Index analysis and reduction of systems of quasi-linear partial-differential and algebraic equations

To reliably solve PDAE models in established equation-oriented modeling environments (i) certain mathematical properties are to be fulfilled and (ii) the specified initial- and boundary conditions are to be consistent. For an assessment of both of these aspects an important theoretical framework is the concept of index. In this contribution we propose a new method for a systematic index reduction of quasi-linear PDAE systems. The general idea is to reveal quasi-linear combinations of the differential quantities in the high-index model which are invariant with respect to a specific independent variable. By using these quasi-linear combinations as templates for symbolic manipulations, additional algebraic constraints become explicit. These explicit constraints are then used for index reduction yielding low-index PDAE models. The procedure is demonstrated in the context of a typical modeling work-flow for modeling problems of a tubular reactor, diffusive charge transport in electrolyte mixtures and incompressible fluid flow.     

基于小波神经网络的污水处理污泥体积指数软测量

污水处理过程具有非线性、时变和滞后等特点,因而无法进行准确的数学建模。现有的污水处理技术中最突出的问题是一些关键的水质参数不能在线监测,只能通过人工间接测量再通过计算获得,耗时较长,不能及时地进行信息反馈,会造成一些严重的后果。为了避免这样的问题,提出了基于小波分析的神经网络(BP)软测量技术,通过建立小波神经网络参数软测量模型,对污水处理中难测水质参数SVI(污泥体积指数)进行在线监测。研究表明,此方法能有效规避单一的BP算法收敛速度慢、容易陷入局部最优解等问题,有助于实现对污水处理的智能控制。     

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.     

Stochastic maximum principle for optimal control under uncertainty

Optimal control problems involve the difficult task of determining time-varying profiles through dynamic optimization. Such problems become even more complex in practical situations where handling time dependent uncertainties becomes an important issue. Approaches to stochastic optimal control problems have been reported in the finance literature and are based on real option theory, combining Ito’s Lemma and the dynamic programming formulation. This paper describes a new approach to stochastic optimal control problems in which the stochastic dynamic programming formulation is converted into a stochastic maximum principle formulation. An application of such method has been reported by Rico-Ramirez et al. (Computers and Chemical Engineering, 2003, 27, 1867) but no details of the derivation were provided. The main significance of this approach is that the solution to the partial differential equations involved in the dynamic programming formulation is avoided. The classical isoperimetric problem illustrates this approach.     

Economic optimal control applied to a solar seawater desalination plant

This paper discusses the formulation of an optimal control strategy taking into account economic objectives in the fresh water production process through a solar seawater desalination plant. It contributes both a linearised model of the solar-field dynamics and a simplified model of the produced distillate as a function of the outlet solar field water temperature. Then such linear models are used to design an economic receding horizon optimal controller. In particular, it comprises incomes related to the production of fresh water and the costs dealing with the electricity. Several simulations validate the proposed models and show the performance of the proposed economic optimal control strategy. In both cases, actual disturbances from physical experiments have been included in the simulations. Notice that the AQUASOL facility available at the Plataforma Solar de Almería (Spain) has been considered in this work as testbed.     

Reducing the energy demand of continuous distillation processes by optimal controlled forced periodic operation

In a continuous distillation process, it is generally believed that steady-state conditions represent the optimal operation mode from the viewpoint of required energy supply and that any disturbance of steady-state conditions (e.g. an oscillating profile of reflux ratio or reboiler heat rate) will cause a higher energy demand if the product specifications (expressed as average values) have to be fulfilled. However, this assumption has been disproven by some theoretical and experimental studies in the past, where the distillation process was studied under unsteady-state conditions, to reduce the energy demand. In these studies, both the reflux and the vapor flow rates have been controlled periodically. In the present paper, dynamic optimization methods are applied to find the optimal profiles for all possible control variables (flow rates of feed, products, reflux and vapor). Two examples are discussed. In the first example, an ideal ternary mixture is separated into two fractions, and in the second example, the same mixture is separated into three fractions using a column with a sidestream. For both examples, it is demonstrated that appropriate control profiles for the main control variables can reduce the required energy supply compared with steady-state conditions. The results were obtained on the basis of a simple mathematical model of a distillation column with the assumption of constant relative volatilities and equimolar evaporation and condensation. To generate the control profiles, a new software package for the solution of large-scale optimal control problems was used. The optimal control profiles represent a decoupling of feed supply, removal of distillate product, removal of bottom product, and, in the second example, withdrawing of the sidestream.     

