being blown over. Fig. 9Ã¥â€¦Â±bÃ¥â€¦Â²

shows the critical U or V under which at least one type of accident may happen when the truck is driven on a snow-covered

road surface. It is easy to find that when U and V are not high, no

rollover or sideslip accidents will happen. If the wind speed is

moderate, sideslip accident will likely happen when the vehicle

driving speed is more than 20 mph. When the wind speed is more

Fig. 9. CDSs on a straight road with various surface conditions: Ã¥â€¦Â±aÃ¥â€¦Â²

dry road surface; Ã¥â€¦Â±bÃ¥â€¦Â² snow-covered road surface; and Ã¥â€¦Â±cÃ¥â€¦Â² icy road

surface

than 50 mph, rollover accidents instead of sideslip will happen

first. Fig. 9Ã¥â€¦Â±cÃ¥â€¦Â² shows the critical U or V when the truck moves on

an icy road surface assuming the CST of sideslip is satisfied. By

comparing Figs. 9Ã¥â€¦Â±aÃ¢â‚¬â€œcÃ¥â€¦Â², it is obvious that sideslip accidents will

be more prone to occur first than rollover accidents when the road

kinetic friction coefficient decreases. Sideslip accidents can happen even when the wind speed is below 20 mph and the vehicle

JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010 / 311

Fig. 10. CDSs on dry roads with different radius and wind conditions

driving speed is 25 mph on icy roads. This observation is consistent with the frequent sideslip accidents observed in cold regions.

Curved Roads

Fig. 10 gives the results of CDS under different wind speeds U

and radiuses R when the road surface is dry. It can be found

that with the increase of wind speeds or the decrease of radius,

the CDS decreases dramatically. When wind is very weak

Ã¥â€¦Â±U Ã¢Â¬Â 10 mphÃ¥â€¦Â², any radius lower than 330 ft will impose considerable safety threats to the truck with a driving speed about

65 mph or higher. A further decrease of the radius to 165 and

100 ft leads to a dramatic decrease of the CDS to around 50 and

37.5 mph, respectively. With the increase of wind speed, the CDS

under the same radius will also significantly decrease compared to

the case only with breeze. For example, when the wind speed

increases from 10 to 40 mph, the CDS for a radius of 360 ft will

decrease from 70 to 35 mph.

Fig. 11 gives the CDS results under different curvature radiuses when the road surface is covered by snow. It can be found

that sideslip will be the only accident type which will happen first

Ã¥â€¦Â±if there is an accidentÃ¥â€¦Â². It is found that depending on the driving

speeds, the curvature radius of 590 ft and lower along with 20mph wind speed will possibly cause accidents. With a radius of

130 ft, 30 mph will be the CDS for the truck in the present study

if there is no wind. Due to the high number of possible combinations of wind, driving speed, and curvature radius, a full parametric study of all possible scenarios will not be discussed here. By

comparing Fig. 11Ã¥â€¦Â±aÃ¥â€¦Â² with Fig. 11Ã¥â€¦Â±bÃ¥â€¦Â², it can be found that if the

driving speed is more than 35 mph and the radius of the curved

road is more than 130 ft, the possibility of sideslip increases dramatically when the wind speed changes from 0 to 20 mph.

Fig. 12 shows the CDS under different radiuses when the road

is covered by ice. Two different wind speeds Ã¥â€¦Â±0 and 20 mphÃ¥â€¦Â² are

studied. Similar to the results for snow-covered curved roads and

icy straight roads, sideslip accidents will dominate and the truck

may experience sideslip accidents when it is driven in a speed of

60 mph on the curved road with a radius of 330 ft or in a driving

speed of 25 mph on the curve with a radius of 130 ft when there

is no wind. We can find that the truck with the driving speed more

than 20 mph is prone to sideslip accidents when the radius is

more than 330 ft and the wind speed is 20 mph. Comparing Figs.

12Ã¥â€¦Â±a and bÃ¥â€¦Â², people can find that even very moderate wind can

affect the stability of the truck significantly on curved roads covered by ice.

Fig. 11. CDSs on snow-covered roads with various radiuses: Ã¥â€¦Â±aÃ¥â€¦Â² U

= 0 mph; Ã¥â€¦Â±bÃ¥â€¦Â² U = 20 mph

Transient Accident-Related Responses

Fig. 13 shows the time-history results of course angle and lateral

displacement of the truck on snow-covered and icy road surfaces,

respectively, when V = 32.5 mph and U = 47.5 mph. Fig. 14 displays the corresponding time history of lateral friction force.

