Time-series analysis of driving data

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University of Amsterdam

Faculty of Science

Time-series analysis of driving data

H.C. Bronk

Supervised by

Dr. E.R. Dugundji & R.J. van Loon, MSc

Thesis submitted for the degree of

Master of Science

in Computational Science

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Abstract

In this thesis we explore the difference between safe and unsafe driving behaviour by applying time-series analysis techniques to data obtained from an experiment in a driving simulator. We survey the research field of driving behaviour as well as its history, identifying the not yet fully explored concept of satisficing driving, which we use in an attempt to better understand the transition from error-neglecting to error-correcting driving behaviour. We develop a model of lateral vehicle control and test it in a simulator experiment with participants in both alert and drowsy states.

Unfortunately the proposed model will prove incapable of detecting a significant change in behaviour. We subsequently turn to exploratory data analysis to learn as much as we can about how driving skills suffer from drowsiness.

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Preface

At this moment in time, there is nothing left for me to write save for this preface. Finishing this project has been a constant battle against perfectionism and the obsessing over details that ultimately proved insignificant. I am therefore extremely pleased to work on this last page.

I would like to start by pointing out that initially my aim was to develop a driver aid that could alert drivers of expected dangerous situations. To this end I developed a software platform for streaming data analysis, which consumed most of the scheduled time for a regular master thesis. An opportunity then presented itself to participate in a simulator experiment, which I accepted, because I would be able to apply my software to the collected data. Ultimately however, I ended up only using standard analysis techniques. Even though the software I wrote had no part in the results as presented in this thesis, I wanted to include the text I had already written. This is why, in addition to about 60 pages in the body of this thesis, there are another 40 or so (non-code) pages in the appendices.

A few people have had a large impact on me over the course of this project. First of all, I would like to tell my parents that I love them and am very grateful for their never ending faith and support. The same goes for my brothers (and friends), who never stopped teasing me: ‘‘When are you finally finished?!’’

My thanks go also to the people at TNO in Soesterberg, the place of my internship. In particular to Roald for his inspiration, discussions, and those two weeks we were locked up in a room with blacked out windows, doing experiments and missing out on summer. The other interns made TNO a very fun place to work. I have formed lasting friendships (looking at you Noel) and met people that have changed me as a person. I miss the summer barbecues in the park and the games we played.

Finally, special thanks go to Elenna. When I asked the university for a supervisor, my request was forwarded to two researchers. I am glad she was the one to reply, since without her I would not be on the path I am today. I would never have had the amazing experience in India, which was instrumental in helping me find the career I want to start. My time there reshaped me and I still have a very strong connection to some of the people there. Thanks for guiding me to the finish line and for always being there as a sounding board. I wish you all the best.

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List of Tables

2.1 An overview of the data gathered in the UBV experiment at TNO. . . 25

2.2 The number of samples per 250 ms time bin. . . 30

3.1 Linear models of the relation between the lateral position of peaks and low frequency steering reversals. Models were fit using least squares, with standard errors obtained from the HAC Newey-West covariance matrix estimator. . . 43

4.1 Standard deviations of lateral position distributions . . . 48

4.2 Fit parameters of the linear dependence of ∆t on PERCLOS. . . 51

4.5 The maximum steering magnitude, as measured by Ω, modeled as a function of rescaled PERCLOS ratings. The coefficients indicate a strong increase in Ω when a participant’s measured PERCLOS rating increases from the minimum to the maximum value. Both the BP and BG tests are positive, which is why the traditional F test of joint significance has been replaced by the Wald test. . . 58

4.6 Peak lateral position fit statistics. . . 60

4.7 Peak lateral position fit statistics (scaled). . . 60

A.1 IVA package command line parameters. . . 66

B.1 Performance measurements for prototype network implementations. . . 102

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List of Figures

1.1 The first case of a pedestrian suffering fatal injuries from a traffic accident . . . 1

2.1 Preprocessing: completeness of data . . . 27

2.2 Preprocessing: data completeness for selected participants . . . 29

2.3 Preprocessing: incomplete bins . . . 31

3.1 Drowsiness: PERCLOS P80 measurements . . . 33

3.2 Drowsiness: KSS and PERCLOS P20 . . . 34

3.3 Drowsiness: meaned PERCLOS compared to KSS . . . 35

3.4 Drowsiness: method comparison for all participants . . . 36

3.5 Drowsiness: driver states . . . 38

3.6 Drowsiness: box plots relating P20, KSS, and state . . . 39

a KSS range per state . . . 39

b P20 range per KSS score . . . 39

3.7 An illustration of the relationship between α(t) and ¯ω(t)from a short segment of driving data. . . 40

3.8 The relation between steering wheel angle and reversal points . . . 41

3.9 Sample driving data with reversal points . . . 42

3.10 Separating low and high frequency reversals . . . 44

3.11 Sample driving data with low frequency reversals . . . 45

3.12 Lateral position peaks and reversals . . . 46

a A histogram of the time difference . . . 46

b Comparing lateral positions . . . 46

4.1 Distributions of reversals in alert and drowsy states . . . 49

4.2 Distributions of peaks and reversals of drowsy driving . . . 50

4.3 Mean time between reversals as a function of drowsiness . . . 52

4.4 Mean reversal ∆t change over scaled drowsiness range . . . 55

4.5 Maximum steering magnitude . . . 57

4.6 Omega increases with drowsiness . . . 59

4.7 Local maximum lateral positions increasing with PERCLOS rating . . . 61

A.1 An example of a complex system built as a network of simple models. . . 65

A.2 Curses Manager: interface overview. . . 75

A.3 Curses Manager: log filtering. . . 76

a Curses Manager: filtering by log level. . . 76

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LIST OF FIGURES LIST OF FIGURES

A.4 GUI Manager: single view. . . 78

A.5 GUI Manager: double view. . . 79

B.1 An example Lane Departure Warning network topology. . . 94

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List of listings

3.1 Sample R code to calculate reversal points from a set of steering wheel angles. . 40

A.1 Example node configurations. . . 67

A.2 Manager: create signal sockets method. . . 68

A.3 Manager: initialize nodes method. . . 70

A.4 Manager: main execution method. . . 71

A.5 Manager: network termination method. . . 72

A.6 Manager: handle fatal logs. . . 74

A.7 Generic Node: main execution order. . . 81

A.8 Generic Node: handshake procedure . . . 82

A.9 Generic Node: synchronization procedure . . . 82

A.10 Generic Node: message stream . . . 82

A.11 FileReader node: message stream . . . 84

A.12 FileReader node: fast message stream . . . 86

A.13 LateralPosition node: entire file . . . 88

A.14 LeastSquares node: data structure initialization . . . 89

A.15 LeastSquares node: main algorithm . . . 91

B.1 A worker implemented using multiprocessing and standard pipes and queues. . 99

B.2 ØMQ worker that uses PUB/SUB, with handshake. . . 101

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Chapter 1

Introduction

On the 17th of August, 1896, Mrs. Bridget Driscoll, aged 44, became the first traffic fatality in the United Kingdom (fig. 1.1). As noted by Andrew McFarlane in a BBC News Magazine article on 17 August 2010, Mrs. Driscoll, on foot, was hit by an imported Roger-Benz, driven by Arthur Edsall of the Anglo-French Motor Co.

