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.

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.

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.

On the maximin distance properties of orthogonal designs via the rotation

Space-filling designs are widely used in computer experiments.They are frequently evaluated by the orthogonality and distance-related criteria.Rotating orthogonal arrays is an appealing approach to constructing orthogonal space-filling designs.An important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal arrays.This paper studies the maximin L_(2)-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three criteria.We provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G_(2)-aberration criterion.New infinite families of orthogonal or 3-orthogonal U-type designs,which also perform well under the maximin distance criterion,are obtained and tabulated.Examples are presented to show the effectiveness of the constructed designs for building statistical surrogate models.

Column-orthogonal designs with multi-dimensional stratifications

The orthogonal Latin hypercube design and its relaxation,and column-orthogonal design,are two kinds of orthogonal designs for computer experiments.However,they usually do not achieve maximum stratifications in multi-dimensional margins.In this paper,we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal arrays.The newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects(quadratic effects and bilinear effects)when the rotated orthogonal arrays have strength larger than two.Besides orthogonality,the resulting designs also preserve better space-filling properties than those constructed by using the existing methods.In addition,we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial designs.Some newly constructed orthogonal Latin hypercube designs are tabulated for practical use.