Currently, most automobiles have automatic transmission systems. The gearshifting strategy used to generate shift patterns in transmission systems plays an important role in improving the performance of vehicles. However, conventional transmission systems have a fixed type of shift map, so it may not be enough to provide an efficient gearshifting pattern to satisfy the demands of driver. In this study, we developed an intelligent strategy to handle these problems. This approach is based on a normalized radial basis function neural network, which can generate a flexible gearshift pattern to satisfy the demands of drivers, including comfortable travel and fuel consumption. The method was verified through simulations.
1. Introduction
The demand for automatic transmission (AT) systems has increased greatly since the invention of the electronic transmission control unit (TCU) developed in the early 1980s by Renault and BMW
[1]
. The representative AT system is stepped transmission (ST)
[2]
where a fixed gearshift map is provided to reduce the engine torque during gearshifting, which correctly matches the oil pressure to the friction elements such as the clutch and band brakes.
However, the fixed gearshifting map of the ST system has several problems, one of which is that the fixed map can’t provide adaptive, flexible shift patterns that are suitable for different driving conditions, so an unnecessary “kick down” phenomenon may occur often. This “kick down” may cause the driver to feel uncomfortable and result in poor fuel efficiency. Another problem is that the ST system cannot adapt the gearshifting time to the habits and inclinations of the driver, which causes drivers discomfort.
One way to alleviate these problems and provide efficient gearshifting is to develop more advanced shift maps that can generate adaptive gearshift patterns and determine the intelligent gearshifting time without changing the transmission hardware and TCU. Methods such as fuzzy logic
[3

6]
and neural networks
[7
,
8]
can be used to develop such an advanced system, but the neural network technique was preferred in this study.
In general, neural networks are recognized as an intelligent method because of their advantages such as selforganization by learning, robustness against uncertainty, and fault tolerance. However, the efficiency of neural networks can be reduced in some applications because of the large numbers of neurons and layers, which incur a long learning period. In
Standard gearshifting map of a fourspeed automatic transmission system.
particular, the problem can be very challenging when many mechanical and environmental factors have to be considered. Given these considerations, the normalized radial basis function neural network (NRBFNN)
[9]
was preferred in this study instead of the conventional multineural network.
The paper is organized as follows. In Section 2, we explain the conventional gearshifting method of the AT system. In Section 3, the proposed intelligent gearshifting method is described that utilizes the NRBFNN. Section 4 presents the overall structure. In Section 5, simulation results are provided that verify the effectiveness of this method. Concluding remarks are given in the final section.
2. GearShifting Control
Gearshifting control means that a shifting point on a given fixed gearshifting map of the TCU is moved to another, as shown in
Figure 1
, in terms of the driving velocity (xaxis) and the throttle valve open rate (yaxis) acquired from the engine control unit (ECU).
The procedure of gearshifting can be understood easily using an example. Assume that the point indicating the current status of the velocity and throttle valve open rate of the vehicle is point A. If a driver steps on the accelerator pedal to increase the current velocity and throttle valve open rate, point A is moved to point B across the upshift line (drawn in solid line) and the shift position of a vehicle changes from the 1st shift position to the 2nd shift position. If a driver steps off the accelerator pedal to decrease the velocity and the throttle valve open rate at point B, point B is moved to point A across the downshift line (shown by the dashed line).
The upshift line is a boundary between the lower position and the higher position, whereas the downshift line is a boundary between the higher position and the lower position. These boundaries are fixed and impossible to change once the shifting map has been installed on the TCU.
As already mentioned, the fixed type map limits the flexibility of the gearshifting strategy to adapt to the driving conditions and the driver’s inclinations. A viable option for avoiding these problems is to change the upshift and downshift boundary lines of a shift map automatically to adapt to different driving conditions and driver inclinations within an admissible range, which is specified by the maximum or minimum limits predetermined by the maximum torque and rotation speed of an engine.
3. Intelligent GearShifting Strategy Based on NRBFNN
In this section, we describe the intelligent gearshifting method based on NRBFNN, which was developed to address the weakness of the fixed gearshifting method. First, a brief description of NRBFNN is provided, as follows.
 3.1 Normalized Radial Basis Function Neural Network
Neural networks are used widely because of their learning capability, their parallel distributed structure, high fault tolerance, etc. Although there are many types of structures in neural networks, the RBFNN adopted by this approach has distinct advantages: a simple structure with a single hidden layer and a local mapping capacity for fast learning.
In general, the standard RBFNN comprises three layers, and a Gaussian radial function is typically used as the activation function of the hidden neuron. In this study, a normalized Gaussian radial function, which may be superior to the standard one
[9
,
10]
, is preferred as the activation function of the hidden neuron. The normalized radial basis function of the hidden neuron shown in
Figure 2
is expressed mathematically as
where x is the input vector of length m, and c
_{q}
and
σ
_{q}
are the center vectors of length m and the standard deviation of the
q
th neuron in the hidden layer, respectively.
The
i
th neuron in the output layer is evaluated as
Normalized radial basis function neural network.
where
ω
_{iq}
denotes the weight between the
q
th neuron of the hidden layer and the
i
th neuron of the output layer and
θ
_{i}
is the threshold value of the
i
th output neuron.
In the NRBFNN, three types of parameters need to be adjusted to adapt the network to the desired purpose:center vectors c
_{q}
, standard deviation
σ
_{q}
, and output weights
ω
_{iq}
. The gradient descent method, which is one of the most popular approaches for updating c
_{q}
and
ω
_{iq}
, is used, where the fixed value of
σ
_{q}
is defined as
where d is the maximum distance between the chosen centers and
l
is the number of centers.
The update rules for learning the centers and weights can be summarized as follows
[9

