Complex Structural Analysis and Structural Reliability

Melchers, Robert E.; Guan, X.L.

doi:10.1061/9780784408506.ch11

Cited by 3 publications

(7 citation statements)

References 21 publications

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“…When the points are obtained, for each direction vector pointing from the origin, it is possible to find the point very close to vector and consider this point as the intersection between the direction vector and the failure surface, thereby eliminating the root-searching process. The random variables that are not standard normal can be converted into standard normal random variables using Rosenblatt or Nataf transformation (Melchers, 1987). The approach is divided into two parts: (i) obtaining the lattice grids crossing the failure surface that are small enough so that the center of gravity of these grids can be considered as locating on the failure surfaces, and (ii) utilizing direction sampling to obtain the failure probability.…”

Section: Novel Approach To Conduct Reliability Analysismentioning

confidence: 99%

“…MPP is a point located on the failure surface (i.e., G(x)=0) with the minimum distance from the origin in the space of standard normal variables (referred to as the U-space). In these two methods, the original random variables are converted to independent standard normal variates using Rosenblatt or Nataf transformation (Melchers, 1987). The rational for this linear approximation is that the probability densities of the random variables located in the region affected by this approximation is small.…”

Section: Introductionmentioning

confidence: 99%

“…For sampling methods, different trials using the same number of samples can result in different probabilities of failure. The coefficient of variation of the failure probability obtained using crude MC simulation, COV(P f ), is expressed as (Melchers, 1987)…”

Section: Introductionmentioning

confidence: 99%

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Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Han

Frangopol

2023

Advances in Structural Engineering

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Multitudes of algorithms have been proposed to evaluate the failure probability of components and systems. Among all these algorithms, direction sampling is a promising one. However, a major computational effort involved in direction sampling is that for each direction sample a root-searching process needs to be conducted to obtain the distance between the origin and the failure surface, which can be computationally expensive. In addition, the failure probability along a direction is hard to obtain when the direction vector intersects the failure surface multiple times. This paper proposes a novel approach to obtain densely populated points locating on the failure surface and utilizing these points to conduct reliability analysis with direction sampling. The process of obtaining the population consists in dividing the initial hypercube space into multiple lattice grids, identifying the grids crossing the failure surface, and dividing these grids into smaller ones. The iterative division process stops when the grids cut across by the failure surface are small enough so that the centers of these grids can be considered located on the failure surface. Several numerical tests are performed to validate the applicability of the proposed approach. Through these tests, it can be concluded that for the situation where the intersection between the direction vector and the failure surface is unique, the proposed approach will lead, with high accuracy, to a failure probability. For the situation where the intersection is not unique, satisfactory estimation of failure probabilities can also be achieved using approximation methods. For high-dimensional reliability problems, clustering techniques can be utilized to reduce the computational cost.

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Section: Novel Approach To Conduct Reliability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Han

Frangopol

2023

Advances in Structural Engineering

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“…where sampling is performed in the region where failures are more likely to occur (see, e.g., [15] for the review of simulation methods in reliability analysis).…”

Section: Since the Limit State Condition Is Also Transformed Intomentioning

confidence: 99%

“…[12,2,15]), into the space U where the probability measure is defined by the probability density function f U (u) = n i=1 ϕ(u i ) being the product of the n one-dimensional standard normal PDFs of random variables U i = T i (X).…”

Section: Reliability Analysis Problem Formulationmentioning

confidence: 99%

Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures

Stocki

Tauzowski

Knabel

2008

International Journal of Crashworthiness

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Possibly the most common application of spot welding is in the automobile manufacturing industry, where it is almost universally used to weld the sheet metal car components.However, due to manufacturing inaccuracies and fatigue failures an important number of spot welds may be missing in an operational vehicle. It seems that in order to properly analyze reliability of such structures, in particular crashworthiness reliability, the spot weld failures must be considered. Representing properties of each spot weld in a stochastic model by corresponding random variables is extremely inefficient. Therefore, in the current paper an approach is proposed for handling spot weld defects in the reliability analysis by accounting for their averaged influence on a failure criterion. The approach consists in appropriate treatment of a random noise component of the limit state function. The noise results from strategy of deleting a certain number of randomly selected spot weld elements from the finite element model each time the limit state function value is computed.Dealing with noisy limit state functions in structural reliability analysis is a challenging task. The only method that seems to be insensitive to this phenomenon is Monte Carlo sampling, which for most of the applications of practical interest is prohibitively expensive. Having this in mind, in the paper a method based on the algorithm proposed by Zou et al. in [23] is investigated. The method combines the best features of the first order reliability method, the response surface technique and the importance sampling method to achieve both accuracy and efficiency. A detailed study on the reliability of thin-walled s-rail subjected to crash is performed. Some suggestions concerning modification of the original algorithm are proposed.

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Bayesian fatigue damage and reliability analysis using Laplace approximation and inverse reliability method

Guan

Jha

et al. 2011

PHM_CONF

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This paper presents an efficient analytical Bayesian method for reliability and system response estimate and update. The method includes additional data such as measurements to reduce estimation uncertainties. Laplace approximation is proposed to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability level. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A numerical example and a practical fatigue crack propagation problem with experimental data are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method is compared with simulation-based methods.

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Complex Structural Analysis and Structural Reliability

Cited by 3 publications

References 21 publications

Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures

Bayesian fatigue damage and reliability analysis using Laplace approximation and inverse reliability method

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