The following hearing [Unknown Author, 1896b] lasted for 6 hours and was directed at the errors that Mrs. Driscoll or Mr. Edsall had made that could explain the outcome of the event. Mrs. Driscoll allegedly froze in bewilderment at the sight of the automobiles, and did not move out of the way of the vehicle. On the other hand, a witness claimed that Mr. Edsall "did not seem to understand what he was doing". The arguments focussed on whether or not Mr. Edsall had warned Mrs. Driscoll by shouting, as well as the speed of the vehicle. The jury settled on a verdict of accidental death, and Mr. Edsall was not prosecuted. The coroner is known to have said that he hoped that "such a thing would never happen again".

Figure 1.1:Bridget Driscoll of Croydon, aged 44, became the first pedestrian to suffer fatal injuries from a traffic accident in the United Kingdom, on 17 August 1896. [Unknown Author, 1896a].

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1.1. MACROSCOPIC ACCIDENT STATISTICS CHAPTER 1. INTRODUCTION

Over one hundred years later, the World Health Organization [2013] reported that 1.24 million people were killed on the world’s roads in 2010. About 93% of accidents are solely (57%) or in part (36%) due to human factors [Rumar, 1985]. An increased understanding of human driving could therefore potentially result in a large reduction in the traffic-related death rate, by for example improved road safety laws, driver training, infrastructure, and car design. It is therefore important to study the role of human behaviour in traffic safety.

The vast majority of traffic safety research is focused on unsafe driving behaviour and accidents. In this thesis we will however concentrate our efforts on understanding regular driving behaviour. Gibson and Crooks [1938] already said (emphasis added):

‘‘The situation which faces highway-safety officials in dealing with a public who insist on killing themselves at an ever-increasing rate is similar to that of a bewildered parent dealing with a bad child. Despite past failure, the only thing the parent knows to do is to admonish him oftener and spank him harder. A wiser procedure would be first to try to understand what is going on in the child’s head. Frequently the child does not want to misbehave, and most assuredly the driver does not want to kill himself. Intelligent measures toward educating the public to drive safely can only be taken when the performance of driving an automobile is thoroughly understood. Programs of testing and experimenting are necessary, but useful only if they have some theory to go on. Discussion of the problem should be disinterested rather than merely admonitory, should adopt the driver’s point of view rather than the safety engineer’s, should start from normal rather than abnormal driving, and should emphasize what the driver ought to do rather than what he ought not to do.’’

We will first review accident analysis research, related psychological models, and ways of quantifying behavioural output. This will show why it is important to focus on safe instead of unsafe driving. We will then develop a computational model that attempts to quantify driver risk, in order to better understand how safe and unsafe driving can be distinguished, and the transition can be detected.

1.1 Macroscopic Accident Statistics

When researching traffic safety, one naturally seeks to compare the level of safety between various geographical locations, time periods, automobile manufacturers, or drivers. In order to do research and compare experimental conditions, the level of safety associated with a particular condition needs to be quantified. The most widely used method of doing this is by using statistics about accidents, frequency and severity in particular, that are provided by local governments, police departments, or hospital records.

Applying statistical analysis to accident numbers collected over a certain time period can provide insight into the effectiveness of a policy or a change in infrastructure, allowing for the evaluation of past traffic safety improvement measures. This type of research has shown, for instance, that the estimated effect of road lighting on injury accidents during darkness on rural roads in the Netherlands is −54% ± 2% [Wanvik, 2009].

Statistical analysis of accident incidence rate can also improve traffic safety by giving a prediction on the effectiveness of proposed policy, thereby enabling cost-benefit analyses. The usual practice is to select crashes that occur in a particular location or time period, develop a statistical

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1.1. MACROSCOPIC ACCIDENT STATISTICS CHAPTER 1. INTRODUCTION

model from which the influence of the chosen explanatory variables can be infered, and subsequently use this knowledge to forecast a reduction in accidents that would be the result of a proposed safety improvement measure [Lord and Mannering, 2010].

A major example of this is the effort by local governments to resolve so called black spots: geographical locations where accidents are concentrated. Black spots can be effectively treated with small scale low-cost engineering measures [Sayer, 1994], such as signs and road markings.

However, statistical effects such as regression toward the mean [Chiolero et al., 2013], and effects pertaining to driver behaviour such as accident migration [Boyle and Wright, 1984] and risk compensation [Wilde, 1982] give reason to doubt the effectiveness of resolving accident black spots. Research by Elvik [1997], citing the ‘‘Iron Law of Evaluation Studies’’ [Rossi, 1987], indicates that the measured effectiveness of black spot treatment programs tends to zero if more and more confounding factors are accounted for. On the other hand, a recent study [De Pauw et al., 2014] on the safety effects of an extensive black spot treatment programme in Belgium, which accounts for confounding factors such as regression to the mean, found a decrease in the number of injury crashes of 24--27%, and a decrease in the number of fatal injuries by 46--57%. The conflicting results indicate that the way drivers deal with accident risk is not fully understood.

Accident statistics are used in traffic safety research outside of public policy as well. For example, Hayakawa et al. [2000] explained cross-national differences in risk perception by looking at the traffic environments in Japan and the United States, and research by van Beeck et al. [2000] shows that there is a nonlinear relation between economic development and traffic accident mortality.

Besides the issues specific to research into the effect of black spot treatments, there are other, more general, potential problems with inferences made from road accident rate statistics. For one, the reliability of these statistics is questionable. The level of accident reporting varies between types of accidents (fatalities, serious injuries, minor injuries, economic damage only), type of victims (car drivers, cyclists, pedestrians), countries and districts, and reporting agencies. Furthermore, the classification of accidents also varies between countries and reporting agencies.

A meta-analysis by Elvik and Mysen [1999], based on 49 studies in 13 countries, concludes that reporting of injuries in official statistics is incomplete at all levels of injury severity. The reporting level for fatalities varied from 87% to over 100%1_{, while the percentage of reported} hospital-treated injury accidents varied from 21% to 88%. The authors conclude that official accident statistics are therefore not, in general, comparable for different countries, and note that despite this being well known, road safety research routinely compares and combines results of studies in order to reach more general conclusions.