11]
:
where c
_{qj}
is the
i
th element of center vector c
_{q}
with length m,
is the desired output of the
i
th output neuron, and
ω
_{iq}
and
Overall structure of the intelligent gearshifting system.
ω
_{iq}
are the connection weights between the
q
th hidden neuron and the
i
th output neuron, respectively.
η
_{1}
and
η
_{2}
are the learning rates, the values of which may vary between 0 and 1.
 3.2 Intelligent GearShifting Map Using NRBFNN
The intelligent gearshifting strategy uses a flexible shift map to adapt to various driving conditions, i.e., the habits or inclination of a driver, road conditions such as uphill or downhill driving, etc. However, it is difficult to develop a neural network that solves all these problems so it is more efficient to classify them into several subfunctions and to construct the corresponding systems using a hierarchical structure.
As shown in
Figure 3
, the intelligent gearshifting system comprises five modules, where each module has its own function as follows.

 Module to decide the status of the engine output (Module 1): to evaluate the proximity between the vehicle’s load and the allowable maximum engine output.

 Module for the driver’s intention (Module 2): to determine the driver’s intention when driving.

 Module for the road condition (Module 3): to determine whether the road is uphill or downhill and whether the engine brakes may be required.

 Module for the degree of satisfaction (Module 4): to determine the degree of driver satisfaction with the current shift map.

 Module for the shift position (Module 5): to decide the final shift position.
More detailed descriptions of each module are given below.
 3.2.1 Deciding the status of the engine output (Module 1)
This module decides the load of a vehicle based on information provided by the ECU. These are represented as follows:

