scholarly journals Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method

Author(s):  
Ronan Keane ◽  
H. Oliver Gao

Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem and compares different algorithms for its solution. The optimization consists of an arbitrary car following model, posed as either an ordinary or delay differential equation, being calibrated to an arbitrary source of trajectory data that may include lane changes. Typically, the calibration problem is solved using gradient free optimization. In this work, the gradient of the optimization problem is derived analytically using the adjoint method. The computational cost of the adjoint method does not scale with the number of model parameters, which makes it more efficient than evaluating the gradient numerically using finite differences. Numerical results are presented that show that quasi-Newton algorithms using the adjoint method are significantly faster than a genetic algorithm and also achieve slightly better accuracy of the calibrated model.

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5539 ◽  
Author(s):  
Mădălin-Dorin Pop ◽  
Octavian Proștean ◽  
Tudor-Mihai David ◽  
Gabriela Proștean

Nowadays, the intelligent transportation concept has become one of the most important research fields. All of us depend on mobility, even when we talk about people, provide services, or move goods. Researchers have tried to create and test different transportation models that can optimize traffic flow through road networks and, implicitly, reduce travel times. To validate these new models, the necessity of having a calibration process defined has emerged. Calibration is mandatory in the modeling process because it ensures the achievement of a model closer to the real system. The purpose of this paper is to propose a new multidisciplinary approach combining microscopic traffic modeling theory with intelligent control systems concepts like fuzzy inference in the traffic model calibration. The chosen Takagi–Sugeno fuzzy inference system proves its adaptive capacity for real-time systems. This concept will be applied to the specific microscopic car-following model parameters in combination with a Kalman filter. The results will demonstrate how the microscopic traffic model parameters can adapt based on real data to prove the model validity.


Author(s):  
Tu Xu ◽  
Jorge Laval

This paper analyzes the impact of uphill grades on the acceleration drivers choose to impose on their vehicles. Statistical inference is made based on the maximum likelihood estimation of a two-regime stochastic car-following model using Next Generation SIMulation (NGSIM) data. Previous models assume that the loss in acceleration on uphill grades is given by the effects of gravity. We find evidence that this is not the case for car drivers, who tend to overcome half of the gravitational effects by using more engine power. Truck drivers only compensate for 5% of the loss, possibly because of limited engine power. This indicates not only that current models are severely overestimating the operational impacts that uphill grades have on regular vehicles, but also underestimating their environmental impacts. We also find that car-following model parameters are significantly different among shoulder, median and middle lanes but more data is needed to understand clearly why this happens.


2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
A. V. Wildemann ◽  
A. A. Tashkinov ◽  
V. A. Bronnikov

This paper introduces an approach for parameters identification of a statistical predicting model with the use of the available individual data. Unknown parameters are separated into two groups: the ones specifying the average trend over large set of individuals and the ones describing the details of a concrete person. In order to calculate the vector of unknown parameters, a multidimensional constrained optimization problem is solved minimizing the discrepancy between real data and the model prediction over the set of feasible solutions. Both the individual retrospective data and factors influencing the individual dynamics are taken into account. The application of the method for predicting the movement of a patient with congenital motility disorders is considered.


2017 ◽  
Vol 24 (13) ◽  
pp. 2873-2893 ◽  
Author(s):  
Austin A Phoenix ◽  
Jeff Borggaard ◽  
Pablo A Tarazaga

As future space mission structures are required to achieve more with scarcer resources, new structural configurations and modeling capabilities will be needed to meet the next generation space structural challenges. A paradigm shift is required away from the current structures that are static, heavy, and stiff, to innovative lightweight structures that meet requirements by intelligently adapting to the environment. As the complexity of these intelligent structures increases, the computational cost of the modeling and optimization efforts become increasingly demanding. Novel methods that identify and reduce the number of parameters to only those most critical considerably reduce these complex problems, allowing highly iterative evaluations and in-depth optimization efforts to be computationally feasible. This parameter ranking methodology will be demonstrated on the optimization of the thermal morphing anisogrid boom. The proposed novel morphing structure provides high precision morphing through the use of thermal strain as the sole actuation mechanism. The morphing concept uses the helical members in the anisogrid structure to provide complex constrained actuations that can achieve the six degree of freedom morphing capability. This structure provides a unique potential to develop an integrated structural morphing system, where the adaptive morphing capability is integrated directly into the primary structure. To identify parameters of interest, the Q-DEIM model reduction algorithm is implemented to rank the model parameters based on their impact on the morphing performance. This parameter ranking method provides insight into the system and enables the optimal allocation of computational and engineering resources to the most critical areas of the system for optimization. The methodology, in conjunction with a singular value decomposition (SVD), provides a ranking and identifies parameters of relative importance. The SVD is used to truncate the nine parameters problem at two locations, generating a five parameter optimization problem and a three parameter optimization problem. To evaluate the ranking, a parameter sweep in conjunction with a simple minimum cost function search algorithm will compare all 120 five parameter ranking orders to the Q-DEIM ranking. This reduced parameter set significantly reduces the parameter complexity and the computational cost of the model optimization. This paper will present the methodology to define the resulting performance of the optimal thermal morphing anisogrid structure, minimum morphing control, and the systems frequency response capability as a function of available power.


Author(s):  
Rachel M. James ◽  
Britton E. Hammit ◽  
Stephen D. Boyles

Microsimulation models help agencies obtain robust estimates of project benefits and spend their resources effectively. The realism of these models depends on the quality of input data and the realism of the sub-models controlling driver behavior. The availability of trajectory-level driving data provides new opportunities to improve car-following models and their application in practice. Procedures for calibrating car-following models using a single driving trajectory are well documented in the literature. However, methods for identifying a representative parameter set to describe a collection of observed driving behavior must be developed and tested before trajectory-level data can be applied in practice. This paper describes eight methods for obtaining representative sets of calibration parameters to describe a group of drivers or a specific driving condition. The methods are tested using a 100-trip sample from the SHRP2 Naturalistic Driving Study and validated with a 10-fold cross-validation procedure. The method capturing the average behavior while preserving underlying correlations between the calibrated model parameters performed the best across all four models. Methods that adequately captured the average behavior while relaxing the assumption of underlying parameter correlations performed better than all other tested methods. Therefore, simply taking the mean or median of the distribution of observed parameter values offers a practical approach for generating a representative parameter set, significantly outperforming default parameter values.


Author(s):  
Ankit Anil Chaudhari ◽  
Karthik K. Srinivasan ◽  
Bhargava Rama Chilukuri ◽  
Martin Treiber ◽  
Ostap Okhrin

We propose a new methodology for calibrating Wiedemann-99 vehicle-following parameters for mixed traffic (different conventional vehicle classes) based on trajectory data. The existing acceleration equations of the Wiedemann model are modified to represent more realistic driving behavior. Exploratory analysis of simulation data revealed that different Wiedemann-99 model parameters could lead to similar macroscopic behavior, highlighting the importance of calibration at the microscopic level. Therefore, the proposed methodology is based on optimizing performance measures at the microscopic level (acceleration, speed, and trajectory profiles) to estimate suitable calibration parameters. Further, the goodness of fit for the observed data is sensitive to the numerical integration method used to compute vehicles’ velocity and position. We found that the calibrated parameters using the proposed methodology perform better than other approaches for calibrating mixed traffic. The results reveal that the calibrated parameter values and, consequently, the thresholds that delineate closing, following, emergency braking, and opening regimes, vary between two-wheelers and cars. The window (in the relative speed versus gap plot) for the unconscious following is larger for cars while the free-flow regime is more extensive for two-wheelers. Moreover, under the same relative speed and gap stimulus, two-wheelers and cars may be in different regimes and display different acceleration responses. Thus, accurate calibration of each vehicle’s parameters is essential for developing micro-simulation models for mixed traffic. The calibration analysis results of strict and overlapping staggered car following signify an impact of staggered car following compared with strict car following which demands separate calibration for strict and staggered following.


2011 ◽  
Vol 22 (09) ◽  
pp. 1005-1014 ◽  
Author(s):  
KEIZO SHIGAKI ◽  
JUN TANIMOTO ◽  
AYA HAGISHIMA

The stochastic optimal velocity (SOV) model, which is a cellular automata model, has been widely used because of its good reproducibility of the fundamental diagram, despite its simplicity. However, it has a drawback: in SOV, a vehicle that is temporarily stopped takes a long time to restart. This study proposes a revised SOV model that suppresses this particular defect; the basic concept of this model is derived from the car-following model, which considers the velocity gap between a particular vehicle and the preceding vehicle. A series of simulations identifies the model parameters and clarifies that the proposed model can reproduce the three traffic phases: free, jam, and even synchronized phases, which cannot be achieved by the conventional SOV model.


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