基于输入轨迹参数化的间歇过程迭代学习控制

针对间歇过程的迭代学习控制问题,提出了一种基于输入轨迹参数化的迭代学习控制策略。根据最优输入轨迹的主要形态特征,将其参数化为较少量的决策变量,降低传统迭代学习控制复杂性的同时维持良好的优化控制效果。基于输入轨迹参数化的迭代学习控制策略能保持算法的简洁性和易实现性,在不确定扰动影响下逐步改善产品质量。对一个间歇反应器的仿真研究验证了本文方法的有效性。     

Optimal Stopping for I.I.D. Random Variables Based on the Sequential Information of the Location of Relative Records Only

Abstract

Let X _j , j = 1,…, n be independent and identically distributed random variables. Like in the classical secretary problem, the optimal stopper only observes Y _j  = 1, if X _j is a (relative) record, and Y _j  = 0, otherwise. The actual X _j values are not revealed. The goal is to maximize the expected X value at which one stops. We show that the optimal number of observations one should skip before considering stopping depends heavily on the underlying distribution.     

Algebraic Structure Count of Cyclobutadienyl Bridged Polyacenes

Abstract

By substitution of the benzene rings in [n]phenylenes with polyacene units (all being of the same length) a new class of compounds is obtained. By analogy we call this class [n]acenylenes. Beside linear (X_n), we also examine angularly linked acenylenes which might be realized in two extreme ways: by connecting the polyacene units in a strictly spiral way (Y_n) or in the so called zig-zag manner (Z_n).

The recursion formulae for the algebraic structure count (ASC) of X_n, Y_n and Z_n are derived here, and they read as:

ASC(X_n) = (h + 1). ASC(X_n-1)—ASC(X_n-2)

ASC(Y_n) = h. ASC(Y_n-1) + ASC(Y_n-2)

ASC(Z_n) = h. ASC(Z_n-1) + ASC(Z_n-2)

where n denotes the number of polyacene units and h the number of hexagons in each polyacene unit.

It is proved that Y_n and Z_n have equal ASCs.     

Optimization of Heat Pump–Assisted Intermittent Drying

In the present study, heat pump–assisted drying of salak fruit was optimized by dividing the dehydration process into three distinct phases, namely, the initial, intermittent, and final stages. Drying variables considered for the optimization were the intermittent duration (X ₁), intermittent ratio (X ₂), and intermittent cycle (X ₃); the response variables studied were the total drying time (Y ₁), total heating time during intermittent drying (Y ₂), total heating time after intermittent drying (Y ₃), total color change (Y ₄), ascorbic acid content (Y ₅), and total phenolic content (Y ₆). Response surface methodology was used to determine the best combination of the drying variables that could provide the shortest drying period and premium product quality. Experimental results showed that all of the response variables were improved under the optimized intermittent drying conditions compared to the conventional method using constant drying conditions. The optimized heat pump–assisted intermittent drying reduced the drying time by 36% and improved phytochemicals retention with ascorbic acid and total phenolic content recorded at 18.4 ± 1.8 mg ascorbic acid/100 g dw and 43.3 ± 2.2 mg gallic acid equivalent (GAE)/g dw, respectively. The color change of the final product was minimum with a ΔE* value of 7.26 ± 2.03.     

Pseudo-prophet Inequalities in Average-Optimal Stopping

Abstract

This note considers the average-optimal expected return of two players observing independent random variables X ₁, … , X _n , whose distributions are generated at random. One player, the pseudo prophet, knows the distributions prior to observing the random variables. The other player, the gambler, has no such foresight. Sharp difference and ratio comparisons of the two players' optimal expected returns are given. The key step in the proof is a reduction to a classical prophet inequality for i.i.d. random variables proved by Hill and Kertz (Hill, T.P.; Kertz, R.P. Comparisons of stop rule and supremum expectations of i.i.d. random variables. Ann. Probab. 1982, 10 (2), 336–345).     

Investigation on process parameters of electrospinning system through orthogonal experimental design

