Bifurcation analysis of index infinity DAE parabolic models describing reactors and reacting flows

We show that most steady‐state models of chemical reactors and reacting flows in which convection effects are dominant and diffusion/conduction is neglected in the flow direction but included in the transverse directions, may change from parabolic type with a unique solution to index infinity differential‐algebraic equation (DAE) type with an infinite number of steady‐state solutions depending on the values of the reaction parameters. When a model is of index infinity, standard numerical methods may find only one of the solutions corresponding to latest possible ignition. We present complete bifurcation analysis of these models, a method for finding all solutions, determine the stability and, for some simpler cases, the domain of initial conditions attracted to these states. We also demonstrate that the various steady‐state solutions of the DAE systems are best found by integrating the transient hyperbolic versions of the models with appropriately selected capacitance terms and initial conditions. © 2016 American Institute of Chemical Engineers AIChE J, 63: 295–305, 2017     

Sliding motion of discontinuous dynamical systems described by semi-implicit index one differential algebraic equations

We have proposed an approach to derive a continuous system of differential algebraic equations (DAE) of index one that is dynamically equivalent to a discontinuous index one DAE system. This involves augmenting the convex combination of the ordinary differential equations with the algebraic equations from individual models. This result is proved by using the implicit function theorem. This procedure is illustrated with the help of an ideal gas-liquid system in which the algebraic variables can be expressed as explicit functions of differential variables. It is also demonstrated with an example from a soft-drink manufacturing process, in which, it is difficult to express the algebraic variables as explicit functions of differential variables. Through computer simulation, it is shown that the equivalent dynamic DAE system and the discontinuous DAE system have identical solutions. The proposed method is several orders of magnitude more efficient than the procedure that works with the discontinuous system of DAEs.     

On Parameter Estimation for Exponential Dispersion Arma Models

Abstract. A class of autoregressive moving‐average (ARMA) models proposed by Jørgensen and Song [Journal of Applied Probability (1998), vol. 35, pp. 78–92] with exponential dispersion model margins are useful to deal with non‐normal stationary time series with high‐order autocorrelation. One property associated with the class of models is that the projection process takes the exact form of the classical Box and Jenkins ARMA representation, leading to considerable ease to establish theories. This paper focuses on the issue of parameter estimation for such models, which has not been thoroughly investigated in Jørgensen and Song's paper. The key of the proposed approach is to treat the residual process associated with the projection essentially as a measurement error, which enables us to formulate directly an ARMA representation for the observed time series. The parameter estimation therefore becomes straightforward using the existing methods for the Box and Jenkins ARMA models such as the quasi‐likelihood method. The approach is illustrated by simulation studies and by an analysis of myoclonic seizure counts.     

Fault diagnosis for distillation process based on CNN–DAE

Distillation is the most widely used operation for liquid mixture separation in the chemical industry. It is of great importance to detect and diagnose faults in distillation process. Due to the strong feedback and coupling of processes in a distillation column, it is difficult to use deep auto-encoders(DAEs) alone to achieve good results in detecting and diagnosing faults, in terms of accuracy and efficiency. This paper proposes a hybrid fault-diagnosis model based on convolutional neural networks(CNNs) and DAEs, by integrating the powerful capability of CNN in feature extraction and of DAE in classification. A case study was carried out with the distillation process of depropanization. It is shown that the proposed hybrid model is of good performance compared to other models, in terms of the accuracy of fault detection in such a process. Also, with the increase of structural layers of the CNN–DAE model, the diagnostic accuracy will be improved, with an optimal accuracy of 92.2%.     

Fault detection of large-scale process control system with higher-order statistical and interpretative structural model

Nonlinear characteristic fault detection and diagnosis method based on higher-order statistical (HOS) is an effec-tive data-driven method, but the calculation costs much for a large-scale process contr...     

基于高阶统计和解释结构模型相结合的大型过程控制系统的故障检测(英文)

Nonlinear characteristic fault detection and diagnosis method based on higher-order statistical (HOS) is an effec-tive data-driven method, but the calculation costs much for a large-scale process control system. An HOS-ISM fault diagnosis framework combining interpretative structural model (ISM) and HOS is proposed:(1) the adja-cency matrix is determined by partial correlation coefficient;(2) the modified adjacency matrix is defined by directed graph with prior knowledge of process piping and instrument diagram;(3) interpretative structural for large-scale process control system is built by this ISM method;and (4) non-Gaussianity index, nonlinearity index, and total nonlinearity index are calculated dynamical y based on interpretative structural to effectively eliminate uncertainty of the nonlinear characteristic diagnostic method with reasonable sampling period and data window. The proposed HOS-ISM fault diagnosis framework is verified by the Tennessee Eastman process and presents improvement for highly non-linear characteristic for selected fault cases.     

