Identification of semi-parametric hybrid process models

Hybrid models are mathematical models that comprise both mechanistic and black-box or data-driven components. Typically, the parameters in the mechanistic part of a hybrid model (if any) are assumed to be known. However in this research, a two-level approach is proposed for the identification of hybrid models where some parameters in the mechanistic part of the model are unknown. At the first level, the black-box component is identified using a regularization method with given values for the regularization and mechanistic parameters. At the second level, the regularization and mechanistic parameters are determined simultaneously and optimized according to a specific criterion placed on the predictive performance of the hybrid model. This approach is tested through the modelling of a toluene nitration process, where a support vector machine (SVM) model is used to represent the chemical kinetics, with the mass transfer-related mechanistic parameters being estimated simultaneously. The case study shows that good results can be obtained in terms of both the prediction of the process variables of interest and the estimates of the mechanistic parameters, when the measurement error in the training data is small whilst when the magnitude of the measurement error increases, the accuracy of the estimates of the mechanistic parameters decreases. However, the predictive performance of the resulting hybrid model in the latter case is still acceptable, and can be much better than that attained from the application of a pure black-box model under certain extrapolation conditions.     

Hybrid convolution model and its application in predictive pH control

This paper presents a new method for synthesising chemical process models that combines prior knowledge and fuzzy models. The hybrid convolution model consists of a fuzzy model based steady-state, and an impulse response model based dynamic part. Prior knowledge enters to the dynamic part as a resident time distribution model of the process. The proposed approach is applied in the modelling and model based control of a highly nonlinear pH process.     

Hybrid fuzzy model-based predictive control of temperature in a batch reactor

Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed.

A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model was made. We established that the latter approach clearly outperforms the approach where a linear model is used.     

A new approach for modeling of multicomponent gas hydrate formation

Several models have been proposed to investigate the kinetics of gas hydrate formation. The main differences between the proposed models are the definition of the driving force, thermodynamics approach and the number of resistances to study the gas consumption by the hydrate phase. This paper concentrates on gas hydrate formation from multicomponent mixture, which has not been much studied before. In the present research, chemical potential has been considered as the driving force and, consequently, a new resistance coefficient was introduced. A complete discussion and reasonable assumptions has been provided to support this modelling.     

Dynamic nonlinear soft sensor modelling method using linear slow feature analysis and least squares support vector regression for batch processes

Data-driven soft sensor models have been extensively utilized in industrial processes. Batch processes are usually employed to manufacture low-volume and high value-added products in chemical, materials, and pharmaceutical industries. The most distinctive features of batch process lie in nonlinear, repetition, and slow time varying characteristics. In this paper, a data-driven soft sensor modelling method based on linear slow feature analysis (LSFA) and least squares support vector regression (LSSVR) is proposed. In this method, LSFA was used to effectively capture the driving force behind the data features that change as slowly as possible. Then, a LSSVR model was constructed between the extracted slow feature variables and quality variables. Finally, a numerical example, industrial penicillin fermentation processes, and cobalt oxalate synthesis process were utilized to confirm the prediction accuracy and model reliability of the proposed approach.     

A global optimization method for model selection in chemical reactions networks

Model inference is a challenging problem in the analysis of chemical reactions networks. In order to empirically test which, out of a catalogue of proposed kinetic models, is governing a network of chemical reactions, the user can compare the empirical data obtained in one experiment against the theoretical values suggested by the models under consideration. It is thus fundamental to make an adequate choice of the decision variables (e.g. initial concentrations of the different species in the tank) in order to have maximal separation between sets of concentrations provided by the theoretical models, making then easier to identify which of the theoretical models yields data closest to those obtained empirically under identical conditions.In this paper we illustrate how global optimization techniques can be successfully used to address the problem of model separation, as a basis for model selection. Some examples illustrate the usefulness of our approach.     

