The braking coordination between tractor and semitrailer is vital to the safety of articulated vehicles. Traditional evaluation about braking coordination is based on the pressure measurement along air braking pipeline, which needs to change original braking structure to install gauges and cannot directly reflect the final braking coordination of different wheels. To overcome these limitations, this paper proposes a novel dynamic measurement system for evaluating the braking coordination of articulated vehicles. During the brake test, all wheel velocities of the whole articulated vehicle are synchronously obtained through a specially designed distributed acquisition platform. To effectively eliminate gross errors and noises in wheel angular velocity data, a 3-order autoregressive (AR) model and an improved-thresholding wavelet filtering algorithm are developed. Further, a novel direct evaluation method about braking coordination is proposed according to the differences in angular velocity dropping time of all wheels. Finally, the overall system is assessed through real field tests. The results validate the feasibility and effectiveness of the proposed system.
To reduce the accidents of tractor-semitrailers and improve their safety, many efforts have been dedicated to investigating active safety systems including antilock braking system or electronic stability control [
Undisputedly, among different performance evaluations, the braking performance is primary and vital. The world’s major economies have issued the standards/rules which hold legal demands regarding braking tests and performance of braking systems, for example, FMVSS 105/121/135 in USA [
The articulated vehicle is a combination of tractor and semitrailer, which are connected with each other through the fifth wheel (kingpin). If the braking system of tractor is not coordinated with that of semitrailer, it may cause severe accidents such as jackknife, snaking, and trailer-swing, which are unique to articulated vehicles [
In this paper, a novel dynamic measurement system for evaluating the braking coordination of articulated vehicles is proposed. It evaluates the braking coordination performance through analyzing the differences in the angular velocity dropping time of all wheels during the dynamic brake of articulated vehicles, which is executed on actual road surfaces. The novel aspects of the proposed system can be summarized as follows. (1) It can directly evaluate the final braking coordination of articulated vehicles because it is executed in real dynamic brake situation and directly measures the differences in the angular velocity dropping time of all wheels. (2) It does not need to change original braking pipeline of tractor-semitrailers and has the advantages of easiness to install, convenient maintenance, low cost, and so forth.
Section
The proposed system consists of an embedded main computer, a brake pedal sensor, a differential global positioning system (DGPS), and a group of wheel velocity units (WVUs). The overall configuration is shown in Figure
Overall configuration of the proposed system.
To realize effective and efficient braking coordination test, the working mechanism of the overall system follows the idea of “centralized control, distributed collection, and postprocessing.” According to this idea, we develop the software on the main computer to control the whole system. Besides, the software collects wheel velocity data based on multithread technique and processes all the data. Specifically, at the beginning of brake coordination test, the centralized-control main computer triggers all WVUs to work as well as the inner AD acquisition card to collect the pedal sensor data. Simultaneously, it starts to collect the velocity data of the tractor through DGPS. During the test, the angular velocity of each wheel is measured and stored by the corresponding WVU. Once the test is finished, the main computer acquires the wheel angular velocity information of each WVU through wireless communication. Finally, data processing and braking coordination evaluation are performed on the main computer.
As more and more articulated vehicles are equipped with active safety systems, it seems easy and convenient to obtain wheel velocity information through the Controller Area Network (CAN) bus. However, for such information, one major problem is that the resolution is low, usually one pulse per revolution. Thus, the measurement accuracy cannot be ensured when the velocity becomes low. To realize reliable evaluation of braking coordination of articulated vehicles, we specially design the WVU module to measure the wheel velocity accurately.
Figure
Developed WVU module. The complete module (a) and the PCB (b).
To measure angular velocity, there are two commonly used methods, that is, frequency measurement and period measurement, respectively. The former is more accurate at high velocity, while the latter is more accurate at low velocity. To take advantage of the two methods and adapt to a wide range of velocities, we adopt a combined method. That is, when the wheel velocity is higher than a certain threshold, the frequency measurement method is utilized. On the contrary, if the velocity is lower than this threshold, the period measurement method is adopted. Through such processing, the measured angular velocity data can achieve high measurement accuracy.