It can be found that when wind gust is applied on the truck moving on the snow-covered surface, after a slight lateral displacement about 0.6 ft in Fig. 13Ã¥â€¦Â±bÃ¥â€¦Â², the joint effect of wind-induced

lateral force and moment will change the vehicle course angle

Ã¥â€¦Â³Fig. 13Ã¥â€¦Â±aÃ¥â€¦Â²Ã¥â€¦Â´ and bring the driving direction of the truck opposite

to the wind direction until the truck moves laterally about 1.8 ft,

when the lateral friction force of the rear tire reaches the sideslip

critical friction force Ã¥â€¦Â±Fig. 14Ã¥â€¦Â². So at 0.8 s after wind gust is

applied on the truck, the truck starts to sideslip after it has traveled laterally about 1.8 ft from its original path. As shown in

Fig. 13Ã¥â€¦Â±aÃ¥â€¦Â², the course angle is lower than 2Ã‚Â° when sideslip just

happens. But 0.6 s after the vehicle starts to sideslip, the course

angle is about 11Ã‚Â°, which suggests that a strong rotational movement of the truck has occurred after the tires start to sideslip.

When the road is covered by ice, as shown in Fig. 13Ã¥â€¦Â±aÃ¥â€¦Â², the

course angle is lower than Ã¢Â«Âº2Ã‚Â° when sideslip happens. But 0.6 s

after the truck starts to sideslip, the course angle is about 4Ã‚Â°,

which means that strong rotational motion of the truck has happened under the strong wind load after the tires start to sideslip.

Fig. 13Ã¥â€¦Â±bÃ¥â€¦Â² suggests that the lateral displacement of the truck on

icy roads is pretty straightforward and gradually increasing along

the wind direction, which is different from that observed on the

312 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

Fig. 13. Time histories of vehicle course angle and lateral distance:

Ã¥â€¦Â±aÃ¥â€¦Â² course angle; Ã¥â€¦Â±bÃ¥â€¦Â² lateral displacement

Fig. 12. CDSs on icy roads with various radiuses: Ã¥â€¦Â±aÃ¥â€¦Â² U = 0 mph; Ã¥â€¦Â±bÃ¥â€¦Â²

U = 20 mph

snow-covered road. It is found that the lateral friction force of the

rear tire increases quickly over time and will exceed the critical

friction forces and start to sideslip at about 0.5 s Ã¥â€¦Â±Fig. 14Ã¥â€¦Â². While

the same truck is driven in the same speed on a snow-covered

road, it requires 0.8 s to start sideslip Ã¥â€¦Â³Fig. 13Ã¥â€¦Â±aÃ¥â€¦Â²Ã¥â€¦Â´. As discussed

earlier, once sideslip starts, the driver usually can do very little to

regain the control of the vehicle.

Discussions

Compared to existing simulation models, the new model has the

following improvements: Ã¥â€¦Â±1Ã¥â€¦Â² adopting a series of dynamic equations to simulate the transient process of accidents; Ã¥â€¦Â±2Ã¥â€¦Â² for the first

time, combining crosswind, different road surfaces, curving, and

excitations from supporting structures in one single model which

can be used to consider more realistic scenarios; Ã¥â€¦Â±3Ã¥â€¦Â² introducing a

new and important variable CST of each specific combination of

adverse environmental and driving conditions in addition to the

CDS which has been adopted in existing studies. Such a new

variable will be helpful on characterizing the accident risks

more realistically; and Ã¥â€¦Â±4Ã¥â€¦Â² as a holistic deterministic model, the

present study can be used directly to provide useful information

for traffic and emergency management as well as accident preventions. Moreover, the developed model also lays a critical basis

for future reliability-based vehicle safety studies under hazardous

environments.

Several assumptions have been made in the proposed model

due to the lack of more detailed information: Ã¥â€¦Â±1Ã¥â€¦Â² driver behavior

uncertainties on steering angle is not considered due to the lack of

a reliable model. Possible solutions include adopting CST to

study driver behavior and consider uncertainties using the reliability theory and Ã¥â€¦Â±2Ã¥â€¦Â² wind loads on a truck during the rollover

process are assumed to be constant. A preliminary sensitive study

conducted by the writers showed the impact from such an assumption is insignificant. If necessary, this could be further improved by conducting more extensive wind tunnel tests or

applying the reliability theory to appropriately simulate the distributions of wind force coefficients during the rollover process.

More comprehensive parametric studies and site-specific analyses

can easily be conducted based on the model developed in the

present study, which will be reported by the writers later.

Conclusions

An integrated vehicle safety behavior simulation model was developed which adopts more realistic dynamic equations and accident criteria to characterize the transient process of accidents.

Numerical analyses on one type of typical trucks under several

representative scenarios were conducted. Major findings from the

numerical studies are summarized as follows:

Fig. 14. Time history of tire lateral force

JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010 / 313

1.

2.

3.

4.

5.

6.

