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It is accepted that the activity of the vehicle pedals (

Driving is one of the essentials in our daily life. Nowadays there are strong research efforts invested in the modeling of the driver behavior using driving signals by means of hidden Markov models (HMMs) [

Observable and measurable driving signals can be divided into three categories [

The instantaneous and simultaneous measurement of the three car pedals is a difficult task in the great majority of vehicles. In fact, there are 3 methods to directly measure the status of the car pedals: using position sensors [

The authors of this paper have the design experience of a universal and non-disturbing solution (Miveco Resesarch Project [

Artificial neural networks (ANNs) are one of the most powerful tools that have been widely employed in recent years in various fields such as sensors [

The main idea of this work is to develop a mathematical model to estimate the pedals activity (

There are other learning machine methods that are beyond the scope of this paper to deal with function approximation problems such as support vector regression (SVR) which uses support vector machines (SVM) [

The paper is arranged as follows. Section 2 shows the methodology followed to collect the PA and MV variables and visualizes the relation between them. Section 3 illustrates the inverse modelling strategy used to develop the neural models using MLP neural networks. Section 4 shows the structure of the proposed models and the results of testing them. Conclusions are included in Section 5.

This section describes the methodology followed to obtain the PA and MV signals. As result of previous research authors’ work [

From these experimental tests, the authors have selected four easily measured variables of the driving dynamics that reflect the activity on the vehicle control pedals: regime engine (RE), instantaneous velocity of the vehicle (VS), frontal inclination (FI), and linear acceleration (LA).

The first subsystem in

The second subsystem (

In

As a result of the previous section, the authors propose an inverse model with four input easily measurable variables (MV) and three output variables (PA). The input variables are the regime engine (RE), frontal inclination (FI), linear acceleration (LA) and vehicle speed (VS). In addition, the output variables are the estimation of the three vehicle pedals activity: throttle, brake, and clutch.

The inverse modelling process followed to develop the neural network estimators in this work is illustrated in

Concerning the data preparation task, the early stopping technique is used to improve the generalization performance. In this technique the entire normalized data set has been divided randomly into training (80%), validation (10%), and testing (10%) subsets. The validation subset is employed during the training phase by monitoring the validation set error. It normally decreases during the initial phase of the training, as does the training set error. However when the network begins to over fit the data, the validation set error begins to rise [

Numerous neural networks are available for function approximation problems. A Multilayer Perceptron MLP neural network trained with backpropagation is chosen as it has many useful properties for the pedals estimation problem. It can efficiently learn large data sets as compared to Radial Basis Function RBF networks and Generalized Regression neural networks GRNN, it has been already shown to be effective for function approximation problems, it can efficiently establish a nonlinear relationship between a group of variables, it has been already used in inverse modeling processes [

Since the backpropagation learning algorithm was first popularized, there have been extensive research efforts to accelerate its convergence because the basic algorithm is too slow for most practical applications. These researches fall into two categories, heuristic techniques and numerical techniques. In this work, the feedforward neural network is trained with the Levenberg-Marquardt numerical optimization method because it is the fastest for function approximation problems of networks containing up to a few hundred weights [

The Levenberg-Marquardt algorithm updates the network weights and biases (x vector) using the formula described in

When a particular training algorithm fails on an MLP, it could be due to one of two reasons. The learning rule fails to converge to the proper values of the network parameters, perhaps due to unsuitable network initialization. Or the inability of the given network to implement the desired function, perhaps due to a insufficient number of hidden neurons. To avoid the first possibility, the neural network models were trained and tested 10 times and the network architecture with the lowest root mean square error (RMSE) on the testing data set is chosen.

