Nonlinear dynamic data reconciliation and parameter estimation through particle swarm optimization: Application for an industrial polypropylene reactor

This work presents a procedure to solve nonlinear dynamic data reconciliation (NDDR) problems with simultaneous parameter estimation based on particle swarm optimization (PSO). The performance of the proposed procedure is compared to the performance of a standard Gauss-Newton (GN) scheme in a real industrial problem, as presented previously by Prata et al. [2006. Simultaneous data reconciliation and parameter estimation in bulk polypropylene polymerizations in real time. Macromolecular Symposia 243, 91-103; 2008. In-line monitoring of bulk polypropylene reactors based on data reconciliation procedures. Macromolecular Symposia 271, 26-37]. Both methods are used to solve the NDDR problem in an industrial bulk propylene polymerization process, using real data in real time for the simultaneous estimation of model parameters and process states. A phenomenological model of the real process, based on the detailed mass and energy balances and constituted by a set of algebraic-differential equations, was implemented and used for interpretation of the actual plant behavior in real time. The resulting nonlinear dynamic optimization problem was solved iteratively on a moving time window, in order to capture the current process behavior and allow for dynamic adaptation of model parameters. Obtained results indicate that the proposed PSO procedure can be implemented in real time, allowing for estimation of more reliable process states and model parameters and leading to much more robust and reproducible numerical performance.     

Kinetic parameter estimation in hydrocracking using hybrid particle swarm optimization

This paper provides a continuous lumping model for hydrocracking using molecular weight and true boiling point as the basis. Isomerization and cracking are the two typical global reactions which occur on acid sites of a bifunctional acid-metal hydrocracking catalyst. The latter reaction is considered to model the hydrocracking process. It is assumed that the rate coefficient of the cracking reactions depend on the size of the feed hydrocarbons. The kinetic parameters involved in the continuous lumping model are estimated by using a hybrid particle swarm optimization method. The proposed kinetic methodology is validated with the experimental data cited in the literature.     

Parameter estimation of methanol transformation into olefins through improved particle swarm optimization with attenuation function

This paper provides two improved mathematical expressions of attenuation function to quantify the effect of water in the process of methanol transformed to olefins on SAPO-34. Comparison between the experimental and predicted data shows that the kinetic models, such as four component lumped kinetic model and six component lumped kinetic model, are fitted well by using the improved attenuation functions. In addition, the effect of the error objective function with different weight factors on parameter estimation has been considered. If the maximum component is 10 times greater than minimum, the real weight of each response is more suitably used in the minimization. Meanwhile, double particle swarm optimization is employed to minimize the error objective function and the calculated values agree well with the experimental data.     

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。     

The use of particle swarm optimization for dynamical analysis in chemical processes

Particle swarm optimization is employed here to evaluate the parametric regions where different dynamic phenomena (periodic oscillations, double-period oscillations, chaos) can be expected in dynamic models. The proposed algorithm comprises two fundamental steps: the rough evaluation of regions where the desired solutions can be found and solution refining. The refining step allows the search for unstable solutions that may coexist with the other stable attractors. No preliminary bifurcation analysis is required. Simulations performed for distinct dynamic models show that the proposed algorithm is indeed able to locate different dynamic phenomena in the parameter space and that the algorithm may be of help for those interested in increasing the speed of more traditional dynamic bifurcation analysis.     

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.     

微粒群算法在干燥器多变量优化设计中的应用

建立了以具有废气循环的回转干燥系统年总费用为目标函数的优化设计数学模型,在此基础上探讨了惯性权因子对微粒群算法性能的影响,并应用微粒群算法求解干燥器优化设计数学模型,对干燥器出口废气温度与循环比进行优化设计。结果表明,带动态非线性惯性因子的微粒群算法对求解多变量的干燥优化设计问题具有方法简单、所需微粒群规模小、收敛速度快等特点;采用部分废气循环并进行优化设计对干燥系统的节能具有十分重要的意义,对湿空气出口温度和废气循环比进行优化设计,其年总费用比无废气循环的常规设计节省18．2%,比循环比为0．2时的常规设计节省12．6%。     

粒子群优化算法的发展及应用

讨论了粒子群优化算法的发展和应用。介绍了粒子群优化算法的基本原理和算法流程,并且与其他演化算法进行了比较,给出了一些经常用到的测试函数。针对粒子群优化算法在搜索后期存在的不足,介绍了改进的粒子群优化算法,重点介绍了在实际应用领域中用到的改进粒子群优化算法。     

