Advanced First Order Reliability Method Research Articles

Performance-Based Reliability of ASME Piping Design Equations

In this paper, we present an exploratory study on the evaluation of reliability levels associated with the piping design equations specified by ASME Boiler and Pressure Vessel (BPV) Code, Section III. Probabilistic analyses are conducted to evaluate reliability levels in straight pipe segments with respect to performance functions that characterize the different failure criteria using advanced first-order reliability method (AFORM). One important failure criterion considered in this study relates to the plastic instability which forms the basis of piping design equations for emergency and faulted load level conditions as defined in the ASME code. The code-specified definition of plastic instability is based on the evaluation of a collapse moment which is defined using the moment–curvature curve for a particular component. In this study, we use elastic-perfectly plastic, bilinear kinematic hardening, and multilinear kinematic hardening stress–strain curves to develop closed-form expressions for the moment–curvature relationship in a straight unpressurized pipe. Both the pressurized and the unpressurized loading conditions are considered. The closed-form reliability is evaluated using Monte Carlo simulation because of the complex nature of the closed-form expression. The reliability values are calculated with respect to the maximum allowable moment specified by the code design equations that use deterministic safety factors.

An evaluation method to predict progressive collapse resistance of steel frame structures

In the current work, a probabilistic assessment method of a steel framed building under abrupt removal of a column due to catastrophic events is developed. A multi-story steel framed model taking into account the influence of catenary effect has been analyzed. Uncertainties in the structural variables are incorporated in the probabilistic simulation approach. Based on the changes of component internal energy, the progressive collapse sensitivity to abrupt removal of a column has been investigated. Besides, a simplified beam damage model is proposed to analyze the energies absorbed and dissipated by structural beams under large deflections. In addition, the correlation incorporating catenary action between bending moment and axial force in a beam during the whole deformation development process is studied. With the methodologies adopted for progressive collapse assessment under removal of a column, a deterministic method has been developed, framed within the Advanced First Order Reliability Method (AFORM). A robustness index (RI) is proposed to evaluate the structural robustness performance based on the acceptable probability of global failure and structural collapse probability.

Sensitivity Analysis by Parametric Study of Load Factor for a Concrete Box Girder Railway Bridge Using Limit State Design

Reliability based limit state design method is replacing traditional deterministic designs such as allowable stress design and/or ultimate strength design methods in world trends. European design code(Eurocode) has adopted limit state design, and Korea road bridge design standard has also recently been transferred to limit state design method. In this trend, Korea railroad design standard is also preparing for adopting the same design concept. While safety factors are determined empirically in traditional design, load combinations as well as load factors are determined by solving limit state equations. General partial safety factors are evaluated by using AFORM(Advanced First Order Reliability Method) in the reliability based limit state design method. In this study sensitivity analysis is carried out for a dead load factor and a live load factor. Relative precisions of the dead load and the live load factors are discussed prior to the AFORM analysis. Furthermore the sectional forces of design and the material quantities required by two different design methods are compared for a PSC box girder railway bridge.

Reliability analysis of marine risers with narrow and long corrosion defects under combined loads

A marine riser, one of the most important components of offshore oil/gas transportation, needs to be designed to eliminate the risks caused by complex ocean environments, platform displacement and internal corrosion, etc. In this study, a new analytical-numerical assessment approach is proposed in order to quantitatively investigate the reliability of internally corroded risers under combined loads including axial tension and internal pressure. First, an analytical solution of the limit state function of intact risers under combined loads is obtained, which is further modified by the non-dimensional corrosion depth (d/t) for the risers with a narrow and long corrosion defect. The relationship between d/t and limited internal pressure is obtained by finite element analysis and nonlinear regression. Through an advanced first-order reliability method (HL-RF) algorithm, reliability analysis is performed to obtain the failure probability, the reliability index and the sensitivity. These results are further verified by Monte-Carlo importance sampling. The proposed approach of reliability analysis provides an accurate and effective way to estimate the reliability of marine risers with narrow and long corrosion defects under combined loads.

개선된 일계이차모멘트법을 적용한 메트릭스 구조물 신뢰도 해석

The wing is a framework composed chiefly of skin, spars, ribs and can be simplified by matrix structure. In this paper, a displacement reliability of matrix structure is analysed by AFORM(Advanced First Order Reliability Method) and applicability is assessed.

