Sequential experimental design based on multiobjective optimization procedures

Model-based sequential experimental designs are frequently applied for discrimination of rival models and/or estimation of precise model parameters. Although the development and use of a single design criterion to perform the simultaneous model discrimination and precise parameter estimation seem appealing, published material indicates that previous attempts to develop such a single design criterion have not been successful. Despite that, this problem has rarely been analyzed with the help of multiobjective optimization procedures. In this work, a multiobjective optimization method based on the particle swarm optimization procedure is used to build the Pareto fronts in experimental design problems where distinct design criteria used for discrimination of rival models and/or estimation of precise model parameters are considered simultaneously. It is shown through the rigorous analysis of the Pareto sets that both design objectives are frequently conflicting, which means that optimum discrimination of rival models and estimation of precise model parameters cannot be performed simultaneously in many cases. However, it is also shown that the use of the posterior covariance matrix of estimated model parameters for model discrimination makes the design of experiments for the simultaneous optimum model discrimination and estimation of model parameters possible in many experimental design problems.     

KINETIC PARAMETER ESTIMATION BY STANDARD OPTIMIZATION METHODS IN CATALYTIC CONVERTER MODELING

The application of mathematical models to the prediction of the performance of automotive catalytic converters is gaining increasing interest, both for gasoline and diesel engined-vehicles. This article addresses converter modeling in the transient state under realistic experimental conditions. The model employed in this study relies on Langmuir-Hinshelwood kinetics, and a number of apparent kinetic parameters must be tuned to match the behavior of each different catalyst formulation. The previously applied procedure of manually tuning kinetics parameters requires significant manpower. This article presents a methodology for kinetic parameter estimation that is based on standard optimization methods. The methodology is being applied in the exploitation of synthetic gas experiments and legislated driving cycle tests and the assessment of the quality of information contained in the test results. Although the optimization technique employed for parameter estimation is well known, the development of the specific parameter estimation methodology that employs the results of the available types of experiments is novel and required significant development. Application of this refined tuning methodology increases the quality and reliability of prediction and also greatly reduces the required manpower, which is important in the specific engineering design process. The parameter estimation procedure is applied to the example of modeling of a diesel catalytic converter with adsorption capabilities, based on laboratory experiments and vehicle driving cycle tests.     

Model selection and parameter estimation for chemical reactions using global model structure

In complex reaction systems, such as those found in heterogeneous catalytic reactions, several alternative kinetic models are usually considered in an effort to describe reaction kinetics. The number of plausible mechanisms can be very large, even for systems with a small number of reactions and components. Usually, only a restricted number of models are investigated in detail, since the evaluation of a large number of complex models is extremely time-consuming. In this work, a methodology is described, which allows performing efficiently a global search within all plausible models and parameter sets using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The developed methodology is applied to the parameter estimation and model optimization of the partial oxidation of ethane reaction network. The present approach allows the reliable investigation of a considerable number of models mechanisms in an automatic manner and in a short computational time. It appears to be a very effective way to optimize complex reaction mechanisms.     

On the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification

Parameter estimation algorithms integrated in automated platforms for kinetic model identification are required to solve two optimization problems: i) a parameter estimation problem given the available samples; ii) a model‐based design of experiments problem to select the conditions for collecting future samples. These problems may be ill‐posed, leading to numerical failures when optimization routines are applied. In this work, an approach of online reparametrization is introduced to enhance the robustness of model identification algorithms towards ill‐posed parameter estimation problems.     

An efficient constraint handling method with integrated differential evolution for numerical and engineering optimization

Constrained optimization problems are very important as they are encountered in many engineering applications. Equality constraints in them are challenging to handle due to tiny feasible region. Additionally, global optimization is required for finding global optimum when the objective function and constraints are nonlinear. Stochastic global optimization methods can handle non-differentiable and multi-modal objective functions. In this paper, a new constraint handling method for use with such methods is proposed for solving equality and/or inequality constrained problems. It incorporates adaptive relaxation of constraints and the feasibility approach for selection. The recent integrated differential evolution (IDE) with the proposed constraint handling technique is tested for solving benchmark problems with constraints, and then applied to many chemical engineering application problems with equality and inequality constraints. The results show that the proposed constraint handling method with IDE (C-IDE) is reliable and efficient for solving constrained optimization problems, even with equality constraints.     

