Optimizing Fine-Tuning of Earth Foundation Models via Multidimensional Latin Hypercube Sampling for Small-Scale Burn Scar Identification

Sampling efficiency in Monte Carlo based uncertainty propagation strategies: Application in seawater intrusion simulations

The convergence properties for Latin Hypercube Sampling (LHS) for reliability analyses is studied and compared with Simple Random Sampling (SRS) which has relatively wellknown error estimates. This paper summarizes the anticipated error of LHS estimates for percentile statistics of the response. For the relatively simple case, LHS yields dramatic improvements where the variance of the estimate is 1/N times that of SRS. However, for cases with many important variables, the improvement is diminished and often tends to a constant such as 1/3. In no case is the performance of LHS worse that SRS, so that one can expect LHS to continue to be a popular alternative to SRS when a direct sampling method is needed. Nomenclature fx = joint density function g = limit state function n = number of samples pf = probability of failure x = input variable(s) Z = response function

Latin hypercube sampling and geostatistical modeling of spatial uncertainty in a spatially explicit forest landscape model simulation

The failure of stress corrosion fraction (SCF) will lead to the ejection of nuclear power plant related equipment, which will affect the safety and economy of nuclear power plant. In this paper, a SCF failure analysis method for primary coolant circuits materials was established based on Paris model, and the uncertainty of fracture toughness was transformed into an integral form to improve the calculation efficiency. Taking the weld of thermowell as an example, the probability of SCF failure was calculated, and the uncertainty was analyzed by Wilks’ method. The influences of simple random sampling (SRS), Latin hypercube sampling (LHS) and Halton low discrepancy sequence on the uncertainty quantification of the calculated results were studied. At the same time, a surrogate model was established based on polynomial chaos expansion (PCE) method to study whether this method was suitable for SCF probability calculation. The results show that Halton sequence with 1000 samples can make the mean and variance convergence of failure probability better than SRS and LHS. When calculating the upper limit of tolerance interval, the mean and median of results corresponding to LHS are similar to those of SRS, but the dispersion degree of LHS is lower than SRS, while the results corresponding to Halton sequence are smaller than those corresponding to SRS and LHS. The increase of Wilks’ order can reduce the conservatism. When the order is 4, both the computational efficiency and the computational accuracy are considered. The results of the surrogate model based on PCE are basically consistent with those of the original program, but the amount of calculation is greatly reduced. This method is suitable for SCF probability analysis.

<p>Reliability of pipe structure is one aspect to be considered in reactor safety analysis. MSC NASTRAN is a computer code that can be used to calculate pipe deflection for reliability evaluation. MSC PATRAN can be used to generate input for this code. Uncertainty evaluation needs to be done in the input variable to understand uncertainty range in the analysis results. A computer code for evaluating structure reliability has been developed in our previous study. The code has implemented latin hypercube sampling (LHS) to assess uncertainty in the input variable, such as load and modulus of elasticity. In this study, comparison of two uncertainty methods, i.e. simple random sampling (SRS) and LHS, was carried out for the developed software. The comparison was subjected to pipe deflection calculation using 100 samples. Comparison analysis shows that LHS method produces a robust mean of variance for all sample size. The results also confirm that variance of pipe deflection using LHS is smaller by 3% than SRS one. It can be concluded that LHS is appropriate to be implemented for uncertainty analysis in the developed code.</p><p><strong> </strong></p>

