Bodil Recke

A systematic approach for soft sensor development

This paper presents a systematic approach based on robust statistical techniques for development of a data-driven soft sensor, which is an important component of the process analytical technology (PAT) and is essential for effective quality control. The data quality is obviously of essential significance for a data-driven soft sensor. Therefore, preprocessing procedures for process measurements are described in detail. First, a template is defined based on one or more key process variables to handle missing data related to severe operation interruptions. Second, a univariate, followed by a multivariate principal component analysis (PCA) approach, is used to detect outlying observations. Then, robust regression techniques are employed to derive an inferential model. A dynamic partial least squares (DPLS) model is implemented to address the issue of auto-correlation in process data and thus to provide smoother estimation than using a static regression model. The proposed methodology is illustrated through applications to a cement kiln system for estimation of variables related to product quality, i.e., free lime, and to emission quality, i.e., nitrogen oxides (NOx) emission. The case studies reveal the effectiveness of the systematic framework in deriving data-driven soft sensors that provide reasonably reliable one-step-ahead predictions.

Data-driven soft sensor design with multiple-rate sampled data: A comparative study

Multi-rate systems are common in industrial processes where quality measurements have slower sampling rate than other process variables. Since inter-sample information is desirable for effective quality control, different approaches have been reported to estimate the quality between samples, including numerical interpolation, polynomial transformation, data lifting and weighted partial least squares (WPLS). Two modifications to the original data lifting approach are proposed in this paper: reformulating the extraction of a fast model as an optimization problem and ensuring the desired model properties through Tikhonov Regularization. A comparative investigation of the four approaches is performed in this paper. Their applicability, accuracy and robustness to process noise are evaluated on a single-input single output (SISO) system. The regularized data lifting and WPLS approaches are implemented to design quality soft sensors for cement kiln processes using data collected from a plant log system. Preliminary results reveal that the WPLS approach is able to provide accurate one-step-ahead prediction. The regularized data lifting technique predicts the product quality of cement kiln systems reasonably well, demonstrating the potential to be used for effective quality control.

Complex nonlinear behaviour of a fixed bed reactor with reactant recycle

Abstract The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks the emergence of a stable periodic solution. This periodic solution in turn undergoes a period doubling leaving it unstable and giving rise to a stable period 2 solution. It is know that if the system possesses one period doubling it often also has the possibility of posessing a chaotic attractor. It is shown, that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported.

Application of Soft Constrained MPC to a Cement Mill Circuit

Abstract In this paper we develop a Model Predictive Controller (MPC) for regulation of a cement mill circuit. The MPC uses soft constraints (soft MPC) to robustly address the large uncertainties present in models that can be identified for cement mill circuits. The uncertainties in the linear predictive model of the cement mill circuit stems from large variations and heterogeneities in the feed material as well as operational variations. These sources of variations give rise to very nonlinear behavior and variations in the dead-times of the cement mill circuit. The uncertainties may be characterized by the gains, time constants, and time delays in a transfer function model. The developed soft MPC is compared to a normal MPC. The comparison is conducted using a rigorous cement mill circuit simulator used for operator training. The simulations reveal that compared to normal MPC, soft MPC regulate cement mill circuits better and in a plant friendly way by using less variations in the manipulated variables (MVs).

Bifurcation Control of Sample Chemical Reaction Systems

Abstract Bifurcation control of Hopf bifurcations is applied to two systems exhibiting a subcritical Hopf bifurcation. A subcritical Hopf bifurcation is characterized by the emergence of an unstable periodic solution, quite often coexisting with a stable periodic solution in a hysteresis scenario. This type of scenario can lead to large amplitude oscillations if the Hopf bifurcation point is crossed. Therefore it is desirable to change this bifurcation scenario, which can be achieved with the bifurcation control described in this paper. The purpose of this type of control is to convert a subcritical Hopf bifurcation to a supercritical one. An additional benefit is that the resulting stable periodic solution will have a relatively small amplitude at least close to the Hopf bifurcation point. The method is first successfully applied to a small example system, to illustrate the calculations and subsequently to an industrial size heat integrated ammonia reactor. For the ammonia reactor the existence region of the sustained oscillation is reduced dramatically and the maximum amplitude is reduced from approximately 200°C to about 60°C. Furthermore the nominal operating point no longer coexist with stable periodic solution.