The new model can be used to predict the safety performance

of vulnerable vehicles under various hazardous weather, topographic, and road surface conditions by using the variables

CST and CDS. The rigorous validation of the new simulation

model depends on the availability of comprehensive experimental data, which is beyond the scope of the present study;

For both straight and curved roads, rollover accidents usually

happen first when the road surface is dry. When the wind

speed is low, the difference of curvature has noteworthy impacts on CST and CDS. With the increase of the wind speed,

wind will gradually replace the curvature to dominate the

impacts on CST and CDS;

Sideslip accidents usually happen first on curved roads when

the road surface is covered by either snow or ice. Both CST

and CDS usually decrease with the increase of the driving

speed or the wind speed significantly. When wind is weak,

the decrease of the curvature radius will cause the CST and

CDS dramatically decrease under the same driving speed.

When wind is strong, the CST and CDS will only slightly

decrease for smaller curvature radiuses. It was found that the

truck is very vulnerable to accidents on curved roads covered

by ice even with the existence of very moderate wind;

On straight roads, the dominant accident type exhibited a

relatively complicated pattern when the road surface is covered by snow or ice. When the wind speed is moderate Ã¥â€¦Â±U is

not more than 50 mphÃ¥â€¦Â², sideslip accidents may happen first

on snow-covered roads depending on the specific combination of wind and driving speeds. On icy roads, sideslip accidents usually happen first when the wind speed is not very

high Ã¥â€¦Â±less than 50 mphÃ¥â€¦Â². When the wind speed exceeds 50

mph, rollover accidents usually will happen first for both

snow-covered and icy road surfaces;

It was found that the road surface condition, wind speed, and

the curvature all play vital roles on the accident risks integrally. Accurately predicting the safety risk under adverse

driving conditions requires a detailed simulation with the developed model on a case by case basis; and

CST was found to be a critical variable which can be used to

conduct a more accurate and personalized risk analysis by

considering the site-specific environmental conditions as

well as reaction time of individual drivers. This will be incorporated into the reliability-based accident model based on

the present study in the future.

Acknowledgments

This publication was partially supported by the Colorado Department of Transportation and the CDC NIOSH Mountain and Plains

Education and Research Center Ã¥â€¦Â±Grant No. 1T42OH009229-01Ã¥â€¦Â².

Its contents are solely the responsibility of the writers and do not

necessarily represent the official views of CDOT or CDC NIOSH

and MAP ERC.

Notation

The following symbols are used in this paper:

a Ã¢Â«Â½ longitudinal distance to axle, measured forward

from center of sprung mass;

ay Ã¢Â«Â½ lateral acceleration caused by the movement of

bridge;

c1 , c2 Ã¢Â«Â½ tire cornering stiffness coefficients, in Fy / Ã¢ÂÂ£ = c1Fz

+ c2Fz2;

cÃ¢ÂÂ£ Ã¢Â«Â½ tire cornering stiffness, measured at rated vertical

tire load;

d Ã¢Â«Â½ track width;

Fw,y Ã¢Â«Â½ lateral wind force;

Fw,z Ã¢Â«Â½ vertical wind force;

Fy Ã¢Â«Â½ lateral tire force;

Fz Ã¢Â«Â½ vertical tire force;

g Ã¢Â«Â½ acceleration due to gravity;

h Ã¢Â«Â½ height of center of sprung mass, measured upwards

from roll center;

hcm Ã¢Â«Â½ height of center of mass for whole truck, measured

upwards from ground;

hs Ã¢Â«Â½ height of center of sprung mass, measured upwards

from ground;

hu Ã¢Â«Â½ height of center of unsprung mass, measured

upwards from ground;

hw Ã¢Â«Â½ height of lateral wind load Fw,y, measured upwards

from roll center;

Ixx Ã¢Â«Â½ roll moment of inertia of sprung mass, measured

about sprung center of mass;

IxÃ¢Â¬ËœxÃ¢Â¬Ëœ Ã¢Â«Â½ roll moment of inertia of sprung mass, measured

about origin of Ã¥â€¦Â±x0 ; y 0 ; z0Ã¥â€¦Â² coordinate system;

Ixz Ã¢Â«Â½ yaw-roll product of inertia of sprung mass,

measured about sprung mass center;

IxÃ¢Â¬ËœzÃ¢Â¬Ëœ Ã¢Â«Â½ yaw-roll product of inertia of sprung mass,

measured about origin of Ã¥â€¦Â±x0 ; y 0 ; z0Ã¥â€¦Â² coordinate system;

Iyy Ã¢Â«Â½ pitch moment of inertia of sprung mass, measured

about sprung mass center;

Izz Ã¢Â«Â½ yaw moment of inertia of sprung mass, measured

about sprung mass center;

IzÃ¢Â¬ËœzÃ¢Â¬Ëœ Ã¢Â«Â½ yaw moment of inertia of total mass, measured

about origin of Ã¥â€¦Â±x0 ; y 0 ; z0Ã¥â€¦Â² coordinate system;

k Ã¢Â«Â½ suspension roll stiffness;

kt Ã¢Â«Â½ tire roll stiffness;

L Ã¢Â«Â½ wheelbase;

l Ã¢Â«Â½ suspension roll damping rate;

M x Ã¢Â«Â½ wind-induced roll moment;