Real-time unsaturated slope reliability assessment considering variations in monitored matric suction

A reliability-based slope stability assessment method considering fluctuations in the monitored matric suction was proposed for real-time identification of slope risk. The assessment model was based on the limit equilibrium model for infinite slope failure. The first-order reliability method (FORM) was adopted to calculate the probability of slope failure, and results of the model were compared with Monte-Carlo Simulation (MCS) results to validate the accuracy and efficiency of the model. The analysis shows that a model based on Advanced First-Order Reliability Method (AFORM) generates results that are in relatively good agreement with those of the MCS, using a relatively small number of function calls. The contribution of random variables to the slope reliability index was also examined using sensitivity analysis. The results of sensitivity analysis indicate that the effective cohesion c\' is a significant variable at low values of mean matric suction, whereasmatric suction (ua-uw) is the most influential factor at high mean suction values. Finally, the reliability indices of an unsaturated model soil slope, which was monitored by a wireless matric suction measurement system, were illustrated as 2D images using the suggested probabilistic model.

이중 쐐기형 초음속 흡입구의 압력회복률에 대한 신뢰성 기반 최적설계

본 연구에서는 이중 쐐기형 초음속 흡입구의 압력회복률에 대한 신뢰성 최적설계를 수행하였다. 주어진 설계영역에서 다양한 설계변수의 불확실성을 고려하여 흡입구의 압력회복률을 확률적으로 모델링하였으며, 목적함수로는 흡입구 항력을 선정하였다. 신뢰성 최적설계에 앞서 전산해석비용을 줄이기 위해 실험계획법과 크리깅 모델을 이용하여 적절한 설계공간을 탐색하였다. 신뢰성 기법의 정확도 검증을 위해 몬테카를로 시뮬레이션을 수행하였으며 이 결과를 신뢰성 기법 결과가 잘 추종함을 확인하였다. 신뢰성 기반 최적설계를 수행한 결과, 설계변수의 불확실성을 고려함으로써 시스템의 신뢰성을 확보하였다. 시스템 설계의 다양한 불확실성을 고려하기 위해서는 신뢰성 기반 최적설계가 유용한 접근방법임을 확인할 수 있었다. In this study, RBDO(Reliability Based Design Optimization) was performed for a supersonic double-wedge inlet. By considering uncertainty of design with given design space, the pressure recovery was transformed into the probabilistic constraint while the inlet drag was considered as a deterministic objective function. To save computational analysis cost and to search good design space, Latin-Hypercube design of experiment and the Kriging model were incorporated and then RBDO was performed. Monte-Carlo simulation was performed to verify the accuracy of AFORM(Advanced First Order Reliability Method). It was found that AFORM result agreed very well with the Monte-Carlo simulation result. The system reliability was guaranteed by considering uncertainty of the design variables. In case of considering diverse uncertainty of system design, RBDO was found to be useful.

Prediction Approach for Corrosion Fatigue Life of Aircraft Structure Based on Probabilistic Fracture Mechanics

The corrosion, corrosion fatigue and fracture failure process of aircraft structure is directly concerned with combined effect of many factors, such as load, material characteristics, corrosive environment and so on. The process is very complicated, and there is typical randomness. Based on probabilistic fracture mechanics, with consideration of the limitation of the conventional probabilistic approaches for prediction of corrosion fatigue life of aircraft structure at present, and a new reliability approach under loading spectrum was proposed, in which corrosion damage and fatigue crack damage was united as a same damage parameter. Short crack and long crack growth behavior was separately discussed, and influence of short crack aspect ratio on structure life was discussed. The Advanced First-Order Reliability Method, Importance Sampling Method and iteratively advanced Second-Order Reliability Method were used to compute the fracture failure probability. The results show that the model is feasible. By sensitivity analysis of random parameter, the important parameter was obtained, which helped to monitor the structure fatigue life.

크리깅 메타모델을 이용한 신뢰도 계산

In this study, the new method for reliability estimation is proposed using kriging metamodel. Kriging metamodel can be determined by appropriate sampling range and sampling numbers because there are no random errors in the Design and Analysis of Computer Experiments(DACE) model. The first kriging metamodel is made based on widely ranged sampling points. The Advanced First Order Reliability Method(AFORM) is applied to the first kriging metamodel to estimate the reliability approximately. Then, the second kriging metamodel is constructed using additional sampling points with updated sampling range. The Monte-Carlo Simulation(MCS) is applied to the second kriging metamodel to evaluate the reliability. The proposed method is applied to numerical examples and the results are almost equal to the reference reliability.

