MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

Analysis of Stopping Behavior at Rural T-Intersections Using Naturalistic Driving Study Data

Rural intersections account for around 30% of crashes in rural areas and 6% of all fatal crashes, representing a significant but poorly understood safety problem. Crashes at rural intersections are also problematic since high speeds on intersection approaches are present which can exacerbate the impact of a crash. Additionally, rural areas are often underserved with EMS services which can further contribute to negative crash outcomes. This paper describes an analysis of driver stopping behavior at rural T-intersections using the SHRP 2 Naturalistic Driving Study data. Type of stop was used as a safety surrogate measure using full/rolling stops compared to non-stops. Time series traces were obtained for 157 drivers at 87 unique intersections resulting in 1277 samples at the stop controlled approach for T-intersections. Roadway (i.e. number of lanes, presence of skew, speed limit, presence of stop bar or other traffic control devices), driver (age, gender, speeding), and environmental characteristics (time of day, presence of rain) were reduced and included as independent variables. Results of a logistic regression model indicated drivers were less likely to stop during the nighttime. However presence of intersection lighting increased the likelihood of full/rolling stops. Presence of intersection skew was shown to negatively impact stopping behavior. Additionally drivers who were traveling over the posted speed limit upstream of the intersection approach were less likely to stop at the approach stop sign.

Analysis on intersections between fractures by parallel computation

The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies all pairs of intersected fractures(the basic components composing the connectivity of a network),is one of its crucial procedures.This paper attempts to improve intersection analysis through parallel computing.Considering a seamless interfacing with other procedures in modeling,two algorithms are designed and presented,of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy.A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations.Moreover,the preferred application conditions for the two algorithms are also discussed.

Adaptive neuro-fuzzy interface system for gap acceptance behavior of right-turning vehicles at partially controlled T-intersections

Gap acceptance theory is broadly used for evaluating unsignalized intersections in developed coun tries. Intersections with no specific priority to any move ment, known as uncontrolled intersections, are common in India. Limited priority is observed at a few intersections, where priorities are perceived by drivers based on geom etry, traffic volume, and speed on the approaches of intersection. Analyzing such intersections is complex because the overall traffic behavior is the result of drivers, vehicles, and traffic flow characteristics. Fuzzy theory has been widely used to analyze similar situations. This paper describes the application of adaptive neurofuzzy interface system （ANFIS） to the modeling of gap acceptance behavior of rightturning vehicles at limited priority Tintersections （in India, vehicles are driven on the left side of a road）. Field data are collected using video cameras at four Tintersections having limited priority. The data extracted include gap/lag, subject vehicle type, conflicting vehicle type, and driver＇s decision （accepted/rejected）. ANFIS models are developed by using 80 % of the extracted data （total data observations for major road right turning vehicles are 722 and 1,066 for minor road right turning vehicles） and remaining are used for model vali dation. Four different combinations of input variables are considered for major and minor road right turnings sepa rately. Correct prediction by ANFIS models ranges from 75.17 % to 82.16 % for major road right turning and 87.20 % to 88.62 % for minor road right turning. Themodels developed in this paper can be used in the dynamic estimation of gap acceptance in traffic simulation models.

Decision-Making Models Based on Meta-Reinforcement Learning for Intelligent Vehicles at Urban Intersections

Behavioral decision-making at urban intersections is one of the primary difficulties currently impeding the development of intelligent vehicle technology.The problem is that existing decision-making algorithms cannot effectively deal with complex random scenarios at urban intersections.To deal with this,a deep deterministic policy gradient(DDPG)decision-making algorithm(T-DDPG)based on a time-series Markov decision process(T-MDP)was developed,where the state was extended to collect observations from several consecutive frames.Experiments found that T-DDPG performed better in terms of convergence and generalizability in complex intersection scenarios than a traditional DDPG algorithm.Furthermore,model-agnostic meta-learning(MAML)was incorporated into the T-DDPG algorithm to improve the training method,leading to a decision algorithm(T-MAML-DDPG)based on a secondary gradient.Simulation experiments of intersection scenarios were carried out on the Gym-Carla platform to verify and compare the decision models.The results showed that T-MAML-DDPG was able to easily deal with the random states of complex intersection scenarios,which could improve traffic safety and efficiency.The above decision-making models based on meta-reinforcement learning are significant for enhancing the decision-making ability of intelligent vehicles at urban intersections.

