Keywords

1 Introduction

With the rapid development of China’s economy and the continuous acceleration of urbanization, urban expressway has developed rapidly in various cities in China. The construction of urban expressway plays an increasingly important role in alleviating urban traffic congestion, reducing environmental pollution and promoting economic development.

Automatic traffic event detection (AID) is one of the important functions of traffic management and control system. In the past 40 years, many experts and scholars both at home and abroad have been devoted to the research of various traffic event detection methods. The traditional automatic detection algorithm of traffic events is mostly based on fixed detector data (such as the data of loop detector), and the development is relatively perfect. But the fixed detector can only collect the traffic data (such as occupancy, speed and flow) of the point, and it is difficult to ensure whether the data based on the point represents the real traffic condition; On the other hand, the layout distance, location and communication of fixed detector are also the key factors affecting the performance of the algorithm. In practical application, the fixed detector data often lacks data for a long time due to communication failure and equipment failure, which can not guarantee the smooth progress of event detection. In addition, the installation and maintenance of detectors will hinder the normal operation of road traffic, sometimes it is necessary to close the road, which will cause inconvenience to the giver. How to detect and confirm the time, place and nature of the event accurately and timely is the key technology for the successful operation of traffic management and control system. The performance of the automatic detection algorithm for traffic events is the core of traffic event management system, and also one of the important evaluation indexes for the successful operation of intelligent transportation system.

2 Related Work

Guerrero-Ibáñez et al. discuss how sensor technology can be integrated with the transportation infrastructure to achieve a sustainable Intelligent Transportation System (ITS) and how safety, traffic control and infotainment applications can benefit from multiple sensors deployed in different elements of an ITS [1]. Several case studies of big data analytics applications in intelligent transportation systems, including road traffic accidents analysis, road traffic flow prediction, public transportation service plan, personal travel route plan, rail transportation management and control, and assets maintenance are introduced [2]. Intelligent transportation is an emerging technology that integrates advanced sensors, network communication, data processing, and automatic control technologies to provide great convenience for the daily lives [3]. Patel et al. survey a set of solutions available in the literature to design of an ITS system using IoT along with challenges and future scope for the improvement of the existing solutions [4]. Veres et al. present a survey that highlights the role modeling techniques within the realm of deep learning have played within ITS [5]. In order to meet the demands of the intelligent transportation big data processing, this paper puts forward a high performance computing architecture of large-scale transportation video data management based on cloud computing, designs a parallel computing model containing the distributed file system and distributed computing system to solve the problems such as flexible server increase or decrease, load balancing and flexible dynamic storage increase or decrease, computing power and great improvement of storage efficiency [7]. Other influential work includes Refs [7,8,9,10].

This paper consists of the following parts. The first part introduces the related background and significance of this paper, the second part is the related work of this paper, and the third part is data analysis. The fourth part is example analysis. The fifth part is conclusion.

Nonlinear dynamic control is a method to study the feedback linearization design of general nonlinear control systems through the concept of “inverse” of dynamic systems. The application research shows that dynamic inversion is a more effective method in nonlinear control, and has good tracking performance for nonlinear rigid spacecraft system. However, the dynamic inverse method is sensitive to the modeling error, and how to improve the robustness of the controller has always been a difficult problem to solve.

2.1 Traditional Traffic Incident Detection Technology

At present, China is actively carrying out its research, hoping to realize the systematization and informatization of expressway management. According to the classification provided in the professional magazine path published by the IT center of the University of California, Berkeley, the road traffic flow parameters can be divided into: vehicle counting, vehicle type identification and accident detection. Automatic incident detection (AID) is one of the main research directions of intelligent transportation. It mainly focuses on the macro road traffic flow information, such as road flow, vehicle occupancy, vehicle flow density, etc. the micro phenomenon of traffic accidents can be detected indirectly.

According to the different sources of traffic flow information, the methods widely studied at present mainly include the following: aid based on ground induction coil; Aid based on global positioning system (GPS) signal; Aid based on video signal. The ground induction coil detects the traffic flow information according to the principle of the change of magnetic field intensity. When the vehicle passes through, the magnetic field intensity of the coil changes, and the parameters such as vehicle speed and flow can be obtained. These parameters can be used to identify traffic events such as vehicle suspension and traffic flow reduction, so as to indirectly detect traffic accidents. During the installation and maintenance of ground induction coil, the road must be excavated to block the traffic, which is very inconvenient and the detection parameters are limited.

