Evaluation of the Risk of Truck Platoon under Crosswind regarding the Lateral Displacement on Horizontal Curves

Driving safety on horizontal curves under crosswinds has always been a concern for researchers. However, previous studies focused on single vehicles, especially single trucks. Te safety of the truck platoon under crosswinds on horizontal curves was rarely examined. To fll such a gap, this study establishes a model for evaluating the safety of truck platoons under crosswinds on curves. After obtaining aerodynamic coefcients, a cosimulation model of a three-truck platoon is established with Trucksim and Simulink. Te infuencing factors on the lateral displacement of the truck platoon were analyzed, and the safety of the truck platoon under crosswinds on horizontal curves was then quantifed with the response surface method. Te results show that the fully autonomous platoon is safer than the human-led platoon. In a three-vehicle platoon, the smaller the lateral displacement of the truck, the further back the truck, and the lateral displacement of the vehicle increases with the loading of the truck. Te safety index is computed to quantify the reliability of the truck platoon. Te results indicate that the safety index increases with a decrease in the mean wind velocity and mean vehicle velocity and increases with an increase in the mean radius. When crosswinds come from the inside of the curve, the safety index increases with an increase in the mean superelevation; for crosswinds from the outside of the curve, the safety index rises with the drop of superelevation. Te proposed approach can quantify the safety level of truck platoons under crosswinds on horizontal curves, and the results provide guidance to support the decision-making of transportation management agencies.


Introduction
Driving safety on horizontal curves under crosswinds has always been a research focus.Horizontal curves are relatively dangerous segments due to the centripetal force exerted on the vehicle driving on curves, leading to excess lateral displacement that can cause accidents [1].Previous studies have shown that design features, including curve radius, superelevation, curve length, and roadside conditions, are found to signifcantly afect accidents [2,3].Te highway safety manual provides safety performance models with diferent curve features.Still, other studies focused on methods of horizontal curve safety using factors such as high-friction surface treatments [4] and spatial considerations [5].However, road surface conditions and geometric features are still the main factors concerning the safety of vehicles under hazardous driving conditions [6].
As compared to passenger cars, the safety of high-sided vehicles on curves is of particular interest, especially under crosswinds.Baker [7,8] defned the accidents of high-sided vehicles in windy environments into three types: sideslip, rollover, and rotational accidents.He carried out a series of research with rigid vehicle simulation models to investigate the risk of vehicle accidents and identifed contributing factors that had the greatest efect on the probability of windinduced accidents.To evaluate the safety performance under various conditions more accurately and comprehensively, reliability models based on the kinetic simulation models are widely used.Snaebjörnsson et al. [9] developed a general probability model and applied it to assess the reliability of road vehicles in harsh environments, analyzing the efects of wind direction, wind velocity, road friction coefcient, and superelevation.Chen et al. [10] developed a framework based on a transient dynamic vehicle simulation model to consider the relationship between vehicles and harsh driving conditions such as wind gusts, ice, and curves.Shin and Lee [11] evaluated the probability of vehicle overturning and sideslip accidents in windy environments considering vehicle speed, tire-road friction coefcient, superelevation, wind speed factors, etc., with design optimization of road radius to improve vehicle safety.Tese results based on traditional heavy trucks focused on the rollover and sideslip accident, but they overlooked another type of wind-induced accident, an incursion into adjacent lanes due to windinduced excessive lateral displacement, which can occur, before the criterion for a rollover accident or sideslip accident is met.Te incursion into adjacent lanes can pose severe threats to safety at wind-prone spots, like long-span bridges and tunnel portals.
Te abovementioned studies focused only on single trucks, while studies on the driving safety of truck platoons under crosswinds on horizontal curves are still lacking.Given the booming development of connected and automated vehicle (CAV) technologies, truck platooning becomes the focus not only for researchers but also for transportation industries.It is important to guarantee the safe operation of truck platoons before their large-scale deployment.Nevertheless, driving safety of truck platoons in harsh conditions, such as on curves under crosswinds, has been largely ignored.Safety studies on platoon vehicles are relatively well conducted for string stability, realistic scenarios [12], and technical failures [13].Axelsson [14] provided an overview of the safety of vehicles in platoons, outlining fault types and ways to improve safety performance.Most of the research focuses on longitudinal safety [15], and another important aspect of safety is the lateral safety of truck platoons, which is rarely concerned.When trucks travel in a platoon, the shortening of the spacing distance leads to changes in the aerodynamic coefcients of vehicles, making truck platoons respond diferently from individual trucks under crosswind, and the characteristics of multivehicle platoon operation make the impact of incursion accidents on surrounding vehicles more serious.Ma et al. [15] studied the lateral displacement of autonomous truck platoons and proposed a reliability-based safety assessment method to quantify the risks of the truck platoon.However, their study focused on the straight segment and ignored the impact of horizontal alignment.
Meanwhile, the impact of driving performance on lateral displacements of trucks under crosswinds cannot be ignored for human-driven and autonomous trucks.As many control algorithms of autonomous trucks also simulated the behaviors of human drivers, previous studies on driver behavior still shed light on autonomous vehicles.Baker [16] proposed a model to describe drivers' steering behavior under the infuence of crosswinds by considering drivers' reaction time and driver characteristics.Based on Baker's model, Chen and Cai [17] used the front wheel steering angle instead of the steering angle at the vehicle's center of gravity, which better captured drivers' steering behavior.Chen et al. [18] later conducted a driving simulation study under crosswind using a high fdelity driving simulator and proposed a method to evaluate the driver's ability to cope with the crosswind.Te drivers' reaction time has been a key indicator of the abovementioned studies.Te importance of drivers' reaction time applies to truck platoons as well, since both human-led truck platoons and fully autonomous truck platoons are both being tested.Although the driving performance of the human-driven vehicle was extensively examined, the diferences between the safety of human-led and autonomous truck platoons under crosswinds are rarely examined, which is worth exploring in the era of mixed trafc of autonomous vehicles and manned vehicles.
Based on the above discussion, the current study aims to fll those identifed research gaps in the existing literature.Specifcally, the present study proposes a reliability-based method to quantify the safety of truck platoons on horizontal curves under crosswinds.In addition, the impact of reaction time and the loading strategy of the truck platoon are also investigated.Driving safety in extreme conditions has been an ongoing issue that has prevented autonomous vehicles from moving to L4 or higher levels of automation.Te current study potentially contributes to the state of the art in that regard.Te results can support the decision-making of trafc management considering platoon operation in harsh conditions.
Te rest of the paper is organized as follows: Section 2 presents the four main steps of the framework proposed.Section 3 displays the results and discussion.Section 4 concludes the main fndings of the paper.

