Consensus-based approach for parameter and state estimation of agro-hydrological systems

The development of advanced closed-loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro-hydrological systems in a robust and reliable manner. A nonlinear state-space model is established based on the discretization of the Richards equation to describe the dynamics of the agro-hydrological systems. We consider that model parameters are unknown and need to be estimated together with the states simultaneously. We propose a consensus-based estimation mechanism, which comprises two main parts: (a) a distributed extended Kalman filtering algorithm used to estimate several model parameters; and (b) a distributed moving horizon estimation algorithm used to estimate the state variables and one remaining model parameter. Extensive simulations are conducted, and comparisons with existing methods are made to demonstrate the effectiveness and superiority of the proposed approach. In particular, the proposed approach can provide accurate soil moisture estimate even when poor initial guesses of the parameters and the states are used, which can be challenging to be handled using existing algorithms.     

超临界CO2二元系统相平衡的数值模拟

应用微扰理论,借助微扰状态方程,对超临界CO2 系统相平衡进行了模拟。编制了求解程序,介绍了状态方程中各参数的确定方法和程序模块的设计思想。针对超临界CO2 /非极性体系、超临界CO2 /极性体系,在不同温度、压力条件下的气液相平衡进行了计算,将计算结果与实验结果进行了比较,结果表明:微扰状态方程适合模拟超高压下的CO2 二元体系的相平衡。     

用FRKS状态方程关联高度非对称二元系超额焓

引言对于组分分子大小、形状、结构相差较大的高度非对称混合物,迄今仍未有计算其超额焓的满意的方法．最近Lin等用转子链立方状态方程计算了高度非对称二元系的超额焓．在他们的工作中,使用两个可调参数虽然明显改进了计算,但对大多数体系,误差仍较大．对于这一类体系,立方状态方程失败的两个主要原因是：一、对于纯物质,立方状态方程中的引力参数α通常表为温度T和偏心因子ω的函数．对于复杂化合物,特别是长链碳氢化合物,由于其性质偏离正常流体较远,偏心因子已不可靠,另外,对于高沸点物质,也难以得到可靠的ω数值;因此,…     

Property prediction of crystalline solids from composition and crystal structure

Kernel regression as a data‐driven and rigorous nonparametric statistical technique to predict properties of atomic crystals is proposed. A key feature of the proposed approach is the possibility of treating predictors not only as continuous, but also as categorical data. The latter specifically allows the predictive model to capture the discrete nature of crystals with regards to composition (number of atoms in the chemical formula) and spatial configuration (finite number of crystallographic space groups). Another important aspect of using kernel regression is the direct access to its explicit mathematical form, which can be directly embedded in optimal inverse problems to design new crystalline materials with given target properties. The property prediction approach is illustrated by training models to predict electronic properties of 746 binary metal oxides and elastic properties of 1173 crystals. As a first approach to solving the inverse problem, an exhaustive enumeration algorithm is described. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2605–2613, 2016     

Use of the empirical slopes approach to predict gas solubility properties in some pure polar solvents and in binary mixtures containing polar solvents

In previous papers^1,2 the theory of Hildebrand and Lamoreaux³ has been developed into the empirical slopes approach. This approach can be used to provide useful predictions of solubility, entropy of solution and related properties for gases in relatively non-polar pure liquids and binary mixtures. It was anticipated¹ that the empirical slopes approach could not be applied to polar solvent systems because the approach is based on regular solution theory,^4,5 which is inapplicable to such systems. In this paper, however, it is shown that the empirical slopes approach can predict the solubility and entropy of solution of gases in polar solvents, and in binary mixtures containing these solvents. The predictions are compared with the experimental values and they are also given for certain gas-pure solvent combinations which have not been studied experimentally. For gas solubilities in the binary mixtures the predictive accuracy and the merits of the empirical slopes approach are compared with those of some other theories.     

