Efficient Spreadsheet Algorithm for First-Order Reliability Method

Low, Bak Kong; Tang, Wilson H.

doi:10.1061/(asce)0733-9399(2007)133:12(1378)

Cited by 318 publications

(185 citation statements)

References 14 publications

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“…Low and Tang (2007) proposed anefficient algorithm for FORM [20], which changes the dimensionless number n i , so that Eq. (12) maybe rewritten as:…”

Section: Form Algorithmsmentioning

confidence: 99%

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Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses

Zhao

Zhang

Zhu

2017

Period. Polytech. Civil Eng.

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IntroductionThe design and performance of tunnels are usually affected by some uncertainties that can be costly and time-consuming for tunnel construction projects. Traditional empirical and deterministic design approaches do not include uncertainty in tunnel support design [1][2][3], but tend to be based on trial-anderror processes that consider safety and cost [4][5][6]. Reliabilitybased optimization (RBO) makes provision for the uncertainty of structures by adding probabilistic constraints. This is quite straight forward if the results of the reliability analysis are accurate and precise so that no question arises as to whether a given design satisfies safety requirements. The purpose of RBO is to find a balanced design that is not only economical but also reliable in the presence of uncertainty [7].Over the past few decades, numerous reliability optimization techniques have been proposed [6,8,9]. Younes and Alaa overviewed the various RBDO approaches using mathematical and finite element models with different levels of difficulties [10]. Marcos and Gerhart (2010) produced a detailed literature review on reliability-based optimization [11]. Although RBO has some evident advantages overdeterministic optimization design, it is often computationally inefficient. Response surface methodology has been applied in RBO in attempts to improve its efficiency [12,13]. Zhang et al. applied the mean first-order reliability method (MFORM) to the optimization of geotechnical systems [6]. Those methods improved the computational efficiency but decreased the accuracy of the reliability analysis, which affects the results of RBO. The selection of an optimization method is critical to RBO applications, especially for complex nonlinear optimization problems. Gen and Yun reviewed the application of soft computing methods in reliability optimization [14]. Genetic algorithms and particle swarm optimization have also been applied to RBO [7,15]. Lee et al. proposed a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by appropriately increasing the input standard deviations for efficient computation in sampling-based RBDO [16].

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“…Low and Tang (2007) proposed anefficient algorithm for FORM [20], which changes the dimensionless number n i , so that Eq. (12) maybe rewritten as:…”

Section: Form Algorithmsmentioning

confidence: 99%

“…The algorithm of Low and Tang (2007) computed the reliability index using Excel Solver in this work. Then, the ABC algorithm was used to search the design variables based on the objective function.…”

Section: Lssvm-based Relationship Between Reliability Index and Desigmentioning

confidence: 99%

Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses

Zhao

Zhang

Zhu

2017

Period. Polytech. Civil Eng.

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“…The index (βHL) can be calculated by minimizing the quadratic form (in this case an ellipsoid) subjected to the constraint that the ellipsoid just touches the surface of the failure region. The matrix formulation of the Hasofer-Lind index (β) as modified in Low and Tang (2007) is:…”

Section: Reliability Analysismentioning

confidence: 99%

Reliability analysis of municipal solid waste landfill settlements

Datta

Ering

Babu

2016

JGS Special Publication

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In the analysis and design of municipal solid waste (MSW) landfills, there are many uncertainties associated with the properties of MSW during and after MSW placement. For the analysis of time dependent settlement response of MSW, a composite compressibility model that accounts for instantaneous compression under the applied load, time dependent mechanical creep and biological decomposition is used. The objective of the present study is to demonstrate the influence of variability in model input parameters on the prediction of MSW settlement and to study the implication of different processes on settlement with an aim to assess landfill capacities and develop landfill closure plans. For this purpose regression equations based on response surface method (RSM) are developed to represent the complex behaviour of MSW. Probabilistic settlement analysis of MSW with due consideration to spatial and temporal variation of geotechnical properties is also performed. The published data on geotechnical properties of MSW are used to define the spatial variation of such parameters. The results of MSW settlements using reliability analysis framework are compared and discussed.

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“…The FORM procedure adopted in the study was given by Low and Tang (2007). The developed reliability-based charts are as shown in Figures (2) to (11).…”

Section: Reliability-based Interaction Curvesmentioning

confidence: 99%

“…Computations of design safety indices were carried as described by Low and Tang (2007). Interaction curves were plotted considering varying safety indices of the columns.…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Interaction Curves for Reinforced Concrete Design of Short Columns to Eurocode 2

Abubakar¹,

Falmata²

2015

SCEA

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The work presented in this paper examined the criteria of Eurocode 2 (EC 2) (2004) for the design of reinforced concrete short columns subjected to axial loads and bending moments using First Order Reliability method (FORM).Individual design variables of the columns were considered random with known probability distributions. Computations of design safety indices were carried as described by Low and Tang (2007). Interaction curves were plotted considering varying safety indices of the columns. The choice of a target reliability index was made to correspond with values recommended by Joint Committee on Structural Safety (JCSS, 2001). A design example was included to demonstrate the applicability of the developed reliabilitybased interaction as against the current EC 2 design charts. It was shown that considering the same loading and geometrical conditions of the column, the reliability-based procedure gave higher steel reinforcements at target safety indices of 2.5, 3.0, 4.0 and 5.0; and are safer than the deterministic design.

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Efficient Spreadsheet Algorithm for First-Order Reliability Method

Cited by 318 publications

References 14 publications

Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses

Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses

Reliability analysis of municipal solid waste landfill settlements

Reliability-Based Interaction Curves for Reinforced Concrete Design of Short Columns to Eurocode 2

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