Research on Pattern Recognition of Automobile Anti-Lock Braking System

A general electronic ABS system is shown in Figure 1, which is mainly composed of three parts: wheel speed sensor, controller (electronic control unit) and brake pressure regulator.

Figure 1.

ABS system block diagram

2.1.2

Electronic control unit (ECU)

The controller (electronic control unit, ECU) is the control core of the ABS system and is the key to the system development process. The main role of the control unit ECU is to calculate and process the wheel speed signal input from the wheel speed sensor, and then output the corresponding control signal from the output to the solenoid valve, so that it performs the function of brake pressure regulation.

The workflow diagram of ECU is shown in Figure 2. As the electronic control unit has a continuous monitoring of the four wheel sensor speed signal function, can be continuously detected from each wheel speed sensor input pulse electrical signals, its processing, calculations will become proportional to the wheel speed of the control signal, from these control signals in the electronic control unit can distinguish between the four wheels of the state of motion, if the input control signals to determine that the wheels will soon be embraced, the ECU will immediately issue a Command, into the anti-lock braking process, according to the analysis of the input wheel speed signal to the hydraulic regulator output an effective control signal so that the solenoid valve to produce the corresponding state response to the wheel braking force on the impact of the braking pressure adjustment to ensure that the system can not always exist in a larger braking force and make the wheels in a purely deadlocked state.

Figure 2.

ECU working flowchart

The ECU also has safety protection circuits that can display their status to the user if a fault occurs. If a fault occurs in the ABS system, the ECU automatically shuts down the ABS system and proceeds to the normal braking state, while the ABS warning light on the dashboard illuminates to warn of a system fault.

In the normal driving process of the car, its actual speed v and wheel speed v_w are equal, at this time the motion state of the car is called pure rolling motion. However, in the actual driving process, when the driver stepped on the brake pedal, the angular velocity of the wheels will be due to the brake friction torque and become smaller, the actual speed and wheel speed is not equal, there will be an unstable speed difference between them, so that the wheels and the road surface between the two appear relative slip.

Wheel slip rate is the actual vehicle speed v and wheel speed v_w difference with the actual vehicle speed v ratio, the expression for: 1S=(v−vwv)×100%=(1−vwv)×100%=(1−rwv)×100%

where S is the wheel slip rate, v is the vehicle speed (longitudinal speed of the wheel center, m/s), v_w is the wheel speed (instantaneous circumferential speed of the wheel, v_w = rw, m/s), r is the radius of the wheel, and w is the angular speed of wheel rotation (rad/s).

When v = v_w, slip rate S = 0, the wheel is in free roll.

At v_w = 0, slip rate S = 100%, the wheel is in full lock.

When v > v_w, slip rate 0 < S < 100%, the wheel is in the state of both locking and slipping. The greater the slip rate, the greater the corresponding degree of wheel slip.

After the use of ABS, so that the car in the braking process automatically adjusts the braking force of the wheels, the wheel slip rate control in a range that can obtain the best braking effect, can effectively avoid the emergence of the wheels of the hold slip, not only to shorten the braking distance, but also to improve the stability of the direction, and enhance the steering control ability.

The ABS anti-lock braking system is shown in Figure 3. Here to four wheels in the right front wheel to illustrate its working principle, if the electronic control unit to determine the right front wheel tends to hold dead, the ECU will make the control of the right front wheel braking pressure inlet solenoid valve energized, so that the right front wheel inlet solenoid valve into the closed state, the braking fluid output from the brake master cylinder is no longer into the right front brake wheel cylinder. At this time, the right front fluid solenoid valve is still not energized and is in the closed state, the right front brake wheel cylinder brake fluid will not flow out, the right front brake wheel cylinder scraping pressure to maintain a certain amount of other braking pressure does not tend to hold the wheel will still increase with the increase in the output pressure of the brake master cylinder.

Figure 3.

