1、文章编号:摇 1007鄄8827(2017)01鄄0077鄄09基于神经网络的炭气凝胶孔结构的预测与优化模型研究杨摇 榛,摇 乔文明,摇 梁晓怿(华东理工大学 化学反应工程国家重点实验室,特种功能高分子材料及相关技术教育部重点实验室,上海 200237)摘摇 要:摇 如何控制和预测孔结构是炭气凝胶研究的重要课题。 然而,由于耗时耗财,导致实验方法研究控制和预测孔结构成为难题。 本文提出一种基于神经网络的炭气凝胶孔结构的预测与优化模型,并采用遗传算法设计和优化模型,对六种典型训练算法模型性能进行比较分析。 利用该模型对孔径和吸附容量进行预测,两者的预测相关系数分别为 0. 992 和 0. 98
2、1,预测均方根误差分别为 0. 077 和 0. 054。 经测试,该模型与实验研究的结果相符,并有效的应用于预测和控制炭气凝胶实验参数。关键词:摇 炭气凝胶; 孔结构; 神经网络; 训练算法; 模型中图分类号: 摇 TQ127. 1+1文献标识码: 摇 A基金项目:国家自然科学基金(21177038).通讯作者:梁晓怿. E鄄mail: xyliang73 sina. comModelling and optimization of the pore structure ofcarbon aerogels using an artificial neural networkYANG Zhen
3、,摇 QIAO Wen鄄ming,摇 LIANG Xiao鄄yi(State Key Laboratory of Chemical Engineering, Key Laboratory for Special functional Polymer Materials and Their Related Technologies,Ministry of Education, East China University of Science and Technology, Shanghai200237, China)Abstract: 摇 An intelligent simulation me
4、thod for predicting and optimizing the pore structure of carbon aerogels is proposed byusing an artificial neural network (ANN) algorithm. The ANN model has been optimized based on an improved genetic algorithmfrom six typical training algorithms. The volumes and diameters of pores in the simulated
5、samples are predicted by the optimizedANN model, which shows correlation coefficients R2of 0. 992 and 0. 981 and root鄄mean鄄square prediction errors (RMSPE) of0. 077 and 0. 054 between the predicted and experimental values for the volumes and diameters of pores, respectively. The proposedmodel is exp
6、ected to have practical applications in the pore structure control of carbon aerogels.Key words:摇Carbon aerogels; Pore structure; Neural network; Training algorithms; ModellingReceived date: 2016鄄10鄄28;摇Revised date: 2017鄄01鄄29Foundation item: National Natural Science Foundation of China (21177038).
7、Corresponding author: LIANG Xiao鄄yi. E鄄mail: xyliang73 sina. comEnglish edition available online ScienceDirect ( http:蛐蛐www. sciencedirect. com蛐science蛐journal蛐18725805 ).DOI: 10. 1016/ S1872鄄5805(17)60108鄄21摇 IntroductionCarbon aerogels have high ratios of surface or in鄄terface atoms owing to their
8、 particles in nanometerscale that form them1. Compared with conventionalgranular materials, carbon aerogels have a series ofexcellent physical and chemical properties such as lowdensities, high electrical conductivity, high specialsurface area, biocompatibility, and anticorrosion byacid and base2,3.
