Optimization of mechanical properties using D-optimal factorial design of experiment: Electromagnetic stir casting process of A357-SiC nanocomposite

Electromagnetic stir casting process of A357-Si C nanocomposite was discussed using the D-optimal design of experiment(DODOE) method. As the main objective, nine random experiments obtained by DX-7 software were performed. By this method, A357-Si C nanocomposites with 0.5, 1.0 and 1.5 wt.% Si C were fabricated at three different frequencies(10, 35 and 60 Hz) in the experimental stage. The microstructural evolution was characterized by scanning electron and optical microscopes, and the mechanical properties were investigated using hardness and roomtemperature uniaxial tensile tests. The results showed that the homogeneous distribution of Si C nanoparticles leads to the microstructure evolution from dendritic to non-dendritic form and a reduction of size by 73.9%. Additionally, based on DODOE, F-values of 44.80 and 179.64 were achieved for yield stress(YS) and ultimate tensile strength(UTS), respectively, implying that the model is significant and the variables(Si C fraction and stirring frequency) were appropriately selected. The optimum values of the Si C fraction and stirring frequency were found to be 1.5 wt.% and 60 Hz, respectively. In this case, YS and UTS for A357-Si C nanocomposites were obtained to be 120 and 188 MPa(57.7% and 57.9 % increase compared with those of the as-cast sample), respectively.

Optimization of Proportion and Formulation Process of Jinweng Granule by D-Optimal Mixture Design

[Objectives] To study the optimal proportion and formulation process of Jinweng granule,the physicochemical properties of the optimal preparing process was observed. [Methods] Adopting the D-optimal mixture design method,selecting the mixing ratio of starch,dextrin,fumei powder and lactose as tested factors,and selecting the most significant factor between hygroscopicity,formability,solubility as the evaluation index,the optimal proportion of filler was examined by system experiments. Granularity,solubility,the angle of repose,and critical relative humidity( CRH) were used to evaluate the optimal proportion and formulation process of Jinweng granule. [Results]The optimal prescription of Jinweng granule is extract∶ starch∶ dextrin∶ lactose∶ fumei powder( 1∶ 0. 5∶ 0. 05∶ 0. 3∶ 0. 15),and the binder was consisted of 1% sodium carboxymethylcellulose( CMC) slurry and 3% starch syrup. The CRH of the optimum formulation process of granule is 72%,and the fluidity,solubility and granularity were qualified. [Conclusions] The process model established by D-optimum mixture design has good predictability,and the granule prepared by the optimal proportion has good repeatability,and the granule proportion and formulation process is stable and reliable.

A New D-optimal Design Scheme for the Identification of Cubic Polynomials

In this paper, the limitations of the single cube D-optimal design scheme is studied, and a double cube D-optimal design scheme is suggested in order to overcome the limitations. For a sort of incomplete cubic polynomials, the test design of the identification is developed with this new scheme, and the comparation with the single cube scheme is also given. This scheme is shown to be perfectly suitable for the optimal identification of the complete cubic polynomials.

The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments;therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model where q is an indicator variable. We have considered an experiment based on the dose-response to a fly insecticide in which males and females respond in different ways, proposed in Atkinson et al. (1995) [1]. To find the D-optimal designs, this problem has been reduced to a canonical form.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

ON CURVED SURFACE APPROXIMATION AND HIDDEN SURFACE ELIMINATION IN 3-D COMPUTER AIDED GARMENT DESIGN

An approximation method for curved surface mannequin and hidden surface eliminationin 3-D computer aided garment design system is described. The mannequin is the basis of the3-D modeling for clothes. In terms of the requirements of computer aided garment design,the authors put forward a method for curved surface approximation in the meaning of leastsquares. Using. this method the computation of geometric modeling is simple andefficient. It is also convenient for curved surface modification and shading.

TWO－LEVEL MULTI－POINT APPROXIMATION METHOD FOR OPTIMUM DESIGN OF COMPLICATED STRUCTURES

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An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

H2 and H∞-Feedback Control Design for Nonlinear Gene Networks via Successive Galerkin’s Approximation

This paper presents a design method of H2 and H∞-feedback control loop for nonlinear smooth gene networks that are in control affine form. Formulaic solution methodology for solving the nonlinear partial differential equations, namely the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations through successive Galerkin’s approximation is implemented and the results are compared. Throughout the implementation, there were several caveats that need to be further resolved for practical applications in general cases. Such issues and the clarification of causes are mathematically established and reviewed.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

EFFICIENT METHOD FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION BY CONSIDERING UNCERTAINTY

A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. The Kriging approximate model with updating is introduced to reduce the computational cost of MDF caused by the complex structure. The computational efficiency is remarkably improved as the lack of iterative process during reliability analysis. Special attention is paid to a turbine blade design optimization by adopting the proposed method. Results show that the method is much more efficient than the commonly used double-loop based RBMDO method. It is feasible and efficient to apply the method to the engineering design.

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.

RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.