Aarts and van Schagen [2006] remarks on the use of ’crash rate’ in meta studies that not all authors use the same operationalisation. For example, crash liability of drivers in the last 3 to 5 years, crash frequency, crash frequency per speed category, and crash frequency per kilometre road length are all used. The different uses of ’crash rate’ is a confounding factor in meta studies, especially because not all studies are explicit about their operationalisation.

1_{Various reasons for over reporting are mentioned, such as not removing victims who died immediately before}

the accident, not removing victims who commit suicide, treatment of accidents involving foreigners, or a mismatch in definitions between road accident statistics and mortality statistics.

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1.2. MODELS OF DRIVING BEHAVIOUR CHAPTER 1. INTRODUCTION

Even within single datasets there are many potential sources for error. If the number of reported accidents within a particular condition, location, or time interval is too low, it is easy to use the wrong statistical model and draw erroneous conclusions. In particular it might be impossible to properly show a significant effect for explanatory variables. A study performed on data from Nordic countries showed that pure randomness accounted for the majority of variation in segments with small accident counts, and exposure, i.e. traffic volume, being the most dominant systematic component. Together these sources account for 80% to 90% of variation in their data sets [Fridstrøm et al., 1995]. The effect of a policy change would be very hard to measure using this data. Additionally, besides the effect of long term economic growth on traffic accident mortality [van Beeck et al., 2000], road mortality also follows the business cycle [Chen, 2014], resulting in another confounding factor.

To summarize, traffic safety research based on accident rate statistics suffers from three problems. First, the available data is unreliable, and not always available in sufficient quantities. The second, related problem, is that there are methodological issues in analyzing the data in a statistically sound way. Third, we do not know enough about the way drivers deal with accident risk.

Fortunately, a recent literature review [Lord and Mannering, 2010] shows that there has been a lot of methodological innovation in statistical accident rate analysis. Eleven potential sources of erroneous conclusions and sixteen types of statistical models are discussed. Recently introduced statistical models can improve the vality of findings, and the authors expect that these models could provide new insights in the coming years. However, they also note that there is a trade-off in the practical side of crash-frequency analysis that may render these innovative methods irrelevant for many researchers whose goal it is to predict an effect on the number of accidents as a result of a policy or infrastructural change. These types of research rely on explanatory variables that can be easily predicted, but the complex models often need much more data and variables that cannot easily be forecast, such as levels of precipitation and friction coefficients.

Lord and Mannering [2010] also note that a real boost in our understanding of traffic safety can be expected when large data sets of regular driving become widely available in the future. Performing the kind of statistical analysis that now happens on accident data on regular driving in various scenarios could provide valuable insights into why some situations result in accidents while other very similar situations do not. These kinds of questions cannot be answered by looking at accident data alone.

Until more data becomes available, it is unlikely that an accident based statistical approach will result in a better understanding of driving behaviour. However, in parallel to the statistical research on traffic safety, there has been a major research effort in developing psychological models of driving.

1.2 Models of Driving Behaviour

The scientific discipline that is concerned with the behavioural aspect of traffic safety research is part of Human Factors, which is defined by the International Ergonomics Association [2014] as:

‘‘Ergonomics (or human factors) is the scientific discipline concerned with the understanding of interactions among humans and other elements of a system, and

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the profession that applies theory, principles, data and methods to design in order to optimize human well-being and overall system performance.’’

More specifically applied to traffic safety, the U.S. Department of Transportation’s National Highway Traffic Safety Administration [2014] explains that Human Factors is

‘‘The application of knowledge about human abilities, limitations, and other human characteristics to the design of equipment, tasks, and jobs.’’

and that

‘‘The role of human factors research is to provide an understanding of how drivers perform as a system component in the safe operation of vehicles. This role recognizes that driver performance is influenced by many environmental, psychological, and vehicle design factors.’’

The concept of driver performance that is mentioned in the above quote is concerned with what a driver can do to influence a situation. It describes the driver as a machine with certain properties: knowledge about the current situation and surroundings, cognitive abilities, perceptual abilities, motor control, et cetera. Actions taken by the driver are not solely attributable to driver performance, as social and psychological factors also play a role in determining a driver’s behaviour.

The complex nature of driver behaviour allows for a driver’s actions to be caused by several underlying factors. For example, a driver might be speeding because the penalty to being late is more severe than the penalty to speeding (social factor), because driving fast is considered more exciting (psychological factor), or because the driver has no knowledge of the current speed limit (performance factor). Models can be developed for (a combination of) any of these factors.

Due to its complex nature, we do not have a good model of general human driving behaviour (e.g. [Hancock and Scallen, 1999], [Ranney, 1994]), in the sense that we cannot predict a driver’s actions in a given traffic situation. Nevertheless, some models that provide an explanation for a particular aspect of driving exist.

1.2.1 A preoccupation with accidents

Historically, the first driver models were based on accidents. Researchers attempted to identify accident prone individuals by using statistical methods. Accident-proneness theories suggested that some drivers were more susceptible to accidents than others, because some people are also more clumsy in other aspects of life, such as dining, or climbing stairs. Driving was considered a perceptual-motor skill, and accidents a failure of this skill [Summala, 1988]. Early traffic safety improvement programs therefore focussed on improving driver skill, or reducing the environmental strain on a driver’s skill.

The statistical study of accident-proneness offered little insight into the psychological aspects of the driving errors associated with crash causation, so the focus gradually shifted to an approach that was based on psychological tests. By subjecting drivers to tests that measured perceptual and motor skills, researchers attempted to predict past accident involvement, hoping to establish a link between measurable characteristics and accident-proneness.

This new approach of individual differences, also referred to as the study of differential accident involvement, became very prominent in the 1970s. Perhaps the most important work in

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identifying accident predictors, according to Ranney [1994], was done by Barrett et al. [1973]. They concluded, based on a conceptual analysis of accident-cause data, that three categories of information-processing measures were relevant predictors for accident-proneness. These categories, perceptual style, selective attention, and reaction time, were later joined by vision, vigilance, and decision making [Panek et al., 1977], to expand the model from accident causation to general driving behaviour. Over time, a new field of driving behaviour developed that was no longer primarily concerned with accident causation and predicting accident involvement [Ranney, 1994; Summala, 1988].

The increase in interest in non-accident based driving behaviour models was important, because it has been suggested in literature that the preoccupation with accidents caused a lack of progress in developing a comprehensive driving model. Several problems have been pointed out. For instance, Hancock and Scallen [1999] claim that accidents are not simply outliers in the distribution of normal driving, but are instead the result of a chain of highly unusual events, some of which can not be avoided by the driver. Furthermore, in addition to the problems pointed out in 1.1, there is a lack of stability of accident data. It has also been suggested that pre-crash driving behaviour is not representative of the limits of driver performance, an implicit assumption when trying to predict accident rates based on performance in information processing tests [Ranney, 1994].

