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Module 1: Safe and Sustainable Transportation Systems

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Road Crash Estimation and Predictive Methods

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In this lecture, what we are going to expose you to, uh, are the different estimation methods of, uh, road crashes in general. Uh, then we will subsequently look at, uh, specifically pedestrians and bicycle crashes, uh, but, uh, you have to, uh, first understand the concepts and definitions are related to road crashes, uh, how they are estimated and what are the parameters involved in these estimation methods? So, uh, you would now notice that most of them, um, uh, transportation, uh, safety, literature, uh, we are using the word crash, uh, rather than accident, uh, because, uh, more and more, uh, research is showing that, uh, all of these accidents. Uh, R may not be, uh, an accident, uh, for example, uh, the word, the meaning of the word, uh, accident in English means that it happens suddenly or without, uh, uh, anybody's, uh, intervention or any things intervention. But, uh, what we are noticing is that many of these accidents, uh, can be predicted, uh, and if they are being, if they can be predicted, that means they can be. Uh, avoided or stopped as well. So hence, uh, this word crash is, seems to be a better fit. Uh, so when we say crash, what we mean is that a set of events that result in injury or property damage due to collision of at least one motorized vehicle and may involve collision with another motorized vehicle, a bicyclist, a pedestrian, or an object. Okay, so a crash, uh, on a totality, uh, is, uh, uh, does not always necessarily, um, lead to an, uh, lead to a fatality or a death. It may be just an, uh, property damage kind of an, uh, crash. Uh, it may be, uh, involving multiple vehicles or just one vehicle crashing with an object, uh, on the road. Or it may be a vehicle crashing with, uh, either a pedestrian or a bicyclist. So everything, uh, Uh, including, uh, inclusive of all of these terminologies is what is it crush? So when do you want to estimate a crash? Right? Uh, one way to know about an, uh, crash or an accident is to, uh, is after the fact that the accident happens now, that is a very reactive way of, uh, understanding or knowing whether, uh, crashes happen. But if you had to predict a crash. Or if you had to estimate that this roadway is likely to have a number of crashes in the next month or in the next year, then you can almost, it's almost a proactive measure and you can almost, uh, then do some, uh, take, make some interventions so that, uh, these crashes can be prevented. Right? So that is why it is very, very important nowadays, uh, in today's, uh, Uh, transportation arena to estimate the crashes. So when we say estimate of crashes, what we are usually trying to do is, uh, we are trying to develop different methodologists to. Predict crash frequency, right? How quick, uh, how frequently, um, a crash can occur. So it can be on an existing roadway for existing conditions, uh, um, during the past or in the future. Right? So if you already have data about, uh, the number of accidents or crashes in the past, then for that particular type of a roadway, you can say, for example, uh, on state highways in such and such. Uh, state, uh, and in this district, uh, there were a number of crashes per year, so that is kind of a crash frequency. That is a very, uh, easy to understand, simple terminology of understanding what a crash frequencies look past. But can you use the same trend and predict that these, uh, the crash frequency will be the same in the future or not? That is what something, uh, we will tell you how to do that. Okay. So it can be for an existing roadway. It can be for existing roadway for alternative conditions, right? Maybe different conditions causes different crash frequencies at all. It could be for totally new roadway as well that a new roadway is being built, uh, between, uh, two piles. So what is the, uh, probability or what is the prediction that how many crashes will occur there? Uh, or how frequently they will occur. So that is also something that has to be taken into account so that if you, I mean, this is the best time to take into account, uh, the crash frequencies for a new roadway because, uh, vehicles have not yet started plying on that doorway so that you can incorporate safety measures proactively. So as to reduce the probability of those crashes happening, Uh, now what are the different contributing factors when it comes to crashes? Right. So what you will see in this, uh, in this picture on the right-hand side is, uh, overall, what are the three different types of factors that we group, um, uh, demander one are the roadway factors. The other are the vehicle factors, and then there are. Driver factors. So you will see this. This is a little bit of a, uh, old, uh, uh, dataset, but this percentages may differ, uh, as we are, uh, uh, improving