道路交通專(zhuān)業(yè)畢業(yè)設(shè)計(jì)外文翻譯--基于od矩陣神經(jīng)網(wǎng)絡(luò)與主成分分析法的路段流量估算（英文）

1、 OD MATRICES ESTIMATION FROM LINK FLOWS BY NEURAL NETWORKS AND PCA Lorenzo Mussone1 , Matteo Matteucci2 1Department of Building Environment Science Technology, Politecnico di Milano, Italy mussone@polimi.it, via Bonardi

2、, 9, 20123 Milano 2 Department of Electronic and Information, Politecnico di Milano, Italy matteucc@elet.polimi.it, via Ponzio,34/5, 20123 Milano Abstract: The paper tackles OD matrix estimation starting from the measur

3、es of flow on road network links and proposes the application of soft-computing techniques. The application scenarios are two: a trial network and the real rural network of the Province of Naples both simulated by a m

4、icro-simulator dynamically assigning known OD matrices. A PCA (Principal Component Analysis) technique was also used to reduce the input space of variables in order to achieve better significance for input data and to

5、study the possible eigengraphs of the road networks. Copyright © 2006 IFAC Keywords: OD estimation, Neural Networks, PCA, Link flow measures, Variance stabilization 1. INTRODUCTION The analysis of urban networks

6、was organically and significantly developed since the middle of 80s in order to solve problems related to road circulation. Many planning and control methodologies both with equilibrium and dynamic approaches are bas

7、ed on the use of an origin destination matrix (OD). Field survey necessary to build this matrix is expensive and cannot be repeated with a high frequency. For this reason, methodological and operating alternatives ha

8、ve been experimented since many years and they aim at building the OD matrix by using link flows that generally cost less to be measured. In order to solve the problem of OD estimation many approaches have been deve

9、loped. Some are based on entropy maximization that is on the maximization of trip distribution dispersion on all available paths; in some cases the built model refers to an OD matrix objective without referring indee

10、d to estimation errors, or to statistic estimation indexes or to likelihood functions (Van Zuylen and Willumsen, 1980). This model was later extended to congested networks by formulating an optimization problem with

11、 variational disequality constraints leading to a bi-level programme. The bi-level approach presents some difficulties to find the optimal solution because of non-convex and non-differential formulation. Florian and

12、Chen (1995) formulated a heuristic approach (of Gauss-Seidel type) capable of converging to optimal solution by limiting the objective to the correction of O/D matrix. Other approaches are based on models that use

13、 the statistical properties of observed variables. For instance Maher (1983) proposed a Bayesian estimation by means of a normal multivariate distribution both for matrix distribution and for link flow; Cascett

14、a (1984) used an estimation based on generalized least squares (GLS). An overview of statistical methods for estimating OD matrix can be found in Cascetta and Nguyen (1988); it regards generalized and constrained lea

15、st squares and estimation of likelihood and Bayesian type. The most of these studies assumes a fixed percentage of link or path choice calculated by a deterministic user equilibrium assignment model. This can cause s

16、ome inconsistency between flows and the OD matrix especially when the network is highly congested. In order to overtake this limitation, Cascetta (1989) proposed to interpret link and path flows like stochastic vari

17、ables and, therefore, values obtained by a SUE assignment like the average values of these variables. On the same line there are other papers such as Yang et al. (1992), and in a successive improvement in (Yang et al

18、., 2001); Lo et al. (1996) proposed a unified statistical approach for the estimation of OD matrix using simultaneously link flow data and information about link choice percentage. Gong (1998) uses a Hopfield neural

19、 network as a tool for solving an optimal problem, components. In the following plots, arcs with a higher contribution are thicker and their color is red if they have a positive contribution otherwise is blue. The vis

20、ualization of eigenflows, i.e., the product of the flow matrix and the eigengraphs, shown in the next chapters, is the projection of traffic flows onto the eigengraph space; in the same way as before, arcs with a hig

21、her contribution to flow are thicker and their color is red if they have a positive contribution otherwise their color is blue. 3. APPLICATION SCENARIOS 3.1 The simulator The scenarios referred to during experimentat

22、ions are produced by a simulation environment for road networks developed by the transport section of the University of Naples. This simulator is able to reproduce dynamic vehicular flow starting from a generic tran

23、sport demand. Setting up the experiments requires the definition of the transport system, demand and supply, by which every model and procedures must be calibrated. For this reason, a trial network with 6 nodes (amon

24、g which there are 3 centroids) and 12 links was firstly used (Figure 1). Fig. 1: The simplified network for first experiments. Fig. 2: Schematic network used for the rural road network of the Province of Naples. Then,

25、with the aim at making more likely the application scenery, a real land system has been surveyed both with its demographic characteristics and activity locations, and actual transport supply. The territorial context

26、is the whole province of Naples from which the rural road network has been extracted (Figure 2). This network has 994 nodes (among which there are 45 centroids) and 1363 links (reduced to 1190 after discharging links

27、with no flow). 3.2 Demand and vehicular flow on links Demand is characterized by within-day and day-to- day dynamic and it is updated each 15 minutes. Flows on link are detected each five minutes. For the trial networ

28、k, demand is described by a 3x3 matrix and the nodes 1 and 6 are origin centroids; the nodes 1, 4 and 6 are destination centroids (for a total of four non-empty cells). Simulation days are 15. For the network of Napl

29、es province (the final network) the scenery is more complex. Demand is described by a 48x48 with 1004 non-empty cells (out of 2304) and with a structure highly variable during the day. Besides the high variability of

30、 demand it must be underlined that non-empty cells sets in the 15 minute intervals are generally not overlapping. Cells with less than 10 vehicles per hour are cancelled for two main reasons: firstly to reduce data d

31、ispersion and secondly because it is very difficult that these low values have a statistical significance while it is likely they don’t give a real information. The final matrix has therefore 726 non empty cells (abo

32、ut the 31% of the total) with a reduction of the number of non- empty cells of about 28%, but with reduction of demand of only about 8.8%. Simulation days are 15 also for this scenario but obviously the amount of dat

33、a to be used is more than ten times higher (total demand is 41,488,230 veh/h). For both networks the number of records is 1440 for OD demand and 4320 for link flows. For this reason each row of OD demand (15 minute i

34、nterval) is related to the three rows of flow of the same 15 interval, leading to 4320 records both for OD demand and link flows. By using the dataset under examination and observing the plot of seasonality, we can a

35、rgue that process variance is low when the seasonality value is low and, conversely, it is high when the seasonality value is high. Assuming this, it is reasonable to look for the existence of an analytical relations

36、hip between seasonality (basically a mean) and variance. The existence of a relationship between these two variables (plotted in Figure 3) confirms that the process is not stationary. From this figure it can be easy

37、 argued that variance and average are related by a non-linear relationship, specifically a quadratic one. In this situation a possible technique to stabilize the variance is to apply a logarithmic transformation. The

38、 following results show that this transformation really allows us to improve performance of about some percentage points for the RMSE index with respect to results obtained without stabilization. However, it must be