A Sensorless State Estimation for A Safety-Oriented Cyber-Physical System in Urban Driving: Deep Learning Approach

Mohammad Al-Sharman, Student Member, IEEE, David Murdoch, Student Member, IEEE, Dongpu Cao,Senior Member, IEEE, Chen Lv, Member, IEEE, Yahya Zweiri, Member, IEEE,Derek Rayside, Member, IEEE, and William Melek, Senior Member, IEEE

Abstract—In today’s modern electric vehicles, enhancing the safety-critical cyber-physical system (CPS)’s performance is necessary for the safe maneuverability of the vehicle. As a typical CPS, the braking system is crucial for the vehicle design and safe control. However, precise state estimation of the brake pressure is desired to perform safe driving with a high degree of autonomy.In this paper, a sensorless state estimation technique of the vehicle’s brake pressure is developed using a deep-learning approach. A deep neural network (DNN) is structured and trained using deep-learning training techniques, such as, dropout and rectified units. These techniques are utilized to obtain more accurate model for brake pressure state estimation applications.The proposed model is trained using real experimental training data which were collected via conducting real vehicle testing. The vehicle was attached to a chassis dynamometer while the brake pressure data were collected under random driving cycles. Based on these experimental data, the DNN is trained and the performance of the proposed state estimation approach is validated accordingly. The results demonstrate high-accuracy brake pressure state estimation with RMSE of 0.048 MPa.

I. INTRODUCTION

WITH the rise of autonomous vehicles, cyber physical systems (CPSs) have become a major research focus,with teams from academia, industry and government organizations studying them [1]-[4]. In electric vehicles (EV),the various subsystems of the EV, like communications,electric powertrain and energy management, sensors, the driver, and the environment all come together to form a tightly coupled, dynamically interacting system [5]-[9]. The resulting system has strong uncertainties, nonlinearities, and difficult to model interactions between its parts, making estimation and control of CPSs in EVs a difficult task.

For CPSs in EVs, we are concerned primarily with safety critical systems, such as the braking system [10]-[12].Braking systems have benefited from numerous technological advances in the last several decades, such as new control schemes, higher safety standards, and other electronic improvements [13]-[15]. With increased autonomy and control authority, however, it becomes increasingly important that the braking system be accurate and safe against faults.Braking control generally uses measurements of the hydraulic pressure in brakes to decide actions to be taken, measured by pressure sensors [16]. If a hardware or software fault occurs in these sensors, however, brake control can be compromised,leading to potentially dangerous safety issues. This can be circumvented by using high precision brake pressure state estimation, with the potential to evolve the system into a sensorless system with sufficiently accurate estimation [17].

This type of estimation has been a hot research topic in the past, generally through the use of control theory-based approaches. A recursive least-squares approach was used in [18]to estimate brake pressure by using characteristics of the pressure response of antilock braking systems. An extended Kalman filter based approach, combining tire dynamics and hydraulic models, was used in [19]. Other approaches have included the design of inverse models for brake pressure [20],modeling the decrease, increase, and hold of brake pressure using experimental data [21], including measuring the amount of fluid passing through the valve to determine brake pressure[22]. All of these, however, are controls based approaches, with none being suitable for a fully sensor-less design. Reference[23] uses a neural net to perform estimation of brake pressure,using data obtained from an EV. However, this paper used conventional back propagation, which suffers from problems with overfitting, vanishing gradient, as well as higher computational complexity in training. Nevertheless, these problems have been resolved by implementing the recent advances of deep learning techniques to augment the training process of the deep neural network (DNN) [24].

Fig. 1. Deep-Learning-Based Training Technique.

Deep learning can be described as a learning approach that employs DNNs which comprise of two or more hidden layers[25]. Deep learning was introduced to resolve the problems associated with the poor training techniques used with DNNs[26]. Among these problems are the overfitting and vanishing gradient problem. The vanishing gradient problem has been resolved using rectified unit functions as activation functions[27]. The overfitting problem has also been tackled by implementing modern regularization techniques, such as dropout [28]. Dropout randomly drops units and their connections during the weight update cycle to reduce overfitting. Similar results were found by [29], which used rectified linear units (ReLUs) and dropout techniques to improve the accuracy of their neural net. These advantages are exploited to improve the training accuracy of the DNN and enhance the brake pressure state estimation.