our, uh, research day by day. But overall, what we have seen is the crashes occur. You do different driver related, uh, uh, factors, different roadway related factors and different vehicles let it factors. So a driver related or human factors include. Uh, a judgment, uh, driver's skill, attention, fatigue, whereas vehicles, uh, vehicle related factors include the design of the vehicle, the maintenance of the vehicle, the manufacturer, uh, uh, what type of vehicle is it? Right. And whereas the road we are, the environment include the geometric alignment. Cross-section traffic control devices. Meaning signals are on signalized intersection, the surface friction grade, whether visibility or not. So these are broadly all of the different types of factors that contribute to crashes Ana uh, on a facility, on a high Vera Arbonne road. The other important thing to, uh, uh, understand is this a whole idea of objective and subjective safety. Right. Uh, objectively when we look at it, something that can be quantified, right? So, uh, when we look at objective safety, essentially what we are trying to do is try to find out, uh, if there are, uh, what are the number of crashes or what are the number of, or what is the crash frequency and how can we reduce that? Whereas there is a totally different, uh, arena of what is called a subjective frequency. That is the perception of how a person feels. Safe on the transportation system. Uh, this is, this may vary, uh, based on the different types of users vary from location to location, but nonetheless is becoming a very, very important, uh, aspect. When we talk about, uh, transportation safety, for example, see if you, uh, if you do a physical improvement on a roadway, what do you expect? You expect that because of that? Improvement. Your crashes were maybe here and it has li it has led to now fewer number of crashes, right? It has gone from here to here and also at the same time, the subjective safety. So now people feel that here they were feeling less safe. Now they are feeling. That they're more safe. So a physical improvement. When you do something, uh, take a measure to, uh, improve safety or physical measure, then it should affect both the objective safety as well as the subjective safety. However, when you say, for example, what TV safety campaign, it has been noticed that if, uh, if the situation was such that you are feeling unsafe or you are feeling safer, You may change the perception of a subjective safety may change, but your objective safety is not changing. Your objective safety is not moving where it is. This line is parallel to your, uh y-axis. So your objective safety is not changing because of her TV safety campaign. Right. So we do, so these are different types of, um, uh, means of understanding how can you improve the safety offer, uh, facility. Similarly, when there is physical deterioration. So when a road is a road or a bridge or anything is deteriorating in age, right? So what you start to suddenly feel is you were feeling safer here, but you suddenly now start to feel less safer because that bridge is getting. Um, um, less and less safer at the same time, maybe objectively as well. There are increasing number of crashes right here. There are fewer crashes. Now there are more crashes, but the slope of the line says that your feeling of safety is reducing by a larger amount than the actual objective safety or the actual number of crashes that are taking place. So different measures give, uh, gives results to different types of. Objective ones, subjective safety, uh, implications. Right? So you're not only look at the objective safety, but all at the same time, you have to look at subjective safety of your, uh, uh, highway or the facility in your area. Then you different descriptive analysis. Uh, our disruptive measures have been developed over the years, which gives you an idea about. Um, the number of crashes or the frequency of crashes that are happening, uh, for example, uh, you may want to, uh, say you have decided that you want to know the number of accidents, uh, divide, uh, as a result of the different types of, uh, intersections that are there in your area. Uh, so it may be, uh, at a mid-block, uh, intersection it maybe at a Y intersection maybe, or a T intersection. It may be at a roundabout four legged. Or even five, like junction. So you can divide it up in that way and understand what are the safety implications, uh, at different types of intersections in your city. So in order to know, uh, or different parameters that are involved in understanding, uh, the road safety may include just purely the number of people that have died at each of these or the percentage of death, number of injuries. Remember all crashes do not lead to death. There may be a lot of crashes that lead to minor injuries, major injuries, uh, and then maybe they lead to death. Okay. So you may not, not, you may want to know either the total number or the percentage, uh, the, just the total number of crashes