水体富营养化控制手段及防治实例

由于人类活动致使自然水体的富营养化，使水质恶化，造成鱼类和其他水生生物大量死亡。富营养化的防治是水污染处理中最为复杂和困难的问题。营养物质去除的高难度．至今还没有任何单一的生物学、化学和物理措施能够彻底去除废水的氮、磷营养物质。介绍了当前水体中磷、氮的控制标准和污水脱氮除磷（生化硝化、反硝化、生物除磷等）技术；同时适当选择了几例德国污水和地表水处理的典型工程实例。     

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems.     

ANNSA: a hybrid artificial neural network/simulated annealing algorithm for optimal control problems

This paper introduces a numerical technique for solving nonlinear optimal control problems. The universal function approximation capability of a three-layer feedforward neural network has been combined with a simulated annealing algorithm to develop a simple yet efficient hybrid optimisation algorithm to determine optimal control profiles. The applicability of the technique is illustrated by solving various optimal control problems including multivariable nonlinear problems and free final time problems. Results obtained for the different case studies considered agree well with those reported in the literature.     

The implementation of an optimal control policy for a batch thermal system

A system comprising a steam heated exchanger through which fluid is pumped into a tank containing a steam heating coil has been constructed. This system has been modelled and the optimal charge rate to bring the tank to known conditions of mass and temperature in minimum time has been calculated by use of Pontryagin's maximum principle.The optimal policies calculated in this way have been implemented on the experimental equipment and comparisons with an equivalent constant charge rate made. Time advantages up to nearly 20% have been achieved over the constant charge rate by use of the optimal policy.Four control schemes have been compared to implement the optimal policy. These have been the control of mass alone, the control of temperature alone an two policies involving switching between mass and temperature. The two policies involving switching have given much closer agreement with predictions t those involving a single control variable.     

OPTIMIZATION OF FEDBATCH CULTURE SYSTEMS WITH TWO FEED RATES

The feed rate optimization of fed batch cultures with two or more feed rates is a numerically difficult problem involving two or more singular control variables. Even when implicit or explicit forms of singular control profiles can be derived, the sequence of control including bang-bang regions and singular regions must be known a priori. Thus, no attempt has been reported in literature.

A nonsingular transformation algorithm has been proposed to convert singular control problems with control variables into nonsingular problems involving nonsingular control variables. Using the proposed transformation and numerical technique, optimization of fed-batch cultures with two feed rales has been carried out succesfully.     

基于模糊满意度的烧结过程多目标优化控制

为实现铁矿石烧结过程中烧结终点和混合料槽料位两个关键参数的综合优化,提出了一种基于模糊满意度的多目标优化控制方法。首先,通过综合运用模糊控制、预测控制的切换控制技术,建立烧结终点的智能优化控制模型;其次,为稳定混合料槽料位,基于专家知识,建立了混合料槽料位专家控制模型;最后通过构造求解多目标优化问题的系统满意度函数,将多目标优化问题转化为单目标优化问题,求取系统的满意解,实现烧结过程多目标优化控制。仿真结果和实际运行结果表明提出的方法是可行而有效的。     

Comparison of fatty acids and lipids of smolting hatchery-fed and wild atlantic salmonSalmo salar

