Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization

Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collaborative Optimization （CO） is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.

Multidisciplinary Design and Optimization of Satellite Launch Vehicle Using Latin Hypercube Design of Experiments

The design of new Satellite Launch Vehicle （SLV） is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Low Earth Orbit （LEO） bound SLV comprising of solid and liquid stages with the use of Genetic Algorithm （GA） as global optimizer. Convergence of GA is improved by introducing initial population based on the Design of Experiments （DOE） Technique. Latin Hypercube Sampling （LHS）-DOE is used for its good space filling properties. LHS is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. In SLV design minimum Gross Lift offWeight （GLOW） concept is traditionally being sought. Since the development costs tend to vary as a function of GLOW, this minimum GLOW is considered as a minimum development cost concept. The design approach is meaningful to initial design sizing purpose for its computational efficiency gives a quick insight into the vehicle performance prior to detailed design.

A new rotation method for constructing orthogonal Latin hypercube designs

Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrelated with each other,and is a stepping stone to the space-filling property for fitting Gaussian process models.Among the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional projections.This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods.Furthermore,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed.Theoretical properties as well as construction algorithms are provided.

Simulation of internal nitrogen release from bottom sediments in an urban lake using a nitrogen flux model

Nutrient release from sediment is considered a significant source for overlying water. Given that nutrient release mechanisms in sediment are complex and difficult to simulate, traditional approaches commonly use assigned parameter values to simulate these processes. In this study, a nitrogen flux model was developed and coupled with the water quality model of an urban lake. After parameter sensitivity analyses and model calibration and validation, this model was used to simulate nitrogen exchange at the sediment–water interface in eight scenarios. The results showed that sediment acted as a buffer in the sediment–water system. It could store or release nitrogen at any time, regulate the distribution of nitrogen between sediment and the water column, and provide algae with nitrogen. The most effective way to reduce nitrogen levels in urban lakes within a short time is to reduce external nitrogen loadings. However, sediment release might continue to contribute to the water column until a new balance is achieved. Therefore, effective measures for reducing sediment nitrogen should be developed as supplementary measures. Furthermore, model parameter sensitivity should be individually examined for different research subjects.

Sensitivity analysis of factors affecting gravity dam anti-sliding stability along a foundation surface using Sobol method

The anti-sliding stability of a gravity dam along its foundation surface is a key problem in the design of gravity dams.In this study,a sensitivity analysis framework was proposed for investigating the factors affecting gravity dam anti-sliding stability along the foundation surface.According to the design specifications,the loads and factors affecting the stability of a gravity dam were comprehensively selected.Afterwards,the sensitivity of the factors was preliminarily analyzed using the Sobol method with Latin hypercube sampling.Then,the results of the sensitivity analysis were verified with those obtained using the Garson method.Finally,the effects of different sampling methods,probability distribution types of factor samples,and ranges of factor values on the analysis results were evaluated.A case study of a typical gravity dam in Yunnan Province of China showed that the dominant factors affecting the gravity dam anti-sliding stability were the anti-shear cohesion,upstream and downstream water levels,anti-shear friction coefficient,uplift pressure reduction coefficient,concrete density,and silt height.Choice of sampling methods showed no significant effect,but the probability distribution type and the range of factor values greatly affected the analysis results.Therefore,these two elements should be sufficiently considered to improve the reliability of the dam anti-sliding stability analysis.

Optimization on the Impeller of a Low-specific-speed Centrifugal Pump for Hydraulic Performance Improvement

In order to widen the high-efficiency operating range of a low-specific-speed centrifugal pump, an optimization process for considering efficiencies under 1.0Qd and 1.4Qd is proposed. Three parameters, namely, the blade outlet width b2, blade outlet angle β2, and blade wrap angle φ, are selected as design variables. Impellers are generated using the optimal Latin hypercube sampling method. The pump efficiencies are calculated using the software CFX 14.5 at two operating points selected as objectives. Surrogate models are also constructed to analyze the relationship between the objectives and the design variables. Finally, the particle swarm optimization algorithm is applied to calculate the surrogate model to determine the best combination of the impeller parameters. The results show that the performance curve predicted by numerical simulation has a good agreement with the experimental results. Compared with the efficiencies of the original impeller, the hydraulic efficiencies of the optimized impeller are increased by 4.18% and 0.62% under 1.0Qd and 1.4Qd, respectively. The comparison of inner flow between the original pump and optimized one illustrates the improvement of performance. The optimization process can provide a useful reference on performance improvement of other pumps, even on reduction of pressure fluctuations.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

