Use Of Latin Hypercube Sampling Research Articles

Microarray classification using genetic algorithm and latin hypercube sampling

Cancer, the second leading cause of global death, requires advanced diagnostic technology. Microarray gene expression technology plays an important role in comprehensively analyzing the genetic aspects of cancer. However, challenges such as high-dimensional attributes, limited samples, and varying gene presence rates hinder the accurate classification of microarray data. This study proposes a model that uses latin hypercube sampling (LHS) in genetic algorithms (GA) for Feature Selection in microarray data classification. LHS makes the chromosome samples in the initial population of GAs representative and diverse. The study used three microarray datasets with different numbers of features and classes. The results reveal that first, the use of GA alone tends to limit the exploration of the resulting feature space, while the use of LHS can expand the feature selection possibilities in the context of feature selection. Secondly, this study shows that microarray classification using GA with LHS (GALHS) consistently outperforms other feature selection methods such as based correlation features (BCF), principal component analysis (PCA), relief, and lasso. Thus, this research contributes to feature selection by applying LHS and GA to optimize the performance of microarray data classification models.

A novel evolutionary algorithm for structural model updating with a hybrid initialization and multi-stage update strategy

Measurement errors, spatial incompleteness, and parameter uncertainties frequently lead to significant deviations between the estimated correction coefficients of structural model updating and their actual values. To address the limitations, a novel multi-objective evolutionary algorithm called MOEA-HiMs is proposed for structural model updating, which incorporates a hybrid initialization and multi-stage update strategy. Two main contributions are summarized: (a) the introduction of optimal point and elite set initialization to enhance population diversity, which is achieved through the use of Latin hypercube sampling and a regularization technique, respectively; (b) the division of the optimization process into multiple stages, where solutions are corrected to improve converging efficiency using an appropriate update strategy. Additionally, the elite set is selected through the execution of sensitivity classification using a novel mathematical sensitivity index. The effectiveness and robustness of the MOEA-HiMs are demonstrated by the numerical offshore jacket platform and an experimentally-scaled platform structure. Both numerical and experimental results prove that the novel proposed MOEA-HiMs is more effective and robust than the traditional MOEA when using limited information, even under heavy noise conditions. The algorithm can serve as preliminary methods for online structural model updating of offshore platforms.

Emulating long-term weather-driven transportation earthworks deterioration models to support asset management

The deterioration of transport infrastructure earthworks is a global problem, with negative impacts for infrastructure resilience, becoming of increasing significance as existing infrastructure ages. Key mechanisms which affect this deterioration include seasonal pore pressure cycling driven by changing weather and climate, and the long-term dissipation of construction induced excess pore pressures. These complex processes lead to significant uncertainty in rates of deterioration and the current state of existing earthworks assets. The objective in this work was to establish a framework to emulate deterministic numerical models of slope deterioration over time using statistical (Gaussian process) emulation. A validated, physically based, deterministic modeling capability has been developed that can replicate the hydro-mechanically coupled behavior of cut and embankment slopes and their deterioration as driven by weather and climate. In parallel, a statistical (Gaussian process) emulator model was developed, and then trained with data from a deterministic modeling parametric study, using a formal experimental design approach, making use of Latin hypercube sampling. Exemplar forecasting outputs are presented to demonstrate application of the approach for use in decision-making. This information can be used in the design of new earthworks and the management of existing earthwork portfolios.

The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles

This work demonstrates the use of Latin Hypercube Sampling and Proper Orthogonal Decomposition in combination with a Radial Basis Function model to perform on vehicle prediction coupled fluid–thermal–structure. We regarded the Mach number, flight altitude and angle of attack as input parameters and established a rapid prediction model. The basic process of numerical simulation of the hypersonic vehicle coupled fluid–thermal–structure was studied to obtain the database of pressure coefficient, heat flux, structural temperature and structural stress as the sample data to train this prediction method. The prediction error was analyzed. The prediction results showed that the data-driven method proposed in this paper based on proper orthogonal decomposition and radial basis function could be used for predicting vehicle coupled fluid–thermal–structure with good efficiency.

Reliability sensitivity analysis using axis orthogonal importance Latin hypercube sampling method

In this article, a combined use of Latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is equivalently solved by reliability sensitivity analysis of a series of hyperplanes through each sampling point parallel to the tangent hyperplane of limit state surface around the design point. The analytical expressions of these hyperplanes are given, and the formulas for reliability sensitivity estimators and variances with the samples are derived according to the first-order reliability theory and difference method when non-normal random variables are involved and not involved, respectively. A procedure is established for the reliability sensitivity analysis with two versions: (1) axis orthogonal Latin hypercube importance sampling and (2) axis orthogonal quasi-random importance sampling with the Halton sequence. Four numerical examples are presented. The results are discussed and demonstrate that the proposed procedure is more efficient than the one based on the Latin hypercube sampling and the direct Monte Carlo technique with an acceptable accuracy in sensitivity estimation of the failure probability.

Simulation-based Bayesian optimal design for multi-factor accelerated life tests

ABSTRACTWe consider simulation-based methods for the design of multi-stress factor accelerated life tests (ALTs) in a Bayesian decision theoretic framework. Multi-stress factor ALTs are challenging due to the increased number of simulation runs required as a result of stress factor-level combinations. We propose the use of Latin hypercube sampling to reduce the simulation cost without loss of statistical efficiency. Exploration and optimization of expected utility function is carried out by a developed algorithm that utilizes Markov chain Monte Carlo methods and nonparametric smoothing techniques. A comparison of proposed approach to a full grid simulation is provided to illustrate computational cost reduction.

