Taguchi optimization approach for Pb(II) and Hg(II) removal from aqueous
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BP神经网络与GA算法相结合的空调风叶翘曲均匀性优化黄立东;周小蓉【摘要】以模具温度、熔体温度、注射时间、保压时间、保压压力5个因素为设计变量,空调风叶叶片尖部Z轴坐标最大差值为目标变量,采用田口方法进行实验设计并根据实验方案进行CAE模拟,根据模拟结果采用BP神经网络构建设计变量与目标变量之间的数学关系模型,并利用GA算法对数学模型进行全局最优求解.求得最优工艺参数为;模具温度45℃、熔体温度205℃、注射时间1.8s、保压时间6s、保压压力50 MPa.模拟验证得到优化工艺参数下的目标变量为0.08 mm,低于各个实验设计方案,且风叶各叶片翘曲均匀性得到提高.【期刊名称】《中国塑料》【年(卷),期】2014(028)007【总页数】5页(P77-81)【关键词】注塑;空调风叶;翘曲均匀性;前馈神经网络;遗传算法;田口方法【作者】黄立东;周小蓉【作者单位】湖南机电职业技术学院机械工程系,湖南长沙410151;湖南机电职业技术学院机械工程系,湖南长沙410151【正文语种】中文【中图分类】TQ320.66+20 前言空调中的风叶作为送风的主要装置,其性能的好坏直接关系到空调工作状况的好坏。
风叶注塑时,由于各个叶片受到的压力可能不同,将使得各个叶片产生的翘曲不一致,这将直接决定着风叶叶片的品质,因此必须确保3个叶片翘曲的平衡性。
关于注塑产品的翘曲优化问题,许多学者都做过相关研究,Fei等[1]利用BP神经网络对产品进行了翘曲预测及优化;Gao等[2]利用Kriging代理模型减少了产品翘曲量;Erzurumlu等[3]采用正交实验、信噪比率和遗传算法得出了最小翘曲和缩痕指数的优化组合;Hakimian等[4]利用正交实验研究了微齿轮的翘曲和收缩性质;Deng等[5]利用MIPS方法及GA算法对产品翘曲量进行了优化。
不过以上研究大多集中于对产品翘曲量最值的优化,而对于注塑产品而言,翘曲的整体均匀性甚至比翘曲量最值更重要,因此,简单的以翘曲量的最大值来衡量最终产品翘曲的好坏,具有一定的局限性。
内置式永磁同步电机双层磁钢结构优化设计李维1,王慧敏2,张智峰1,邓强1,张志强1,唐源1,付国忠1(1.中国核动力研究设计院核反应堆系统设计重点实验室,成都610213;2.天津工业大学电气工程与自动化学院,天津300387)摘要:为有效改善永磁同步电机的转矩输出能力和弱磁扩速能力,将双层磁钢结构用于电动车辆用内置式永磁同步电机中,在不增加转子径向尺寸的前提下放置更多的永磁体,从而提高了永磁体工作点和电机凸极率。
同时,以提高电机输出转矩性能和增强电机弱磁扩速能力为优化目标,以双层磁钢磁极结构参数为优化变量,基于Taguchi 法实现了内置式永磁同步电机转子磁极结构的多目标优化设计,在有效抑制电机电磁转矩波动的同时扩大了电机转速运行范围。
在此基础上,对空载运行、额定负载运行、最大转矩运行、最高转速运行等4种电动车辆用内置式永磁同步电机典型工况进行了有限元仿真分析。
结果表明:通过优化磁极结构,电机最大转矩点和最高转速点的电磁转矩平均值分别达到164.18N ·m 和34.81N ·m ,均高于设计要求,最大转矩点和最高转速点性能得到了提升,验证了所提双层磁钢结构和优化设计方案的有效性。
关键词:电动车辆;内置式永磁同步电机;双层磁钢结构;Taguchi 法中图分类号:TM351文献标志码:A 文章编号:员远苑员原园圆源载(圆园20)园6原园园76原07第39卷第6期圆园20年12月Vol.39No.6December 2020DOI :10.3969/j.issn.1671-024x.2020.06.012天津工业大学学报允韵哉砸晕粤蕴韵云栽陨粤晕GONG 哉晕陨灾耘砸杂陨栽再Optimization design of double-layer interior permanent magnet synchronous motor LI Wei 1,WANG Hui-min 2,ZHANG Zhi-feng 1,DENG Qiang 1,ZHANG Zhi-qiang 1,TANG Yuan 1,FU Guo-zhong 1(1.Science and Technology on Reactor System Design Technology Laboratory ,Nuclear Power Institute of China ,Chengdu 610213,China ;2.School of Electrical Engineering and Automation ,Tiangong University ,Tianjin 300387,China )Abstract :In order to improve the performances of the permanent magnet synchronous motor 渊PMSM冤such as high torqueoutput and wide speed range袁the double-layer structure is adopted as the magnetic pole structure for the interior PMSM applied in electric vehicles.More permanent magnets are placed under the same size of the rotor to im鄄prove the working point of the permanent magnet and obtain the higher motor salient rate.Meanwhile the geomet鄄rical parameters of the double-layer structure are chosen as the optimization variables.And the multi-objective optimization design of the double-layer pole structure for the interior PMSM is realized based on the Taguchi method袁to improve the performance of output torque as well as the ability of flux weakening and speed expand鄄ing.On this basis袁the finite element simulation analyses are carried out for four typical working conditions of the interior PMSM applied in electric vehicles袁including no-load operation袁rated load operation袁maximum torque operation and maximum speed operation.It is shown that by the optimization of the double-layer structure the av鄄erage values of electromagnetic torque at the maximum torque point and maximum speed point of the motor reach 164.18N 窑m and 34.81N 窑m袁respectively袁which were higher than the design requirements.The performances ofthe maximum torque point and maximum speed point are improved袁and the effectiveness of the proposed structure and its optimization design are verified by the simulation results.Key words :electric vehicle曰interior permanent magnet synchronous motor渊PMSM冤曰double-layer pole structure曰Taguchimethod收稿日期:2020-06-29基金项目:国家自然科学基金资助项目(51507111)第一作者:李维(1983—),男,高级工程师,主要研究方向为反应堆结构设计。
教学案例一:田口参数实验设计1 田口方法源起实验设计是以概率论与数理统计为理论基础,经济地、科学地制定实验方案以便对实验数据进行有效的统计分析的数学理论和方法。
其基本思想是英国统计学家R. A. Fisher在进行农田实验时提出的。
他在实验中发现,环境条件难于严格控制,随机误差不可忽视,故提出对实验方案必须作合理的安排,使实验数据有合适的数学模型,以减少随机误差的影响,从而提高实验结果的精度和可靠度,这就是实验设计的基本思想。
在三十、四十年代,英、美、苏等国对实验设计法进行了进一步研究,并将其逐步推广到工业生产领域中,在冶金、建筑、纺织、机械、医药等行业都有所应用。
二战期间,英美等国在工业试验中采用实验设计法取得了显著效果。
战后,日本将其作为管理技术之一从英美引进,对其经济复苏起了促进作用。
今天,实验设计已成为日本企业界人士、工程技术人员、研究人员和管理人员必备的一种通用技术。
实验计划法最早是由日本田口玄一(G. Taguchi)博士将其应用到工业界而一举成名的。
五十年代,田口玄一博士借鉴实验设计法提出了信噪比实验设计,并逐步发展为以质量损失函数、三次设计为基本思想的田口方法。
田口博士最早出书介绍他的理论时用的就是“实验计划法─DOE”,所以一般人惯以实验计划法或DOE来称之。
但随着在日本产业界应用的普及,案例与经验的累积,田口博士的理论和工具日渐完备,整个田口的这套方法在日本产业专家学者的努力之下,早已脱离其原始风貌,展现出更新更好的体系化内容。
日本以质量工程(Quality Enginerring)称之。
但是,严格来讲,田口方法和DOE是不同的东西。
田口方法重视各产业的技术,着重快速找到在最低成本时的最佳质量。
DOE则重视统计技术,着重符合数学的严谨性。
虽然学术界普遍认为田口方法缺少统计的严格性,但该方法还是以其简单实用性广为工业界所应用和推广。
先进国家对田口方法越来越重视,并且也已经取得了很好的效果。
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tipped tool(硬质合金刀) tool bits (车刀)Tool wearFrom Wikipedia, the free encyclopediaTool wear describes the gradual failure of cutting tools due to regular operation. It is a term often associated with tipped tools, tool bits, or drill bits that are used with machine tools.刀具磨损是用来描述刀具在正常加工过程中的一种逐渐失效的形似。
主要是用以描述硬质合金刀,车刀和钻铣刀等的逐渐失效的术语。
Types of wear include:∙flank wear in which the portion of the tool in contact with the finished part erodes.Can be described using the Tool Life Expectancy equation.∙刀具的侧面/后刀面磨损是刀具和工件已切削完的部分接触磨损中的一部分,可以用刀具寿命公式表示。
∙crater wear in which contact with chips erodes the rake face. This is somewhat normal for tool wear, and does not seriously degrade the use of a tool until it becomes serious enough to cause a cutting edge failure.∙剥落磨损或(前刀面磨损/月牙洼磨损)是由于和切屑相接处而磨损出现的一个凹坑(月牙洼),月牙洼和切削刃之间有一小的棱边,在磨损过程中月牙洼逐渐扩大使得棱边逐渐变窄,切削刃的强度大为增加,极易导致崩刀现象。
翻译以下英文术语,并深入了解术语的含义。
1.optimal solution:最优解,使目标函数取得最大值的可行解。
P352.objective function:目标函数,指需优化的量,即欲达的目标,用决策变量的表达式表示。
P123.feasible region:可行域,指所有可行解的集合。
P284. simplex method:单纯形法:是一种迭代的算法,其核心思想是不仅将取值范围限制在顶点上,而且保证每换一个顶点,目标函数值都有所改善.P1175. BF solutions:基可行解,满足变量非负约束条件的基解称为基可行解。
P1816. sensitivity analysis:敏感性分析:指对系统或事物因周围条件变化显示出来的敏感程度的分析。
P1467. algorithm:算法,指系统的求解过程。
p1078. spanning tree:生成树,若有限图的生成子图是一棵树,则称为该图的生成树。
树指不含有圈的连通网。
P3799. states:状态,各阶段开始时的客观条件. P44510.directed arc:有向弧,指通过一条弧的流只有一个方向的弧。
P37611. unbounded:无界,指约束条件不能阻止目标函数值在有利的方向上(正的或者负的)增长。
P3512. CPF solution:顶点(角点)可行解,指位于可行域顶点的解。
P3713. functional constraints:约束条件,指决策变量取值时受到的各种资源条件的限制,通常表达为含决策变量的等式或不等式。
P3414 multiple optimal solutions:多个最优解的问题,指有无穷多解,每一个解都有相同的目标函数值的问题。
P12215. slack variable:松弛变量,添加x i到约束条件的不等式中使其变为等式的变量P10816. augmented solution:增广解,指原始变量(决策变量)取值再加入相应的松弛变量取值后而形成的解。
基于Taguchi方法的电机转子铸铝工艺参数优化设计摘要:运用taguchi方法对电机转子铸铝工艺中的铝液浇注温度和主要模具温度进行优化设计,根据凝固时间的实验结果,获取最佳的浇注温度和模具温度组合,为提高铸铝转子质量提供参考。