Anti-lock brake system

If the braking pressure in the right front brake wheel cylinder to maintain a certain, ECU determined that the right front wheel still tends to hold dead, ECU and make the right front discharge solenoid valve is also energized and transferred to the open state, the right front brake wheel cylinder in part of the braking wave will be in the state of the opening of the discharge solenoid valve flow back to the reservoir, so that the right front brake wheel cylinder braking pressure is rapidly reduced, the right front wheel tendency to hold will begin to eliminate, with the right front brake wheel cylinder brake pressure is reduced, and the right front wheel tendency will begin to eliminate, with the right front brake wheel cylinder braking pressure is reduced. With the reduction of braking pressure of the right front brake cylinder, the right front wheel will gradually accelerate under the action of the inertia force of the car, when the ECU according to the wheel speed sensor input signal to determine that the right front wheel holding tendency has been completely eliminated, the ECU will make the right front liquid solenoid valve and the discharge solenoid valve are de-energized, so that the inlet solenoid valve into the open state, so that the discharge solenoid valve into the closed state, and at the same time, also make the electric pump is energized to run, to the brake wheel cylinder At the same time, it also energizes the electric pump to deliver brake fluid to the brake wheel cylinder, and the brake fluid output from the brake master cylinder enters into the right front brake wheel cylinder through the solenoid valve, so that the braking pressure of the right front brake wheel cylinder increases rapidly, and the right front wheel starts to decelerate again.

ABS anti-lock device is not a completely independent system, it is mainly through the control of the brake braking system, braking pressure to achieve the braking of the wheels.

In the tire model, the nonlinear relationship between the road adhesion coefficient and the wheel slip rate can be fitted by the following simplified “magic formula”: 2μ=Asin{Barctan[Cλ−arctanDλ]}

Where μ denotes the roadway adhesion coefficient, the magnitude of which depends on its different roadway characteristics. λ represents the wheel slip rate. A, B, C, D are state parameters.

The experimental data for fitting the adhesion coefficients of high, medium and low road surfaces based on this formula are shown in Table 1.

The curves of roadway adhesion coefficient versus slip rate during braking on high, medium and low road surfaces are shown in Fig. 4.

Figure 4.

The relation curve between pavement adhesion coefficient and slip rate

In this paper, the road surface with moderate adhesion coefficient is selected for the simulation of anti-lock braking system, braking initial speed v = 25 m/s, wheel moment of inertia I_w = 2.4 kg · m², wheel radius R=0.35 m, 1/4 body mass 280kg, A = 0.5, B = 1.4, C = 8, D = 6. The simulation results of the braking process of the obtained car are shown in Fig. 5 to Fig. 9.

Figure 5.

Simulation results of vehicle speed and wheel speed equipped with ABS

Figure 6.

Angular acceleration and braking force of vehicles equipped with ABS

Figure 7.

Comparison of braking distance with or without ABS

Figure 8.

Comparison with or without ABS slip rate

Figure 9.

Comparison of wheels angular speeds with or without ABS

The simulation results of the speed and rotational speed of the vehicle equipped with ABS are shown in Fig. 5. From Fig. 5, it can be seen that the wheels of the ABS-equipped vehicle are not locked during the braking process, and a certain speed is maintained all the time, which ensures a better maneuverability and stability of the car during the braking process.

The results of the comparison of braking distances of vehicles with and without ABS are shown in Figure 6. As can be seen from Fig. 6, in the braking process of the vehicle equipped with ABS, when the angular acceleration of the wheels reaches the control threshold of the controller, the control system sends out a command to control the braking pressure through the opening and closing of the hydraulic control unit (solenoid valve), thus controlling the angular acceleration of the wheels at -75~75rad/s².

The simulation results of angular acceleration and braking force of the vehicle equipped with ABS are shown in Fig. 7. From Fig. 7, it can be clearly seen that during braking, the braking distance of the vehicle equipped with ABS braking system is smaller than that of the vehicle without ABS, in which the braking distance with ABS is about 205m and the braking time is 11s, and the braking distance without ABS is about 250m and the braking time is 14s.

The results of the comparison of slip rates of vehicles with and without ABS are shown in Figure 8. With the brake pedal to the bottom, the wheel slip rate of the vehicle without ABS will quickly become 100%, while the vehicle with ABS in the first 6s of braking, the slip rate has been controlled at 0.2~0.5, according to the curve in Fig. 4, it can be seen that the maximum coefficient of adhesion can be obtained when the wheel slip rate is in the range of 0.2~0.5.

The results of wheel angular velocity comparison with and without ABS are shown in Figure 9. As can be seen from Figure 9, the vehicle without ABS in the brake pedal to the end, the wheel speed quickly becomes 0, that is, the wheel hold, wheel hold will seriously affect the safety of the vehicle driving, and equipped with ABS vehicles in the braking wheel will not hold, to ensure that the vehicle’s braking stability, and enhance the safety of the vehicle driving.