or you want to divide it up into different types of injuries, minor injuries, mean of the injuries or mean of the, that. So you can develop different types of descriptive statistics, which will give you a clearer picture based on. Uh, where you want to, um, know about the safety of your facility in the city. So similarly, you can do it for different types of roads. You can do it for a daytime, nighttime, so you can do it for multiple, uh, multiple parameters and you can calculate all these so that these are all done so that the, uh, measure that you implement to improve it. Uh, should be very, very specific. So in this type of care situation, you have to look at possibly a mid-block section is the most vulnerable section in this case. So you have to improve the safety of the, uh, pedestrians crossing at mid-block, for example, maybe. So what type of intervention do you put? You do not, you should not go for an intervention that is more effective at a signalized intersection versus now you have to think of something that is. More, uh, practical for mid-block section. So that is the reason why you develop all different types of descriptive statistics. Uh, you also have to know quantitatively, uh, how well to predict, right? Prediction always has a lot of errors now, uh, when you're trying to predict anything, you need essentially a lot of input values, right? The better the input values. The more precise, the input values, the better will be your prediction. So, uh, a system that we are moving towards is to have, is to capture, uh, all incidents are all crashes that happen, uh, at a roadway and write down the parameters then and there. Right? So when an accident happens, you would see that, uh, not only the police arrives, maybe the ambulance, uh, at the spot. Uh, we are also trying to have, uh, an engineer along with them, uh, arrive at the spot so that, uh, the engineer can help, uh, point out some deficiencies in the roadway design or the intersection design or whatever it is so that all the parameters have captured at the same time, um, of the, of the crash by collecting all those parameters, then you can, uh, hope to develop a predictive model. Which will give you better results. Right? So it is very, very important, so that, uh, for us to do such kind of, uh, accident investigation, right at that spot, and you have to have different types of people come there. So, uh, not only, uh, the ambulance, not only the police, uh, but also maybe, uh, engineers on the spot so that they can, uh, verify how, uh, different parameters or what are the different parameters that were involved in that. Uh, for that particular type of crash? No. How the different crash estimating methods evolve, right? We have already talked about crash frequency. The other thing that, uh, people now look at rather than just crash frequency is something called a crash rate that tells you that, uh, how many crashes have happening, but, uh, So, uh, a number of miles off vehicles, uh, driven on that road, right?

So the point is the more, the number of vehicles, the likelihood that the number of crashes will increases higher. So it's not just the frequency or how many accidents are happening per year or per month. It is also how many vehicles are on that road or how many vehicles have been driven on that road. So that is something is called a crash rate. And then there are, of course, a lot of indirect safety measures. Known as surrogate measures, uh, that have been developed, right. Surrogate measures usually mean, uh, for example, uh, if you don't wear a helmet, you're more, more likely to be involved in a, uh, injury aura, fatality related crash. Uh, if you're on a two Wheeler, right? So now, so people are trying to relate the wearing of helmet or the wearing of a seatbelt when you're in a car to the probability of you being involved in it. Um, uh, major, uh, crash or a major injury crash, right? So different types of crashes. You can categorize that into, so these are called a surrogate measures or indirect measures. So when you, when you don't have good information, good data on your, uh, roadway segment, direct, uh, number of accidents are, uh, information that is available firsthand. If you don't have that kind of data, then what you do usually is try to predict an accident using different types of. Uh, indirect measures and those indirect measures usually call, uh, surrogate measures. And then there are of course, uh, statistical techniques, uh, which looks at, uh, what is the best model that fits the existing number of accidents. Right? Usually people will see that, uh, can, can regression models, uh, estimate crash frequency, um, uh, can, uh, um, uh, uh, pies and models, uh, are negative exponential models. Uh, fit, uh, the crash frequency that is happening. So those are all statistical tools. Then again, if those are, those are can also help in predicting future crashes. If, if the models fit is very good, right with the models, fit is very good. Then you can predict these