abstract: aluminum liquid pouring temperature and mold temperature were optimized on the motor rotoraluminum-casting process by using the taguchi method. according to the results of solidification time, the best pouring temperature and mold temperature combination were determined which provided reference for improving the quality of aluminum-casting rotor.关键词: taguchi方法;工艺参数优化;浇注温度;模具温度key words: taguchi method;technological parameters optimization;pouring temperature;mold temperature中图分类号:tm303 文献标识码:a 文章编号:1006-4311(2013)24-0034-020 引言电机铸铝转子的加工质量是影响电机整体质量的关键要素之一,转子铸铝方法主要有离心铸铝和压力铸铝两种,其中压力铸铝用压力将融化好的金属铝液注入型腔,待冷却凝固成铸件。
该方法质量问题最突出的表现是转子内部存在的气孔,其次是转子内部的笼条细条、断条、夹渣以及端环部分的缩孔、冷裂、热裂、缺肉等问题。
这些问题最终导致整机的电气性能下降、转速不够、效率降低。
CHAPTER 10: ARBITRAGE PRICING THEORY ANDMULTIFACTOR MODELS OF RISK AND RETURN PROBLEM SETS1. The revised estimate of the expected rate of return on the stock would be the oldestimate plus the sum of the products of the unexpected change in each factor times the respective sensitivity coefficient:Revised estimate = 12% + [(1 × 2%) + (0.5 × 3%)] = 15.5%Note that the IP estimate is computed as: 1 × (5% - 3%), and the IR estimate iscomputed as: 0.5 × (8% - 5%).2. The APT factors must correlate with major sources of uncertainty, i.e., sources ofuncertainty that are of concern to many investors. Researchers should investigatefactors that correlate with uncertainty in consumption and investment opportunities.GDP, the inflation rate, and interest rates are among the factors that can be expected to determine risk premiums. In particular, industrial production (IP) is a goodindicator of changes in the business cycle. Thus, IP is a candidate for a factor that is highly correlated with uncertainties that have to do with investment andconsumption opportunities in the economy.3. Any pattern of returns can be explained if we are free to choose an indefinitelylarge number of explanatory factors. If a theory of asset pricing is to have value, itmust explain returns using a reasonably limited number of explanatory variables(i.e., systematic factors such as unemployment levels, GDP, and oil prices).4. Equation 10.11 applies here:E(r p) = r f + βP1 [E(r1 ) −r f ] + βP2 [E(r2 ) – r f]We need to find the risk premium (RP) for each of the two factors:RP1 = [E(r1 ) −r f] and RP2 = [E(r2 ) −r f]In order to do so, we solve the following system of two equations with two unknowns: .31 = .06 + (1.5 ×RP1 ) + (2.0 ×RP2 ).27 = .06 + (2.2 ×RP1 ) + [(–0.2) ×RP2 ]The solution to this set of equations isRP1 = 10% and RP2 = 5%Thus, the expected return-beta relationship isE(r P) = 6% + (βP1× 10%) + (βP2× 5%)5. The expected return for portfolio F equals the risk-free rate since its beta equals 0.For portfolio A, the ratio of risk premium to beta is (12 − 6)/1.2 = 5For portfolio E, the ratio is lower at (8 – 6)/0.6 = 3.33This implies that an arbitrage opportunity exists. For instance, you can create aportfolio G with beta equal to 0.6 (the same as E’s) by combining portfolio A and portfolio F in equal weights. The expected return and beta for portfolio G are then: E(r G) = (0.5 × 12%) + (0.5 × 6%) = 9%βG = (0.5 × 1.2) + (0.5 × 0%) = 0.6Comparing portfolio G to portfolio E, G has the same beta and higher return.Therefore, an arbitrage opportunity exists by buying portfolio G and selling anequal amount of portfolio E. The profit for this arbitrage will ber G – r E =[9% + (0.6 ×F)] − [8% + (0.6 ×F)] = 1%That is, 1% of the funds (long or short) in each portfolio.6. Substituting the portfolio returns and betas in the expected return-beta relationship,we obtain two equations with two unknowns, the risk-free rate (r f) and the factor risk premium (RP):12% = r f + (1.2 ×RP)9% = r f + (0.8 ×RP)Solving these equations, we obtainr f = 3% and RP = 7.5%7. a. Shorting an equally weighted portfolio of the ten negative-alpha stocks andinvesting the proceeds in an equally-weighted portfolio of the 10 positive-alpha stocks eliminates the market exposure and creates a zero-investmentportfolio. Denoting the systematic market factor as R M, the expected dollarreturn is (noting that the expectation of nonsystematic risk, e, is zero):$1,000,000 × [0.02 + (1.0 ×R M)] − $1,000,000 × [(–0.02) + (1.0 ×R M)]= $1,000,000 × 0.04 = $40,000The sensitivity of the payoff of this portfolio to the market factor is zerobecause the exposures of the positive alpha and negative alpha stocks cancelout. (Notice that the terms involving R M sum to zero.) Thus, the systematiccomponent of total risk is also zero. The variance of the analyst’s profit is notzero, however, since this portfolio is not well diversified.For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor willhave a $100,000 position (either long or short) in each stock. Net marketexposure is zero, but firm-specific risk has not been fully diversified. Thevariance of dollar returns from the positions in the 20 stocks is20 × [(100,000 × 0.30)2] = 18,000,000,000The standard deviation of dollar returns is $134,164.b. If n = 50 stocks (25 stocks long and 25 stocks short), the investor will have a$40,000 position in each stock, and the variance of dollar returns is50 × [(40,000 × 0.30)2] = 7,200,000,000The standard deviation of dollar returns is $84,853.Similarly, if n = 100 stocks (50 stocks long and 50 stocks short), the investorwill have a $20,000 position in each stock, and the variance of dollar returns is100 × [(20,000 × 0.30)2] = 3,600,000,000The standard deviation of dollar returns is $60,000.Notice that, when the number of stocks increases by a factor of 5 (i.e., from 20 to 100), standard deviation decreases by a factor of 5= 2.23607 (from$134,164 to $60,000).8. a. )(σσβσ2222e M +=88125)208.0(σ2222=+×=A50010)200.1(σ2222=+×=B97620)202.1(σ2222=+×=Cb. If there are an infinite number of assets with identical characteristics, then awell-diversified portfolio of each type will have only systematic risk since thenonsystematic risk will approach zero with large n. Each variance is simply β2 × market variance:222Well-diversified σ256Well-diversified σ400Well-diversified σ576A B C;;;The mean will equal that of the individual (identical) stocks.c. There is no arbitrage opportunity because the well-diversified portfolios allplot on the security market line (SML). Because they are fairly priced, there isno arbitrage.9. a. A long position in a portfolio (P) composed of portfolios A and B will offer anexpected return-beta trade-off lying on a straight line between points A and B.Therefore, we can choose weights such that βP = βC but with expected returnhigher than that of portfolio C. Hence, combining P with a short position in Cwill