Reliability index for non-normal distributions of limit state functions

Seyed Hooman Ghasemi,Andrzej S. Nowak 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.62 No.3

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are nonnormal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

PSSC 거더 교량의 한계상태별 신뢰도 비교

황철성,백인열 한국구조물진단유지관리공학회 2007 한국구조물진단유지관리공학회 논문집 Vol.11 No.1

처짐, 응력 및 휨강도 한계상태에 대한 PSSC(prestressed steel and concrete)거더의 신뢰도해석을 수행한다. PSSC 거더는 시공비용과 형하공간의 확보 면에서 지간 40m이상인 교량에 적용하는데 커다란 장점을 가지고 있는 형식이다. 이 논문에서는 다양한 지간, 단면 및 설계 응력수준을 가지는 PSSC 거더를 설계하여 중앙점 처짐, 응력 및 단면 휨모멘트 해석을 수행하고, 각각에 대한 한계상태를 가정한 후, Monte-Carlo 시뮬레이션과 Rackwitz-Fiessler 방법을 이용하여 신뢰도지수를 구한다. 결과를 분석하면 PSSC 거더에 대한 처짐한계상태는 응력한계상태보다 적절하게 큰 신뢰도지수 값을 보이며, 휨강도에 대한 신뢰도지수가 매우 큼을 알 수 있다. Reliability analysis of prestressed steel and concrete(PSSC) girders is conducted for deflection, stress and moment strength limit state. PSSC girder has strong advantages in terms of construction cost and vertical clearance for the span length of over 40 meters. In this paper, example PSSC girders with different span lengths, section dimensions and design stress levels are designed and analyzed to calculate the midspan deflection, stress and the section moment strength. Deflection limit state, stress limit state and strength limit state functions are assumed and the reliability indexes are obtained by Monte-Carlo simulation and Rackwitz-Fiessler procedure. The results show that the reliability of PSSC girder for deflection limit state is appropriately higher than the stress limit state and the reliability for moment strength is significantly conservative.

A New Adaptive Importance Sampling Monte Carlo Method for Structural Reliability

Ehsan Jahani,Mohsen A. Shayanfar,Mohammad A. Barkhordari 대한토목학회 2013 KSCE Journal of Civil Engineering Vol.17 No.1

Monte Carlo simulation is a useful method for reliability analysis. But in Monte Carlo, a large number of simulations are required to assess small failure probabilities. Many methods, such as Importance sampling, have been proposed to reduce the computational time. In this paper, a new importance sampling Monte Carlo method is proposed that reduces the numbers of calculation of the limit state function. On the other hand, the proposed algorithm does not need the knowledge about the position of the design point or the shape of the limit state function. The key-idea of the proposed algorithm is that the mean of sampling density function is changed throughout the simulation. In fact, in random point generating process each point with lower absolute value of limit state function and nearer distance from space center is considered the mean of the sampling density function. Based on this, the centralization of the sampling will be on the important area.

Efficient slope reliability analysis using a surrogate-assisted normal search particle swarm optimization algorithm

Yuan Yi-li,Hu Chang-ming,LI LIANG,Hou Xu-hui 한국CDE학회 2024 Journal of computational design and engineering Vol.11 No.1

Sampling of training data is the most important step in active learning slope reliability analysis, which controls the analysis accuracy. In this study, a novel surrogate-assisted normal search particle swarm optimization (SANSPSO) was proposed to enhance the accuracy and robustness of existing methodologies. In SANSPSO, the sampling process was considered a minimum problem with an objective function defined as the absolute value of the performance function. Initiated with a normal search paradigm and supplemented by three algorithm strategies, this approach seeks to preserve the continuity of the solution while refining the algorithm’s efficacy and efficiency. To reduce computation cost, surrogate-assistance was used, in which a surrogate model substitutes the objective function in most iterations. This surrogate model evolves during the iteration process and ultimately replaces the actual performance function within Monte Carlo simulation. Finally, this study presents a comparative study with five state-of-the-art methods across four explicit problems and three engineering cases, where test data suggest that the SANSPSO methodology yields a 20% improvement in accuracy and a 30% rise in stability under different dimensional problems relative to the most efficacious of the alternate methods assessed because of the improved and more consistent prediction of limit state function. These findings substantiate the validity and robustness of the SANSPSO approach.