Motivational models in particular became more prominent. Where earlier models attempted to link a driver’s skill to his or her accident rate, these new models used the more abstract notion of risk, and the driver’s motivation to reduce this risk.

1.2.2 Driving as self-paced task

Gibson and Crooks [1938] were the first to write an influential paper on the theory of driving behaviour. They focussed on driver vision, defining a field of safe travel and minimum stopping zone. The road can be seen as an infinitely bounded field of safe travel. Other road users, obstacles, but also lines, the curve of a corner, and the presence of potential obstacles that can not currently be seen, place limits on this field. Each vehicle driving at a nonzero speed necessarily also has a stopping zone: the minimum area covered by the vehicle before stopping. Both fields extend in front of the vehicle and pass through space with it. When the field of safe travel contracts because of another vehicle coming up, or because the driver is reaching the top of a hill that might contain an obstacle just beyond the horizon, the driver has to decelerate, in order to prevent the minimum stopping zone from extending further than the field of safe travel. In other words, drivers should choose their speed such that the depth-of-field to depth-of-zone ratio (the field-zone ratio) is greater than one.

The authors note that the field-zone ratio is probably to a large extent habitual, dependent on how much of a hurry the driver is in, and that it might be thought of as an index of caution. This theory fueled the controversial argument that trying to improve traffic safety by improving infrastructure is pointless, because the drivers will maintain the same field-zone ratio by driving faster [Smeed, 1949]2_{. Driving, according to this principle, was seen as a self-paced task. This} notion gained popularity in the 1960s and 1970s. It was suggested that drivers adjust their

2_{Smeed [1949] disagrees with this notion: ‘‘There is a body of opinion that holds that the provision of better roads,}

for example, or the increase in sight lines merely enables the motorist to drive faster, and the result is the same number of accidents as previously. I think there will nearly always be a tendency of this sort but I see no reason why this regressive tendency should always result in exactly the same number of accidents as would have occurred in the absence of active measures for accident reduction.’’

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level of risk taking to keep their anxiety at a constant level. This was later expanded to the compensation principle [Summala, 1988].

The principle of risk compensation, in its original form [Cownie and Calderwood, 1966], states that people train their behaviour in a closed loop. Observations lead to decisions, based on the associated risk and pay-off for each possible decision. The decision leads to an event, which in turn influences future decisions based on new observations. When a decision leads to a positive outcome, such as more comfortable driving, the driver is more likely to make the same decision in similar circumstances. Negative motivations are those that lead to (near) accidents, delays, uncomfortable driving, and so on. The driver gradually trains this loop through experience and conditioning.

1.2.3 Risk homeostasis theory

These ideas gained more traction when they were discussed by Wilde [1982], who labeled the concept of a closed loop risk compensation mechanism as Risk Homeostasis Theory (RHT). Although the underlying ideas remained largely the same, he clarified and expanded upon them. For example, the author was more explicit in defining a target risk level that drivers optimize their payoff for. The risk level should be thought of as a homeostatic process, with minor variations due to randomness, faulty estimations due to newly introduced accident countermeasures, transient psychological states, and so on. It should also be noted that RHT does not attempt to explain the occurence of individual accidents, nor their causes. Rather, RHT attempts to explain accident rate per capita from a population’s risk acceptance [Wilde, 1989].

A later paper [Wilde, 1986] contains the following synoptic description:

‘‘RHT posits that the traffic accident rate per time unit of road-user exposure is the output of a closed-loop regulatory process in which the target level of risk operates as the unique controlling variable. . . . Thus, it is argued that road-users, equipped with their perceptual skills, perceive a certain level of accident risk which they compare with the level of accident risk they wish to accept. The latter is determined by the pattern of trade-offs between expected costs and benefits associated with the available alternatives for action and is equivalent to that level of perceived accident risk at which the overall utility of manner and amount of mobility is perceived as maximal. The expected costs and benefits are a function of economic, cultural and person-related variables—and their long-term, short-term and momentary fluctuations—which thus control the desired or target level of risk and its variations.’’

Wilde [1986] cites various other studies, as well as illustrations, that ‘‘. . . add strength to the plausibility of RHT . . . ’’, but concedes that when considered separately, they may be interpreted in other directions. Furthermore, ‘‘Against the yardstick of more cogent predictive experimentation, . . . the theory of risk homeostasis remains largely untested.’’ A later overview article [Wilde, 1998], contains several examples of results that can be explained using RHT. For example, when Sweden changed from left to right hand traffic in 1967, there was a marked reduction in traffic fatality rate, which returned to previous levels just 18 months later. According to RHT, road users associated driving with a much higher risk, and consequently chose less risky actions, leading to a reduction in fatality rate. Eventually the homeostatic process returned to normal when drivers had experienced that traffic had not become more risky due to the change. Driver training, childproof medicine bottles, and traffic safety education for children

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all faild to limit the number of accidents, because drivers became more confident, parents less careful, and children more mobile as a result of them. ‘‘On the other hand, incentive systems for accident-free operation have been shown to be a very powerful method for reduction of injury rates.’’ These kinds of programs reduce the risk level people are willing to tolerate, reducing the total accident rate.

Both Cownie and Calderwood [1966] and Wilde [1998] argue that, similar to the concerns raised following the model by Gibson and Crooks [1938], that safety measures merely remove inhibitions from the loop, causing a driver to exhibit more dangerous behaviour. Going back to the example of traffic safety black spots (section 1.1), improving infrastructure only causes accidents to migrate to other locations. Due to the time-lagged nature of the closed loop, safety measures result in a temporary reduction in fatalities at best. While this notion is supported by several examples cited by Wilde, there are also studies that counter it. For example, Wanvik [2009] shows a significant effect of road lighting on injury accidents by using data spanning 19 years of accidents on Dutch roads. De Pauw et al. [2014] show the effects of an extensive black spot programme in Flanders, Belgium on traffic safety.

1.2.4 Zero-risk theory and satisficing driving

Another motivational theory of driving that also started from the concept of driving as a self-paced task, first hinted at in Näätänen and Summala [1974], is Zero-Risk Theory, although not yet under that name. The key concept of the paper is the ‘‘Subjective Risk Monitor’’, a part of their driver control flow model that monitors risk. They specifically distinguish between the risk monitor and actually perceived risk, because contrary to the prevailing ideas at the time (still present in Wilde’s risk homeostasis theory), they claim that most of the time the driver’s subjective risk equals nil, hence the theory’s name.

The authors note that they see no other way of understanding drivers’ reluctance in wearing seat belts or maintaining large safety margins, since they have been shown to greatly reduce objective risk with little effort by the driver. ‘‘And what about the easy decrement of vigilance, sudden drowsiness, even sleep, under natural (but not corresponding experimental) driving conditions . . . ? Even a very slight subjective risk of death or severe injury should, presumably, be a guarantee against at least an early vigilance decrement.’’ Instead of continuously evaluating risk, driving happens habitually. Time goals, conservation of effort, maintenance of speed and progress, and pleasure of driving, all tend to push drivers towards more risky behaviour. It is only when subjective risk passes a threshold that drivers actively consider risk and, after enough reinforcement, alter their habits.

