Continuous stirred tank reactor fault detection using higher degree Cubature Kalman filter

Continuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible. A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results

Polymer Reactor Modeling, Design and Monitoring

Polymers range from synthetic plastics, such as polyacrylates, to natural biopolymers, such as proteins and DNA. The large molecular mass of polymers and our ability to manipulate their compositions and molecular structures have allowed for producing synthetic polymers with attractive properties. new polymers with remarkable characteristics are synthesized. Because of the huge production volume of commodity polymers, a little improvement in the operation of commodity-polymer processes can lead to significant economic gains. On the other hand, a little improvement in the quality of specialty polymers can lead to substantial increase in economic profits

A Novel Diagnostic and Prognostic Framework for Incipient Fault Detection and Remaining Service Life Prediction with Application to Industrial Rotating Machines

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Data-driven machine health monitoring systems (MHMS) have been widely investigated and applied in the field of machine diagnostics and prognostics with the aim of realizing predictive maintenance. It involves using data to identify early warnings that indicate potential system malfunctioning, predict when system failure might occur, and pre-emptively service equipment to avoid unscheduled downtime. One of the most critical aspects of data-driven MHMS is the provision of incipient fault diagnosis and prognosis regarding the system’s future working conditions. In this work, a novel diagnostic and prognostic framework is proposed to detect incipient faults and estimate remaining service life (RSL) of rotating machinery. In the proposed framework, a novel canonical variate analysis (CVA)-based monitoring index, which takes into account the distinctions between past and future canonical variables, is employed for carrying out incipient fault diagnosis. By incorporating the exponentially weighted moving average (EWMA) technique, a novel fault identification approach based on Pearson correlation analysis is presented and utilized to identify the influential variables that are most likely associated with the fault. Moreover, an enhanced metabolism grey forecasting model (MGFM) approach is developed for RSL prediction. Particle filter (PF) is employed to modify the traditional grey forecasting model for improving its prediction performance. The enhanced MGFM approach is designed to address two generic issues namely dealing with scarce data and quantifying the uncertainty of RSL in a probabilistic form, which are often encountered in the prognostics of safety-critical and complex assets. The proposed CVA-based index is validated on slowly evolving faults in a continuous stirred tank reactor (CSTR) system, and the effectiveness of the proposed integrated diagnostic and prognostic method for the monitoring of rotating machinery is demonstrated for slow involving faults in two case studies of an operational industrial centrifugal pump and one case study of an operational centrifugal compressor

Moving Horizon Estimation for JModelica.org

In this thesis a Moving Horizon Estimator (MHE) has been implemented for the JModelica.org platform. JModelica.org is an open-source software platform for simulation and optimization of systems described in the modeling language Modelica. MHE is an optimization-based strategy for state estimation where, at each time step, a finite horizon optimization problem is solved to generate an estimate of the current state values. The goal has been to implement an MHE that works with many already existing Modelica models and that has an intuitive user interface. The performance of the implemented MHE is evaluated using both linear and nonlinear systems in a series of simulation examples. The results indicate that the MHE performs well