基于全局优化改进混沌粒子群遗传算法的物料平衡数据校正

结合遗传算法（GA）和粒子群算法（PSO）的优点以及混沌运动的特性,提出了加入混沌扰动的混沌粒子群遗传算法（DCPSO-GA）,并使用5个高维非线性测试函数考察全局优化混合算法的性能。DCPSO-GA解决了在寻优搜索时出现的停滞现象,扩大了全局优化的搜索空间,丰富了粒子的多样性,且不需要函数梯度信息。测试结果证明,针对本文的5个测试函数DCPSO-GA能找到全局最优解,其收敛速度很快,大大减少了计算量。而且,经过与其他相关算法比较可知,当总的目标函数调用次数较接近或更少时,改进算法不论在计算精度还是收敛速度上,均有很大的提高。并将DCPSO-GA算法应用到重油裂解参数估计和预测中,测试结果证明,其提高了参数估计和预测的准确性,降低了误差,能有效找到全局最优解,收敛速度快,大大减少计算量。     

Real-time optimization for a laboratory-scale flotation column

In this paper, a supervisory layer with real-time optimization (RTO) has been implemented in an experimental laboratory-scale flotation column for copper concentration. A two-stage and modifier adaptation (MA) methodology for RTO has been compared under structural, experimental and dynamic uncertainty. In addition, a gradient-free alternative for MA, called nested modifier optimization, has been proposed and tested. The results show that the KKT updates of the MA approach allow the process optimum to be determined under uncertain scenarios, unlike the two-stage approach. From the perspective of gradient modifiers, the performance of the nested methodology is comparable to the dual approach because previous past values are used to update the modifiers without requiring the gradient estimation step. In addition, the interaction of RTO with the regulatory layer must be considered to propose an optimal implementation.     

Inverse problems of biological systems using multi-objective optimization

Mathematical modeling for dynamic biological systems is a central theme in systems biology. There are still many challenges in using time-course data to obtain an inverse problem of nonlinear dynamic biological systems. In this study, a multi-objective optimization technique is introduced to determine kinetic parameter values of biochemical reaction systems. The multi-objective parameter estimation was converted into the minimax problem through the satisfying trade-off method. The aspiration value was assigned as the minimum solution to the corresponding single objective estimation. The aim of this trade-off estimation was to obtain a compromised result by simultaneously minimizing both concentration and slope error criteria. Hybrid differential evolution was applied to solve the minimax problem and to yield a global estimation.     

A comparative study of teaching-learning-self-study algorithms on benchmark function optimization

In typical optimization problems, the number of design variables may be large and their influence on the specific objective function can be complicated; the objective function may have some local optima while most chemical engineers are interested only in the global optimum. For any new optimization algorithms, it is essential to validate their performance, compare with other existing algorithms and check whether they provide the global optimum solutions, which can be done effectively by solving benchmark problems. In this work, seven typical optimization algorithms including the newly proposed TLBO (Teaching-learning-based optimization) based algorithms such as the TLSO (Teaching-learning-self-study optimization) algorithm have been reviewed and tested by using a set of 20 benchmark functions for unconstrained optimization problems to validate the performance and to assess these optimization algorithms. It was found that the TLSO algorithm shows the fastest convergence speed to the optimum and outperforms other algorithms for most test functions.     

On the feasibility and reliability of nonlinear kinetic parameter estimation for a multi-component photocatalytic process

Nonlinear kinetic parameter estimation plays an essential role in kinetic study in reaction engineering. In the present study, the feasibility and reliability of the simultaneous parameter estimation problem is investigated for a multi-component photocatalytic process. The kinetic model is given by the L-H equation, and the estimation problem is solved by a hybrid genetic-simplex optimization method. Here, the genetic algorithm is applied to find out, roughly, the location of the global optimal point, and the simplex algorithm is subsequently adopted for accurate convergence. In applying this technique to a real system and analyzing its reliability, it is shown that this approach results in a reliable estimation for a rather wide range of parameter value, and that all parameters can be estimated simultaneously. Using this approach, one can estimate kinetic parameters for all components from data measured in only one time experiment.     

