Stochastic analysis and robust optimization for a deck lid inner panel stamping

FE-simulation and optimization are widely used in the stamping process to improve design quality and shorten development cycle. However, the current simulation and optimization may lead to non-robust results due to not considering the variation of material and process parameters. In this study, a novel stochastic analysis and robust optimization approach is proposed to improve the stamping robustness, where the uncertainties are involved to reflect manufacturing reality. A meta-model based stochastic analysis method is developed, where FE-simulation, uniform design and response surface methodology (RSM) are used to construct meta-model, based on which Monte-Carlo simulation is performed to predict the influence of input parameters variation on the final product quality. By applying the stochastic analysis, uniform design and RSM, the mean and the standard deviation (SD) of product quality are calculated as functions of the controllable process parameters. The robust optimization model composed of mean and SD is constructed and solved, the result of which is compared with the deterministic one to show its advantages. It is demonstrated that the product quality variations are reduced significantly, and quality targets (reject rate) are achieved under the robust optimal solution. The developed approach offers rapid and reliable results for engineers to deal with potential stamping problems during the early phase of product and tooling design, saving more time and resources.     

Process analysis and optimization for failure energy of spot welded titanium alloy

Titanium and its alloys have been applied in many industrial fields because of their high specific strength, good corrosion resistance and high thermal stability. Whereas, there is limited valuable references for recommendations of welding parameter selection and specific standards of the small scale resistance spot welding (SSRSW) of titanium alloy though it has been applied in many industrial production fields. Seventeen tests were designed according to the three-level three-factor Box–Behnken experimental design and the mathematical model correlating the process parameters and the failure energy was established on the basis of response surface methodology (RSM) technique. And then this model was used to analyze the effects/interactions of the welding parameters on the failure energy. The verification test results which were conducted with completely new welding parameters verified that the model presented in this paper was effective and robust. Sensitivity analysis was also carried out to explore the impact of each process parameter on the quality of welding joint. The optimal combination of process parameters for maximum failure energy of the welded joint was obtained using the model based on artificial fish swarm algorithm (AFSA).     

A different view of ridge analysis from numerical optimization

This research falls into the gap between applied statistics and numerical optimization in a specific topic—Ridge Analysis (RA). This article proposes using the trust-region (TR) methods in numerical optimization to solve the RA problem, arising from the literature of response surface methodology (RSM) in applied statistics, where its goal is to help engineers for ‘process improvement’ to find the better response value of the predicted response function within the boundary of experimentation. In the field of numerical optimization, as the family of TR approaches always exhibits excellent mathematical properties during optimization steps, thus the algorithm presented in this study guarantees global optima for the RA problem. Two examples found in the RSM literature are included to illustrate the algorithm, demonstrating its capability of locating better operating conditions than existing computing methods and pointing out particular circumstances (termed the ‘hard case’) where the classical RA procedure fails. An important application to the response modeling problem arising from the philosophy of Taguchi's quality engineering illustrates the hard case. Finally, the utility of the presented TR algorithm is demonstrated through a sequential framework with iterative updates of the TR model under local approximation provided that the predicted response model is a high-order or even non-polynomial function.     

Response surface modeling and optimization of a new impact-toughened mould material used in the shaping of sanitary ware

This paper reports the synthesis of a high-impact epoxy composite toughened by the combination of amines, of which SiO₂, H₂O, Tween-80 and WD-60 were used as particulate filler, pore-forming agent, surface active agent and silane coupling agent, respectively. Concept of three-levels-six-factors Box-Behnken response surface design was applied for modeling and optimization of impact strength of the new impact-toughened mould material. A second-order mathematical model between the response (impact strength) and variables (SiO₂, H₂O, Tween-80, WD-60, epoxy resin and amines contents) was derived. Analysis of variance (ANOVA) showed a high coefficient of determination value (R² = 91.09%). The maximum impact strength was found to be 35.7 MPa at the optimum content of raw materials of SiO₂ (20.21%), H₂O (31.28%), Tween-80 (2.02%), WD-60 (6.06%), epoxy resin (30.29%) and hardener (10.14%). The predicted values thus obtained were close to the experimental values indicating suitability of the model. Geometrical representation of the mathematical models in three-dimensional response surface plots and isoresponse contour plots served as a good aid in understanding the behavior of reaction under different conditions. Besides, the optimum product was characterized by thermal analysis and pore size distribution analysis. This study clearly showed that the epoxy composite could be applied in the shaping of sanitary ware.     