Electrospinning is a very simple and versatile method of creating polymer‐based high‐functional and high‐performance nanofibers. But most of the investigations are not systematic and describe the electrospinning process without quantitative accuracy. Inconsistent and even opposite results have been reported, which has hindered the consistent interpretation of the experiments. Orthogonal experimental method was used to investigate qualitative and quantitative correlations between fiber characteristics (diameters and morphologies) and the processing and materials parameters. Uniform fibers can be obtained without any beads by proper selection of the processing parameters, and a lower glass transition temperature was observed for electrospun fibers than that of native polymer. Results of statistical analysis showed that significant influences were observed for polymer molecular weight and solution concentration on fiber diameters, and there were significant effects of polymer molecular weight, solution concentration, and solvent system on fiber morphologies. Meanwhile, solution concentration and polymer molecular weight, and polymer molecular weight and solvent system had obvious interaction effects. Regression analysis revealed quantitative relations of fiber diameters and beads percent, that is, Y₁ = 72.8X₁ ? 8.1X₂ + 138.8, Y₂ = ?3.2X₁ + 0.4X₂ + 60.5, where Y₁ is fiber diameter (nm), Y₂ beads percent (%), X₁ solution concentration (%, w/w), and X₂ polymer molecular weight (kDa). Validation test showed that the experimental values of fiber size and beads percent were in good agreement with the calculated ones. Based on these results, optimal conditions could be obtained for predetermined diameters and morphologies for electrospun fibers. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3105–3112, 2007     

Effects of α‐amylase and glycerol levels on the composition optimization of poly(β‐hydroxybutyrate‐co‐valerate)/starch blended biodegradable resin analyzed with response surface methodology

Response surface methodology was used to analyze the effects of the enzyme level (X₂) and glycerol level (X₁) on objective attributes [water solubility index (WSI), water absorption index (WAI), and maximum loading (Y₃)] of a cornstarch/poly(β‐hydroxybutyrate‐co‐valerate) blended composite. A rotatable central composite design was used to develop models for the objective responses. The experiments were run at barrel temperatures of 160, 160, 165, and 165°C, with a screw speed of 40 rpm and complete feeding (filling ratio = 1). Responses were most affected by changes in X₂ and to a lesser extent by X₁. Individual contour plots of the different responses were overlaid, and regions meeting the optimal WSI of 8.73%, WAI of 3.94 g of gel/g of dry weight, and Y₃ of 304.17 N were established at an X₂ of 5.43 g and an X₁ of 120.79 mL. These predicted values for the optimal process conditions were in good agreement with the experimental data. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Comparison of Values of Independent Random Variables in a Bayesian Setting

Abstract

An optimal stopping problem for independent observations in a Bayesian setting is considered. One optimal stopper knows only the prior distributions of the independent X _i 's, while the other stopper knows the conditional distributions of the X _i 's. We show that the extremal relationship of the returns to the two different optimal stoppers is the same as the relationship between an optimal stopper and a “prophet” in a usual corresponding optimal stopping setting.     

Optimization and modeling of UV-TiO2 mediated photocatalytic degradation of golden yellow dye through response surface methodology

In this article, heterogeneous photocatalysis of golden yellow (GY) dye by Evonik p25 titanium dioxide (PTD) and UV radiations was optimized by using central composite design of response surface methodology. The GY dye photocatalysis was expressed as the function of amount of PTD loading (X₁), GY dye initial concentration (X₂), and UV irradiance intensity (X₃). The optimization of degradation conditions was done by measuring two different responses, that is, color removal (Y₁) and chemical oxygen demand removal (Y₂). The effect of X₁, X₂, and X₃ were studied in the range 0.5–1.5?g/L, 15–35?W/m², and 10–30?mg/L, respectively. The quadratic model was suggested for Y₁ and Y₂. The numerical optimization of results was done via Design Expert software. The predictive results obtained were verified by performing actual experiments. The photodegradation kinetics, total organic carbon disappearance, effect of inorganic salts, and H₂O₂ concentration on GY dye photodegradation were also studied.     

Polymer-Solid Interface Connectivity and Adhesion: Design of a Bio-Based Pressure Sensitive Adhesive

Adhesion at polymer-solid interfaces was explored for a new bio-based pressure sensitive adhesive (PSA) in terms of sticker groups, φ_X, on the polymer phase, receptor groups, φ_Y, on the solid surface, and the bond strength of the sticker-receptor X-Y acid-base interaction, χ. The polymer-solid interface restructuring models of Gong and Lee et al. were extended with new percolation models of entanglements and interface strength to determine the optimal sticker group concentration, φ?_X. For the general case where φ_Y and χ are constant, it is predicted that when φ_X < φ?_X, that the critical peel energy behaves as G_1c ～ φ_X/φ?_X and the locus of failure is adhesive between the polymer and the solid. However, when φ_X > φ?_X, failure occurs cohesively in a polymer-polymer interface adjacent to the solid and the strength decreases as G_1c ～ φ?_X/φ_X. The switch from adhesive to cohesive failure can be understood in terms of the changes in the chain conformations of the adhered chains and their decreasing interpenetration, X_i, with the bulk chains, via X_i ～ 1/r, where r = χφ_Xφ_Y. The optimal value of φ_X which maximizes the adhesion and determines the mode of failure is given by φ?_X ≈ 0.129/C_∝, and for typical values of the characteristic ratio C_∝ in the range 7–20, φ?_X ≈ 1% mole fraction, corresponding to about 2 sticker groups per entanglement molecular weight, M_e. This result was verified for a bio-based PSA synthesized from an acrylated high oleic fatty acid, which was copolymerized with maleic anhydride as the sticker group. The observed behavior is counterintuitive to the current wisdom for the effect of acid-based interactions on adhesion, where the strength is expected to increase with the number of X-Y contacts. The surprisingly low value of φ?_X ≈ 1% sticker groups which maximizes the adhesion strength can now be readily calculated using the percolation model of entanglements and fracture.     

