الفهرس 
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Abstract
The principle component analysis (PCA) method is the most popular one of the data driven
approaches. Basically, PCA is a method for extracting information from data by compressing
large data matrices in such a way the most important data is preserved while the redundant
and noisy data is discarded. In fact, classical PCA method is not suitable for time varying
process, however, the normal process is usually time-varying owing to drifts and equipment
aging. It is sometimes difficult to distinguish between slow drifts that are normal and
incipient process degradation that can lead to more severe abnormal situations. Although,
the Recursive Principle Component Analysis (RPCA) algorithms are commonly used, the
outliers and the computation cost are of the most important challenges face them. One of
the main objectives of this thesis is to dealing with the time-varying behavior in order to
reduce false alarms. This thesis introduced a set of methods for designing PCA models for
fault detection and isolation for time varying industrial processes. These methods can be
briefly described below.
A robust Recursive PCA-based fault detection model is proposed in two steps. Step-1, a
complete adaptive monitoring based on PCA model is introduced. Step-2, outlying samples,
which are recorded from real processes, are pretreated by means of employing one of the
statistical measurements such that the model is insensitive to the outliers and is correctly
updated. This proposed model is evaluated by applying to both a static multivariate system
and a simulated non-isothermal continuous stirred tank reactor (CSTR) system. The results
demonstrate the superiority of the proposed model to the classical PCA for monitoring the
slow and the fast system variations.
Three proposed recursive fault detection approaches are introduced to reduce the computation
cost. The first approach introduces a recursive PCA model that is constructed
based on First-order Perturbation Analysis. The second approach develops a recursive
PCA model based on a simple and reliable subspace tracking method, i.e., Data Projection
Method (DPM). The third approach presents a new index that is used for fault detection.
The last approach does not need constructing the PCA model, it only benefits from the
last principal components. The simulation results have demonstrated the adaptability, reliability,
credibility, and applicability of the proposed recursive fault detection approaches
compared to the traditional methods.
Two isolation methods are developed for time varying process monitoring. The proposed
isolation methods depend on recursive calculating of the contribution of each process variable
in the monitoring indices that are used to measure the processes healthy. The proposed
isolation methods are: (i) Recursive Partial Decomposition Contributions (RPDC), (ii) Recursive
Diagonal Contributions (RDC). Moreover, an integrated fault detection and isolation
approach is introduced for monitoring time varying industrial processes. The proposed
recursive monitoring methods are effective in detecting and isolating simple and complex
faults. Four types of sensor faults: bias, drift, precision degradation, and complete failure
are considered. Two indices based on the Hotelling’s T2 and SPE statistics are applied
for representing the contribution of the variables. The overall performance of the proposed
scheme was validated by using a non-isothermal continuous stirred tank reactor system. The
simulation results demonstrate the effectiveness of the proposed algorithms with respect to
the traditional methods. Most industrial processes are time-varying. So, the proposed
adaptive monitoring schemes are expected to have broad applicability in industry.
PCA based methods are basically linear. Nonlinearity in most chemical and biological
processes is still a significant problem. Kernel principal component analysis (KPCA) has
recently proven to be a powerful tool for monitoring nonlinear processes with numerous
mutually correlated measured variables. Kernel PCA model maps a nonlinear input space
into a high-dimensional feature space where the data structure is likely to be linear. Principal
components in the feature space can be calculated by means of integral operators and
nonlinear kernel functions. They require only linear algebra to develop a process monitoring
system compared to other nonlinear methods that involve nonlinear optimization. This
thesis proposes a kernel PCA method for determining the dimension of principal subspace.
The developed Kernel PCA method is tested using three different applications. The validity
of the developed method is measured through two indices: false alarm and missed detection
rates. On the basis of these error rates, the developed Kernel PCA method gives a better
monitoring performance than the linear PCA model.
Different applications are used to measure the validity, reliability and credibility of the
proposed approaches in this thesis. These applications implies a MATLAB/SIMULINK
model of a non-isothermal Continuous Stirred Tank Reactor (CSTR) system. The CSTR
is commonly process employed in literature for data driven-based methods. The successful
application of the proposed PCA methods to the CSTR process has demonstrated the
feasibility and effectiveness of these methods for process monitoring. The proposed methodologies
are fairly general and are applicable to most chemical processes. In short, many fault
detection and isolation approaches are proposed in this thesis. The main notable features of
these approaches are stemmed from their simplicity, low computational cost, and credibility
to real industrial processes monitoring.