In order to identify whether the automobile anti-lock braking system (ABS) is in normal operation mode, this paper simulates the changes of vehicle speed and wheel speed of each wheel when the actuator and sensor of the ABS system fail.When the actuator of the ABS system fails, step down the brake pedal and the pressure of the brake fluid enters into the brake pump chamber directly, and the wheels will suddenly lock.When the sensor of the ABS system fails, the corresponding wheel speed will not be recognized as the signal of the sensor cannot be transmitted to the pressure regulator, and the ABS valve will be very dangerous if it does not receive the speed signal. ABS system sensor failure, due to the sensor signal can not be transmitted to the pressure regulator, the corresponding wheel speed is not recognized, the wheels are in independent operation, when the ABS valve can not receive the speed signal will be very dangerous. Due to time constraints, this paper only focuses on braking at the start of the car, with a simulation of a single actuator failure.

3.2.1

ABS fault-free simulation

Firstly, simulate the emergency braking scenario of a high-speed vehicle on a road with a low coefficient of adhesion.

Parameters of the simulation experiment: the simulation time is 15 seconds. The 9th second is considered to apply braking force. The road surface adhesion coefficient is 0.4, the initial speed is 75km/h, and the interval is 0.1 seconds. The simulation results are shown in Fig. 10. Where, (a) ~ (f) represent the simulation results of longitudinal speed, steering wheel angle, left front wheel speed, right front wheel speed, left rear wheel speed, and right rear wheel speed, respectively.

From Fig. 10, it can be seen that under normal conditions, the car is still in a stable state at the 9th second due to the large braking force applied, but the braking force of the four wheels is adjusted under the control of the ABS.

Figure 10.

Simulation results of no fault condition

3.2.2

Actuator ABS valve fault simulation

Simulation conditions: The basic setup is the same as in the no-fault case. Braking pressure increases momentarily when the corresponding wheel actuator fails at the start of braking. 1)

Left front wheel actuator ABS valve failure

The simulation results of the left front wheel actuator failure case are shown in Fig. 11, where (a) ~ (d) represent the simulation results of the left front wheel speed, the right front wheel speed, the left rear wheel speed and the right rear wheel speed, respectively.

From the simulation results, it can be seen that the left front actuator during braking fails and the left front wheel braking force increases instantaneously and cannot be reduced, which is due to the solenoid valve not working. The speed of the left front wheel decreases instantly, and the wheel tends to hold on around the 10th second. The traction of the tire becomes poor, and the car gradually loses control. At this time, the ABS system controls the braking force of the other wheels to improve the vehicle’s braking performance. But in the end, the vehicle remained out of control.

2)

Right front wheel actuator ABS valve failure

The simulation results of the right front wheel actuator failure case are shown in Figure 12. The simulation results show that when the actuator of the right front wheel fails in the 9th second, the braking force on the right front wheel increases and no longer decreases, which is due to the solenoid valve not working. The speed of the right front wheel decreases instantly, the 10th second tends to deadlock, the tire traction becomes poor, the car gradually lost control. At this point, the ABS system controls the braking force of the other wheels to improve the vehicle’s braking performance. But eventually the vehicle went out of control.

3)

Left rear wheel actuator ABS valve failure

The simulation results of the left rear wheel actuator failure case are shown in Figure 13. The simulation results show that the left rear wheel actuator fails in the 9th second, the braking force acting on the left rear wheel increases and no longer decreases, which is due to the solenoid valve can not work. The speed of the left rear wheel decreases instantly, and the 10th second is close to deadlock. The adhesion of the tires decreases, and the car gradually loses control. At this point, the ABS system controls the braking force of the other wheels to improve the vehicle’s braking performance. But in the end, the vehicle went out of control.

4)

Right rear wheel actuator ABS valve failure

The simulation results of the right rear wheel actuator failure case are shown in Figure 14. The simulation results show that the right rear actuator malfunctions at the 9th second, and the braking force on the right rear wheel increases rapidly and no longer decreases, which is caused by the solenoid valve not working. The speed of the right rear wheel decreases instantly, and at the 10th second it is close to locking, the traction of the tire decreases, and the car gradually loses control. At this point, the ABS system controls the braking force of the other wheels to improve the vehicle’s braking performance. But eventually the vehicle went out of control.

Figure 11.

Left front wheel actuator fault simulation results

Figure 12.

Right front wheel actuator fault simulation results

Figure 13.

Left rear wheel actuator fault simulation results

Figure 14.

