Improved Latin Hypercube Sampling Research Articles

Accurate Oil Temperature Prediction Model and Oil Refilling Parameters Optimization for Hydraulic Closed-Circuit System

Oil temperature plays a crucial role in hydraulic closed-circuit systems (HCS), and conventional thermal equilibrium models and coupled simulation models face challenges in terms of accuracy, efficiency, and cost when calculating oil temperature. This study introduces an innovative HCS oil temperature precise prediction model and oil refilling parameter optimization method. The initial sample space was determined through a Sobol sensitivity analysis and improved Latin hypercube sampling, leading to the development of a combinatorial agent model (CAM) suitable for oil temperature prediction with superior accuracy and stability compared to other methods. Based on CAM, the optimal oil refilling flow rates under various operational conditions are computed. To validate the efficacy of the theoretical analysis, an HCS experiment platform was established. The data indicates that the temperature prediction error range of the CAM model falls between 0.30 °C and 1.05 °C, and optimizing the oil refilling flow rate can effectively enhance system efficiency while ensuring that the oil temperature remains within permissible limits. The research methodology and findings are applicable in engineering practice and can be extended to optimize the design of other hydraulic systems.

Improved Latin hypercube sampling initialization-based whale optimization algorithm for COVID-19 X-ray multi-threshold image segmentation

Image segmentation techniques play a vital role in aiding COVID-19 diagnosis. Multi-threshold image segmentation methods are favored for their computational simplicity and operational efficiency. Existing threshold selection techniques in multi-threshold image segmentation, such as Kapur based on exhaustive enumeration, often hamper efficiency and accuracy. The whale optimization algorithm (WOA) has shown promise in addressing this challenge, but issues persist, including poor stability, low efficiency, and accuracy in COVID-19 threshold image segmentation. To tackle these issues, we introduce a Latin hypercube sampling initialization-based multi-strategy enhanced WOA (CAGWOA). It incorporates a COS sampling initialization strategy (COSI), an adaptive global search approach (GS), and an all-dimensional neighborhood mechanism (ADN). COSI leverages probability density functions created from Latin hypercube sampling, ensuring even solution space coverage to improve the stability of the segmentation model. GS widens the exploration scope to combat stagnation during iterations and improve segmentation efficiency. ADN refines convergence accuracy around optimal individuals to improve segmentation accuracy. CAGWOA's performance is validated through experiments on various benchmark function test sets. Furthermore, we apply CAGWOA alongside similar methods in a multi-threshold image segmentation model for comparative experiments on lung X-ray images of infected patients. The results demonstrate CAGWOA's superiority, including better image detail preservation, clear segmentation boundaries, and adaptability across different threshold levels.

System reliability analysis of Cable-stayed bridge using pair Copula and ICLHS with unequal weights under seismic loading

Considering the correlation between different components, quantifying the failure probability of a high-level hyper-static structure under non-stationary seismic loading is of great significance in guiding earthquake-resistant design and fortification of bridges. In this study, a high-pier and large-span railway cable-stayed bridge in the mountainous region were employed to evaluate the seismic performance. First, the basic theoretical methods of the non-stationary random seismic motion simulation, equivalent extreme value theory based on extreme value distribution (EVD), improved Latin hypercube sampling (ICLHS) with unequal weighted fractional moment estimation and Pair Copula technique are presented. Second, the finite element analysis model of the cable-stayed bridge was established based on the OpenSees platform, the seismic response samples of the bridge were calculated under three levels of seismic ground motion to determine the first passage failure probability of the main components of the bridge under the design failure modes. Finally, the Pair Copula function was introduced to estimate the seismic system reliability of the cable-stayed bridge. The optimal Copula type that can describe the correlation between the bridge components was selected through goodness-of-fit tests such as AIC, BIC, and the minimum distance method. The failure probability of the entire system was obtained by calculating the selected Copula function type under seismic loading.

AOK‐ES: Adaptive optimized Kriging combining efficient sampling for structural reliability analysis

AbstractThe pivotal problem in reliability analysis is how to use as few actual assessments as possible to obtain an accurate failure probability. Although adaptive Kriging provides a viable method to address this problem, unsatisfied Kriging surrogate accuracy and reliability modeling samples often lead to an unacceptable computing burden. In this paper, an adaptive optimized Kriging combining efficient sampling (AOK‐ES) is proposed: first, to enhance the Kriging approximation ability, a high‐fidelity optimized Kriging model (OKM) is established; further, to ensure the samples quality of OKM modeling and reliability calculation, an improved Latin hypercube sampling method and an optimized importance sampling approach are developed correspondingly. Six different types of case studies demonstrate the superiority of the proposed AOK‐ES. The analysis results demonstrate that the proposed AOK‐ES holds the potential to reduce computing cost while ensuring accuracy.