Deep learning techniques are commonly used in the field of intelligent vehicles, most commonly in perception algorithms[8], [30], [31]. In past years, networks like AlexNet [32] and GoogLeNet [33] have achieved good results using deep learning for image classification, with image segmentation networks like YOLO9000 [34] and SSD [35] coming to the fore.Deep learning is also being used prominently in various forms in industrial applications [36]. Fault detection and classification is an active research topic, with deep learning being used both to identify faults and to classify them, as well as for learning features to be used in fault classification [37], [38]. LiftingNet uses a multilayer neural network to extract deep features from noisy data for use in fault classification in motor bearings[39]. Other approaches have also been used, such as one that used unsupervised learning vibration images to perform intelligent feature extraction for fault diagnosis in rotor systems[40]. Semi-supervised learning is a more common approach,with one approach using semi-supervised learning based on hierarchical extreme learning machines for soft sensor modelling [41]. Recently, dendritic neuron model (DNM) with learning schemes has shown significant ability in solving classification and estimation problems [42].

In this paper, a sensorless deep-learning-based approach is proposed for precise state estimation of the brake pressure of the electric vehicles (see Fig. 1). The term “sensorless” refers to that there is no sensor required to capture the changes in the braking pressure cycle while driving. Due to immense noise associated with the onboard vehicle’s sensors, developing sensorless data-driven estimation algorithm is highly needed to design robust control schemes [23], [43]. To the best of the authors’ knowledge and after exploring the existent literature,utilizing recent DL techniques for state estimation of brake pressure has not been addressed. The main novel contributions of the proposed state estimation algorithm can be concluded as follow: 1) A sensorless novel deep-learning-based algorithm is developed for brake pressure state estimation of an electric vehicle; 2) This state estimation technique uses current DL techniques and functions, such as dropout and ReLU to provide overfitting-free models of the state estimator; 3) The implementation of the proposed network is based on experimental data acquired using a real experimental vehicle testing environment; 4) Compared with conventional training methods, the proposed approach demonstrates more accurate brake pressure state estimation with RMSE errors of 0.048 MPa; 5) The proposed deep learning structure is expandable, hence, it can estimate other EV states in urban and high-way environments.

The rest of the paper is formed as follows. Section II reviews the structure of the DNN, dropout, and adaptive moment estimation (ADAM) optimization technique. Section III illustrates the experimental setup and data collection system. Section IV presents the proposed DL brake pressure estimation technique. In Section IV, the proposed and the future works are presented. In Section V, the preliminary results of the proposed brake pressure state estimation approach.

II. DEEP NEURAL NETWORK DESIGN

Neural networks have demonstrated good performance for state estimation of the brake pressure [23]. However, obtaining highly expressive state estimator’s model is linked, in practice,to the accuracy of the utilized training method. Despite the effectiveness of conventional training techniques, modern deeplearning-based structures have shown superiority in terms of minimizing the associated overfitting and achieving fast convergence. In this section, a DNN is proposed using dropout regularization to improve the quality of the brake pressure estimation. As described in Fig. 1, the DNN uses the vehicle states and powertrain states as inputs and the ground truth of the brake pressure values are the outputs while conducting the training experiment of the neural network. In this section, the standard structure of the DNN is illustrated. Dropout and the ADAM optimization technique are also presented.

A. Deep Neural Networks

A deep neural network was chosen in this study to perform brake pressure state estimation. Fig. 2 illustrates the basic architecture design of the multilayer neural network which is composed of a single input layer, one or more hidden layers and a single output layer.

Fig. 2. Structure of multilayer neural network.

