Won-Hee Kang

Network reliability analysis of complex systems using a non-simulation-based method

Civil infrastructures such as transportation, water supply, sewers, telecommunications, and electrical and gas networks often establish highly complex networks, due to their multiple source and distribution nodes, complex topology, and functional interdependence between network components. To understand the reliability of such complex network system under catastrophic events such as earthquakes and to provide proper emergency management actions under such situation, efficient and accurate reliability analysis methods are necessary. In this paper, a non-simulation-based network reliability analysis method is developed based on the Recursive Decomposition Algorithm (RDA) for risk assessment of generic networks whose operation is defined by the connections of multiple initial and terminal node pairs. The proposed method has two separate decomposition processes for two logical functions, intersection and union, and combinations of these processes are used for the decomposition of any general system event with multiple node pairs. The proposed method is illustrated through numerical network examples with a variety of system definitions, and is applied to a benchmark gas transmission pipe network in Memphis TN to estimate the seismic performance and functional degradation of the network under a set of earthquake scenarios.

Further development of matrix-based system reliability method and applications to structural systems

In efforts to estimate the risk and reliability of a complex structure or infrastructure network, it is often required to evaluate the probability of a ‘system’ event, i.e. a logical function of multiple component events. Its sensitivities with respect to design parameters are also useful in decision-making processes for more reliable systems and in reliability-based design optimisation. The recently developed, matrix-based system reliability (MSR) method can compute the probabilities of general system events including series, parallel, cut-set and link-set systems, and their parameter sensitivities, by use of efficient matrix-based procedures. When the component events are statistically dependent, the method transforms the problem into an integral in the space of random variables which cause the statistical dependence, termed as the common source random variables (CSRVs). One can identify CSRVs by fitting a generalised Dunnett-Sobel (DS) model to a given correlation coefficient matrix. This article introduces two further developments of the MSR method: First, for efficient evaluation, it is proposed that the integral in the CSRV space can be performed using the first- or second-order reliability methods. Second, a new matrix-based procedure is developed to compute the sensitivity of the system failure probability with respect to the parameters that affect the correlation coefficients between the components. In addition, an extensive parametric study is performed to investigate the effect of the error in fitted generalised DS model on the accuracy of the estimates by the MSR method. The further developed MSR method is demonstrated by two examples: system reliability analysis of a three-storey Daniels system structure, and finite element reliability analysis of a bridge pylon system.

A rapid reliability estimation method for directed acyclic lifeline networks with statistically dependent components

Lifeline networks, such as transportation, water supply, sewers, telecommunications, and electrical and gas networks, are essential elements for the economic and societal functions of urban areas, but their components are highly susceptible to natural or man-made hazards. In this context, it is essential to provide effective pre-disaster hazard mitigation strategies and prompt post-disaster risk management efforts based on rapid system reliability assessment. This paper proposes a rapid reliability estimation method for node-pair connectivity analysis of lifeline networks especially when the network components are statistically correlated. Recursive procedures are proposed to compound all network nodes until they become a single super node representing the connectivity between the origin and destination nodes. The proposed method is applied to numerical network examples and benchmark interconnected power and water networks in Memphis, Shelby County. The connectivity analysis results show the proposed methods reasonable accuracy and remarkable efficiency as compared to the Monte Carlo simulations.

Evaluation of Multinormal Integral and Sensitivity by Matrix-based System Reliability Method

In efforts to estimate the system-level risk and reliability of an engineering system, it is often required to evaluate multinormal integrals efficiently and accurately. Their sensitivities with respect to design parameters are also important in decision-making processes for more reliable systems. This paper proposes to use the recently developed matrix-based system reliability (MSR) method for evaluating multinormal integrals and their sensitivities with respect to design parameters. While most of the existing multinormal calculation methods are applicable to parallel or series system events only, the proposed approach can compute the probabilities of any general system events. The correlation coefficient matrix of the normal random variables is fitted by a generalized Dunnett-Sobel correlation model. This transforms the multinormal problem into an integral in the space of statistically independent standard normal random variables, termed as common source random variables (CSRVs). If many CSRVs are needed for accurate representation of the given correlation coefficient matrix, first- and second-order reliability methods (FORM/SORM) can be used for efficient numerical integration. The paper demonstrates the proposed approach through numerical examples.

Assessment of seismic risk and importance measures of interdependent networks using a non simulation-based method

Infrastructure networks are critical backbones of urban society that support virtually every economic and societal activity. Recent events have shown that these systems are susceptible to natural and man-made hazards such as earthquakes, hurricanes, and terrorist attacks, and have the potential risk of creating cascading failures due to their interdependent nature. Therefore, analyzing the vulnerability of these complex interacting infrastructures under potential hazards is critical for the development of risk mitigation strategies and effective response and recovery. To assess the seismic risk on the infrastructure, non simulation-based methods have the merit of rapid risk assessment for infrastructures and the associated decision making, because they are efficient in estimating sensitivities and conditional probabilities which are often used for identifying critical components. This article presents a non simulation-based method to assess the system reliability of complex interdependent infrastructure networks under seismic hazards. Also proposed are methods to compute importance measures to gauge the relative contribution of components to system reliability. A case study is presented to demonstrate the proposed approach that can efficiently estimate the reliability of a network system, the effect of interactions between two networks, and the importance measures of components.

