Reliability Assessment Based on the Concept of Failure Surface Frontier

2005 ◽  
Author(s):  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
High Efficiency ◽  
Limit State ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Test Results ◽  
Limit States ◽  
Failure Region ◽  
Novel Concept ◽  
Quadratic Approximations ◽  
State Functions

This work proposes a novel concept of failure surface frontier (FSF), which is a hyper-surface consisting of the set of the non-dominated failure points on the limit states of a given failure region. FSF better represents the limit state functions for reliability assessment than conventional linear or quadratic approximations on the most probable point (MPP). Assumptions, definitions, and benefits of FSF are discussed first in detail. Then, a discriminative sampling based algorithm was proposed to identify FSF, from which reliability is assessed. Test results on well known problems show that reliability can be accurately estimated with high efficiency. The algorithm is also effective for problems of multiple failure regions, multiple most probable points (MPP), or failure regions of extremely small probability.

Failure Surface Frontier for Reliability Assessment on Expensive Performance Function

2006 ◽  
Vol 128 (6) ◽  
pp. 1227-1235 ◽  
Author(s):  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
State Of The Art ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Test Results ◽  
Approximation Model ◽  
Limit States ◽  
Performance Function ◽  
Failure Region ◽  
Novel Concept ◽  
Quadratic Approximations

This work proposes a novel concept of failure surface frontier (FSF), which is a hyper-surface consisting of the set of non-dominated failure points on the limit states of a failure region. Assumptions, definitions, and benefits of FSF are described first in detail. It is believed that FSF better represents the limit states for reliability assessment (RA) than conventional linear or quadratic approximations on the most probable point. Then, a discriminative sampling based algorithm is proposed to identify FSF, based on which the reliability can be directly assessed for expensive performance functions. Though an approximation model is employed to approximate the limit states, it is only used as a guide for sampling and a supplementary tool for RA. Test results on well-known problems show that FSF-based RA on expensive performance functions achieves high accuracy and efficiency, when compared with the state-of-the-art results archived in literature. Moreover, the concept of FSF and proposed RA algorithm are proved to be applicable to problems of multiple failure regions, multiple most probable points, or failure regions of extremely small probability.

A Radial-Based Centralized Kriging Method for System Reliability Assessment

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Yao Wang ◽  
Dongpao Hong ◽  
Xiaodong Ma ◽  
Hairui Zhang
Keyword(s):  
System Reliability ◽  
High Efficiency ◽  
Reliability Assessment ◽  
System Failure ◽  
Kriging Method ◽  
Limit States ◽  
Density Region ◽  
High Probability Density ◽  
Failure Region ◽  
Computationally Intensive

System reliability assessment is a challenging task when using computationally intensive models. In this work, a radial-based centralized Kriging method (RCKM) is proposed for achieving high efficiency and accuracy. The method contains two components: Kriging-based system most probable point (MPP) search and radial-based centralized sampling. The former searches for the system MPP by progressively updating Kriging models regardless of the nonlinearity of the performance functions. The latter refines the Kriging models with the training points (TPs) collected from pregenerated samples. It concentrates the sampling in the important high-probability density region. Both components utilize a composite criterion to identify the critical Kriging models for system failure. The final Kriging models are sufficiently accurate only at those sections of the limit states that bound the system failure region. Its efficiency and accuracy are demonstrated via application to three examples.

An Integrated Performance Measure Approach for System Reliability Assessment

2014 ◽  
Author(s):  
Zequn Wang ◽  
Pingfeng Wang
Keyword(s):  
System Reliability ◽  
Limit State ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Performance Measure ◽  
State Function ◽  
Analysis Tool ◽  
Performance Measure Approach ◽  
Performance Function ◽  
Integrated Performance

This paper presents an integrated performance measure approach (iPMA) for system reliability assessment considering multiple dependent failure modes. An integrated performance function is developed to envelope all component level failure events, thereby enables system reliability approximation by considering only one integrated system limit state. The developed integrated performance function possesses two critical properties. First, it represents exact joint failure surface defined by multiple component failure events, thus no error will be induced due to the integrated limit state function in system reliability computation. Second, smoothness of the integrated performance on system failure surface can be guaranteed, therefore advanced response surface techniques can be conveniently employed for response approximation. With the developed integrated performance function, the maximum confidence enhancement based sequential sampling method is adopted as an efficient component reliability analysis tool for system reliability approximation. To furthermore improve the computational efficiency, a new constraint filtering technique is developed to adaptively identify active limit states during the iterative sampling process without inducing any extra computational cost. One case study is used to demonstrate the effectiveness of system reliability assessment using the developed iPMA methodology.