B. Conventional Training

The backpropagation algorithm is commonly used for updating the weights of the NN. The operation of a neural network can be described using

where amand am+1represent the outputs of the m th and(m+1)th layers of the FFNN, and bm+1is the bias weights for the (m+1)th layer. While training, the aim is to train the network with associations between the specific input-output mappings {(p1, t1),…, (pQ, tQ)}, where p is the input vector and t is the associated output. The backpropagation algorithm adopts the mean squared error (MSE) as the performance index for optimization, which can be approximated as

The final recurrence relation can thus be summarized as

The training procedure of the neural network is deemed sensitive, and utilizing the conventional backpropagation (BP)as a stand-alone training approach may result in inaccurate performance of the obtained model [44]. BP experiences some problems pertaining to overfitting and computational complexity, which was recently tackled using some innovative DL training techniques, namely the use of dropout.

C. Dropout-Based Training

This section illustrates the basic dropout neural network model. Dropout is a DL technique that was introduced as a simple way to resolve the problem of overfitting [24]. As shown in Fig. 3, Dropout considers randomly selected units for training rather than all units [29].

Fig. 3. Dropout training technique.

In each layer m, pmdenotes a vector of independent Bernoulli random variables which represents the probability of the dropped-out nodes. This vector is multiplied elementwise with the output of the associated layer, am, to form the thinned outputs, a ˆm, as

Dropout has shown its usefulness for Bayesian approximation and estimation purposes [45]. Incorporating adaptive gradient-based optimization techniques, such as,ADAM with dropout has shown an excellent regression performance with a minimum training cost [46]. Hence, in this study, ADAM is adopted for gradient-based training optimization due to its fast convergence in regression problems compared to the conventional stochastic gradient descent (SGD) [46].

Based on the estimation of the first and the second moment of the gradients, ADAM calculates the adaptive learning rates for specific parameters. The optimization algorithm has been considered suitable in applications where data contains a large number of parameters. ADAM optimization is also well-suited to state estimation problems where the measurements are associated with immense noise sequences and sparse gradients[46]. Fig. 4 represents the flowchart of the ADAM optimization scheme. α and t define the step size and time step, respectively. θ0,m0, and v0represent the initial parameter vector, 1st, and 2nd moment vectors.

The main aim of the ADAM optimization technique is to minimize the expected value of the noisy objective f(θ) with regard to its parameters θ . f1(θ), …, fN(θ) represent the outputs of the stochastic function of following timestamps 1, …, N. The sources of stochasticity might be associated with evaluation of the randomly selected batches of data points and/or from the associated noise sequence of the objective function. The vector of the partial derivatives of the objective function ftcan be described as the gradient with respect to θ.

Fig. 4. ADAM optimization scheme.

The squared gradient ( vt) and the mean and the moving averages of ( mt) the mean represent the estimates of the variance and the mean of the gradient, respectively. The exponential decay of these averages are controlled by using hyper-parameters β1and β2.

III. EXPERIMENTAL SETUP AND DATA COLLECTION

In this section, the experimental setup as well as the data collection procedure is presented. The proposed DNN is trained using real vehicle driving data. Several experiments were performed to collect training data using an electric passenger vehicle with a chassis dynamometer attached. The testing vehicle, data collection methods, selected feature methods, testing scenarios, and data pre-processing are described in the following sections.

A. Testing Vehicle and the Electric Powertrain

The data were collected via conducting real driving experiment using an electric car with chassis dynamometer, as exhibited in Fig. 5 . The chosen vehicle is driven by a permanent-magnet synchronous motor, which can operate either in driving or generating modes. The electric motor is powered via battery via a DC bus, which releases or absorbs the electric power during driving or braking cycles,respectively. Relevant specifications of the test vehicle and power train are shown in Table I.

Fig. 5. EV testing using a chassis dynamometer.

TABLE I EV AND POWERTRAIN LIST OF SPECS

Several driving cycles standards can be used to set up the testing scenarios. The new European drive cycle (NEDC)which comprises of four repeated urban driving cycles was used for brake pressure estimation using NN [23]. However,arbitrary driving style imposes more challenges for NN to predict the brake pressure. In this paper, random driving cycles were adopted to better represent the urban driving environment with a range of speed up to 45 km/h. The proposed DL based brake pressure estimation is designed to capture the relevant trends of the urban driving behavior.