Dynamic Response and Optimal Design of Radio Telescope Structure under Wind Load Excitation

The dynamic response of a radio telescope structure under wind load excitation significantly impacts the accuracy of signal reception. To address this issue, this study established a parametric finite element model of a radio telescope to simulate its dynamic response under wind load excitation. An improved Latin hypercube sampling method was applied in the design of experiments (DOEs) to optimize the structural dimensional parameters of various components of the radio telescope with the aim of reducing the dynamic response to wind load. A response surface model and multi-objective genetic algorithm (MOGA) were employed for multi-objective structural optimization of the radio telescope structure. The findings reveal that the thickness of the stiffening ribs, the length of the side of the square hollow pole, the thickness of the middle pole, and the inner diameter of the thin pole are the most influential structural parameters affecting the first-order frequency (F1), second-order frequency (F2), maximum deformation in the x-direction (DX), and maximum deformation in the z-direction (DZ) of the radio telescope, respectively. Optimizing the radio telescope results in a 40.00% improvement in F1 and a 24.16% enhancement in F2, while reducing DX by 43.94% and DZ by 64.25%. The study outcomes offer a comprehensive scheme for optimizing the structural dimensional parameters of various radio telescope components in regions characterized by multiple wind fields.

A boundary identification approach for the feasible space of structural optimization using a virtual sampling technique-based support vector machine

To improve the computational efficiency of structural optimization, this study treats the feasibility evaluation of the solutions as a two-class classification problem and proposes a boundary identification approach (BIA) to identify the feasible region boundary of search space. The BIA includes a virtual sampling technique (VST), an improved Latin hypercube sampling (ILHS) method, and a support vector machine (SVM) classifier. The VST can generate cheap samples based on a mapping strategy from actual samples without time-consuming structural analysis. To enhance the global performance of the SVM, the ILHS yields the sample set on the normalized hypersphere of the original design space. An optimization framework based on the BIA hybridized with the harmony search algorithm is presented, and two numerical and three truss examples are utilized to examine the performances of the proposed optimization framework. The prediction accuracy of the BIA reaches about 99% in two numerical examples, and 97%, 90%, and 80% in the 10-bar, 72-bar, and 600-bar truss optimization examples, respectively. The results also show that the number of structural analyses required by the proposed optimization approach is reduced by more than 80% compared to the conventional metaheuristics optimization algorithms while obtaining a similar quality of optimal designs.

Bi-level optimization model of integrated biogas energy system considering the thermal comfort of heat customers and the price fluctuation of natural gas

Biogas is a pervade renewable energy source in rural areas, which can be used to generate power, heating and gas to satisfy the multi-energy needs of users. However, the energy efficiency and thermal comfort of heat customers after the connection of biogas digester is a challenging modelling problem. This paper establishes a bi-level optimization model of integrated biogas energy system considering the thermal comfort of heat customers and the price fluctuation of natural gas. In detail, using the penalty factor to describe the thermal comfort and using the DBN (Dynamic Bayesian network) model to predict natural gas fluctuations. The upper optimization target is the largest profit of the energy agency, and the lower objective is the minimum heating cost considering the penalty factor. The uncertainty of weights and biases in DBN prediction is addressed using the Sparrow search algorithm, and the uncertainty in probability results is tackled using an improved Latin hypercube sampling method. The optimization results show the proposed bi-level model can greatly increase the profit of energy agency by 18.5%, and the DBN prediction model has 89.3% prediction accuracy. Furthermore, the influence of diverse biogas scales and operation modes of the system, fluctuated natural gas price effects and various penalty factors of the user economy and comfort during heating are also analyzed.

Probabilistic Power Flow Method for Hybrid AC/DC Grids Considering Correlation among Uncertainty Variables

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with different meteorological characteristics in the AC/DC interconnected grid significantly increases the difficulty of establishing a steady-state model. Therefore, this study proposes an improved Latin hypercube sampling algorithm using the van der Waerden scores and diffusion kernel density estimation to overcome the limitations of a priori assumption on probability distributions in uncertainty modeling and to retain the correlations among random variables in the sampling data. Interconnected grids are constructed with IEEE 9-bus and IEEE 14-bus and modified with IEEE 57-bus to describe common application cases of aggregated renewable energy. On this basis, the approximation errors of the proposed probabilistic power flow algorithm to the statistical characteristics of the power parameters are evaluated by setting the Nataf algorithm and the Latin hypercube algorithm using adaptive kernel density estimation as the control group. The results show that the improved Latin hypercube sampling algorithm can exhibit high computational accuracy and strong adaptability, both in severe operating scenarios with large amplitude of load fluctuations and with nonlinear power balance equations incorporating high dimensional random variables.

