System Identification Based on Errors-In-Variables System Models

We study the identification problem for errors-in-variables (EIV) systems. Such an EIV model assumes that the measurement data at both input and output of the system involve corrupting noises. The least square (LS) algorithm has been widely used in this area. However, it results in biased estimates for the EIV-based system identification. In contrast, the total least squares (TLS) algorithm is unbiased, which is now well-known, and has been effective for estimating the system parameters in the EIV system identification. In this dissertation, we first show that the TLS algorithm computes the approximate maximum likelihood estimate (MLE) of the system parameters and that the approximation error converges to zero asymptotically as the number of measurement data approaches infinity. Then we propose a graph subspace approach (GSA) to tackle the same EIV-based system identification problem and derive a new estimation algorithm that is more general than the TLS algorithm. Several numerical examples are worked out to illustrate our proposed estimation algorithm for the EIV-based system identification. We also study the problem of the EIV system identification without assuming equal noise variances at the system input and output. Firstly, we review the Frisch scheme, which is a well-known method for estimating the noise variances. Then we propose a new method which is GSA in combination with the Frisch scheme (GSA-Frisch) algorithm via estimating the ratio of the noise variances and the system parameters iteratively. Finally, a new identification algorithm is proposed to estimate the system parameters based on the subspace interpretation without estimating noise variances or the ratio. This new algorithm is unbiased, and achieves the consistency of the parameter estimates. Moreover, it is low in complexity. The performance of the identification algorithm is examined by several numerical examples, and compared to the N4SID algorithm that has the Matlab codes available in Matlab toolboxes, and also to the GSA-Frisch algorithm

Fault detection for the Benfield process using a closed-loop subspace re-identification approach

Closed-loop system identification and fault detection and isolation are the two fundamental building blocks of process monitoring. Efficient and accurate process monitoring increases plant availability and utilisation. This dissertation investigates a subspace system identification and fault detection methodology for the Benfield process, used by Sasol, Synfuels in Secunda, South Africa, to remove CO2 from CO2-rich tail gas. Subspace identification methods originated between system theory, geometry and numerical linear algebra which makes it a computationally efficient tool to estimate system parameters. Subspace identification methods are classified as Black-Box identification techniques, where it does not rely on a-priori process information and estimates the process model structure and order automatically. Typical subspace identification algorithms use non-parsimonious model formulation, with extra terms in the model that appear to be non-causal (stochastic noise components). These extra terms are included to conveniently perform subspace projection, but are the cause for inflated variance in the estimates, and partially responsible for the loss of closed-loop identifiably. The subspace identification methodology proposed in this dissertation incorporates two successive LQ decompositions to remove stochastic components and obtain state-space models of the plant respectively. The stability of the identified plant is further guaranteed by using the shift invariant property of the extended observability matrix by appending the shifted extended observability matrix by a block of zeros. It is shown that the spectral radius of the identified system matrices all lies within a unit boundary, when the system matrices are derived from the newly appended extended observability matrix. The proposed subspace identification methodology is validated and verified by re-identifying the Benfield process operating in closed-loop, with an RMPCT controller, using measured closed-loop process data. Models that have been identified from data measured from the Benfield process operating in closed-loop with an RMPCT controller produced validation data fits of 65% and higher. From residual analysis results, it was concluded that the proposed subspace identification method produce models that are accurate in predicting future outputs and represent a wide variety of process inputs. A parametric fault detection methodology is proposed that monitors the estimated system parameters as identified from the subspace identification methodology. The fault detection methodology is based on the monitoring of parameter discrepancies, where sporadic parameter deviations will be detected as faults. Extended Kalman filter theory is implemented to estimate system parameters, instead of system states, as new process data becomes readily available. The extended Kalman filter needs accurate initial parameter estimates and is thus periodically updated by the subspace identification methodology, as a new set of more accurate parameters have been identified. The proposed fault detection methodology is validated and verified by monitoring process behaviour of the Benfield process. Faults that were monitored for, and detected include foaming, flooding and sensor faults. Initial process parameters as identified from the subspace method can be tracked efficiently by using an extended Kalman filter. This enables the fault detection methodology to identify process parameter deviations, with a process parameter deviation sensitivity of 2% or higher. This means that a 2% parameter deviation will be detected which greatly enhances the fault detection efficiency and sensitivity.Dissertation (MEng)--University of Pretoria, 2008.Electrical, Electronic and Computer Engineeringunrestricte