LARGE SAMPLE ANALYSIS OF AUTOREGRESSIVE MOVING-AVERAGE MODELS WITH ERRORS IN VARIABLES

Abstract. We consider estimation of parameters of an unobservable ARMA(p, q) process {U_t; t= 1,2,…} based on a set of n observables, X₁, …, X_n, where X_t=U_t, +ε_t, 1 ≤t≤n, it being assumed that {ε_t} is independent of {U_t}. We examine the asymptotic properties of these ARMA estimators under a set of weak regularity conditions on {ε_t}.     

Reversibly crosslinked self‐healing PCL‐based networks

Poly(ε‐caprolactone) (PCL)‐based thermoreversible networks with self‐healing properties were prepared through Diels–Alder (DA) and retro‐DA reactions. Bis‐ or Tris‐maleimide compounds and a series of copolymer(caprolactone‐diene) PCL_XF_Y (X: degree of polymerization and Y: furan‐average functionality) with Y between 2.4 and 4.9 were used. The successive sequences of formation and dissociation of polycaprolactone networks via DA and retro‐DA reactions were observed repeatedly by dynamic mechanical analyses (DMA) and their gel‐temperatures determined. The cross‐linking densities, thermal properties, and thermal reversibility of the PCL_XF_Y/multimaleimide polymers have been modulated by the structure and functionalities of the used diene and dienophile moieties. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Determination of Intrinsic Minimum Bubbling Velocity in Fine Powder Aerations Based on Experimentally Measured Elastic Deformation Coefficients

It is found that the minimum bubbling velocity of aerated fine powder can be defined by experimentally measuring incremental elastic deformation coefficient (Y). The value of Y starts changing at a certain degree of powder expansion. The sudden change of Y indicates the initiation of the fractures in the homogeneously aerated expanded (HAE) emulsion phase. The intrinsic minimum gas velocity (U_mb*), which causes this fracture initiation, can be significantly smaller than the so‐called minimum bubbling velocity (U_mb) defined by the classical concepts.     

Concentration of ω-3 polyunsaturated fatty acids of marine oils using Candida cylindracea lipase: Optimization of reaction conditions

Production of ω-3 fatty acid concentrates from seal blubber oil (SBO) and menhaden oil (MHO) upon enzymatic hydrolysis by Candida cylindracea lipase was optimized. In this process, the content of total ω-3 fatty acids, Y ₁; eicosapentaenoic acid, Y ₂; and docosahexaenoic acid, Y ₃, in the final product was maximized. A three-factor central composite rotatable design was used to study the effect of enzyme concentration (X ₁), reaction time (X ₂), and reaction temperature (X ₃). Second-order polynomial regression models for Y ₁, Y ₂, and Y ₃ were employed to generate response surfaces. After hydrolysis, a maximum of 54.3% total ω-3 fatty acids was obtained from SBO at an enzyme concentration of 308 U/g oil, a reaction time of 40 h, and a reaction temperature of 37°C. Similarly, a maximum of 54.5% total ω-3 fatty acids was obtained from MHO at an enzyme concentration of 340 U/g oil, a reaction time of 45 h, and a reaction temperature of 38°C.     

Application of the percolation model to gelation of an epoxy resin

The percolation model has been applied to the study of gelation of the TGDDM-DDS system (tetraglycidyldiaminodiphenylmethane–diaminodiphenylsulfone) at a mass concentration of 100–30. For each temperature the experimental viscosity curves are satisfactorily described by a percolation law. Using the degree of chemical reactions, X, as a variable, a very clear change in the reaction mechanism with temperature can be shown. Then a rate of advancement of effective reactions, Y, is defined. This value only takes intermolecular-type reactions into account, and is probably the only variable on which viscosity depends in a percolation law: η = B(1 ? Y/Y_c)^?p. We obtain Y_c= 0.45 and p= 2.0. Comparing X_c and Y_c at the gel point, we obtain information on the proportion of intramolecular reactions with temperature. It is also demonstrated that the critical percolation threshold agrees closely with the gel point determined experimentally on log G″= f(t) curves.     