Aerodynamic Characteristics of Truck Platoons.
When trucks are traveling in platoons, their aerodynamic responses difer from that of a single truck due to shortened vehicle spacing.To accurately simulate the truck platoon's response under crosswinds, the relationship between aerodynamics and slip angles should be developed.In this study, computational fuid dynamic (CFD) simulations are conducted to obtain the aerodynamic features of the three-truck platoon, where a typical Scania truck model is adopted.For details of the setting of the CFD simulation, readers are referred to a previous study [15], where various simulation scenarios for a three-truck platoon were carried out and validated.
Figure 1 presents the aerodynamics of the truck platoon when intervehicle spacing between trucks is half the truck length.It shows that the drag coefcients of a single truck are signifcantly diferent from those of platoon vehicles.Tere is also a signifcant diference between the leading truck, the middle one, and the trailing one within the platoon.Te 2 Journal of Advanced Transportation aerodynamic coefcient of the lead vehicle is the largest within the truck platoon, while it is still smaller than that of the single truck.Te diference in aerodynamic coefcients indicates that the responses of trucks within a platoon also difer accordingly under crosswinds compared to those of a single truck.
Truck spacing (measured as vehicle length L, L � 16.5 m) equal to 0.5 L with a range of sideslip angles between 0 °and 35 °in increments of 5 °was tested in CFD simulations.A similar virtual wind tunnel is set up, and a calculation domain is used.As a result, the aerodynamic coefcients used in this paper were obtained.