System Reliability Analysis of an Offshore Jacket Platform

This study investigates strategies for solving the system reliability of large three-dimensional jacket structures.These structural systems normally fail as a result of a series of different components failures.The failure characteristics are investigated under various environmental conditions and direction combinations.Theβ-unzipping technique is adopted to determine critical failure components,and the entire system is simplified as a series-parallel system to approximately evaluate the structural system reliability.However,this approach needs excessive computational effort for searching failure components and failure paths.Based on a trained artificial neural network(ANN),which can be used to approximate the implicit limit-state function of a complicated structure,a new alternative procedure is proposed to improve the efficiency of the system reliability analysis method.The failure probability is calculated through Monte Carlo simulation(MCS)with Latin hypercube sampling(LHS).The features and applicability of the above procedure are discussed and compared using an example jacket platform located in Chengdao Oilfield,Bohai Sea,China.This study provides a reference for the evaluation of the system reliability of jacket structures.

Multi-objectives nonlinear structure optimization for actuator in trajectory correction fuze subject to high impact loadings

This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.

Peak shaving operation optimization of high proportion new energypower generation considering wind-solar complementationand source-load coupling

To optimize peaking operation when high proportion new energy accesses to power grid,evaluation indexes are proposed which simultaneously consider wind-solar complementation and source-load coupling.A typical wind-solar power output scene model based on peaking demand is established which has anti-peaking characteristic.This model uses balancing scenes and key scenes with probability distribution based on improved Latin hypercube sampling(LHS)algorithm and scene reduction technology to illustrate the influence of wind-solar on peaking demand.Based on this,a peak shaving operation optimization model of high proportion new energy power generation is established.The various operating indexes after optimization in multi-scene peaking are calculated,and the ability of power grid peaking operation is compared whth that considering wind-solar complementation and source-load coupling.Finally,a case of high proportion new energy verifies the feasibility and validity of the proposed operation strategy.

Prediction of snow water equivalent using artificial neural network and adaptive neuro-fuzzy inference system with two sampling schemes in semi-arid region of Iran

Direct measurement of snow water equivalent(SWE)in snow-dominated mountainous areas is difficult,thus its prediction is essential for water resources management in such areas.In addition,because of nonlinear trend of snow spatial distribution and the multiple influencing factors concerning the SWE spatial distribution,statistical models are not usually able to present acceptable results.Therefore,applicable methods that are able to predict nonlinear trends are necessary.In this research,to predict SWE,the Sohrevard Watershed located in northwest of Iran was selected as the case study.Database was collected,and the required maps were derived.Snow depth(SD)at 150 points with two sampling patterns including systematic random sampling and Latin hypercube sampling(LHS),and snow density at 18 points were randomly measured,and then SWE was calculated.SWE was predicted using artificial neural network(ANN),adaptive neuro-fuzzy inference system(ANFIS)and regression methods.The results showed that the performance of ANN and ANFIS models with two sampling patterns were observed better than the regression method.Moreover,based on most of the efficiency criteria,the efficiency of ANN,ANFIS and regression methods under LHS pattern were observed higher than the systematic random sampling pattern.However,there were no significant differences between the two methods of ANN and ANFIS in SWE prediction.Data of both two sampling patterns had the highest sensitivity to the elevation.In addition,the LHS and the systematic random sampling patterns had the least sensitivity to the profile curvature and plan curvature,respectively.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

Reliability and sensitivity analysis of wedge stability in the abutments of an arch dam using artificial neural network

In this study,the seismic stability of arch dam abutments is investigated within the framework of the probabilistic method.A large concrete arch dam is considered with six wedges for each abutment.The seismic safety of the dam abutments is studied with quasi-static analysis for different hazard levels.The Londe limit equilibrium method is utilized to calculate the stability of the wedges in the abutments.Since the finite element method is time-consuming,the neural network is used as an alternative for calculating the wedge safety factor.For training the neural network,1000 random samples are generated and the dam response is calculated.The direction of applied acceleration is changed within 5-degree intervals to reveal the critical direction corresponding to the minimum safety factor.The Latin hypercube sampling(LHS)is employed for sample generation,and the safety level is determined with reliability analysis.Three sample numbers of 1000,2000 and 4000 are used to examine the average and standard deviation of the results.The global sensitivity analysis is used to identify the effects of random variables on the abutment stability.It is shown that friction,cohesion and uplift pressure have the most significant effects on the wedge stability variance.