Random Traffic Flow Simulation of Heavy Vehicles Based on R-Vine Copula Model and Improved Latin Hypercube Sampling Method

The rationality of heavy vehicle models is crucial to the structural safety assessment of bridges. To establish a realistic heavy vehicle traffic flow model, this study proposes a heavy vehicle random traffic flow simulation method that fully considers the vehicle weight correlation based on the measured weigh-in-motion data. First, a probability model of the key parameters in the actual traffic flow is established. Then, a random traffic flow simulation of heavy vehicles is realized using the R-vine Copula model and improved Latin hypercube sampling (LHS) method. Finally, the load effect is calculated using a calculation example to explore the necessity of considering the vehicle weight correlation. The results indicate that the vehicle weight of each model is significantly correlated. Compared to the Monte Carlo method, the improved LHS method better considers the correlation between high-dimensional variables. Furthermore, considering the vehicle weight correlation using the R-vine Copula model, the random traffic flow generated by the Monte Carlo sampling method ignores the correlation between parameters, leading to a weaker load effect. Therefore, the improved LHS method is preferred.

Machine Learning Analysis of Reaction Parameters in UV-Mediated Synthesis of Gold Nanoparticles

Gold nanoparticles represent an important class of functional nanomaterials for optoelectronics, biomedical applications, and catalysis. Therefore, controllable synthesis of nanoparticles with specified size and shape is important. Though reduction of gold ions is quite a simple process and may be performed with many different protocols, the reproducibility of the results and transfer of protocols between independent research groups remains a challenging task. Machine learning analysis based on statistical approaches is hardly applicable to the published data, since most of the researchers report only successful syntheses. In this work, we apply uniform sampling of the reaction parameter space. The concentrations of gold precursor, reducing agent, and surfactant were varied via an improved Latin hypercube sampling, and each run was performed under in situ UV–vis control. Based on the resulting set of optical spectra, we address the relevant chemical questions about nanoparticle formation, their shape, and period of growth. Our work demonstrates a data driven approach applied to the space of reaction parameters in a limited available set of experiments.

Efficient seismic reliability analysis of non-linear structures under non-stationary ground motions

The seismic reliability assessment (SRA) of complex nonlinear structures which possess structural and seismic uncertainty is an open challenge for academics and practical engineers. This paper proposes an improved maximum entropy method (IMEM) for the SRA of nonlinear structures. Non-stationary ground motions are first generated via a random-function-based spectral representation method. High-dimensional random variables in the ground motion simulation are then converted into two basic random variables as the high-dimensional probability space is reduced to a low-dimensional probability space. A two-step IMEM constrained with fractional moments is deployed to estimate the extreme value distribution (EVD) of the nonlinear structural dynamic system. An improved Latin hypercube sampling approach is also established to calculate the fractional moments of the complex nonlinear dynamic system. The first-passage probability of the structural nonlinear seismic response can be computed conveniently by a numerical integration using the EVD. Two numerical examples, 1) a three-story nonlinear shear frame structure and 2) a real-world high-pier continuous rigid frame bridge model, both of which exhibit strong nonlinearity under seismic action, are analyzed to show that the proposed method is efficient and accurate.

Improved probabilistic load flow method based on D‐vine copulas and Latin hypercube sampling in distribution network with multiple wind generators

In this study, a D-vine copulas modelling based probabilistic load flow (PLF) computation method is proposed, which considers the dependence among multiple wind generators. Furthermore, this method is not restricted by the type of wind speed distribution, i.e. allow random variables to comply with any types of distribution model. Copula theory plays an important role on dependency modelling. However, when high-dimensional correlation is taken into account, standard multivariate copula suffers from the problems of inflexible structure. Vine copula is flexible to build high-dimensional dependence and able to construct complicated dependence structure by applying bivariate copulas. For marginal distributions of wind speed, non-parametric model can provide a better estimation than those parametric models. An improved Latin hypercube sampling based Monte Carlo simulation method is utilised to solve PLF problems. A modified IEEE 33-node distribution system is used to conduct the numerical experiments for the accuracy and efficiency verification of the proposed PLF method, under the MatlabR2016a platform. The simulation results verify the outstanding accuracy, efficiency and robustness of the proposed PLF method.