Contributing Factors.
While diferences in aerodynamic coefcients signifcantly afect the motion of platoon vehicles, factors with impacts on single vehicles have efects on platoons as well.Except for crosswinds that have a signifcant impact on lateral displacements of vehicles, rain and snow on the road may reduce the friction coefcient [19] between tires and the road surface, which in turn reduces friction and increases the lateral displacement of curves.Tus, the wind heading, wind velocity, and friction coefcient are taken as contributing factors to the safety of the truck platoon.
Apart from environmental factors, the characteristics of the truck platoon will undoubtedly afect its motion under crosswinds.As the velocity of the truck directly afects the result of lateral displacements, vehicle velocity is considered a contributing factor to the safety of the truck platoon.Te size of the truck unit, spacing distance, load, and position in a platoon also afect the results, as the aerodynamic drag coefcient of the rear vehicle can be greatly reduced after entering the wake area of the front vehicle [20].When the vehicle is fully loaded, halfloaded, and empty in the leading, middle, and trailing position, the diferences in the vehicle's center of gravity height and position within a platoon also have a signifcant impact on the results of lateral displacement, so the impact of the formation strategy on the truck platoon's response is considered.As the motion results are determined by the truck's control model as well, the current study focuses on the infuence of reaction time, the key parameter of the control model, to explore the diferences in lateral displacements between a human-driven truck and an autonomous truck.
As the magnitude of superelevation and radius have an impact on the force in the lateral direction of the vehicle force analysis, the road alignment design factors of a horizontal curve are very important for the safety of the vehicle.Terefore, superelevation and radius are taken as contributing factors to the safety of the truck platoon.Te speed and direction of the crosswind will have an impact on the operation status of the vehicle; therefore, its time-varying relationship needs to be considered.Te velocity of the crosswind is set to increase linearly from 5 s to 7 s, reaching its peak of 40 km/h, stay stable for 3 seconds, and then drop to 0 at 12 s.

Truck Model.
Trucks with semitrailers are widely used in cargo transportation, but they are a prominent hazard source, thus becoming one of the most concerning research topics among many trucks.Te center of gravity of the semitrailer is located high, contributing to the poor stability of trucks; thus, the proportion of accidents related to lateral instability is higher in semitrailers.Tree homogeneous semitrailers make up the truck platoon model used in this paper, and the selected truck model is consistent with the truck model used in the CFD simulation [15], which is a Scania truck commonly found in China.Te relevant parameter settings for the truck models are shown in Table 1.

Platooning Algorithms.
Commonly used longitudinal control methods when truck platoons are in automatic operation mode include adaptive cruise control (ACC), cooperative adaptive cruise control (CACC), and cooperative look-ahead control (CLAC).Te ACC mode is adopted in the simulation of the middle truck and tail truck in the platoon, which has a clear logic and has been widely used to control the speed of platoon vehicles.If the distance is less than the threshold, the throttle is closed and the brake is applied.Te lead truck is set to be manually driven in the current study, as the complex driving condition has blocked the use of full self-driving on open roads in practice.
Lateral control methods for autonomous trucks have undergone a certain development process.Current methods applied to vehicle lateral control include [21] proportionalintegral-diferential (PID) control methods, linear quadratic regulator (LQR), optimal preview control (OPC), and model predictive control (MPC) methods.In addition, robust control, adaptive control, sliding mode control, and fuzzy control methods are also commonly used.Optimal control has a good tracking efect and has become the main method for landing applications, and the lateral control model in this study is accomplished by Macdam's [22] optimal preview control model.Te model has a clear physical meaning and a simple structure, and it has been used in numerous studies and products based on Trucksim.Diferent reaction time values can be set to simulate the diference between human driver and autonomous vehicle reaction characteristics considering safety infuences.

Reliability-Based Assessment Model.
Based on the simulation model above, a reliability-based model can be set up to measure the safety level of truck platoons.Te safety index of platoon vehicles can be given, with the uncertainties of infuencing factors taken into consideration.

Limit State Function.
Te current study focused on the incursion into the neighboring lane; thus, the limit state of the safety performance under crosswinds can be defned as the lateral displacement equaling the maximum allowable threshold.Baker [7]considered lateral displacements beyond 0.5 m as unsafe domains.Tis result has been followed by researchers in this feld.Terefore, the safety performance function is set as f(X) � 0.5 − lat vehicle. ( Since the safety performance of the three-truck platoon is a tandem relationship, an accident of one truck is considered an accident of the platoon, and thus, the limit state is set as the maximum value of the lateral displacement of the three trucks in the truck platoon.If the lateral displacement of one or more trucks exceeds 0.5 m, it is considered to have invaded adjacent lanes and entered the dangerous domain.Considering the width of a lane, the lateral displacement after the vehicle has already invaded the adjacent lane is meaningless, so the cases that exceed this upper bound value are processed in the data preprocessing stage.