If drivers do not normally feel risk, and therefore do not optimize their driving for a target risk level, then how do they control their driving? Following Gibson and Crooks [1938], Näätänen and Summala [1976] proposed that drivers use safety margins as control measure. According to proxemics theory by Hall [1966], people have comfort or safety zones around them in all environments, not just in traffic. Hall defined four zones: the intimate, personal, social, and public zones. The public zone is accessible to anyone, but zones become more restricted the closer they are to the person, with the intimate zone being reserved to close friends and family. A person intruding in another person’s comfort zone will cause an increase in perceived threat and trigger an avoidance response. People have similar comfort zones while driving, but elongated instead of circular. The act of driving increases the size of these margins, especially in front of the vehicle, to account for the minimum stopping distance [Summala, 2007].

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On the road, these comfort zones serve a dual purpose. They function as a warning mechanism when, for example, a fast car approaches from the opposite direction and passes at a short distance. When judging whether a gap is large enough to overtake a slower vehicle or cross a road, the same zone shows us the opportunities to achieve our goals.

To summarize: according to zero-risk theory, regular driving behaviour consists of learned habits, mostly aimed at increasing mobility and efficient transportation, but inhibited by safety margins. Once a safety margin has shrunk to below a critical level, the subjective risk level will cross a threshold, and the driver will switch from error neglecting to error correcting behaviour. This corresponds with the views of Hancock and Scallen [1999], who notes that humans rarely operate in an optimizing way, as is a common assumption in models across scientific disciplines, but rather in a satisficing manner. The term satisficing behaviour (following Simon [1955, 1969]), is used to denote behaviour that keeps performance on a level that is considered good enough. Driving behaviours such as lanekeeping or maintaining a particular speed can be thought of as satisficing. Drivers rarely care where in the lane they are, as long as they are not outside of it, and not too close to other traffic or obstacles. Drivers also generally do not care about their precise speed. Instead they match their speed to other vehicles in the lane they are driving in, or attempt to drive as fast as possible. It is not until the situation suddenly becomes less safe that drivers start to actively and consciously correct their movement. The more unsafe a situation becomes, the more safety becomes the primary goal. Once a satisfactory level of safety has been reached, the driver will switch back to regular, satisficing driving.

These views provide a basis for traffic safety improvement strategies. Instead of lowering the amount of risk drivers are willing to optimize for through incentives, as suggested by Wilde [1998], Näätänen and Summala [1974] present an example with two possible ways of improving safety. Many road shoulders in Finland have a dangerous drop on the edge of a few inches, concealed by tall grass. Safety should be increased without simultaneously decreasing subjective risk, in this case by raising the surface next to the road. This would cause an increase in safety, but not decrease the subject risk, due to the same visual appearance. Alternatively, the grass could be cut, so even though objective risk remains the same, subjective risk increases, causing drivers to be more careful. Similarly, a very effective safety measure would be the installation of crash barriers between lanes of traffic in opposing direction. They would prevent head on collisions between swerving vehicles, but result in significantly more minor accidents, decreasing objective and increasing subjective risk.

Since the first paper by Näätänen and Summala [1974] provided a basis, zero risk theory has been refined and expanded. A recent work by Summala [2007] provides a comprehensive overview of the theory, including the effects of emotion, workload, multilevel control theory, traffic laws, and an extension of the safety margins concept into the time domain. However, the introduced concepts of behavioural thresholds, zones, and satisficing driving, are sufficient for the research in this thesis.

If we are to use the above concepts to research traffic safety, we need to be able to quantify behavioural output, so that we may pose and validate a hypothesis. We will present and explain the most widely used measures in the next section.

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1.3. QUANTIFYING DRIVING BEHAVIOUR CHAPTER 1. INTRODUCTION

1.3 Quantifying Driving Behaviour

To make the study of traffic safety more tractable, researchers generally only consider the output of driving behaviour, which can be quantified using proximal indicators. Indeed, traffic safety is often defined as a set of these indicators, without considering the underlying behaviour [Martens et al., 2012].

Behavioural indicators are broadly classified in two categories, longitudinal and lateral, associated with car following and lane keeping performance of the driver, respectively.

We will discuss several metrics from both categories, as well as several miscellaneous indicators. For other overviews of behaviour and performance metrics, see Martens et al. [2012], Liu et al. [1999, 2009], and Östlund et al. [2005].

1.3.1 Longitudinal proximal indicators

The longitudinal proximal indicators quantify the risk of an accident by movement in the longitudinal driving direction. Longitudinal indicators apply to car following situations, where there is a risk of a head-tail collision. Measures specific to these situations are time headway and time-to-collision, which quantify the ability of a driver to keep a safe distance from the leading vehicle. Speed and speed variablity are tangentially related, but they also play a role in non-car following situations.

Speed

Vehicle speed is a behavioural indicator that is linked to general road safety. It is limited by law on public roads in many countries, and is often targeted by government road safety campaigns.

Nilsson [2004] has shown that accident risk increases with increasing mean driving speed on rural highways, by comparing accident rates and speed limit changes on various roads in Sweden. The resulting data were fit to a power law model, with coefficients depending on the type of injury resulting from the accident.

Studies by Kloeden et al. [1997, 2001] on the effect of individual vehicle speed shows an exponential increase of accident risk with an increase in speed.

A meta-analysis study conducted by Elvik et al. [2004] demonstrated that a single speed parameter such as mean speed is not sufficient for representing the influence of speed on crashes on urban roads. On these roads, it is also necessary to incorporate the variation of the speed into Nilsson’s model. Publications by Kloeden et al. [2001] and Larsen et al. [1990] also present models for accident risk as a function of speed variability.

The results from Nilsson [2004] may also indicate that the effect of a particular increase in speed on accident rate depends on the speed design of the road, with the effect being smaller on roads that are designed for high speeds, such as motor ways, than on lower speed roads. The exact relationship between speed and crash rate is not clear, and depends on actual road and traffic characteristics. Even though general inferences can be made from aggregated data, current vehicle speed is not a reliable indicator of driver safety.

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For an excellent overview of current the current literature of the effect of speed and speed dispersion on accident risk, see [Aarts and van Schagen, 2006].

Time headway

Time headway (TH) is an indicator of the distance between a vehicle and its lead vehicle. In an attempt to improve road safety, some authorities use it to impose fines on drivers that do not keep a sufficient distance between their vehicle and the car in front of them. It is defined in Evans [1991] (appearing in Vogel [2003]) as the elapsed time between the front of the lead vehicle passing a point on the roadway and the front of the following vehicle passing the same point.