PSSC 합성거더 교량의 프리스트레스 효과 및 신뢰도 해석

황철성,백인열 한국구조물진단유지관리공학회 2008 한국구조물진단유지관리공학회 논문집 Vol.12 No.6

프리스트레스하중이 작용되는 강합성교인 PSSC 교량에서 프리스트레스의 효과와 단면의 변형에 따른 텐던의 변형의 영향을 밝히기 위해 교량지간 25m~45m의 최적화된 표준단면에 대해 고정하중 및 활하중이 작용될 때 합성전·후에 발생하는 부재내의 변형도 및 응력변화와 허용응력 한계상태, 항복응력 한계상태 및 강도한계상태의 단면력과 부재내의 변형도 및 응력변화를 구한다. 또한 거더의 처짐 및 응력과 휨강도를 변수로 하는 한계상태들을 가정하고 이에 대한 신뢰도 분석을 수행하였다. 표준 PSSC 교량의 경우 하중 및 저항계수를 적용하여 설계하는 미국 설계기준의 목표신뢰도지수 값이 3.5 임과 비교하면, 허용응력을 ember force, strain and stress distribution of a section are obtained for optimized standard 25m~45m PSSC composite bridge subjected to dead and live load in order to interpret the effect of prestressing and deformation of tendon. The stress and strain distribution and moment capacity are obtained for both noncomposite and composite section and for allowable stress limit state, yield limit state and strength limit state. Reliability analysis is conducted after assuming limit states for stress and flexural strength. The reliability index for standard PSSC composite bridge which is designed to satisfy the allowable stress for flexural strength are higher than 3.5 which is required reliability indexes on American code for LRFD. Reliability of PSSC girder which is designed based on allowable stress of bridge design code is high for flexural strength.

PSSC 합성거더 교량의 비선형 거동 분석 및 신뢰도 해석

황철성,백인열 한국구조물진단유지관리공학회 2008 한국구조물진단유지관리공학회 논문집 Vol.12 No.1

프리스트레스하중이 작용되는 강합성교인 PSSC 교량에서 프리스트레스의 효과와 단면의 변형에 따른 텐돈의 변형의 영향을 밝히기 위해 사하중 및 활하중이 작용될 때 합성전·후에 발생하는 부재내의 변형도 및 응력변화와 허용응력 한계상태, 항복응력 한계상태 및 강도한계상태의 단면력과 부재내의 변형도 및 응력변화를 구한다. 또한 거더의 처짐 및 응력과 휨강도를 변수로 하는 한계상태들을 가정하고 이에 대한 신뢰도 분석을 수행한다. 허용응력에 맞추어 설계한 예제 단면의 응력에 대한 신뢰도 지수가 0 부근임에 비하여, 처짐 및 휨강도에 대한 신뢰도 지수는 높은 값을 주고 있어서 도로교설계기준의 허용응력에 대하여 설계한 PSSC 거더는 처짐 및 휨강도에 대하여 높은 신뢰도를 얻을 수 있음을 알 수 있다. Member force, strain and stress distribution of a section are obtained for prestressed steel and concrete(PSSC) composite bridge subjected to dead and live load in order to interpret the effect of prestressing and deformation of tendon. The stress and strain distribution and moment capacity are obtained for both noncomposite and composite section and for allowable stress limit state, yield limit state and strength limit state. Reliability analysis is conducted after assuming limit states for deflection, stress and flexural strength. Comparing that the reliability index for stress is near 0 for example section which is designed to satisfy the allowable stress exactly, the reliability indexes for deflection and flexural strength are high. Reliability of PSSC girder which is designed based on allowable stress of bridge design code is high for deflection and flexural strength.

전산유체역학 배관 곡면 침식 모사를 통한 배관 실패 주기 분석

남정용,이용규,박건희,이건학,이원보,Nam, Chongyong,Lee, Yongkyu,Park, Gunhee,Lee, Gunhak,Lee, Won Bo 한국화학공학회 2018 Korean Chemical Engineering Research(HWAHAK KONGHA Vol.56 No.1

2000년대 이후 대두된 안전, 환경 이슈들로 인해 안전 관리는 더욱 더 중요해졌다. 하지만 안전 관리는 많은 경험적 데이터들을 요구하므로 한계점들이 많다. 안전 분야 중 하나인 배관 안전의 경우 현재 배관을 관리하는 시뮬레이션 프로그램들이 존재하지만, 배관 내부 침식에 대해서는 데이터를 얻기 힘들어 시뮬레이션에 반영이 잘 되어있지 않은 상태이다. 이러한 문제점에서 착안해 본 연구에서는 전산유체역학(CFD)을 이용하여 배관 내부의 곡면에 일어나는 침식을 모사하였고, 계산한 침식 속도를 바탕으로 한계상태함수를 이용하여 배관의 실패 주기를 분석하였다. CFD 대상 배관의 경우 여수 산업 단지에 실제로 운영되고 있는 표본을 사용하였다. DPM (Discrete Phase Model)과 부식 모델을 이용하여 CFD 결과로 $3.093mm{\cdot}yr^{-1}$ 수치의 침식 속도를 얻을 수 있었고, 이 결과를 한계상태함수에 적용한 결과 배관에 누출(leak)을 유발하는데 14.2년, 파열(burst)를 유발하는데 28.2년이라는 실패 주기를 얻어낼 수 있었다. 이러한 과정들을 통해 배관 곡면 침식이 배관 안전 진단에 유효한 실패 모드임을 도출할 수 있었다. 본 연구는 실패 연도를 구할 수 있는 방법론들을 제시하여 데이터의 한계점을 극복하고, 배관 안전 진단에 좀 더 정밀하고 발전된 방법을 제시한 것에 대해 의의를 가진다. Safety management has become even more important because of the safety and environmental issues that have arisen since the 2000s. However, the safety study requires many empirical data, so there are many limitations. In the case of pipe safety, simulation programs exist, but it is difficult to get data about the pipe internal erosion of the pipe. In this study, the erosion rate of the pipe elbow was simulated using computational fluid dynamics (CFD). Also, the failure period of the pipe was calculated by the limit state function using erosion rate. In the case of CFD pipe, a sample which is actually operated in Yeosu industrial complex was used, and the geometry and mesh formation were rationalized in terms of typical fluid dynamics simulations. Using the Discrete Phase Model (DPM) and the corrosion model, the erosion rate ($3.09227mm{\cdot}yr^{-1}$) was obtained from CFD simulations. As a result of applying the erosion rate to the limit state function, we obtained the pipe failure period value, 14.2 years to trigger a leak and 28.2 years to trigger a burst. Through these processes, we concluded that pipe erosion is one of the major failure modes. In addition to the results, this study has significance for suggesting the methodology of the pipe safety study.