M z Ã¢Â«Â½ wind-induced yaw moment;

m Ã¢Â«Â½ total mass;

ms Ã¢Â«Â½ sprung mass;

mu Ã¢Â«Â½ unsprung mass;

NÃ¢ÂÂ¤ Ã¢Â«Â½ Ã¢Â³Âµ M z / Ã¢Â³ÂµÃ¢ÂÂ¤ = Ã¥â€¦Âº jaÃ¢Â¬Ëœj cÃ¢ÂÂ£,j, partial derivative of net tire yaw

moment with respect to sideslip angle;

NÃ¢ÂÂ¦ Ã¢Â«Â½ Ã¢Â³Âµ M z / Ã¢Â³ÂµÃ¢ÂÂ¦ = Ã¢Ë†â€™aÃ¢Â¬Ëœ1cÃ¢ÂÂ£,1, partial derivative of net tire yaw

moment with respect to steer angle;

NÃ¢ÂÂºÃ‹â„¢ Ã¢Â«Â½ Ã¢Â³Âµ M z / Ã¢Â³ÂµÃ¢ÂÂºÃ‹â„¢ = Ã¥â€¦Âº jaÃ¢Â¬Ëœ2cÃ¢ÂÂ£,j / U, partial derivative of net tire

j

yaw moment with respect to yaw rate;

r Ã¢Â«Â½ height of roll axis, measured upwards from ground;

U Ã¢Â«Â½ forward speed;

u Ã¢Â«Â½ active roll torque;

Y Ã¢ÂÂ¤ Ã¢Â«Â½ Ã¢Â³ÂµFy / Ã¢Â³ÂµÃ¢ÂÂ¤ = Ã¥â€¦Âº jcÃ¢ÂÂ£,j partial derivative of net tire lateral

force with respect to sideslip angle;

Y Ã¢ÂÂ¦ Ã¢Â«Â½ Ã¢Â³ÂµFy / Ã¢Â³ÂµÃ¢ÂÂ¦ = Ã¢Ë†â€™cÃ¢ÂÂ£,1 partial derivative of net tire lateral

force with respect to steer angle;

Y Ã¢ÂÂºÃ‹â„¢ Ã¢Â«Â½ Ã¢Â³ÂµFy / Ã¢Â³ÂµÃ¢ÂÂºÃ‹â„¢ = Ã¥â€¦Âº jaÃ¢Â¬ËœcÃ¢ÂÂ£,j / U partial derivative of net tire

j

lateral force with respect to yaw rate;

Ã¢ÂÂ£ Ã¢Â«Â½ tire slip angle;

Ã¢ÂÂ¤ Ã¢Â«Â½ sideslip angle;

Ã¢ÂÂ¦ Ã¢Â«Â½ steer angle;

Ã¢ÂÂª Ã¢Â«Â½ road superelevation;

314 / JOURNAL OF TRANSPORTATION ENGINEERING Ã‚Â© ASCE / APRIL 2010

Ã¢ÂÂ¾ Ã¢Â«Â½ absolute roll angle of sprung mass;

Ã¢ÂÂ¾t Ã¢Â«Â½ absolute roll angle of unsprung mass;

Ã¢ÂÂ¾Ã¢Â´Â±t Ã¢Â«Â½ roll angle of unsprung mass when one wheel lift

up;

Ã¢ÂÂ¾cri

Ã¢Â«Â½ critical roll angle of unsprung mass;

t

Ã¢ÂÂº Ã¢Â«Â½ heading angle; and

Ã¢ÂÂºÃ‹â„¢ Ã¢Â«Â½ yaw rate.

Subscripts

f Ã¢Â«Â½ front;

j Ã¢Â«Â½ jth axle, counted from front; and

r Ã¢Â«Â½ rear.

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Published 03/28/2017

Copyright Ã‚Â© 2017 SAE International

doi:10.4271/2017-01-0221

saetransaf.saejournals.org

A Comprehensive Validation Method with Surface-Surface Comparison for

Vehicle Safety Applications

Junqi Yang, Zhenfei Zhan, Ling Zheng, and Gang Guo

Chongqing University

Changsheng Wang

Tongji University

ABSTRACT

Computer Aided Engineering (CAE) models have proven themselves to be efficient surrogates of real-world systems in automotive

industries and academia. To successfully integrate the CAE models into analysis process, model validation is necessarily required to

assess the modelsÃ¢â‚¬â„¢ predictive capabilities regarding their intended usage. In the context of model validation, quantitative comparison

which considers specific measurements in real-world systems and corresponding simulations serves as a principal step in the

assessment process. For applications such as side impact analysis, surface deformation is frequently regarded as a critical factor to be

measured for the validation of CAE models. However, recent approaches for such application are commonly based on graphical

comparison, while researches on the quantitative metric for surface-surface comparison are rarely found. To deal with this problem, a

validation metric, which combines the discrepancies measurements in magnitude and shape, is proposed to evaluate the inconsistence

between two deformed surfaces. For magnitude error, an exploited 2-Dimensional Dynamic Time Warping (2D-DTW) method is

applied to address the mismatch in surface features between two surfaces. Geometric features, say mean curvatures of surfaces, are

extracted for shape comparison. For decision making, the original assessments are then transformed into scores through a linear

regression method. An analytical case is employed to verify the employed algorithms in the proposed method. Furthermore, the method

is implemented on a real-world case involving surface comparison to show its potential in vehicle safety applications.