The electric powertrain comprises the fundamental components that generate electrical power. This comprehends a gearbox, an electric motor, a differential and a couple of two half shafts. At the center of the front axle, the electric motor is placed. In acceleration scenarios, accelerating the vehicle, the electric motor produces a propulsion torque that is transmitted to the axle to propel the vehicle through the drivetrain. While the electric motor switches to the regenerative brake mode to apply a braking toque in the vehicle deceleration scenarios[47], [48].

The hydraulic brake system installed in the testing vehicle includes wheel cylinders, a master brake cylinder, and inlet/outlet valves. As illustrated in Fig. 6 which represents the hydraulic brake structure, a spring and a piston are used to model the wheel cylinder movements. Based on the hydraulic valve dynamics and fluid flow, the pressure of the wheel cylinder can be expressed by (20). Detailed models can be found in [1]

Fig. 6. Structure of the hydraulic brake system.

B. Data Collection and Pre-Processing

The vehicle was run through several random driving cycles,giving a total of 10 000 s of data. Vehicle states and powertrain data were collected using the CAN bus, at a frequency of 100 Hz. In order to enhance the training performance, the raw unbalanced features data were smoothed and subsequently scaled from 0 to 1 to reduce the effect of the dissimilar units of the used signals. Fig. 7 shows an example of the collected raw data of the vehicle speed and corresponding brake pressure.

Fig. 7. The vehicle speed and corresponding brake pressure.

C. Process of Feature Selection

Selecting unique, and redundancy-free features contribute to a successful training of the state estimator model. The main states of the vehicle and powertrain were selected to train the model of brake pressure state estimator, while the measured brake pressure value is used as a ground truth. In addition to the vehicle and powertrain parameters, the motor speed and torque, the battery voltage and current, and the state of charge(SoC) of the battery are used as unique features. This is because when the EV is in the deceleration mode, the electric motor works as a generator, recapturing the kinetic energy.This causes the motor and battery current to change from positive to negative, which indicates that the battery is being recharged by regenerated energy from braking. The mean and standard deviations of some vehicle states are also added as features.IV. DEEP LEARNING BASED STATE ESTIMATOR MODEL

State estimation algorithms and sensor fusion schemes are required for designing robust control algorithms for dynamic systems [49], [50]. Obtaining precise state estimates in highly dynamic systems is challenging due to sensor drifts and immense bias sequences [51]-[53]. In this section, the proposed deep-structured neural network is evaluated for the purpose of brake pressure state estimation. The scaled EV features along with the ground truth brake pressure are considered for the training process of the DNN. The proposed DNN uses the vehicle states and powertrain states and the ground truth brake pressure values as target outputs while training the DL state estimator model. Fig. 8 illustrates some key features from the training data for one natural driving cycle.

Fig. 8. Sample of pre-scaled key features training data.

Designing an accurate DL-based state estimator model to estimate the brake pressure is not straightforward. Obtaining an accurate model is linked to the accuracy of the utilized training datasets, the structure of the network, training and optimization techniques. In this study, innovative deep learning techniques are exploited to enhance the training process of the DNN. Dropout regularization and ReLUs are implemented to improve the prediction of the brake pressure state estimator’s model. As shown in Fig. 9, the proposed DNN consists of visible input and output layers and 3 hidden layers, along with the visible inputs and outputs layers.

Fig. 9. DNN training scheme.

The ReLU activation function is used to generate the output signal of the hidden values, it can be expressed as follows:

The ReLU activation function is used to ensure accurate training for all hidden layers’ nodes. Dropout regularization method is implemented to reduce the training cycle’s computations by considering arbitrarily selected nodes for the training rather than the entire net. This means that the dropped-out units have temporally no contribution to the forward path and any weight updates are not applied to the neuron on the backward path. The implementation of dropout is not cumbersome; it is based on picking random units with a predefined probability (p) to be excluded from the training process. A low probability value has small impact and high values may cause under-learning by the network. However,with respect to the size of the DNN and number of units, a probability value of 10%-50% can provide good performance.

V. EXPERIMENTAL RESULTS AND DISCUSSIONS

This section presents the training and testing results of the implemented DL-based approach for the brake pressure state estimation. Discussions of dropout probability tuning are also included.