In Atlantic Canada the Atlantic salmonSalmo salar change from the parr stage to the smolt stage while still in fresh water, preparatory to migration to salt water. In some stocks this takes place during the second overwintering. In several hatcheries where the water temperature drops to 0–0.5 C and the ponds ice over, there is a high incidence of erosion of the dorsal and pectoral fins and sometimes of the caudal fin. No disease organism has been identified, and the lesions heal over in most cases. Dietary fatty acids were thought, to be a factor. A detailed study of lipid recoveries and classes has shown that in the skins of abnormal fish the total lipid, is 7.8% compared to 4.7% in control fish. Unexpectedly, an analysis of one lot of healthy smoltstage wild fish showed that whole bodies have only a quarter of the lipid of comparble hatchery fish. Comparison of fatty acids showed that wild fish lipids include a higher proportion of arachidonic acid than those of the hatchery fish. in the latter, linoleic acid is provided readily by diet but the elongation to arachidonic acid evidently does not proceed. These results suggest that the smolt lipid, is involved intimately with either the cause of the dermal lesion or is a defense mechanism, possibly mediated through oxygenase activity.     

Preparation of microbial silage from fish of underutilized species

Fish silage was produced by microbial means from a mixture of several fish species which are not used for human consumption, and form part of the shrimp by-catch. The fish was mixed with a carbohydrate source (molasses) and a starter culture of Lactobacillus plantarum 8014. The mixture was fermented at 30 +/- 2 degrees C. Several tests were undertaken to determine the optimal conditions and concentration of molasses (5, 10 and 15%) and Lactobacillus (0.5, 1.0, 2.5, 5.0 and 10.0%). Results indicated that 1% of microorganisms and 15% of molasses were the optimal proportions to produce a stable fish silage. The production process and stability study of fish silage were followed through chemical, physical and microbiological tests. As findings revealed, the first six days of the process are related to acid production, pH reduction and microbial control, while after this period the process is basically related to protein hydrolysis. In addition, sensory tests of flavor and color were performed. The results of this study suggest the feasibility of utilizing this marine resource at present discarded, through a technological scheme, to produce fish silage for animal feed.     

Bang‐Bang solution of nonlinear time‐optimal control problems using a semi‐exhaustivesearch

At times, the objective is to seek a bang‐bang control policy for nonlinear time‐optimal control problems. The usefulness of iterative dynamic programming (IDP) has been shown in the literature for solving such problems. However, the convergence to the optimal solution has been obtained from about 50% of the guessed values near the optimum. In this paper, we present a semiexhaustive search method for seeking such solutions and a comparison is made with the IDP. The results show that the convergence can be obtained from a significantly higher number of guessed values chosen over a much wider region around the optimum.     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

自制交联阳离子淀粉絮凝剂处理含油废水

以自制的马铃薯交联阳离子淀粉为絮凝剂,对某炼油厂的含油废水进行絮凝实验,以COD去除率和油去除率为指标,得到絮凝剂最佳投加量,在此基础上考察了pH和水温的影响.实验结果表明:絮凝剂的最佳投加量为4 650 mg/L、pH为1.5～4、温度为50℃时,该絮凝剂对含油量和COD的去除效果较好.     

沉水植物对水体净化效果的研究进展

文章综述了沉水植物对富营养化水体及其他受污水体中的N、P和有机物的去除,及对水体叶绿素a、溶解氧等影响的研究的进展,并分析沉水植物对其的去除率,沉水植物在水质改善和水体生态修复中较高的应用价值。同时指出沉水植物净化水质中存在的问题,展望了沉水植物净化水质的应用前景。     

pH值对强化混凝去除水中微量有机物的影响

通过烧杯试验,分别以聚合氯化铝(PAC)和FeCl3为混凝剂研究了pH值对水中有机物去除的影响。研究结果表明:PAC的最佳投加量为8 mg/L,此时有机物和浊度的去除率分别为51.8%和93.6%;FeCl3的最佳投加量为50 mg/L,此时有机物和浊度的去除率分别为57.8%和95.0%。有机物去除的最佳pH值范围为5.5～6.5,浊度去除的最佳pH值范围为7～8;相对于原水而言,调节pH值能够使有机物的去除率提高10%左右,因此调节pH值是一种经济有效的去除水中有机物的强化混凝方法。