create an arbitrage portfolio with zero investment, zero beta, and positiverate of return.b. The argument in part (a) leads to the proposition that the coefficient of β2must be zero in order to preclude arbitrage opportunities.10. a. E(r) = 6% + (1.2 × 6%) + (0.5 × 8%) + (0.3 × 3%) = 18.1%b.Surprises in the macroeconomic factors will result in surprises in the return ofthe stock:Unexpected return from macro factors =[1.2 × (4% – 5%)] + [0.5 × (6% – 3%)] + [0.3 × (0% – 2%)] = –0.3%E(r) =18.1% − 0.3% = 17.8%11. The APT required (i.e., equilibrium) rate of return on the stock based on r f and thefactor betas isRequired E(r) = 6% + (1 × 6%) + (0.5 × 2%) + (0.75 × 4%) = 16% According to the equation for the return on the stock, the actually expected return on the stock is 15% (because the expected surprises on all factors are zero bydefinition). Because the actually expected return based on risk is less than theequilibrium return, we conclude that the stock is overpriced.12. The first two factors seem promising with respect to the likely impact on the firm’scost of capital. Both are macro factors that would elicit hedging demands acrossbroad sectors of investors. The third factor, while important to Pork Products, is a poor choice for a multifactor SML because the price of hogs is of minor importance to most investors and is therefore highly unlikely to be a priced risk factor. Betterchoices would focus on variables that investors in aggregate might find moreimportant to their welfare. Examples include: inflation uncertainty, short-terminterest-rate risk, energy price risk, or exchange rate risk. The important point here is that, in specifying a multifactor SML, we not confuse risk factors that are important toa particular investor with factors that are important to investors in general; only the latter are likely to command a risk premium in the capital markets.13. The formula is ()0.04 1.250.08 1.50.02.1717%E r =+×+×==14. If 4%f r = and based on the sensitivities to real GDP (0.75) and inflation (1.25),McCracken would calculate the expected return for the Orb Large Cap Fund to be:()0.040.750.08 1.250.02.040.0858.5% above the risk free rate E r =+×+×=+=Therefore, Kwon’s fundamental analysis estimate is congruent with McCracken’sAPT estimate. If we assume that both Kwon and McCracken’s estimates on the return of Orb’s Large Cap Fund are accurate, then no arbitrage profit is possible.15. In order to eliminate inflation, the following three equations must be solvedsimultaneously, where the GDP sensitivity will equal 1 in the first equation,inflation sensitivity will equal 0 in the second equation and the sum of the weights must equal 1 in the third equation.1.1.250.75 1.012.1.5 1.25 2.003.1wx wy wz wz wy wz wx wy wz ++=++=++=Here, x represents Orb’s High Growth Fund, y represents Large Cap Fund and z represents Utility Fund. Using algebraic manipulation will yield wx = wy = 1.6 and wz = -2.2.16. Since retirees living off a steady income would be hurt by inflation, this portfoliowould not be appropriate for them. Retirees would want a portfolio with a return positively correlated with inflation to preserve value, and less correlated with the variable growth of GDP. Thus, Stiles is wrong. McCracken is correct in that supply side macroeconomic policies are generally designed to increase output at aminimum of inflationary pressure. Increased output would mean higher GDP, which in turn would increase returns of a fund positively correlated with GDP.17. The maximum residual variance is tied to the number of securities (n ) in theportfolio because, as we increase the number of securities, we are more likely to encounter securities with larger residual variances. The starting point is todetermine the practical limit on the portfolio residual standard deviation, σ(e P ), that still qualifies as a well-diversified portfolio. A reasonable approach is to compareσ2(e P) to the market variance, or equivalently, to compare σ(e P) to the market standard deviation. Suppose we do not allow σ(e P) to exceed pσM, where p is a small decimal fraction, for example, 0.05; then, the smaller the value we choose for p, the more stringent our criterion for defining how diversified a well-diversified portfolio must be.Now construct a portfolio of n securities with weights w1, w2,…,w n, so that Σw i =1. The portfolio residual variance is σ2(e P) = Σw12σ2(e i)To meet our practical definition of sufficiently diversified, we require this residual variance to be less than (pσM)2. A sure and simple way to proceed is to assume the worst, that is, assume that the residual variance of each security is the highest possible value allowed under the assumptions of the problem: σ2(e i) = nσ2MIn that case σ2(e P) = Σw i2 nσM2Now apply the constraint: Σw i2 nσM2 ≤ (pσM)2This requires that: nΣw i2 ≤ p2Or, equivalently, that: Σw i2 ≤ p2/nA relatively easy way to generate a set of well-diversified portfolios is to use portfolio weights that follow a geometric progression, since the computations then become relatively straightforward. Choose w1 and a common factor q for the geometric progression such that q < 1. Therefore, the weight on each stock is a fraction q of the weight on the previous stock in the series. Then the sum of n terms is:Σw i= w1(1– q n)/(1– q) = 1or: w1 = (1– q)/(1– q n)The sum of the n squared weights is similarly obtained from w12 and a common geometric progression factor of q2. ThereforeΣw i2 = w12(1– q2n)/(1– q 2)Substituting for w1 from above, we obtainΣw i2 = [(1– q)2/(1– q n)2] × [(1– q2n)/(1– q 2)]For sufficient diversification, we choose q so that Σw i2 ≤ p2/nFor example, continue to assume that p = 0.05 and n = 1,000. If we chooseq = 0.9973, then we will satisfy the required condition. At this value for q w1 = 0.0029 and w n = 0.0029 × 0.99731,000In this case, w1 is about 15 times w n. Despite this significant departure from equal weighting, this portfolio is nevertheless well diversified. Any value of q between0.9973 and 1.0 results in a well-diversified portfolio. As q gets closer to 1, theportfolio approaches equal weighting.18. a. Assume a single-factor economy, with a factor risk premium E M and a (large)set of well-diversified portfolios with beta βP. Suppose we create a portfolio Zby allocating the portion w to portfolio P and (1 – w) to the market portfolioM. The rate of return on portfolio Z is:R Z = (w × R P) + [(1 – w) × R M]Portfolio Z is riskless if we choose w so that βZ = 0. This requires that:βZ = (w × βP) + [(1 – w) × 1] = 0 ⇒w = 1/(1 – βP) and (1 – w) = –βP/(1 – βP)Substitute this value for w in the expression for R Z:R Z = {[1/(1 – βP)] × R P} – {[βP/(1 – βP)] × R M}Since βZ = 0, then, in order to avoid arbitrage, R Z must be zero.This implies that: R P = βP × R MTaking expectations we have:E P = βP × E MThis is the SML for well-diversified portfolios.b. The same argument can be used to show that, in a three-factor model withfactor risk premiums E M, E1 and E2, in order to avoid arbitrage, we must have:E P = (βPM × E M) + (βP1 × E1) + (βP2 × E2)This is the SML for a three-factor economy.19. a. The Fama-French (FF) three-factor model holds that one of the factors drivingreturns is firm size. An index with returns highly correlated with firm size (i.e.,firm capitalization) that captures this factor is SMB (small minus big), thereturn for a portfolio of small stocks in excess of the return for a portfolio oflarge stocks. The returns for a small firm will be positively correlated withSMB. Moreover, the smaller the firm, the greater its residual from the othertwo factors, the market portfolio and the HML portfolio, which is the returnfor a portfolio of high book-to-market stocks in excess of the return for aportfolio of low book-to-market stocks. Hence, the ratio of the variance of thisresidual to the variance of the return on SMB will be larger and, together withthe higher correlation, results in a high beta on the SMB factor.b.This question appears to point to a flaw in the FF model. The model predictsthat firm size affects average returns so that, if two firms merge into a largerfirm, then the FF model predicts lower average returns for the merged firm.However, there seems to be no reason for the merged firm to underperformthe returns of the component companies, assuming that the component firmswere unrelated and that they will now be operated independently. We mighttherefore expect that the performance of the merged firm would be the sameas the performance of a portfolio of the originally independent firms, but theFF model predicts that the increased firm size will result in lower averagereturns. Therefore, the question revolves around the behavior of returns for aportfolio of small firms, compared to the return for larger firms that resultfrom merging those small firms into larger ones. Had past mergers of smallfirms into larger firms resulted, on average, in no change in the resultantlarger firms’ stock return characteristics (compared to the portfolio of stocksof the merged firms), the size factor in the FF model would have failed.Perhaps the reason the size factor seems to help explain stock returns is that,when small firms become large, the characteristics of their fortunes (andhence their stock returns) change in a significant way. Put differently, stocksof large firms that result from a merger of smaller firms appear empirically tobehave differently from portfolios of the smaller component firms.Specifically, the FF model predicts that the large firm will have a smaller riskpremium. Notice that this development is not necessarily a bad thing for thestockholders of the smaller firms that merge. The lower risk premium may bedue, in part, to the increase in value of the larger firm relative to the mergedfirms.CFA PROBLEMS1. a. This statement is incorrect. The CAPM requires a mean-variance efficientmarket portfolio, but APT does not.b.This statement is incorrect. The CAPM assumes normally distributed securityreturns, but APT does not.c. This statement is correct.2. b. Since portfolio X has β = 1.0, then X is the market portfolio and E(R M) =16%.Using E(R M ) = 16% and r f = 8%, the expected return for portfolio Y is notconsistent.3. d.4. c.5. d.6. c. Investors will take on as large a position as possible only if the mispricingopportunity is an arbitrage. Otherwise, considerations of risk anddiversification will limit the position they attempt to take in the mispricedsecurity.7. d.8. d.。
拓扑优化(topology optimization)1. 基本概念拓扑优化是结构优化的一种。
结构优化可分为尺寸优化、形状优化、形貌优化和拓扑优化。
其中尺寸优化以结构设结构优化类型的差异计参数为优化对象,比如板厚、梁的截面宽、长和厚等;形状优化以结构件外形或者孔洞形状为优化对象,比如凸台过渡倒角的形状等;形貌优化是在已有薄板上寻找新的凸台分布,提高局部刚度;拓扑优化以材料分布为优化对象,通过拓扑优化,可以在均匀分布材料的设计空间中找到最佳的分布方案。
拓扑优化相对于尺寸优化和形状优化,具有更多的设计自由度,能够获得更大的设计空间,是结构优化最具发展前景的一个方面。
图示例子展示了尺寸优化、形状优化和拓扑优化在设计减重孔时的不同表现。
2. 基本原理拓扑优化的研究领域主要分为连续体拓扑优化和离散结构拓扑优化。
不论哪个领域,都要依赖于有限元方法。
连续体拓扑优化是把优化空间的材料离散成有限个单元(壳单元或者体单元),离散结构拓扑优化是在设计空间内建立一个由有限个梁单元组成的基结构,然后根据算法确定设计空间内单元的去留,保留下来的单元即构成最终的拓扑方案,从而实现拓扑优化。
3. 优化方法目前连续体拓扑优化方法主要有均匀化方法[1]、变密度法[2]、渐进结构优化法[3](ESO)以及水平集方法[4]等。
离散结构拓扑优化主要是在基结构方法基础上采用不同的优化策略(算法)进行求解,比如程耿东的松弛方法[5],基于遗传算法的拓扑优化[6]等。
4. 商用软件目前,连续体拓扑优化的研究已经较为成熟,其中变密度法已经被应用到商用优化软件中,其中最著名的是美国Altair公司Hyperworks系列软件中的Optistruc t和德国Fe-design公司的Tosca等。
前者能够采用Hypermesh作为前处理器,在各大行业内都得到较多的应用;后者最开始只集中于优化设计,而没有自己的有限元前处理器,操作较为麻烦,近年来和Ansa联盟,开发了基于Ansa的前处理器,但在国内应用的较少。
Journal of Hazardous Materials 192 (2011) 1046–1055Contents lists available at ScienceDirectJournal of HazardousMaterialsj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /j h a z m atTaguchi optimization approach for Pb(II)and Hg(II)removal from aqueous solutions using modified mesoporous carbonGhasem Zolfaghari a ,Abbas Esmaili-Sari a ,Mansoor Anbia b ,∗,Habibollah Younesi a ,Shahram Amirmahmoodi b ,Ali Ghafari-Nazari caDepartment of Environment,Faculty of Natural Resources and Marine Sciences,Tarbiat Modares University,Noor,Mazandaran,P.O.Box:46414-356,Iran bResearch Laboratory of Nanoporous Materials,Faculty of Chemistry,Iran University of Science and Technology,Farjam Street,Narmak,Tehran 16846,Iran cLoabiran Company,Research and Development Group,Shiraz,Irana r t i c l ei n f oArticle history:Received 22January 2011Received in revised form 2June 2011Accepted 6June 2011Available online 12 June 2011Keywords:Lead Mercury Zn-OCMK-3Taguchi method Adsorptiona b s t r a c tUsing the Taguchi method,this study presents a systematic optimization approach for removal of lead (Pb)and mercury (Hg)by a nanostructure,zinc oxide-modified mesoporous carbon CMK-3denoted as Zn-OCMK-3.CMK-3was synthesized by using SBA-15and then oxidized by nitric acid.The zinc oxide was loaded to the modified CMK-3by the equilibrium adsorption of Zn(II)ions from aqueous solution followed by calcination to convert zinc nitrate to zinc oxide.The CMK-3had porous structure and high specific surface area which can accommodate zinc oxide in a spreading manner,the zinc oxide connects to the carbon surface via oxygen atoms.The controllable factors such as agitation time,initial concentration,temperature,dose and pH of solution have been optimized.Under optimum conditions,the pollutant removal efficiency (PRE)was 97.25%for Pb(II)and 99%for Hg(II).The percentage contribution of each controllable factor was also determined.The initial concentration of pollutant is the most influential factor,and its value of percentage contribution is up to 31%and 43%for Pb and Hg,respectively.Our results show that the Zn-OCMK-3is an effective nanoadsorbent for lead and mercury pollution ngmuir and Freundlich adsorption isotherms were used to model the equilibrium adsorption data for Pb(II)and Hg(II).