Response surface approximations for structural optimization

Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to find the region of interest containing the optimal design, and techniques for finding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the ‘best’ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-effective. In a further attempt to improve efficiency, different regression models were investigated. The results indicate that the use of the two methods investigated does not significantly improve the results. Finding an accurate global approximation is challenging, and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space. © 1998 John Wiley & Sons, Ltd.     

D-optimal mixture design: optimization of ternary matrix blends for controlled zero-order drug release from oral dosage forms

The objective of the present study was to develop a tablet formulation with a zero-order drug release profile based on a balanced blend of three matrix ingredients. To accomplish this goal, a 17-run, three-factor, two-level D-Optimal mixture design was employed to evaluate the effect of Polyox^™ (X₁), Carbopol® (X₂), and lactose (X₃) concentrations on the release rate of theophylline from the matrices. Tablets were prepared by direct compression and were subjected to an in vitro dissolution study in phosphate buffer at pH 7.2. Polynomial models were generated for the responses Y₄ (percent released in 8 h) and Y₆ (similarity factor or f₂). Fitted models were used to predict the composition of a formulation that would have a similar dissolution profile to an ideal zero-order release at a rate of 8.33% per hour. When tested, dissolution profile of the optimized formulation was comparable to the reference profile (f₂ was 74.2, and n [release exponent] was 0.9). This study demonstrated that a balanced blend of matrix ingredients could be used to attain a zero-order release profile. Optimization was feasible by the application of response surface methodology, which proved efficient in designing controlled-release dosage forms.     

CFD simulation and performance optimization of a new horizontal turbo air classifier

A new horizontal turbo air classifier equipped with two inclined air inlets has been introduced. The flow field and classification performance of the classifier have been investigated using CFD method and response surface methodology (RSM). Simulation results show that the flow field is composed of the primary swirling flow and the secondary upward washing air, and the uniformly distributed swirling flow occupies the classifying chamber. The tangential gas velocity reaches the maximum value on the outer surface of the rotor cage, generating strong centrifugal force for the particle classification. The discrete phase model (DPM) can predict the cut sizes, but cannot present the fish-hook phenomenon. The desirable experimental condition by targeting the cut size of 20 μm and minimizing the classifying accuracy index is, rotor speed of 1373.6 rpm, primary air volume flow rate of 261.8 m³/h and secondary air volume flow rate of 42.4 m³/h. The corresponding fine and coarse fraction loss are less than 1.42% and 7.24%, respectively. This study provides a new strategy to design the horizontal turbo air classifier.     

Application of rotatable central composite design in the preparation and optimization of poly(lactic-co-glycolic acid) nanoparticles for controlled delivery of paclitaxel

Context: Polymeric carrier systems of paclitaxel (PCT) offer advantages over only available formulation Taxol® in terms of enhancing therapeutic efficacy and eliminating adverse effects. Objective: The objective of the present study was to prepare poly (lactic-co-glycolic acid) nanoparticles containing PCT using emulsion solvent evaporation technique. Methods: Critical factors involved in the processing method were identified and optimized by scientific, efficient rotatable central composite design aiming at low mean particle size and high entrapment efficiency. Twenty different experiments were designed and each formulation was evaluated for mean particle size and entrapment efficiency. The optimized formulation was evaluated for in vitro drug release, and absorption characteristics were studied using in situ rat intestinal permeability study. Results: Amount of polymer and duration of ultrasonication were found to have significant effect on mean particle size and entrapment efficiency. First-order interactions of amount of miglyol with amount of polymer were significant in case of mean particle size, whereas second-order interactions of polymer were significant in mean particle size and entrapment efficiency. The developed quadratic model showed high correlation (R² > 0.85) between predicted response and studied factors. The optimized formulation had low mean particle size (231.68 nm) and high entrapment efficiency (95.18%) with 4.88% drug content. The optimized formulation showed controlled release of PCT for more than 72 hours. In situ absorption study showed faster and enhanced extent of absorption of PCT from nanoparticles compared to pure drug. Conclusion: The poly (lactic-co-glycolic acid) nanoparticles containing PCT may be of clinical importance in enhancing its oral bioavailability.     