Gaussian Process Regression-Based Response Surface
Method.Common response surface methods for taking sample points include the Box-Behnken design (BBD) method and the central composite design (CCD) method [23], both of which aim to select 2n + 1 points to meet the requirements of the ftting response surface.Since the CCD method involves operating conditions that would exceed the experimental safety threshold, the BBD method is used to take sample points.Te sample points obtained from the BBD experiments and the sample points in experiments only considering single factors were all used to develop the response surface model.Te classical response surface-ftting method uses a quadratic polynomial without cross terms as a performance function [24].However, the accuracy of this method is not high enough, especially when it is impossible to iterate sample points for experiments.With the development of machine-learning methods and the improvement of computational ability, researchers have introduced artifcial neural networks [25] (ANNs), radial basis functions (RBFs), and support vector machines (SVMs).Neural network regression models have better regression capabilities than classical RSM models but are less efective in solving small sample problems [25,26].SVM is efective in the small sample case [26], but its efectiveness is strongly infuenced by the choice of the kernel function.Su [27] et al. introduced Gaussian process regression (GPR) into the ftting of performance functions and achieved good results.As a probabilistic model suitable for small sample regression, its independent variables are all set as random variables and have good interpretability and practicality [27].Terefore, GPR is adopted as the response surface method and compared with SVM and the classical response surface model.Te compared metrics are the mean absolute error (MAE) and root mean squared error (RMSE): where Y i is the true value and Y * i is the estimated value.It is assumed that all statistical characteristics of GPR are fully specifed by the mean and covariance functions.Te joint Gaussian prior distribution of m training samples and one output sample is where K(X, x * ) is an m × m symmetric positive defnite covariance matrix with any element K ij of the matrix measuring the correlation between x i and x j (i, ) is an m × 1 covariance matrix generated from all the input training samples x of the input test samples X, and k(x * , x * ) is the covariance matrix x * of itself.Te covariance function k y (x i , x j ) is the kernel of the Gaussian process regression.Te optimal hyperparameters of the model can be obtained by the maximum likelihood method.Te predicted posterior distribution can be obtained by

Safety Index.
A typical frst-order reliability method is chosen to calculate the safety index.Defned as the vector consisting of standard deviations of the variables, the safety index at the point of the mean can be expressed as [9] β � g(x) Te relationship between the probability of failure and the safety index can be approximated by the following equation [28]: where Φ is the standard normal probability distribution function.A positive value of the safety index corresponds to a failure probability between 0 and 0.5, while a negative value of the safety index corresponds to a failure probability between 0.5 and 1.  Journal of Advanced Transportation time; thus, steering wheel angles generated by the control model used are delayed by the amount of time on the x-axis to simulate the neuromuscular delay in human drivers.

Results and Discussion
Figure 2 shows the relationship between the reaction time and the maximum lateral displacement of the truck platoon when the vehicle speed is set as 70 km/h and wind speed is set as 40 km/h.It can be observed in Figure 2 that the maximum lateral displacement in the case of the reaction time corresponding to the autonomous truck (below 0.1 s [29]) is signifcantly smaller than the maximum lateral displacement in the case of the reaction time of the manually driven truck (0.2 s-0.3 s [29]), and the maximum lateral displacement of three platoon vehicles gradually increases as the reaction time increases, refecting the better safety of the autonomous trucks.

Te Impact of the Formation Strategy on the Truck Platoon's Response.
Te response of trucks is afected not only by the driver reaction time but also by the formation strategy.Characteristics of trucks with diferent loading vary signifcantly in diferent positions within a platoon, which afects the results of the lateral displacement.From Figure 3, it can be seen that the maximum lateral displacement of platoon vehicles is the largest when the load is concentrated on the lead truck.When the load is concentrated on the tail truck, the maximum lateral displacement of platoon vehicles is the smallest.When both the middle and tail trucks are fully loaded with an empty lead truck, the platoon experiences the smallest lateral displacement.
Furthermore, Figure 3 shows that the lateral displacement of a truck within a platoon increases with loading.Moreover, the further back a truck is in the platoon, the smaller the maximum lateral displacement when all trucks have the same loads.Te order of trucks with diferent loading infuences the maximum lateral displacement of the platoon.Tese fndings can be useful to guide the formation strategy of the truck platoon with diferent loading situations when reorganizing the platoon.When reorganizing the platoon, vehicles with more cargo should be arranged at the rear of the platoon, and loaded trucks should avoid the lead truck position to minimize the maximum lateral displacement of trucks in the platoon.