© 2011 Elsevier B.V. All rights reserved.1.IntroductionHeavy metal contamination such as lead (Pb)and mercury (Hg)has been identified as a concern in environment,due to discharges from industrial wastes,agricultural and urban sewage [1].Pb has been well recognized for its negative effect on the environment where it accumulates readily in living systems [2].There is a great concern about Hg pollution,which is due to its toxicity,persistent character in the environment and biota as well as biomagnifica-tion along the food chain [3].Increasing pollution by Pb and Hg has been reported in recent years in Iran [4,5].The results from the data collected in the rivers around Caspian Sea and Anzali Wetland,North Iran,show the various degrees of Pb and Hg con-centrations [6].Thus,the increased awareness of toxicity of heavy metal and the stringent environmental safety regulations demand the removal of them from the various discharges to avoid con-tamination of the biological ecosystem.Several methods such as coagulation [7],chemical oxidation [8],photocatalytic degradation [9],adsorption [10],etc.are being used for the removal of heavy∗Corresponding author.Tel.:+982177240516;fax:+982177491204.E-mail address:anbia@iust.ac.ir (M.Anbia).metal from water.Among these methods,adsorption is still the most versatile and widely used.Alternative adsorbents studied include biosorbents [11],clays [12],activated carbon [13],resins [14]and zeolites [15].Increasingly stringent standard on the quality of drinking water has stimulated a growing effort on the develop-ment of new high efficient adsorbents.The development of porous materials with large surface areas is currently an area of exten-sive research,particularly with regard to potential applications as environmental remediation.An upsurge began in 1992with the development by the Mobil Oil Company of the class of silicate meso-porous materials known as the M41S phase [16].It was reported that ordered mesoporous silica (OMS)can be used as an adsorbent for removal of numerous compounds [17–19].Recently,the syn-thesis of ordered mesoporous carbons (OMC)using OMS as hard templates has attracted a great deal of attention.Ryoo et al.[20]first used MCM-48silica as the template to synthesize CMK-1carbon.Subsequently,this research group reported the synthesis of CMK-2[21],CMK-3[22],CMK-4[23],and CMK-5[24].Very recently,Guo et al.[25]reported the synthesis of OMC by using SBA-16.Some researchers modified and functionalized the surface of the OMC for more applications [26,27].In the present study,CMK-3was synthesized using SBA-15,modified by HNO 3treatment and then functionalized by Zn(NO 3)2·4H 2O.This modified nanostructure,0304-3894/$–see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.jhazmat.2011.06.006G.Zolfaghari et al./Journal of Hazardous Materials 192 (2011) 1046–10551047zinc oxide-modified mesoporous carbon CMK-3called Zn-OCMK-3.The novelty of the present study consists of Taguchi optimization method for the removal of lead and mercury from aqueous solution and experimental data are presented in order to demonstrate the practical usage of zinc oxide-modified mesoporous carbon CMK-3.The optimum conditions with the higher pollutant removal effi-ciency (PRE)for batch adsorption studies were determined using the Taguchi method.In this study,agitation time,initial concentra-tion,temperature,dose and pH were studied as the controllable factors.Accordingly,the percentage contribution of each afore-mentioned experimental parameter to the process is determined using the Taguchi method.Furthermore,Langmuir and Freundlich adsorption isotherms were studied to explain the sorption mecha-nism.2.Design of experiments (DOE)Design of experiments (DOE)is developing a scheme of experiment different conditions.The Taguchi method which was established by Genichi Taguchi has been generally adopted to optimize the design variables because this approach can signifi-cantly minimize the overall testing time and the experimental costs [28–31].The Taguchi crossed array layout consists of an inner array and an outer array [32].The inner array is made up of the orthogonal array (OA)selected from all possible combinations of the control-lable ing the orthogonal array specially designed for the Taguchi method,the optimum experimental conditions can be eas-ily determined [28].Accordingly,an analysis of the signal-to-noise (S/N)ratio is needed to evaluate the experimental u-ally,three types of S/N ratio analysis are applicable:(1)lower is better (LB),(2)nominal is best (NB),and (3)higher is better (HB)[33].Because the target of this study is to maximize the pollutant removal efficiency,the S/N ratio with HB characteristics is required,which is given by Eq.(1):S /N =−10log 101n1PRE i2 (1)where n is the number of repetitions under the same experimentalconditions,and PRE represents the results of measurements.3.Experimental3.1.MaterialsThe reactants used in this study were tetraethyl orthosilicate (TEOS,98%)as a silica source,distilled water (DW),Pluronic ®P123(EO 20PO 70EO 20)as a surfactant and phosphoric acid (H 3PO 4,85%)from Aldrich (U.K.),sucrose as a carbon source,sodium hydroxide (NaOH),ethanol,sulfuric acid (H 2SO 4,98%)and zinc nitrate tetrahy-drate (Zn(NO 3)2·4H 2O)from Merck,Germany.Hydrochloric acid (HCl,37%)and sodium hydroxide were used to control the pH of water samples.3.2.Ordered mesoporous silica:SBA-15SBA-15was synthesized as reported by Colilla et al.[34].The synthesis procedure was based on the use of P123as direct-ing agent of the silica and phosphoric acid as catalyst.The molar compositions of the initial solutions here presented are as follows:SiO 2/P123/H 3PO 4/H 2O =1/0.017/1.5/208.These solutions were stirred at 35◦C for 24h in sealed Teflon beakers and then fur-ther heated at 100◦C for 24h.The obtained products were filtered,washed with DW and then dried at 90◦C for 12h in air.The surfac-tant removal was done by heating first at 250◦C (3h)and then at 550◦C (4h)in air.3.3.Ordered mesoporous carbon:CMK-3CMK-3was prepared according to the synthesis procedure described by Jun et al.