9、 It is considered as a promising ma鄄terial for various electrochemical applications, catalystsupports,adsorbents,andchromatographypack鄄ings4,5,6.In this study, a new type of carbon aerogels wasprepared by sol鄄gel polymerization method using phe鄄nol, melamine and formaldehyde as raw materials.Pore st
10、ructure of carbon aerogels is essential to carbonaerogels because it will directly affect their perform鄄ance. However, it is difficult to control practicallypore structure parameters of carbon aerogels due to theconstraints of time and cost.In recent years, interest using artificial neuralnetworks (
11、ANNs) as a tool in material technologyhas increased. ANNs have been successfully used inseveral types of material applications like analysis,classifications, predictions or control and others7,8.ANNs are mathematical models that have the ca鄄pabilities to relate input to output parameters. They摇第 32
12、卷摇 第 1 期2017 年 2 月新摇 型摇 炭摇 材摇 料NEW CARBON MATERIALSVol. 32摇 No. 1Feb. 2017摇can learn from examples by iteration without requiringa prior knowledge of the relationships between processparameters and properties of materials9.The neural network is determined by the architec鄄ture, training algorithms an
13、d learning rule. The mostoften used ANN for material applications is a fullyconnected and supervised network with a back propa鄄gation learning rule. The neural network architectureis designed by means of a trial鄄and鄄error process witha human intervention. Although there are some stud鄄ies carried out
14、 on the automatic design of architec鄄tures10, how to design an appropriate architecturesystematically and autonomously remains a challeng鄄ing problem. The genetic algorithm (GA) is quite ef鄄fective in solving optimization problems owing to itsinherent property of implicit parallelism11. In thispaper
15、, we have established an optimal structure ofANN by GA. Plumb et al.12have shown that aproper selection of the training function has a signifi鄄cant effect on the predictive ability of a network.Therefore, one of the aims of this paper is to obtainan optimized ANN to control and predict the porestruc
16、ture for carbon aerogels through selecting trainingalgorithms. To do this, six training algorithms havebeen evaluated.Performances of ANN have been optimized byvarying the numbers of neurons in the hidden layer,optimizing the architecture of neural network and se鄄lecting a proper training algorithm.
17、 Then, the numeri鄄cal simulation results from the optimal controlling andpredicting model are compared with experimentalones. The purpose of this paper is to investigate thebehaviors of pore structure for carbon aerogels and es鄄tablish controlling and predicting model using the neu鄄ral network metho
18、d. The flowchart of this study isshown in Fig. 1.2摇 Experimental2. 1摇 Preparation and experimental designIn the present experiments, the total reactantconcentration is 20%, and the molar ratio of phenoland m鄄cresol is 1 颐 2. The catalyst concentration is100 mmol/ L. We investigate the effect of the
19、reactantconcentration, the molar ratio of phenol and m鄄cresolin the solution on pore structure of carbon aerogels.The reactants are mixed in propyl alcohol to formtransparent solutions. The solutions are poured intosealed glass ampoules (8 cm伊2 cm, internal diame鄄ter, each filled with 20 mL solution
20、) and heated at90 益 for 48 h in a water bath. Then, the black or鄄ganic gels are moved into a pressure vessel and super鄄critically dried at 270 益 and 8 MPa. Finally, with aheating rate of 5 益 / min, the carbon aerogels areformed by pyrolysis of the organic aerogels in a hori鄄zontal tube furnace at 80
21、0 益 for 3 h under nitrogenprotection. As a comparison, phenol鄄furfural (m鄄C/P=0) and m鄄cresol鄄furfural (m鄄C/ P=肄 ) are poly鄄merized in 1鄄propanol under the same conditions13.Fig. 1摇 Flowchart of this study.摇摇Samples are named MP/ RC/ CC in accordancewith preparation conditions, in which MP is mela鄄m
22、ine/ phenol molar ratio, RC is the concentration ofthe reactants and CC is the catalyst concentration.Under certain conditions (solvent exchange, super鄄critical drying and pyrolysis), the influences of dif鄄ferent reaction temperatures, reaction times, variousmelamine/ phenol molar ratios (M/ P) on p
23、ore struc鄄ture of carbon aerogels are studied.2. 2摇 Analysis and characterizationMain analysis and characterization methods ofthis paper are as follows:Laser particle size analyzer. Particle size distri鄄bution and average particle size were measured by alaser particle size analyzer.Nitrogen adsorpti
24、on. Adsorption and desorptionisotherms of nitrogen were measured at 77 K using acommercial adsorption apparatus (ASAP2020M, Mi鄄cromeritics). Samples were degassed at 200 益 undervacuum for 12 h. The BET surface areas (SBET) wereanalyzed bytheBrunauer鄄Emmett鄄Teller( BET )method from the adsorption iso
