On the bounds for structural system reliability

The potential applications and challenges of uncertain data mining have recently attracted interests from researchers. Most uncertain data mining algorithms consider aleatory (random) uncertainty of data, i.e. these algorithms require that exact probability distributions or confidence values are attached to uncertain data. However, knowledge about uncertainty may be incomplete in the case of epistemic (incomplete) uncertainty of data, i.e. probabilities of uncertain data may be imprecise, coarse, or missing in some applications. The paper focuses on uncertain data which miss probabilities, specially, value-uncertain discrete objects which miss probabilities (for short uncertain objects). On the other hand, classification is one of the most important tasks in data mining. But, to the best of our knowledge, there is no method to learn Naïve Bayesian classifier from uncertain objects. So the paper studies Naïve Bayesian classification of uncertain objects. Firstly, the paper defines interval probabilities of uncertain objects from probabilistic cardinality point of view, and bridges the gap between uncertain objects and the theory of interval probability by proving that interval probabilities are F-probabilities. Secondly, based on the theory of interval probability, the paper defines conditional interval probabilities including the intuitive concept and the canonical concept, and the conditional independence of the intuitive concept. Further, the paper gives a formula to effectively compute the intuitive concept. Thirdly, the paper presents a Naïve Bayesian classifier with interval probability parameters which can handle both uncertain objects and certain objects. Finally, experiments with uncertain objects based on UCI data show satisfactory performances.

Studies on the theory of structural system reliability includes identifi- cation of main the failure modes and calculation of inclusive failure probabilities for the structural system. The efficient and accurate identification of failure modes in structural systems is difficult and represents a key focus for research in sys- tem reliability. The fundamental theory of the branch and bound algorithm for stage critical strength is reviewed in this paper. Some deficiencies in this method are highlighted. Corresponding approaches to overcome these deficiencies are pro- posed. Calculated system reliability solutions to the classical model, a truss with 10 elements, indicate that the improvement measures proposed in this paper increase the efficiency of recognising the main failure modes of the structural system, and are readily validated. The outcomes of this type of benchmark analysis suggest that the proposed methodology may be capable of representing a suitable basis for the structural system reliability analysis of complex truss-like structures, includ- ing transmission towers. Using the proposed approach, the principal failure modes and system reliability of a transmission tower are calculated. Based on practical engineering considerations, effective methods to improve this structural system re- liability are proposed.

Reliability of corrosion-damaged steel structures using interval probability theory

In most mechanical and structural systems, a certain amount of uncertainty exists in both strength and load values. The uncertainty of these values must be taken into consideration when quantifying the safety and reliability of a system. Fuzzy set theory has been used for the description and analysis of such systems. A means for comparing fuzzy strength and load values is needed to determine the safety and reliability of fuzzy mechanical and structural systems. The concepts of fuzzy bounds and subsethood are used here to define a safety index for mechanical or structural systems based on fuzzy load and strength values. Similarly, a criticality index for fracture damage assessment is defined based on fuzzy stress intensity factors. The concept of a fuzzy factor of safety is also introduced. The proposed safety and criticality indices and the fuzzy factor of safety could provide useful measures for rating designs in terms of strength-based reliability and damage tolerance. The application of the proposed measures in the assessment of damage as reported by online structural damage detection systems is also suggested.

Failure-mode importance measures in structural system with multiple failure modes and its estimation using copula

Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

The present paper studies the reliability-based structural optimization of the civil engineering in the seismic zone. The objective is to minimize the sum of construction material cost and the expected failure loss under severe earthquake, which is obtained by the sum of the products of the failure probability and its failure losses for the important failure modes. The set of constraints includes the deterministic constraints, and the constraints based on structural reliability—the reliability index constraints of structural element failure for the serviceability state under minor earthquake and the failure probability of the structural system for the ultimate limit state under severe earthquake. By introducing the load roughness index, the structural system reliability computation under hazard load can be greatly simplified, which is approximately determined by its weakest failure mode. Finally, the numerical example of high rising shear RC frame is calculated.

An equivalent linear method for structural system reliability with nonlinear safety margins

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

Over the last four decades, structural system reliability (SSR) has been an active research topic as engineering systems including structures and infrastructure networks become more complex, and the computational power has been remarkably advanced. Among many efforts to advance SSR technologies, the research by Prof. Armen Der Kiureghian in the early 2000s is considered to have built critical pathways to the development of next-generation SSR methods by revisiting the topic of SSR. As demonstrated in Der Kiureghian (Structural system reliability, revisited. Proceedings, 3rd ASRANet International Colloquium, Glasgow, UK, July 10-12, 2006), his research efforts led to new insights and perspectives on critical topics of structural system reliability. This has encouraged researchers to perform a variety of research activities to develop new SSR technologies that can address challenges and needs in risk management of real-world systems. This chapter provides a review on such efforts to reload the research community with SSR technologies, which were made possible by the revisit. The chapter reviews the following SSR methods: linear programming bounds, matrix-based system reliability method, sequential compounding method, cross-entropy-based adaptive importance sampling, selective recursive decomposition algorithm, branch-and-bound employing system reliability bounds, and genetic-algorithm-based selective search for dominant system failure modes. For each of the reviewed methods, their main concepts, applications and follow-up research activities are presented along with discussions on merits, remaining challenges, and future research needs.

This paper develops a model validation method in the case of the full scale tests for the system model are infeasible. The Bayesian network with uncertain conditional probability parameters is used to represent the relations between the large computational model and its smaller modules. The interval probability theory is adopted to extrapolate the posterior probability of the interested variable in the uncertain Bayesian network. An interval valued Bayes factor is obtained to be the metric for model validation.

Network arch bridges are extremely slender bridge structures with a very efficient load-carrying structure. This configuration can carry loads that are several times greater than traditional tied-arch bridges with vertical hangers. These bridges are seen as an attractive structure due to their slenderness, which potentially also make them vulnerable to global system buckling. Thus, the buckling reliability of network arch bridges is here further investigated with emphasis on geometric and load uncertainties. In principle, the reliability of structural systems can be accurately predicted by standard Monte Carlo simulation. This method has several attractive features for structural system reliability. One is that the system failure criterion is easy to control, almost irrespective of the complexity of the system. However, the computational cost involved may be prohibitive for highly reliable structural systems if standard Monte Carlo simulation is used. In this chapter a recently developed enhanced Monte Carlo method has been applied for calculating the reliability. This method drastically reduced the computational burden of the standard Monte Carlo approach and thereby made it practically feasible to estimate the reliability of the bridge against buckling.

Dominant mechanisms in stochastic plastic frames

System reliability of timber structures with ductile behaviour

This study deals with an economic analysis of structural systems on using a reliability-based design method. Although the expected total cost which is composed of the initial cost and the cost of failure for the structural system has been investigated, it is crucial to consider the annual prediction cost with life cycle cost (LCC) during the life duration. It is also important to evaluate the cost not only on structural failure but also on designer's faults. Furthermore, it is necessary that the cost of the reliability test is taken into account in determining the expected total cost because uncertainties of parameters are strongly dependent upon the quality control or material test. In this paper, a new expected total cost concept which includes the cost mentioned above is proposed. In the proposed formulation, an optimization problem for economic evaluation during the life duration with the capital rate of interest and rate of price fluctuations can be solved by applying the present currency and annual prediction concepts. For a comparative evaluation, from the numerical analyses of a truss bridge structure, it is pointed out that not only optimization by present value but also that by annual value is useful for decision making in practical design.