Over the recent decades, Topology Optimization (TO) has become an important tool in the design and analysis of mechanical structures. Although structural TO is already used in many industrial ...applications, it needs much more investigation in the context of vehicle crashworthiness. Indeed, crashworthiness optimization problems present strong nonlinearities and discontinuities, and gradient-based methods are of limited use. The aim of this work is to present an in-depth analysis of the novel Kriging-Assisted Level Set Method (KG-LSM) for TO. It is based on an adaptive optimization strategy using the Kriging surrogate model and a modified version of the Expected Improvement (EI) as the update criterion, which allows for embedding opportune constraints. The adopted representation using Moving Morphable Components (MMCs) significantly reduces the dimensionality of the problem, enabling an efficient use of surrogate-based optimization techniques. A minimum compliance cantilever beam test case of different dimensionalities is used to validate the presented strategy, as well as identify its potential and limits. The method is then applied to a 2D crash test case, involving a cylindrical pole impact on a rectangular beam fixed at both ends. Compared to the state-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the KG-LSM optimization algorithm demonstrates to be efficient in terms of convergence speed and performance of the optimized designs.
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•An active failure-pursuing Kriging modeling method is proposed for time-dependent reliability analysis.•An equivalent stochastic process transformation is developed to form a uniform high ...probability density region.•An active failure-pursing strategy is proposed to identify the most valuable samples.•Correlation-based screening and space partition are applied to represent the sensitive local regions.
Some time-dependent reliability analysis methods use surrogate models to approximate the implicit limit state functions of complex systems. However, the performance of these methods is usually affected by the situations that the used models are not accurate and some samples have no significant contribution to the accuracy improvement. To construct a more suitable model for reliability analysis, this work proposes an active failure-pursuing Kriging modeling method to identify the most valuable samples for improving the accuracy of the predicted failure probability. On the one hand, a global predicted failure probability error index calculated through the real-time reliability result is proposed to pursue the sensitive sample and the corresponding local region that is most likely to maximize the improvement of the accuracy of the reliability result. A fault-tolerant scheme is further applied to ensure the accuracy of the failure-pursuing process. On the other hand, the correlation-based screening and space partition strategy is developed to describe the local regions and avoid the clustering of samples. In each iteration, the Kriging model is updated with the exploitation of new sample from the local regions around the sensitive samples. Additionally, an equivalent stochastic process transformation is developed to form a uniform high probability density sampling space. The results of three cases demonstrate the efficiency, accuracy and stability of the proposed method.
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Arsenic (As) and antimony (Sb) often co-occur in floodplain depositional environments that are contaminated by legacy mining activities. However, the distribution of As and Sb throughout floodplains ...is not uniform, adding complexity and expense to management or remediation processes. Identifying floodplain morphology predictor variables that help quantify and explain As and Sb spatial distribution on floodplains is useful for management and remediation. We developed As and Sb risk maps estimating concentration and availability at a coastal floodplain wetland impacted by upper-catchment mining. Significant predictors of As and Sb concentrations included i) distance from distributary channel-wetland intersection and ii) elevation. Distance from channel explained 53 % (P < 0.01) and 28 % (P < 0.01), while elevation explained 42 % (P < 0.01) and 47 % (P < 0.01) of the variability in near-total Sb and As respectively. As had a higher extractability than Sb across all tested soil extractions, suggesting that As is more environmentally available. As and Sb dry mass estimates to a depth of 0.1 m scaled to the lower coastal Macleay floodplain ranged from 113–192 tonnes and 14–24 tonnes respectively. Landscape-scale modelling of metalloid distribution, informed by morphology variables, presented here may be a useful framework for the development of risk maps in other regions impacted by contaminated upper-catchment sediments.
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•We examine drivers of As and Sb spatial variability in floodplain wetland sediments.•Wetland elevation and distance from channel help to predict As and Sb distribution.•Integrating these landscape morphology components aids model prediction accuracy.•As is more environmentally available than Sb based on selective soil extractions.
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4.
Rare Event Estimation Using Polynomial-Chaos Kriging Schöbi, R; Sudret, B; Marelli, S
ASCE-ASME journal of risk and uncertainty in engineering systems. Part A, Civil Engineering,
06/2017, Volume:
3, Issue:
2
Journal Article
Open access
AbstractStructural reliability analysis aims at computing the probability of failure of systems whose performance may be assessed by using complex computational models (e.g., expensive-to-run ...finite-element models). A direct use of Monte Carlo simulation is not feasible in practice, unless a surrogate model (such as kriging, also known as Gaussian process modeling) is used. Such metamodels are often used in conjunction with adaptive experimental designs (i.e., design enrichment strategies), which allows one to iteratively increase the accuracy of the surrogate for the estimation of the failure probability while keeping low the overall number of runs of the costly original model. This paper develops a new structural reliability method based on the recently developed polynomial-chaos kriging (PC-kriging) approach coupled with an active learning algorithm known as adaptive kriging Monte Carlo simulation (AK-MCS). The problem is formulated in such a way that the computation of both small probabilities of failure and extreme quantiles is unified. Different convergence criteria for both types of analyses are discussed, and in particular the original AK-MCS stopping criterion is shown to be overconservative. A multipoint enrichment algorithm is elaborated, which allows the addition of several points in each iteration, thus fully exploiting high-performance computing architectures. The proposed method is illustrated on three examples, namely a two-dimensional case that allows underlining of the advantages of this approach compared to standard AK-MCS. Then the quantiles of the eight-dimensional borehole function are estimated. Finally the reliability of a truss structure (10 random variables) is addressed. In all cases, accurate results are obtained with approximately 100 runs of the original model.