부식기반 복합고장을 고려한 가스배관의 신뢰도 평가

김성준,김도현,김우식,김영표,김철만 한국품질경영학회 2019 품질경영학회지 Vol.47 No.4

Purpose: The purpose of this paper is to develop a reliability estimation procedure for the underground gas pipeline in the presence of corrosion defects. Methods: Corrosion is one of the major causes of the gas pipeline failure. Several failure forms caused by corrosion have been studied. Among them, small leak and burst are considered in this paper. The composite failure of the two is defined by limit state function, and it is expressed with pipe parameters. Given a modified corrosion dataset, in order to obtain reliability estimations, the method of first order and second moment is adopted because of its simplicity. The computation processes are conducted with MATLAB coding. Results: According to numerical results, the probability of composite failure is affected by both small leak and burst. In particular, when corrosion depth stays at low level, it is consistent with the probability of burst failure. On the contrary, it is more influenced by the small leak failure as corrosion depth is increasing. In such case, the probability of composite failure is fast approaching to the safety limit. Conclusion: By considering the composite failure, more practical predictions of remaining life can be obtained. The proposed method is useful for maintenance planning of the underground gas pipeline.

노출형 철골기둥-베이스 플레이트 접합부의 내력평가를 위한 수치적 연구

이광호,유영찬,최기선,구혜진,유미나 한국구조물진단유지관리공학회 2016 한국구조물진단유지관리공학회 논문집 Vol.20 No.5

철골기둥-베이스 플레이트 접합부의 파괴유형은 베이스 플레이트 압축면과 인장면의 휨파괴, 앵커볼트의 인장파괴, 뽑힘, 전단파 괴, 그리고 콘크리트 기초파괴 및 철골기둥의 소성힌지발생에 따른 파괴이다. 본 연구에서는 핀접합 또는 강접합으로 가정하여 설계되는 노출 형 철골기둥-베이스 플레이트 접합부가 받을 수 있는 모멘트의 크기를 구하기 위하여, 한계상태 함수를 이용하여 철골기둥-베이스 플레이트 접합부의 휨성능 및 파괴유형을 예측하고 실험결과와 비교하였다. 한계상태함수를 이용하여 노출형 철골기둥-베이스 플레이트 접합부의 휨 성능을 비교적 정확히 예측할 수 있는 범위는 축력이 있는 경우, 앵커볼트의 항복 또는 철골기둥의 항복으로 판별되었을 때이며 축력이 없는 경 우, 베이스 플레이트의 항복으로 판별된 경우이다. 파괴유형까지 같이 고려할 경우, 축력이 있으며 앵커볼트의 항복으로 판별된 경우에만 한계 상태함수의 사용이 가능하다. The failure modes of steel column-base plate connection arranged on the basis of AISC Design Guide-#1 and -#10 are base plate tension and compression side flexural yielding, yielding, pull-out and shear failure of anchor rod, concrete crushing in concrete footing and steel column yielding. The bending moment capacity and failure mode in this connection are predicted using limit-state function and we compare these results and test result. In the case that thickness of base plate is relatively thick, bending moment capacity and failure mode in steel column-base plate connection accurately predicted. But in the case that thickness of base plate is relatively thin and axial force do not exist, prediction of failure mode in this connection is somewhat inaccurate.

Reliability analysis of steel cable-stayed bridges including soil-pile interaction

Jin Cheng,Xiao-luan Liu 국제구조공학회 2012 Steel and Composite Structures, An International J Vol.13 No.2

An efficient and accurate algorithm is proposed to evaluate the reliability of cable-stayed bridges accounting for soil-pile interaction. The proposed algorithm integrates the finite-element method and the response surface method. The finite-element method is used to model the cable-stayed bridge including soilpile interaction. The reliability index is evaluated based on the response surface method. Uncertainties in the superstructure, the substructure and load parameters are incorporated in the proposed algorithm. A long span steel cable-stayed bridge with a main span length of 1088 m built in China is considered as an illustrative example. The reliability of the bridge is evaluated for the strength and serviceability performance functions. Results of the study show that when strength limit states for both girder and tower are considered, soil-pile interaction has significant effects on the reliability of steel cable-stayed bridges. Further, a detailed sensitivity study shows that the modulus of subgrade reaction is the most important soil-pile interaction-related parameter influencing the reliability of steel cable-stayed bridges.