25、therm of nitrogen at p/p0from 0. 05 to 0. 2. Micropore volumes (Vmic), mi鄄cropore surface areas (Smic), and external surface ar鄄eas (Sext) were obtained by the t鄄plot method usingan adsorption branch of the isotherms. Mesopore sizedistributions, mesopore volumes (Vmes) and averagepore diameters ( Dp
26、) were obtained with the BJH(Barrett鄄Johner鄄Halendar) model using the desorptionbranch of the isotherms.3摇 ANN description摇 摇 An ANN concept, which is from artificial intelli鄄87摇新摇 型摇 炭摇 材摇 料第 32 卷gence family, has been developed to model nonlinearprocesses in many areas. An ANN is a parallel鄄dis鄄tr
27、ibuted information processing system. It stores thesamples with distributed coding, thus forming a train鄄able nonlinear system. The main idea of the neuralnetwork resembles the functions of human brains. It isself鄄adaptive to the environment so as to respond dif鄄ferent inputs rationally14.An overvie
28、w of neural network algorithms wasprovided by McCulloch15. A neuron as a unit withprocess of stimulus and reaction is generalized in thissystem. A set of training data for learning is per鄄formed with weight (connection strength), transferfunction and biases. In this study, a back鄄propagation(BP) alg
29、orithm is used for the neural network, whichis simple from the viewpoint of structure and easyanalysis with mathematics. The back propagation neu鄄ral network scheme, which has a great learning abilityin training and mapping the relations between inputsand outputs, is the most commonly used networkmo
30、dels16,17. The basic structure of BP neural net鄄work is shown in Fig. 2.Fig. 2摇 Basic structure of BPNN.摇 摇 The neuron shown in Fig. 2 can be classified in鄄to three types, input, output and hidden neurons. In鄄put neurons are the ones that receive input signal fromexternal sources. Output neurons are
31、 those that sendthe signals to external sources. Neurons, which haveinputs and outputs, are called hidden neurons. Thereare one or several nodal points in the output layer,which generate output data.In this network, each input value is connected toeach input neuron by the weight matrix. Usually, BPn
32、eural network is represented by the following model(Eq. (1),Nj=移WjiIiHj=f(Nj+Bj)Ok=f(移WkjHj+Bk)(1)where Iiand Okare input and output values, Hjis the output of activation function of the jthneuron inthe hidden layer , Wjiand Wkjare weights , f is thetransfer function and Bjand Bkare biases.The optim
33、al ANN configuration is selected fromvarious ANN configurations based on their predictiveperformance. Mean square prediction error (MSE)defined as Eq. (2) is used to evaluate prediction ac鄄curacy of the model:MSE=移Nk=1(Ok-Tk)2/ N(2)where N is the number of prediction data, Tkisthe actual value of th
34、e kthexperimental data and Okisthe kthestimated value of the prediction model. MSEis easily computed and it can give a precise descrip鄄tion of the predictive performance of the network.Also, the linear regression coefficient R2betweenthe predicted values of the ANN model and the de鄄sired output is u
35、sed to evaluate the predictive abilityof the network.MSE and R2are frequently calculated until erroris acceptable. Finally, the test data are used to verifythe nonlinear relationship between the input and out鄄put data sets.Steps of optimization procedure andlearning algorithm are listed in detail in
36、 Ref. 18.ANN is self鄄adaptive to the environment so as torespond different inputs rationally. In other word, adesigned neural network can give a rapid response forany given input. Some advantages of a neural net鄄work are adoption, learning, generalization, easy toimplementation, and self鄄organizatio
37、n.Implementation of a neural network needs a deci鄄sion of two main features, the structure in other wordtopology of the network and the type of learning algo鄄rithm. In this article, the topology of the network isoptimized by an improved genetic algorithm. Six dif鄄ferent training algorithms are teste
38、d by comparing pre鄄dicting results.4 摇Methodology design of the neuralnetwork摇 摇 In this study, the neural network is used to pre鄄dict diameters and volumes of pores in the MP/ RC/CC carbon aerogels. There are 24 experimental datain training and test sets (Table 1). Six different train鄄ingalgorithms
39、areusedtopredictexperimentalresults.A neural network is implemented with a threelayer feed鄄forward structure, an input layer, a hiddenlayer and an output layer. The designed neural net鄄work has 3 input and 2 output neurons as shown inFig. 3.97第 1 期YANG Zhen et al: Modelling and optimization of the p
40、ore structure of . . . . . .摇Table 1摇The experimental data used to form the training and test sets.SamplesInput 1 of NNM/ PInput 2 of NNReactant content(g/100mL)Input 3 of NNCatalyst content(mol/ L)Output 1 of NNPore diameter(nm)Output 2 of NNVolume adsorbed(cm3/ g)S(1)0.0550. 0210.31.5S(2)0.05100.
