First-order Second-moment Approximation Research Articles

Comparison of First-Order and Second-Order Derived Moment Approaches in Estimating Annual Runoff Distribution

AbstractThe first-order second-moment approximation (FOSM) has been proposed to estimate the annual runoff (Q) distribution from the statistical information of annual precipitation (P), annual pote...

Accuracy of First-Order Second-Moment Approximation for Uncertainty Analysis of Water Distribution Systems

AbstractThis study performs an extensive investigation to explore critical factors that affect the accuracy of the first-order second-moment (FOSM) approximation when it is used as a nodal pressure...

Probability risk assessment of landslides: A case study at Finneidfjord

Probabilistic risk assessments are increasingly being considered the most appropriate framework for engineers to systematically base decisions on hazard mitigation issues. This paper aims to show the advantages of a quantitative risk assessment by application to a historical case study. The generalized integrated risk assessment framework has been applied retrospectively to a submarine landslide that occurred in 1996 near the village of Finneidfjord in northern Norway. Over 1 million cubic metres of predominantly quick clay was displaced. Even though it was triggered underwater on the embankment of the Sørfjord, the retrogressive nature of the slide resulted in it encroaching 100–150 m inland. The triggering mechanism is believed to have been the placement of fill, from a nearby tunnelling project, on the foreshore of the embankment. This paper is a retrospective quantitative evaluation of the risk to the neighbouring houses, the persons in those houses, and the persons in open spaces caused by the placement of increasing levels of embankment fill. A probabilistic approach, making use of second-moment modelling and first-order second-moment approximation is adopted. It aims to demonstrate the advantages of this type of risk assessment in understanding complex and integrated hazards, particularly those in populated environments.

Scenario-based probabilistic estimation of direct loss for geohazards

A general probabilistic framework for the estimation of scenario-based direct loss induced by a geohazard on the physical environment is proposed. The approach allows explicit consideration of the uncertainties that exist in the parameters and models which are representative of the intensity of the hazardous event, in the vulnerability of the physical environment to the geohazard and in post-event restoration costs. Such parameters, which are user-defined, are modelled as second-moment random variates. The propagation of model and parameter uncertainties is addressed through first-order second-moment approximation. The second-moment perspective allows efficient quantification of the uncertainty in estimates of vulnerability and direct loss. An overview of the main current challenges encountered in loss estimation methods for geohazards is provided, as well as a series of reference definitions for subsequent use in the methodology. A general description of the sources of uncertainty relevant to loss estimation is made available.

A Global Robust Optimization Using Kriging Based Approximation Model

The current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies but it may produce uncontrollable uncertainties. To increase manageability of such uncertainties, the Taguchi method, reliability-based optimization and robust optimization are commonly being used. The main functional requirement of a mechanical system is to obtain the target performance with maximum robustness. In this research, a design procedure for global robust optimization is developed using kriging and global optimization approaches. Robustness is determined by kriging model to reduce a number of real functional calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust optimum of a surrogate model. As the postprocess, the global optimum is further refined by applying the first-order second-moment approximation method. Mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

Response variability of an SSI system with uncertain structural and soil properties

A non-classical modal-analysis-based formulation including an additional random vector to represent the system uncertainties is used to quantify the effect of uncertain soil–foundation and superstructure properties on structural response for seismically excited soil–structure interacting (SSI) systems. It is shown that the pertinent equations are essentially the same as those for only soil parameter uncertainty and very similar to those for only structural parameter uncertainty. The method is implemented here by using an effective Gaussian quadrature method to find accurate frequency-domain stochastic response properties of the SSI systems. Numerical examples of multiple-degree-of-freedom SSI systems with quite large parameter uncertainty illustrate that the unconditional spectral density of the structural response is often very similar to that in the absence of uncertainty. However, deterministic variations of parameters may cause large changes in the response spectral density. In particular, when the parameter uncertainty is not negligible, there may be significant uncertainty about the spectral density of structural response near the system's resonant frequencies. It is shown that the effects of uncertainty about multiple parameters can generally be adequately and efficiently approximated by applying a simple first-order second-moment approximation to the results for single-parameter uncertainty.

Probabilistic analysis of rock slope stability with first-order approximation

Based on the theory of probability, the probabilistic analysis of slope stability is conducted. Equations for the estimation of slope failure probability are first derived using direct integrations. However, the complexity of the integrations is formidable. In order to overcome the limitation of the direct integration, the first-order second-moment approximation of the slope failure probability is employed for more complex slope stability problems. The study indicates that the distributions of parameter values play a significant role in slope stability, which can not be disclosed by the conventional methods of stability analysis. Greater dispersiveness of the parameter values will lead to a different probability of failure, although the factor of safety estimated by conventional methods remains the same if the mean values of the parameters are unchanged. By taking consideration of the distributions of the parameters, the probability model can provide more reliable designs of rock slopes.

Probabilistic analysis of underground excavation stability

Abstract The deterministic description of rock excavation stability with a safety factor is frequently insufficient and, sometimes, misleading. The applications of the probabilistic analysis to determine the likelihood of a rock excavation failure have been proposed by many researchers. The probabilistic analysis will lead to a better understanding of excavation stability and provide more complete information. The difficulty in estimating the failure probability of a underground excavation is the complexity of mathematics involved. In order to overcome this limitation, the first-order second-moment approximation of the failure probabilities is utilized. The technique simplifies the computation significantly and allows for the analysis of relatively complex stability problems. Two underground excavation stability problems are investigated in the study, including the stability of a horizontally layered rock roof and the stability of a underground rock prism. The study indicates that the distributions of parameter values play a significant role in the excavation stability, which can not be disclosed by the conventional methods of stability analysis. Greater dispersiveness of the parameter values will lead to a different probability of failure, although the factor of safety estimated by conventional methods remains the same if the mean values of the parameters are unchanged.

On the application of probabilistic fracture mechanics to the reliability and inspection of pressure vessels

A probabilistic fracture mechanics model was developed to analyse the failure probability of a typical high power density reactor pressure vessel. The major causes for the nuclear reactor pressure vessel failure include fatigue, corrosion fatigue and brittle failure. All these causes are greatly affected by the stress loading conditions, material properties (aged by neutron damage), and defects embedded in the structure. Both an analytical first-order second-moment approximation and a hybrid methodology were employed in this study. In addition to the static scatter of the pre-existing cracks and material properties, a random walk model based on the operating history was introduced to represent the random occurrence of the abnormal transient stresses. The failure mode is defined as the brittle failure caused by a critical crack, meaning the stress intensity factor around a critical crack exceeding the fracture toughness of the pressure vessel material. Through a sample study on a typical high power density nuclear power plant, it was found that the vessel failure probability is about 4 × 10 −4 at the 40th year of operation and the failure rate is in the order of 5 × 10 −6 per vessel per year, which had reasonable agreement with the value of 10 −4−10 −6 as reported based on real-world statistics. In addition to the failure probability caused by fatigue crack growth, the reliability of a Low Temperature Overpressure incident was also evaluated.

Reliability analysis of wind-sensitive structures

The theoretical background of practical structural reliability methods encompassing numerical integration, approximate methods and simulation techniques is reviewed in the context of wind-excited structures. Their relative merits, shortcomings and limitations are addressed from the standpoint of their accuracy and computational efficiency. Quantitative reliability estimates of a concrete chimney are made, using different analysis procedures. Multiple potential failure modes are represented by the exceeding of the ultimate moment capacity at any level of the chimney height. The general bounds on the system failure probability are expressed in terms of the failure probability of the individual modes. The narrower bounds are established based on the existing theory by taking into account not only the failure probability of the individual modes, but also the joint failure probabilities in any two modes. Based on the findings of this study, it is suggested that the advanced first-order second-moment approximation and the simulation methods, which combine the Monte Carlo technique with variance reduction techniques, may provide accurate results for practical reliability analysis of wind-excited structures.

Comments on “first-order second-moment approximation in reliability of structural systems: critical review and alternative approach”, by Krzysztof Dolinski

Comments on “first-order second-moment approximation in reliability of structural systems: critical review and alternative approach”, by Krzysztof Dolinski

First-order second-moment approximation in reliability of structural systems: Critical review and alternative approach

The objective of the paper is to present and discuss the methods originated from the first-order second-moment approximation that are commonly used in the reliability analysis of structural systems. The approach is formulated as an optimization problem. The consequences of this formulation and some objections concerning the methods are investigated and illustrated on the examples. The lack of uniqueness and some difficulties with error estimation are considered as the main disadvantages of the approach. An alternative approach is given for the independent random variables. The approach yields the upper and lower bounds for the structural reliability. Its application is presented in the case of the linear conditions of structural failure. It is shown that the bounds remain sometimes a sole verification of the correctness of the first-order second-moment approximation.