crashes in the future as well. Uh, so crash frequency or crash rates are often used, uh, for crash estimation and evaluation. Uh, they are very simplistic. So for example, you may, uh, many times see such statistics in the newspapers or in the, uh, or in the, uh, uh, digital media or TV or in the TV showing the number of accidents that have happened per city per year, uh, and how well they rank. So these are, uh, these are easy to understand, uh, And since these crashes have already happened. So, uh, the validity, the acceptance of these numbers are high. People do believe in these numbers. Uh, but you know, it, it, it, it does not, it does not provide a means of, uh, uh, predicting crashes. It is just a very reactive method. So just to know about the crash after the crash has happened, Right. That is a very old way of, uh, trying to deal with, uh, reducing the number of crashes. So it does not give you alternatives. It does not give you different methods of prediction or, uh, anything like that. Uh, however, so those, if you look at each of those methods to crash frequency, he's, uh, simply the number of crashes are divided by the period in either years or months or whatever. You're looking at crash rate, which is a better, uh, which is a better. Um, uh, measure than crash frequency. What it says is that a crash rate per hundred million vehicles miles traveled, right? So if the more, the number of vehicle miles VMT or VKT traveled on the road, the number of crashes, uh, is likely to be higher, right? So number of crashes by a hundred million into a hundred million divided by the volume on that road, uh, every day, a number of years you wanted for an. The total length segment that you are looking at. So that is essentially how you determine the crash rate. So if you're given like simple problems like this, say for example, on, on road segment a, which is a three mile section, uh, it has had four crashes over five years and has a traffic volume of 4,000 vehicles per day. Whereas, uh, the next segment segment B is also a three mile section, but it has had 10 crashes over five years. And has a traffic volume of 12,000 vehicles per day. So if you determine crash frequency and crash rate, what do you expect to see? Which is the worst segment or which is the better segment, right? That is what you essentially want to compare these two segments to see, which is the worst segment, and then maybe prioritize, uh, usually you want to help both of the segments, but if you are only prioritized, then you would have to pick which segment to, uh, improve. So, uh, if you purely looked at crash frequency, Then you would have seen that segment a, uh, where four out of four patches in five years pointed, whereas, uh, uh, 10 crashes in five years, uh, is two. So you would've, you would've thought that segment Baeza, uh, worst segment. However, if we start now looking at, uh, the crash rate, which is. Uh, with depends upon how many vehicles are traveling on that road. Then you will see that segment a, uh, the crash rate and segment is 18.2 crashes per hundred million vehicle starboard. Whereas segment B's only 15.2 per hundred million vehicles, styles that will give you that gives you an idea of, uh, maybe a road segment, a hazard, um, is a more serious, uh, situation. And we have to. Focus more there because the crash rate is higher on segment a, although it is crash, frequencies lower. So that's why people are more and more people are looking at crash rates rather than just the frequency of crashes. Uh, what are the indirect means of, uh, understanding, uh, safety? Like we said, the surrogate surrogate methodology is used primarily because maybe a road or a facility is not yet in service. So it's a. A road that is just being built. So you don't have any previous data on the road. So how can you predict what the crashes will be on that road? Or? It has been only just, just a, um, open for the last few months or few weeks. So you don't have a lot of data on it. So how can you then predict. Uh, or maybe crash frequencies are low, uh, frequencies are low. However, people are complaining that, uh, there are a lot of, uh, accidents that are leading to fatalities maybe. Right. So you don't know how to then, uh, well, how do you deal with it? Uh, or if it has some unique features, uh, it has lots of curves. Horizontal curves are vertical curves, uh, more than the average amount number of curves. So such a unique features may also lead to developing. Uh, unique surrogate measures, which tells you about the safety of that area. Right? So here you're seeing that, uh, people have, uh, like we were talking, not wearing helmet versus not wearing a seatbelt. They have seen, and also drivers using cell phone. So it has been noticed that, uh, if you are, um, uh, if you are using a cell phone, uh, then the number of previous injuries are higher than when you are. Uh, and then even the number of killed. Uh, is that much, so you can then use these surrogate measures to predict how