基于归一分解的并行多目标Dividing Rectangles算法

多目标优化问题普遍存在且难以解决,目前多采用多目标进化算法进行求解.然而,这些方法通常在种群初始化阶段和进化过程中包含随机操作以保持多样性,导致了其结果不可复现且缺乏全局收敛的理论保证.鉴于此,提出了一种基于归一分解的多目标Dividing Rectangles(DIRECT)算法,首先通过一种可较好捕捉复杂前沿的归一分解方法将原问题分解为一系列子问题,以降低问题计算复杂度;其次,采用Dividing Rectangles算法同时优化分解得到的子问题,并在优化过程中基于全局关联机制将生成的候选解分配给相应的子问题,以更好地保留优秀候选解并提高算法搜索效率;最后,证明了算法的收敛性.此外,为了进一步提高计算效率,提出了一种基于自适应关联迁移策略的多层次多粒度并行方案,并基于该方案对所提出的算法进行了并行化.将所提算法应用于多个基准优化问题,实验结果表明,相比于NSGA-II,所提串行算法能够产生收敛性、多样性更为优越的帕累托最优解集,并行算法可在大规模缩短问题求解时间的同时,进一步提升帕累托前沿近似精度.

基于Dividing Rectangles的多模态医学图像配准算法

为了准确、可靠地配准多模态医学图像,提出了一种基于互信息的全局优化配准算法。该算法首先提取出目标物体的外轮廓面,再用迭代最近点方法初步对齐图像;然后用确定性的全局优化方法—Dividing Rectangles搜索归一化互信息的全局最优解。该算法利用图像的特征信息,为Dividing Rectangles方法提供了一个较好的初始配准位置,并充分利用了Dividing Rectangles方法在小范围内的高效搜索能力。实验结果表明,对于3维人体脑部数据,该算法配准精度高、速度快,而且有效地避免了配准过程中出现的局部极值。

Energy conserving effects of dividing wall column

The energy-conserving performance of dividing wall column(DWC) is discussed in this paper. The heat transfer through the dividing wall is considered and the results are compared with that of common heat insulation dividing wall column(HIDWC). Based on the thermodynamic analysis of heat transfer dividing wall column(HTDWC) and HIDWC, both computer simulation and experiments are employed to analyze the energyconserving situation. Mixtures of n-hexane, n-heptane and n-octane are chosen as the example for separation.The results show that the energy consumption of HTDWC is 50.3% less than that of conventional distillation column, while it is 46.4% less than that of HIDWC. It indicates that DWC is efficient on separating threecomponent mixtures and HTDWC can save more energy than HIDWC. Thus it is necessary to consider the heat transfer while applying DWC to industry.

Experimental and simulation of the reactive dividing wall column based on ethyl acetate synthesis

Reactive dividing wall column(RDWC) is a highly integrated unit which combines reaction distillation(RD) with dividing wall column separation technology into one shell, and it realized the chemical reaction and the separation of multiple product fractions simultaneously. In this paper, the reaction of esterification with acetic acid and ethanol to produce ethyl acetate was used as the research system, experiments and simulations of the RDWC were carried out. This system in the traditional process mostly used the homogeneous catalyst(e.g. sulfuric acid). However, in view of the corrosion of the equipment caused by the acidity of the catalyst, we used the heterogeneous catalysts – iron exchange resins – Amberlyst15 and proposed a novel catalyst loading method. Firstly,the reliability of the model of the simulation was verified by the experimental study on the change of liquid split ratio and reflux ratio. After that, the four-column model was established in Aspen Plus to analyze the effects of the amount of azeotropic agent, reflux ratio and acetic acid concentration. Finally, for a fair comparison, the economic analysis was conducted between traditional RD column and RDWC. The results showed that RDWC can save34.7% of total operating costs and 18.5% of TAC.

Numerical Investigation on Effect of Vapor Split Ratio to Performance and Operability for Dividing Wall Column

Operability problem of dividing wall column (DWC) raised by vapor split was investigated by numerically analyzing four cases defined by different compositions of a three-component mixture. DWCs were firstly designed for each case by optimizing the vapor split to the two sides of the dividing wall, and then their feasibilities and total annual costs in operation were evaluated against different vapor split ratios. The analysis on the operability of the DWC for four cases was made based on two scenarios: (1) vapor split is shifted by the vapor resistance difference between the column sections in the two sides of the dividing wall and (2) the feed composition is changed. It was demonstrated that the positioning of the dividing wall and the decision on the vapor split may affect significantly the operability of a DWC.

