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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina


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Volume 15, Issue 1

Issues

Volume 13 (2015)

Research on identification method of heavy vehicle rollover based on hidden Markov model

Zhiguo Zhao / Yeqin Wang / Xiaoming Hu / Yukai Tao / Jinsheng Wang
Published Online: 2017-07-07 | DOI: https://doi.org/10.1515/phys-2017-0054

Abstract

Aiming at the problem of early warning credibility degradation as the heavy vehicle load and its center of gravity change greatly; the heavy vehicle rollover state identification method based on the Hidden Markov Model (HMM, is introduced to identify heavy vehicle lateral conditions dynamically in this paper. In this method, the lateral acceleration and roll angle are taken as the observation values of the model base. The Viterbi algorithm is used to predict the state sequence with the highest probability in the observed sequence, and the Markov prediction algorithm is adopted to calculate the state transition law and to predict the state of the vehicle in a certain period of time in the future. According to combination conditions of Double lane change and steering, applying Trucksim and Matlab trained hidden Markov model, the model is applied to the online identification of heavy vehicle rollover states. The identification results show that the model can accurately and efficiently identify the vehicle rollover state, and has good applicability. This study provides a novel method and a general strategy for active safety early warning and control of vehicles, which has reference significance for the application of the Hidden Markov theory in collision, rear-end and lane departure warning system.

Keywords: Hidden Markov model; rollover; driving status identification; heavy vehicle

PACS: 07.05.Tp

1 Introduction

Because of: a high center of gravity; large load capacity; and relatively high aspect ratio, when the heavy vehicle encounters extreme conditions, such as excessive speed; small turning radius; and avoiding obstacles, it is prone to rollover accidents. US Highway Safety Bureau statistics show that in all traffic accidents, vehicle rollover accident hazards rank second only to the car crash. The vehicle rollover is a major traffic accident leading to the loss of life and property, and has become an important problem affecting traffic safety [1, 2].

At present, most of the rollover warning status recognitions are based on roll angle or lateral acceleration limits that are greater than a set value for the rollover conditions. Preston-Thomas J [3], Dunwoody [4], Dongyong Hyun [5], and others, focus on the lateral load transfer rate (LTR). They use the LTR as the criterion to analyze the parameters which affect the LTR value, so as to judge the vehicle rollover degree; In 2001, Chen B and Peng H proposed a rollover real-time early warning algorithm based on TTR rollover time predictions. This algorithm is characterized with simple logic and good practicability [6]; In 2003, Eger and Kiencke proposed a time-series-based rollover warning algorithm, which determines the mathematical relationship between the roll angle and roll angular velocity based on the boundary condition of vehicle stability [7]; In 2008, H. Yu proposed a real-time TTR matrix based rollover warning algorithm, and the use of Kalman filter technology to improve the accuracy of the TTR matrix [8]; In 2011, at Jilin University, Zhu Tianjun proposed a modified TTR and Kalman filter technology based rollover early warning method, and the test results show that the method can be a real-time warning [9].

HMM is a statistical model based on the Markov chain, which has a simple dynamic Bayesian network structure and has been widely used in pattern recognition and fault diagnosis [10]. In this paper, the vehicle rollover as a “fault-like” state, introducing the GMM correlation analysis method, presents a method of vehicle rollover state identification and prediction based on HMM.

2 Hidden Markov model and Markov prediction method

The Hidden Markov model consist of two processes, one is the Markov process, the other one is a general stochastic process(which may be discrete or continuous), and therefore has a double stochastic [1113]. A typical hidden Markov model (HMM) can be described by the following five parameters:

  1. Number of states N. The number of states the system may be in during the Markov process. Suppose aij = P(qt+1 = Sj | qt = Si). qt is the state at time t. aij = P(qt+1 = Sj | qt = Si). The state of the system can only be expressed by the observed value.

  2. Possible number of observations M. ot is the observed value at time t during the discrete process. Assuming tot is finite, so the observed value of the system at time t must be an element in {O}.

  3. State transition matrix A. The transition probability from state Si to state Sj is aij = P(qt+1 = Sj | qt = Si), 1 ≤ i, jN. Because the total number of transfer states for one system is N, the number of value aij can reach N × N, expressed as a matrix: a11a1nan1annN×N

    And j=1n aij = 1.

  4. Confusion matrix B. The observed probability of the observed value Ot = Ok in the state Sj is bjk = P(ot = Ok|qt = Sj), where 1 ≤ jN, 1 ≤ kM.

    In the state Sj, the number of random process can be M, then the number of value bjk can reach N × M, expressed as a matrix b11b1mbn1bnmN×M

    And k=1n bjk = 1.

  5. Vector of the initial state probabilities π. The probability that the first state q1 take S = {S1, S2, …, SN}, and if πi = P(qi = SI), then π = {π1, π2, …, πN}, is a 1 × N vector.

There are three main problems in HMM application, the first two are pattern recognition problems, the last one is parameter training [14]:

  1. Evaluation problem. To calculate the probability of an observed sequence based on the known HMM. This problem is assumed to have a series of HMM solutions to describe the different systems, and need to know which system has the greatest probability of the current observation sequence.

  2. Decoding problem. To observe the sequence of states that is most likely to occur in the specified model based on the observed sequence.

  3. Learning problem. That is the parameter training problem. HMM was obtained from the observation sequence, and the hidden state of its representation generated a three tuple (A, B, π) to describe the phenomena law.

In practice, the majority of cases are continuous signals and data. For example, as the vehicle is operating, signal data, which can reflect the vehicle speed, roll, and lateral acceleration, are continuous in the time axis. This continuity exists in a general stochastic process where the probability of occurrence of observations in each state can be expressed as a function of the probability density function. One of the most common methods is to use a linear combination of multiple Gaussian functions to estimate the probability density function of the observed value. Setting O as the observation sequence, the probability density function can be expressed as bj (O) = m=1M cjm N(O, μjm, COVjm), 1 ≤ jN.

Where μjm, COVjm, cjm represent mean vector, covariance matrix, and weight coefficient of the m-th Gaussian component, the state Sj. cjm satisfies the constraint condition: cjm0,m=1Mcjm=1

Since the representation structure of bj(O) is changed, the method of parameter updating in model training process also changes. For bj(O), it is mainly determined by three parameters, so the update for bj(O) is actually the update for μjm, COVjm, cjm. The introduced parameter γt(j, m) represents the probability of the k-th Gaussian component function ot. The state SJ represents ot at time t, namely: γtj,m=αtjβtjj=1Nαtjβt(j)×cjmN(O,μjm,COVjm)m=1McjmN(O,μjm,COVjm).

The core concept of the Markov prediction method, is the state transition. The vehicle state can be S1, S2, …, SN, and each time it can only be in one state. Each state has n steering directions (including itself), and state transition is stochastic. State transition probability aij = P(Sj | Si) is used to describe the size of state transition possibility, which is the origin of state transition matrix A in the Hidden Markov Model. A=a11a1nan1annN×N

The state transition probability matrix has the following characteristics:

  1. 0 ≤ aij ≤ 1 (i, j = 1, 2, ⋯, N),

  2. j=1Naij=1(i,j=1,2,,N).

The state transition probability matrices completely describe the change process of the objects under study. The above matrix A, may be a one step transition probability matrix. For a multi-step transition probability matrix, the following definitions can be interpreted:

If the system is in the Si state at time t0, it changes to be in the Sj state at time tn after the n-step transfer. Then, the description of the number of possibilities of such a transition is called the nstep transition probability. Recorded as: aij(n) = P(Sj | Si).

There are: An=a11na1nnan1nannnN×N

Let A(n) be an n-step transition probability matrix, and have:

  1. A(n) = A(n−1)A;

  2. A(n) = An.

For a Markov process, if the initial probability ai(n) = P(qn = Si) and transition probability matrix are known, the state after n steps can be predicted. That is the state of the vehicle at any time within the effective range of the vehicle system.

For n ≥ 1, as ai(n) = P(qn = Si), so that: ai(n)=j=1Naj(0)ajin,i=1,2,,N

It is a long-term process to monitor and pre-alarm the running state of a vehicle. Considering the influence of the state transition matrix, the definition of stationary distribution is introduced: Such as the existence of non-zero vector X = (x1, x2, ⋯, xn), so that : X = (x1, x2, ⋯, xn).

A is a probability matrix and X is a fixed probability vector.

In particular, let X = (x1, x2, ⋯, xn) be a state probability vector and A be a state transition probability matrix.

If XA = X, then i=1N xi aij = xj, i = 1, 2, ⋯, N.

Then X is a stationary distribution of the Markov chain. If the state probability vector X at some time of the stochastic process is a stationary distribution, the process is said to be in an equilibrium state. And once the process is in equilibrium, the state probability distribution remains unchanged even after many step transitions, that means once the process is in equilibrium it will always be in equilibrium.

3 Vehicle rollover model

According to the state of the vehicle steering motion, the hierarchical HMM is constructed from bottom to top (illustrated in Figure 1). The lower structure describes the influence factors in the vehicle steering movement, and the superstructure describes a state of the vehicle turning movement. Superstructure is used to describe a state in which the car is in a turning motion. When the car is rollover, the probability of “hidden state” for rollover is larger.

Vehicle layered HMM rollover model
Figure 1

Vehicle layered HMM rollover model

4 Identification method of vehicle rollover state

The roll angle and lateral acceleration are used to characterize the vehicle rollover state. Based on the HMM theory, the method of the vehicle rollover state identification is built up, as shown in Table 1. The dynamic data of Lateral acceleration and roll angle, obtained by the sensor in the running vehicle, according to a certain step segment, is used as the observed value of a continuous HMM state model library. Using the algorithm of “evaluation problem” introduced in HMM application problem, we can get the HMM state model with the best observation value within a certain step, which acts as the current state of the vehicle. A number of stepwise vehicle states are obtained over a longer period of time, this can be used as part of the vehicle state Markov chain and conclude the state transfer law to predict the state of the vehicle for a certain time in the future.

Vehicle state identification method
Figure 2

Vehicle state identification method

Table 1

LZ3254M5DA2 Some parameters

According to the Markov prediction method, the step of predicting the state of the vehicle steering process using the hidden Markov chain in the HMM is as follows:

  1. Dividing the state of vehicle in the process of turning. According to the risk of possible rollover and the specific circumstance in training processes, the four states are determined: Normal State S1, Intermediate State one S2, Intermediate State two S3, and Rollover State S4.

  2. Calculating real-time status. The observed sequence is obtained from the HMM library of lower sub-movement. Then, according to the Viterbi algorithm, introduce the “decoding problem”, and a best path is figured out. The sequence is the state sequence of the largest probability of occurrence. The prediction begins with the last state SN of the state sequence, but the SN is the only one state that appears to be the largest, not a probability vector. In practice, let SN−1 = Si. Then the initial state probability used to predict can be expressed as : π0 = Ai, where Ai is the ith line of the transfer matrix A.

  3. Predicting the state according to the transition probability. The initial state of the current time is π0, then the state probability at time t can be expressed as πt = π0 AAA = π0 A(t). The elements in π0 represent the probability values of the three states at time t, and the one with the largest probability are the state in which the vehicle is most likely to be at time t.

5 Rollover model training

5.1 Simulation conditions

Considering the safety, this paper uses: the heavy vehicle dynamics simulation software Trucksim; selects the typical heavy-duty vehicle driving conditions; and collects the corresponding driving cycle experimental data. In order to make the simulation as close as possible to the actual situation, the LZ3254M5DA2 dump truck is chosen as the research object. The Trucksim simulation model is constructed, as shown in Table 1.

5.2 Simulation on operating conditions

According to the provisions of the United States NCAP, a dynamic test mainly includes a J-type steering test and a hook test. The hook test was adopted by NCAP as a dynamic test because it was close to the actual situation [15]. The vehicle rollover process is relatively short, in order to properly simulate the vehicle operating conditions under complex conditions. Operating conditions combining Double Lane Change and Hook Steering are adopted, as shown in Figure 3.

Double Lane Change and Hook Steering
Figure 3

Double Lane Change and Hook Steering

The roll angle and lateral acceleration corresponding to the operating conditions obtained through the joint simulation of Trucksim and Matlab, are investigated, as shown in Figure 4 and Figure 5.

Lateral acceleration under Double Lane Change and Hook Steering
Figure 4

Lateral acceleration under Double Lane Change and Hook Steering

Roll angle under Double Lane Change and Hook Steering
Figure 5

Roll angle under Double Lane Change and Hook Steering

5.3 Model training

Five parameters describe hidden Markov model (HMM), they are π, A, μ, COV and, c. The HMM for the characterization of four lateral states, is trained by applying Trucksim and Matlab. They are recorded as S1, S2, S3, and S4. The paper takes S4 as an example, where the data structure of S4 is as follows: π=0.60110.39850.0004A=0.46510.53130.00360.31800.38970.29220.17220.53380.2940c=0.27640.72360.52450.47550.37890.6211

μ is a 2 × 3 × 2 matrix, and COV is a 2 × 2 × 3 × 2 matrix. Interception of part of the data are as follows: μ(:,:1)=0.07710.01190.015661.826370.852874.9786COV(:,:,2,1)=0.01110.17230.172331.139

Four training models are stored in the model library, which can not only be used to identify the vehicle condition under other working conditions, but also update the model and improve the accuracy of description.

6 Simulation test

After obtaining the four state models through training, the simulations and rollover state identification tests were carried out for the same vehicle under other operating conditions. Taking high-speed double-shift line conditions as an example (70 km/h), the working conditions are shown as Figure 6.

Hyperbolic condition
Figure 6

Hyperbolic condition

The lateral acceleration and the roll angle are taken as observation features, and the data segments of 90 steps before 9s are selected for each step in 0.1s. The data of each data segment in four models. The statistical results are used to calculate the confusion matrix of the Markov chain, which can be used to compute the state of the vehicle for the current time. 89 times transition can happen among 90 data. statistics of before and after the transition state are shown in Table 2, and this can be a confusion matrix.

Table 2

State transition

Confusion matrix: A=0.94230.01920.038500.05260.89480.052600.062500.870.06250001

Since the 90th data state presents the “state 4” of the rollover state, and the “state 4” in the confusion matrix can only be converted to itself. It means in kinematic that the rollover state of the state “4” is irreversible, therefore, it can be predicted that the vehicle is in the rollover state at the moment of step 91, 92 and 93, and it is irreversible. The prediction is also consistent with simulation using Trucksim.

7 Conclusion

In this paper, the roll angle and lateral acceleration are chosen as parameters to characterize the rollover state of the vehicle, and a method is proposed to identify the rollover state of the heavy vehicle based on the hidden Markov model, which can dynamically identify the driving state of the heavy vehicle in complex operating conditions. The experimental results show that the proposed algorithm can identify the rollover state of heavy vehicles effectively and have high accuracy.

In this paper, the variations in road surface and vehicle load are not considered. If there is any difference in identification results of rollover state in this case it is not studied. In the future research, we need to improve the identification algorithm to achieve a variety of loads and driving conditions to accurately identify the status of a heavy vehicles rollover target.

Acknowledgement

Part of the research funding is funded by the National Natural Science Foundation of China (51675212)), Major Project of Natural Science Research in Universities of Jiangsu Province (16KJA460004) and Jiangsu province six talent peak project (2013-ZBZZ-020).

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About the article

Received: 2016-12-06

Accepted: 2017-04-06

Published Online: 2017-07-07


Citation Information: Open Physics, Volume 15, Issue 1, Pages 479–485, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2017-0054.

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© 2017 Zhiguo Zhao et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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