P.H.A.J.M. van Gelder

An overview of quantitative risk measures for loss of life and economic damage.

A comprehensive overview of methods to quantify and limit risks arising from different sources is still missing in literature. Therefore, a study of risk literature was carried out by the authors. This article summarises about 25 quantitative risk measures. A risk measure is defined as a mathematical function of the probability of an event and the consequences of that event. The article focuses mainly on risk measures for loss of life (individual and societal risk) and economic risk, concentrating on risk measurement experiences in The Netherlands. Other types of consequences and some international practices are also considered. For every risk measure the most important characteristics are given: the mathematical formulation, the field of application and the standard set in this field. Some of the measures have been used in a case study to calculate the flood risks for an area in The Netherlands.

The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

Abstract The paper evaluates the effectiveness of the method of L-moments for estimating parameters of the Pareto distribution model of peaks over a sufficiently high threshold, and compares its performance against a widely used method of de Haan (de Haan L. Extreme value statistics. In: Galambos J, Lechner J, Simin E, editor. Extreme value theory and applications, vol. 1. 1994. p. 93–122). Monte Carlo simulations and actual wind speed data collected at various stations in the United States have been utilized in this study. In the de Haan method, the first two moments of peaks of log-transformed data are used for the parameter estimation, whereas the L-moment method utilizes linear combinations of expectations of order statistics of peaks in the original data. Despite the procedural differences, the paper shows that the de Haan and two L-moments based estimates of the tail shape parameter are in fairly close agreement in simulated data as well as in the US wind speed data. Furthermore, higher order estimates of the shape parameter are obtained using the L-skewness of peaks data. Such estimates appear to provide a more stable upper bound, which can be useful in identifying meaningful values of design quantiles.

Societal Risk and the Concept of Risk Aversion

It seems generally accepted that the FN-curve is a fairly accurate description of the societal risk. However in the communication with the public and representative decisionmakers a schematisation of the FN-curve to one or two numbers may bring certain advantages. Various measures like Potential loss of Life, the area under the FN-curve, the Risk Integral etc. are proposed in the literature. Although the formulae look distinctly different at first sight a more thorough inspection reveals, that all schematisations contain as building blocks the two familiar statistical moments of the FN-curve, the expected value of the number of deaths E(N) and the standard deviation σ(N). In the paper the linear combination E(N) + k.σ(N) is proposed as a simple risk averse measure of the societal risk.

Evaluation of tunnel safety: towards an economic safety optimum

The aim of this paper is to propose a method for the evaluation of tunnel safety using probabilistic risk assessment. The framework includes three criteria; personal-, societal- and economic risk. The use of personal and societal risk is becoming more and more widespread. There are however, still some difficulties in using the economic risk criterion. As a first step towards economic risk optimisation, the cost effectiveness of addition and removal of safety measures in tunnels is investigated. Finally, the application of the three proposed criteria is further discussed for some tunnelling projects currently underway in the Netherlands.

Time-dependent reliability analysis of flood defences

This paper describes the underlying theory and a practical process for establishing time-dependent reliability models for components in a realistic and complex flood defence system. Though time-dependent reliability models have been applied frequently in, for example, the offshore, structural safety and nuclear industry, application in the safety-critical field of flood defence has to date been limited. The modelling methodology involves identifying relevant variables and processes, characterisation of those processes in appropriate mathematical terms, numerical implementation, parameter estimation and prediction. A combination of stochastic, hierarchical and parametric processes is employed. The approach is demonstrated for selected deterioration mechanisms in the context of a flood defence system. The paper demonstrates that this structured methodology enables the definition of credible statistical models for time-dependence of flood defences in data scarce situations. In the application of those models one of the main findings is that the time variability in the deterioration process tends to be governed the time-dependence of one or a small number of critical attributes. It is demonstrated how the need for further data collection depends upon the relevance of the time-dependence in the performance of the flood defence system.