Multiscale modelling of mass transfer in gas jets and bubble plumes

The injection of high‐speed gas streams into liquids is common in many industrial applications, such as sparging in multiphase reactors and contacting in mass transfer devices. Modelling the fluid dynamics and associated heat and mass transfer processes in such a system is complex because it involves many governing scales and drastic changes in physical properties. In this study, one formulation of a multiscale computational fluid dynamics model is proposed to simulate the fluid dynamics and mass transfer in such systems. The model uses volume‐of‐fluid interface capturing in regions where high mesh resolution can be attained and the drift‐flux or mixture model approximation in regions where mesh resolution is too low to directly resolve interface dynamics. The model was developed to provide a tunable, automatic transition between the two modelling approaches for both fluid dynamics and mass transfer predictions. The approach was validated through a comparison with results from two published studies. In the first case, the implementation of the drift‐flux model was validated through the simulation of a dispersed gas bubble plume injected into a cylindrical tank. In the second case, the fluid dynamics and mass transfer predictions were compared to results from an experimental study involving the horizontal injection of air into a rectangular tank filled with water for the application of aeration. The results show that the modelling approach can provide a good prediction of the experimental data using only limited fitting of empirical parameters, making it applicable to a broad range of other applications.     

Comprehensive Fischer–Tropsch reactor model with non-ideal plug flow and detailed reaction kinetics

This paper presents a detailed first principle Fischer–Tropsch reactor model including detailed heat transfer calculations and detailed reaction kinetics. The model is based on a large number of components and chemical reactions. The model is tuned to a fixed bed nearplug flow reactor but can also be applied to slurry and micro-channel reactors.The presented model is based on a cascade of ideally stirred reactors. This modelling approach is novel for Fischer–Tropsch reactors and has the advantage of being able to represent none-ideal reactors. Using a large number of components and reactions makes it possible to better represent the product slate than with conventional modelling based on distribution models.The results of the simulations emphasise that temperature control is important. Global conversion and product yields are dependent on operating conditions especially the temperature. The model is used to calculate the dimensions of an industrial reactor from a laboratory scale reactor.     

HYBRID NEURAL MODELLING OF FLUIDISED BED DRYING PROCESS

The aim of this study was to investigate the applicability of hybrid neural models in modelling of drying process. A study aimed at extending a neural network mapping was also carried out. In this approach dimensionless numbers (Re, Ar, H/d) were used as inputs to predict the heat transfer coefficient in a fluidised bed drying process. To produce a data set necessary to train the networks, trials of drying different materials in a fluidised bed were carried out. On the basis of this network, a hybrid model describing the process of drying in a fluidised bed dryer was built. Results obtained were compared not only with available experimental data but also with results obtained using other types of models: a pseudo-dynamic neural model and a classical mathematical model. The analysis of results leads to a conclusion that hybrid models constitute a solid alternative method of process modelling.     

HYBRID NEURAL MODELLING OF FLUIDISED BED DRYING PROCESS

The aim of this study was to investigate the applicability of hybrid neural models in modelling of drying process. A study aimed at extending a neural network mapping was also carried out. In this approach dimensionless numbers (Re, Ar, H/d) were used as inputs to predict the heat transfer coefficient in a fluidised bed drying process. To produce a data set necessary to train the networks, trials of drying different materials in a fluidised bed were carried out. On the basis of this network, a hybrid model describing the process of drying in a fluidised bed dryer was built. Results obtained were compared not only with available experimental data but also with results obtained using other types of models: a pseudo-dynamic neural model and a classical mathematical model. The analysis of results leads to a conclusion that hybrid models constitute a solid alternative method of process modelling.     