Comparison of Equilibrium and Nonequilibrium Models in the Simulation of Multicomponent Sorption Processes

Abstract

A mathematical model has been developed to describe the process of equilibrium adsorption from a finite bath. A nonlinear Fritz-Schluender isotherm model was used to describe the equilibrium between solid and liquid phases. Finite-difference numerical solutions for single, binary, and ternary systems were obtained and shown to match previously published experimental data satisfactorily. These solutions were also compared with nonequilibrium models for the three cases. It was shown that the nonequilibrium model is superior to the equilibrium one since 1) it is applicable to both equilibrium and nonequilibrium conditions, 2) its computer program is general and can be used for any number of sorbates, 3) it can be used for any type of linear or nonlinear equilibrium isotherms without the need to any modifications in the program, and 4) its numerical solutions are of high accuracy compared to experimental data.     

An algorithm for the optimization of kubelka-munk absorption and scattering coefficients

A new approach to the calculation of Kubelka-Munk absorption and scattering coefficients based on linear-leastsquares techniques is proposed. This algorithm characterizes colorants by determining the coefficients from typical mixtures. Several advantages are gained over traditional methods: Absorption and scattering can be determined without use of primary binary mixtures by using production-mixture history; colorants are characterized in the same manner in which they are used; and the approach is quite flexible in terms of manipulating the calculation.     

Thermodynamic modeling of the BaO-SiO<Subscript>2</Subscript> and SrO-SiO<Subscript>2</Subscript> binary melts

The evaluation of the thermodynamic properties and the phase diagrams for the binary BaO-SiO₂ and SrO-SiO₂ systems is carried out using a structural model for silicate melts and glasses. This thermodynamic model is based on the assumption that an addition of metal oxides to silica results in the depolymerization of the silicon-oxygen network, with a characteristic free energy change. A least squares optimization program permits all available thermodynamic and phase diagram data to be optimized simultaneously. In this manner, data for the above binary systems have been analysed and represented with a small number of parameters. The resulting equations represent the thermodynamic and phase diagram data for the alkaline-earth oxide-silica systems within error limits for most of the experimental data. In particular, the measured limiting liquidus slope, at X _{SiO 2} = 1, is well reproduced.     

Continuous optimization using a dynamic simplex method

Most chemical processes are operated under continuously changing conditions and thus the optimal operating conditions change with time. On-line optimization techniques of various types which are used to track these kinds of moving optimum, have sparked significant interest in recent years. However, most of these strategies deal only with static optimum or optimum that move so slowly that they can be considered static.The model-based optimization algorithms, such as SQP, use first-principle models to optimize the process in a sequential steady-state mode, and hence rely on accurate process models. But for many circumstances, a process model is either too complex or expensive to obtain or changes quickly with time. This can limit the model-based approach and points to the ‘direct search’ optimization methods, since for these methods no explicit model is required. Moreover, direct search methods need very few new measurements to calculate a new movement toward the optimum. However, little work has been done on optimizing dynamic systems with moving optima using direct search methods. In this work, the traditional Nelder-Mead simplex method is modified and extended to allow tracking of moving optima, which results in a so-called dynamic simplex algorithm. Various simulation examples demonstrate the capability and flexibility of this new direct search algorithm in tracking moving optima in multiple dimensions.     

Synthesis and optimization of utility system using parameter adaptive differential evolution algorithm☆

Synthesis and optimization of utility system usual y involve grassroots design, retrofitting and operation optimi-zation, which should be considered in modeling process. This paper presents a general method for synthesis and optimization of a utility system. In this method, superstructure based mathematical model is established, in which different modeling methods are chosen based on the application. A binary code based parameter adaptive differential evolution algorithm is used to obtain the optimal configuration and operation conditions of the sys-tem. The evolution algorithm and models are interactively used in the calculation, which ensures the feasibility of configuration and improves computational efficiency. The capability and effectiveness of the proposed approach are demonstrated by three typical case studies.     