CITATION: Yang, J., Zhan, Z., Zheng, L., Guo, G. et al., “A Comprehensive Validation Method with Surface-Surface Comparison for

Vehicle Safety Applications,” SAE Int. J. Trans. Safety 5(1):2017, doi:10.4271/2017-01-0221.

INTRODUCTION

As a crucial step in validation activity, metric development for

quantitative comparison between test and corresponding simulation

needs to consider various features of responses. For vehicle safety

applications, considerable researchers have paid their efforts to

develop numerous potential metrics with various case studies. Cheng

[2] utilized a wavelet decomposition based method to extract the

features of crash pulses, and introduced a metric in the form of rating

score. Yang [3] reviewed several popular metrics in safety

applications, and proposed a metric to address the bias introduced by

Subject Matter Expert and quantitative metric itself. More recently,

Xi et al. [4] and Xu et al. [5] paid efforts on the metrics development

involving uncertainty consideration. Moreover, several previously

introduced metrics, say CORA [6], EARTH [7] and EEARTH [8]

become the foundations of the published ISO standards Ã¢â‚¬Å“Road

vehicles – Objective rating metrics for dynamic systemsÃ¢â‚¬Â. Though

great progress has been achieved in the field of curve-curve

comparison based validation, the development of quantitative metric

for surface-surface comparison has not been well studied.

With the ever growing concerns about occupant protection,

automotive manufacturers have to meet several increasingly strict

vehicle safety regulations and laws, such as the mandatory Federal

Motor Vehicle Safety Standards FMVSS and the market-driven New

Car Assessment Program (NCAP). Traditional approach to assess

whether these requirements are satisfied is commonly based on costly

and time-consuming physical tests. To shorten the development time,

Computer Aided Engineering (CAE) models based virtual prototype

tests to evaluate the vehicle crashworthiness are on the rise. To

maximize the use of these models, the validity and predictive

capabilities of these models need to be assessed objectively and

quantitatively. This calls for the process of CAE model validation.

The fundamental concept of model validation has been introduced

mainly by several professional societies and institutions, including the

U.S. Department of Energy (DOE), the American Institute of

Aeronautics and Astronautics (AIAA), the U.S. Department of Defense

(DOD), and the American Society of Mechanical Engineers Standards

Committee (ASME). It is commonly defined as the process of

determining the degree to which a model is an accurate representation

of the real world from the perspective of its intended uses.

For many vehicle safety applications, surface deformation is

frequently regarded as a critical factor to be measured for validating

the CAE models. For instance, to ensure occupant protection, besides

39

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Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

time histories responses, modeler would also concern the deformed

door surfaces of vehicle in side impact test and accident. Currently,

validation methods for these applications are commonly based on

graphical comparison, which is neither objective nor accurate. Ideal

metric should provide quantitative indication for the degree of

agreement between computational and experimental data. For such

purpose, a comprehensive validation metric for surface-surface

comparison is proposed in this paper. The proposed metric for

surface-surface comparison combines the measurements of errors in

magnitude and shape. For magnitude error, a 2-Dimensional Dynamic

Time Warping (2D-DTW) method is proposed to address the effect of

shape features on magnitude. As for shape error, curvature based

measurement is introduced to characterize the geometric features of

surfaces. For convenient decision making, the two error measurements

are transformed into scores through a linear regression method.

The rest of this paper is organized as follows. The proposed surface

validation method is introduced in the following section. The third

section demonstrates the validity of the techniques involved in this

metric through an intuitive case. Then the proposed method is applied

to a case to show its potential in real-world engineering application.

PROPOSED SURFACE-SURFACE

VALIDATION METHOD

Let DR = [xR, yR, zR] and DC = [xC, yC, zC] be the coordinates of the

nodes on real-world surface and corresponding CAE model based

surface. For the convenience of formulation, the original coordinates

data are projected onto respective principal planes, so that to

represent the original data by the height information of the

transformed nodes [9]. The other two dimensions are transformed as

the mesh indexes of the surfaces. Therefore, the following validation

activities are performed based on the projected and meshed CAE and

test data, say ZR and ZC, which are both m Ãƒâ€” n matrices.

The proposed surface-surface validation process contains two main

parallel assessment procedures for magnitude error and shape error,

respectively. For magnitude error, an exploited 2D-DTW method is

applied to address the mismatch regarding surface features (i.e. peaks

and valleys) between two surfaces. Then the pre-processed surfaces

are submitted to the following Euclidean distance calculation. In

terms of shape error, geometric feature, say mean curvatures of

surfaces, are extracted for topology comparison. Since the ranges of

two errors are quite different, the original assessments are

transformed into scores through a linear regression method.