GPS uses the triangulation principle of multiple satellites to work, and can accurately locate the geographical coordinates of GPS receiving terminal. With the progress of GPS technology, it has been more and more applied to the field of transportation. By installing GPS receiving terminal on the vehicle, the monitoring center can obtain the vehicle position information in real time, and calculate the vehicle motion information according to the position information at different times, so as to realize the detection of traffic events. Video detection is more and more widely used in traffic monitoring. Through the background modeling, moving target extraction and classification, moving target tracking and so on, the vehicle information, including vehicle shape, size, driving condition and traffic flow, can be detected. Finally, the vehicle behavior is analyzed by the methods of pattern matching and state estimation. However, because video detection is easily affected by difficulties such as weather conditions, object occlusion and color similarity between the target and the environment, the detection rate is not high. The analysis of vehicle behavior can only be aimed at simple situations and the accuracy is not high. Video based traffic flow detection technology is relatively mature, so the current video based aid technology still uses the macro information of traffic flow for indirect detection.

2.2 Overview of Linear Dynamic Control

In the local sense, a. Isidori and others consider the nonlinear regulation problem of nonlinear system under the assumption that the external system is Poisson stable, and the internal system dynamic index can stabilize the assumption of nonlinear regulation. The necessary conditions for the general local tracking of unrestricted external signals are obtained by J w. grizle, It is worth noting that local nonlinear regulation cannot track the unbounded external signals, which is essentially different from linear systems. In order to realize the tracking of unstable (unbounded) external signals, the adjustment problem in the global sense must be considered. In the global sense, the models considered by M. D. dayawansa and a. r.tee are as follows:

$$\left\{\begin{array}{c}x=\varphi (x,y)\\ {y}_{1}={y}_{2}\\ ...\\ {y}_{m}=\alpha (x,y)+\beta (x,y)u\end{array}\right.$$
(1)

In recent years, topological Photonics and non Hermite optics have become the two most active emerging research fields of photonics. The concept of topology originally came from mathematics and was used to study the properties of geometric shapes that remain unchanged under continuous deformation. For example, if a doughnut is not torn, no matter how it expands, rubs or contracts, it cannot be equivalent to a solid ball. The most famous topological invariant in topology is the “Chen number” named after Mr. Chen Shengshi of Nankai University. The development of topological photonics originated from the study of topological states in condensed matter physics. At first, the concept of topology was introduced into physical science to explain the famous quantum Hall effect. Therefore, the 2016 Nobel Prize in physics was also awarded to pioneer scientists in topological materials research.

Subsequently, the concept of topology was extended to the fields of optics, acoustics, metamaterials and cold atomic systems, which greatly promoted the development of topological physics. Especially in the field of optics. Topological photonics has gradually become an important frontier and cross field in optics and related scientific fields from the initial unidirectional transmission electromagnetic wave topological state experiment to the recent topological laser. On the other hand, the concept of non Hermite comes from quantum mechanics. It is generally believed that non Hermite systems have no physical meaning, and the introduction of parity time Pt symmetry has changed people’s traditional understanding of non Ö Mi open systems. When the concept of Pt symmetry in non Hermite quantum mechanics is introduced into the optical field, the carefully designed IPS symmetry with reciprocal loss and easy to control system continues to bring new discoveries. The development of non Hermite optics also brings new prospects for a series of application technologies, such as sensing and detection, wireless transmission energy and single-mode laser.

Due to the difficulties in experiment and theory, most studies of topological Photonics and non Hermite optics in the past were carried out by an Shengye, almost focusing on the on-line effect. However, nonlinear effects can be found everywhere in both the classical world and the quantum world. The diversity of the natural world also promotes the development of Applied Science. For example, nonlinear response is the key to the powerful function of digital electronic technology. It is the fundamental reason why artificial neural network can perform complex operations and the basis for the development of many new photonics technologies. Until recently, it has been found that there are many interesting phenomena when considering nonlinearity in optical topological systems, such as topological optical solitons, topological lasers and nonlinear topological insulators. However, the “marriage” between topology and non Hermite has just begun. For complex systems with topological and non Hermitian characteristics, the research on nonlinear effects is almost blank. Even in the field of optics, it has not found or built an adjustable nonlinear non Hermite topology photonics experimental platform.

2.3 Global Adjustment of Nonlinear Dynamic Control System

Considering that the external dynamic control system w = r(w) is free and uncontrolled, if the solution flow of the system is \({\varphi }_{t}^{r}(w)\), \(\varOmega =\{w|{\varphi }_{t}^{r}\left({w}_{0}\right)\,\text{is a limit point and }{\text{w}}_{0}\in {R}^{r}\}\), then q is the invariant manifold of the external dynamic control system, and any bounded solution w(T) of the system has w(t) → \(\varOmega\)(t → ∞), so the following proposition can be obtained.

The necessary conditions for global adjustment problem to be solvable by state feedback are: existence of maps c(w) ∈ L and S(w) ∈ C′, which makes

$$\left\{\begin{array}{c}\frac{\partial S(w)}{\partial w}r(w)=f(S(w)),w,c(w))\\ h(S(w),w)=0\end{array}\right.$$
(2)

Due to the difficulties in experiment and theory, most studies of topological Photonics and non Hermite optics in the past were carried out by an Shengye, almost focusing on the on-line effect. However, nonlinear effects can be found everywhere in both the classical world and the quantum world. The diversity of the natural world also promotes the development of Applied Science. For example, nonlinear response is the key to the powerful function of digital electronic technology. It is the fundamental reason why artificial neural network can perform complex operations and the basis for the development of many new photonics technologies. Until recently, it has been found that there are many interesting phenomena when considering nonlinearity in optical topological systems, such as topological optical solitons, topological lasers and nonlinear topological insulators. However, the “marriage” between topology and non Hermite has just begun. For complex systems with topological and non Hermitian characteristics, the research on nonlinear effects is almost blank. Even in the field of optics, it has not found or built an adjustable nonlinear non Hermite topology photonics experimental platform.

To address this gap, researchers at Nankai University used the self-developed continuous laser direct writing technology to prepare non Hermite topological photonic lattices in nonlinear crystals for the first time, realizing the regulation of parity time and non Hermite topology. The influence of nonlinear effect and the resistance of sensitivity and robustness between outliers and singular points further reveal the nonlinear effect. The results show that the local nonlinear effect can affect and change the overall Pt symmetry of the system, resulting in the emergence and disappearance of topology and abnormal non Hermitian singularity dynamic control. This result changes people’s understanding of the interaction of multiple characteristics in nonlinear complex systems, and provides a new research direction for topological Photonics and non Hermite optics.

3 Data Analysis

3.1 Data Analysis and Selection of Input Parameters

According to the data base of Sect. 3, the microwave detector data on Beijing Expressway can collect the traffic, speed, occupancy and traffic volume of a certain point on the road. Among them, the flow, speed and occupancy can be used to describe the characteristics of traffic flow. The changing law of these parameters can reflect the operation state of traffic flow. When the traffic flow is in the normal and stable state, the change of traffic parameters is relatively stable or not obvious; When traffic events occur and affect the upstream detector, the traffic parameters detected by the upstream detector change obviously, and the traffic parameters detected by the downstream detector are not obvious. Therefore, the event detection can be carried out by considering the change rate of traffic parameters with time and the change rate of upstream and downstream traffic parameters.

3.2 Bayesian Algorithm

In the method of statistical analysis, the method of discriminant analysis is used to establish a better discriminant function according to a batch of samples with clear classification, so that the cases of misjudgment are the least. Then, for a given new sample, it can be judged which population it comes from. The main methods include Fisher, Bayesian, distance and so on. Among them, Bayesian discriminant thought is to calculate the posterior probability according to the prior probability and make statistical inference based on the distribution of posterior probability. The so-called prior probability is to describe the degree of people’s understanding of the object studied in advance by probability; The so-called posterior probability is the probability calculated according to the specific data, prior probability and specific discrimination rules. It is the result of the correction of prior probability. Because Bayesian discriminant method considers the loss after misjudgment, it has certain superiority. Here, Bayesian discriminant analysis method is adopted.

$$ \begin{aligned} & OCCRDF = \frac{{OCC(i,t) - OCC(i + 1,t)}}{{OCC(i,t)}} \\ & VOLRDF = \frac{{VOL(i + 1,t) - VOL(i,t)}}{{VOL(i,t)}} \\ \end{aligned} $$
(3)

3.3 Improved Algorithm Based on Multi Parameters

California algorithm is the most classic and practical algorithm based on Discriminant recognition. It has been used as a comparison algorithm of other newly developed algorithms. The only disadvantage of this algorithm is that it only uses one traffic parameter of occupancy rate, and only one parameter is easy to cause high misjudgment rate, In this study, the occupancy rate, the change rate of vehicle speed with time and the change rate of upstream and downstream are used as the judgment conditions. This paper uses the improved California algorithm based on multi parameters to judge the relative difference of the upstream and downstream occupancy rate, the relative difference of the upstream and downstream speed, the change rate of the upstream occupancy rate with time, and whether the change rate of the upstream speed with time is greater than the specified threshold to give an event alarm. The flow chart of the algorithm is shown in Fig. 1

Fig. 1.
figure 1

Flow chart of multi parameter discrimination algorithm based on fixed detector

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4 Example Analysis

4.1 Algorithm

This paper first introduces the relatively mature normal deviation method (SND). The normal deviation method uses the arithmetic mean of the traffic parameter values of the N sampling periods before the time t as the prediction value of the traffic parameter at the time t, and then uses the standard normal deviation to measure the change degree of the parameter in time. When it exceeds the corresponding threshold, the alarm will be triggered. Based on the analysis of the travel speed of expressways in the previous section, if only considering the change of traffic parameters in time dimension, it will cause false alarm in morning and evening peak, resulting in a high false alarm rate. Therefore, the space-time two-dimensional discrimination algorithm based on floating car proposed in this paper is as follows:

(1) From the time dimension, we first judge the speed value, then use the arithmetic mean of the driving speed of the N sampling periods before the time t to predict the traffic parameter value at the time t, and then use the standard normal deviation to measure the change degree of the driving speed relative to its previous average value. Algorithm is shown in Fig. 2.

Fig. 2.
figure 2

Algorithm diagram

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Let the actual value of the driving speed at time t be v (t), and the actual values of the traffic parameters in the n sampling periods before time t are v(t − n), v(t − n + 1),… v (t − 1).

$$\begin{gathered} v\left( t \right) \le K_{1} \hfill \\ SND(t) = \frac{{\bar{v}(t) - v(t)}}{S} \ge K_{2} \hfill \\ \end{gathered}$$
(4)

(2) From the spatial dimension, based on the drastic change of the upstream and downstream driving speed when the event occurs, the following formula is used for discrimination;

$$VRDF(t)\frac{V(i+1,t)-V(i,t)}{V(i,t)}\ge {K}_{3}$$
(5)
$$ \begin{aligned} E\left( t \right)\dot{x}_{{d + 1}} \left( t \right) - & \,E\left( t \right)\dot{x}_{{k + 1}} \left( t \right) = E\left( t \right)\Delta \dot{x}_{{k + 1}} \left( t \right) = f\left( {t,x_{d} \left( t \right)} \right) + B\left( t \right)u_{d} \left( t \right) - f\left( {t,x_{k} \left( t \right)} \right) \\ - & \,B\left( t \right)u_{k} \left( t \right) = f\left( {t,x_{d} \left( t \right)} \right) - f\left( {t,x_{{k + 1}} \left( t \right)} \right) + B\left( t \right)\Delta u_{{k + 1}} \left( t \right) \\ \end{aligned} $$
(6)
$$\Vert \Delta {x}_{k+1}\left(t\right)\Vert \le \left(p{k}_{f}+{m}_{2}+{m}_{3}\right){\int }_{0}^{t}\Delta {x}_{k+1}\left(\tau \right)d\tau +{\int }_{0}^{t}{(m}_{1}\Vert \Delta {u}_{k}\left(\tau \right)\Vert +pd)d\tau$$
(7)

4.2 Algorithm Effectiveness Analysis

There are two methods to test and verify the event detection algorithm, one is based on simulation data, the other is based on actual data. However, under the simulation condition, the traffic condition is ideal, which is far from the real situation. Therefore, the algorithm verification based on the measured data is carried out, that is, the event detection algorithm is verified by collecting and processing the floating car detection data, fixed detector data and real event information in Beijing, and different threshold combinations are used to detect the algorithm, On the premise of ensuring a certain error rate, improve the detection rate, so as to determine the national value of the algorithm, and obtain the detection effect of the multi parameter discrimination algorithm based on fixed detector and the spatiotemporal two-dimensional discrimination algorithm based on floating car.

In 1996, through a survey of the traffic management center of the United States, abdulhai proposed that the acceptable average indicators of incident detection were Dr Z 88% and far s 1.8%. This index is also called TMC acceptable index. Here, this paper takes this as the index of the effectiveness analysis of the algorithm. If the algorithm meets this requirement, the algorithm can meet the needs of practical application (Fig. 3).

Fig. 3.
figure 3

Algorithm effectiveness analysis

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5 Conclusions

Due to the fixed detector spacing, communication failure caused by the serious lack of data and the number of floating cars and other issues, if the simple use of a single data source for expressway incident detection, the effect is not ideal, often resulting in long-term interruption of detection, can not smoothly carry out detection and other issues. Therefore, in this paper, the fixed detector data and floating car data are effectively combined, and a good detection algorithm is proposed respectively. Finally, the D-S theory is applied to the fusion of algorithm results, which can effectively solve the problems of low coverage and reliability of single data source event detection algorithm. Finally, the effectiveness of the algorithm is analyzed with the data of Beijing Expressway. It is expected that the algorithm proposed in this study can provide some reference for automatic event detection of urban expressway.