A novel metamodel management strategy for robust trajectory design of an expendable launch vehicle

Uncertainty-based design optimization has been widely acknowledged as an advanced methodology to address competing objectives of aerospace vehicle design, such as reliability and robustness. Despite the usefulness of uncertainty-based design optimization, the computational burden associated with uncertainty propagation and analysis process still remains a major challenge of this field of study. The metamodeling is known as the most promising methodology for significantly reducing the computational cost of the uncertainty propagation process. On the other hand, the nonlinearity of the uncertainty-based design optimization problem's design space with multiple local optima reduces the accuracy and efficiency of the metamodels prediction. In this article, a novel metamodel management strategy, which controls the evolution during the optimization process, is proposed to alleviate these difficulties. For this purpose, a combination of improved Latin hypercube sampling and artificial neural networks are involved. The proposed strategy assesses the created metamodel accuracy and decides when a metamodel needs to be replaced with the real model. The metamodeling and metamodel management strategy are conspired to propose an augmented strategy for robust design optimization problems. The proposed strategy is applied to the multiobjective robust design optimization of an expendable launch vehicle. Finally, based on non-dominated sorting genetic algorithm-II, a compromise between optimality and robustness is illustrated through the Pareto frontier. Results illustrate that the proposed strategy could improve the computational efficiency, accuracy, and globality of optimizer convergence in uncertainty-based design optimization problems.

Prediction of Surficial Pressure Loading for an Underwater Projectile Using CFD-Based Database

In the present study, a CFD-based database is proposed to predict surficial pressure loading. To evaluate flow properties, a three-dimensional multi-phase Navier–Stokes flow solver based on unstructured meshes was utilized. Relative motion between a platform and a projectile was described using six degrees of freedom (6-DOF) equations of motion and an overset mesh technique. Accuracy of the 6-DOF module in the flow solver was validated by solving a benchmark problem. Four major parameters related to the surficial pressure loading were selected, which are escaping velocity, pressure of compressed gas flows, freestream velocity, and depth of water. Initial sample points were estimated by applying an improved Latin hypercube sampling method. To evaluate a flow condition with the maximum surficial pressure loading in a given database, a genetic algorithm and an artificial neural network were utilized. Then, accuracy of the database was iteratively evaluated by comparing the maximum pressure loading with those by the CFD prediction. It was found that the relative errors are less than 0.1% for both the projectile and the platform with 24 resultant sample points. It was also found that the escaping velocity and the freestream velocity significantly affect the characteristics of the surficial pressure loading due to the rotational disturbance around the projectile.

Reliability and variance-based sensitivity analysis of arch dams during construction and reservoir impoundment

The static performance of arch dams during construction and reservoir impoundment is assessed taking into account the effects of uncertainties presented in the model properties as well as the loading conditions. Dez arch dam is chosen as the case study; it is modeled along with its rock foundation using the finite element method considering the stage construction. Since previous studies concentrated on simplified models and approaches, comprehensive study of the arch dam model along with efficient and state-of-the-art uncertainty methods are incorporated in this investigation. The reliability method is performed to assess the safety level and the sensitivity analyses for identifying critical input factors and their interaction effects on the response of the dam. Global sensitivity analysis based on improved Latin hypercube sampling is employed in this study to indicate the influence of each random variable and their interaction on variance of the responses. Four levels of model advancement are considered for the dam-foundation system: 1) Monolithic dam without any joint founded on the homogeneous rock foundation, 2) monolithic dam founded on the inhomogeneous foundation including soft rock layers, 3) jointed dam including the peripheral and contraction joints founded on the homogeneous foundation, and 4) jointed dam founded on the inhomogeneous foundation. For each model, proper performance indices are defined through limit-state functions. In this manner, the effects of input parameters in each performance level of the dam are investigated. The outcome of this study is defining the importance of input factors in each stage and model based on the variance of the dam response. Moreover, the results of sampling are computed in order to assess the safety level of the dam in miscellaneous loading and modeling conditions.