一种混杂系统数据校正新方法

对于既包含连续生产过程又包含离散事件的混杂系统,尤其是对于带有生产方案切换的实际生产过程,通过在物料平衡模型中引入随机调度方程,从而构造出包含随机调度方程参数变量θ的新型协调模型,然后利用一种不确定模型的协调算法对此模型进行求解,最后,通过仿真研究证实了该方法的有效性和鲁棒性.     

A perturbation approach for consistent initialization of index-1 explicit differential-algebraic equations arising from battery model simulations

Estimation of consistent initial conditions is very crucial for the successful solution of differential-algebraic equation (DAE) systems that arise in many fields of science and engineering. In this paper, an efficient perturbation approach for initialization of DAE systems of index-1 is proposed and implemented for DAE models governing batteries. In addition, different existing solvers are compared for consistent initialization of DAE systems. The proposed approach does not necessarily require a nonlinear solver for initialization and builds on the applicability and usability of robust and efficient explicit, linearly implicit and semi-implicit integrators in time. Three different problems are presented wherein the proposed approach is observed to work for a wider range of inconsistent initial conditions compared to other existing generally used routines. It is also observed that the present approach is computationally efficient compared to the other existing approaches in a given environment.     

Structural modeling and analysis of FRP composite product subsystems—A systems approach

This study derives a new mathematical model aimed to consider virtual design and manufacturing procedures for developing highly competitive, complex geometry composite products for various engineering applications. The fiber‐reinforced polymer (FRP) composite industry faces several critical issues right from selection (of product, process, equipment, tooling, materials) to manufacturing the final products by meeting several design criteria and customer requirements. An attempt has been made in this article to identify different subsystems and other constituents of five main systems–resin system, reinforcement system, process equipment, tooling system, and product design of total composite product system. Intermediate processes, alternative designs, process sequence, technological changes, chemical reactions, and other performance affecting parameters have been discussed. Graph theoretical models, variable permanent adjacency matrix models, and permanent functions of these systems based on graph theory–matrix algebra–permanent function methodology are developed. Analytical tests for structural analysis of composite product system are derived to select optimum constituents in each of these five systems of composite product. Coefficient of similarity and dissimilarity are useful aid to take right decision between alternative solutions. Permanent function is a unique representation and to be used by composite industry for coding, evaluation, comparison, ranking, and optimum selection. Structural models are useful for basic understanding of complete composite product system, leading to right decisions for manufacturing and business strategies. Step‐by‐step procedure is developed to assist composite industry to implement the proposed method in a right way. Usefulness of the proposed methodology to composite industry is also presented. POLYM. COMPOS., 27:681–699, 2006. © 2006 Society of Plastics Engineers     

Multiproduct batch plants design using linear process performance models

In this contribution, a novel linear generalized disjunctive programming (LGDP) model is developed for the design of multiproduct batch plants optimizing both process variables and the structure of the plant through the use of process performance models. These models describe unit operations using explicit expressions for the size and time factors as functions of the process variables with the highest impact. To attain a linear formulation, values of the process variables as well as unit sizes are selected from a set of meaningful discrete values provided by the designer. Regarding structural alternatives, both kinds of unit duplications in series and in parallel are considered in this approach. The inclusion of the duplication in series requires different detailed models that depend on the structure selected. Thus, in a new approach for the multiproduct batch plant design, a set of potential structural alternatives for the plant is defined. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Recursive state estimation techniques for nonlinear differential algebraic systems

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. While state and parameter estimation of ODE systems has been studied extensively, differential algebraic equation (DAE) systems have received much less attention. However, most realistic chemical engineering processes are modelled as DAE systems and hence state and parameter estimation of DAE systems is a significant problem. Becerra et al. (2001) proposed an extension of the extended kalman filter (EKF) for estimating the states of a system described by nonlinear differential-algebraic equations (DAE). One limitation of this approach is that it only utilizes measurements of the differential states, and is therefore not applicable to processes in which algebraic states are measured. In this paper, we address the state estimation of constrained nonlinear DAE systems. The novel aspects of this work are: (i) development of a modified EKF approach that can utilize measurements of both algebraic and differential states, (ii) development of a recursive approach for the inclusion of constraints, and (iii) development of approaches that utilize unscented sampling in state and parameter estimation of nonlinear DAE systems; this has not been attempted before. The utility of these estimators is demonstrated using electrochemical and reactive distillation processes.     