Magnitude Error Measurement

Given two surfaces data to be compared, the most direct way to

assess the discrepancy is computing Euclidean distance, which forms

the foundation of distance measure [10]. However, Euclidean

distance is quite sensitive to even small mismatches between two

data. For example, slightly misaligned phase of time histories or

shifted shape features (i.e. peaks and valleys) of surfaces would lead

to unreasonably large Euclidean distance measurement [11]. To

address such problem, a 2D-DTW is exploited to separate the

interaction between the features of shape and magnitude.

2D-DTW based Euclidean distance measurement

Dynamic Time Warping (DTW) is originally an algorithm for

measuring similarity between two temporal sequences which may

vary in speed and was initially used in context with speech

recognition [12, 13]. It shows remarkable potential in various

applications, e.g., data mining [14], medical imaging [15], and

geological monitoring [16]. The key idea of DTW is that any point of

a time history can be (forward and/or backward) aligned with

multiple points of the other time history that lie in different temporal

positions, so as to compensate the temporal shifts [17]. With such

advantage, DTW has also proven itself to be an exceptionally useful

tool in the field of model validation to map the samples of two time

history curves [18]. However, for surface-surface comparison, the

matching process needs to be performed in a higher dimensionality

space. For such purpose, a 2D-DTW method is developed to

minimize the effect of mismatched surfaces features on the

magnitude error measurement.

In the context of DTW for one dimensional problems, the warping

path that minimize the cost to match two curves needs to be

calculated. Similarly, the proposed 2D-DTW evaluates the warping

paths in two dimensionalities, say horizontal and vertical , as

shown in Figure. 1.

Figure 1. Dimensionalities definition for surfaces to be compared.

For the two directions, the distance matrices of the two surfaces are

calculated as:

(1)

where ||Ã¢â‚¬Â¢||2 indicates L2-norm operation.

imply that the

original matrices ZR and ZC are both sliced as n-column vectors,

while

imply ZR and ZC are partitioned as m-row vectors.

For each dimensionality, respective distance matrix can be obtained.

The alignments of the two surfaces are optimized in the sense that it

minimizes the cumulative distance. To optimize the warping paths

Ã¢â‚¬Å“verticallyÃ¢â‚¬Â and Ã¢â‚¬Å“horizontallyÃ¢â‚¬Â, the matrices that minimize the

Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

cumulative distances to match two surfaces are required to be

calculated based on dh and dv. For each warping step, the cumulative

distance is expressed as:

(2)

Dh and Dv indicate the cumulative distances regarding the two

dimensionalities. The optimal warping paths to match the two

surfaces can be determined based on Dh and Dv.

In practice, backtracking is needed to identify the indexes for each

step. Taking the horizontal warping process as example, backtracking

along the minimum cumulative index pairs (ih, jh) starting from the

top-right corner indexes (n, n) of Dh yields the DTW results. In case

that the original sequences of matrices indexes are not optimal,

certain sample indexes of

will be repeated for several

times to make the two surfaces matched, which will results in the

prolongation of the original matrix. Assume the obtained matrices be

in the size of mÃ¢â‚¬Â² Ãƒâ€” nÃ¢â‚¬Â² (mÃ¢â‚¬Â² Ã¢â€°Â¥ m, nÃ¢â‚¬Â² Ã¢â€°Â¥ n), the following magnitude

comparison is conducted based on the warped surfaces data ZÃ¢â‚¬Â²R and

ZÃ¢â‚¬Â²C. Then the discrepancy in magnitude can be calculated based on

Euclidean distance, as shown in Equation (3).

(3)

Shape Error Measurement

In the context of differential geometry, curvature is a critical attribute

to describe the shape of a surface [19]. In this study, mean curvature

is employed to characterize the surfaces to be compared.

Geometric Features Extraction

At any point on a surface, its normal planes that contain the normal

vector would certainly intersect with the surface. The intersection

forms a curve called a normal section. Different normal sections

correspond to different curvatures at the evaluated point, and the

maximum and minimum values of these curvatures are called the

principal curvatures k1 and k2, respectively. As expressed in

Equation (4), the mean curvature is defined as the average of the

two principal curvatures:

(4)

Mean curvature is employed in this study as it is a physically

meaningful quantity. In the theory of differential geometry, the

implication of M related to geometry is provided in Table 1.

41

Table 1. Implication of mean curvature related to geometry.

Let S (DR, DC Ã¢Å â€ S), which belongs to 3-dimensional Euclidean space,

represent the surface data to be evaluated, the mean curvature matrix

of the surface can be calculated as:

(5)

where

is the gradient of S , while

is the Hessian matrix of S .

Trace (Ã¢â‚¬Â¢) denotes the trace of the matrix correspondingly. Details can

be referred to ref. [20, 21].