Offset-free model predictive control using Koopman-Wiener models

Abstract. This master’s thesis was built on the previously developed Koopman-Wiener nonlinear model predictive controller, and the goal of this thesis was to find a suitable strategy for rejecting steady-state offset, caused by plant model mismatch. This thesis also aimed to enable the controller to perform in applications where the full state is not measured and the available measurements are corrupted with noise. The work in this thesis considered multiple strategies for handling plant model mismatch, but disturbance rejection was selected as the main approach. It is proposed in this thesis that the disturbance model for disturbance rejection can be chosen by calculating empirical observability Gramian at a single initial point for every considered augmented model option and then picking the model which is interpreted as the most observable. The proposed observability analysis provides information about weak observability of the disturbance augmented model only at the single initial point. Nevertheless, it was argued in this thesis that the results can be assumed to represent the relevant operation region, and thus the method is applicable for choosing a disturbance model. As an alternative to compare against disturbance rejection, this thesis also investigated recursive least squares method that adapts the Koopman-Wiener model within the controller online. For state estimation, this thesis utilized unscented Kalman filter. This thesis demonstrated performance of the chosen methods with two nonlinear system case studies commonly studied in the literature: a simulated continuous stirred tank reactor and a simulated distillation column. This paper provides three main results. Firstly, the controller with disturbance rejection is successful in eliminating steady-state offset in a closed-loop system. Secondly, the controller is unable to reach satisfactory performance while using the recursive least squares method. Thirdly, the results from case studies support the chosen disturbance modeling approach, since the disturbance models chosen with the approach lead to improved or equal controller performance compared to using other disturbance models. Furthermore, the results support presenting a useful heuristic about how to perform disturbance modeling with Koopman-Wiener models by having the disturbances affect the slow dynamics of the model.Säätöpoikkeamasta vapaa malliprediktiivinen säädin käyttäen Koopman-Wiener malleja. Tiivistelmä. Tämä diplomityö perustui aiemmin kehitettyyn epälineaariseen Koopman-Wiener malliprediktiiviseen säätimeen. Diplomityön tavoitteena oli löytää sopiva strategia eliminoimaan tasapainotilan säätöpoikkeama, joka on seurausta tilanteesta, jossa säätimen käyttämä malli ei vastaa ohjattavaa prosessia. Työssä tavoiteltiin myös säätimen toiminnan mahdollistamista sovelluksissa, joissa prosessin jokaista tilamuuttujaa ei mitata, ja saatavilla olevissa mittauksissa on kohinaa. Diplomityössä harkittiin useita eri strategioita vastaamaan säätimen ja prosessin mallien yhteensopimattomuuteen, mutta häiriön torjunta valikoitui pääasialliseksi lähestymistavaksi. Diplomityössä ehdotetaan, että häiriön torjuntaan käytettävä häiriömalli voidaan valita laskemalla empiirinen havaittavuus Gramin matriisi yhdessä alkupisteessä jokaiselle harkitulle häiriömallille ja sitten valitsemalla malli, joka tulkitaan eniten havaittavaksi. Ehdotettu havaittavuusanalyysi tuottaa tietoa heikosta havaittavuudesta häiriöaugmentoidulle mallille vain valitussa alkupisteessä. Siitä huolimatta, tässä työssä argumentoitiin, että tulosten voidaan olettaa kuvastavan olennaista prosessin toiminta-aluetta, ja menetelmä soveltuu täten häiriömallin valitsemiseen. Vaihtoehtona häiriön torjunnalle, tässä työssä tutkittiin myös rekursiivista pienimmän neliösumman menetelmää adaptoimaan säätimessä käytettävää Koopman-Wiener-mallia ajon aikana. Tilaestoimointiin tässä työssä käytettiin hajustamatonta Kalman suodinta. Diplomityö demonstroi valittujen menetelmien suorituskykyä kahdella epälineaarisella tapaustutkimuksella: simuloitu jatkuvatoiminen sekoitusreaktori ja simuloitu tislauskolonni. Tässä työssä esitetään kolme tärkeää tulosta. Ensimmäiseksi, säädin joka käyttää häiriön torjuntaa, onnistuu poistamaan tasapainotilan säätöpoikkeaman takaisinkytketyssä systeemissä. Toiseksi, säädin ei saavuta tyydyttävää suorituskykyä rekursiivista pienimmän neliösumman menetelmää käytettäessä. Kolmanneksi, tapaustutkimukset tukevat ehdotettua lähestymistapaa häiriömallinnukseen, koska valitut häiriömallit johtavat parempaan tai yhtä hyvään säätimen suorituskykyyn verrattuna muiden häiriömallien käyttämiseen. Lisäksi tulokset tukevat hyödyllisen heuristisen säännön esittämistä Koopman-Wiener-mallien häiriömallintamiselle siten, että häiriömuuttujat vaikuttavat mallin dynaamisesti hitaisiin tilamuuttujiin

Early warning generation for process with unknown disturbance

Process safety has paramount importance in a chemical process. A well designed control system is the first layer in a process system. The warning system works as the upper protection layer above the control system. It alerts the operators when the control system fails to prevent an undesired situation. A typical warning system issues warnings when a monitored variable exceeds the threshold. Often these do not allow operators sufficient lead-time to take corrective actions. With the motivation of improving the operator’s working environment by providing lead-time, the current research develops a predictive warning scheme using a moving horizon technique. The main hypothesis proposed in this thesis is given the current state of process system, the future states of the system can be predicted using a suitable model of process system. If an external input disturbs the system state, the controller will try to bring the system within the desired control/safety limits of the system. A warning is issued if it is determined that the control system will not be able to keep the system withing the safety limits. Based on the hypothesis, warning systems were developed for both linear and nonlinear systems. For linear systems, using the gain of the models, a linear constrained optimization problem was formulated. Linear programming (LP) was used to determine if the system will remain within the safety limits or not. In case the LP determines that there is no feasible solution within the constrained limits, warnings are issued. The predictive warning scheme was also extended for nonlinear systems. A non-linear receding horizon predictor was used to predict the future states of the nonlinear system. However, for nonlinear system formulation leads to nonlinear constrained optimization problem, where the constraints are the safety limits. Controller’s ability to keep the predicted states inside the safety limit was checked using a feasibility test algorithm. The algorithm uses a constraint separation method with weighting functions to determine the existence of a feasible solution. The algorithm calculates the global minimum of the objective function. If the global minimum of the objective function is positive, it signifies no feasible solution within the input and output constraints of the system and a warning is issued. Prediction of the effect of the disturbances requires the knowledge of the disturbances. In process industries, disturbances are often unmeasured. This thesis also investigates the estimation of unknown disturbances. An iterative Expectation Minimization (EM) algorithm was proposed for the estimation of the unknown states and disturbances of nonlinear systems. Efficacy of the proposed methods was shown through a number of case studies. The warning system for the linear system was simulated on a virtual plant of a continuous stirred tank heater (CSTH). The nonlinear warning system was implemented on a continuous stirred tank reactor (CSTR). Both case studies showed that, the proposed method was capable of providing a warning earlier than the traditional methods that issues warning based on the measured signals