Comparison of Response Surface Models.
Te choice of the kernel has a signifcant efect on the ftting results of the response surface.Tree kernels are used for comparison in the current research.Te squared exponential kernel is of the same form as the RBF kernel, and its hyperparameters are length scale parameters l: Te rational quadratic kernel can be viewed as a mixture of RBF kernels with diferent characteristic length scales, where the scale mixing parameter a is a scalar and must be positive.Te kernel is of the form: Te Matern kernel is a generalization of the squared exponential kernel: where Γ is the gamma function, K v is the modifed Bessel function, and ρ and ] are the positive parameter of the covariance.Te parameter ] controls the smoothness of the learning function, and the Matern kernel of size ] � 2.5 is used in this paper.All regression models based on machinelearning methods are conducted ten-fold cross-validation to evaluate their generalizability.Te comparison reveals that the RMSE and MAE of GPR with the Matern kernel are optimal as shown in Table 3. Terefore, the GPR function paired with the Matern kernel was chosen as the regression model for ftting the response surface in this paper.

Reliability Analysis.
Once the response surface model is determined, it is possible to assess the probability of a lateral accident in a truck platoon.When the safety index is equal to 0, it means that the probability of an accident is 0.5 [28].Te larger the safety index is, the safer the truck platoon is under crosswinds.Te mean road friction coefcient of the road is set as 0.6, which corresponds to a dry road condition.Since it obeys a truncated normal distribution, it is transformed into a normal distribution with the method proposed by the Joint Committee on Structural Safety, and the transformed mean value is 0.5 with a mean wind direction of 70 Te mean radius of the curve is set as 400 m, and the mean superelevation is set as 3%.As Figure 4 shows, the safety index usually increases with a decrease in the mean wind velocity and the mean vehicle velocity.Te safety index increases where the mean vehicle velocity and mean wind velocity both decrease, which confrms the reasonableness of the speed limit.Te efect of the road friction coefcient on truck lateral safety has been studied, so the current study focuses on the efect of radius and superelevation and combines it with wind velocity to facilitate the set of reasonable management measures according to the actual and forecast wind level.Te efect of these two geometric features is also explored combined with vehicle speed to provide the basis for setting speed limits.
Te results of ftting the safety index as a function of the mean wind velocity and the mean radius at the mean vehicle velocity of 70 km/h and the mean superelevation of 3% are shown in Figure 5.With an increase in wind velocity and decrease in radius, the safety index gradually decreases.When the radius is less than 500 m, the safety index decreases rapidly with an increase in wind velocity; thus, truck platoons have a higher risk level on curves with a radius of less than 500 m.When the mean wind velocity is 60 km/h, the safety index is ftted as a function of the mean radius and mean as shown in Figure 6; at this time, no matter how the platoon speed changes, the safety index is less than 0, which indicates that the risk of wind-caused accidents of the truck platoon is higher than 0.5 in this case.
Curves with small radii are usually paired with superelevation, which can have an impact on the lateral stability of the vehicle.Terefore, the relationship between the safety index and the mean superelevation is also worth studying.Tere is a signifcant diference in the safety index law of the vehicle between the conditions when the wind comes from the inside and the outside of the curve; thus, the two situations are discussed separately.Te directions of winds from the inside and outside of the curves, namely, "inside wind" and "outside wind," is illustrated in Figure 7. Te mean vehicle velocity is set as 70 km/h, and the mean radius is set as 300 m; the results of ftting the safety index as a function of the mean wind velocity and the mean superelevation of winds from the inside of the curve are shown in Figure 8.With a gradual increase in superelevation, the safety index increases due to the crosswind from the inside of the curve, as extra centripetal force is needed from superelevation to compensate for the efects of the crosswind.As   the wind speed increases, the safety index decreases.Similarly, the results of ftting the safety index with the mean velocity and the mean superelevation are shown in Figure 9, where the mean wind velocity is still fxed at 60 km/h.Under crosswind from the outside of the curves, the safety index drops with an increase in superelevation, as shown in Figures 10 and 11, because the crosswind can counteract the centrifugal force of the vehicle running on the curve; thus, too large superelevation will only weaken the lateral safety of the vehicle and cause a larger lateral displacement.Te above results show that there is a signifcant diference in the safety index rule of the vehicle when the wind comes from the inside and the outside of the curve.When calculating reliability, we should not only  8 Journal of Advanced Transportation focus on the magnitude of wind velocity but also distinguish whether the wind comes from the inside or outside of the curve.