To effectively evaluate the braking coordination, it is vital to obtain accurate angular velocity data of all wheels. However, during emergent brake test, it will inevitably cause measurement noises and even gross errors at the beginning of brake due to fluctuations of braking air pressure, vibrations of vehicle body, imperfections of fixture, changes of tire-road friction conditions, and so forth. To eliminate these adverse effects, a data processing algorithm based on time series analysis is first proposed to detect and correct the potential gross errors. Then, an improved-thresholding wavelet filtering algorithm is developed to further remove the noises in the wheel angular velocity measurements.
Due to the advantages of low computational burden, good real-time performance, and high prediction accuracy, autoregressive (AR) model is one of the most popular models in time series analysis and has been widely used in practical applications, such as traffic flow forecast and gyroscope drift modeling [
Traditional methods such as
For AR model, the estimation of AR model parameters
Obviously, the wheel angular velocity data can be regarded as a sequence of data points indexed by time. From the point of time series, there is a certain temporal correlation among consecutive wheel angular velocity data in a long enough time interval. Taking this point into consideration, current wheel angular velocity data may have some relationship with past wheel angular velocity data. Therefore, the wheel angular velocity data can be modeled as AR process.
Assuming
After stationary processing, the next step is to determine the order of AR model. To identify the AR model order, the autocorrelation (ACF,
Then, according to the judge rule based on ACF and PACF, the order of AR model can be determined. If PACF cuts off to zero after
When the order of AR model has been determined, the model parameters can be estimated. Because the length of
Further, we can estimate the
The initial condition is
The parameters are calculated as
Update
If
When the five steps above are completed, the
For further clarification, the recursive structure of parameter estimation process can be described by Burg’s lattice filter, which is shown in Figure
Burg’s lattice filter for parameters estimation of
Once the process of modeling the wheel angular velocity data is completed, the developed
If
Applying the proposed
As a useful mathematical tool, wavelet transform has quickly spread to a whole spectrum of applications in science and engineering fields in a relatively brief period [
To achieve wavelet filtering processing, a suitable wavelet should be selected first to perform discrete wavelet transform (DWT) of wheel angular velocity signal. To obtain both good decomposition and reconstruction of wheel angular velocity signal, the selected wavelet should be orthogonal. Moreover, the selected wavelet should have compact support and high-order vanishing moment, which is the benefit of detecting singular point in wheel angular velocity signal. In addition, a wavelet with moderate supporting length is preferred so as to reduce the computational burden. In this paper, the “Daubechies5” wavelet in the Daubechies family is chosen to perform DWT.
In addition to wavelet function, the number of the levels of decomposition (LOD) for DWT also has a significant influence on the filter performance. In the vehicle application, an appropriate LOD can be selected when the noises are removed and all true motion dynamics components of the vehicle are preserved in the filtered signal. Unfortunately, there is no coherent methodology to determine how many levels of decomposition should be used at present. In this paper, a proper LOD is achieved by analyzing the frequency band property after DWT. According to DWT, each level of decomposition divides the spectrum of the original signal into different subbands. If one LOD is applied for the wheel angular velocity signal with sampling frequency
Since the fundamental vehicle dynamics are generally below 2~3 Hz, these motion dynamics are preserved in low-frequencies components (approximation parts) after DWT. After applying four LOD, the output band of approximation coefficients is limited to 3.125 Hz, which nearly reaches 3 Hz. Therefore, using four LOD is proper when taking into account the fact that a sampling frequency of
Moreover, the selection of an appropriate threshold is another crucial task as it directly affects the denoising results. In current study, the threshold is selected based on the heuristics variant of Stein’s Unbiased Risk Estimate (SURE), which is a conservative method and can avoid the loss of wavelet coefficients associated with vehicle motion. The calculation steps of the threshold
The noise intensity of wheel angular velocity signal at level of
According to the method proposed by Donoho and Johnstone [
Through computing the square of detail coefficients at
The final heuristic Stein unbiased likelihood threshold
After obtaining the suitable threshold, we can adopt shrinkage scheme to perform thresholding on detail coefficients to suppress or remove the noise component. Soft-thresholding is the most commonly used shrinkage scheme for threshold denoising because hard-thresholding causes discontinuity in the thresholded coefficients. However, soft-thresholding generates biased outputs, which may result in additional error sources in certain conditions. To overcome this limitation, a new improved-thresholding technique is proposed:
The proposed thresholding scheme above is a more continuous approach which preserves the highest amplitude coefficients and has smooth transition from noisy to important coefficients. Thus, it can help keep the continuity and reduce the impact of a biased signal.