Surrogate-model-based,particle swarm optimization,and genetic algorithm techniques applied to the multiobjective operational problem of the fluid catalytic cracking process

Abstract

This article provides a concise multiobjective optimization methodology for an industrial fluid catalytic cracking unit (FCCU) considering stochastic optimization techniques, genetic algorithms (GA) and particle swarm optimization (PSO), based on surrogates or meta-models in order to approximate the objective function. A FCCU was considered and simulated in an AspenONE process simulator. In addition the article examines the claim that PSO has the same effectiveness (finding the optimal global solution) as GA, but with significantly better computational efficiency (fewer function evaluations). The optimization results obtained with the PSO technique, based on the evaluation of less functions and adjustment of less parameters, showed a 3% increase in yield of naphtha as compared to results obtained with the GA technique. Finally, the results of the optimization obtained with the stochastic optimization techniques were compared and analyzed with a deterministic one. The performance targets of the multiobjective operational optimization supported the FCCU design and production planning to ensure refinery profitability and a regulatory environment.     

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.     

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.     

Refrigeration system synthesis based on de-redundant model by particle swarm optimization algorithm

Simultaneous optimization of refrigeration system (RS) and its heat exchanger network (HEN) leads to a large-scale non-convex mixed-integer non-linear programming (MINLP) problem. Conventionally, researchers usually adopted simplifications to confine problem scale from being too large at the cost of reducing solution space. This study established an optimization framework for the simultaneous optimization of RS and HEN. Firstly, A more comprehensive and compact model was developed to guarantee a relatively complete solution space while reducing model scale as well as its solving difficulty. In this model, a tandem arrangement of connecting sub-coolers and expansion valves was considered in the superstructure; and the pressure/temperature levels were optimized as continuous variables. On this basis, we proposed a “two-step transformation method” to equivalently transform the cross-level structure into a non-cross-level structure, and the de-redundant superstructure was established with ensuring comprehensiveness and rigor. Furthermore, the MINLP model was developed and solved by Particle Swarm Optimization algorithm. Finally, our methodology was validated to get better optimal results with less CPU time in two case studies, an ethylene RS in an existing plant and a reported propylene RS.     

混合粒子群优化算法及其应用

提出了一种通过改进全局最优位置粒子寻优策略而提高粒子群优化计算效率的混合粒子群优化算法。针对流程工业典型设备的状态跟踪预报等有计算时间限制的优化问题,混合粒子群优化算法在不改变原有粒子群粒子寻优策略的前提下,将粒子群整体已搜寻到的全局最优位置看作一个特殊的粒子,令该粒子执行梯度下降寻优的寻优策略。在粒子群的寻优迭代计算中增加全局最优位置粒子单独的梯度下降寻优过程,从而将粒子群优化算法的全局寻优特性与梯度下降算法的邻域寻优特性相结合,以提高粒子群优化算法的整体寻优效率,进而缩短寻优计算的时间。针对流程工业典型设备的实际应用表明,混合粒子群优化算法能够减少寻优迭代次数,进而缩短优化计算时间。     

基于LCPSO算法的相稳定性判别

相稳定性判别为相平衡计算的基本课题,常采用Gibbs自由能曲面与切平面的距离函数（TPDF）最小化方法求解。对于强非理想体系,或在高压条件下,其TPDF表现出复杂形态,有平凡解和多极值,传统方法难以求得满足约束的全局最小值,从而导致判别失误。粒子群算法（PSO）虽有全局优化性能,但也会陷于局部极小,且缺少约束处理机制。为此,分析了PSO内在蕴含的线性特点,在种群初化、粒子运动等环节提出应对策略,构建线性约束粒子群算法（LCPSO）,确保种群在可行空间内搜索。还增设调变参数、局部加速等措施,以兼顾算法的全面探测和细化挖掘的能力,提高其全局优化效能。经多个实例的测试表明,LCPSO适用面广,既可用于超额自由能、状态方程等各类热力学模型,又能克服混合模型一阶不连续的困难,应用范围从液液相分裂拓展到汽液液相分裂。与确定性全局算法IN/GB相比,LCPSO速率高,效果好,尤对多元体系更具优势。     