Uncertainty is endemic in geospatial data due to the imperfect means of recording, processing, and representing spatial information. Propagating geospatial model inputs inherent uncertainty to uncertainty in model predictions is a critical requirement in each model's impact assessment and risk-conscious policy decision-making. It is still extremely difficult, however, to perform in practice uncertainty analysis of model outputs, particularly in complex spatially distributed environmental models, partially due to computational constraints.In the field of groundwater hydrology, the "stochastic revolution" has produced an enormous number of theoretical publications and greatly influenced our perspective on uncertainty and heterogeneity; it has had relatively little impact, however, on practical modeling. Monte Carlo simulation using simple random (SR) sampling from a multivariate distribution is one of the most widely used family of methods for uncertainty propagation in hydrogeological flow and transport model predictions, the other being analytical propagation.Real-life hydrogeological problems however, consist of complex and non-linear three dimensional groundwater models with millions of nodes and irregular boundary conditions. The number of Monte-Carlo runs required in these cases, depends on the number of uncertain parameters and on the relative accuracy required for the distribution of model predictions. In the context of sensitivity studies, inverse modelling or Monte-Carlo analyses, the ensuing computational burden is usually overwhelming and computationally impractical. These tough computational constrains have to be relaxed and removed before meaningful stochastic groundwater modeling applications are possible.A computationally efficient alternative to classical Monte Carlo simulation based on SR sampling is Latin hypercube (LH) sampling, a form of stratified random sampling. The latter yields a more representative distribution of model outputs (in terms of smaller sampling variability of their statistics) for the same number of input simulated realizations. The ability to generate unbiased LH realizations becomes critical in a spatial context, where random variables are geo-referenced and exhibit spatial correlation, to ensure unbiased outputs of complex models. On this regard, this dissertation offers a detailed analysis of LH sampling and compares it with SR sampling in a hydrogeological context. Additionally, two alternative stratified sampling methods, here named stratified likelihood (SL) sampling and minimum energy (ME) sampling, are examined (proposed in a spatial context) and their efficiency is further compared to SR and LH in a hydrogeological context; also accounting for the uncertainty related to the particular model at hand via a two step sampling method. All three stratified sampling methods (accounting for model sensitivity in the second case study) were found in this work to be more efficient than simple random sampling.Additionally, this thesis proposes a novel method for the expansion of the application domain of LH sampling to very large regular grids which is the common case in environmental (hydrogeological or not) models. More specifically, a novel combination of Stein's Latin Hypercube sampling with a Monte Carlo simulation method applicable over high discretization domains is proposed, and its performance is further validated in 2D and 3D hydrogeological problems of flow and transport in a mid-heterogeneous porous media, both consisting of about $1$ million nodes. Last, an additional novel extension of the proposed LH sampling on large grids is adopted for conditional high discretized problems. In this case too, the performance of the proposed approach is evaluated in a 3D hydrogeological model of flow and transport. Results indicate that both extensions (conditional and not) of LH sampling on large grids facilitate efficient uncertainty propagation with fewer model runs due to more representative model inputs. Overall, it could be argued that all the proposed methodological approaches could reduce the time and computer resources required to perform uncertainty analysis in hydrogeological flow and transport problems. Additionally, since it is the first time that stratified sampling is performed over high discretization domains, it could be argued that the proposed extensions of LH sampling on large grids could be considered a milestone for future uncertainty analysis efforts. Moreover, all the proposed stratified methods could contribute to a wider application of uncertainty analysis endeavors in a Monte Carlo framework for any spatially distributed impact assessment study.

In this paper, two sampling methods which are Latin hypercube sampling (LHS) and simple random sampling were. compared to improve the modeling speed of neural network model. Sampling method was used to generate initial weights and bias set. Electrical characteristic data for <TEX>$HfO_2$</TEX> thin film was used as modeling data. 10 initial parameter sets which are initial weights and bias sets were generated using LHS and simple random sampling, respectively. Modeling was performed with generated initial parameters and measured epoch number. The other network parameters were fixed. The iterative 20 minimum epoch numbers for LHS and simple random sampling were analyzed by nonparametric method because of their nonnormality.