crash frequency will happen and what type of crash will happen. Uh, for example, um, uh, say for example, at an intersection, The encroachment time. That is a time during which a turning vehicle infringes on the right-of-way of another vehicle can be used as a surrogate estimate. So for example, if you have a, you know, free left turns and many intersections you have, so the three left turn time and the true vehicle is coming, uh, on the main main road. So there is a possibility that these two, uh, vehicles may, uh, collide or during the free left turn, maybe somebody is trying to. Grass a pedestrian. It started to cross that road. So they may interact, uh, uh, collide with each other. So that is, so the encroachment time may be seen as a surrogate measure for safety at an intersection. And we've already looked at, uh, or talked about wearing seatbelts or, uh, not wearing helmets, being a surrogate measure. Uh, when we start looking at the statistical method, uh, we have already told you that, uh, they may be a, um, uh, these may be, uh, either simple regression equations or they may also be, uh, poison or negative binomial. Uh, we, people are tending to look at negative binomial and Pizer because, uh, usually when we look at the number of crashes that happen on, on one roadway, for example, Uh, over the year or two years, they are usually termed as rare events. Uh, I mean, rare events as in you would see that there are a lot of accidents happening, uh, but, uh, in terms of count or in terms of, if you count each, uh, crash as an event. So for our three 65 days, you may fall, you may find only, uh, there are 50 accidents that have happened. So three 65, 50 out of three 65 days. Seems like a rare event. So that's why some, uh, researchers are modeling them as modeling crashes, where events, however, it is a, it is imperative that a, these statistical models, uh, have a good fit, uh, otherwise, uh, you, uh, they may not be able to predict. Uh, the future crashes, uh, very, uh, accurately, uh, and calibration to local data is very, very important. So once you have your statistical model, you are then calibrated, calibrated, uh, to, uh, maybe the model was developed in another city, in another town, in another country, you have to calibrate it to local conditions, uh, then validated with, uh, the actual number of accidents that have happened. Uh, only then, uh, statistical models can be. Uh, used very, uh, used with confidence, uh, right. Uh, so in these predictive models, what people use in general, uh, are these are what are called safety performance functions. So, uh, if you are really a person that is working in transportation, safety arena, then, uh, you, uh, will be, uh, dealing with a lot of these. Safety performance functions, right? SPF. This is there. These are statistical base models used to estimate average crash frequency for a particular facility with specified based conditions. Right? These are equations, most likely regression equations. Sometimes they are a, um, uh, exponential equation, negative, exponential equations that. I've been developed for a certain base condition. Now, if you take that to another condition, then like we said, you have to calibrate it to those conditions and then use it in order to predict. Uh, so these are, uh, we'll show you what safety performance functions are. Uh, then, uh, accident modification functions are, uh, AMS are the ratio of the effectiveness of one condition in comparison to the other conditions.All right. So now you have, uh, developed a countermeasure. Maybe you have implemented a counter measure to reduce safety. So what is the modification factor, uh, as a result of that, um, uh, implementation of that, um, safety measure, right? Maybe you have increased police patrolling. So as a result of increased police patrolling on that, uh, on that roadway, How have accidents changed? So the ratio of before and after, uh, gives you the actual modification practice, then somebody else in some other neighborhood, uh, or in some of the city can also think that, well, if I have more, uh, Uh, police, uh, patrolling this roadway. Maybe my accidents will also go down. So those are called accident modification factors. The calibration factors are, these are multiplied with the crash frequency predicted by the SPF, right to account for differences between them jurisdiction and that time period for Vista, they were developed. So maybe this was developed five years ago, uh, for a different city. Uh, however, now you want to use it. I guess later for a different city. So you have to calibrate it to your area, to the, your time period. So all those calibrations are involved in this, uh, usually, yeah, this is how, uh, you will, uh, uh, see, uh, uh, predictive, uh, a statistical model. So predict, uh, and predicted or the number of, uh, crash or the crash frequency for a specific year on a specific type will be given by your. Uh, SPF function, safety performance function, which is then multiplied by your, uh, accident