[22].SBA-15was used as a hard template.1g SBA-15was added to a solution obtained by dissolving 1.25g of sucrose and 0.14g of H 2SO 4in 5g H 2O.The resultant mixture was dried in an oven at 100◦C (6h),and subsequently,the oven temperature was increased to 160◦C (6h).After that,the SBA-15containing the partially carbonizing organic masses was added in aqueous solution consisting sucrose (0.75g),H 2SO 4(0.08g)and water (5g).The resultant mixture was dried again at 100◦C (6h),and subsequently,the oven temperature was increased to 160◦C (6h).This powder sample was heated to 900◦C using a fused quartz reactor.The carbon–silica composite obtained was washed with 1M aqueous ethanolic NaOH solution (50vol.%NaOH solution and 50vol.%ethanol)twice at 90◦C,in order to remove the silica tem-plate.The carbon samples obtained after the silica removal were filtered,washed with ethanol and dried at 120◦C.3.4.Modification of CMK-3:OCMK-3The texture and surface chemistry of synthesized CMK-3was modified by HNO 3to optimize their ability of dispersing active metal particles [35].0.1g of dried CMK-3powder was treated with 15ml of HNO 3solution (2M)at 80◦C under refluxing.Samples were recovered and washed thoroughly with DW until the pH was close to 7.Finally,carbon supports were filtered,washed with distilled water and dried at 108◦C.It was denoted as OCMK-3.3.5.Functionalization of OCMK-3:Zn-OCMK-3The zinc oxide was loaded to the OCMK-3by the equilibrium adsorption of Zn(II)ions from aqueous solution followed by calci-nation in air at 350◦C (2h)to convert zinc nitrate to zinc oxide.The Zn(II)solution was prepared by dissolving Zn(NO 3)2.4H 2O in THF (1.5mol/l).80ml of Zn(II)solution including 2g of the OCMK-3was agitated at 150rpm for 3days to reach the equilibrium state.The solid was separated by filtration and then dried in oven at 110◦C before calcinations at 350◦C.The ZnO functionalized OCMK-3was referred as Zn-OCMK-3.The filtrate was analyzed by Inductively Coupled Plasma to ensure complete adsorption.It was observed that the Zn was taken up by OCMK-3.3.6.CharacterizationThe X-ray powder diffraction (XRD)patterns were recorded on a Philips 1830diffractometer using Cu K ␣radiation.The diffractograms were recorded in the 2Ârange of 0.5–10◦with a 2Âstep size of 0.01◦.The surface area was measured by nitro-gen adsorption/desorption at 77K using Brunaure–Emmet–Teller (BET)method.Scanning electron microscopy (SEM)images were obtained with JEOL 6300F SEM.Transmission electron microscopy (TEM)images for determination of ZnO dispersion and morphology of samples were obtained using a 300kV Philips CM-30TEM.Table 1Controllable factors and their levels.Factor DescriptionLevel 1Level 2Level 3Level 4A Agitation time (min)1030120240B Concentration (mg/l)10100200400C Dose (g/l)0.10.30.50.7D Temperature (◦C)20253035EpH24671048G.Zolfaghari et al./Journal of Hazardous Materials 192 (2011) 1046–10553.7.Adsorption procedure3.7.1.Optimization studiesThis study considers five controllable factors,and each factor has four levels (Table 1).Therefore,an L 16(45)orthogonal array is chosen,and the experimental conditions (Table 2)can be obtained by combining Table 1and the L 16(45)orthogonal array.Stock solu-tions of 1000mg/l Pb(II)and Hg(II)were prepared from Pb(NO 3)2as the Pb source and Hg(NO 3)2as the Hg source in deionized water.A series of aqueous solutions of Pb and Hg with the agita-tion time of 10–240min,initial concentration of 10–400mg/l,dose of 0.1–0.7g/l,temperature of 20–35◦C,and pH of 2–7were pre-pared (Table 2).Batch adsorption tests were performed by shaking 500ml Amber Winchester bottles containing 100ml of the Pb(II)and Hg(II)in a Gallenkamp incubator shaker,stirring at 150rpm.The concentration of heavy metal in the supernatant was analyzed with an Inductively Coupled Plasma Atomic Emission Spectrome-ter (ICP-AES –Perkin-Elmer 4300DV Model).The PRE is calculated using Eq.(2):PRE =C 0−C e C 0×100(2)where C 0and C e are the initial and equilibrium concentrations of pollutant (mg/l),respectively.The analysis of mean (ANOM)statistical approach is adopted herein to develop the optimal conditions [31].Initially,the mean of the S/N ratio of each factor at a certain level should be calculated.For example,(M )Level =iFactor =I,the mean of the S/N ratio of factor I in level i ,is given by Eq.(3):(M )Level =iFactor =I =1n Iin Iij =1S NLevel =iFactor =Ij(3)where n Ii represents the number of appearances of factor I in thelevel i ,and [(S /N)Level =iFactor =I ]j is the S/N ratio of factor I in level i ,andits appearance sequence in Table 2is the j th.By the same measure,the mean of the S/N ratios of the other factors in a certain level can be determined.Thereby,the S/N response table is obtained,and the optimal conditions are established.Finally,the confirmation experiments on solidification under these optimal conditions are carried out.In addition to ANOM,the analysis of variance (ANOVA)[31]statistical method is also used to analyze the influence of eachcontrollable factor on removal of lead and mercury.The percentage contribution of each factor,R F ,is given by Eq.(4):R F =SS R −(DOF R V ER )SS T×100(4)In Eq.(4),DOF R represents the degree of freedom for each factor,which is obtained by subtracting one from the number of the level of each factor (L ).The total sum of squares,SS T ,is given by Eq.(5):SS T =mj =1⎛⎝nj =1PRE 2i⎞⎠−mn (PRE T )2(5)where PRE T =˙m j =1(˙n i =1PRE i )j /(mn ),m represents the number of experiments carried out in this study,and n represents the numberof repetitions.The factorial sum of squares,SS F ,is given by Eq.(6):SS F =mn LLk =l PRE Fk −PRE T2(6)where PRE Fk is the average value of the measurement results of a certain factor in the k th level.Additionally,the variance of error,V Er ,is given by Eq.(7):V Er =SS T −EF =ASS Fm (n −1)(7)3.7.2.Sorption isotherm studiesFor sorption isotherm studies,a series of aqueous solutions of lead and mercury with the initial concentration of 10,100,200and 400mg/l,were prepared.The experiments were carried out under stirring at 150rpm at temperature of 25◦C for 120min contact time,dose 0.5g/l Zn-OCMK-3and pH 6.The amount of lead and mercury adsorption at equilibrium,q e (mg/g)was calculated by Eq.