Data cleaning and knowledge discovery in process data

This dissertation presents several methods for overcoming the Big Data challenges, with an emphasis on data cleaning and knowledge discovery in process data. Data cleaning and knowledge discovery is chosen as a main research area here due to its importance from both theoretical and practical points of view. Theoretical background and recent developments of data cleaning methods are reviewed from four aspects: missing data imputation, outlier detection, noise removal and time delay estimation. Moreover, the impact of contaminated data on model performance and corresponding improvement obtained by data cleaning methods are analyzed through both simulated and industrial case studies. The results provide a starting point for further advanced methodology development. It is hard to find a universally applicable method for data cleaning since every data set may have its own distinctive features. Thus, we have to customize available methods so that the quality of the data set is guaranteed. An integrated data cleaning scheme is proposed, which incorporates model building and performance evaluation, to provide guidance in tuning the parameters of data cleaning methods and prevent over-cleaning. A case study based on industrial data has been used to verify the feasibility and effectiveness of the proposed new method, during which a partial least squares (PLS) model was built and three univariate data cleaning procedures is tested. A time series Kalman filter (TSKF) is proposed that successfully handles outlier detection in dynamic systems, where normal process changes often mask the existence of outliers. The TSKF method combines a time series model fitting procedure with a modified Kalman filter to deal with additive outlier (AO) and innovational outlier (IO) detection problems in dynamic process data set. A comparative analysis of TSKF and available methods is performed on simulated and real chemical plant data. Root cause diagnosis of plant-wide oscillations, as a concrete example of data cleaning and knowledge discovery in the process data, is provided. Plant-wide oscillations can negatively influence the overall control performance of the process and the detection results are often affected by noise at different frequency ranges. To address such a problem, an information transfer method combining spectral envelope algorithm with spectral transfer entropy is proposed to detect and diagnose such oscillations within a specific frequency range, mitigating the effects from measurement noise. The feasibility and effectiveness of the proposed method are verified and compared with available methods through both simulated and industrial case studies.Chemical Engineerin

Measurements, Models, Systems and Design

531 s.

Methodology for utilising prior knowledge in constructing data-based process monitoring systems with an application to a dearomatisation process

Global competition is forcing the process industry to optimise the production processes. One key factor in optimisation is effective process state monitoring and fault detection. Another motivator to improve process monitoring systems are the substantial losses of revenue resulting from abnormal process conditions. It has been estimated that the petrochemical industry in the US alone loses 20 billion dollars per year because of unoptimal handling of abnormal process situations. Traditionally, the monitoring systems have been based on first principle models, constructed by specialists with process specific expertise. In contrast, the use of data-based modelling methods require less expertise and offers the possibilities to build and update the monitoring models in a short period of time, thus allowing more efficient development of monitoring systems. The aims of this thesis are to augment data-driven modelling with existing process knowledge, to combine different data-based modelling methods, and to utilise calculated variables in modelling in order to improve the accuracy of fault detection and identification (FDI) and to provide all necessary diagnostic information for fault tolerant control. The suggested improvements are included in a methodology for setting up FDI systems. The methodology has been tested by building FDI systems for detecting faults in two online quality analysers in a simulated and in a real industrial dearomatisation process at the Naantali oil refinery (Neste Oil Oyj). In developing an FDI system, background information about the user requirements for the monitoring system is first acquired. The information is then analysed and suitable modelling methods are selected according to the guidelines given in the methodology. Second, the process data are prepared for the modelling methods and augmented with appropriate calculated variables. Next, the input variable sets are determined with the introduced method and the models are constructed. After the estimation accuracy of the models is validated, the values of the fault detection parameters are determined. Finally, the fault detection performance of the system is tested. The system was evaluated during a period of one month at the Naantali refinery in 2007. The monitoring system was able to detect all the introduced analyser faults and to provide the information needed for a fault tolerant control system, thus validating the methodology. The effects of a number of suggested improvements in data-based modelling are analysed by means of a comparison study

Improving time efficiency of feedforward neural network learning

Feedforward neural networks have been widely studied and used in many applications in science and engineering. The training of this type of networks is mainly undertaken using the well-known backpropagation based learning algorithms. One major problem with this type of algorithms is the slow training convergence speed, which hinders their applications. In order to improve the training convergence speed of this type of algorithms, many researchers have developed different improvements and enhancements. However, the slow convergence problem has not been fully addressed. This thesis makes several contributions by proposing new backpropagation learning algorithms based on the terminal attractor concept to improve the existing backpropagation learning algorithms such as the gradient descent and Levenberg-Marquardt algorithms. These new algorithms enable fast convergence both at a distance from and in a close range of the ideal weights. In particular, a new fast convergence mechanism is proposed which is based on the fast terminal attractor concept. Comprehensive simulation studies are undertaken to demonstrate the effectiveness of the proposed backpropagataion algorithms with terminal attractors. Finally, three practical application cases of time series forecasting, character recognition and image interpolation are chosen to show the practicality and usefulness of the proposed learning algorithms with comprehensive comparative studies with existing algorithms

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67