다분야 통합해석 시스템의 효율적인 신뢰성 해석기법 연구

다분야 통합해석 시스템의 신뢰성 해석에 대한 기존의 연구들은 대부분 비선형 최적화 기법을 기반으로 하고 있다. 이들은 다분야 통합최적설계 프레임워크를 이용하여 신뢰성을 직접 해석하기 때문에 효율적인 AFORM기법을 적용하는 것이 불가능하다. 본 논문은 AFORM기법을 적용한 다분야 통합시스템의 순차적 신뢰성 해석기법(SARAM)을 제안한다. 이를 위해 신뢰성 해석과 다분야 통합시스템의 해석(MDA)을 분리하고, 순차적으로 배열하여, 되풀이구조를 가지는 해석구조를 구성하였다. 제안된 방법의 효율성은 계산량, 정확도, 그리고 동시 수행기능의 관점에서 평가하였다. 3개의 다분야 통합시스템 예제를 계산한 결과, 제안된 기법은 정확도를 보장하면서 기존의 방법에 비해 우수한 계산효율을 보였다. Existing methods have performed the reliability analysis using nonlinear optimization techniques. This is mainly due to the fact that they directly apply Multidisciplinary Design Optimization(MDO) frameworks to the reliability analysis formulation. Accordingly, the reliability analysis and the Multidisciplinary Analysis(MDA) are tightly coupled in a single optimizer, which hampers utilizing the recursive and function-approximation based reliability analysis methods such as the Advanced First Order Reliability Method(AFORM). In order to utilize the efficient reliability analysis method under multidisciplinary analysis systems, we propose a new strategy named Sequential Approach on Reliability Analysis under Multidisciplinary analysis systems(SARAM). In this approach, the reliability analysis and the MDA are decomposed and arranged in a sequential manner, making a recursive loop. The efficiency of the SARAM method was verified using three illustrative examples taken from the literatures. Compared with existing methods, it showed the least number of subsystem analyses over other methods while maintaining accuracy.

Sequential approach to reliability analysis of multidisciplinary analysis systems

The goal of this study is to present an efficient strategy for reliability analysis of multidisciplinary analysis systems. Existing methods have performed the reliability analysis using nonlinear optimization techniques. This is mainly due to the fact that they directly apply multidisciplinary design optimization (MDO) frameworks to the reliability analysis formulation. Accordingly, the reliability analysis and the multidisciplinary analysis (MDA) are tightly coupled in a single optimizer, which hampers the use of recursive and function-approximation-based reliability analysis methods such as the first-order reliability method (FORM). In order to implement an efficient reliability analysis method for multidisciplinary analysis systems, we propose a new strategy named sequential approach to reliability analysis for multidisciplinary analysis systems (SARAM). In this approach, the reliability analysis and MDA are decomposed and arranged in a sequential manner, making a recursive loop. The key features are as follows. First, by the nature of the recursive loop, it can utilize the efficient advanced first-order reliability method (AFORM). It is known that AFORM converges fast in many cases and requires only the value and the gradient of the limit-state function. Second, the decomposed architecture makes it possible to execute concurrent subsystem analyses for both the reliability analysis and MDA. The concurrent subsystem analyses are conducted by using the global sensitivity equation (GSE). The efficiency of the SARAM method was verified using two illustrative examples taken from the literatures. Compared with existing methods, it showed the least number of subsystem analyses over the other methods while maintaining accuracy.

Assessing uncertainty in subsurface solute transport: efficient first-order reliability methods

Due to the heterogeneity of natural groundwater systems, any quantitative description of aquifer hydraulic properties is subject to uncertainty. Consequently, prediction of groundwater contaminant transport is also subject to uncertainty. Stochastic approaches to transport simulation quantify this uncertainty in terms of random variables and processes. An important practical consideration in the application of such methods is their large computational cost. In recent years the first-order reliability method (FORM) has been introduced as a possible technique for obtaining stochastic results with low computational expense. Specifically, the implementation of FORM known as advanced FORM (AFORM) has been shown to produce reasonably accurate results when applied to simple problems. However, recently published results indicate that the computational burden of AFORM can equal, or even exceed, that of Monte Carlo simulation when applied to groundwater contamination problems with a large number of variables. If FORM is to be a viable alternative, the computational costs of the method must be lowered. In this work we propose two alternative implementations of FORM that have a higher computational efficiency. The primary numerical difficulty that arises in AFORM is locating the linearization point, a procedure that requires the solution of a non-linearly constrained optimization problem. We minimize this difficulty by zoning spatially variable aquifer parameters and by defining a new linearization point that can be found more easily. The new approaches are shown to produce results that are comparable to those obtained with AFORM when applied to a one-dimensional transport problem. Future work will be aimed at generalizing the procedures described herein.