Right rear wheel actuator fault simulation results

In this paper, after categorizing the regulator fault types, fault cause Y=(y1,y2,y3,y4,y5) is taken as output and y₁, y₂, y₃, y₄, y₅ represents no fault, left front regulator fault, right front regulator fault, left rear regulator fault and right rear regulator fault respectively. The number of output nodes is equal to the number of identified types, so five output nodes are taken, and the corresponding fault types correspond to the output results of the output neurons, and the fault mode X=(x1,x2,…,x6) is taken as input, and x₁, x₂, …, x₆ represents the corresponding changes in longitudinal speed, lateral speed, and four-wheel wheel speed, respectively. After classifying the sensor fault type, the fault cause Y=(y6,y7,y8,y9,y10) is the output, y₆, y₇, y₈, y₉, y₁₀ represents no fault respectively, the left front sensor is faulty, the right front sensor is faulty, the left rear sensor is faulty, the right rear sensor is faulty, the number of output nodes is equal to the number of identification types, so five output nodes are taken, and the corresponding fault type corresponds to the output result of the output neuron, with the fault mode X=(x7,x8,…,x12) as the input, x₇, x₈, …, x₁₂ represents the corresponding change of longitudinal vehicle speed, lateral vehicle speed and four-wheel wheel speed respectively, The failure modes caused by multiple sets of different fault causes are used as training samples to learn, so as to establish the mapping relationship between the failure modes and the fault causes.

For the regulator (ABS valve) in total there are 6 failure modes corresponding to 6 input nodes and there are 5 failure causes corresponding to 5 output nodes and 10 samples are taken for each failure cause, hence there are 50 samples. In this paper, 9 sets of samples are taken as training samples for the velocity values at 0.3s, 0.4s, 0.5s, 0.6s, 1.8s, 3.2s, 3.8s, 4.2s, 4.5s, and 1.5s as detection samples.

For the sensor, again 50 samples are taken and 9 sets of samples of velocity values at start, 0.5s, 1s, 2.5s, 3s, 3.5s, 4s, 4.5s, 4.7s are taken as training samples and velocity values at 2s are taken as detection samples.

The neurons of the BP network all use the Sigmoid activation function, which is processed to prevent saturation of the neuron outputs due to the absolute value of the net input being too large, and then the weights are adjusted to enter the flat region of the error surface. Commonly used input data preprocessing methods are: 1)

All sample values are divided identically by a larger benchmark to ensure that the data is between (0, 1). However, the benchmark value of the method is more difficult to determine, if the benchmark value is too large, part of the original data may tend to be very small, if the benchmark value is too small, part of the data may be very close to 1, and, when adding a new set of samples, there may be a need to change the original value of the benchmark has been determined.

In this paper, the normalization method shown in equation (3) is used to transform the input and output data into the interval (0,1), which is the ratio of the data at each position of the training sample minus the minimum value of the row in which it is located to the difference between the maximum and minimum values of the data in that row: 3aji=aji−ajminajmax−ajmin

Where a_ji, a_jmax, a_jmin are the normalized, actual, maximum and minimum values in each group of sample data, m is the number of samples, n is the number of samples. This method ensures that the data are between (0,1) or (-1,1), but also maximizes the possibility of widening the differences between the individual data in the same set of samples.

For this problem, this paper uses the trial-and-error method, where the same sample set is used for training with other parameters unchanged, the convergence accuracy is fixed, and the number of iterations is compared, from which the number of nodes in the hidden layer corresponding to the minimum network error is determined. The neural network model for fault pattern recognition is divided into three layers: the input layer, the hidden layer, and the output layer. For regulator faults the number of nodes in the input layer is 6, which corresponds to 6 fault phenomena, and the number of nodes in the output layer is 5, which corresponds to 5 fault causes. The magnitude of output layer node values is influenced by the likelihood of fault occurrence. First of all, this paper refers to an empirical formula for determining the number of implied layer nodes, which is calculated as a rough estimation, and the range of values for the number of implied layer nodes can be initially obtained. Namely: 4m=n+l+α

Where m is the number of nodes in the hidden layer, n is the number of nodes in the input layer, l is the number of nodes in the output layer, and α is a constant between 1 and 10. At this point, for the same training sample, different numbers of hidden layer neurons are selected, and the traingda adaptive modification learning rate algorithm is used, the activation function is tansig, the objective error is used 1e-5, and the learning rate is used 0.0001, and the network is trained 400 times respectively, and the optimal value of the 400 training processes corresponding to the number of neurons in each hidden layer is recorded.