(8):q e =C 0−C eWV (8)where C 0and C e (mg/g)are the liquid phase initial and equilibrium concentrations of the heavy metals respectively.V is the volume of the solution (l),and W is the mass of dry adsorbent used (g)[36].The sorption equilibrium data of Pb(II)and Hg(II)onto theTable 2The S/N ratio of each test.Tests FactorPRE (%)S/NPb(II)Hg(II)ABCDEPRE 1PRE 2PRE 1PRE 2Hg(II)Tests 110100.120228.0028.3030.5030.3828.9829.66Tests 2101000.325431.0028.7435.7535.5029.4831.03Tests 3102000.530663.0063.0147.5447.9535.9833.57Tests 4104000.735748.4046.5047.2047.1033.5133.46Tests 530100.330765.5065.3574.2574.1336.3137.40Tests 6301000.135655.5055.4555.5055.0034.8834.84Tests 7302000.720432.5032.4945.5045.4030.2333.15Tests 8304000.525226.6026.0035.0035.3028.3930.91Tests 9120100.535478.5078.3597.2097.0037.8839.74Tests 101201000.730268.5066.3051.5051.4036.5634.22Tests 111202000.125751.0051.1045.5045.7434.1533.18Tests 121204000.320641.0041.1043.0043.5032.2632.71Tests 13240100.725695.7595.7597.4097.6739.6239.78Tests 142401000.520768.0068.9864.0064.0036.7136.12Tests 152402000.335248.5048.0034.1034.1433.6630.66Tests 162404000.130432.7032.6045.0043.4030.2732.90PRE 1and PRE 2for both pollutants represent the pollutant removal efficiency at first and second test pieces,respectively.The boldfaces correspond to the maximum value of S/N ratio among the 16tests.G.Zolfaghari et al./Journal of Hazardous Materials192 (2011) 1046–10551049Fig.1.XRD patterns of CMK-3,OCMK-3and Zn-OCMK-3.Zn-OCMK-3were analyzed in terms of Langmuir and Freundlich isotherm models[37].The Langmuir model is given by Eq.(9):C eq e=1q m b+1q mC e(9)where q e and C e are the equilibrium concentrations of metal ions in the adsorbed and liquid phases in mg/g and mg/l,respectively.q m (mg/g)and b(l/mg)are the Langmuir constants.In other word,q m is the maximum monolayer capacity and b is the adsorption affinity onto the adsorption sites and it is related to energy of adsorption. The Langmuir constants can be calculated from the slope and inter-cept of the linear plot,C e/q e versus C e.The essential characteristics of the Langmuir isotherm can also be expressed in terms of a dimen-sionless constant of separation factor or equilibrium parameter,R L, which is defined asR L=11+C0b(10) where b is the Langmuir constant and C0is the initial concentra-tion of metal ions.The R L value indicates the shape ofisothermFig.2.Images of samples.(A)SBA-15:SEM,(B)CMK-3:SEM,(C)ZnO supported on OCMK-3(Zn-OCMK-3):SEM,(D)hexagonal structure of CMK-3:TEM,(E)oxidized mesoporous carbon(OCMK-3):TEM(F)zinc oxide-modified mesoporous carbon(Zn-OCMK-3):TEM.1050G.Zolfaghari et al./Journal of Hazardous Materials192 (2011) 1046–1055 Table3S/N ratio response table for Pb(II).Factor/level[(S/N)LevelFactor ]j(M)LevelFactorj=1j=2j=3j=4A/128.9829.4835.9833.5132.00 A/236.3134.8830.2328.3932.46 A/337.8836.5634.1532.2635.22 A/439.6236.7133.6630.2735.07 B/128.9836.3137.8839.6235.70 B/229.4834.8836.5636.7134.41 B/335.9830.2334.1533.6633.51 B/433.5128.3932.2630.2731.12 C/128.9834.8834.1530.2732.08 C/229.4836.3132.2633.6632.93 C/335.9828.3937.8836.7134.75 C/433.5130.2336.5639.6234.99 D/128.9830.2332.2636.7132.05 D/229.4828.3934.1539.6232.92 D/335.9836.3136.5630.2734.79 D/433.5134.8837.8833.6634.99 E/128.9828.3936.5633.6631.91 E/229.4830.2337.8830.2731.97 E/335.9834.8832.2639.6235.69 E/433.5136.3134.1536.7135.18 The boldface corresponds to the maximum value of the mean of the S/N ratios of a certain factor among the four levels.[38].R L values between0and1indicate favorable adsorption,while R L>1,R L=1,and R L=0indicate unfavorable,linear,and irreversible adsorption isotherms.Also,the Freundlich model is given by Eq.(11):ln q e=ln k f+1nln C e(11)where q e and C e are the equilibrium concentrations of metal ions in the adsorbed and liquid phases in mg/g and mg/l,respectively.k f (mg/g)and n(l/mg)are the Freundlich constants which are related to the sorption capacity and intensity,respectively.The Freundlich constants k f and n can be calculated from the intercept and slope of the linear plot with ln q e versus ln C e.4.Results and discussion4.1.Characterization4.1.1.XRD patterns and BET surface areaThe XRD of synthesized samples are shown in Fig.1.The XRD patterns of CMK-3showed three diffraction peaks that can be indexed to(100),(110),and(200)in the2Ârange from0.5◦to10◦,representing well-ordered hexagonal mesopores[22].The XRD patterns show well-resolved reflections indicating that CMK-3 nicely maintains its original structure even after the modification with HNO3and functionalization with ZnO.CMK-3had porous structure and high surface area(998m2/g)which can accommodate ZnO in a spreading manner,the ZnO connects to the carbon surface via oxygen atoms.The lower surface area of OCMK-3(985m2/g) compared with pure CMK-3is mainly attributed to the presence of dense carboxylic surface groups.It is considered that calcina-tion at350◦C makes the Zn(II)ions adsorbed on the carbon bind to the mesoporous carbon via oxygen atoms upon the formation of zinc oxide,in which the surface area of Zn-OCMK-3also may progressively increase(1030m2/g).4.1.2.SEM and TEM imagesSEM images of the synthesized samples are shown in Fig.2A–C. Fig.2A reveals that the SBA-15sample consists of many rope-like domains with relatively uniform sizes of≈1m,which are aggregated into wheat-like macrostructures.The preservation of Table4S/N ratio response table for Hg(II).Factor/level[(S/N)LevelFactor]j(M)LevelFactorj=1j=2j=3j=4A/129.6631.0333.5733.4631.94A/237.4034.8433.1530.9134.08A/339.7434.2233.1832.7134.97A/439.7836.1230.6632.9034.87B/129.6637.4039.7439.7836.65B/231.0334.8434.2236.1234.06B/333.5733.1533.1830.6632.64B/433.4630.9132.7132.9032.50C/129.6634.8433.1832.9032.65C/231.0337.4032.7130.6632.96C/333.5730.9139.7436.1235.09C/433.4633.1534.2239.7835.16D/129.6633.1532.7136.1232.92D/231.0330.9133.1839.7833.73D/333.5737.4034.2232.9034.53D/433.4634.8439.7430.6634.68E/129.6630.9134.2230.6631.37E/231.0333.1539.7432.9034.21E/333.5734.8432.7139.7835.23E/433.4637.4033.1836.1235.05 The boldface corresponds to the maximum value of the mean of the S/N ratios of a certain factor among the four levels.rope-like morphology during the SBA-15templating synthesis of CMK-3from sucrose provides additional confirmation that carbon is faithful replica of the SBA-15(Fig.2B).Furthermore,the carbon replica possesses the same wheat-like shape similar to the SBA-15.Fig.2C is the SEM picture of the ZnO particle on CMK-3.TEM image showed in Fig.2D confirm that the structure of CMK3is well-ordered hexagonal arrays of mesopores.Fig.2E shows that after oxidation treatment,ordered structure is maintained.Fig.2F clearly demonstrates the ZnO particulates deposited in the pores of the carbon.As it can be seen,ZnO is well dispersed on the carbon support.4.2.Optimization4.2.1.Optimum conditionsThe pollutant removal efficiency in Tests1–16measured for Pb(II)and Hg(II)according to the method and Eq.