Regression Based Rating

As the ranges of these two errors, say D and M, are nondeterministic

and quite different, it is difficult for engineers to interpret how good

or how bad a CAE model is based on these raw error data. To provide

more intuitive rating based on the original measurements, a rating

score method is employed (Zhan et al., 2011b). The regression based

method translates the original errors into one score between 0 and

100%, so that it can provide an intuitive rating score. In this study,

Equation (6) is used to calculate the magnitude score Sm,

(6)

where D* is the maximum allowable magnitude error, km defines the

order of the regression. In this way, the best magnitude score is

100%. If the magnitude is equal to or greater than the maximum

allowable threshold M*, then the score is 0%. In between, the score is

calculated by regression method. Equation (7) provides the similar

rating rule for shape error.

(7)

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Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

ILLUSTRATIVE CASE

In the proposed method, the validity of 2D-DTW would largely affect

the calculated magnitude score, while the capability of curvature

extraction algorithm is the core of shape score calculation. In this

section, the validity of 2D-DTW and curvature calculation algorithms

is verified through a demonstrative case study.

Two free surfaces in the size of 64 Ãƒâ€” 64 are provided in this case, as

shown in Figure 2. These two surfaces are globally similar in terms of

the surface features. However, it is observed that several geometric

characteristics cannot be well matched. The proposed 2D-DTW is

utilized to address such problem. Based on the 2D-DTW algorithm,

the optimum paths in directions and are obtained, as shown in

Figure 3. The dash lines indicate the reference paths in two

directions, while the dotted lines are the optimal warping paths. It is

noted that when the matrices to be matched are consistent, the

optimal warping path will be identical with the diagonal line of the

chessboard. Under such condition, sequentially matching the samples

can result in the minimum distance. As the warping paths are not

identical with the reference ones, the two surfaces need to be

expanded to make the global features matched. Through the warping

process, the sizes of surface matrices Z1 and Z2 are automatically

changed into 71 Ãƒâ€” 69. Figure 4 shows the resultant surfaces.

To obviously show the effectiveness of the warping process, contours

of surfaces are presented in Figure 5. Figure 5(a) is the original

surface contours, while Figure 5(b) shows the resultant contours. In

these figures, Ã¢â‚¬Å“PÃ¢â‚¬Â indicates Ã¢â‚¬Å“peakÃ¢â‚¬Â, and Ã¢â‚¬Å“VÃ¢â‚¬Â means Ã¢â‚¬Å“valleyÃ¢â‚¬Â. As

shown in Figure 5(a), the locations of

on Z1 are different

from that of

on Z2. Through warping, the surfaces are

modified and the geometric features of peak and valley can be

maximally matched, as shown in Figure 5(b). Therefore, it can be

concluded that the proposed 2D-DTW method has the capability to

minimize the effect of shape mismatch on magnitude evaluation.

Figure 3. Warping paths of surfaces in two directions.

Figure 4. Matched surfaces based on 2D-DTW.

a.

b.

Figure 5. Contours of the (a) original surfaces, and (b) warped surfaces.

Figure 2. Surfaces to be compared.

In terms of shape error, the ability to extract surface features correctly

is critical to the resultant measurements. Curvatures are able to

represent the geometric characteristics of a surface. For each point on

the surface, mean curvature can be evaluated to show whether it is a

convex or concave point according to the sign of the evaluated value.

In this case study, the mean curvatures of nodes on surfaces Z1 and

Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

43

Z2 are calculated, as provided in Figure 6. According to the

implications of mean curvature, positive mean curvature indicates

convex region, while negative value corresponds to concave region.

Figure 8. Deformed door surfaces to be compared.

Error Measurement

Figure 6. Extracted mean curvatures for the two surfaces.

The evaluated results in Figure 6 are consistent with the intuitive

observations. Based on the reliable evaluations, differences between

the two surfaces regarding mean curvature can be calculated.

As shown in Figure 8, ZR and ZC are globally similar according to

visual comparison, except for several slight differences in local

details. For the purpose of quantitative evaluation, 2D-DTW is firstly

performed for ZR and ZC to match the two surfaces. As shown in

Figure 9, in total 17 shifting steps are needed in the matching process.

The two warped surfaces are provided in Figure 10. The mismatches

in geometric features have been globally compensated. Then,

magnitude errors at each points of the surfaces can be calculated.

ENGINEERING CASE

In this section, a real-word test based deformed surface and

corresponding FE surface are employed to demonstrate the method

for model fidelity quantification. The left-front door after crash and

corresponding FE surface are presented in Figure 7. The real-world

deformed door is scanned by laser scanning facility and represented

as a set of coordinates. Meanwhile, the nodes coordinates are

extracted through post-processing the FE model based crash results.

After transforming the two surfaces into the same space, the

validation activity can be conducted. The surfaces and in the size of

64Ãƒâ€”64 are presented in Figure 8.