modification factors and also your calibration factor. So these will be, I mean, this is a basic cross level, uh, model. If you try, if you try to, uh, if you're trying to develop a predictive model for your area, it will have all of these elements, but different factors would be there for your case calibration. Uh, the, uh, value of calibration, maybe less, maybe high. So this is basically, but this is how the, your model. Sure look like then if you have looking at developing these, uh, safety performance functions, they are usually, they will look like something like this. So for example, a safety performance function for roadway segment on rural two lane highways. Right? This is as specific as that, right. You're happy. It has to be. For a particular type of a facility. So if you have to develop a, um, um, SPF, uh, uh, for, uh, uh, two lane, rural highway, maybe this will look like the, so, uh, it has the, uh, uh, vehicles per day ADT. The, your length of stretch. It is for all three 65 days. And then these have been developed based on all the, uh, data that has been collected. So it looks like, uh, it is some, some form of, uh, uh, exponential function that you're using to predict the, uh, average crash frequency for the base conditions. Right. This is for base conditions for rural to Lynn. Now, like we said, Uh, those are all for base conditions. If you have to now, uh, improve those conditions, you have taken certain strategies, uh, maybe a year to estimate the effect of particular geometry design or traffic control feature on the effectiveness of the particular treatment. So essentially you have to have accident modification factors that is the expected average crash frequency with condition B condition. B's the improved condition. Where they have a frequency condition by the, uh, divided by the expected average crash frequency with condition. So that will give you how much by how much, how effective was your, uh, implementation on that roadway? Right. Simple examples, uh, using a SPF for tooling, uh, roadways, the expected average crash frequency of existing conditions is 10 injury crashes per year. Assumed observed data is not available, right? This is just using an SPF, the base condition in the absence of automated speed enforcement. So these are base conditions where automated speed enforcement was not available. However, if automated speed and Forstmann was installed, installed the AMF or the engineer 0.83, it has been noticed that it is pointed. So how many crash freaks, what is the average crash frequency that you can expect? You just have to. You'll know that, uh, this is the formula, which will give you the expected of the predicted, uh, average crash frequency, you know, your, a SPF, right. Your SPF, and you'll know you're a SPFs 10 and, you know, you're, uh, accident modification factor for this kind of, uh, intervention, right? This is the kind of intervention for which . So now you can expect that. There'll be 8.3 crashes per year, which are down from and crashes. But yeah, so that is a very simple similarly, uh, if there is a, uh, a treatment X which consists of providing left turn lane on both major road approaches, uh, to Ann Arbor for six, four legged signalized intersection and treatment, why is permitting left? Turn on Redmond where, so you have three left turns. That you can do, both of these treatments are to be implemented. And it is assumed that the effects are independent of each other. So if both of them are, uh, implemented what will happen, right. And if you assume that the effects are independent. So, uh, yeah. Ann Arbor, four legged in signalized intersection is expected to have. So you have seen from other data somewhere else, then it is expected to have 7.9 accidents in a year. But at your location, you have implemented these two treatments. So how much do you expect it to change by? Right. So if you have, this is what, uh, is the base condition. You have these two accident modification factors, since they are independent of each other, you can multiply both of them and you can see that your accidents might reduce to 6.8 accidents. But yeah, so that is a very simple, uh, understanding of how to. Um, Gadi out the statistical modeling, uh, calibration, uh, last thing, uh, in your, uh, um, uh, in understanding, uh, how to Reddick, uh, crash frequencies is a process of adjusting the SPF to reflect different crash frequencies or different jurisdictions. Okay. Calibration can be undertaken for a single state. Are were appropriate for different, within different geographical areas within the status as well. It accounts for factors such as climate driver, population, animal population accident, reporting thresholds and accident reporting system procedures. So all of these may vary from, uh, different, uh, from place to place. So in order to take into account all of this, you have to adjust your. Uh, uh, safety, uh, your SPF, your safety performance functions, right? Only then you can use it for your jurisdiction.