(2)(Table2).Sub-stituting the number of experimental repetitions and results of the measurement(PRE)into Eq.(1),the S/N ratio of each test condition are determined(Table2).The boldfaces in Table2refer to the maxi-mum value of S/N ratio among the16tests.Subsequently,the values of the S/N ratio were substituted into Eq.(3)and the mean of theS/N ratios of a certain factor in the i th level,(M)LevelFactor,was obtained(Table3(Pb)and Table4(Hg)).The(M)LevelFactorshows the effect of each level of each factor on the response,independently.It is calculated by averaging the S/N ratio values of all the experiments where the level of that factor has been used.In Tables3and4the boldfaces refer to the maximum value of the mean of the S/N ratios of a cer-tain factor among four levels,and thus it indicates the optimum conditions for adsorption process.From these Tables,the optimum conditions for removal of Pb(II)and Hg(II)are as follows:(1)The agitation time is120min;(2)the initial concentration is10mg/l;(3)the temperature is35◦C;(4)the dose is0.7g/l;and(5)the pH is6.The confirmation experiment was carried out according to the aforementioned optimum conditions,the PRE of Pb and Hg regis-tered,and the S/N ratio was calculated(Table5).The value of the S/N ratio under optimum conditions(Pb:39.75and Hg:39.91)slightly exceeds that in Test13(Pb:39.62and Hg:39.78),and the average PRE under optimum conditions(Pb:97.25%and Hg:99%)indeed exceeds that in Test13(Pb:95.75%and Hg:97.54%).Although the difference of the S/N ratio between the optimum conditions andG.Zolfaghari et al./Journal of Hazardous Materials192 (2011) 1046–10551051 Table5The optimum conditions for Pb(II)and Hg(II)adsorption.A B C D E PRE1PRE2S/NTest13for Pb(II)240100.725695.7595.7539.62 Optimization condition for Pb(II)120100.735697.0097.5039.75 Test13for Hg(II)240100.725697.4097.6739.78 Optimization condition for Hg(II)120100.735698.5099.5039.91PRE1and PRE2for both pollutants represent the pollutant removal efficiency atfirst and second test pieces,respectively.Test13is very little,the agitation time substantially decreases from 4h(Test13)to2h(optimum conditions).Furthermore,the PRE increases from95.75to97.25%and from97.54to99%for Pb(II)and Hg(II),respectively.These results are pretty exciting due to the fact the lower agitation time corresponds to a better adsorption system.4.2.2.Agitation timeThe(M)LevelFactorare shown in Figs.3–7for the experimental con-ditions proposed by Taguchi method.Fig.3shows the effect of agitation time on the S/N ratio in the removal of Pb(II)and Hg(II). The distribution of adsorbate between adsorbent and solution is influenced by agitation time.It is seen that the time required for equilibrium is120min.In the other words,the optimum time is 2h.This is obvious from the fact that a large number of vacant sur-face sites are available for the adsorption during the initial stage and with the passage of time,the remaining vacant surface sites are difficult to be occupied due to repulsive forces between the solute molecules on the solid phase and in the bulk liquid phase. Heavy metal adsorption slightly decreases after120min.It may be related to desorption process at upper time.4.2.3.Initial concentrationFig.4shows that the S/N for Pb concentration decreases from 35.70to31.12by increasing concentration from10to400mg/l and the S/N for Hg concentration decreases from36.65to32.50 by increasing concentration from10to400mg/l.The efficiency of metal removal is affected by the initial metal concentration,with the removal percentage decreases as the concentration increases. This effect has been attributed to the surface binding of low-affinity surface sites as high-affinity ones begin to reach saturation,lead-ing to a reduction in the removal efficiency.Seco et al.[39]have reported that the amount of adsorption was decreased with the increase in initial concentration.4.2.4.Adsorbent amountThe present study shows that the Zn-OCMK-3is an effective adsorbent for the removal of Pb(II)and Hg(II)from aqueous solu-tion(97.25%for Pb and99%for Hg).It can be seen from Fig.5that the dose for Pb(II)and Hg(II)was increased with the increase in adsorbent.Amount of Zn-OCMK-3was varied from0.1to0.7g/l. It is apparent that the equilibrium concentration in solution phase decreases with increasing carbonous adsorbents amount for a given initial Pb(II)and Hg(II)concentration.Since the amount of metals removed from the aqueous phase increases as the sorbent amount is increased in the batch vessel with afixed initial heavy metal concentration.This result was anticipated because for afixed ini-tial solute concentration,increasing amount of adsorbent provides greater surface area.4.2.5.TemperatureThe plot of adsorption capacity as a function of temperature is shown in Fig.6.The uptake of Pb and Hg onto the Zn-OCMK-3 increased with increase in temperature from20to35◦C,indicat-ing more chemical interaction between the sorbate and the surface functionalities of the Zn-OCMK-3.Adsorption efficiency is observed to increase on raising the temperature,as previously reported [40,41].Seco et al.[39]have investigated the adsorption of heavy metals onto activated carbon.They concluded that increase in tem-perature results in greater removal efficiency.The adsorption of Pb(II)onto another carbon material has been reported by Wang et al.[42].In their study,the Pb(II)adsorption capacity increased with the rise of temperature.4.2.6.Solution pHOne of the critical parameter in the treatment of heavy metals by the sorption medium is pH,because the surface charge of an adsorbent could be modified by changing pH of the solution.Fig.7 shows that the S/N ratio increased with the pH value from2to6.The removal of Pb(II)and Hg(II)from water by Zn-OCMK-3was found to be dependent on the solution pH value.This can be explained on the basis of Surface Complex Formation(SCF)theory[39].In the SCF theory,adsorption of inorganic species onto hydrous solids is described as a chemical coordination and electrostatic process involving specific interactions at the solid/solution interface.The increase in the metal removal as the pH increases is on the basis of a decrease in competition between proton and metal species for the surface sites,and by the decrease in positive surface charge, which results in a lower coulombic repulsion of the sorbingmetal. Fig.3.The effect of agitation time on the S/N ratio in the removal of Pb(II)(left)and Hg(II)(right).Circles onfigures indicate optimum time for adsorption process.。