Extracting dynamic features with switching models for process data analytics and application in soft sensing

In recent decades, soft sensors have been profoundly studied and successfully applied to predict critical process variables in real‐time. While dealing with various application scenarios, data‐driven methods with representation learning possess great potentials. Latent features are formulated in these approaches to predict outputs from correlated input variables. In this study, a probabilistic framework of feature extraction is proposed in the context of process data analysis. To address switching behaviors in industrial processes, multiple emission models are utilized to construct latent space. To address temporal correlations from continuously operating processes, a dynamic model is implemented in latent space. Bayesian learning strategy is then developed for parameters estimation, where modeling preferences and uncertainties from multiple models are considered. The effectiveness and practicability of the proposed feature extraction algorithm are illustrated through numerical simulations, as well as an industrial case study. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2037–2051, 2018     

基于负荷划分数据和支持向量机的火电厂燃烧过程建模

为建立燃烧过程稳态模型,首先利用稳态检测算法提取稳态样本;针对稳态数据中的不均衡性,提出了一种基于负荷划分数据的方法,即根据负荷工况将样本划分成训练子集与测试子集,以提高模型的泛化性能。利用单因素图形分析方法确定3个模型参数的搜索范围,将网格搜索与交叉验证相结合选择最优的模型参数,在此基础上建立了一个300 MW燃煤火电厂机组锅炉燃烧过程的支持向量机模型,包括锅炉效率、NO_x排放量、排烟温度和飞灰含碳量4个过程输出。结果表明,经过参数优化的4个输出模型均具有很好的泛化性能。     

Kinetic Modeling of Large‐Scale Reaction Systems

This review gives a brief account of basic ideas underlying approaches to analysis and modeling of large‐scale reaction systems. The emphasis is on model simplification and mechanism/dimension reduction via heuristic concepts and formal mathematical techniques. Among the key topics discussed are: top‐down and bottom‐up modeling approaches, graph/matrix representation of chemical reactions, mechanistic vs. pathways models, quantitative structure‐reactivity relationships, mathematical reduction of dimensionality, high‐fidelity surrogate models, continuum approximation, lumping of nonlinear kinetics, overall behavior/kinetics of many reactions, effect of pore diffusion, steady state multiplicity and stability. Some common features of dimension reduction methodologies are noted. Areas where further work will be valuable are identified.     

Time representations and mathematical models for process scheduling problems

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented with corresponding strengthened formulations that rely on exploiting the non-overlapping graph structure of these problems through maximum cliques and bicliques. These formulations are compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stopping criterion used. Computational results show that the multi-operation sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.     

Semi-supervised dynamic latent variable modeling: I/O probabilistic slow feature analysis approach

Modeling of high dimensional dynamic data is a challenging task. The high dimensionality problem in process data is usually accounted for using latent variable models. Probabilistic slow feature analysis (PSFA) is an example of such an approach that accounts for high dimensionality while simultaneously capturing the process dynamics. However, PSFA also suffers from a drawback that it cannot use output information when determining the latent slow features. To address this lacunae, extension of the PSFA by incorporating outputs, resulting in Input-Output PSFA (IOPSFA) is proposed. IOPSFA can use both input and output information for extracting latent variables. Hence, inferential models based on IOPSFA are expected to have better predictive ability. The efficacy of the proposed approach with an industrial and a laboratory scale soft sensing case studies that have both complete and incomplete output measurements is evaluated, respectively. © 2018 American Institute of Chemical Engineers AIChE J, 65: 964–979, 2019     

环保芳烃油RAE在轮胎中的应用研究

2010年1月1日起，进入欧洲市场的轮胎必须满足8种多环芳烃的含量不超过10ppm，苯并芘含量不能超过1ppm的规定。当前轮胎行业普遍使用环保的芳烃油或者环烷油代替以蒴使用的PAH含量很高的DAE。其中，环烷油替代品不利于抓地力的提高，而TADE的价格又相对较高。因此，RAE是一种很好的替代品。通过配方微调和工艺改善，RAE替代DAE可以取得很好的效果。     

Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.     

Bias Correction Estimation for a Continuous‐Time Asset Return Model with Jumps

In this article, local linear estimators are adapted for the unknown infinitesimal coefficients associated with continuous‐time asset return models with jumps, which can correct the bias automatically due to their simple bias representation. The integrated diffusion models with jumps, especially infinite activity jumps, are mainly investigated. In addition, under mild conditions, the weak consistency and asymptotic normality are provided through the conditional Lindeberg theorem as the time span T→∞ and the sample interval Δ _n →0. Furthermore, our method presents advantages in bias correction through simulation whether jumps belong to the finite activity case or infinite activity case. Finally, the estimators are illustrated empirically through the returns of stock index under 5‐minute high sampling frequency for real application.