41、059.51.3S(3)0.05150.17.51.1S(4)0.05200.26.90.9S(5)0.150. 028.71.4S(6)0.1100. 057.61.1S(7)0.1150.15.40.75S(8)0.1200.23.80.68S(9)0.250. 0214.11.9S(10)0.2100. 0511.21.6S(11)0.2150.18.11.0S(12)0.2200.27.30.96S(13)0.450. 028.62.1S(14)0.4100. 0515.31.9S(15)0.4150.111.91.6S(16)0.4200.28.10.79S(17)0.650. 02
42、20.82.6S(18)0.6100. 0519.22.4S(19)0.6150.117.12.1S(20)0.6200.215.41.6S(21)0.850. 0228.62.9S(22)0.8100. 0524.22.6S(23)0.8150.122.12.5S(24)0.8200.216.51.3Fig. 3摇 The topology of involved neural network.4. 1摇 Architecture optimization of neural networkIn the neural network based model, too few hid鄄den
43、neurons will hinder the learning process and toomany will depress the predictive abilities of the ANNowing to the overtraining. To make the model com鄄putationally efficient, experiments show that a con鄄stant bias added to the input signal can affect learningtime.Bias is set up to improve the accurac
44、y and speedof convergence. For choosing the best bias, the MSEof network simulation and actual results are tested.According to the demand of material design accuracy,MSE is less than 0. 2. Normally, bias should be set toa small value, and the smaller is the value, the higheris the precision, but too
45、 small of the value would af鄄fect the convergence speed. However, if bias is toobig, it will speed up convergence at the beginning ofthe simulation, but when it is near the optimum pointof 0. 37, it will produce an oscillation and a reduceconvergence. Therefore, bias is chosen as 0. 37 inthis paper.
46、In this paper, bias is added to the input signalsthat are near the centers of the training functions,where the learning rate is highest. Another way to08摇新摇 型摇 炭摇 材摇 料第 32 卷make the model computationally efficient is to searchfor a theoretical optimal number of hidden units.The coefficient of the le
47、arning rate (滋) and itscorresponding decrease factor (滋d) are two importantparameters and play an important role in the design ofa structure based on diameters and volumes of poresin the prediction model. In general, the architectureof a neural network in the model is predeterminedbased on a prior k
48、nowledge of nonlinear system or de鄄signer爷 s experience.In this section, a GA鄄basedmethod is developed to optimize the architecture ofneural network based models. The aim of this sectionis to search for the feed鄄forward network architecturewith an optimal hidden layer neuron number and otherstructur
49、e parameters by GA.4. 1. 1摇 Genetic algorithmGA, based on a direct analogy to Darwinian nat鄄ural selection and genetics in biological systems, is apromising alternative to conventional heuristic meth鄄ods. Based on the Darwinian principle of survival ofthe fittest爷19,20, one of the most important pro
50、blemsof GA is, as in the ANN case, the premature conver鄄gence to local minima due mainly to the tendency ofthe best individuals to maintain their genetic informa鄄tion across generations. In this paper, to avoid thisproblem, genetic algorithm is improved as following.N individuals are ranked from the
