4.1 PRESENTACIÓN DE RESULTADOS
4.1.7 Séptima etapa
4.1.7.3 Determinación de la variable de respuesta a través del Modelo Matemático
In the following section prominent trip modelling techniques are described and reviewed.
3.4.3.1 Markov process
A Markov process is a stochastic process with the following properties:
The number of possible outcomes or states is finite.
The outcome at any stage depends only on the outcome of the previous stage.
38 Markov process is useful to analyse dependent random events – events whose likelihood
depends upon what happened last. A Markov model can look at a series of events and
analyse the likelihood that one kind of event is followed by another based on probabilities.
The model output stream of events would reflect the transition probabilities derived from
the observed data. This stream of events is called as Markov chain (Grinstead and Snell,
1997).
For EMS, Markov model is used for trip modelling where the transition probabilities of
vehicle speed are determined based on legislative and/or non-legislative driving cycles
(Chan-Chiao et al., 2004, Dean et al., 2008, Cairano et al., 2013). In this set up it is called as
Markovian driver. However in real world driving the vehicle speed is not deterministic and
transition happens based on various driving factors and some of these may be fixed for a
given route and time. Transition of vehicle speeds in real world driving is dynamic and
difficult to model especially based on driving cycles.
Similarly a trip prediction model was presented (Johannesson, 2009) for a prescribed route.
In the study vehicle speed profiles were collected 37 times for a given route and driver. The
route considered was divided into several sections. For each section a Markov position
dependent transition matrix as a function of speed and acceleration was developed. Based
on current vehicle location and speed, acceleration was predicted. Effect of dynamic
factors like traffic or time of travel and influence of driver style was not considered. The
prediction model was not validated against an individual logged vehicle speed profile to get
insight about effectiveness of prediction. However this method may be applicable for a
known mean and variance of the speed. Further this method requires a set of Markov
transition models for each section in the route composed of many sections. This may be
Introduction to Driving Cycles, Real World Driving and Review of Trip Modelling
39 Note that these models perform only limited prediction at each time and not the entire trip
vehicle speed profile. These limited predictions are dependent on current and past data.
3.4.3.2 Model predictive control (MPC)
Model predictive control (MPC) can easily handle non-linear time varying system, since the
controller is explicitly the function of the model that can be modified in real time.
Future values of output variables are predicted using a dynamic model of the process and
current measurements. A history of past system data is required. A reference trajectory to
the prediction has to be defined. The predictions are made for more than one time delay
ahead as shown in Figure 3-5.
Figure 3-5: Model predictive control - Basic concept (Re et al., 2009)
The window of time (or distance) considered for prediction is known as prediction horizon
(P). Then there is control horizon (M) which revises prediction made based on the
deviations in predictions from the reference trajectory over the next prediction horizon
while satisfying the constraint. Based on the control action, prediction horizons are revised.
However only the prediction variable values u(k) (input) corresponding to the next
40 control horizon is re-calculated to take control action. This continues with each time step
and this approach is known as receding horizon approach (Qina and Badgwellb, 2003,
Allgöwer et al., 2004). Set point in trip modelling is the trip destination point.
One of the techniques used in the prediction horizon is assuming constant speed and
elevation using geographical position system (GPS)(Koot et al., 2005). MPC may also use
detailed navigation system with curve radius, speed limits, crossing, traffic light, etc., In
MPC updated prediction is made at each time step over a limited prediction horizon during
the trip (Koot et al., 2005, Maciejowski, 2001). MPC requires high computational effort
(Serrao et al., 2011).
3.4.3.3 Artificial Neural Network (ANN)
Artificial Neural Network (ANN) is a system based on the operation of biological neural
networks. A neural network is a parallel system, capable of resolving models that linear
computing cannot. When an element of the network fails, it continues to perform without
any problem due to parallel nature as shown in Figure 3-6. A neural network learns on its
own and may not require reprogramming.
