Multivariate Simulation and Multimodal Dependence Modeling of Vehicle Axle Weights with Copulas
01 Dec 2006-Journal of Transportation Engineering-asce (American Society of Civil Engineers)-Vol. 132, Iss: 12, pp 945-955
TL;DR: A transformation invariant approach using copula functions is proposed for the multivariate simulation of dependent axle weights of different vehicle classes and is found to be in very good agreement with the observed data.
Abstract: 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.
Citations
More filters
173 citations
TL;DR: In this article, the authors present a comprehensive model for Monte Carlo simulation of bridge loading for free-flowing traffic and show how the model matches results from measurements on five European highways.
Abstract: 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.
113 citations
Cites methods from "Multivariate Simulation and Multimo..."
...Correlation between axle loads is modelled for each vehicle class by Crespo-Minguillón and Casas (1997) and by Srinivas, Menon, and Prasad (2006) who use copula functions....
[...]
TL;DR: In this paper, a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure was proposed for serviceability limit state reliability analysis of piles, and four load-test datasets of load-displacement curves of piles were used to illustrate the proposed procedure.
Abstract: 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.
108 citations
Cites methods from "Multivariate Simulation and Multimo..."
...[13] used the copula approach for modeling the multivariate and multimodal vehicle axle weight data....
[...]
TL;DR: The Copula Bayesian Network method is proposed to construct a disruption length prediction model to assist the Dutch Operational Control Center Rail (OCCR) during disruptions and its prediction power is sound.
Abstract: 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.
87 citations
TL;DR: Using a database of weigh-in-motion measurements collected at two European sites for over 1 million trucks, this paper examines the relationships between adjacent vehicles in both lanes in terms of vehicle weights, speeds and inter-vehicle gaps.
85 citations
Cites background from "Multivariate Simulation and Multimo..."
...[18] to model dependence between axle weights and spacings on vehicles....
[...]
References
More filters
TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
47,133 citations
TL;DR: Introduction.
Abstract: Introduction. Aspects of Interpretation. Technical Considerations. Statistical Analysis. Special Methods for Joint Responses. Some Examples. Strategical Aspects. More Specialized Topics. Appendices.
3,913 citations
TL;DR: In this article, a related model for association in bivariate survivorship time distributions is proposed for the analysis of familial tendency in disease incidence, which is related to more specifically epidemiological models.
Abstract: SUMMARY The application of Cox's (1972) regression model for censored survival data to epidemiological studies of chronic disease incidence is discussed. A related model for association in bivariate survivorship time distributions is proposed for the analysis of familial tendency in disease incidence. The possible extension of the model to general multivariate survivorship distributions is indicated. This paper is concerned with a problem in the analysis of epidemiological studies of chronic disease incidence. In contrast with problems in the epidemiology of infectious disease, such analysis usually assumes that incidence of disease in different individuals represents independent events, the occurrence of which is influenced by measurable factors describing individuals and their environment. However, in the study of familial tendency in chronic disease incidence, this assumption is called into question. Comparisons of parents and offspring and sibling comparisons investigate possible relationships between disease incidence in related individuals and such studies provide interesting analytical difficulties. Here, this problem is treated as one of estimating association in multivariate life tables. In ? 2 it is shown that epidemiological incidence studies may be regarded as being concerned primarily with the study of the distribution of the age at incidence and that Cox's (1972) regression model for the analysis of censored survival time data may readily be applied to incidence data and is closely related to more specifically epidemiological models. In later sections, a related model for bivariate life tables is developed and applied to the problem of demonstrating association in disease incidence in ordered pairs of individuals. The possible extension of the model into more dimensions is indicated.
2,013 citations
Book•
01 Jun 1996TL;DR: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometricreliability Index Generalized Reliability index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis.
Abstract: Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometric Reliability Index Generalized Reliability Index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis Introduction to Process Descriptions.
1,852 citations
TL;DR: It is found that null hypothesis testing is uninformative when no estimates of means or effect size and their precision are given, and an alternative paradigm of data analysis based on Kullback-Leibler information is described.
Abstract: This paper presents a review and critique of statistical null hypothesis testing in ecological studies in general, and wildlife studies in particular, and describes an alternative. Our review of Ecology and the Journal of Wildlife Management found the use of null hypothesis testing to be pervasive. The estimated number of P-values appearing within articles of Ecology exceeded 8,000 in 1991 and has exceeded 3,000 in each year since 1984, whereas the estimated number of P-values in the Journal of Wildlife Management exceeded 8,000 in 1997 and has exceeded 3,000 in each year since 1994. We estimated that 47% (SE = 3.9%) of the P-values in the Journal of Wildlife Management lacked estimates of means or effect sizes or even the sign of the difference in means or other parameters. We find that null hypothesis testing is uninformative when no estimates of means or effect size and their precision are given. Contrary to common dogma, tests of statistical null hypotheses have relatively little utility in science and are not a fundamental aspect of the scientific method. We recommend their use be reduced in favor of more informative approaches. Towards this objective, we describe a relatively new paradigm of data analysis based on Kullback-Leibler information. This paradigm is an extension of likelihood theory and, when used correctly, avoids many of the fundamental limitations and common misuses of null hypothesis testing. Information-theoretic methods focus on providing a strength of evidence for an a priori set of alternative hypotheses, rather than a statistical test of a null hypothesis. This paradigm allows the following types of evidence for the alternative hypotheses: the rank of each hypothesis, expressed as a model; an estimate of the formal likelihood of each model, given the data; a measure of precision that incorporates model selection uncertainty; and simple methods to allow the use of the set of alternative models in making, formal inference. We provide an example of the information-theoretic approach using data on the effect of lead on survival in spectacled eider ducks (Somateria fischeri). Regardless of the analysis paradigm used, we strongly recommend inferences based on a priori considerations be clearly separated from those resulting from some form of data dredging.
1,848 citations