Macro-scale computations of shocked particulate flows require closure laws that model the exchange of momentum/energy between the fluid and particle phases. Closure laws are constructed in this work ...in the form of surrogate models derived from highly resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that if the input data is noise-free, the DKG method converges monotonically; convergence is less robust in the presence of noise. The MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. This work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows.
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Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined ...as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging.
•The Tellus and LUCAS databases were used to explore soil spatial variability.•Elevation was the most influential covariate to model target soil properties.•Spatial maps produced from kriging ...techniques showed high accuracy.•Generated maps would be useful for site-specific management options evaluation.•A strong spatial structure was found for the fractal parameters.
Understanding how topography affects the distribution of soil properties is essential in the management of landscape hydrology and establishment of sustainable soil management practices. This study investigated the impact of topography on the variation in particle size distribution, coarse fragments, and soil bulk density using different interpolation techniques and fractal analysis. It also evaluated the performance of various interpolation techniques in predicting and characterizing the distribution of soil properties. The study was conducted using data from 620 samples extracted from the Tellus and LUCAS databases in Eglinton and Castlederg counties, Northern Ireland. Terrain attributes were obtained at a 30 × 30 m resolution using a global digital elevation model (GDEM) reintroduced to the Universal Transverse Mercator (UTM) projection. Interpolation analyses were conducted using inverse distance weighting (IDW), ordinary kriging (OK), block kriging (BK) and co-kriging (CK). Among the terrain attributes, elevation was the most influential covariate for CK. In addition, fractal analysis was conducted to assess the self-similarity of the soil properties. Prediction accuracy of the interpolation methods was evaluated using the Nash-Sutcliffe efficiency, mean absolute error, index of agreement, and Pearson correlation coefficient. Spatial maps produced from the kriging techniques showed high accuracy in the prediction of soil particle size distribution and bulk density. The use of elevation as an auxiliary variable was successful in producing accurate soil property distribution maps with CK. The fractal parameters showed that the soil properties had short range spatial variability, anti-persistent nature, and strong spatial structure. Additionally, the fractal dimension was strongly correlated with sand, silt and clay contents and bulk density, and weakly correlated with the coarse fragments.
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The present paper discusses a new methodology to assess stress-cycle fatigue design using meta-modelling. Research on its application is presented for offshore wind turbine towers. Kriging models are ...used to surrogate the complex time-domain stress-cycle fatigue assessment that demands multiple evaluations in the design phase.
The presented development highlights the importance of having a notion of improvement for the problem of meta-modelling. Literature shows that, when meta-modelling complex engineering problems, the idea of improvement is not always considered. To tackle the problem of assessing fatigue in the design phase, a learning criterion is introduced. It has the particularity of relating to the physical description of the stress-cycle fatigue. Results of the proposed criterion are compared with meta-modelling using a Latin hypercube sampling, and with the standard design approach that bins environmental conditions for fatigue design calculations. A full 1 year validation sample is used to study convergence.
As surrogate models for stress-cycle fatigue, Kriging models significantly decrease the efforts of the design procedure. Results showed that computational efforts can be reduced consistently by a factor of 5–8 without compromising accuracy. This may correspond to a reduction of up to approximately 85% of the effort needed to assess stress-cycle fatigue in the design phase.
To conclude, it is important to highlight that the methodology presented has a universal character. It can be implemented to reduce computational time or assess the probabilistic response with only one requirement, the definition of a single representative indicator. In the case of fatigue, the short-term stress-cycle damage rate was considered.
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We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method ...builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.
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•An active learning method combining Kriging and Subset Simulation (AK–SS) is proposed.•AK–SS takes advantages of Subset Simulation and the Kriging metamodel.•The proposed method is applied to ...several benchmark functions and a tunnel lining structure.•AK–SS is shown to be more efficient than the other methods in the literature.•AK–SS can deal with small probability problems with time-consuming function evaluations.
With complex performance functions and time-demanding computation of structural responses, the estimation of small failure probabilities is a challenging problem in engineering. Although Subset Simulation (SS) is a powerful tool for small probabilities, the computation amount is still large for time-consuming numerical procedures. Metamodelling is an important approach to increase the computational efficiency for engineering problems, however, a larger set of sample points is required for higher accuracy. This is a time-consuming task when the performance function needs to be numerically evaluated. To address this issue, AK–SS: an active learning method combining Kriging model and SS is proposed in this paper. The efficiency of this new method relies upon the advantages of SS in evaluating small failure probabilities and the Kriging model with active learning and updating characteristic for approximating the true performance function. The proposed method is applied to several benchmark functions in the literature, and to the reliability analysis of a shield tunnel, which requires finite element analysis. The results demonstrated that as compared to the other approaches in literature, AK–SS can provide accurate solutions more efficiently, making it a promising approach for structural reliability analyses involving small failure probabilities, high-dimensional performance functions, and time-consuming simulation codes in practical engineering.
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