Concerning the second possibility, there is no theory yet to explain how many hidden neurons are needed to approximate any given function. If there are too few hidden neurons, a high training error and high generalization error would result due to underfitting and high statistical bias. On the other hand, if there are too many hidden neurons, there would be a low training error, but there would still be a high generalization error, due to overfitting and high variance. In most situations, there is no way to determine the best number of hidden neurons without training several networks and estimating the generalization error of each [

Once the optimum number of hidden neurons is obtained, a neural network with that optimum number of hidden neurons is trained several times in order to determine the best learning parameters. Finally, a neural network with the optimal number of hidden neurons and learning parameters is trained several times in order to determine the best number of training epochs. At this point, three neural network models were developed to estimate the pedals activity (

Moreover a linear regression analysis was done between the model-estimated values and the real values. A model that exactly reproduces the actual observations has slope ‘a’ as 1 and intercept ‘b’ as 0. The parameters ‘a’ and ‘b’ are calculated following the least square procedure as given in

Below are the results of the ANN models obtained for pedals signals estimation due to the driver activity from the driving dynamics variables mentioned above. Concerning the training process of the throttle, brake, and clutch models, the maximum number of training epochs is 50 epochs; the number of patterns used in the training and testing phases are 92840 and 9284 respectively.

The optimum number of hidden neurons is seven for the throttle pedal activity ANN model, as can be seen in

Moreover linear regression analysis is done between the model-estimated data and the captured data as shown in

The results of testing the ANN model of the clutch pedal developed using the same methodology as the throttle and brake, show that this prediction approach fails. Therefore the clutch pedal information has to be estimated using a different approach from that followed with the throttle and brake pedals. This is because in the case of the clutch pedal, it is not important to know the relative position of the clutch rather than the instant at which it was depressed and its continuity. This is an on/off (digital) behaviour, not a continuous behaviour like the throttle and brake, which requires different processing to obtain a good model.

An alternative approach is to use the regime engine (rpm) and vehicle speed (km/h) signals to deduce the gear position signal (discrete amplitude signal), as described in [

The main contribution of this work is the presentation of a solution to estimate the driving activity avoiding the use of onboard sensors directly applied to the control pedals. The solution is based on an alternative sensorial system (easily measured variables), and on a neural network estimator (a specific neural model related to each pedal).

In this way, after a training period using the registered variables, the proposed system of models provides information about the driver’s activity in a simple and accurate way.

From the alternative variables point of view, observable and measurable driving signals such as the regime engine (RPM meter), vehicle speed (GPS), frontal inclination of the chassis and linear acceleration of the vehicle (inertial sensor) have been chosen. Instead of using

From the ANN modelling point of view, three inverse neural models based on multilayer perceptron with one hidden layer are designed. To validate the obtained models, well known criteria are utilized such as RMSE and regression analysis parameters. The model structure is valid for any vehicle (car, van, bus, lorry, industrial,

The system has been tested with experiments using commercial vehicles, in a chassis dynamometer as well as on urban circuits; consequently this ensures the validity of the proposed models.

This work has been supported by the Spanish Ministry of Environment through the MIVECO Project (MMA 071/2006/3-13.2).

Example of potentiometers used as position sensors for vehicle pedal activity.

Processes involved in pedals activity estimation: (a) experimental test and (b) modelling.

Block diagram of the measurement system.

Relation between the regime engine and the clutch pedal activity.

Relation between the regime engine and the throttle pedal activity (2nd gear position).

Relation between the engine regime and the brake pedal activity.

Relation between the frontal inclination and the brake and accelerator pedals activity.

Relation between the linear acceleration and the brake and throttle pedals activity.

Block diagram to develop the inverse modelling system.

Flow chart of the ANN modeling methodology.

RMSE vs number of hidden neurons of the throttle pedal ANN model.

Structure of the proposed ANN model for the throttle pedal activity.

Results of testing the proposed throttle model.

Results of linear regression analysis of the throttle model.

RMSE

Structure of the proposed model for the brake pedal activity.

Results of testing the proposed brake model.

Results of linear regression analysis of the brake model.

The alternative system used to model the clutch pedal activity.

Results of testing the proposed clutch model.

Comparison between the performances of different learning algorithms.

0.12767 | 0.14698 | 0.14245 | 0.13939 | 0.23885 | ||

0.10806 | 0.13919 | 0.13629 | 0.13127 | 0.32242 |