PREDICTION OF LIQUID-PHASE MASS-TRANSFER COEFFICIENTS IN MULTICOMPONENT ION EXCHANGE: COMPARISON OF MATRIX, FILM-MODEL, AND EFFECTIVE-DIFFUSIVITY METHODS

Several methods are evaluated for predicting or correlating liquid-phase mass-transfer coefficients in multicomponent ion exchange. Comparisons are made of methods based on matrix generalizations of binary results, methods using the film-model relation between multicomponent fluxes and binary mass-transfer coefficients, and effective-diffusivity methods. It was determined that methods based on the film model give results in good agreement with matrix generalization methods and, where comparisons can be made, both of these methods give results in good agreement with exact calculations. Effective-diffusivity methods were found to be less reliable. The film-model methods developed in this study are analogous to methods commonly used in nonelectrolyte systems.     

基于遗传算法的快速X射线计算机层析成像多相流测试技术(Ⅰ)测试原理和数值仿真

针对局部浓度场具有二值分布特征的特定多相流体系,提出引入多相流物理特征的快速X射线计算机层析成像（XCT）技术,基于围绕被测物有限角度的X射线投影数据,建立了改进的遗传算法（GA）求解不完整投影数据集的二值图像重构算法。通过有限角度的同时投影,实现对两相流浓度场的瞬间图像冻结和快速图像采集,既拥有XCT的高空间分辨率特征,同时满足高时间分辨率的动态测量要求,并由于投影角度数要求的大幅度缩减而降低了XCT的硬件成本。以气液两相流的多泡体系为研究对象,通过详细的数值仿真实验获得了较理想的图像重构效果,验证了GA-XCT的理论可行性。在3～24个有限角度投影数据的情况下,GA-XCT表现出明显优于传统CT图像重构算法（即滤波反投影算法）的二值图像重构能力。同时,GA-XCT具有很好的抗噪声能力,而且不依赖于气泡形状。     

用改进的基团贡献法计算二元体系液相分子扩散系数

一种改进的用基团贡献原理计算二元体系液相分子扩散系数的方法,可用于大部分非理想液相体系。用150多个体系的1000多个实验点对此方法进行了验证,结果表明对于理想体系和无限稀释溶液的分子扩散系数,计算值与实验值平均相对误差不超过5%,对于大部分的非理想体系其平均相对误差小于10%。与原有的经验、半经验关联式相比,改进的方法具有更大的适用范围,能更准确地预测液相分子扩散系数。     

Mathematical framework for higher order breakage scenarios

Droplet breakage has been widely studied due to its relevance to the gas purification industry. This phenomenon appears inside scrubbers on the mesh pad, due to the interaction of the droplets with the liquid drainage film or the walls of the equipment. The breakage process that has been most widely studied in the previous publications is binary breakup, mostly due to its simplicity and because it is the most common one in diluted systems.In this work, higher order breakups like ternary, quaternary, etc. have been considered. A higher order breakage model was developed based on an existing binary breakage model, and it was shown that this approach is suitable for higher order breakage computations. Despite the fact that this procedure is reasonably accurate for the first preliminary results, a more accurate mathematical model based on a detailed physical analysis of the problem in question should be developed.     

Batch Kinetics of Metal Biosorption: Application of the Bohart-Adams Rate Law

The most common rate model formulations for metal biosorption in batch systems assume that the uptake process is limited by surface reaction, with the so-called pseudo first order and second order rate equations being the most popular. However, from a modeling perspective the rate coefficients of these equations are of limited use as it is not clear how they can be utilized in the modeling of other process configurations such as fixed bed columns. As an alternative, we advocate a modeling approach predicated on the Bohart-Adams surface reaction rate law because it is of a form that can be readily integrated with the governing equations for batch and fixed bed systems, allowing explicit analytical solutions to be obtained. In this work we fit the batch solution of the Bohart-Adams rate law to kinetic data taken from the literature using a genetic algorithm. The resultant parameter estimates can be used in the fixed bed solution of the Bohart-Adams rate law to generate breakthrough predictions. Moreover, the batch Bohart-Adams rate law is compared with a general nth order surface reaction rate law using the Akaike information criterion approach.     