Nonlinear dynamics and control of a recycle fixed bed reactor

The purpose of this paper is twofold. Primarily to describe the dynamic behaviour that can be observed in a fixed bed reactor with recycle of unconverted reactant. Secondly to describe the possibilities of model reduction in order to facilitate control design. Reactant recycle has been shown to introduce periodic solution to the fixed bed reactor, a phenomenon which is not seen for the system without the recycle, at least not within the Peclet number range investigated in the present work. The possibility of model reduction by the methods of modal decomposition, and by characteristics are investigated in the paper for the present case. Finally a criterion for actuator selection is formulated, and a simulated control example is given.

Physical Implications of Periodic Solutions in a Fixed Bed Reactor with Recycle

Abstract Recycling is often used in industrial processes to reduce cost of raw material and energy supply. The nonlinear effects of introducing recycling on a fixed bed reactor are investigated in the present work. A first order exothermic reaction is chosen as a model reaction. The three cases of recycling investigated are recycling of unconverted reactant, external heat exchange and combined mass and energy. The findings are that bifurcations occur as the operational variables are changed. Investigating the periodic solutions show, that the limit cycle periods in all the investigated cases of recycling, are simple fractions(1, ½, ⅓) of the thermal residence time. Consequently three periodic solutions appear in various sections of the operational space. A physical interpretation of the periodic solutions is that they correspond to one, two and three ignition points respectively in the reactor. These periodic solutions are further investigated and compared to see if it is the same dynamic effect that causes them to appear in the three recycle cases. The implications of the periodic solutions upon the control structure selection for mass recycle will also be considered.

Soft Constrained based MPC for Robust Control of a Cement Grinding Circuit

Abstract In this paper, we develop a novel Model Predictive Controller (MPC) based on soft output constraints for regulation of a cement mill circuit. The MPC is first tested using cement mill simulation software and then on a real plant. The model for the MPC is obtained from step response experiments in the real plant. Based on the experimental step responses an approximate transfer function model for the system is identified. The performance of the MPC in the real plant compares favorably to the existing control system based on fuzzy logic. Compared to the other controllers, soft MPC handles the real time uncertainties effectively. It also regulates the cement mill circuits better and in a plant friendly way by using less variation in the manipulated variables (MVs).

Robust statistics for soft sensor development in cement kiln

Abstract This paper presents a systematic approach of developing data-driven soft sensor using robust statistical technique. Data preprocessing procedures are described in detail. First, a template defined with a key process variable is used to handle missing data. Second, a univariate, followed by a multivariate approach, principal component analysis (PCA), is used to detecting outlying observations. Then, regression technique is employed to derive an inferential model. The proposed methodology is applied to a cement kiln system for realtime estimation of free lime, demonstrating improved performance over a standard multivariate approach.

Product quality estimation using multi-rate sampled data

Abstract This paper investigates different approaches to develop soft sensors from multi-rate sampled data. The data lifting approach consists of two steps, identifying a model with a slow/lifted sampling period and extracting a fast model. Approaches based on direct extraction and linear regression are briefly reviewed, followed by reformulating the task as an unconstrained optimization problem. An illustrative example concerning design of a free lime soft sensor for cement kiln systems is presented. Using data collected from a simulation system based on first principles models, a weighted partial, least squares (WPLS) approach for soft sensor development is compared with data lifting techniques. Case studies reveal the superior performance of the WPLS approach. In addition the product quality for cement kiln systems can be estimated reasonably well, demonstrating the potential to be used for effective quality control.