Multivariate Statistical Simulation

The accurate estimation of site-specific lifetime extreme traffic load effects is an important element in the cost-effective assessment of bridges. A common approach is to use statistical distributions derived from weigh-in-motion measurements as the basis for Monte Carlo simulation of traffic loading. However, results are highly sensitive to the assumptions made, not just with regard to vehicle weights but also to axle configurations and gaps between vehicles. This paper presents a comprehensive model for Monte Carlo simulation of bridge loading for free-flowing traffic and shows how the model matches results from measurements on five European highways. The model has been optimised to allow the simulation of many years of traffic and this greatly reduces the variance in calculating estimates for lifetime loading from the model. The approach described here does not remove the uncertainty inherent in estimating lifetime maximum loading from data collected over relatively short time periods.

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Monte Carlo simulation of extreme traffic loading on short and medium span bridges

SUMMARY


This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best-fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula-based procedure can model and simulate the bivariate probability distribution of two curve-fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best-fit copula for modeling the dependence structure underlying two curve-fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best-fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve-fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley & Sons, Ltd.

http://swrh.whu.edu.cn/dianqing/images/pdf-files/Bivariate%20simulation%20using%20copula%20and%20its%20application%20to%20probabilistic%20pile%20settlement%20analysis.pdf

Bivariate simulation using copula and its application to probabilistic pile settlement analysis

Decreasing the uncertainty in the lengths of railway disruptions is a major help to disruption management. To assist the Dutch Operational Control Center Rail (OCCR) during disruptions, we propose the Copula Bayesian Network method to construct a disruption length prediction model. Computational efficiency and fast inference features make the method attractive for the OCCR’s real-time decision making environment. The method considers the factors influencing the length of a disruption and models the dependence between them to produce a prediction. As an illustration, a model for track circuit (TC) disruptions in the Dutch railway network is presented in this paper. Factors influencing the TC disruption length are considered and a disruption length model is constructed. We show that the resulting model’s prediction power is sound and discuss its real-life use and challenges to be tackled in practice.

Modeling railway disruption lengths with Copula Bayesian Networks

https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1043&context=engschcivart

Modeling Same-Direction Two-Lane Traffic for Bridge Loading

Safety assessment and rational design of bridge structures requires the uncertainty associated with vehicle loads to be modeled as accurately as possible. This modeling is rendered difficult by the presence of vehicle axle weights that involve different combinations of unimodal and multimodal probability distributions with different dependence structures. In this paper, a transformation invariant approach using copula functions is proposed for the multivariate simulation of dependent axle weights of different vehicle classes. Copula based dependence modeling, which is widely used in the financial risk analysis, is applied to model and simulate three different vehicle cases with different combinations of marginal probability distributions for axle weights. The database of observed vehicle weights is based on the data collected at five locations on national highways in India. The dependence between multimodal distributions of axle weights is accurately considered and simulations are carried out. The simulated axle weights are found to be in very good agreement with the observed data. This type of simulation is useful in carrying out simulation-based reliability analysis of bridges and pavements.

S. Srinivas

Papers

Multivariate Simulation and Multimodal Dependence Modeling of Vehicle Axle Weights with Copulas