ANNs combine artificial neurons in order to process information. The higher the weight of
an artificial neuron is, the stronger the input which is multiplied by. Weights can also be
negative, so we can say that the signal is inhibited by the negative weight. Depending on
the weights, the computation of the neuron will be different. By adjusting the weights of an Figure 3-6: Artificial neural network
Output Weights Activation Function In p u ts Output In p u ts
Introduction to Driving Cycles, Real World Driving and Review of Trip Modelling
41 artificial neuron, the desired output is obtained for a set of specific inputs. For a large
network algorithms are used to find appropriate weights in order to obtain the desired
output from the network. This process of adjusting the weights is called learning or training
(Gershenson, 2008). The limitations of ANN are a large data is required to train ANN to
operate and requires high computational time for large networks (Wirasingha and Emadi,
2011).
For vehicle speed profile prediction, function of vehicle speed like location, speed limits,
vehicle and other parameters speed can be considered as input. The weights to inputs can
be identified based on training over actual data.
A feed forward artificial neural network (ANN) was used for trip modelling using ITS data
(Qiuming and Yaoyu, 2009) and compared against real test data for extra urban driving.
Real test data is GPS logged data (10 days) for the same route as the ITS data considered.
ANN is trained using real test data and ITS data of that particular destination. The
prediction method was validated against real test data with ITS data which were not part of
the training. In the study trip prediction of ANN model with ITS data was more accurate
than ITS data alone. In this study vehicle speed profile for the whole trip was predicted. In
the study the scope for the trip prediction update on the fly was not considered.
Considering real world driving being dynamic and uncertain in nature, prediction correction
is necessary. However, ANN approach needs a large processor and slow processing times
adding to the system complexity (Wirasingha and Emadi, 2011). More importantly prior
knowledge of the trip vehicle speed profile is required to make prediction.
3.4.3.4 Summary of trip modelling
Trip prediction models are studied most of the time in predicting known vehicle speed
profile such as legislative driving cycles. In such cases there is no role for disturbance or
42 considered in a few studies. However prediction validation was considered in one of the
ANN study. But the validation was done for the same trip of which historic measured and
ITS data was considered. Hence for the current trip modelling techniques prior knowledge
of the trip vehicle speed profile is required. In other words these trip modelling approaches
are vulnerable outside the destination (or historic) data considered. These methods are
data intensive and for varied trip conditions like in real world driving it becomes
aggravated. In addition they are computationally demanding to operate in real time.
In both Markovian and MPC models predictions are for a limited period (or window) which
gets updated during the journey. They do not predict the entire vehicle speed profile. In
the ANN study the entire vehicle speed profile was predicted.
MPC updates the prediction to minimise the deviation and this is necessary consider
dynamic and uncertainty of real world driving. However the prediction updates depends on
the reference value considered in the MPC model. Similarly in Markovian driver’s
prediction depends on the data set considered. In ANN study prediction correction was not
considered which is required in real world driving. But this can complicate the computation
further.
Further in trip modelling, trip demand is modelled to predict in terms of vehicle speed
profile. In real world driving vehicle speeds are highly dynamic and uncertain nature risks
prediction accuracy (discussed earlier in section 3.3).
3.5
Summary
In driving cycles vehicle speeds are predefined over time or distance; v(t) or v(d). In real
world driving vehicle speed is a function of driving information such as driver style, vehicle
type, road type and traffic. Many of these factors are dynamic and hence not possible to
Introduction to Driving Cycles, Real World Driving and Review of Trip Modelling
43 consider the trip demand not in terms of vehicle speed profile for real world driving. Trip
demand in real world driving has no correlation to driving cycles. It is a function of series of
situation or events such as road types for a given vehicle and driver. For real world driving
trip demand is not exact and has variation; natural driver induced or due to external
factors. Therefore from the EMS point of view as the trip demand is uncertain it has to be
adaptive in real world driving. Driving information is to be considered in the design and
formulation of a proposed EMS.
Most of the trip modelling studies used driving cycles. In a few studies real world logged or
ITS data was used for prediction. MPC has the ability to update the prediction which is
necessary considering uncertain and dynamic nature of real world driving. Prediction
correction was not considered in ANN model. Only in one of the ANN trip modelling
predicted vehicle speed profile was validated against real test data of the destination
considered.
In all trip modelling techniques prior knowledge of the trip vehicle speed profile is required
to make the prediction. No model was validated for the destination outside the test
destination considered for modelling. Hence prediction outside the historic data or trip
destination considered is a suspect.
Trip modelling methods are data intensive and computationally demanding. Trip modelling
techniques predict trip demand in terms of vehicle speed profile which has limitations in
44