A. State Estimator Model Training

The proposed brake pressure state estimation method is implemented in Python with Keras. Several DL models were developed and trained by importing the experimental data to the Keras environment. A DL structure of 3 hidden layers with 60, 40, and 20 neurons, respectively, was chosen based on its smallest MSE of 0.087. All the experiments shown were run on an AMD Radeon™ HD 6800 Series GPU. The ADAM optimization algorithm is used to update the weights and biases based on the MSE loss function [54].

Dropout technique can be implemented for the hidden layers as well as for the visible layers. In order to investigate the best implementation with appropriate probability p, several batch training tests are performed with probabilities ranging from 0.1 to 0.5. The tests are performed with dropout being applied to both the visible input layer alone, and to the visible input and the hidden layers. Fig. 10 exhibits the average RMSE values over 200 epochs for both cases. As can be seen, the RMSE values increases as the dropout probability increases. It can be noticed that dropout is more feasible to be incorporated for hidden and visible input layers, based on the lower RMSE values. The dropout probability can be optimized through cross validation.

Fig. 10. RMSE in validation with different dropout probabilities.

The proposed model is trained using 8500 experimental data points over 200 epochs. Fig. 11 illustrates the accuracy of the training performance of the DNN. As shown, the losses represented by MSE values decrease as the DNN’s weights and biases updated. This proves the accurate update of the weight and biases while training the DNN. Based on the small MSE values, it can be concluded that the training process has obtained an expressive neural network model based on the training set used.

Fig. 11. MSE in training over 200 epochs.

B. State Estimator Model Testing

In this section, the proposed DL-based state estimation algorithm is tested and evaluated. A testing environment is developed for the trained model. A 20 % of the collected data points was selected for testing the proposed state estimator model. The testing data includes the vehicle states and the power train states. The output of the proposed DL-based state estimator has been compared to the ground truth values of the brake pressure. Fig. 12 shows the scaled brake pressure state estimation. The x-axis represents the number of samples while the y-axis represents the scaled brake pressure. As can be observed, the results of the proposed DL-based state estimation approach show a significant coincidence with the ground truth values of the brake pressure.

Fig. 12. DL-based brake pressure state estimation.

Fig. 13 shows the state estimation error magnitudes. To evaluate the accuracy of the proposed approach, regression performance errors are quantified using two main indices,namely, the RMSE and the coefficient of determination R2. R2is a measure of the model’s predication accuracy. It falls between 0 and 1, and the higher the value of the coefficient R2, the better the model at predicting the observations. R2is described as

Fig. 13. Error values of the proposed state estimation method.

The proposed model has achieved a regression accuracy with R2of 0.994, indicating that the proposed model of the brake pressure state estimator can achieve high predicationaccuracy of the brake pressure. Compared with the conventional training technique [23], the proposed has achieved more accurate state estimation with RMSE of 0.048 MPa. Based on the presented results, the proposed method demonstrates an accurate sensorless brake pressure state estimation.

VI. CONCLUSION

This paper proposes a novel DL-based state estimation algorithm for a safety-critical cyber-physical system. Using dropout and other DL modern elements such as ReLU activation functions, a novel DL-based model is introduced for brake pressure state estimation purposes. Real experiments for data collection are conducted via testing the EV on a chassis dynamometer under random driving cycles. The obtained data of the powertrain systems and vehicle states, as well as the ground truth values of the brake pressure are used for the training process. The DL-based state estimator model is trained using dropout with different probabilities. The training results show a high fitting accuracy. The trained model is tested, and the performance of brake pressure state estimation technique is evaluated. The state estimation results demonstrate the applicability and effectiveness of the proposed brake pressure state estimation approach.

As a future work of this research, the proposed state estimation can be further implemented and integrated with the onboard brake control system. The proposed DL-based model can also be flexibly expanded to estimate other states of the vehicle under several road conditions in urban and high-way scenarios. Furthermore, the estimated brake pressure information can be utilized in designing decision-making schemes for optimal braking in complex urban multiagent driving environment.