Reliability-based assessment of flexural timber components with ultimate deflection performance

2020 ◽  
Vol 23 (16) ◽  
pp. 3469-3480
Author(s):  
Pan-Pan Tian ◽  
Hong-Xing Qiu ◽  
Zhou-Zhou Liang ◽  
Jian Sun
Keyword(s):  
Probabilistic Model ◽  
Reliability Index ◽  
Limit State ◽  
Main Beam ◽  
Live Load ◽  
Limit States ◽  
Live Loads ◽  
Deflection Criteria ◽  
State Functions

Assessing the deflection performance of existing flexural timber components is of paramount importance for making better, reliable, and substantiated decisions. The main purpose of this article is to propose four-level reliability index β and deflection criteria for updating existing flexural timber components (main beam, joist, purlin, and rafter) based on long-term deflection probabilistic model, limit state functions, and load combinations. The long-term deflection probabilistic model was obtained through creep deflection and short-term deflection model. Limit state functions were considered to be ultimate limit states of load-bearing capacity. In addition, four-level reliability index β were calculated by three live loads (residential live load, office live load, and snow live load) and seven load ratios ρ (0.2, 0.3, 0.5, 1.0, 2.0, 3.0, and 4.0). The results of proposed four-level criterion were illustrated with the reliable safety assessment for flexural timber components.

A Monte Carlo Reliability Assessment for Multiple Failure Region Problems Using Approximate Metamodels

2007 ◽  
Author(s):  
Ramon C. Kuczera ◽  
Zissimos P. Mourelatos ◽  
Michael Latcha
Keyword(s):  
Monte Carlo ◽  
Limit State ◽  
Reliability Assessment ◽  
Random Variables ◽  
Principal Component ◽  
Sampling Technique ◽  
Engineering Systems ◽  
Limit States ◽  
Global And Local ◽  
Actual Limit

An efficient Monte Carlo reliability assessment methodology is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit, nonlinear limit-state functions, with correlated or non-correlated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels which serve as indicators to determine the failure and safe regions. Samples close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions which can be in general disjoint, and local metamodels of the actual limit states are generated for each transition region. A Monte Carlo simulation calculates the probability of failure using the global and local metamodels. A robust maximin “space-filling” sampling technique is used to construct the metamodels. Also, a principal component analysis addresses the problem dimensionality making therefore, the proposed method attractive for problems with a large number of random variables. Two numerical examples highlight the accuracy and efficiency of the method.

On Estimating the Reliability of Multiple Failure Region Problems Using Approximate Metamodels

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Ramon C. Kuczera ◽  
Zissimos P. Mourelatos
Keyword(s):  
Limit State ◽  
Estimation Method ◽  
Sampling Technique ◽  
Computational Effort ◽  
Reliability Estimation ◽  
Accurate Estimation ◽  
Limit States ◽  
Failure Region ◽  
Sample Points ◽  
Global And Local

In a complex system it is desirable to reduce the number of expensive function evaluations required for an accurate estimation of the probability of failure. An efficient reliability estimation method is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit nonlinear limit state functions with correlated or noncorrelated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels, which serve as indicators to determine the failure and safe regions. Sample points close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions, which can be, in general, disjoint, and local metamodels of the actual limit states are generated for each transition region. Importance sampling generates sample points only in the identified transition and failure regions, thus, allowing the method to focus on the areas near the failure region and not expend computational effort on the sample points in the safe domain. A robust maximin “space-filling” sampling technique is used to construct the metamodels. Two numerical examples highlight the accuracy and efficiency of the method.