Figure 9. Warping paths of the two deformed door surfaces.

In terms of shape error, the extracted curvatures of ZR and ZC are

presented in Figure 11. It is observed that the features of Ã¢â‚¬Å“convexÃ¢â‚¬Â

and Ã¢â‚¬Å“concaveÃ¢â‚¬Â can be correctly represented by the evaluated

curvatures. Similarly, shape errors can be calculated according to the

discrepancies in curvatures evaluated for ZR and ZC.

Figure 7. Deformed real-world door and simulated door.

44

Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

Sensitivity Study

Figure 10. Feature-matched door surfaces for magnitude comparison.

It is known that only one parameter, say the meshing size of the

surface, needs to be determined by engineers in the validation

process. The meshing size, which can be regarded as the resolution of

the evaluation, will certainly affect the precision of assessment

results. Therefore, it is necessary to perform sensitivity study on the

resolution of the surface. As introduced before, the results in Table 2

are obtained based on the surfaces which are meshed in the size of 64

Ãƒâ€” 64. In this subsection, the matrix size is modified for comparison.

The data are shown in Table 3, while corresponding results are

provided in Figure 12 to show the tendency. It is observed in Figure

12(a) that magnitude score is insensitive to the resolution of surfaces.

In terms of shape assessment, as resolution increases, the score

initially shows its uptrend, then keeps in stable value when the

resolution becomes higher than 64 Ãƒâ€” 64. It is reasonable to choose a

high resolution for accurate assessment. However, the increase of

entries in matrix would lead to the increase of computational cost. To

ensure robustness with relatively high computational efficiency, the

size of 64 Ãƒâ€” 64 is preferable for this case. It is suggested that, when

dealing with practical validation problem, performing sensitivity

study in advance is able to specify a resolution correspondingly that

helps obtain robust evaluation results.

Table 3. Magnitude and shape scores evaluations evaluated based on different

resolutions.

Figure 11. Extracted mean curvatures on (a) real-world door surface, and (b)

FE-based door surface.

Based on the evaluations for magnitude and shape discrepancies,

corresponding error measurements are obtained by specifying D* and

M*. D* and M* are defined as the discrepancies between the

maximum and minimum values of D and M, respectively. The values

of the thresholds and the calculated scores are provided in Table 2.

Table 2. Defined thresholds values and corresponding assessed scores.

a.

Figure 12. Scores evaluated based on different resolutions: (a) Magnitude

score, (b) Shape score.

Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

5.

6.

7.

8.

9.

10.

b.

Figure 12 (cont). Scores evaluated based on different resolutions: (a)

Magnitude score, (b) Shape score.

11.

12.

SUMMARY

13.

For safety applications, such as side impact and rollover analysis,

surface deformation is a critical factor to be measured in tests and

corresponding simulations. Model validation activities for such

applications need to compare the deformed surfaces obtained in

simulations with that of real-world tests. However, how to assess the

discrepancy between two surfaces quantitatively is still an

outstanding issue in the field of model validation. This paper presents

a comprehensive validation metric for models involving surfacesurface comparison. The metric is composed of 2D-DTW based

magnitude error measurement and geometric feature based shape

measurement. An illustrative case study is to show the validity of the

algorithms employed in the validation procedure. Furthermore, the

proposed method is applied to the validation an impact model.

Sensitivity study is performed on the resolution parameter of the

proposed method for this case. It is suggested that with appropriate

resolution, robust assessment results can be obtained with no increase

in computational cost.

14.

The scope of this paper is to introduce a metric for surface-surface

comparison to be integrated in existing validation framework. Further

efforts will be paid to integrate the proposed metric with the

well-established curve-curve comparison based metrics to formulate

a more comprehensive validation framework for safety applications

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CONTACT INFORMATION

Corresponding author:

Zhenfei Zhan, Ph.D.

Research Professor

State Key Laboratory of Mechanical Transmission, Chongqing

University, Chongqing, PR China

zhenfeizhan@cqu.edu.cn

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation

of China under Grant NO. 51405041, and the Ford project

Ã¢â‚¬Å“Development of a Validation Method for 3D Surface Comparison in

Vehicle SimulationsÃ¢â‚¬Â.

46

Yang et al / SAE Int. J. Trans. Safety / Volume 5, Issue 1 (April 2017)

DEFINITIONS/ABBREVIATIONS

D* – Threshold of magnitude error.

DR, DC – Coordinates data of surfaces

dh, dv – Distances matrices in 2 directions

Dh, Dv – Optimal cumulative distances in 2 directions

M* – Threshold of shape error.

D, D – Euclidean based magnitude error.

Sm – Magnitude score.

M, M – Mean curvature of surface.

Ss – Shape score.

ZR, ZC – Surfaces Matrices

k1 , k2 – Principal curvatures

ZÃ¢â‚¬Â²R, ZÃ¢â‚¬Â²C – Warped surfaces matrices.

km, ks – Regression order

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