Report : stochastic analysis of road asset data for maintenance cost prediction

Reliable budget/cost estimates for road maintenance and rehabilitation are subjected to uncertainties and variability in road asset condition and characteristics of road users. The CRC CI research project 2003-029-C ‘Maintenance Cost Prediction for Road’ developed a method for assessing variation and reliability in budget/cost estimates for road maintenance and rehabilitation. The method is based on probability-based reliable theory and statistical method. The next stage of the current project is to apply the developed method to predict maintenance/rehabilitation budgets/costs of large networks for strategic investment. The first task is to assess the variability of road data. This report presents initial results of the analysis in assessing the variability of road data. A case study of the analysis for dry non reactive soil is presented to demonstrate the concept in analysing the variability of road data for large road networks. In assessing the variability of road data, large road networks were categorised into categories with common characteristics according to soil and climatic conditions, pavement conditions, pavement types, surface types and annual average daily traffic. The probability distributions, statistical means, and standard deviation values of asset conditions and annual average daily traffic for each type were quantified. The probability distributions and the statistical information obtained in this analysis will be used to asset the variation and reliability in budget/cost estimates in later stage. Generally, we usually used mean values of asset data of each category as input values for investment analysis. The variability of asset data in each category is not taken into account. This analysis method demonstrated that it can be used for practical application taking into account the variability of road data in analysing large road networks for maintenance/rehabilitation investment analysis.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

Stochastic analysis of transit route segments' passenger load variation for capacity and quality of service assessment

This paper investigates stochastic analysis of transit segment hourly passenger load factor variation for transit capacity and quality of service (QoS) analysis using Automatic Fare Collection data for a premium radial bus route in Brisbane, Australia. It compares stochastic analysis to traditional peak hour factor (PHF) analysis to gain further insight into variability of transit route segments’ passenger loading during a study hour. It demonstrates that hourly design load factor is a useful method of modeling a route segment’s capacity and QoS time history across the study weekday. This analysis method is readily adaptable to different passenger load standards by adjusting design percentile, reflecting either a more relaxed or more stringent condition. This paper also considers hourly coefficient of variation of load factor as a capacity and QoS assessment measure, in particular through its relationships with hourly average and design load factors. Smaller value reflects uniform passenger loading, which is generally indicative of well dispersed passenger boarding demands and good schedule maintenance. Conversely, higher value may be indicative of pulsed or uneven passenger boarding demands, poor schedule maintenance, and/or bus bunching. An assessment table based on hourly coefficient of variation of load factor is developed and applied to this case study. Inferences are drawn for a selection of study hours across the weekday studied.

Stochastic analysis of transit route segments' passenger load variation for capacity & quality of service assessment

This study uses weekday Automatic Fare Collection (AFC) data on a premium bus line in Brisbane, Australia •Stochastic analysis is compared to peak hour factor (PHF) analysis for insight into passenger loading variability •Hourly design load factor (e.g. 88th percentile) is found to be a useful method of modeling a segment’s passenger demand time-history across a study weekday, for capacity and QoS assessment •Hourly coefficient of variation of load factor is found to be a useful QoS and operational assessment measure, particularly through its relationship with hourly average load factor, and with design load factor •An assessment table based on hourly coefficient of variation of load factor is developed from the case study

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.