Reliability Analysis of Compliant Offshore Tower Under Earthquake Loads

2009 ◽  
Author(s):  
Syed Danish Hasan ◽  
Nazrul Islam ◽  
Khalid Moin
Keyword(s):  
Seismic Analysis ◽  
Limit State ◽  
Reliability Assessment ◽  
Failure Surface ◽  
Probabilistic Methods ◽  
State Function ◽  
Limit State Function ◽  
Universal Joint ◽  
Sea Bed ◽  
Water Particle Kinematics

Articulated offshore tower with universal joints in the intermediate level leads to a multi-hinged configuration that can be used for a variety of deep water application. They are flexibly linked to the sea-bed by a universal joint and comply with the oscillatory environmental loads causing large fluctuating seismic demands at the articulating joints. This paper investigates the dynamic response and the reliability assessment of articulated joint (s) of such structures under seismic sea environment. The analysis includes the influence of sea bed shaking on the water-particle kinematics by using Californian earthquakes. The sea state is characterized by DNV version of Pierson Moskowitz spectrum. The dynamic equation of motion is derived using Lagrangian approach, taking into the account the nonlinearities associated with structure and loads. A limit-state function for seismic demand for a universal joint has been derived. Using the derived limit-state function and the responses obtained after time-domain seismic analysis, reliability assessment of the articulated joint has been carried out, using efficient MPP-based probabilistic methods. Design point, important for probabilistic design of articulated joint, located on the failure surface has been worked out. Stochastic sensitivity analysis has been performed to assess the relative importance of design parameter on the stochastic response of articulated joint.

Combined flexure and torsion of I-shaped steel beams

1989 ◽  
Vol 16 (2) ◽  
pp. 124-139 ◽  
Author(s):  
Robert G. Driver ◽  
D. J. Laurie Kennedy
Keyword(s):  
Limit State ◽  
Bending Moment ◽  
Phase Behaviour ◽  
Inelastic Interaction ◽  
Steel Beams ◽  
Ultimate Limit State ◽  
Second Phase ◽  
Design Standards ◽  
Limit States ◽  
Interaction Diagram

Design standards provide little information for the design of I-shaped steel beams not loaded through the shear centre and therefore subjected to combined flexure and torsion. In particular, methods for determining the ultimate capacity, as is required in limit states design standards, are not presented. The literature on elastic analysis is extensive, but only limited experimental and analytical work has been conducted in the inelastic region. No comprehensive design procedures, applicable to limit states design standards, have been developed.From four tests conducted on cantilever beams, with varying moment–torque ratios, it is established that the torsional behaviour has two distinct phases, with the second dominated by second-order geometric effects. This second phase is nonutilizable because the added torsional restraint developed is path dependent and, if deflections had been restricted, would not have been significant. Based on the first-phase behaviour, a normal and shearing stress distribution on the cross section is proposed. From this, a moment–torque ultimate strength interaction diagram is developed, applicable to a number of different end and loading conditions. This ultimate limit state interaction diagram and serviceability limit states, based on first yield and on distortion limitations, provide a comprehensive design approach for these members. Key words: beams, bending moment, flexure, inelastic, interaction diagram, I-shaped, limit states, serviceability, steel, torsion, torque, ultimate.

Anchor rod forces and maximum bending moments in sheet pile walls using the factored strength approach

1996 ◽  
Vol 33 (5) ◽  
pp. 815-821 ◽  
Author(s):  
A B Schriver ◽  
A J Valsangkar
Keyword(s):  
Water Pressure ◽  
Limit State ◽  
Bending Moment ◽  
Ultimate Limit State ◽  
Sheet Pile ◽  
Limit States ◽  
Working Stress ◽  
Geotechnical Design ◽  
Ultimate Limit State Design ◽  
Sheet Pile Wall

Recently, the limit states approach using factored strength has been recommended in geotechnical design. Some recent research has indicated that the application of limit states design using recommended load and strength factors leads to conservative designs compared with the conventional methods. In this study the influence of sheet pile wall geometry, type of water pressure distribution, and different methods of analysis on the maximum bending moment and achor rod force are presented. Recommendations are made to make the factored strength design compatible with conventional design. Key words: factored strength, working stress design, ultimate limit state design, anchored sheet pile wall, bending moment, anchor rod force.

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