Various criteria for safety based on time headway exist, with some governments adopting a standard of less than 2s as critical, such as the United States and the Netherlands, and less than 1s in Sweden. Additionally, results from an algorithm by Janssen [2000] (appearing in Martens et al. [2012]) show that the risk of a car crash rises sharply when TH drops below 1.5s.

The concept of time headway corresponds to the use of safety margins and comfort in Summala [2007]. He cites a study by Ohta [1993] that links time headway to the Proxemics concept [Hall, 1966]. Ohta asked drivers to follow a car at various distances (e.g. most comfortable distance, minimum safe distance), and defined driver comfort zones based on this data. The comfortable zone is between 1.1 and 1.7 seconds time headway, below 1.1s is felt as critical, and below 0.6s is considered dangerous by drivers. Longer headways were considered uncomfortable for car following purposes, ‘‘because they are against the social norm’’.

There are several limitations to the use of TH as a measure of safety. For instance, a very low time headway is safer than a time headway of approximately 1s, as the speed difference at the moment of impact will be much lower. Additionally, like speed, TH only describes a single aspect of driving. Furthermore, a small TH can be maintained over long periods of time under stable traffic conditions [Vogel, 2003].

Time-to-collision

Vogel [2003] presents the following definition of to-collision (TTC), also known as time-to-contact: the time span left before two vehicles collide, if nobody takes evasive action (first appearing in Hayward [1972]). It is the time that is needed to cover the distance between the lead and the following vehicle with the relative speed between the vehicles. TTC is undefined if the speed of the lead vehicle is higher than the speed of the following vehicle. Note that TTC does not only apply to car-following situations, but can also be applied to for example head on collisions.

Time-to-collision and time headway are independent of each other [Vogel, 2003]. Since TTC can never be lower than TH, and headway is easy to measure, TH should be used by authorities as a tailgating criterion. Although a small TH does not necessarily indicate a dangerous situation, a small TTC means that action has to be taken in order to avoid a collision. TTC therefore serves as a better safety criterion.

Time to collision has been employed to evaluate safety by determining the minimum TTC during a maneuver, and as a method to compare safety associated with different drivers, environments, or situations. See Vogel [2003] for an overview.

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The cutoff TTC value that is to be used as safety limit is unclear. Analyses show that minimum TTC values less than 1.5s indicate a potentially dangerous situation in urban areas [Svensson, 1998]. On the other hand, Maretzke and Jacob [1992] (appearing in Vogel [2003]) suggest a 5s threshold.

Time-to-collision is clearly inversely related to accident risk in many driving situations, but limitations similar to those of time headway apply. TTC only measures one dimension of traffic safety, and should therefore be combined with other criteria. For instance, two vehicles driving close together can have undefined TTC if the lead vehicle is driving slightly faster, but the short distance would still result in an accident if the lead car were to suddenly brake. On the other hand, a low TTC is acceptable in predictable situations, for instance when approaching a traffic light or stop sign. The lead vehicle’s breaking is predictable, and as such a driver could be comfortable with a low TTC. Traffic jams may also lead to low TTC values if the distance between cars is close and the following car moves forward to close a gap left by the lead car.

Finally, TTC is also an example of a safety margin indicator that can be used in zero-risk theory [Summala, 2007].

1.3.2 Lateral proximal indicators

Safety indicators that capture the lateral component of driving all relate to lane keeping behaviour. They try to give an indication of lateral vehicle control and the level of safety related to the distance to the lane boundaries. We discuss lateral position, time-to-line crossing, lane exceedance rate, steering rate reversals, and steering entropy.

Lateral position

Lateral position, and its standard deviation SDLP, indicate the driving position of a vehicle with respect to the lane center. Large absolute lateral position is considered more dangerous than a small lateral position, because of the increased proximity of the vehicle to vehicles in other lanes, and the increased likelihood of lane departure. A large SDLP indicates strong vehicle swerving, which is commonly assumed to have an adverse effect on traffic safety [Martens et al., 2012].

SDLP is commonly used as indicator for lateral vehicle control. Its use was pioneered by O’Hanlon et al. [1982], who used an instrumented car to measure lateral position of expert drivers under the influence of a psychotropic drug. They found that lateral position was more variable, with deviations as far as 0.5m outside the lane, when drivers were subjected to the drug.

Liu et al. [2009] differentiates between two definitions of SDLP. One definition separates the measure of the driver’s ability to maintain a straight path, precision, from the driver’s ability to track the lane center, or bias. The other definition of SDLP calculates deviations with respect to the lane center, and is a composite measure of precision and bias. Liu et al. [2009] recommends the use of separate measures for bias (mean lateral position) and precision (standard deviation of lateral position), because they are likely to indicate different aspects of driving behaviour. This was done by Pilutti and Ulsoy [1999], among others, who found that six out of twelve drivers tended to the right of the lane center, and that driving precision decreased over time during a two hour drive.

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Of all vehicle-based indicators, SDLP is most consistently associated with drowsiness. One study [Ingre et al., 2006] even reports precise numerical estimates for SDLP as a function of drowsiness levels based on the Karolinska Sleepiness Scale (KSS) [Åkerstedt and Gillberg, 1990]. See Liu et al. [2009] for an overview of driver drowsiness.

Just as the other indicators, lateral position and SDLP have several limitations. Foremost, it is not clear whether an increase or decrease of the SDLP always relates to a respective increase or decrease in safety. Is the increased SDLP that is a result of navigating a curved section of road really indicative of a reduction in safety? What is the relation between a large SDLP in a wide lane and a small SDLP in a narrow lane [Martens et al., 2012]? Which SDLP values should be considered unsafe? How long should the interval over which SDLP is calculated be? An interval that is too long can not be used to detect a change in safety in a short time span, whereas a short interval may prove too volatile. Possibly, a combination of both could be used. Furthermore, the calculation of a standard deviation of the lateral position requires the lateral position to be normally distributed, but distributions are skewed for some drivers (e.g. Pilutti and Ulsoy [1999]3_).

Time-to-line crossing

A measure that is better able to detect lateral risk early is the Time-to-Line Crossing (TLC), developed by Godthelp et al. [1984]. This indicator is a measure of the time until a vehicle crosses the lane boundary, given constant speed and vehicle heading. Short TLC values imply a lane departure is imminent, which, provided the lane departure is unintended, indicates reduced lateral control and increased safety risk, with a threshold value of 1s as a rule of thumb [Martens et al., 2012]. Summala [2007] also uses TLC as a safety margin that might trigger the transition from passive to active driving once it crosses a particular threshold.

Time-to-line crossing values can be estimated as the ratio of the lateral distance from the line to lateral velocity. Alternatively there is the more complex ratio of the Distance-to-Line Crossing (DLC) along the vehicle path to the vehicle forward speed.