Simultaneous hybrid modeling of a nosiheptide fermentation process using particle swarm optimization

Hybrid modeling approaches have recently been investigated as an attractive alternative to model fermentation processes. Normally, these approaches require estimation data to train the empirical model part of a hybrid model. This may result in decreasing the generalization ability of the derived hybrid model. Therefore, a simulta-neous hybrid modeling approach is presented in this paper. It transforms the training of the empirical model part into a dynamic system parameter identification problem, and thus al ows training the empirical model part with only measured data. An adaptive escaping particle swarm optimization (AEPSO) algorithm with escaping and adaptive inertia weight adjustment strategies is constructed to solve the resulting parameter identification problem, and thereby accomplish the training of the empirical model part. The uniform design method is used to determine the empirical model structure. The proposed simultaneous hybrid modeling approach has been used in a lab-scale nosiheptide batch fermentation process. The results show that it is effective and leads to a more consistent model with better generalization ability when compared to existing ones. The performance of AEPSO is also demonstrated.     

Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems

Multi-scenario optimization is a convenient way to formulate and solve multi-set parameter estimation problems that arise from errors-in-variables-measured (EVM) formulations. These large-scale problems lead to nonlinear programs (NLPs) with specialized structure that can be exploited by the NLP solver in order to obtained more efficient solutions. Here we adapt the IPOPT barrier nonlinear programming algorithm to provide efficient parallel solution of multi-scenario problems. The recently developed object oriented framework, IPOPT 3.2, has been specifically designed to allow specialized linear algebra in order to exploit problem specific structure. This study discusses high-level design principles of IPOPT 3.2 and develops a parallel Schur complement decomposition approach for large-scale multi-scenario optimization problems. A large-scale case study example for the identification of an industrial low-density polyethylene (LDPE) reactor model is presented. The effectiveness of the approach is demonstrated through the solution of parameter estimation problems with over 4100 ordinary differential equations, 16,000 algebraic equations and 2100 degrees of freedom in a distributed cluster.     

Towards the integration of process design,control and scheduling: Are we getting closer?

The integration of design and control, control and scheduling and design, control and scheduling, all have been core PSE challenges. While significant progress has been achieved over the years, it is fair to say that at the moment there is not a generally accepted methodology and/or “protocol” for such an integration – it is also interesting to note that currently, there is not a commercially available software [or even in a prototype form] system to fully support such an activity.Here, we present the foundations for such an integrated framework and especially a software platform that enables such integration based on research developments over the last 25 years. In particular, we describe PAROC, a prototype software system which allows for the representation, modeling and solution of integrated design, scheduling and control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers for mixed continuous/integer problems; (iv) a state-space modeling representation capability for scheduling and control problems; and (v) an advanced toolkit for multi-parametric/explicit Model Predictive Control and moving horizon reactive scheduling problems. Algorithms that enable the integration capabilities of the systems for design, scheduling and control are presented on a case of a series of cogeneration units.     

Determination of kinetics in batch cooling crystallization processes—A sequential parameter estimation approach

A comprehensive methodology to carry out a sequential parameter estimation approach has been developed and validated for the determination of the kinetic parameters of the crystallization of a generic organic compound. The strength of the approach lies in the thorough design of isothermal experiments which facilitate the isolation and/or decoupling of the different crystallization phenomena. This methodology has been applied for the parameter estimation of primary and secondary nucleation, growth and agglomeration kinetics. The resulting crystallization model has been able to reproduce the quantiles , and of the volume‐based particle size distribution of an independent seeded validation experiment with an error below 10 μm. The deviation in the prediction has been increased in the case of an independent unseeded experiment, although errors below the uncertainty of the measurement have been always obtained. The methodology here proposed is intended to be an efficient strategy for rapid modeling of batch crystallization processes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3992–4012, 2016     

