Robust identification for multi-section freeway traffic models

1IntroductionIt is important to estimate the densityandspeed oftrafficfor the safetyandtraffic control .For decades ,manyresearchwork have been done to estimate traffic density, trafficvolume ,average speed,and other parameters[1,2] .Theproblemof estimating dynamic traffic has been involved inparts of those research work[1 ~4] .By means of O_Dmatrix,some researchers have also made a series of studiesof traffic prediction and traffic layout estimation[5] .However , most of the research work m…     

An adaptive freeway traffic state estimator

Real-data testing results of a real-time nonlinear freeway traffic state estimator are presented with a particular focus on its adaptive features. The pursued general approach to the real-time adaptive estimation of complete traffic state in freeway stretches or networks is based on stochastic nonlinear macroscopic traffic flow modeling and extended Kalman filtering. One major innovative aspect of the estimator is the real-time joint estimation of traffic flow variables (flows, mean speeds, and densities) and some important model parameters (free speed, critical density, and capacity), which leads to four significant features of the traffic state estimator: (i) avoidance of prior model calibration; (ii) automatic adaptation to changing external conditions (e.g. weather and lighting conditions, traffic composition, control measures); (iii) enabling of incident alarms; (iv) enabling of detector fault alarms. The purpose of the reported real-data testing is, first, to demonstrate feature (i) by investigating some basic properties of the estimator and, second, to explore some adaptive capabilities of the estimator that enable features (ii)-(iv). The achieved testing results are quite satisfactory and promising for further work and field applications.     

New identification approaches for disturbed models

Recently, much research has been conducted in the field of identification of the linear models. In general, these methods use a time-domain estimate or a frequency-domain estimate. In this paper, the time-domain estimate and the frequency-domain estimate were combined to identify the autoregressive exogenous noise (ARX) interference model. The concept of a general prediction error criterion is introduced for the time-domain estimate. An optimal frequency estimation is introduced for the frequency-domain estimate. A new identification method, called the empirical frequency-domain optimal parameter estimate, is proposed for disturbed systems. It is fully applied and developed for the output error model and a specific case or the ARX model. The algorithm theoretically provides the globally optimum frequency-domain estimate of the model. Some simulations are included to illustrate the new identification method.     

Robust control oriented identification of errors-in-variables models based on normalised coprime factors

A robust control oriented identification approach is proposed to deal with the identification of errors-in-variables models (EIVMs), which are corrupted with input and output noises. Based on normalised coprime factor model (NCFM) representations, a frequency-domain perturbed NCFM for an EIVM is derived according to a geometrical explanation for the v-gap metric. As a result, identification of the EIVM is converted into that of the NCFM. Besides an identified nominal NCFM, its worst case error has to be quantified. Unlike other traditional control-oriented identification methods, the v-gap metric is employed to measure the uncertainties including a priori information on the disturbing noises and the worst case error for the resulting nominal NCFM. Since this metric is also used as an optimisation criterion, the associate parameter estimation problem can be effectively solved by linear matrix inequalities. Finally, a numerical simulation shows the effectiveness of the proposed method.     

Robust optimal experiment design for system identification

This paper develops the idea of min-max robust experiment design for dynamic system identification. The idea of min-max experiment design has been explored in the statistics literature. However, the technique is virtually unknown by the engineering community and, accordingly, there has been little prior work on examining its properties when applied to dynamic system identification. This paper initiates an exploration of these ideas. The paper considers linear systems with energy (or power) bounded inputs. We assume that the parameters lie in a given compact set and optimise the worst case over this set. We also provide a detailed analysis of the solution for an illustrative one parameter example and propose a convex optimisation algorithm that can be applied more generally to a discretised approximation to the design problem. We also examine the role played by different design criteria and present a simulation example illustrating the merits of the proposed approach.     

高速公路交通状态的联合估计方法

提出一种有效的高速公路交通密度预测估计方法。通过分析交通模型，建立了系统的离散化状态和误差模型表达式，并采用推广Kalman滤波方法进行估计．为进一步增强数值稳定性以及提高计算效率，根据系统矩阵分块的特点，采用分块的正交化U-D分解算法实现时间更新，同时采用序列U-D分解方法进行测量更新．仿真计算和实际应用表明，该方法可以给出工程实用结果。     

Parameter identification for a traffic flow model

In this paper, a macroscopic model is presented which describes the traffic flow on a freeway by a set of nonlinear, deterministic difference equations. The model is deduced from simple physical and empirical considerations and contains a set of free parameters which have to be estimated using real traffic data. This identification procedure is formulated here as a parameter optimization problem which is solved by nonlinear programming. In addition, the sensitivity of the model with respect to parameter changes and structural changes is investigated. Although stochastic events play a role in traffic dynamics, the results demonstrate that the validated model copes surprisingly well with real traffic behaviour.     

Robust identification of continuous-time low-order models using moments of a single rectangular pulse response

This paper presents a simple method for identifying first- and second-order processes with dead-time by using moments of a single rectangular pulse response in an open-loop system. A closed-form formula is proposed to determine all parameters of four types of process models for a stable linear time-invariant process. It is shown that the same approach can be extended to the identification of multi-input, multi-output linear processes. It is demonstrated through a comparative analysis that the proposed identification method results in good accuracy with a noisy output, and is also able to closely approximate various high-order processes in those low-order models.     