Optimization of Well Position and Sampling Frequency for Groundwater Monitoring and Inverse Identification of Contamination Source Conditions Using Bayes’Theorem

Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity(M),release location(0 X,0 Y)and release time(0 T),based on monitoring well data.To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters,a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy.To demonstrate how the model works,an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed.The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index.The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events.Based on the optimized monitoring well position and sampling frequency,the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach.The case study results show that the following parameters were obtained:1)the optimal monitoring well position(D)is at(445,200);and 2)the optimal monitoring frequency(Δt)is 7,providing that the monitoring events is set as 5 times.Employing the optimized monitoring well position and frequency,the mean errors of inverse modeling results in source parameters(M,X0,Y0,T0)were 9.20%,0.25%,0.0061%,and 0.33%,respectively.The optimized monitoring well position and sampling frequency canIt was also learnt that the improved Metropolis-Hastings algorithm(a Markov chain Monte Carlo method)can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization,which significantly improved the accuracy and numerical stability of the inverse modeling results.

An Artificial Neural Network-Based Response Surface Method for Reliability Analyses of c-φ Slopes with Spatially Variable Soil

This paper presents an artificial neural network（ANN）-based response surface method that can be used to predict the failure probability of c-φslopes with spatially variable soil.In this method,the Latin hypercube sampling technique is adopted to generate input datasets for establishing an ANN model;the random finite element method is then utilized to calculate the corresponding output datasets considering the spatial variability of soil properties;and finally,an ANN model is trained to construct the response surface of failure probability and obtain an approximate function that incorporates the relevant variables.The results of the illustrated example indicate that the proposed method provides credible and accurate estimations of failure probability.As a result,the obtained approximate function can be used as an alternative to the specific analysis process in c-φslope reliability analyses.

Post-failure analysis of landslides in spatially varying soil deposits using stochastic material point method

This paper presents the probabilistic analysis of landslides in spatially variable soil deposits, modeled by a stochastic framework which integrates the random field theory with generalized interpolation material point method(GIMP). Random fields are simulated using Cholesky matrix decomposition(CMD) method and Latin hypercube sampling(LHS) method, which represent material properties discretized into sets of random soil shear strength variables with statistical properties. The approach is applied to landslides in clayey deposits under undrained conditions with random fields of undrained shear strength parameters, in order to quantify the uncertainties of post-failure behavior at different scales of fluctuation(SOF) and coefficients of variation(COV). Results show that the employed approach can reliably simulate the whole landslide process and assess the uncertainties of runout motions. It is demonstrated that the natural heterogeneity of shear strength in landslides notably influences their post-failure behavior. Compared with a homogeneous landslide model which yields conservative results and underestimation of the risks, consideration of heterogeneity shows larger landslide influence zones. With SOF values increasing, the variances of influence zones also increase, and with higher values of COV, the mean values of the influence zone also increase, resulting in higher uncertainties of post-failure behavior.

Placement Optimization Method of FPSO Gas Detectors Based on Leakage Risk

As the first step of the fire/gas-detection systems of floating production storage and offloading(FPSO)units is to iden-tify leakage accidents,gas detectors play an important role in controlling the leakage risk.To improve the leakage scenario detection rate and reduce the cumulative risk value,this paper presents an optimization method of the gas detector placement.The probability density distribution and cumulative probability density distribution of the leakage source variables and environmental variables were calculated based on the Offshore Reliability Data and the statistical data of the relevant leakage variables.A potential leakage sce-nario set was constructed using Latin hypercube sampling.The typical FPSO leakage scenarios were analyzed through computational fluid dynamics(CFD),and the impacts of different parameters on the leakage were addressed.A series of detectors was deployed according to the simulation results.The minimization of the product of effective detection time and gas leakage volume was the risk optimization objective,and the location and number of detectors were taken as decision variables.A greedy extraction heuristic algo-rithm was used to solve the optimization problem.The results show that the optimized placement had a better monitoring effect on the leakage scenario.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

Reliability-Based Optimization:Small Sample Optimization Strategy

The aim of the paper is to present a newly developed approach for reliability-based design optimization. It is based on double loop framework where the outer loop of algorithm covers the optimization part of process of reliability-based optimization and reliability constrains are calculated in inner loop. Innovation of suggested approach is in application of newly developed optimization strategy based on multilevel simulation using an advanced Latin Hypercube Sampling technique. This method is called Aimed multilevel sampling and it is designated for optimization of problems where only limited number of simulations is possible to perform due to enormous com- putational demands.

Sequential good lattice point sets for computer experiments

Sequential Latin hypercube designs(SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point(SGLP) sets. Moreover, we provide efficient approaches for identifying the(nearly)optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability.