ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
OutLine
Abstract
Objective
1. Introduction
2.The System
2.1 Define Fuzzy Sets
2.1.1 Membership function of visibility
2.1.2 Membership function of Pavement Condition
2.1.3 Membership function of Traffic flow/ Link capacity
2.1.4 Membership function of Speed Impact
2.2 Fuzzy Inference System
2.3 Defuzzification
3. Conclusion & Future Research
Reference
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Figures
Figure 1. The Fuzzy system. This figure is from the MATLAB fuzzy logic tool
box and it indicates the relationship of inputs, outputs and the fuzzy inference.
Figure 2. The membership function of Visibility.
Figure 3. The membership function of Pavement Condition.
Figure 4. The membership function of Traffic Flow/ Capability.
Figure 5. The membership function of Speed Impact.
Figure 6. The rule base.
Figure 7. The fuzzy inference system and the output of speed impact after
defuzzification.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Application of fuzzy logic on traffic impacts from adverse weather
Abstract
We have developed an Expert System based on fuzzy logic to predict the impact of
adverse weather on traffic, given the parameters of visibility, pavement condition, and
traffic flow/link capacity. Fuzzy theory and fuzzy logic were used to establish the model.
Fuzzy tool box build in MATLAB was used to implement the fuzzy theory. All the data
includes visibility, pavement condition, and traffic flow could be obtained from Internet.
There are tons of websites providing the weather forecast and the http://traffic.tann.net/
website provides the real time data. Minneapolis’s traffic data is used for analyzing.
All the membership functions (fuzzy sets) could be generated by the historical data and
expert experience. Based on the observed data and expert experience, we will define the
fuzzy rules (fuzzy inference) and obtain the output. Here we will have a parameter, which
is traffic flow/link capacity to maintain the link without congestion.
Objective
The impact of adverse weather to traffic flow has long been a problem for transportation
management. Having the traffic impact of adverse weather helps us to evaluate the traffic
condition and speed predicting. Problems have been encountered in cases where the
effectiveness of traffic speed prediction in terms of heavy fog, flooding, heavy raining,
snowing and strong winds. Precisely predicting the impact of adverse weathers would be
helpful in traffic management, operations and so on. Moreover, the ITS (intelligent
Transportation System) will also be improved by having those information.
Fuzzy logic is suggested to predict the impact of adverse weathers. The advantage of
using the fuzzy approach is that very little calculations need to be done and is also easier
to use, once the fuzzy system has been established. MATLAB, along with the Fuzzy
Logic toolbox is the software used to create the fuzzy inference system.
In order to quantify how serious adverse weather affects traffic, we describe impact in
term of traffic speed. Assuming traffic speed remains the same curve shape while there
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
are without incidents or specific events or anything else that will largely affect traffic
speed. In addition, the condition of congestion will not be considered here because other
factors will be involved with it. That means the only variable is weather condition. Based
on the difference of weather condition, we can get the impact on traffic speed.
1. Introduction
There are two major parameters caused by adverse weather that will affect traffic speed:
visibility and pavement condition. Those data are sometimes not crisp, that means there
are not well defined and clear. For instance, probably we will hear that “the visibility is
good or bad” or “the pavement is slippery or a little bit slippery”. Those linguistic
descriptions are vague and not easy to interpret into crisp definition. Therefore, fuzzy
logic is adopted because of its easily modeling and calculating.
This project is divided into 3 sections. Section one gives some overview about Fuzzy
logic especially the mamdani model, Section 2 explains the system that was developed,
Section 3 describe the conclusion and future research.
Fuzzy Logic- Dr. Lotfi Zadeh of University of California, Berkeley, introduced fuzzy
logic in the 1960s’. Fuzzy logic is a superset of conventional (Boolean) logic that has
been extended to handle the concept of partial truth – truth-values between “completely
true” and “completely false”. In fuzzy logic the truth of any statement becomes a matter
of degree.
The Mamdani Model- The Mamdani fuzzy model, similar to the other (Sugeno and
Tsukomoto model) fuzzy models, has a set of inputs, each with its own membership
functions. The Mamdani model differs from the others in the fact that the output also has
a set of its own membership functions. In the case of the Sugeno model, the output is a
function of the input membership function and in the case of Tsukomoto’s model; the
output is a linear function of the input.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Mamdani’s Method:
Rc  A  B  
U V
 A (u)   B (v)/(u, v)
 AB (u, v)   A (u )   B (v) where "" can be Min. or Product.
2. The System
In order to set up the whole fuzzy system, there are three things:
1. Define fuzzy sets (Membership Functions).
2. Set up the fuzzy inference system (rule base).
3. Defuzzifier. After those procedures, we defuzified the traffic impact fuzzy sets
and obtain a crisp speed impact as output. The output indicates the speed
reduction under the adverse weather in a link with specific traffic flow. Figure1
shows the relationships of the system.
Figure 1. The Fuzzy system. This figure is from the MATLAB fuzzy logic tool box
and it indicates the relationship of inputs, outputs and the fuzzy inference.