基于Gath-Geva算法和核极限学习机的多阶段间歇过程软测量

间歇过程具有较强的非线性,多阶段、慢时变及批次间存在变化,采用单一预测模型不能反映间歇过程的多阶段特性及阶段间过渡特性。提出一种基于Gath-Geva聚类和核极限学习机（kernel extreme learning machine,KELM）的多模型软测量方法。首先采用主成分分析（principal component analysis,PCA）对输入做特征提取,然后利用Gath-Geva算法对间歇过程进行多阶段工况划分,根据生产工况特性划分为不同的操作阶段后,分别建立局部KELM模型。对任一待预测样本,分别计算其对应各局部模型的预测值,最后采用贝叶斯集成,将其隶属于各局部模型的模糊隶属度作为权重和预测值融合得到最终预测值。以青霉素发酵数据进行实验测试,结果表明所提多模型算法相较于单一模型,具有更高的预测精度。     

Blends of aliphatic polyesters. I. Physical properties and morphologies of solution-cast blends from poly(DL-lactide) and poly(ε-caprolactone)

Effects of the mixing ratio of poly(DL-lactide) (PDLLA) and poly (ε-caprolactone) (PCL) on the thermal and mechanical properties and morphologies of the solution-cast blends were investigated by differential scanning calorimetry (DSC), polarizing microscopy, tensile tests, and dynamic mechanical analysis. The presence of amorphous PDLLA did not disturb crystallization of PCL over the PDLLA content [X_PDLLA = PDLLA/(PCL + PDLLA)] from 0.1 to 0.9 and allowed PCL to form spherulites over X_PDLLA ranging from 0.1 to 0.6. The spherulite radius was larger for the blends than for the nonblended PCL. Phase separation occurred for the blends with X_PDLLA between 0.1 and 0.9 T^m of PCL remained unchanged in the X_PDLLA range up to 0.6 but decreased at X_PDLLA above 0.6, whereas the crystallinity of PCL was constant around 60%, irrespective of X_PDLLA. The tensile strength (σ_B, the yield stress (σ_Y), the Young's modulus(E), and the storage modulus (G′) of the blends increased monotonously with X_PDLLA if σ_B at X_PDLLA = 0 and 0.6 and σ_Y at X_PDLLA = 0.6 were excluded. Elongation-at-break (ε_B) of PDLLA increased dramatically, while ε_B of PCL decreased remarkably when a small amount of the other component was added. Equations and parameters predicting σ_Y, E, and G′ of the PCL-PDLLA blends were proposed as a function of X_PDLLA. © 1996 John Wiley & Sons, Inc.     

A Polymath Approach for the Prediction of Optimized Transesterification Process Variables of Polanga Biodiesel

An attempt has been made to employ an artificial neural network (ANN) combined with a genetic algorithm (GA) in MATLAB 7.0 for predicting the optimized reaction variables for maximum biodiesel production of polanga oil by the transesterification process. The developed ANN is a multilayer feed-forward back-propagation network (5-10-1) with five input, ten hidden and one output layers. The input variables are the molar ratio of ethanol to oil (X ₁ in % v/v), the catalyst concentration (X ₂ in % w/v), the reaction temperature (X ₃ in °C), the reaction time (X ₄ in min), the agitation speed (X ₅ in rpm) and the output parameter is biodiesel yield (% by weight) of polanga oil. The experimental data used in the developed ANN were obtained from response surface methodology (RSM) based on a central composite design. The trained ANN was tested using different training functions from the MATLAB to predict the best correlation coefficients of training, testing and validation. The data generated by trained ANN is used by GA with regards to the best response (for predicting biodiesel yield greater than predicted by RSM) for different combinations of variables (X ₁, X ₂, X ₃, X ₄, and X ₅) to attain optimization. The average biodiesel yield (by performing experiments under optimized conditions) of 92 % by weight was produced against the proposed value of 91.08 % by weight.     

Sensitivity analysis on a sequencing batch reactor model. II: Effect of stoichiometric and operating parameters

A previously developed model for sequencing batch reactors was used in this study to investigate the effect of some of the model stoichiometric and operating parameters on the performance of the system. With regard to the effluent chemical oxygen demand (COD) concentration, the model predictions were determined to be correct for the parameters Y_p, f_p and S_sf. However, the stoichiometric parameters α, Y_h and the operating parameter X_ao were determined to have significant effect on the effluent COD concentrations. The intermediate COD concentrations are affected by the parameters Y_p, Y_h, S_sf and X_ao. To use the model for design or control purposes, special attention should be given to the parameters that affect the effluent COD concentration. © 1999 Society of Chemical Industry