Nanostructured materials are extensively applied in many fields of material science for new industrial applications, particularly in the automotive, aerospace industry due to their exceptional physical and mechanical properties. Experimental testing of nanomaterials is expensive, timeconsuming,challenging and sometimes unfeasible. Therefore,computational simulations have been employed as alternative method to predict macroscopic material properties. The behavior of polymeric nanocomposites (PNCs) are highly complex. The origins of macroscopic material properties reside in the properties and interactions taking place on finer scales. It is therefore essential to use multiscale modeling strategy to properly account for all large length and time scales associated with these material systems, which across many orders of magnitude. Numerous multiscale models of PNCs have been established, however, most of them connect only two scales. There are a few multiscale models for PNCs bridging four length scales (nano-, micro-, meso- and macro-scales). In addition, nanomaterials are stochastic in nature and the prediction of macroscopic mechanical properties are influenced by many factors such as fine-scale features. The predicted mechanical properties obtained by traditional approaches significantly deviate from the measured values in experiments due to neglecting uncertainty of material features. This discrepancy is indicated that the effective macroscopic properties of materials are highly sensitive to various sources of uncertainty, such as loading and boundary conditions and material characteristics, etc., while very few stochastic multiscale models for PNCs have been developed. Therefore, it is essential to construct PNC models within the framework of stochastic modeling and quantify the stochastic effect of the input parameters on the macroscopic mechanical properties of those materials. This study aims to develop computational models at four length scales (nano-, micro-, meso- and macro-scales) and hierarchical upscaling approaches bridging length scales from nano- to macro-scales. A framework for uncertainty quantification (UQ) applied to predict the mechanical properties of the PNCs in dependence of material features at different scales is studied. Sensitivity and uncertainty analysis are of great helps in quantifying the effect of input parameters, considering both main and interaction effects, on the mechanical properties of the PNCs. To achieve this major goal, the following tasks are carried out: At nano-scale, molecular dynamics (MD) were used to investigate deformation mechanism of glassy amorphous polyethylene (PE) in dependence of temperature and strain rate. Steered molecular dynamics (SMD)were also employed to investigate interfacial characteristic of the PNCs. At mico-scale, we developed an atomistic-based continuum model represented by a representative volume element (RVE) in which the SWNT’s properties and the SWNT/polymer interphase are modeled at nano-scale, the surrounding polymer matrix is modeled by solid elements. Then, a two-parameter model was employed at meso-scale. A hierarchical multiscale approach has been developed to obtain the structure-property relations at one length scale and transfer the effect to the higher length scales. In particular, we homogenized the RVE into an equivalent fiber. The equivalent fiber was then employed in a micromechanical analysis (i.e. Mori-Tanaka model) to predict the effective macroscopic properties of the PNC. Furthermore, an averaging homogenization process was also used to obtain the effective stiffness of the PCN at meso-scale. Stochastic modeling and uncertainty quantification consist of the following ingredients: - Simple random sampling, Latin hypercube sampling, Sobol’ quasirandom sequences, Iman and Conover’s method (inducing correlation in Latin hypercube sampling) are employed to generate independent and dependent sample data, respectively. - Surrogate models, such as polynomial regression, moving least squares (MLS), hybrid method combining polynomial regression and MLS, Kriging regression, and penalized spline regression, are employed as an approximation of a mechanical model. The advantage of the surrogate models is the high computational efficiency and robust as they can be constructed from a limited amount of available data. - Global sensitivity analysis (SA) methods, such as variance-based methods for models with independent and dependent input parameters, Fourier-based techniques for performing variance-based methods and partial derivatives, elementary effects in the context of local SA, are used to quantify the effects of input parameters and their interactions on the mechanical properties of the PNCs. A bootstrap technique is used to assess the robustness of the global SA methods with respect to their performance. In addition, the probability distribution of mechanical properties are determined by using the probability plot method. The upper and lower bounds of the predicted Young’s modulus according to 95 % prediction intervals were provided. The above-mentioned methods study on the behaviour of intact materials. Novel numerical methods such as a node-based smoothed extended finite element method (NS-XFEM) and an edge-based smoothed phantom node method (ES-Phantom node) were developed for fracture problems. These methods can be used to account for crack at macro-scale for future works. The predicted mechanical properties were validated and verified. They show good agreement with previous experimental and simulations results.

ContextBirds, as indicators of biodiversity, are experiencing habitat reduction and loss due to landscape changes. Evidence is mounting that the response of bird richness to landscape patterns remains controversial on a global scale. In this study, we conducted a quantitative global synthesis to gain a comprehensive understanding of this relationship. Our findings contribute to the development of bird conservation strategies that align with the objectives of SDG15.ObjectiveThrough a quantitative review, this study investigated the effects of landscape patterns on bird richness and analyzed the sources of heterogeneity in the results.MethodsA random-effects model was utilized to merge the impacts of landscape metrics on bird richness, and a meta-regression analysis was performed to investigate the origins of heterogeneity.ResultsThe review encompassed 101 articles from 51 countries worldwide. Field sampling emerged as the primary method for acquiring bird data, with multiple linear regression and generalized linear models as the main analytical approaches. The meta-analysis results highlighted landscape area as a crucial factor influencing bird richness. Regarding landscape composition, the proportions of forests, shrublands, and water bodies positively impacted bird richness, while agricultural land and urban land had negative effects. The relationship between landscape complexity and bird richness is influenced by factors, including net primary productivity (NPP) and precipitation. Landscape heterogeneity was identified as a contributing factor to increased species richness.ConclusionCompared to landscape complexity, indicators of landscape composition and heterogeneity are more suitable as reference tools for bird conservation. The results of landscape complexity exhibit variation. Moreover, our findings underscore the crucial role of preserving forested areas in supporting bird diversity, emphasizing the necessity to account for regional variations when establishing forest cover thresholds.