Robustness analysis of chemical process systems based on complex network non-linear load capacity model

In the complex network of chemical process systems, if a node fails, it may trigger cascading failures and affect normal operation. To enhance the ability of chemical process systems to maintain normal operation after the cascading failure, this paper presents cascading failure modelling and robustness analysis of chemical process systems based on the complex network non-linear load capacity model. First, based on complex network theory, a complex network model of the chemical process is constructed; then, three cascading failure models are constructed using a combination of linear and non-linear load capacity models and initial load and initial residual capacity redistribution strategies; and finally, the nodes with the maximum node degree are deliberately attacked to analyze the robustness of the chemical process system in response to cascading failure. The case study shows that the proposed models are valid and feasible, and the robustness of the chemical process system is enhanced as the load and capacity parameters are increased. By reasonably setting the initial load and adjusting the model parameters, the robustness can be effectively improved, providing a theoretical reference for improving the robustness of the actual chemical process system in response to cascading failure.     

基于LS-SVM和Pensim仿真平台的青霉素发酵过程建模

从青霉素发酵过程仿真平台(Pensim)得到的结果作为出发点,采用最小二乘支持向量机(LS-SVM)对青霉素发酵过程进行建模研究。分别研究丁利用溶解氧浓度、排气二氧化碳浓度等变量对青霉素产物浓度、菌体浓度和底物浓度等重要过程变量的建模问题,在3种不同的仿真条件下分别建立了相应的在线预报模型,并对其进行了分析和比较。基于 Pensim 的仿真结果表明采用 LS-SVM 方法所建立的在线预报模型均具有良好的预测精度,对后续发酵过程的控制和优化能起到一定的参考作用。     

Optimal modelling and experimentation for the improved sustainability of microfluidic chemical technology design

Optimization of the dynamics and control of chemical processes holds the promise of improved sustainability for chemical technology by minimizing resource wastage. Anecdotally, chemical plant may be substantially over designed, say by 35–50%, due to designers taking account of uncertainties by providing greater flexibility. Once the plant is commissioned, techniques of nonlinear dynamics analysis can be used by process systems engineers to recoup some of this overdesign by optimization of the plant operation through tighter control. At the design stage, coupling the experimentation with data assimilation into the model, whilst using the partially informed, semi-empirical model to predict from parametric sensitivity studies which experiments to run should optimally improve the model. This approach has been demonstrated for optimal experimentation, but limited to a differential algebraic model of the process. Typically, such models for online monitoring have been limited to low dimensions.Recently it has been demonstrated that inverse methods such as data assimilation can be applied to PDE systems with algebraic constraints, a substantially more complicated parameter estimation using finite element multiphysics modelling. Parametric sensitivity can be used from such semi-empirical models to predict the optimum placement of sensors to be used to collect data that optimally informs the model for a microfluidic sensor system. This coupled optimum modelling and experiment procedure is ambitious in the scale of the modelling problem, as well as in the scale of the application – a microfluidic device. In general, microfluidic devices are sufficiently easy to fabricate, control, and monitor that they form an ideal platform for developing high dimensional spatio-temporal models for simultaneously coupling with experimentation.As chemical microreactors already promise low raw materials wastage through tight control of reagent contacting, improved design techniques should be able to augment optimal control systems to achieve very low resource wastage. In this paper, we discuss how the paradigm for optimal modelling and experimentation should be developed and foreshadow the exploitation of this methodology for the development of chemical microreactors and microfluidic sensors for online monitoring of chemical processes. Improvement in both of these areas bodes to improve the sustainability of chemical processes through innovative technology.     

On minimal models of process systems

Minimal representations are known to have no redundant elements, and are therefore of great importance. Based on the notions of performance and size indices and measures for process systems, the paper proposes conditions for a process model being minimal in a set of functionally equivalent models with respect to a size norm.Generalized versions of known procedures to obtain minimal process models for a given modelling goal, model reduction based on sensitivity analysis and incremental model building are proposed and discussed.The notions and procedures are illustrated and compared on a simple example, that of a simple nonlinear fermentation process with different modelling goals and on a case study of a heat exchanger modelling.     

Estimation of parameters in monte carlo modelling

This paper presents a general method for estimating model parameters from experimental data when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. From a statistical point of view a Bayesian approach is used in which the distribution of the parameters is handled in discretized form as elements of an array in computer storage. The stochastic nature of the Monte Carlo model allows only an estimate of the distribution to be calculated from which the true distribution must then be estimated. For this purpose an exponentiated polynomial function has been found to be useful. The method provides point estimates as well as joint probability regions. Marginal distributions and distributions of functions of the parameters can also be handled. The motivation for exploring this alternative parameter estimation technique comes from the recognition that for some systems, particularly when the underlying process is stochastic in nature, Monte Carlo simulation often is the most suitable way of modelling. As such, the Monte Carlo approach increases the range of problems which can be handled by mathematical modelling. The technique is applied to the modelling of binary copolymerization. Two models, the Mayo-Lewis and the Penultimate Group Effects models, are considered and a method for discriminating between these models in the light of sequence distribution data is proposed.     

Disaggregation-aggregation based model reduction for refinery-wide optimization

In this paper, reduced nonlinear refinery models are developed by generating and using input-output data from a process simulator. In particular, rigorous process models of continuous catalytic reformer (CCR) and naphtha splitter units are used for generating the data. To deal with complexity associated with large amounts of data, that is usually available in the refineries, a disaggregation-aggregation based approach is presented. The data is split (disaggregation) into smaller subsets and reduced artificial neural network (ANN) models are obtained for each of the subset. These ANN models are then combined (aggregation) to obtain an ANN model which represents all the data originally generated. The disaggregation step can be carried out within a parallel computing platform. Refinery optimization studies are carried out to demonstrate the applicability and the usefulness of the proposed model reduction approach.     

Neural network approach to support modelling of chemical reactors: problems,resolutions, criteria of application

New aspects of neural modelling of chemical reactors have been investigated in this study. An universal method to create a family of neural models, useful for the reactor and reacting system of any type, has been elaborated and presented. Based on this method a detailed analysis of the neural models has been performed. The proposed methods of modelling as well as a comparative analysis of the obtained results have been illustrated with the data obtained for a complex, catalytic hydrogenation of 2,4-dinitrotoluene performed at non-steady state conditions in a multiphase stirred tank reactor. The methods of choosing the input–output signals, the net architecture, the learning method, the number and quality of learning data have been proposed and their influence on the accuracy of obtained predictions have extensively been discussed. A comparison of two types of neural models: a global neural model and a hybrid neural model to a conventional reactor modelling has been performed. General conclusions and useful criteria have been formulated.     

Validation of continuous-time models with delay

This article is a continuation of an earlier work by Huang [2000. Multivariate model validation in the presence of timevariant disturbance dynamics. Chemical Engineering Science 55, 4583-4595] for validation of discrete time models. We present validation method for continuous-time transfer models with time delay. The proposed procedure is based on the local approach for change detection of model parameters. Both single input single output (SISO) and multiple input multiple output (MIMO) models are considered. The special feature of the proposed algorithm is its ability to detect and isolate changes in the time delay as well as in other parameters. The performance of the proposed method is demonstrated using Monte-Carlo simulations and by application to experimental data from a laboratory scale process.     

Model predictive control with non-uniformly spaced optimization horizon for multi-timescale processes

Many chemical processes exhibit disparate timescale dynamics with strong coupling between fast, moderate and slow variables. To effectively handle this issue, a model predictive control (MPC) scheme with a non-uniformly spaced optimization horizon is proposed in this paper. This approach implements the time intervals that are small in the near future but large in the distant future, allowing the fast, moderate and slow dynamics to be included in the optimization whilst reducing the number of decision variables. A sufficient condition for ensuring stability for the proposed MPC is developed. The proposed approach is demonstrated using a case study of an industrial paste thickener control problem. While the performance of the proposed approach remains similar to a conventional MPC, it reduces the computational complexity significantly.