Risk-Based Maintenance of a Cross-Country Petroleum Pipeline System

This paper proposes a data-driven approach in determining an optimal inspection interval for a petroleum pipeline system. The approach accounts for the determination of both the probability of failure and its associated consequences. The probability of failure is estimated by fitting the historical data of failure of the pipeline into either a homogenous Poisson process or non-homogenous Poisson process (power law). The analysis of historical data reveals the Poisoneous form that gives better description of the failure process. The consequences of failure are calculated in terms of economic loss, environmental damage and loss of human life. Both the failure probability and consequences are utilized to estimate the total loss of an operating pipeline system. A risk based integrity maintenance optimization of the pipeline is achieved by minimizing the economic loss, while taking the human risk and maintenance budget as constraints. The proposed framework is utilized in the maintenance planning of a very long cross country petroleum pipeline system. The outcomes are robust and well validated. The framework can be applied to any engineering system that requires inspection and maintenance planning.

Linking Three Gorges Dam and downstream hydrological regimes along the Yangtze River, China

The magnitude of anthropogenic influence, especially dam regulation, on hydrological system is of scientific and practical value for large river management. As the largest dam in the world by far, Three Gorges Dam (TGD) is expected to be a strong evidence on dam impacts on downstream hydrological regime. In this study, statistical methods are performed on the pre- and post-TGD daily hydrological data at Yichang, Hankou, and Datong stations to detect the daily, monthly, yearly, and spatial fluctuations in river hydrology along the Yangtze River during the period of 2000–2013. It is found that TGD makes a significant hydrological variation along the Yangtze River following the dam operation since 2003. Specifically, the daily discharge and water level are gathered to normal event ranges with less extreme events than before 2003. Both maximum and minimum daily water levels at the study stations have decreased due to TGD-induced riverbed incision. The operation of TGD shifts the maximum monthly discharge and water level from August to July at Yichang station. The significance of TGD effect on discharge and water level relationship presents spatial variation. The rating curves at upstream reach experience the most significant effects with a substantial upward shift, while those at lower reach only suggest slight modification. Of the potential drivers considered in this study, dam regulation is responsible for the changes in downstream river hydrology. Moreover, the tributary and adjoining riparian lakes of the Yangtze River contribute to weaken the effect of TGD on downstream hydrological behavior.

Robust detection of discordant sites in regional frequency analysis

[1] The discordancy measure in terms of the sample L-moment ratios (L-CV, L-skewness, L-kurtosis) of the at-site data is widely recommended in the screening process of atypical sites in the regional frequency analysis (RFA). The sample mean and the covariance matrix of the L-moments ratios, on which the discordancy measure is based, are not robust against outliers in the data, and consequently, this measure can be strongly affected by the discordant sites present in the region. We propose to replace the classical mean and covariance matrix estimates by their robust alternatives on the basis of the minimum covariance determinant estimator. The performance of the classical and robust measures for discordant sites identification is assessed in a series of Monte Carlo simulation experiments within the framework of the RFA. The simulation study shows that the robust discordant measure outperforms the classical one and is consistent with the heterogeneity measure H. Thus we recommend its use as a tool for discordant sites detection and formation of homogeneous regions in RFA.

Risk- and Simulation-Based Optimization of Channel Depths: Entrance Channel of Cam Pha Coal Port

We present a simulation model for long-term optimal design of channel depths in which the risk of ship grounding due to wave impacts can be assessed for every ship transit. This new model includes four main components: (1) an eXponential probability law for the number of ship departures; (2) a parametric model of the wave-induced ship motions; (3) modeling effects of tidal variations on the channel performance; and (4) a Poisson probability law for the grounding model in a single random ship departure. A key procedure of the simulation process is to define a minimum underkeel clearance allowance for ship entrance and simultaneously determine downtimes that correspond to an acceptable grounding risk for a specified ship and a generated environment condition. The final results derived from the simulation model can be considered as the key parameters in analysis and selection of an optimal depth. The model has been applied to the entrance channel of Cam Pha Coal Port, Vietnam, as a case study.

Dynamic bounds coupled with Monte Carlo simulations

For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.