一种新的DNA遗传算法及其在参数估计中的应用

化工过程的参数估计是十分棘手的问题,为此常将这类问题转化为非线性优化问题来解决。遗传算法是一种适应性强的全局搜索方法,常被用于解决非线性系统的参数估计问题。但其局部搜索能力较差,易早熟。针对遗传算法的缺点,提出了一种新的DNA遗传算法。该方法使用碱基对个体进行四进制编码,受DNA分子操作启发设计了新的交叉和变异算子。两个经典测试函数的计算结果表明,该算法的搜索能力相对于其他两种算法有了明显提高。使用该算法来估计重油热解三集总模型中的参数,结果表明所建模型拟合精度高。     

自适应混合粒子群约束优化算法及其在软测量模型参数估计中的应用

对于软测量模型参数估计问题, 针对传统梯度法求解非线性最小二乘模型时依赖初值、需要追加趋势分析进行验证和无法直接求解复杂问题的缺陷, 提出将参数估计化为约束优化问题, 使用混合优化算法求解的新思路。为此提出一种自适应混合粒子群约束优化算法(AHPSO-C)。在AHPSO-C算法中, 为平衡全局搜索(混沌粒子群)和局部搜索(内点法), 引入自适应内点法最大函数评价次数更新策略。对12个经典测试函数的仿真结果表明, AHPSO-C是求解约束优化问题的一种有效算法。将算法用于淤浆法高密度聚乙烯(HDPE)串级反应过程中熔融指数软测量模型参数估计, 验证了方法的可行性与优越性。     

A FLOWSHEET MODEL OF A WELL-MIXED FLUIDIZED BED DRYER: APPLICATIONS IN CONTROLLABILITY ASSESSMENT AND OPTIMIZATION

A model of a well-mixed fluidized-bed dryer within a process flowsheeiing package (SPEEDUP(tm)) has been developed and applied to a parameter sensitivity study, a steady-state controllability analysis and an optimization study. This approach is more general and would be more easily applied to a complex flowsheet than one which relied on stand-alone dryer modelling packages. The simulation has shown that industrial data may be fitted to the mode outputs with sensible values of unknown parameters. For this case study, the parameter sensitivity study has found that the heat loss from the dryer and the critical moisture content of the material have the greatest impact on the dryer operation at the current operating point. An optimization study has demonstrated the dominant effect of the heat loss from the dryer on the current operating cost and the current operating conditions, and substantial cost savings (around 50% ) could be achieved with a well-insulated and airtight dryer, for the specific case studied here.     

基于微粒群优化算法的不确定性调和调度

Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimization problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization （PSO） algorithm is developed for nonlinear optimization problems with both continuous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.     

SIMOP: Efficient reactive distillation optimization using stochastic optimizers

A methodology to improve the efficiency of stochastic methods applied to the optimization of chemical processes with a large number of equality constraints is presented. The methodology is based on two steps: (a) the optimization of the simulation step, which involves the optimum choice of design variables and subsystems to be simultaneously solved; (b) the optimization of the nonlinear programming (NLP) problem using stochastic methods. For the first step a flexible tool (SIMOP) is used, whereby different numerical procedures can be easily obtained, taking into account the problem formulation and specific characteristics, the need for specific initialization schemes and the efficient solution of systems of nonlinear equations. This methodology was applied to the optimization of a reactive distillation process for the production of ethylene glycol. Due to the complexity of the mathematical model, several different numerical procedures were generated, and their influence on the computational burden and on the reliability and accuracy of the optimization to reach the global optimum were studied. The results obtained suggest that in addition to the choice of design variables, the structure of subsystems associated to numerical procedures has a considerable impact on the performance of the optimizers.     

Dynamic parameter estimation and optimization for batch distillation

This work reviews a well-known methodology for batch distillation modeling, estimation, and optimization but adds a new case study with experimental validation. Use of nonlinear statistics and a sensitivity analysis provides valuable insight for model validation and optimization verification for batch columns. The application is a simple, batch column with a binary methanol–ethanol mixture. Dynamic parameter estimation with an ℓ₁-norm error, nonlinear confidence intervals, ranking of observable parameters, and efficient sensitivity analysis are used to refine the model and find the best parameter estimates for dynamic optimization implementation. The statistical and sensitivity analyses indicated there are only a subset of parameters that are observable. For the batch column, the optimized production rate increases by 14% while maintaining product purity requirements.