A simple and unified algorithm to solve fluid phase equilibria using either the gamma–phi or the phi–phi approach for binary and ternary mixtures

A new algorithm is proposed for calculating phase equilibria in binary systems at a fixed temperature and pressure. This algorithm is then extended to ternary systems (in which case, the mole fraction of one constituent in a given phase must be fixed in order to satisfy the Gibbs’ phase rule). The algorithm has the advantage of being very simple to implement and insensitive to the procedure used to initialize the unknowns. Most significantly, the algorithm allows the same solution procedure to be used regardless of the thermodynamic approach considered (γ–φ or φ–φ), the type of phase equilibrium (VLE, LLE, etc.) and the existence of singularities (azeotropy, criticality and so on).     

Closed‐loop Fault Detection Using the Local Approach

Fault detection and isolation (FDI) has become a crucial issue for industrial process monitoring in order to increase availability, reliability and production safety. Model‐based FDI methods rely on a mathematical model and input‐output data of a process to perform detection. The local approach is a new model‐based FDI method that aims to detect slight changes of a system's parametric properties. Closed‐loop detection is an important issue for the local approach since all control systems work under closed‐loop conditions. A new algorithm was proposed to revise the original detection algorithm in order to make it work for closed‐loop data. Simulation results show that the proposed method can detect the changes of parameters of a system that can affect closed‐loop performance.     

Closure equations in the estimation of binary interaction parameters

Binary interaction parameters used in the UNIQUAC activity coefficient model are found to be dependent on each other and related by a linear relation termed as the closure equation. For a ternary system, six binary interaction parameters are related by one closure equation. Similarly for quaternary systems, three independent closure equations are obtained for the twelve binary interaction parameters and for quinary systems there are six closure equations for twenty parameters. Each closure equation consists of six parameters. The binary interaction parameters that do not satisfy the closure equations may lead to a less accurate prediction of liquid-liquid equilibria. In this work the binary interaction parameters have been estimated with and without closure equations for few ternary and quaternary systems. Parameters that satisfy the closure equations exhibit better root mean square deviation than those that do not satisfy the closure equations in most of the cases. A similar behavior is observed for NRTL model also.     

A simple correlation for solids holdup in a gas-liquid-solid fluidized bed

A simple empirical model was established which allows solids holdup in a gas-liquid-solid fluidized bed containing large and dense particles to be readily predicted based on the equation of Richardson and Zaki (1954, Trans. Inst. Chem. Engrs32, 35) for liquid-solid fluidized bed systems. The approach is applicable both to monocompnent particle systems and to binary mixtures of particles. For a monocomponent system, a correlation for model parameters was proposed which is expressed as a function of particle diameter, particle density, bed diameter and liquid density. For a binary mixture of particles, the averaging and serial approaches were shown to predict the solids holdup equally well within the range of the gas and liquid velocities considered. Experiments were also performed using eight solid particles for the monocomponent system and five binary mixtures of particles differing in diameter and/or density for the mixture system to substantiate the model.     

A modified “inside-out” algorithm for simulation of multistage multicomponent separation processes using the UNIFAC group-contribution method

A computational procedure using a modification of Boston and Sullivan's “inside-out” multistage multicomponent separation algorithm (1974) is developed. In order to improve convergence behavior for problems involving mixtures with highly nonideal liquid phases, a two-parameter model is used to describe liquid-phase compositional effects upon the K-factor. The quasi-Newton methods of Mehra et al. (1983) and Nghiem (1983) are applied to solving various sets of solution variables in the proposed algorithm. Activity coefficients are calculated using the UNIQUAC activity-coefficient model (1975) with parameters obtained from the UNIFAC group-contribution method (1975). The computational procedure is applicable to distillation, absorption and reboiled-absorption configurations. The proposed algorithm was implemented in a FORTRAN 77 program and tested on the Honeywell DPS 8/70M computer at the University of Calgary. Inclusion of the liquid-phase model resulted in improved convergence behavior for nonideal systems in which the original “inside-out” method failed to converge.