Crashworthiness design optimization using successive response surface approximations

 Finite Element (FE) method is among the most powerful tools for crash analysis and simulation. Crashworthiness design of structural members requires repetitive and iterative application of FE simulation. This paper presents a crashworthiness design optimization methodology based on efficient and effective integration of optimization methods, FE simulations, and approximation methods. Optimization methods, although effective in general in solving structural design problems, loose their power in crashworthiness design. Objective and constraint functions in crashworthiness optimization problems are often non-smooth and highly non-linear in terms of design variables and follow from a computationally costly (FE) simulation. In this paper, a sequential approximate optimization method is utilized to deal with both the high computational cost and the non-smooth character. Crashworthiness optimization problem is divided into a series of simpler sub-problems, which are generated using approximations of objective and constraint functions. Approximations are constructed by using statistical model building technique, Response Surface Methodology (RSM) and a Genetic algorithm. The approximate optimization method is applied to solve crashworthiness design problems. These include a cylinder, a simplified vehicle and New Jersey concrete barrier optimization. The results demonstrate that the method is efficient and effective in solving crashworthiness design optimization problems. Received: 30 January 2002 / Accepted: 12 July 2002 Sponsorship for this research by the Federal Highway Administration of US Department of Transportation is gratefully acknowledged. Dr. Nielen Stander at Livermore Software Technology Corporation is also gratefully acknowledged for providing subroutines to create D-optimal experimental designs and the simplified vehicle model.     

基于响应面法的H13模具钢激光增材再制造工艺优化

本研究采用中心复合响应面法对H13模具钢的激光增材再制造工艺参数进行优化,将激光功率(A),扫描速度(B)和送粉量(C)等激光再制造工艺参数作为优化变量,修复层宽度(W)、高度(H)和显微硬度(HAR)等成形特征作为响应值,通过方差分析构建了工艺参数与修复层成形特征值之间的回归预测模型。通过建立摄动图与三维响应面图分析了工艺参数之间的交互作用对修复层成形特征的影响规律。结果表明,修复层的宽度和高度均随激光功率的增加而增加,随扫描速度的增加而减少。提高送粉量有助于提高修复层高度,但是不利于修复层宽度的增加。同时提高扫描速度和激光功率情况下容易获得较高的硬度值。最后,H13模具钢的最佳激光增材再制造工艺参数确定为:激光功率为2.8 kW,扫描速度为4 mm/s,送粉量为16 g/min。     

Formulation optimization and pharmacokinetics evaluation of oral self-microemulsifying drug delivery system for poorly water soluble drug cinacalcet and no food effect

The present research indicated that a new self-microemulsifying drug delivery systems (SMEDDS) were used to reduce the food effect of poorly water-soluble drug cinacalcet and enhance the bioavailability in beagle dogs by oral gavage. Ethyl oleate, OP-10, and PEG-200 was selected as the oil phase, surfactant and co-surfactant of cinacalcet-SMEDDS by the solubility and phase diagram studies. Central Composite Design-Response Surface Methodology was used to determine the ratio of surfactant and co-surfactant, the amount of oil for optimizing the SMEDDS formation. The prepared formulations were further characterized by the droplet size, self-microemulsifying time, zeta potential, polydispersity index (PDI), and robustness to dilution. The in vitro release profile of cinacalcet-SMEDDS was determined in four different release medium and in fasted state and fed state of simulated gastrointestinal fluid. Cinaclcet-SMEDDS were implemented under fed and fasted state in dogs and product REGPARA^® was used as a comparison to the prepared formulation in the pharmacokinetics. The result showed the components of SMEDDS, the amount of oil, the ratio of surfactant, and co-surfactant was optimized using solubility, pseudo-ternary phase diagram studies, and response surface methodology. In vitro drug release studies indicated that the cinacalcet-SMEDDS eliminated the effect of pH variability in release medium and variational gastroenteric environments with improved drug release performance. Pharmacokinetic studies revealed that the profiles of cinacalcet-SMEDDS were similar both in the fasted and fed state compared with commercial product, indicating the formulation significantly promoted the absorption, enhanced bioavailability and had no food effect essentially. It is concluded that poorly water-soluble drug cinacalcet was improved in the solubility and bioavailability by using a successful oral dosage form the SMEDDS, and eliminated food effect as well.     

Anti-hyperuricemic property of 6-shogaol via self-micro emulsifying drug delivery system in model rats: formulation design,in vitro and in vivo evaluation