TMRS(n): Current transmission output rotation speed

TMRS(n– 1): Previous transmission output rotation speed

TE: Engine torque

TEMAX: Maximum engine torque

TEACC: Engine torque for acceleration

Lve: Load of a vehicle
In the mathematical approach, the load of a vehicle (0 <
L_{ve}
< 1) is defined as the ratio of the acceleration torque to the maximum torque, which can be modeled as (according to the manufacturer: Hyundai Motor Company)
where
RA
is the acceleration resistance;
r
is the radius of the tire;
i_{T}
is the current transmission ratio, which varies according to the current shift position;
i_{F}
is the ratio of the velocity at the endpoint;
η
is the coefficient of the transmission efficiency at each shift position;
t
is the torque elasticity;
W
is the total weight of a vehicle;
W’
is the partial weight of the rotating part
Module 1 to decide the status of engine output.
Normalized radial basis function neural network for submodule M2 A and M2B of Module 2.
of a vehicle, and
g
is the acceleration due to gravity. However, these mathematical models are based on approximations and the parameters may be altered by the driving conditions, so it is difficult to determine the optimal value of the load for a vehicle. Neural networks solve this type of problem via adaptive learning from experimental data.
Figure 4
shows the corresponding NRBNN used to determine the load of the vehicle. As mentioned earlier, the gradient descent method is used to learn the neural network.
 3.2.2 Deciding the driver’s intention (Module 2)
This module is designed to decide the driver’s intention (M
_{A}
), which can be classified into a dynamic mode and a safety mode, which evaluate the driver’s willingness to accelerate (M
_{m}
) simultaneously. This module comprises two submodules: submodule M2A to decide the driver’s dynamic inclination and submodule M2B to evaluate the degree of the driver’s willingness to accelerate, as shown in
Figure 5
and
Table 1
.
Submodule M2A evaluates the driver’s inclination MA based on four inputs: the throttle valve open rate (TH
_{0}
), the
Input/output variables of submodules of Module 2
Input/output variables of submodules of Module 2
Structure of Module 3, which decides the road condition.
variation in the throttle valve open rate (ΔTH
_{0}
), the brake’s deceleration resistance (R
_{b}
), and the brake switch (B
_{sw}
). The relationship between the specified inputs and the output M
_{A}
can be determine by learning the neural network using the experimental data. If output M
_{A}
is close to 1, the system decides that the driver strongly favors a dynamic mode.
Submodule M2B is designed to judge whether the driver desires acceleration or deceleration. This module evaluates the degree of the driver’s willingness to accelerate based on three inputs: the throttle valve opening rate (TH
_{0}
), the current shift position (SHIFT
_{COM}
), and the vehicle’s velocity (V
_{S}
). The nonlinear relationship between the corresponding inputs and the output M
_{m}
can be obtained by learning the neural network using the experimental data. The proximity of output M
_{m}
to 1 indicates that the driver wants to accelerate the vehicle.
 3.2.3 Deciding the road condition (Module 3)
The role of this module is to decide the road condition and it comprises five submodules, as shown in
Figure 6
. The function of each submodule, as shown in
Figure 7
and
Table 2
, can be described briefly as follows.
NRBNN for all submodules of Module 3.
Input/output variables of submodules of Module 3
Input/output variables of submodules of Module 3