Discounted Iterative Adaptive Critic Designs With Novel Stability Analysis for Tracking Control

The core task of tracking control is to make the controlled plant track a desired trajectory.The traditional performance index used in previous studies cannot eliminate completely the tracking error as the number of time steps increases.In this paper,a new cost function is introduced to develop the value-iteration-based adaptive critic framework to solve the tracking control problem.Unlike the regulator problem,the iterative value function of tracking control problem cannot be regarded as a Lyapunov function.A novel stability analysis method is developed to guarantee that the tracking error converges to zero.The discounted iterative scheme under the new cost function for the special case of linear systems is elaborated.Finally,the tracking performance of the present scheme is demonstrated by numerical results and compared with those of the traditional approaches.

Design and Experiments of Ultrasound Image-Guided Multi-DOF Robot System for Brachytherapy

To implant radioactive seeds through a needle precisely and safely, a novel multi-DOF surgical robotic system is presented in this paper for percutaneous prostate intervention through the patient’s perineum under real-time ultrasound image guidance. The proposed robot, which is designed with 9-DOF, consists of a 3-DOF automatic location platform for position adjustment, 2-DOF for automatic ultrasonic probe adjustment mounted with electromagnetic trackers, and 4-DOF for manually adjusting the guided template. Meanwhile, a new registration method based on the quaternion algorithm and least square method is developed, and the needle insertion is performed under the real-time guidance of a navigation system. Furthermore, the robot system has undergone some preliminary experiments with a laser tracker to evaluate the repeatability and accuracy of the robot system. The location error of the puncture needle tip can be controlled under 0.7 mm in air for the whole robotic system. The acquired results endorse the precision of the robot system for prostate seed implantation brachytherapy. © 2017, Tianjin University and Springer-Verlag GmbH Germany.

Formulation of self-nanoemulsifying drug delivery systems containing monoacyl phosphatidylcholine and Kolliphor^(■) RH40 using experimental design

The development of self-nanoemulsifying drug delivery systems(SNEDDS) to enhance the oral bioavailability of lipophilic drugs is usually based on traditional one-factor-at-a-time approaches. These approaches may be inadequate to analyse the effect of each excipient and their potential interactions on the emulsion droplet size formed when dispersing the SNEDDS in an aqueous environment. The current study investigates the emulsion droplet sizes formed from SNEDDS containing different levels of the natural surfactant monoacyl phosphatidylcholine to reduce the concentration of the synthetic surfactant polyoxyl 40 hydrogenated castor oil(Kolliphor ~? RH40). Monoacyl phosphatidylcholine was used in the form of Lipoid S LPC 80(LPC, containing approximately 80% monoacyl phosphatidylcholine, 13% phosphatidylcholine and 4% concomitant components). The investigated SNEDDS comprised of long-chain or medium-chain glycerides(40% to 75%), Kolliphor ~? RH40(5% to 55%), LPC(0 to 40%) and ethanol(0 to 10%). D-optimal design, multiple linear regression, and partial least square regression were used to screen different SNEDDS within the investigated excipient ranges and to analyse the effect of each excipient on the resulting droplet size of the dispersed SNEDDS measured by dynamic light scattering. All investigated formulations formed nano-emulsions with droplet sizes from about 20 to 200 nm. The use of mediumchain glycerides was more likely to result in smaller and more monodisperse droplet sizes compared to the use of long-chain glycerides. Kolliphor~? RH40 exhibited the most significant effect on reducing the emulsion droplet sizes. Increasing LPC concentration increased the emulsion droplet sizes, possibly because of the reduction of Kolliphor~? RH40 concentration. A higher concentration of ethanol resulted in an insignificant reduction of the emulsion droplet size. The study provides different ternary diagrams of SNEDDS containing LPC and Kolliphor ~? RH40 as a reference for formulation developers.

AN ITERATIVE ALGORITHM FOR OPTIMAL DESIGN OF NON-FREQUENCY-SELECTIVE FIR DIGITAL FILTERS

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.

Inverse Design of Electron Lens

The inverse design of electron lens is realized by two different methods in this paper. One is damped least square method and the other is the artificial neural network method. Their merits and defects are discussed according to our calculation results in the paper. In the condition of selecting the learning samples properly, the artificial neural network has obvious advantages in the inverse design of electron lens. It is an effective method to solve the inverse design problem in the electron optic system.

Recent developments in optimal experimental designs for functional magnetic resonance imaging

Functional magnetic resonance imaging(fMRI)is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli.For neuroimaging studies utilizing this pioneering technology,there is a great demand of high-quality experimental designs that help to collect informative data to make precise and valid inference about brain functions.This paper provides a survey on recent developments in experimental designs for fMRI studies.We briefly introduce some analytical and computational tools for obtaining good designs based on a specified design selection criterion.Research results about some commonly considered designs such as blocked designs,and m-sequences are also discussed.Moreover,we present a recently proposed new type of fMRI designs that can be constructed using a certain type of Hadamard matrices.Under certain assumptions,these designs can be shown to be statistically optimal.Some future research directions in design of fMRI experiments are also discussed.

Assessing the Performance of Some Ranked Set Sampling Designs Using Hybrid Approach

In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.