交通流模型参数的近似动态规划辨识方法

针对交通流模型的强非线性、不确定性等特点,提出了基于近似动态规划的交通流模型参数辨识算法.该算法具有自学习和自适应的特性,不依赖于被控对象的解析模型.严格的理论推导证明了这种参数辨识方案的收敛性,仿真结果验证了所提出算法的有效性.     

Projection-based identification algorithm for grey-box continuous-time models

In this paper, a new identification method for continuous-time models, which can handle various grey-box structures and has strong robustness, is presented. The proposed method is based on an incremental model update scheme and the projection onto the subspace which reflects the model structure. By utilising these schemes, robustness of other continuous-time system identification methods and versatility of generic optimisation algorithms can be integrated into the proposed method. The effectiveness of the proposed method is demonstrated through numerical examples related to a grey-box model in closed-loop system and systems with unknown time-delay.     

Robust multi-variable identification: Optimal experimental design with constraints

Model identification for use in the design of multi-variable controllers should utilize an experimental design that optimizes the resulting robust control stability and performance, irrespective of the eventual controller structure or tuning. Previous research has shown that a key factor is to identify a steady-state gain matrix with minimal mismatch in the multi-variable gain directionality. In particular, for ill-conditioned systems, precise estimation of the weak process directions is essential.This research extends prior work to provide two alternative design formulations for robust multi-variable identification that allow seamless inclusion of any linear inequality constraints in the inputs, outputs or combinations thereof. These designs, based on D-optimality theory, produce highly correlated input sequences, and accommodate the input and output constraints by using highly unbalanced replications at the various input condition support-points.The superior effectiveness of the proposed designs over prior methods in the literature is demonstrated on a two-input, two-output binary distillation case study. In addition, the seamless extension of the method to higher-order systems is exhibited via a four-input, four-output fluid catalytic cracking example.Uncertainty in the prior estimate of the steady-state gain matrix and in design implementation is addressed in both of the proposed formulations. Furthermore, the second formulation provides a single tuning parameter to balance the efficacy of robust identification versus minimizing sensitivity to uncertainty. Finally, guidelines are presented for the extension of these methods to non-square systems.     

快速路网交通管理策略的环境效益仿真评价方法*

提出了用于评价城市快速路网交通管理策略环境效益的仿真方法。该方法采用宏观动态交通网络建模思想,将考虑车辆行驶速度的机动车排放模型及燃油消耗模型与宏观交通模型有效衔接,并用货币价值量化排放减少所带来的直接经济价值（包括大气污染治理费的节省和燃油消耗费用的节省）。以可变情报板路径诱导策略为例,对一个算例路网进行仿真。仿真结果表明,路径诱导策略尽管导致NOX增排了0.799 t,但减排了0858 t的CO和0087 t的HC,同时节省燃油消耗185 335166 L,产生直接经济价值逾129万元。研究表明     

Robust likelihood inference for regression parameters in partially linear models

A robust likelihood approach is proposed for inference about regression parameters in partially-linear models. More specifically, normality is adopted as the working model and is properly corrected to accomplish the objective. Knowledge about the true underlying random mechanism is not required for the proposed method. Simulations and illustrative examples demonstrate the usefulness of the proposed robust likelihood method, even in irregular situations caused by the components of the nonparametric smooth function in partially-linear models.     

A new identification method for fuzzy linear models of nonlinear dynamic systems

The most promising methods for identifying a fuzzy model are data clustering, cluster merging and subsequent projection of the clusters on the input variable space. This article proposes to modify this procedure by adding a cluster rotation step, and a method for the direct calculation of the consequence parameters of the fuzzy linear model. These two additional steps make the model identification procedure more accurate and limits the loss of information during the identification procedure. The proposed method has been tested on a nonlinear first order model and a nonlinear model of a bioreactor and results are very promising.     

Open-loop worst-case identification of nonSchur plants

This paper presents an LMI based algorithm for deterministic worst-case identification of nonSchur plants in an open-loop setting. Contrary to other approaches dealing with this problem, the proposed technique does not require prior knowledge of a stabilizing controller. The main result of the paper shows that, as the information is completed, the identified model converges, in the ?₂-induced topology, to the actual plant. Additional results include upper bounds on the worst-case identification error on the finite horizon. The usefulness of the proposed approach is illustrated with a practical example arising in the context of robust visual tracking.     

Parameter identification for models with bounded errors in all variables

In this paper, the problem of parameter identification for models with bounded measurement errors both on the input and on the output is addressed and some corrections to previously published results are presented. In particular, it is shown that only parameter overbounds can in general be computed for systems of the form y = (φ + δφ)θ + δy when the bounded measurement errors δφ and δy are correlated. Since ARMAX and bilinear systems can be represented in this form, it turns out that tight parameter bounds are in general not available for these systems. Finally, we show that it is possible to check a posteriori whether the obtained bounds are tight or not.     

A new mechanism for metastability of under-saturated traffic responsible for time-delayed traffic breakdown at the signal

In this paper we introduce a new mechanism of metastability of under-saturated traffic at the signal that is responsible for a time-delayed traffic breakdown revealed by Kerner (2011). In our model, we assume that the metastability of under-saturated traffic at the signal is caused by a dependence of the mean time of driver acceleration from a queue at the signal on the driver’s stopped time within the queue. With the use of Nagel–Schreckenberg model, we demonstrate that this mechanism of the metastability of city traffic can lead to the time-delayed traffic breakdown at the signal.