Design and Experimental Investigations of a Vibration Based Wireless Measurement System for Bridge Cable Tension Monitoring

Cables are important components of a cable-stayed bridge, and the cable tension is a crucial factor in determining the overall condition assessment of a cable-stayed bridge structure. Based on the vibration frequency method, a wireless monitoring system for bridge cable tension force monitoring has been investigated and experimentally validated through laboratory and field tests in this paper. The vibration frequency-based method for cable tension measurement, the design method of the wireless measurement system with embedded identification algorithm, the test procedures, and relevant results are discussed, respectively. The developed wireless monitoring system is verified by a bridge model test in the laboratory and full-scale bridge tests in the field. Field experimental results show that the relative error between this wireless monitoring system and the reference wired system values is within 0.5%. Therefore, the developed wireless measurement system can provide an estimation of cable tension with sufficient accuracy. Moreover, the developed system is highly integrated and convenient in terms of installation and dismantling, and it has potential applicability prospects in emergency for the quick detection of cable tension.

Computer-Aided Analysis of Flow in Water Pipe Networks after a Seismic Event

This paper proposes a framework for a reliability-based flow analysis for a water pipe network after an earthquake. For the first part of the framework, we propose to use a modeling procedure for multiple leaks and breaks in the water pipe segments of a network that has been damaged by an earthquake. For the second part, we propose an efficient system-level probabilistic flow analysis process that integrates the matrix-based system reliability (MSR) formulation and the branch-and-bound method. This process probabilistically predicts flow quantities by considering system-level damage scenarios consisting of combinations of leaks and breaks in network pipes and significantly reduces the computational cost by sequentially prioritizing the system states according to their likelihoods and by using the branch-and-bound method to select their partial sets. The proposed framework is illustrated and demonstrated by examining two example water pipe networks that have been subjected to a seismic event. These two examples consist of 11 and 20 pipe segments, respectively, and are computationally modeled considering their available topological, material, and mechanical properties. Considering different earthquake scenarios and the resulting multiple leaks and breaks in the water pipe segments, the water flows in the segments are estimated in a computationally efficient manner.

Safety factors for the resistance of steel sections

AbstractThe performance of the design equations given in the Australian Bridge and Steel Standards AS 5100.6 and AS 4100 have been evaluated when structural steel is used that conforms with the tolerances within the following overseas manufacturing standards: EN 10034, KS D 3502, JIS F 3192, JIS A 5526, ASTM A6/A6M-07 and AS/NZS 5100.6. From a consideration of the experimental results from full-scale bending tests, reliability analyses according to AS 5104:2005/IS0 2394:1998 and EN 1990 were conducted. From these analyses, a capacity factor of between 0.93 and 0.95 was determined for beams that have compact, not-compact and non-compact cross-sections when a target reliability index of 3.04 was used, based on the standardised FORM (first order reliability method) sensitivity factor for resistance given in AS 5104:2005/IS0 2394:1998. This finding demonstrates that the capacity factor of 0.90 given in AS 4100 and AS 5100.6 for beams in bending is on the conservative side for steel sections complying with ove...

HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

This study proposes an algorithm to solve inverse reliability problems with a single unknown parameter. The proposed algorithm is based on an existing algorithm, the inverse first-order reliability method (inverse-FORM), which uses the Hasofer Lind Rackwitz Fiessler (HLRF) algorithm. The initial algorithm analyzed in this study was developed by modifying the HLRF algorithm in inverse-FORM using the Broyden-Fletcher-Goldarb-Shanno (BFGS) update formula completely. Based on numerical experiments, this modification was found to be more efficient than inverse-FORM when applied to most of the limit state functions considered in this study, as it requires comparatively a smaller number of iterations to arrive at the solution. However, to achieve this higher computational efficiency, this modified algorithm sometimes compromised the accuracy of the final solution. To overcome this drawback, a hybrid method by using both the algorithms, original HLRF algorithm and the modified algorithm with BFGS update formula, is proposed. This hybrid algorithm achieves better computational efficiency, compared to inverse-FORM, without compromising the accuracy of the final solution. Comparative numerical examples are provided to demonstrate the improved performance of this hybrid algorithm over that of inverse-FORM in terms of accuracy and efficiency.

Reliability analysis for load factors in steel bulk material handling structures with respect to AS4324.1

Abstract AS 4324.1 Mobile equipment for continuous handling of bulk materials Part 1: General requirements for the design of steel structures allows the adoption of both permissible stress design (PSD) and limit state design (LSD) philosophies for the design of structural steel members. To assess the cost-safety balance of the load and capacity factors provided in AS 4324.1 for steel column sections subjected to concentrated axial compression and bi-axial bending, this study estimates the reliability of steel columns based on AS 4324.1, considering both PSD and LSD methods based on a statistical rationale. In addition, this study estimates the reliability of steel columns when using the newly proposed load factors for LSD design to ensure that they improve the performance of the current code in terms of the optimal cost-safety balance. This study incorporates the Monte Carlo simulations to consider the uncertainties in design parameters, loads and resistance and load prediction models. As representative examples, five load combinations (I, II/1, III/6, III/8 and III/10) for two design scenarios are considered for an 1850t reclaimer and a 400t stacker. For load combinations I and II/1, the reliability indices that are achieved by the current safety margins of AS 4324.1 for LSD and PSD methods are relatively high compared with the target reliability index, β = 3.8. For load combinations III/6, III/8 and III/10, reliability indices are close to the target reliability if the existing capacity factors and the factors of safety are used. The proposed capacity factors enable one to achieve a consistent safety level for all load combinations. Based on these results, it is recommended to update the current safety margins with the proposed values to ensure consistent safety levels especially, for load cases III/6, III/8 and III/10.