Parameter estimation in batch process using EM algorithm with particle filter

This paper investigates a parameter estimation problem for batch processes through the maximum likelihood method. In batch processes, the initial state usually relates to the states of previous batches. The proposed algorithm takes batch-to-batch correlations into account by employing an initial state transition equation to model the dynamics along the batch dimension. By treating the unmeasured states and the parameters as hidden variables, the maximum likelihood estimation is accomplished through the expectation–maximization (EM) algorithm, where the smoothing for the terminal state and the filtering for the initial state are specially considered. Due to the nonlinearity and non-Gaussianity in the state space model, particle filtering methods are employed for the implementation of filtering and smoothing. Through alternating between the expectation step and the maximization step, the unknown parameters along with states are estimated. Simulation examples demonstrate the proposed estimation approach.     

一种求解化工动态优化问题的迭代自适应粒子群方法

智能优化方法因其简单、易实现且具有良好的全局搜索能力,在动态优化中的应用越来越广泛,但传统的智能方法收敛速度相对较慢。提出了一种迭代自适应粒子群优化方法（IAPSO）来求解一般的化工动态优化问题。首先通过控制变量参数化将原动态优化问题转化为非线性规划问题,再利用所提出的迭代自适应粒子群优化方法进行求解。相比传统的粒子群优化方法,该种迭代自适应粒子群优化方法具有收敛速度更快的优点,主要原因是：该算法根据粒子种群分布特性自适应调整参数;该算法通过缩减搜索空间并迭代使用粒子群算法搜索最优解。将提出的迭代自适应粒子群方法应用到多个经典动态优化问题中,测试结果表明,该方法简单、有效,精度高,且收敛速度比传统粒子群算法有显著提升。     

Soft sensor for ammonia concentration at the ammonia converter outlet based on an improved particle swarm optimization and BP neural network

Ammonia synthesis production is a critical chemical industry around the world. As the key process variable, the ammonia concentration at the ammonia converter outlet reflects the production status and provides good advices for the operators. However, it cannot be easily measured because of high expenditure and deficient reliability of online sensors in a real-world ammonia synthesis process. Due to this, a soft sensor, which is used to predict the outlet ammonia concentration, is developed using BP neural network (BPNN). An improved particle swarm optimization with expansion and constriction operation (PSOEC) is proposed to optimize the weights and thresholds of BPNN. The PSOEC and BPNN based soft-sensing model (PSOEC-NN) is applied to inferring the outlet ammonia concentration in a fertilizer plant. Results using other modeling methods (BPNN and PSO-NN) are presented for comparison purpose. The proposed PSOEC-NN based soft sensor shows high precision and good generalization capability. PSOEC-NN model would offer great help for further work like advanced control and operational optimization in the ammonia synthesis process.     

混沌粒子群算法及其在生化过程动态优化中的应用

化工过程的动态优化,大多较为复杂,有相当的难度.新近发展的粒子群优化算法,基于群智能机理,适于求解连续问题,但它不具备遍历特性,影响了全局搜索能力.本文拟引入混沌机制,以混沌变量的遍历性改进粒子群算法,使其更全面地获取目标函数的有用信息,并反映到逐代更新的个体极值和群体极值中,可更有效地带领粒子群移向最优解,提高了全局搜优效率.由此构建为混沌粒子群算法,经多个性能测试,表明其搜索能力优于经典粒子群算法,引入混沌机制是有效的.将其用于Park-Ramirez生物反应器补料流率的动态优化,也取得了满意的效果.     

Nonlinear kinetic parameter estimation using simulated annealing

The performance of simulated annealing (S-A) in nonlinear kinetic parameter estimation was studied and compared with the classical Levenberg–Marquardt (L–M) algorithm. Both methods were tested in the estimation of kinetic parameters using a set of three kinetic models of progressively higher complexity. The models describe the catalytic wet air oxidation of phenol carried out in a small-scale trickle bed reactor. The first model only considered the phenol disappearance reaction, while the other two included oxidation intermediate compounds. The number of model parameters involved increased from 3 to 23 and 38, respectively, for the three models. Both algorithms gave good results for the first model, although the L–M was superior in terms of computation time. In the second case the algorithms achieved convergence, but S-A resulted in a better criterion and kinetic parameters with physical meaning. In the more complex model, only S-A was capable of achieving convergence, whereas the L–M failed. For the second and third model the solution of S-A could be further improved, when used as an initial guess for the L–M algorithm.