Simulation Optimization and Experimental Study of Cross-Wall Adiabatic Dividing Wall Column Used to Separate Hexane-Heptane-Octane System

Through separation of the hexane-heptane–octane system in a cross-wall adiabatic dividing wall column, the effects of feed position, side-draw position, liquid split ratio, vapor split ratio and their interactions on the energy consumption were analyzed by Aspen Plus under the constant product purity, and the response surface model for the energy consumption was regressed. Based on the restriction on the optimal operating zone, the comparison of different combinations of surrogate models and optimization methods showed that, the combination of the Kriging model and multi-island genetic algorithm(Kriging-MIGA) had better prediction ability than the combination of the response surface model and partial derivative method(RSM-PD), and RSM-PD had better optimization effect than Kriging-MIGA. With a self-made cross-wall adiabatic dividing wall column, the temperature at measuring points and the energy consumption were measured during experiments, the comparison between measured values and simulated ones demonstrated that the optimized values of variables searched by RSM-PD and Kriging-MIGA could be both used as the optimum technological conditions since the experimental reliability was ensured, with the optimum technological conditions shown below: The feed position is 6, the side-draw position is 7, the combinations of liquid split ratio and vapor split ratio are [0.14, 0.5] and [0.16, 0.52], respectively. RSM-PD and Kriging-MIGA can provide the appropriate optimization methods for the dividing wall column.

A novel kind of multiple steady states characteristics in the dividing wall column

In this article, one kind of multiple steady states(MSS) phenomenon was investigated for a dividing wall column(DWC). The four-section model constructed in Aspen Plus was employed to simulate two DWC cases: mixture of n-hexane, n-heptane and n-octane;system of methanol, ethanol and n-propanol. It can be seen that there is a range of vapor split ratio in which multiple solutions of reflux ratio exist for fixed DWC configuration with the same feed and product streams. The width and the curve shapes of the MSS region, and the number of solutions change with the liquid split ratio. This MSS phenomenon was further explained using the component recovery around the prefractionator and the component recycling flow inside the DWC. This MSS phenomenon is helpful for DWC design by knowing the probable existence of multiple solutions in advance.

Infinitesimal dividing modeling method for dual suppliers inventory model with random lead times

As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.

Reactive dividing wall column for hydrolysis of methyl acetate:Design and control

Reactive distillation and dividing wall column distillation are two kinds of effective separation technologies,and their integrated configuration,reactive dividing wall column(RDWC),presents attractive advantages.In this study,the rigorous simulation of RDWC for methyl acetate hydrolysis is performed,and sensitivity analysis is conducted to obtain the minimum reboiler duty.Then a comparison is made between the conventional process and RDWC process,and it shows that 20.1% energy savings can be achieved by RDWC process.In addition,the dynamic characteristic of RDWC is studied and an effective control strategy is proposed.The simple PI control scheme with three temperature loops can obtain reasonable control performance and maintain products at desired purities.It is proved that this RDWC process is an energy efficiency alternative with good controllability.

Composition control and temperature inferential control of dividing wall column based on model predictive control and PI strategies

The dividing wall column （DWC） is considered as a major breakthrough in distillation technology and has good prospect of industrialization. Model predictive control （MPC） is an advanced control strategy that has acquired extensive applications in various industries. In this study, MPC is applied to the process for separating ethanol, n-propanol, and n-butanol ternary mixture in a fully thermally coupled DWC. Both composition control and tem- perature inferent/al control are considered. The multiobjective genetic algor/thm function ＂gamult/obj＂ in Matlab is used for the weight tuning of MPC. Comparisons are made between the control performances of MPC and PI strategies. Simulation results show that although both MPC and PI schemes can stabilize the DWC in case of feed disturbances, MPC generally behaves better than the PI strategy for both composition control and tempera- ture inferential control, resulting in a more stable and superior performance with lower values of integral of squared error （ISE）.

Optimization of Dividing Wall Column with Heat Transfer Process Across the Wall for Feed Properties Variation

This paper investigates the thermal-coupled effect across the wall and the optimal heat transfer region of the wall for enhancing the energy saving effect of dividing wall column (DWC), and also studies the effects of feed thermal condition (q) and middle component composition of feed (cB) on the heat transfer process, the optimal heat transfer region, and the maximum heat transfer quantity across the wall. The simulation results show that the maximum heat transfer quantity across the wall and the potential for energy saving increase with the increase of q, while with the limitation of temperature difference across the wall, the beneficial heat transfer effect between certain range of stages, which are involved in the optimal heat transfer region, cannot be realized completely for a specific value of q. Besides, compared with q, a changing cB does not change the degree of realizing the beneficial heat transfer effect, but can bring about the variation of liquid split ratio (RL) and vapor split ratio (Rv). Thus, for achieving a maximum energy-saving effect of DWC, different q and cB need to find its own corresponding suitable heat transfer process across the wall.

Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.