A novel evolution control strategy for surrogate-assisted design optimization

Optimization solutions of real-world engineering problems mainly suffer from the large computational cost, the curse of dimensionality, and the multi-disciplinary nature of the involved disciplines. These issues may be intensified by incorporating uncertainties into the design and optimization of the problem. In this context, Surrogate-Assisted Optimization (SAO) methods and Evolution Control Strategies (ECS) have been considered as powerful paradigms to overcome or at least to alleviate the mentioned issues over the last two decades. This paper presents a novel ECS strategy based on the meta-models along with the real models. This strategy calculates the accuracy of the meta-model at each design point and determines if the real-model needs to be replaced with the meta-model. Moreover, the SAO and ECS are integrated to develop an augmented strategy to solve complex problems like Uncertainty-based Multidisciplinary Design Optimization (UMDO). In this context, the artificial neural networks are used along with the improved Latin hypercube sampling technique. Performance benefits of the proposed strategy in achieving the near-global optimum solution are shown by solving two simple mathematical problems and an engineering benchmark problem. To demonstrate the potential capability of this strategy, it applies to the UMDO problem of a space transportation system. Simulation results illustrate that the proposed strategy improves the computational efficiency as well as the globality of the optimal solution by proper management of the meta-models and real-models within the optimization process.

A Robust Multimodal Optimization Algorithm Based on a Sub-Division Surrogate Model and an Improved Sampling Method

The characteristics analysis of an electric machine requires the finite-element method. Hence, a large amount of computation occurs in the design process to take into account uncertainties as the manufacturing tolerances. In this paper, an efficient and useful multimodal optimization algorithm using the kriging surrogate model is proposed for the robust optimization of an electric machine. However, the conventional kriging (CK) method has a memory problem in multi-dimensional problem due to the enlarged correlation matrix. Thus, a sub-domain kriging (SDK) strategy and improved Latin hypercube sampling (ILHS) are proposed not only to solve the memory problem of the CK method, but also to increase the convergence speed. In addition, a gradient-free sensitivity index is proposed for robust optimization in order to address the conventional first and second gradient index which causes a numerical error. The outstanding performance of the proposed algorithm is verified by comparing with other optimization methods via several mathematical test functions which includes multi-dimensional problem. Moreover, the proposed algorithm is applied to a cogging torque reduction design case for interior permanent magnet motor.

Robust ascent trajectory design and optimization of a typical launch vehicle

Robustness and reliability of the designed trajectory are crucial for flight performance of launch vehicles. In this paper, robust trajectory design optimization of a typical LV is proposed. Two formulations of robust trajectory design optimization problem using single-objective and multi-objective optimization concept are presented. Both aleatory and epistemic uncertainties in model parameters and operational environment characteristics are incorporated in the problem, respectively. In order to uncertainty propagation and analysis, the improved Latin hypercube sampling is utilized. A comparison between robustness of the single-objective robust trajectory design optimization solution and deterministic design optimization solution is illustrated using probability density functions. The multi-objective robust trajectory design optimization is executed through NSGA-II and a set of feasible design points with a good spread is obtained in the form of Pareto frontier. The final Pareto frontier presents a trade-off between two conflicting objectives namely maximizing injection robustness and minimizing gross lift-off mass of launch vehicle. The resulted Pareto frontier of the multi-objective robust trajectory design optimization shows that with 1% increase in gross mass, the robustness of the design point to the considered uncertainties can be increased about 80%. Also, numerical simulation results show that the multi-objective formulation is a necessary approach to achieve a good trade-off between optimality and robustness.

Probabilistic Computational Model for Correlated Wind Farms Using Copula Theory

This paper proposed a probabilistic load flow analysis of correlated wind farms based on Copula theory. This method addresses the linear and non-linear dependence between random variables more efficiently and accurately than other methods. The proposed method is nearly unconstrained to the marginal probability distribution types of the input random variables. The dependency between the input random variables is established using Copula theory in this paper. An improved Latin hypercube sampling is adopted due to the real discrete data. Uncertainty and dependence factors are considered to access the load flow of the power system accurately and comprehensively. The validity of the probability distribution between the correlated random variables is evaluated by adopting the power output of wind farms located in New Jersey. The effectiveness and accuracy of the proposed model are investigated using the comparative test in modified IEEE 14-bus and IEEE 118-bus test systems.

An Improved Latin Hypercube Sampling Method to Enhance Numerical Stability Considering the Correlation of Input Variables

Latin hypercube sampling (LHS) method has difficulty in dealing with non-positive definite correlation matrices by traditional Cholesky decomposition, whereas it may often happen with the increasing scale of input variables. In order to improve the numerical stability of LHS, an improved LHS with modified alternating projections method (L-Mapm) is proposed in this paper. Compared with other two existing modified algorithms, L-Mapm is considered to possess accuracy, speediness, and controllability at the same time. The accuracy and effectiveness of L-Mapm applied to probabilistic load flow are proven by the comparative tests in the IEEE 33-bus system and PG&E 69-bus system. The simulation results show that L-Mapm has the best performance in modification and expands the application of LHS.