Analysis of the hydrological response of a distributed physically-based model using post-assimilation (EnKF) diagnostics of streamflow and in situ soil moisture observations

Summary Data assimilation techniques not only enhance model simulations and forecast, they also provide the opportunity to obtain a diagnostic of both the model and observations used in the assimilation process. In this research, an ensemble Kalman filter was used to assimilate streamflow observations at a basin outlet and at interior locations, as well as soil moisture at two different depths (15 and 45 cm). The simulation model is the distributed physically-based hydrological model CATHY (CATchment HYdrology) and the study site is the Des Anglais watershed, a 690 km 2 river basin located in southern Quebec, Canada. Use of Latin hypercube sampling instead of a conventional Monte Carlo method to generate the ensemble reduced the size of the ensemble, and therefore the calculation time. Different post-assimilation diagnostics, based on innovations (observation minus background), analysis residuals (observation minus analysis), and analysis increments (analysis minus background), were used to evaluate assimilation optimality. An important issue in data assimilation is the estimation of error covariance matrices. These diagnostics were also used in a calibration exercise to determine the standard deviation of model parameters, forcing data, and observations that led to optimal assimilations. The analysis of innovations showed a lag between the model forecast and the observation during rainfall events. Assimilation of streamflow observations corrected this discrepancy. Assimilation of outlet streamflow observations improved the Nash–Sutcliffe efficiencies (NSE) between the model forecast (one day) and the observation at both outlet and interior point locations, owing to the structure of the state vector used. However, assimilation of streamflow observations systematically increased the simulated soil moisture values.

Slope Instability Risk Analysis in Earth Dams Using LHS-MC Method

Risk analysis of slope instability in earth dams is presented using LHS –MC method. Latin hypercube sampling (LHS) is suggested as a tool to improve the efficiency of MC random sampling method. One example of risk analysis for dam slope instability is presented to demonstrate the validity and capability of the proposed method. By means of numerical example, it is shown that about 25% of the calculations can be saved by using LHS –MC method instead of simple MC. The exact savings, however, are dependent on details in the use of LHS and on the shape of the failure surfaces of the problems.

Surrogate-Assisted Evolutionary Optimizers for Multiobjective Design of a Torque Arm Structure

This paper presents two surrogate-assisted optimization strategies for structural constrained multiobjective optimization. The optimization strategies are based on hybridization of multiobjective population-based incremental learning (MOPBIL) and radial-basis function (RBF) interpolation. The first strategy uses MOPBIL for generating training points while the second strategy uses a Latin hypercube sampling (LHS) technique. The design case study is the shape and sizing design of a torque arm structure. A design problem is set to minimize structural mass and displacement while constraints include stresses due to three different load cases. Structural analysis is carried out by means of a finite element approach. The design problem is then tackled by the proposed surrogate-assisted design strategies. Numerical results show that the use of MOPBIL for generating training points is superior to the use of LHS based on a hypervolume indicator and root mean square error (RMSE).

Improvement of overtopping risk evaluations using probabilistic concepts for existing dams

Hydrologic risk analysis for dam safety relies on a series of probabilistic analyses of rainfall-runoff and flow routing models, and their associated inputs. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated in order to evaluate the probability of dam overtopping. Typically, parametric density estimation methods have been applied in this setting, and the exhaustive Monte Carlo simulation (MCS) of models is used to derive some of the distributions. Often, the distributions used to model some of the random variables are inappropriate relative to the expected behaviour of these variables, and as a result, simulations of the system can lead to unrealistic values of extreme rainfall or water surface levels and hence of the probability of dam overtopping. In this paper, three major innovations are introduced to address this situation. The first is the use of nonparametric probability density estimation methods for selected variables, the second is the use of Latin Hypercube sampling to improve the efficiency of MCS driven by the multiple random variables, and the third is the use of Bootstrap resampling to determine initial water surface level. An application to the Soyang Dam in South Korea illustrates how the traditional parametric approach can lead to potentially unrealistic estimates of dam safety, while the proposed approach provides rather reasonable estimates and an assessment of their sensitivity to key parameters.

Stochastic Modeling of Exposure and Risk in a Contaminated Heterogeneous Aquifer. 2: Application of Latin Hypercube Sampling

ABSTRACT This research has developed a numerical stochastic methodology for analyzing the uncertainty of groundwater flow and transport parameters and their effects on exposure and risk assessment. The Monte Carlo method is commonly used to analyze exposure uncertainty based on the uncertainty of each groundwater parameter measured. If the Monte Carlo method was used for all parameters in this study, it would have required an extremely large number of simulations. Therefore, a stochastic modeling approach based on Latin Hypercube Sampling was used to reduce the number of simulations required and to make uncertainty analysis feasible. This technique was adapted to use samples from both the statistical distributions of nonspatial stochastic parameters and spatial and discrete hydraulic conductivity field simultaneously. The use of Latin Hypercube Sampling proved to be very efficient for modeling uncertainty in exposure and risk assessment related to groundwater contamination. Key words: Risk assessment; exp...

Computational implementation of a systems prioritization methodology for the Waste Isolation Pilot Plant: a preliminary example

A systems prioritization methodology (SPM) is under development for the Waste Isolation Pilot Plant (WIPP). The SPM is based on a large numerical integration problem that must be repeatedly evaluated to determine compliance probabilities associated with different experimental programs and design modifications. Due to the complexity and computational cost of the underlying integration problem, the implementation of the SPM must be planned very carefully. This presentation describes a preliminary application of the SPM, designated SPM-l, performed to provide insights to facilitate the development and implementation of the methodology. Topics illustrated by SPM-1 include definition of probability spaces on which the SPM is based, use of Latin hypercube sampling and simple random sampling to integrate over different probability spaces, selection of mechanistic calculations to be performed, efficient use of the limited number of mechanistic calculations that can be performed, and assembly of many individual calculations into a complete analysis.