Simulated annealing-based optimal design of energy efficient ternary extractive dividing wall distillation process for separating benzene-isopropanol-water mixtures

This article investigates the performances of different extractive distillation processes intensified with dividing-wall column for separating benzene-isopropanol-water ternary mixtures.All the processes with ethylene glycol as solvent are optimized with the minimal total annual cost(TAC)as target.In order to get the global optimal solution intelligently,an improved simulated annealing algorithm is adopted,which is programmed in MATLAB and linked to Aspen Plus.The results show that the extractive dividing wall column-solvent(EDWC-S)process consisting of an extractive dividing wall column and a solvent recovery column is the best scheme.It can reduce the TAC by 28.65%and CO_(2) emissions by 32.84% compared to the conventional triple-column extractive distillation process.

Control of reactive dividing wall column for selective hydrogenation and separation of C3 stream

In our previous work, the reactive dividing wall column(RDWC) was proposed and proved to be effective for selective hydrogenation and separation of C3 stream. In the present paper, the dynamics and control of the proposed RDWC are investigated. Four control structures including composition and temperature controls are proposed. The feed forward controllers are employed in the four control strategies to shorten the dynamic response time, reduce the maximum deviations and offer an immediate adjustment. The control structures are compared by applying them into the RDWC system with 20% disturbances in both the feed flow rate and the feed compositions, and the results are discussed.

Shortcut Method of Design and Energy-Saving Analysis of Sargent Dividing Wall Column

The Sargent dividing wall column can implement four products separation sequences in one column based on Fully Thermally Coupled Distillation Column. The initial design parameters are required for the design optimization or dynamic control of the Sargent dividing wall column, and in order to make the rigorous simulation of the Sargent dividing wall column more conducive to convergence, a ten column model for complex Sargent column is established in this paper,and the shortcut design method of this model is proposed. The internal minimum vapor and liquid flow are obtained by the Underwood equations and the mass balance method and the V-min method. The separation for a 4-component shortcut mixture of pentane, hexane, heptane and octane was considered, while the initial values of design parameters and the ratio of vapor-liquid distribution of each column were calculated by using the shortcut design method of a ten column model. And by comparing the shortcut calculations with rigorous simulation results, the practicality and reliability of shortcut calculations were verified. The reason for energy saving was analyzed based on back-mixing. A virtual heat exchanger is proposed to make the Sargent dividing wall column more energy efficient.

Application of the dividing wall column to olefin separation in fluidization methanol to propylene(FMTP) process

Dividing wall column(DWC)is shown to be energy efficient compared to conventional column sequence for multi components separation,which is used for olefin separation in fluidization methanol to propylene process in the present work.Detailed design for pilot DWC was performed and five control structures,i.e.composition control(CC),temperature control(TC),composition-temperature control(CC-TC),temperature difference control(TDC),double temperature difference control(DTDC)were proposed to circumvent feed disturbance.Sensitivity analysis and singular value decomposition(SVD)were used as criterion to select the controlled temperature locations in TC,CC-TC,TDC and DTDC control loops.The steady simulation result demonstrates that 25.7% and 30.2% duty can be saved for condenser and reboiler by substituting conventional column sequence with DWC,respectively.As for control structure selection,TC and TDC perform better than other three control schemes with smaller maximum deviation and shorter settling time.

Fast image retargeting based on strip dividing and resizing

Based on image strip dividing, an effective and fast image retargeting algorithm is proposed for resizing images. First,we construct the image energy map using gradient magnitude of the pixels and calculate the accumulated energy of each column,dividing the image into several strips by integrating similar energy columns. The reduced amount of dimension is decided in inverse proportion to the average energy for each strip. Then we retarget the image combining scaling with cropping in terms of each strip＇s reduced ratio. Experiment results show that the proposed algorithm is capable of implementing fast image retargeting and preserving both the local structures and the global visual effect of the image.

FLOW CHARACTERISTICS IN DIVIDING FLOW MANIFOLDS

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Investigation of the operability for four-product dividing wall column with two partition walls

For separating some specific four component mixtures into four products, the four-product dividing wall column(FPDWC) with two partition walls can provide the same utility consumption with the extended Petlyuk configuration, although with structure simplicity. However, the reluctance to implement this kind of four product dividing wall column industrially also consists in the two uncontrollable vapor splits associated with it. The vapor split ratios are set at the design stage and might not be the optimal value for changed feed composition, thus minimum energy consumption could not be ensured. In the present work, a sequential iterative optimization approach was initially employed to determine the parameters of cost-effective FPDWC. Then the effect of maintaining the vapor split ratios at their nominal value on the energy penalty was investigated for the FPDWC with two partition walls, in case of feed composition disturbance. The result shows that no more than + 2% above the optimal energy requirements could be ensured for 20% feed composition disturbances, which is encouraging for industrial implementation.

FLOOD ROUTING MODELS IN CONFLUENT AND DIVIDING CHANNELS

By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded. In this manner, a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction. The meeting of flood peaks in the mainstream and tributary can be analyzed with this model.The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood. Subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well. As a result, flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated.It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.