 Submodule M3A: to decide the slope of the road

 Submodule M3B: to decide the driver’s willingness to accelerate downhill

 Submodule M3C: to decide the driver’s willingness to decelerate downhill

 Submodule M3D: to decide the driver’s intention to use the engine brake

 Submodule M3E: to make the final decision to operate the engine brake
Next, each submodule is explained in detail, and it should be noted that all of the submodules are trained using the gradient descent method.
 1) Submodule M3A
In this module, the slope of the road (C
_{sd}
) is computed from four inputs: the acceleration of the vehicle (V
_{a}
), the output velocity of the AT(TM
_{RS}
), the throttle valve opening rate (TH
_{0}
), and the slope resistance(R
_{g}
). The relationship between the specified inputs and the output C
_{sd}
can be obtained by learning the corresponding neural network using experimental data, which are derived from experiments under various road conditions.
 2) Submodules M3B and M3C
In submodule M3B, the driver’s willingness to accelerate downhill can be determined from the timer, the throttle valve opening rate (TH
_{0}
), and the velocity of the vehicle (V
_{S}
). The driver’s willingness to decelerate downhill in submodule M3C can also be decided from the timer, the brake switch (B
_{sw}
), and the acceleration of the vehicle (V
_{a}
). The relationship between the specified inputs and the corresponding outputs can be obtained by learning the relevant neural networks using experimental data.
 3) Submodule M3D
This module evaluates the degree of the driver’s willingness (i.e., engine brake selection) to decelerate based on three inputs: AD
_{i}
, BS
_{ops}
, and BS
_{opi}
. The willingness to decelerate depends on the number of driver brake operations, so the outputs of the previous submodules M3B and M3C become the inputs of this module. The degree can be classified into three levels: high deceleration (DCC
_{big}
), low deceleration (DCC
_{small}
), and zero deceleration (DCC
_{zero}
).
 4) Submodule M3E
In this module, the degree of downshift when operating the engine brake (D
_{ACC}
) and the road condition (D
_{m}
) are determined from the slope of road C
_{sd}
and the outputs of Module M3D. D
_{m}
= 1 and D
_{m}
= 0 denote a downhill road and a flat road, respectively. The output D
_{ACC}
is determined as follows: ·When D
_{m}
= 0, D
_{ACC}
= K
_{0}
·When D
_{m}
= 1,
where K
_{0}
, K
_{1}
, and K
_{2}
indicate no shift, one downshift, and two downshifts by operating the engine brake, respectively. The relationships between the inputs stated above and the corresponding outputs can be obtained by learning the neural networks using experimental data.
Module 4 to decide the degree of satisfaction.
 3.2.4 Deciding the degree of satisfaction (Module 4)
This module (
Figure 8
) determines the degree (S
_{k}
) of driver satisfaction with the current shift map. The outputs (D
_{M}
, D
_{ACC}
) of Module 3 and other variables, such as the throttle valve opening rate (TH
_{0}
), brake deceleration resistance (R
_{b}
), brake switch (B
_{sw}
), and current shift position (SHIFT
_{COM}
), are used to decide the S
_{k}
. This module plays a role in analyzing the driver’s inclination, and the results are used to make the next adjustment of the shift map. When S
_{k}
is relatively high, the current shift map remains unchanged. Otherwise, some adjustment will be made.
 3.2.5 Decision module for the shift position (Module 5)
This module (
Figure 3
) determines the final gearshifting rate
M_{p}
based on all of the outputs from Modules 1–4. The rate
M_{p}
has a value between 0 and 1, which is computed as follows:
where
δ
(≜ S
_{d}
 S
_{k}
) is the difference between the highest degree (S
_{d}
) and the current degree (S
_{k}
) of the driver’s satisfaction.
Using the rate
M_{p}
, the final shift map position is decided as follows:
where
SM_{current}
is the current shift map position and
SM_{max}
is the maximum shift map position within the admissible range.
4. Simulation Results
A dynamic model of the Hyundai Sonata with a Ricardo engine was used in the simulation to verify the effectiveness of the
Slope of road.
Wheel revolutions per minute (RPM).
proposed approach. The simulation results are examined from several important aspects, particularly the number of times that gearshifting occurred during the test. In general, it is very important to reduce the number of times that unnecessary gearshifts occur because the “jerk” phenomenon caused by gearshifting makes a driver uncomfortable. The second aspect is how long a vehicle remains at a highspeed in the high gearstage. It is wellknown that remaining in the highgear stage during highspeed driving leads to greater fuel economy. The last aspect considers how long the vehicle can keep accelerating in the lowergear stage. Acceleration in the lowgear stage increases the torque of the engine to change the velocity of the vehicle smoothly.
Figure 9
shows the slope of the road where the simulation was performed, and
Figure 10
shows the wheel revolutions per minute (RPM) for the vehicle. In these figures, the xaxis denotes the number of clocks (or iterations) generated in the TCU. It should be noted that each clock is equivalent to 0.016 sec and the number of clocks can be considered as a proxy of time.
Figure 10
shows that the driver required an abrupt acceleration between the 4,000th and 5,000th iterations, before maintaining an almost constant speed after 6,000 iterations. Thus, to
Standard shift map.
Intelligent shift map.
increase the degree of satisfaction, the lower gearstage must be maintained between the 4,000th and 5,000th iterations, whereas the higher gearstage is required after 6,000 iterations to reduce the fuel consumption.
Figures 11
and
12
show the gearshifting results derived from the standard shift map and the intelligent shift map produced in this study, respectively.
Figure 11
shows that the total number of gearshifts was 16 and that the gear4 stage with two gear shifts was maintained after 6000 iterations.
Figure 12
also shows that the number of gearshifts was reduced to 12 and that the gear4 stage was maintained longer than the previous one. These results indicate that the proposed approach is more effective than the conventional method in several respects.
5. Conclusions
In this study, we developed an intelligent gearshifting strategy, which may have a major role in AT systems. To improve the capacity to adapt to different driving conditions and driver inclinations, the proposed method was developed using a NRBFNN, which has distinct advantages, including a simple structure, fast learning, local mapping, and fault tolerance. Compared with the standard method, the intelligent shift map can reduce the total number of gearshifts, which makes a driver more comfortable and provides sufficient driving power. The effectiveness of the proposed method was verified through simulations.
In the future, we will study how to reduce the number of hidden neurons. In general, the radial basis function has no orthogonal properties and does not require unnecessary neurons. The optimal structure of NRBF will make the intelligent shift map more advanced, and it has wide applications.
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