By comparing the number of iterations, error performance of these parameters, it can be seen that when the number of neurons in the implicit layer is 13, the network training error is the lowest, at this time after 152 iterations to achieve the training goal. So the number of neurons in the hidden layer is selected as 13, i.e., the network model used for regulator failure in this paper is 6-13-5.

For the sensor failure input layer node number 6, corresponding to 6 fault phenomenon data, the output layer node number 5, corresponding to 5 causes of failure, using the same method of training, when the number of neurons in the implied layer is 13, the training error is minimized, at this time after a minimum of 141 iterations to reach the training goal. So the number of neurons in the hidden layer is selected as 13, i.e., the network model used for sensor fault pattern recognition in this paper is 6-13-5.

In this study, the inputs and outputs are functionally transformed by means of an activation function, which turns the inputs of a possibly infinite domain into inputs within a specified finite range. The simulations are compared by using purelin for the output layer and tansig and logsig for the implicit layer.

In order to improve the range of the input vector and to make the range of the output vector within (0,1) and to ensure that the step size is less error. The comparison results show that the implicit layer activation function is tansig is less than the implicit layer activation function is logsig with less step size and less error, so in this paper the implicit layer activation function is tansig and the output layer activation function is purelin.

The traditional BP network algorithm has the problems of slow convergence speed during learning, the existence of local extreme value phenomenon and the difficulty of determining the number of nodes in the hidden layer and the hidden layer. For this reason, many improvement methods have emerged in practical applications, which can be divided into two categories: optimization based on gradient descent method and numerical-based optimization, the former mainly includes adaptive adjustment of the learning rate method and elastic BP method, and the latter mainly includes the simulated Newton method, the conjugate gradient method and Levenberg-Marquart method, etc., and in this paper, we select the Levenberg-Marquart method for model construction.

The Levenberg-Marquardt method, abbreviated as LM method, is actually a combination of the gradient descent method and the Newton method [27]. Its search direction is set as: 5S(X(k))=−(H(k)+λ(k)I)−1∇f(X(k)) 6X(k)=X(k)+η(k)S(X(k))

Let η^(k) = 1, then X(k)=X(k)+S(X(k))

The algorithm avoids the direct computation of the Hessian matrix, thus reducing the amount of computation and memory requirement in training. Since the performance function of the BP neural network is the mean square error of the network, the Hessian matrix H can be obtained by approximating the Jacobi matrix J, i.e.: 7H=JTJ

The Jacobi matrix contains the first-order derivatives of the network error with respect to the weights and biases.The LM algorithm requires a large amount of storage because the Jacobi matrix uses a matrix of Q*n (Q is the number of training samples, and n is the total number of all weights and biases in the network).

At the beginning, λ takes a very large number, which at this point corresponds to a gradient descent with a very small step size; as the optimal point is approached and λ decreases to zero, the search direction shifts from a negative gradient to the direction of Newton’s method. Typically, λ is decreased when f(X(k+1))<f(X(k)), otherwise, it is increased by λ. This ensures that the value of the performance function of the network is always decreasing. As the LM algorithm combines the advantages of gradient descent and Newton’s method, the performance becomes even better, the algorithm has a very fast convergence speed for medium-sized neural networks, and it makes good use of Matlab’s computing advantages for matrices.

By comparing the trial calculations, this paper selected to use the Levenberg-Marquardt algorithm to train the network. The training process error is shown in Figure 15. The selected samples were used as inputs and outputs to train the neural network model, and after 400 iterations of calculations, the error basically reached the predetermined value of 0.0001.

Figure 15.

Training process error

The network function approximation is shown in Fig. 16. The simulation output during training matches very well with the target output.

Figure 16.

Network function approximation diagram

The model is determined after reaching the training accuracy requirements, and the determined model is applied for simulation. During the simulation, 1 data is selected every 50 points in the actual collected signals, and a total of 160 sets of data are used as the input of the network to detect the degree of agreement between the output results and the standard filtered outputs, and the simulation results are shown in Fig. 17, and the errors between the simulation results and the target outputs are shown in Fig. 18.

Figure 17.

Simulation output and target output results

Figure 18.

Relative error curve between simulation output and target output

As can be seen from Fig. 18, the error between the simulation results and the target output is very small, and the relative error is mostly below 3%, which indicates that the established network can reflect the relationship between the input and the target output well, and the network can be used to replace the wavelet filtering, and the network’s generalization ability is also very strong.