2.1 Define Fuzzy Sets
In the Mamdani model, every input and output is a fuzzy set. That means there are totally
4 fuzzy sets, which are visibility, pavement condition, traffic flow/ capability and speed
impact.
2.1.1
Membership function of visibility
The terminologies of describing fog are used to define the visibility, and all of them are
listed below. Figure 2 shows the membership function of visibility’s fuzzy set.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
1. 1.Dense Fog (DF) <40m
2. 2.Thick Fog (TF) 40~200m
3. 3.Fog (FO) 200~1000m
4. 4.Mist (MI) 1000~2000m
5. 5.Poor Visibility (PV) 2000~4000m
6.
6.Moderate Visibility (MV) 4000~10000m
Figure 2. The membership function of Visibility.
2.1.2
Membership function of Pavement Condition
Generally, pavement condition is described by surface friction. However, the same
friction will cause different impact of traffic because different kinds of condition. For
instance, pavement covered with water or snow will cause different influence.
Nevertheless, the conditions are treated the same here. Pavement condition has been
divided into four fuzzy sets and they are listed below. Figure 3 shows the membership
function of pavement condition.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
1.Icy (IC)
2.Very Slippery (VS)
3.Slippery (SL)
4.Not Slippery (NS)
Figure 3. The membership function of Pavement Condition.
2.1.3 Membership function of Traffic flow/ Link capacity
Traffic flow is known as number of vehicle passed by a cutting surface in a specific time
period per lane. Link capacity means that the maximum number of vehicle passed a
cutting surface. The parameter of traffic flow/ link capacity is impossible to be greater
than 1. Therefore, the fuzzy set support of the parameter is constrained between 0 and 1.
All the fuzzy sets of the parameter are listed below. Figure 4 shows the membership
function of Traffic flow/ Link capacity.
1.Free Flow (FF)
2.Normal (NO)
3.Light Heavy (LH)
4.Heavy (HE)
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Figure 4. The membership function of Traffic Flow/ Capability. The parameter will
be maintained in the range 0~1.
2.1.4
Membership function of Speed Impact
Traffic impact data came from the difference between same link under same conditions
but different weather conditions. Plus, this is the output of this fuzzy theory model. There
are totally six fuzzy sets for this parameter and they are listed below. Figure 5 shows the
membership function of speed impact.
1.Tremendously Impact (TI)
2.Seriously Impact (SE)
3.Impact (IM)
4.Somehow Impact (SO)
5.Slight Impact (SI)
6.No Impact (NI)
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Figure 5. The membership function of Speed Impact.
2.2 Fuzzy Inference System
A fuzzy inference system includes fuzzy rule base and fuzzy inference engine. A fuzzy
rule base consists of a collection of fuzzy if-then rules. A fuzzy inference engine
combines these rules into a mapping from the inputs of the system into its output. Our
rule base will base on the conditions below.
1. If the visibility is worse, then speed impact is larger.
2. If the pavement condition is worse, then the speed impact is larger.
3. If the coefficient of Traffic Flow/ Capacity is bigger, then the speed
impact is larger.
Figure 6 shows the rules.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Figure 6. The rule base.
2.3 Defuzzification
In order to get a crisp solution of speed impact, we need to defuzzify the solution fuzzy
set. There are various techniques available. The center of area (COA) method, which
finds the center of gravity of the solution fuzzy sets, is used here. The equation is as
following,
*
yCOA

 y *  ( y)dy
  ( y)dy
B'
B'
By this procedure, we can get a crisp solution of speed impact such as shown in figure 7.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Figure 7. The fuzzy inference system and the output of speed impact after
defuzzification.
3. Conclusion & Future Research
Because of the fuzziness of those input data, fuzzy theory is suited for this problem. In
order to obtain more precise solution, well define the fuzzy sets become the most
important issue. It is heuristic to define the shapes of membership functions, but we still
have other methods to improve.
Use ANN to train the data will be one of the feasible ways to make improvement. If we
can train those fuzzy sets by historic data, then it is possible to get a much better solution.
And this is so called “fuzzy-neural” model.
There are different kinds of adverse weathers. They will generate various visibility and
pavement conditions and cause different speed impact. That means if we are going to
predict the traffic impact more accurately, we need to define different fuzzy models for
different weather conditions. For instance, probably we need to establish the Snowing
model, Raining Model, Fog Model and other hybrid models.
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ECE/CS 539
Final Project
Shan-Huen Huang
December 20, 2001
Reference:
1. Hongxing Li, C.L. Philip Chen, Han-Pang Huang, Fuzzy Neural Intelligent Systems,
2000
2. Ernest Czogala, Jacek Leski, Fuzzy and Neuro-Fuzzy Intelligent Systems, 2000
3. Kaur, D.; Tekkedil, D. Fuzzy expert system for asphalt pavement performance
prediction, 2000
4. Bernhard Krause, Martin Pozybill, Constantin von Altrock, Fuzzy application library/
Technical Applications/ Traffic Control, 1996
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