Estimation of failure probabilities by local approximation of the limit state function

Proppe, Carsten

doi:10.1016/j.strusafe.2007.04.001

Cited by 21 publications

(7 citation statements)

References 25 publications

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“…Therefore, in order to eliminate the fluctuations, smoothing techniques [17,29] which employ to improve the response surface methods is applied [105]. Here, the smoothing procedure has been conducted by the Moving Least Squares method [106][107][108][109]. The reliability index * is smoothed with respect to the design space and has been shown in Figure 11(a).…”

Section: Reliability Control Analysismentioning

confidence: 99%

Probability Based Survey of Braking System: A Pareto-Optimal Approach

2020

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Active brake control systems are able to use more accurate control designs on the real-time knowledge of wheel slip such as tire braking forces and external momentums. A multi-objective Pareto type optimization approach is used to evaluate the inconsistent points of the optimization design namely those of minimizing the directional deviation while achieving maximum braking forces on wheels. Moreover, the optimal target slip values defined by the braking purposes like as shorter stopping distance and stability increment by keeping the vehicle in the straight line. This gets by the control of the longitudinal and lateral slip dynamics of each wheel concerning to the road conditions. A controller is optimally brought up by manipulating optimal control law with weights of two control inputs with mathematical and probabilistic characterization. The first-passage probability of critical response levels is used to directly control the vehicle directional stability. An impressive simulation technique based on Monte Carlo method named asymptotic sampling is applied to define the required first-passage probabilities and the Latin Hypercube sampling is used to design of experiments and to cover the design space. Afterwards, a Pareto-type optimization approach is applied to a trade-off between the inconsistent points of the optimization design. The simulation is conducted by the validated vehicle model and the results are indicated that the probability-based control design is represented as a preferable braking performance in comparison with the other systems for braking in sever conditions.

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Section: Reliability Control Analysismentioning

confidence: 99%

Probability Based Survey of Braking System: A Pareto-Optimal Approach

2020

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“…In general, multivariate uniform or multivariate normal distribution is a good choice for the proposal distribution. However, the results obtained with uniform density may be sensitive with respect to the parameters of the uniform distribution (Proppe, 2008). Thus, the Gaussian proposal distribution is employed in this study.…”

Section: Generation Of Samples By Adaptive Markov Chain Simulationmentioning

confidence: 99%

“…Therefore, when constructing a surrogate model, it is wise to use a finer approximation in the likely failure region, and coarser approximation for other regions. Based on this idea, Proppe (2008) proposed a local approximation method, in which the Markov chain simulation is used to generate the training samples around the region of most interest. A moving least‐square method is then used to approximate the local feature of the limit state function.…”

Section: Introductionmentioning

confidence: 99%

“…A moving least‐square method is then used to approximate the local feature of the limit state function. The classical Markov chain simulation used by Proppe (2008) has several limitations, including the convergence issue, and the difficulty of choosing an appropriate proposal distribution and its parameters. Moreover, the moving least‐square regression method has the problem of the curse of dimensionality , that is, the efficiency of the method diminishes as the number of random variables increases.…”

Section: Introductionmentioning

confidence: 99%

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Structural Reliability Assessment by Local Approximation of Limit State Functions Using Adaptive Markov Chain Simulation and Support Vector Regression

Dai

Zhang

Wang

et al. 2012

Computer aided Civil Eng

122

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The surrogate model method is widely used in structural reliability analysis to approximate complex limit state functions. Accurate results can only be obtained when the surrogate model for the limit state function is approximated sufficiently close to the failure region. This study develops a novel local approximation method for efficient structural reliability assessment. The adaptive Markov chain simulation is utilized to generate samples in the failure region (the “region of most interest”). The support vector regression technique is then used to obtain an explicit approximation of the original complex limit state function around the region of most interest. Four examples are given to demonstrate the application and efficiencies of the proposed method.

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“…Hence, Proppe [12] recommends the use of adaptive importance sampling (AIS) instead of FORM. The basic idea is to reduce the variance ˆf p σ by introducing a weighting function h x into a Monte Carlo simulation so that the sampling points are concentrated in the failure domain f Ω .…”

Section: Adaptive Importance Samplingmentioning

confidence: 99%

A Response Surface Methodology for Probabilistic Life Safety Analysis using Advanced Fire Engineering Tools

Albrecht¹,

Hosser²

2011

Fire Safety Science - Proceedings of the 10th International Sym

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In the paper, we evaluate the reliability of a successful evacuation using a CFD fire simulation tool and an evacuation model. Obviously, it is not possible to perform Monte Carlo analysis in a reasonable amount of time because of the high computational costs. Hence, we utilize an adaptive response surface method based on moving least squares in order to compute the reliability. To further decrease the necessary number of numerical evaluations, a preceding sensitivity analysis yields information about the variance of the results and the relevance of the input parameters and hence helps to identify a surrogate model of optimal prognosis. The preliminary scan of the random space for the sensitivity analysis can also be used to obtain information about the approximate location of the design point so that further support points can be concentrated in this relevant area. Using this information for the subsequent reliability analysis leads to a faster convergence. The methodology described will be utilized to evaluate the reliability of a typical example in fire protection engineering.

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Estimation of failure probabilities by local approximation of the limit state function

Cited by 21 publications

References 25 publications

Probability Based Survey of Braking System: A Pareto-Optimal Approach

Probability Based Survey of Braking System: A Pareto-Optimal Approach

Structural Reliability Assessment by Local Approximation of Limit State Functions Using Adaptive Markov Chain Simulation and Support Vector Regression

A Response Surface Methodology for Probabilistic Life Safety Analysis using Advanced Fire Engineering Tools

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