While TLC provides an indication of the likelihood of a lane departure, it can be unreliable in scenarios where the driver is naturally close to the lane boundaries, e.g. when navigating corners, or with a natural driving position that is away from the lane center. Furthermore, TLC can be hard to calculate due to difficulties in obtaining the required vehicle state variables Mammar et al. [2006]. They provide an excellent overview of TLC computations, difficulties, and sensitivities. They also propose a distance based calculation that could, with the help of an onboard video camera, be used to calculate TLC even in difficult situations.

Finally, it is not clear how TLC should be used in situations where the driver changes lanes. Incorporating TLC in a driver warning system, for example, might introduce an unacceptable amount of false positive warnings.

Lane exceedance rate

Wierwille et al. [1996] defines lane exceedance rate as the number of times the vehicle crosses the lane boundary within a certain time interval, while Östlund et al. [2004] as the proportion of time any part of the vehicle is outside the lane. Alternatively, Liu et al. [1999] measured

3_{lateral position ‘‘distribution shapes have normal tendencies’’ for some drivers, but not for all, nor are any statistical}

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the frequency of minor and major lane deviations, where minor deviations are defined as any part of the vehicle exceeding either the central line or the roadside lane boundary, while major deviations were defined as exceeding the line by more than half the width of the vehicle. Since lane exceedance events are rare in normal driving, they are unlikely to produce statistical effects. They are therefore not suitable for assessing driver safety in regular driving situations. However, they may still be used to evaluate experiments with impaired drivers, or be used as triggers to capture valuable information in case such an event occurs [Östlund et al., 2005]. Steering rate reversals

Change in driver attention is associated with changes in steering behaviour [Macdonald and Hoffmann, 1980] and thereby with traffic safety. Normal driving is characterized by continuous small steering corrections, to correct for roadway variance and driving conditions, typically between 2 and 6 degrees. As attention decreases, the vehicle heading is corrected less often, resulting in larger steering corrections, typically in the range of 6 to 12 degrees.

In an experiment related to modality and complexity of information display, Liu et al. [1999] measured the frequency of large (greater than 10 degrees) steering reversals, and showed a significant three-way interaction between age, modality, and complexity. Presenting drivers with complex information on a visual display resulted in significantly more large steering reversals for older than younger drivers. The same occurred with simple versus complex information, regardless of modality.

Based on these results, it seems likely that steering reversals can be used as a metric for driver attention. The link between driver attention and traffic safety is firmly established, see for instance McKnight and McKnight [1993], who report that lapses in driver attention have been identified as a significant contributing factor in as many as 90 percent of traffic accidents, and that 37 percent of drivers from a 1982 dataset took no action to avoid a collision, which suggests that attentional lapses are a major factor in the causation of highway accidents. A change from small to large steering corrections therefore indicates increased risk of an accident. However, it is unclear how useful these results are to monitor the decrease in attention of a single driver during a single trip.

Steering entropy

Entropy is a measure of the uncertainty of a random variable, or the rate at which information is produced. Nakayama et al. [1999] developed a method of measuring steering entropy that can be used to quantify cognitive workload while driving. The approach is to predict a steering wheel angle based on the previous three values, then and calculate the difference between the predicted and measured steering wheel angle. The distribution of these errors, based on a control condition, can be used as baseline within a subject. The distribution is divided in bins, and the error frequency in each bin is calculated. A similar procedure, with the same bins as the baseline, is performed for data taken from the same subject while performing an additional task. This results in another list of error frequencies, which are then used to calculate the entropy, as a summary of the difference between the distributions.

Using this method, they found that steering entropy showed high correlation with existing dual task and subjective evaluation methods. They also found that steering entropy values increased in direct proportion to the degree of task difficulty. The method was further improved

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by Boer [2000], who incorporated more advanced signal processing techniques, and used it to significantly quantify the effect of several workload inducing tasks. He then used steering entropy in combination with an event detection performance measure, in the form of reaction times, to quantify the level of driver distraction caused by wide range of extra-driving activities.

Dawson et al. [2010] attempted to distinguish between a group of regular drivers and a group of drivers suffering from Alzheimer’s disease by using Boer’s entropy method on lateral position data. They found no significant effect in the entropy measure, but suggested that other entropy measures could be used. For instance, the sample entropy developed by Richman and Moorman [2000], that measures complexity and regularity of experimental time series data, might be useful in characterizing (groups of) drivers.

There are some limits to the use of entropy to characterize driving behaviour. As noted by Dawson et al. [2007], some unsafe driving behaviours are negatively associated with entropy, because safe driving often involves making frequent minor corrections to the vehicle heading. These small movements might lead to an increase in entropy. Furthermore, driving rigidly and making infrequent large corrections result in relatively long sections of data with a fixed steering wheel position and linearly changing lane position, leading to reduced entropy measures. It is also not clear that entropy provides a criterion that can be used to differentiate between safe and unsafe driving. Entropy has only been successfully used in within subjects studies, and as such there is no scale on which to judge the safety associated with a certain measured entropy. Certainly, there is no clear cut off value above which driving behaviour can be seen as unsafe.

1.3.3 Model specific metrics

It is also possible to use non-standard model specific parameters as driving behaviour indicators. For instance, Dawson et al. [2010] used a third order autoregressive time series model with a signed error term to model lateral vehicle control. Using this model, they were able to distinguish between two groups of drivers, a group composed of people suffering from Alzheimer’s disease, and a control group composed of neurologically normal, aged drivers. The parameters in their model, the coefficients for flat, linear, and quadratic components, suggested that drivers with Alzheimer’s disease (AD) maintained less control over their vehicle, because their movements were more exaggerated and less dampened compared to the control group. Drivers from the group with AD were also less vigilant in re-centering their vehicle, and maintained an average lateral position closer to oncoming traffic in the left lane.

1.3.4 Situational Awareness

Another method of determining how safely someone is driving is to not use behavioural outputs, but to look at the driver directly. A driver needs to pay attention in order to drive safely, in other words, a driver needs good situational awareness.

According to Gugerty [2011], situational awareness is the updated, meaningful knowledge of an unpredictably-changing, multifaceted situation that operators use to guide choice and action when engaged in real-time multitasking. It is a type of knowledge in psychological terms. Three levels of cognitive processing are involved in situational awareness. At the base level there are automatic, unconscious processes that probably use ambient vision. These do not

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demand cognitive resources, as they opperate at the pre-attentive stage. Then there are recognition-primed decision processes, based on detected events, that are conscious for brief periods at a time, and place few demands on cognitive resources. Finally there are conscious, controlled processes with heavy demands on cognitive resources. The latter two stages depend on focal view [Leibowitz and Owens, 1977, via Gugerty, 2011].