This study aims to determine the effectiveness of the learning model that is influenced by the level of students' initial abilities and the combined influence (interaction effect) between the learning model and the students' initial level of ability to the students' mathematics learning outcomes. The learning model has a central function in learning, namely as a tool and a way to achieve learning goals. The type of research used in this study is quasi-experimental. The research subjects used as the subject of the trial were Yogyakarta State and Private Middle School Students. The object of this research is the students' initial abilities and learning outcomes of mathematics by using Write and Conventional Think Talk learning models. Data collection techniques used are test techniques and documentation techniques. Data were analyzed by two factors, both for initial ability test scores and learning outcome test scores and post anava test using Scheffe Test. The results of the study with α = 5% indicate: 1) The Think Talk Write learning model is more effective than the conventional learning model. (2) Learning outcomes of high-skilled students are better than students who have moderate and low initial abilities, and (3) there is no interaction between learning methods and students' initial level of ability based on learning outcomesKeywords: Effectiveness, Think Talk Write, AnavaAbstractThis study aims to determine the effectiveness of the learning model that is influenced by the level of students' initial abilities and the combined influence (interaction effect) between the learning model and the students' initial level of ability to the students' mathematics learning outcomes. The learning model has a central function in learning, namely as a tool and a way to achieve learning goals. The type of research used in this study is a quasi-experimental. The research subjects used as the subject of the trial were Yogyakarta State and Private Middle School Students. The object of this research is the students' initial abilities and learning outcomes of mathematics by using Write and Conventional Think Talk learning models. Data collection techniques used are test techniques and documentation techniques. Data were analyzed by two factors, both for initial ability test scores and learning outcome test scores and post anava test using Scheffe Test. The results of the study with α = 5% indicate: 1) The Think Talk Write learning model is more effective than the conventional learning model. (2) Learning outcomes of high-skilled students are better than students who have moderate and low initial abilities, and (3) there is no interaction between learning methods and students' initial level of ability based on learning outcomes. Keywords: Effectiveness, Think Talk Write, Anava

Leveraging Monte Carlo Simulation (MCS) combined with simple random sampling (SRS) to evaluate probabilistic locational marginal price (P-LMP) requires long computation time and large computer storage. The paper proposes the joint usage of Latin hypercube sampling (LHS) with sample reduction techniques called the fast forward selection (FFS) algorithm into Monte Carlo simulation for calculation of the P-LMP. This fast forward selection algorithm is needed to cut down the number of samples while keeping most of the stochastic information embedded in such samples. The LHS-FFS-based P-LMP is investigated using IEEE 6-bus and 24-bus systems. This method is compared with SRS and LHS only. The LHS-FFS approach is found to be efficient and flexible; therefore, it has the potential to be applied in many power system probabilistic problems.

Monte Carlo simulation method combined with simple random sampling (SRS) suffers from long computation time and heavy computer storage requirement when used in probabilistic load flow (PLF) evaluation and other power system probabilistic analyses. This paper proposes the use of an efficient sampling method, Latin hypercube sampling (LHS) combined with Cholesky decomposition method (LHS-CD), into Monte Carlo simulation for solving the PLF problems. The LHS-CD sampling method is investigated using IEEE 14-bus and 118-bus systems. The method is compared with SRS and LHS only with random permutation (LHS-RP). LHS-CD is found to be robust and flexible and has the potential to be applied in many power system probabilistic problems.

In this paper, Latin hypercube sampling (LHS) is investigated in connection with reliability evaluation of a power system. A new sampling technique called discrete Latin hypercube (DLHS) is also proposed. Distributions of reliability indexes resulting from two sampling techniques are presented and analyzed along with those from Monte Carlo (MC) sampling. A comparison among LHS, DLHS and traditional MC for reliability analysis is made. The LHS and DLHS are shown to be more effective than MC for obtaining distributions of indices that are close to the real distributions. The distributions of indices are useful in risk analysis and certain stochastic optimization problems. The test system is a 12-area power system which is based on the data from an actual multi-area system.

Estimating the Fair Insurance Premium for Dungeness Crab Yields in the Western U.S. Coast

Latin hypercube sampling (McKay, Conover, and Beckman 1979) is a method of sampling that can be used to produce input values for estimation of expectations of functions of output variables. The asymptotic variance of such an estimate is obtained. The estimate is also shown to be asymptotically normal. Asymptotically, the variance is less than that obtained using simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. A method for producing Latin hypercube samples when the components of the input variables are statistically dependent is also described. These techniques are applied to a simulation of the performance of a printer actuator.