The prevalence of hyperuricemia is relatively high worldwide, and a great number of patients are suffering from its complications. 6-shogaol, an alkylphenol compound purified from the root of ginger (Zingiber officinale Roscoe), has been proved to possess diverse pharmacological activities. However, its poor aqueous solubility usually leads to low bioavailability, and further clinical applications will be greatly discounted. The current study aimed to formulate a 6-shogaol-loaded-Self Microemulsifying Drug Delivery System (SMEDDS) to amend low aqueous solubility and bioavailability orally, as well as, potentiate the hyperuricemic activity of the 6-shogaol. SMEDDS was developed with central composite design established on a two system components viz., 18.62% W/W ethyl oleate (oil phase) and ratio of tween 80 (surfactant) to PEG 400 (co-surfactant) (1.73:1, W/W). Based on quadratic model, the navigation of the design space could generate spherically-shaped and homogenous droplets with respective mean particle diameter, polydispersity and of 20.00?±?0.26?nm and 0.18?±?0.02. The 6-shogaol-SMEDDS showed significant elevation of cumulative release compared with the free 6-shogaol and more importantly a 571.18% increment in the relative oral bioavailability of the drug. The predominant accumulation of 6-shogaol-SMEDDS in the liver suggested hepatic-targeting potentiality of the drug. Oral administration of 6-shogaol-SMEDDS in hyperuricemic rats also significantly decreased uric acid level and xanthine oxidase activity. Histological studies confirmed formulation groups indeed could provide better protection of kidney than free drug groups. Collectively, these findings indicated that the SMEDDS hold much promise in enhancing the oral delivery and therapeutic efficacy of 6-shogaol.     

Multiobjective optimization of multi-cell sections for the crashworthiness design

Plastic deformation of structures absorbs substantial kinetic energy when impact occurs. For this reason, energy-absorbing components have been extensively used in the structural design of vehicles to intentionally absorb a large portion of crash energy to reduce the severe injury of occupants. On the other hand, high peak crushing force may to a certain extent indicate the risk of structural integrity and biomechanical damage of occupants. For this reason, it is of great significance to maximize the energy absorption and minimize the peak force by seeking for optimal design of these components. This paper aims to design the multi-cell cross-sectional thin-walled columns with these two crashworthiness criteria. An explicit finite element analysis (FEA) is used to derive higher-order response surfaces for these two objectives. Both the single-objective and multi-objective optimizations are performed for the single, double, triple and quadruple cell sectional columns under longitudinal impact loading. A comparative analysis is consequently given to explore the relationship between these two design criteria with the different optimization formulations.     

基于复合优化方法立式数控加工中心的多目标优化设计

为实现加工中心动静态性能不低于优化前性能,达到整机重量最轻的要求,本文提出了一种复合优化方法来研究多变量、多约束和多目标的数控加工中心优化设计。采用有限元分析和实验模态测试方法分析各大件动态性能,并验证了有限元模型的精确性。然后以该有限元模型为基础进行静态分析,得出各大件的最大变形及应力等。以柔度为目标,采用变密度法拓扑优化设计立柱结构的外形框架;以固有频率为目标,基于元结构的可适应性动态优化方法设计加工中心的筋板结构;以固有频率和质量为目标,基于响应面法的尺寸优化确定各结构的最优尺寸。最后将优化后的各大件进行整机装配,分析校核整机动静态性能。分析结果表明,优化后的整机在保证加工中心动静态性能的条件下,整机质量从12749kg减少到12127kg,减重达到4.9%,达到了整机的优化设计要求,说明该方法具有较高的精度和较强的工程实用性。     

Quality Management: Tools and Methods for Improvement

Results from the comparison of D, G, and A efficiencies and the scaled average prediction variance IV criterion are presented for the central composite, small composite, Notz, Hoke, Box–Draper, and computer-generated designs. These design optimality criteria are evaluated over the cuboidal design region for three, four, and five design variables.     

Adaptive improved response surface method for reliability-based design optimization

Reliability-based design optimization (RBDO) requires the evaluation of probabilistic constraints (or reliability), which can be very time consuming. Therefore, a practical solution for efficient reliability analysis is needed. The response surface method (RSM) and dimension reduction (DR) are two well-known approximation methods that construct the probabilistic limit state functions for reliability analysis. This article proposes a new RSM-based approximation approach, named the adaptive improved response surface method (AIRSM), which uses the moving least-squares method in conjunction with a new weight function. AIRSM is tested with two simplified designs of experiments: saturated design and central composite design. Its performance on reliability analysis is compared with DR in terms of efficiency and accuracy in multiple RBDO test problems.     