Conclusions
Based on reliability theory, a method for evaluating the safety of truck platoons on curved sections of highways under crosswinds is established.Te proposed method includes three main steps.First, based on the aerodynamic simulation results of the truck platoon, the truck platoon model is built based on the joint simulation of Trucksim and Simulink.Te infuencing factors of safety are then analyzed.Finally, the response surface model is established, and the safety index is calculated by Gaussian process regression; the reliability of the truck platoon on the curved section of highway under crosswinds is analyzed considering the effects of diferent factors based on the safety index.Te main research fndings are summarized as follows: (1) Te results show that the maximum lateral displacement of the truck platoon gradually increases with an increase in the reaction time, refecting the lower safety of manually driven trucks.At the same time, truck position and truck loading also signifcantly afect the lateral safety of the platoon.In a three-vehicle platoon, the further back the truck is, the smaller the lateral displacement is; the lateral displacement of the vehicle is the largest when the truck is fully loaded and the smallest when it is empty.Tis conclusion can be used to guide the cargo loading and the positioning strategy of trucks when reorganizing the platoon.(2) A response surface based on Gaussian process regression was established, and the reliability of lateral deviation accidents of truck platoons operating in curved sections of highways was assessed by safety indices.Te evaluation results show that the safety index usually increases with the fall in the mean wind velocity and increases with the drop in the mean vehicle velocity.Tis result can provide a quantitative basis for trafc management.
(3) Te curve radius and superelevation of the highway signifcantly afect the lateral safety of truck platoons.With a decrease in the average radius, the safety index gradually decreases.When the radius is less than 500 m, the safety index decreases rapidly with an increase in wind velocity.If the wind comes from the inside of the curve, the safety index increases with an increase in superelevation, and if the wind comes from the outer side, the safety index decreases with an increase in superelevation.Terefore, attention should be paid to diferentiating the wind direction to give the reliability index.
In summary, the reliability-based approach proposed in this paper quantifes the safety level of truck platoons on curved sections of highways under crosswinds.Te results of the study are as expected, and the given assessment method is easy to operate, which provides a quantitative basis for ensuring the safety of truck platoons on mountainous highways.
Tere are still some limitations in this study: (1) Te efect of vertical curves on safety has not been considered in this study because the braking performance of platoon vehicles was not considered.(2) Multiple simulations are used for analysis, while there is still a lack of validation based on actual measurement data.(3) Only ACC-based platoon control and optimal preview lateral control are implemented, and more advanced longitudinal and lateral control algorithms have not been considered.

2. 3 .
Truck Platoon Simulation.Te impact of the selected safety elements needs to be explored based on the simulation program.Te simulation model used in the current study is built based on the cosimulation of Trucksim and Simulink.In Trucksim software, the vehicle model, lateral control model, and road model can be set and the wind speed and direction can be adjusted.Simulink can realize the platoon control of trucks.

Figure 1 :
Figure 1: Simulation results of aerodynamic coefcients for truck platoons.

3. 1 .
Te Impact of the Reaction Time.Te characteristics of the truck platoon include the driver reaction time, vehicle speed, vehicle spacing, and vehicle load of the lateral control model.Manually driven trucks and autonomous trucks react differently under crosswinds due to diferences in their reaction

MFigure 4 :
Figure 4: Safety index as a function of the mean wind velocity and mean vehicle velocity.

Figure 5 :Figure 6 :Figure 7 :Figure 8 :Figure 9 :
Figure 5: Safety index as a function of the mean wind velocity and mean radius.

Figure 10 :
Figure 10: Safety index as a function of the mean wind velocity and mean superelevation (outside wind).

M 6 -Figure 11 :
Figure 11: Safety index as a function of the mean vehicle velocity and mean superelevation (outside wind).

Table 1 :
Truck model geometry.Considering the magnitude of the efects on the safety of vehicle operation under the efect of crosswinds, wind velocity, wind direction, road friction coefcients, radius, superelevation, and vehicle speed are selected as the infuencing factors for the study.Combined with the existing studies, appropriate variance and mean values are set, as shown in Table2.

Table 3 :
Results of ten-fold cross-validation.