To provide a more clear description, the improved-thresholding wavelet filtering algorithm developed above is summarized briefly as follows.
Utilizing all wheel angular velocity data processed by the algorithms presented above, we can carry out the braking coordination evaluation under unified time frame.
During braking coordination test, the brake beginning time of the whole articulated vehicle, which is represented by
However, it is very difficult to accurately determine the time
Angular velocity of one wheel and braking pedal force during one braking coordination test.
From Figure
Ascertain the brake beginning time of the whole articulated vehicle, that is,
Determine the average braking delay time (ABDT) of all wheel axles.
First, the angular velocity region from
Besides, considering that the left and right wheels on the same axle almost have the same average braking delay time in practice, we can further define the ABDT of the
Calculate maximal ABDT difference of any two wheel axles, that is,
To verify the performance of the proposed dynamic measurement system for evaluating the braking coordination, field tests were conducted on an articulated vehicle. It consists of a FOTON AUMAN 6 × 4 tractor, pulling a CIMC 3-axle semitrailer. That is, it totally had 6 wheel axles (
Articulated vehicle and test platform.
The tests were carried out in an open and flat area at the Proving Ground for Highway and Traffic, Ministry of Transport, China. During the tests, the tractor-semitrailer first accelerated smoothly to reach a certain preset velocity and then the emergent brake maneuver was executed to evaluate its whole braking coordination. The specific testing and operating conditions satisfy the requirements of GB7258, GB/T 26778, and GB 12676 in China [
Since all wheel angular velocity data have the same processing procedure, we choose the right-rear wheel of the semitrailer to demonstrate the effectiveness of processing algorithms developed in Section
The results of detecting and correcting gross errors through Grubbs and
The denoising results through wavelet algorithms.
From Figure
From Figure
When all wheel angular velocity data have been processed by the proposed
Four processed wheel velocities and brake pedal force in the unified time frame.
Local enlarged plot of Figure
According to the procedures presented in Section
(1) To achieve reliable evaluation, it is suitable to carry out 5-6 repeated tests in the same testing and operating conditions and then make statistical average processing to assess the final braking coordination.
(2) The accuracy and reliability of the proposed evaluation system are also verified by experimental results, which can actually be demonstrated from the following two aspects.
(a) According to the results of multiple field tests, it can be found that although the ABDT of each wheel is obtained and processed independently, there is only a slight difference (less than 0.015 s) between ABDTs of any two wheels located at the same axle (i.e., left and right wheels at the same axle). Such result is consistent with the characteristics that the wheels located at the same axle have almost the same braking pipeline delay structure in this case. If the measuring accuracy about the wheel ABDT is larger than 0.015 s, such consistent result cannot be obtained.
For instance, in the same test shown in Figure
(b) Also based on the results of multiple field tests, it can be found that the time difference between the ABDT of any wheel located at the
As the same test shown in Figure
Many severe accidents of articulated vehicles such as jackknife, snaking, and trailer-swing are caused by braking incoordination between tractor and semitrailer. To realize direct, reliable, and accurate evaluation about braking coordination, a novel dynamic measurement system is proposed in this paper.
The specially designed distributed acquisition platform is first developed to synchronously collect all wheel velocities. To obtain more accurate wheel angular velocities, the
The authors declare that they have no competing interests.
This work was supported in part by the Science and Technology Major Project of the Ministry of Transportation of China (Grant no. 2011318223450), the National Natural Science Foundation of China (Grant no. 61273236), the Jiangsu Provincial Basic Research Program (Natural Science Foundation, Grant no. BK2010239), and the Scientific Research Foundation of Graduate School of Southeast University (no. YBJJ1637).