3D preform shape optimization in forging using reduced basis techniques

Three-dimensional preform shape optimization of complex forgings with a weighted summation of multiple basis shapes is presented in this article. Currently, 2D preform shape optimization is well developed; however, in cases in which the parts are neither axisymmetric nor plane strain, 2D assumptions do not hold well. The number of design variables required to define the 3D preform shape is high, making most iterative design methods impractical for shape optimization. The goal here is to make design optimization practical and efficient by developing reduced-order modeling techniques for 3D preform shape optimization. The preform shape is treated as a linear combination of various billet shapes, called basis shapes, with the weights for each basis shape used as design variables, thereby reducing the number of design variables. It is very difficult to obtain the necessary gradient information for 3D forging simulations, so a non-gradient method is used to build the surrogate model on which optimization is performed. The optimization problem is formulated to minimize strain variance while placing constraints on underfill. Representative problems are used to demonstrate the effectiveness of the approach.     

Multicriteria evaluation and optimization of the ultrasonic sealing performance based on design of experiments and response surface methodology

Proper closure is an essential packaging quality aspect and can, amongst others, be achieved with ultrasonic sealing. The ultrasonic sealing performance depends on the film type, and the seal settings, such as seal time, applied force and ultrasonic amplitude. Because these parameters are less intuitive than heat seal parameters and optimal settings are undefined for many films, this work presents an efficient approach to evaluate the effect of these settings on the ultrasonic sealing performance. An experimental design defines the experiments to perform. A response surface methodology is then used to model the relation between seal settings and sealing performance. Based on these models, the seal settings are optimized. As there are several criteria to express sealing performance, single‐criteria and multicriteria optimizations are described. The approach was illustrated for a polyethylene terephthalate/linear low‐density polyethylene‐C4 film. The seal settings were optimized to obtain high seal strength, limited ultrasonic horn displacement, and low seal energy. The optimum settings were 0.1 seconds (seal time), 4.32 N/mm (force), and 28.75 μm (amplitude). The predicted optimum strength, horn displacement, and energy were 2.32 N/mm, 40 μm, and 11.66 J, respectively. Besides the optimum, the seal window is also of interest. A broad seal window ensures sufficient seal strength for a wide range of settings. For the polyethylene terephthalate/linear low‐density polyethylene‐C4 film, a strength of ≥90% of the optimum was obtained for 39% of the input combinations within the design space. The presented approach is widely applicable (other films and sealing processes) since it is flexible in the input parameters, design, and responses.     

复合材料带缠绕成型工艺参数耦合机制及优化

基于复合材料缠绕成型工艺过程研究,分别对成型过程中紧密接触与自粘接过程进行理论分析,提出影响复合材料缠绕制品质量的关键工艺参数:缠绕温度、缠绕压力和缠绕张力;以层间剪切强度(ILSS)为优化目标,根据响应面法Box-Behnken Design(BBD)原理设计实验,建立工艺参数耦合对剪切强度的回归模型,通过对残差、方差(ANVOA)、预测值与实际值对比等检验分析,验证回归模型的可靠性及有效性,进而获得缠绕成型最优工艺参数。结果表明:在最优工艺参数作用下,层间剪切强度达到22.9 MPa,缠绕制品结合强度最高。     

Development of a solid self-microemulsifying drug delivery system (SMEDDS) for solubility enhancement of naproxen

Context: Comparative evaluation of liquid and solid self-microemulsifying drug delivery systems (SMEDDS) as promising approaches for solubility enhancement.

Objective: The aim of this work was to develop, characterize, and evaluate a solid SMEDDS prepared via spray-drying of a liquid SMEDDS based on Gelucire® 44/14 to improve the solubility and dissolution rate of naproxen.

Material and methods: Various oils and co-surfactants in combination with Gelucire® 44/14 were evaluated during excipient selection study, solubility testing, and construction of (pseudo)ternary diagrams. The selected system was further evaluated for naproxen solubility, self-microemulsification ability, and in vitro dissolution of naproxen. In addition, its transformation into a solid SMEDDS by spray-drying using maltodextrin as a solid carrier was performed. Scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and X-ray diffraction (XRD) were used to evaluate the physical characteristics of the solid SMEDDS obtained.

Results: The selected formulation of SMEDDS was comprised of Miglyol 812®, Peceol?, Gelucire® 44/14, and Solutol® HS 15. The liquid and solid SMEDDS formed a microemulsion after dilution with comparable average droplet size and exhibited uniform droplet size distribution. In the solid SMEDDS, liquid SMEDDS was adsorbed onto the surface of maltodextrin and formed smooth granular particles with the encapsulated drug predominantly in a dissolved state and partially in an amorphous state. Overall, incorporation of naproxen in SMEDDS, either liquid or solid, resulted in improved solubility and dissolution rate compared to pure naproxen.

Conclusion: This study indicates that a liquid and solid SMEDDS is a strategy for solubility enhancement in the future development of orally delivered dosage forms.