THE MAXIMUM NUMBER OF INTERSECTIONS BETWEEN TWO PLANE RECTANGULAR PATHS

We show that the maximum number of intersections between two plane rectangular paths with lengths m and(mod 3); and it is mn+1 otherwise.

Coordinated Control of Traffic Signals for Multiple Intersections

The proper phase difference of traffic signals for adjacent intersections could decrease the time of operational delay. Some theorems show how to minimize the total average delay time for vehicle operating at adjacent intersections under given conditions. If the distance and signal cycles of adjacent intersections satisfy with specific conditions, the total average delay time would achieve zero. If the signal cycles of adjacent intersections and the phase difference of them are co-prime numbers, the total average delay time would be a constant. In general, if signal cycles of adjacent intersections and the phase difference of them are reducible numbers, the minimum total average delay time would be solved by the given algorithm. Numerical experiments have verified the rationality of these theorems.

Experimental and numerical investigation of groundwater head losses on and nearby short intersections between disc-shaped fractures

Discrete fracture models are used for investigating precise processes of groundwater flow in fractured rocks,while a disc-shaped parallel-plates model for a single fracture is more reasonable and efficient for computational treatments.The flow velocity has a large spatial differentiation which is more likely to produce non-linear flow and additional head losses on and nearby intersections in such shaped fractures,therefore it is necessary to understand and quantify them.In this study,both laboratory experiments and numerical simulations were performed to investigate the total head loss on and nearby the intersections as well as the local head loss exactly on the intersections,which were not usually paid sufficient attention or even ignored.The investigation results show that these two losses account for 29.17%-84.97%and 0-73.57%of the entire total head loss in a fracture,respectively.As a result,they should be necessarily considered for groundwater modeling in fractured rocks.Furthermore,both head losses become larger when aperture and flow rate increase and intersection length decreases.Particularly,the ratios of these two head losses to the entire total head loss in a fracture could be well statistically explained by power regression equations with variables of aperture,intersection length,and flow rates,both of which achieved high coefficients of determination.It could be feasible through this type of study to provide a way on how to adjust the groundwater head from those obtained by numerical simulations based on the traditional linear flow model.Finally,it is practicable and effective to implement the investigation approach combining laboratory experiments with numerical simulations for quantifying the head losses on and nearby the intersections between disc-shaped fractures.

Study on Geometric Factors Influencing Saturation Flow Rate at Signalized Intersections under Heterogeneous Traffic Conditions

The main objective of intersection design is to facilitate the convenience, comfort, and safety of people traversing the intersection by enhancing the efficient movement of road users. The intersections on urban roads in India generally cater to heterogeneous motorized traffic, along with slow-moving traffic including pedestrians. It is therefore necessary to consider saturation flow for mixed traffic conditions to evaluate the overall operation of signalized intersections. A proper traffic model must consider varying characteristics of all the road users to effectively design and efficiently manage signalized intersections. This paper presents the results of the study on analyses of saturation flow rate conducted at signalized intersections with mixed traffic conditions in the city of Bangalore, India. Studies were carried out at 15 signalized intersections in the city of Bangalore with varying geometric factors such as width of road (w), gradient of the road (g), and turning radius (r) for right turning vehicles. Saturation flow rate computed as per Highway Capacity manual (HCM: 2000), Indonesian highway capacity manual (IHCM), and IRC SP: 41-1994 was compared with the field observations. The geometric factors, which affect the saturation flow, have been considered in this study and accordingly a new model has been proposed for determining saturation flow. It has been shown that by the introduction of the suggested adjustment factors in this paper, the saturation flow rate can give better picture of the field conditions, especially under heterogeneous traffic conditions of an urban area.

Model of Traffic Speed-Flow Relationship at Signal Intersections

Speed-flow relationship is the fundamental for the traffic simulation and traffic volume forecast. Traditional quadratic polynomial model can’t reflect the saturate flow at signal intersections. In order to determine the speed-flow relationship at signal intersections, the speed and time-headway of vehicles at two signal intersections were investigated and the accuracy of software used to get the speed was tested. After vehicle starting-up from queuing, the time-headway reduces gradually with the increase of speed. The relationship of power exponential function between speed and time-headway is formulated. Traffic volume can be calculated by the vehicle time-headway. Then the speed-flow relationship was developed and an S-shaped curve model was built in this paper. In the S-shaped curve model, traffic flow approaches to the saturate when the speed doesn’t increase. Thus, S-shaped curve model is better to describe the speed-flow relationship at signal intersection. The results can provide a reference to determine the parameters in traffic simulation and for the study of level of service of intersections.

Examining the Risk Factors of Rear-End Crashes at Signalized Intersections

Rear-end crashes are among the most common crash types at signalized intersections. To examine the risk factors for the occurrence of this crash type, this study involved the analysis of nine years of intersection crash records in the state of Wyoming. With that, the contributing factors related to crash, driver, environmental, and roadway characteristics, including pavement surface friction, were investigated. A binomial logistic regression modeling approach was applied to achieve the study’s objective. The results showed that three factors related to crash and driver’s attributes (commercial vehicle involvement, speeding, and driver’s age) and four factors related to environmental and roadway characteristics (lighting, weather conditions, area type, whether urban or rural and pavement friction) are associated with the risk of rear-end crash occurrence at signalized intersections. This study provides insights into the mitigation measures to implement concerning rear-end crashes at signalized intersections.

Vehicle Motion Prediction at Intersections Based on the Turning Intention and Prior Trajectories Model

Intersections are quite important and complex traffic scenarios,where the future motion of surrounding vehicles is an indispensable reference factor for the decision-making or path planning of autonomous vehicles.Considering that the motion trajectory of a vehicle at an intersection partly obeys the statistical law of historical data once its driving intention is determined,this paper proposes a long short-term memory based(LSTM-based)framework that combines intention prediction and trajectory prediction together.First,we build an intersection prior trajectories model(IPTM)by clustering and statistically analyzing a large number of prior traffic flow trajectories.The prior trajectories model with fitted probabilistic density is used to approximate the distribution of the predicted trajectory,and also serves as a reference for credibility evaluation.Second,we conduct the intention prediction through another LSTM model and regard it as a crucial cue for a trajectory forecast at the early stage.Furthermore,the predicted intention is also a key that is associated with the prior trajectories model.The proposed framework is validated on two publically released datasets,next generation simulation(NGSIM)and INTERACTION.Compared with other prediction methods,our framework is able to sample a trajectory from the estimated distribution,with its accuracy improved by about 20%.Finally,the credibility evaluation,which is based on the prior trajectories model,makes the framework more practical in the real-world applications.

Double-directional control bolt support technology and engineering application at large span Y-type intersections in deep coal mines

Under deep and complex geological conditions,severe deformation occurs at intersection points of Y-type roadways with large cross sections during engineering projects in coal mines,especially at junction arches.Based on in-situ investigations and theoretical studies,we have summarized typical forms of destruction and identified high stress and unrestricted support at both sides of junction arch as its main causes.In this study,we also presented double-directional control bolt support technology for a large Y-type span intersection,applied to deep intersection engineering in the Jiahe Coal Mine,which has proved effective.

Planning and Decision-making for Connected Autonomous Vehicles at Road Intersections:A Review

Planning and decision-making technology at intersections is a comprehensive research problem in intelligent transportation systems due to the uncertainties caused by a variety of traffic participants.As wireless communication advances,vehicle infrastructure integrated algorithms designed for intersection planning and decision-making have received increasing attention.In this paper,the recent studies on the planning and decision-making technologies at intersections are primarily overviewed.The general planning and decision-making approaches are presented,which include graph-based approach,prediction base approach,optimization-based approach and machine learning based approach.Since connected autonomous vehicles(CAVs)is the future direction for the automated driving area,we summarized the evolving planning and decision-making methods based on vehicle infrastructure cooperative technologies.Both four-way signalized and unsignalized intersection(s)are investigated under purely automated driving traffic and mixed traffic.The study benefit from current strategies,protocols,and simulation tools to help researchers identify the presented approaches’challenges and determine the research gaps,and several remaining possible research problems that need to be solved in the future.

INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS

Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.

Failure analysis and control technology of intersections of large‑scale variable cross‑section roadways in deep soft rock

In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupling action of multiple factors such as deep high stress,adjacent faults,cross-layer design,weak lithology,broken surrounding rock,variable cross-sections,wide sections up to 9.9 m,and clusters of nearby chambers,there was severe deformation and breakdown in the No.10 intersection of the roadway of large-scale variable cross-section at the−760 m level in a coal mine.As there are insufcient examples in engineering methods pertaining to the geological environment described above,the numerical calculation model was oversimplifed and support theory underdeveloped;therefore,it is imperative to develop an efective support system for the stability and sustenance of deep roadways.In this study,a quantitative analysis of the geological environment of the roadway through feld observations,borehole-scoping,and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model.This model is combined with the strain softening constitutive(surrounding rock)and Mohr–Coulomb constitutive(other deep rock formations)models to construct a compression arch mechanical model for deep soft rock,based on the quadratic parabolic Mohr criterion.An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modifed cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting,based on the Heok-Brown criterion.As a result of on-site practice,the following conclusions are drawn:(1)The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment,the tectonic stress is nearly 30 MPa,and the surrounding rock is severely fractured.(2)The deformation of the roadway progressively increases from small to large cross-sections,almost doubling at the largest cross-section.The plastic zone is concentrated at the top plate and shoulder and decreases progressively from the two sides to the bottom corner.The range of stress concentration at the sides of the intersection roadway close to the passageway is wider and higher.(3)The 7 m-thick reinforced compression arch constructed under the strengthening support scheme has a bearing capacity enhanced by 1.8 to 2.3 times and increase in thickness of the bearing structure by 1.76 times as compared to the original scheme.(4)The increase in the mechanical parameters c andφof the surrounding rock after anchoring causes a signifcant increase inσt;the pulling force of the cable bolt beneath the new grouting material is more than twice that of ordinary cement grout,and according to the test,the supporting stress feld shows that the 7.24 m surrounding rock is compacted and strengthened in addition to providing a strong foundation for the bolt(cable).On-site monitoring shows that the 60-days convergence is less than 30 mm,indicating that the stability control of the roadway is successful.

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

Traffic Organization Optimization of Urban Road Combined Intersections

With the development of the economy and the acceleration of urbanization, the number of vehicles in cities is increasing rapidly, which greatly increases the pressure on urban traffic. Solving traffic accidents and problems to keep smooth travel and safe travel has become a top priority in road construction. In this paper, how to optimize the traffic at the intersection of the urban road was discussed with the aim of reducing traffic accidents and problems to keep peoples’ smooth travel and safe travel.

Intersections of two offset parametric surfaces based on topology analysis

Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topological relations between different intersection loops and calculates intersection loops with the help of previously calculated intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing algorithm. The proposed algorithm could calculate intersection curves robustly and effectively, and has been tested to be capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional algorithms.