Eric Mai

Algorithm for Finding Optimal Paths in a Public Transit Network with Real-Time Data

Recently, transit agencies have begun opening their route configuration and schedule data to the public, as well as providing online application programming interfaces to real-time bus positions and arrival estimates. On the basis of this infrastructure for providing transit data over the Internet, the authors developed an algorithm to calculate the travel times of K shortest paths in a public transportation network where all wait and travel times were known only in real time. Although there was a large body of work on routing algorithms in transit networks, the authors took cues from an algorithm to find the shortest paths in road networks, called transit node routing. This approach was based on observation of intuitive behavior by humans: when taking transit, travelers looked for a particular set of transfer points that connected transit routes that led from the origin and destination. A lookup table was precomputed of feasible paths between the origin stop of every bus route to the terminus of every other bus route by using the transfer points. This precomputation of paths significantly reduced the computation time and number of real-time arrival requests to transit agency servers, the bottleneck in computing this problem. The computational complexity of the algorithm is linear in real time, and implementation results show that queries from a web server are returned in 3 s in the worst case.

Neural Network Initialization with Prototypes - Function Approximation in Engineering Mechanics Applications

A prototype-based initialization methodology is proposed to approximate functions that are used to characterize nonlinear stress-strain, moment-curvature, and load-displacement relationships, as well as restoring forces and time histories in engineering mechanics applications. Three prototypes are defined by exploiting the capabilities of linear sums of sigmoidal functions. By using the proposed prototypes either individually or combinatorially, successful training can take place for ten specific types of nonlinear functions and far beyond when the required number of hidden nodes and initial values of weights and biases can always be derived before the training starts. Some mathematical insights to this initialization methodology and a few prototypes are offered, while training examples are provided to demonstrate a clear procedure that is used to implement this methodology. With the derived numbers of hidden nodes in each approximation, applying the Nguyen-Widrow algorithm is enabled and the training performance is compared between the existing and the proposed initialization options.

A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics

This paper introduces a heuristic methodology for designing multilayer feedforward neural networks to model the types of nonlinear functions common to many engineering mechanics applications. It is well known that a perfect way to determine the ideal architecture to initialize neural network training has not yet been established. This could be because this challenging issue can only be properly addressed by looking into the features of the function to be approximated and thus might be hard to tackle in a general sense. In this study, the authors do not presume to provide a universal method approximate an arbitrary function, rather the focus is given to modeling nonlinear hysteretic restoring forces, a significant domain function approximation problem. The governing physics and mathematics of nonlinear hysteretic dynamics as well as the strength of the sigmoidal basis function are exploited to determine both an efficient neural network architecture (e.g., the number of hidden nodes) as well as effective initial weight and bias values for those nodes. Training examples are presented to demonstrate and validate the proposed initial design methodology. Comparisons are made between the proposed methodology and the widely used Nguyen-Widrow Initialization. Future work is also identified.

Simulating the Travel Time Impact of Missed Transit Connections

It is well established that transit passengers dislike transferring, in part because of the inherent risk that the connecting vehicle will be missed, a risk that can increase overall travel time. Despite the problems that missed transfers cause, such transfers across a system are rarely tracked in transit performance monitoring programs. The likelihood of a missed transfer depends on combinations of several factors and thus is hard to estimate. In practice, transit systems are most often evaluated according to the performance of individual vehicles, stops, and routes, not the interactions between them. This paper describes a systems approach to quantify the effects of travel time reliability, schedule adherence, and schedule design on missed transit connections, and the resulting travel time distributions. To determine the effects of vehicle interactions on transfers and the role that transfers play in travel time, a series of simulations based on automatic passenger counting data from the bus system in San Diego, California, was performed. Travel times on two transfer trips in downtown San Diego were simulated. The effects of passenger arrival rate, on-time vehicle performance, and schedule design on the likelihood of a transfer being missed were investigated in a sensitivity analysis. This research is expected to lead to a better understanding of the passenger effects of schedule adherence on transfer trips. Practically speaking, this methodology could aid in the identification of pairs of buses whose chronic schedule deviations at a particular location are likely causing missed transfers.

Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

This paper continues the development of a heuristic initialization methodology for designing multilayer feedforward neural networks aimed at modeling nonlinear functions for engineering mechanics applications as presented previously at SPIE 2003, and 2005 to 2007. Seeking a transparent and domain knowledge-based approach for neural network initialization and result interpretation, the authors examine the efficiency of linear sums of sigmoidal functions while offering constructive methods to approximate functions in engineering mechanics applications. This study provides details and results of mapping the four arithmetic operations (summation, subtraction, multiplication, division) as well as other functions including reciprocal, Gaussian and Mexican hat functions into multilayer feedforward neural networks with one hidden layer. The approximation and training examples demonstrate the efficiency and accuracy of the proposed mapping techniques and details. Future work is also identified. This effort directly contributes to the further extension of the proposed initialization procedure in that it opens the door for the approximation of a wider range of nonlinear functions.

Toward constructive methods for sigmoidal neural networks - function approximation in engineering mechanics applications

This paper reports a continuous development of the work by the authors presented at IJCNN 2005 & 2007 [1, 2]. A series of parsimonious universal approximator architectures with pre-defined values for weights and biases called “neural network prototypes” are proposed and used in a repetitive and systematic manner for the initialization of sigmoidal neural networks in function approximation. This paper provides a more in-depth literature review, presents one training example using laboratory data indicating quick convergence and trained sigmoidal neural networks with stable generalization capability, and discusses the complexity measure in [3, 4]. This study centers on approximating a subset of static nonlinear target functions - mechanical restoring force considered as a function of system states (displacement and velocity) for single-degree-of-freedom systems. We strive for efficient and rigorous constructive methods for sigmoidal neural networks to solve function approximation problems in this engineering mechanics application and beyond. Future work is identified.