Measuring properties of a driver’s focal view should then give some insight into how much attention a driver has for the driving task, and therefore into how likely he or she is to be driving safely.

Eye trackers can be used to measure a driver’s eye movements (saccades) and fixations. Although focal attention can shift without a saccade, the assumption that focal attention is tracked by fixations is safe for driving because of the wide field of view, which makes large eye and head movements necessary for driving safely. A common variable that indicates attention is the dwell time, the percentage of time spent fixated on particular locations. This method is suitable for use during regular driving on the road.

In simulator studies it is also possible to use performance and event detection based measures. Inferences can be made based on actions taken in pre-defined driving scenarios, or by measuring the speed and accuracy of reported events in a hazard perception test.

There are many more methods of determining driver attention. For a complete overview of situational awareness in driving, the underlying cognitive processes, methods of measuring situational awareness, and understanding the component parts of situational awarness, see [Gugerty, 2011].

If driving happens habitually, in a satisficing manner, as zero-risk theory posits, the change from error neglecting to error correcting behaviour may be detected from a driver’s eye movements, and correlated with safety margin indicators such as TTC, TH, and TLC.

1.3.5 Measuring safety as a function of proximal indicators

We have discussed the most commonly used behavioural safety indicators, and as shown, they all have limited applicability to detect a change in safety levels for single vehicles. To summarize, the following common problems exist:

• Measures can be suitable for macroscopic analysis of traffic, but not for detecting changes in safety on a microscopic level, i.e. for a single driver.

• Indicators can be inaccurate, because they are sensitive or hard to measure.

• Measures can be ambiguous, changes can be interpreted as more safe or less safe, depending on the situation.

• Measures can lack a threshold value for the distinction between safe and unsafe behaviour. • Proximal indicators, such as TH or TTC, only measure a single aspect of driving.

• Metrics can be unstable between and within subjects, which leads to reproducibility issues. Most importantly, these indicators are usually validated against accident records, and given the previously discussed problems with infering safety levels from accident data, it is unclear whether these indicators can be used to accurately measure a driver’s safety risk.

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1.4. MODELING SATISFICING DRIVING CHAPTER 1. INTRODUCTION

Above problems might arise due to individual problems with the respective proximal indicators, but it is also suggested [Hancock and Scallen, 1999] that there is a fundamental problem with the research methodology in traffic safety research.

The approach of trying to model individual outputs of driving behaviour might be based too much on standard methods from mathematics and physics, and not enough on a theoretical understanding of the way humans operate vehicles.

Assuming that human driving behaviour is satisficing recognizes that behaviour can not be captured in simple mathematical models that relate traffic safety to trying to maintain a certain time headway, speed or preferred lane position. Instead, trying to infer when drivers perceive a situation to change from safe to unsafe, and attempting to model that change might be a more promising path.

1.4 Modeling Satisficing Driving

In order to better understand human driving, and thereby improve our ability to prevent or alleviate road accidents, we need to research regular instead of extreme driving situations. The data for macroscopic statistical research on regular driving is not yet available, so we will focus on individual drivers in a microscopic study instead. Drivers are very proficient in distinguishing safe from unsafe situations, provided they are paying attention. Therefore, the driver itself may be a source of valuable insight into which situations are safe and which are unsafe.

We will take the position of Näätänen and Summala [1974] and Hancock and Scallen [1999] and assume that drivers do not normally feel any risk, and drive in a satisficing, error neglecting manner until certain safety margins reach a threshold, causing drivers to prioritize safety. By investigating the transition from error neglecting to error correcting behaviour, we hope to be able to distinguish safe from unsafe situations, providing a basis for research into which behavioural indicators best predict current driver risk.

Since the change in driving priority is governed by the process of maintaining adequate safety margins, we will base our investigation on this concept. We restrict our scope to the lateral component, since less work has been done in this area.

A driver has the most direct control over lateral safety margins through the steering wheel, which will therefore be our primary source of data. By further restricting our research to a highway driving scenario, we obtain a reliable method of measuring lateral safety margins, i.e. the lateral position within a lane. Of course, a driver will feel more anxious while driving with large trucks to the left and right side than when both adjacent lanes are empty. Nevertheless, we assume drivers are so trained in lane keeping that they feel uncomfortable to cross lane boundaries, even when no other traffic is present.

Lateral position and steering wheel data can be combined to produce a lateral distribution of heading error corrections. In this thesis we investigate whether this distribution can be used to detect the moment in which a driver transitions error neglecting to error correcting behaviour, indicating the change from a safe to an unsafe situation.

We pose the following research question: can we detect the transition from error-neglecting to error-correcting behaviour by using a distribution of significant heading corrections?

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1.4. MODELING SATISFICING DRIVING CHAPTER 1. INTRODUCTION

We start by expanding on this idea in section 2.1 where we discuss the proposed model. The following sections chapter 2 and section 2.3 present the experiment we performed to test the model, as well as the necessary pre-processing steps. Chapter 3 contains a discussion on the independent variables that are necessary to validate the model, which itself is presented in section 4.1. Finally, the rest of chapter 4 is an overview of our most promising exploratory data analysis results.

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Chapter 2

Experiment

2.1 Model

In the previous chapter, in section section 1.4, we set out to investigate how steering corrections are laterally distributed, and attempt to find a lateral position boundary that is associated with a change in behaviour from error-neglecting to error-correcting driving.

One could take any significant change in the steering wheel orientation, α, as a significant driver action. However, we look at the steering wheel’s angular velocity ω instead, as it likely corresponds better with a driver’s intention. From the assumption that drivers attempt to maintain safety margins we can say that it seems more likely that they steer left or right by some amount, rather than setting the steering wheel to a certain angle.

We therefore define a steering correction as a period of time in which the steering wheel keeps turning in the same direction. The correction starts and ends with a sign change of the steering wheel’s angular velocity ω. The most important difference with a definition based on significant changes in steering angle is that a series of multiple rotations in the same direction is considered one correction, instead of a series of corrections.

This leads to the following mathematical definition of a steering correction: c(t) =

(

sign ω(t), when ω(t) 6= 0

c(t − ∆t), when ω(t) = 0. (2.1)

where t is a sample’s time stamp, and ∆t is the time between samples. The last line causes a series of rotations in the same direction to be part of a single correction.1

We assume significant steering corrections to entail a change in steering wheel angle that is noticable over a period of time, since they are meant to have a significant impact on vehicle heading. Additionally, we want to filter out minor movements due to a driver moving his hands without intending a change in heading, as well as mechanical and sensor noise. Data gathered from a pilot project in naturalistic driving conditions suggests that a one-second rolling time

1_{The possible singularity in c(0), when ω(0) = 0 never occurs in practice due to how the algorithm we use is}

Time-series analysis of driving data

University of Amsterdam

Faculty of Science