An extended stochastic response surface method for random field problems

Huang, Shupei; Kou, Xin-jian

doi:10.1007/s10409-007-0090-5

Cited by 15 publications

(6 citation statements)

References 7 publications

(10 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such realizations can be chosen at collocation points according to the SSG in Section 3.2.2, or a much simpler heuristic rule in [96], which is selected in this paper. For the approximation in (19) the rule generates 17 collocation points to form a stochastic response surface, which was very close to the target output [95].…”

Section: Stochastic Response Surface Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Robust reliability-based topology optimization under random-field material model

Pham,

Hoyle

2022

Preprint

View full text Add to dashboard Cite

This paper proposes an algorithm to find robust reliabilitybased topology optimized designs under a random-field material model. The initial design domain is made of linear elastic material whose property, i.e., Young's modulus, is modeled by a random field. To facilitate computation, the Karhunen−-Loève expansion discretizes the modeling random field into a small number of random variables. Robustness is achieved by optimizing a weighted sum of mean and standard deviation of a quantity of interest, while reliability is employed through a probabilistic constraint. The Smolyaktype sparse grid and the stochastic response surface method are applied to reduce computational cost. Furthermore, an efficient inverse-reliability algorithm is utilized to decouple the double-loop structure of reliability analysis. The proposed algorithm is tested on two common benchmark problems in literature. Finally, Monte Carlo simulation is used to validate the claimed robustness and reliability of optimized designs.

show abstract

Section: Stochastic Response Surface Methodsmentioning

confidence: 99%

“…The SRSM deals with this difficulty by approximating the output by a polynomial chaos expansion [82]. The below formulations follows [95]. The multidimensional Hermite polynomials of degree p are used in the SRSM and defined as:…”

Section: Stochastic Response Surface Methodsmentioning

confidence: 99%

Robust reliability-based topology optimization under random-field material model

Pham,

Hoyle

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The SRS method overcomes this problem by approximating the outputs by a polynomial chaos expansion (Xiu, 2010). The below formulations follows Huang and Kou (2007). The multidimensional Hermite polynomials of degree p are used in the SRS method and defined as:…”

Section: Stochastic Response Surface Methodsmentioning

confidence: 99%

Reliability-based topology optimization under random-field material model

Pham,

Hoyle

2021

Preprint

View full text Add to dashboard Cite

This paper presents an algorithm for reliabilitybased topology optimization of linear elastic continua under random-field material model. The modelling random field is discretized into a small number of random variables, and then the interested output is estimated by a stochastic response surface. A single-loop inverse-reliability algorithm is applied to reduce computational cost of reliability analysis. Two common benchmark problems in literature are used for demonstration purposes. Different values of target reliability and ranges of Young's modulus are considered to investigate their effects on resulting optimized topologies. Lastly, Monte Carlo simulation tests the proposed algorithm for correctness and accuracy.

show abstract

“…The number of truncated terms depends on the ratio between the correlation length and model geometric size 49 . Considering that soil properties commonly change gently in space, it is pointed out that this spatial variability can be captured by just a few terms in K‐L expansion 50 …”

Section: Simulation Of the Spatially Varied Soil Strength Via Rfmentioning

confidence: 99%

Efficient reliability analysis of slopes integrating the random field method and a Gaussian process regression‐based surrogate model

Zhu

Hiraishi

Pei

et al. 2020

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Efficient evaluation of slope stability is a frontier in geo‐disaster prevention fields. While many slope stability evaluation methods, ranging from deterministic to probabilistic, have been proposed, reliability methods are particularly advantageous as they can account for uncertainties during slope stability evaluation. To address the problem of the low efficiency of direct Monte Carlo simulations and overcome the defects of the traditional response surface method, in this work, a novel probabilistic procedure that integrates a Gaussian process regression‐based surrogate model and the random limit equilibrium method for slope stability evaluation while accounting for the spatial variability of soil strength is proposed. The novel Gaussian process regression‐based surrogate model is efficiently used in the Monte Carlo simulation to reduce the number of calls for direct stability analysis of a slope with spatially varied soil strength. To verify the accuracy and efficiency of the proposed procedure, it was applied to three case studies: the first one is a slope in saturated clay under undrained conditions; the second one is a slope for which the friction angle and cohesion values are cross‐correlated; and the third one is a real slope with multiple soil layers. The results obtained from the comparisons with other methods confirmed the precision and feasibility of the proposed procedure.

show abstract

An extended stochastic response surface method for random field problems

Cited by 15 publications

References 7 publications

Robust reliability-based topology optimization under random-field material model

Robust reliability-based topology optimization under random-field material model

Reliability-based topology optimization under random-field material model

Efficient reliability analysis of slopes integrating the random field method and a Gaussian process regression‐based surrogate model

Contact Info

Product

Resources

About