20 research outputs found
Model based fault detection for two-dimensional systems
Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial
systems. Extensive research has been carried out on FDI for one dimensional (1-D)
systems, where variables vary only with time. The existing FDI strategies are mainly focussed
on 1-D systems and can generally be classified as model based and process history data based
methods. In many industrial systems, the state variables change with space and time (e.g., sheet
forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter
systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented
by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems
represent a great challenge in both theoretical development and applications and only limited
research results are available.
In this thesis, model based fault detection strategies for 2-D systems have been investigated
based on the F-M and the Roesser models. A dead-beat observer based fault detection has been
available for the F-M model. In this work, an observer based fault detection strategy is investigated
for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique,
a dead-beat observer is developed and the state estimate from the observer is then input to a
residual generator to monitor occurrence of faults. An enhanced realization technique is combined
to achieve efficient fault detection with reduced computations. Simulation results indicate
that the proposed method is effective in detecting faults for systems without disturbances as well
as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems
but strict conditions are required in order for an observer and a residual generator to exist. These
strict conditions may not be satisfied for some systems. The effect of process noises are also not
considered in the observer based fault detection approaches for 2-D systems. To overcome the
disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation
error variances. Based on the state estimate from the Kalman filter, a residual is generated
reflecting fault information. A model is formulated for the relation of the residual with faults
over a moving evaluation window. Simulations are performed on two F-M models and results
indicate that faults can be detected effectively and efficiently using the Kalman filter based fault
detection.
In the observer based and Kalman filter based fault detection approaches, the residual signals
are used to determine whether a fault occurs. For systems with complicated fault information
and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault
detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component
analysis (DPCA). Based on historical data, the reference residuals are first generated using
either the observer or the Kalman filter based approach. Based on the residual time-lagged
data matrices for the reference data, the principal components are calculated and the threshold
value obtained. In online applications, the T2 value of the residual signals are compared with
the threshold value to determine fault occurrence. Simulation results show that applying DPCA
to evaluation of 2-D residuals is effective.Doctoral These
On the connection between discrete linear repetitive processes and 2-D discrete linear systems
A direct method is developed that reduces a polynomial system matrix describinga discrete linear repetitive process to a 2-D singular state-space form such that all the relevant properties, including the zero structure of the system matrix, are retained. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D singular form is zero coprime system equivalence. The exact nature of the resulting system matrix in singular form and the transformation involved are established
Computational and algebraic aspects of two-dimensional, linear, multivariable control systems
There are at present a large number of theoretical and
algorithmic results relating to one-variable polynomial
matrices arising from one-dimensional multivariable systems.
In recent years many of the theoretical results have been
extended to two-variable polynomial matrices arising from
two-dimensional multi variable systems, such as delay-differential
or partial differential systems. However there
has been no major attempt to extend the algorithmic results
associated with single variable polynomial matrices to two-variable or multivariable polynomial matrices.
This thesis investigates further some of the extensions
of the algebra of one-dimensional multivariable systems to
two-dimensional multivariable systems. [Continues.
Sliding Mode Control
The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area
Structure-Preserving Model Reduction of Physical Network Systems
This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p
Modeling, Estimation, and Pattern Analysis of Random Texture on 3-D Surfaces
To recover 3-D structure from a shaded and textural surface image involving textures, neither the Shape-from-shading nor the Shape-from-texture analysis is enough, because both radiance and texture information coexist within the scene surface. A new 3-D texture model is developed by considering the scene image as the superposition of a smooth shaded image and a random texture image. To describe the random part, the orthographical projection is adapted to take care of the non-isotropic distribution function of the intensity due to the slant and tilt of a 3-D textures surface, and the Fractional Differencing Periodic (FDP) model is chosen to describe the random texture, because this model is able to simultaneously represent the coarseness and the pattern of the 3-D texture surface, and enough flexible to synthesize both long-term and short-term correlation structures of random texture. Since the object is described by the model involving several free parameters and the values of these parameters are determined directly from its projected image, it is possible to extract 3-D information and texture pattern directly from the image without any preprocessing. Thus, the cumulative error obtained from each pre-processing can be minimized. For estimating the parameters, a hybrid method which uses both the least square and the maximum likelihood estimates is applied and the estimation of parameters and the synthesis are done in frequency domain. Among the texture pattern features which can be obtained from a single surface image, Fractal scaling parameter plays a major role for classifying and/or segmenting the different texture patterns tilted and slanted due to the 3-dimensional rotation, because of its rotational and scaling invariant properties. Also, since the Fractal scaling factor represents the coarseness of the surface, each texture pattern has its own Fractal scale value, and particularly at the boundary between the different textures, it has relatively higher value to the one within a same texture. Based on these facts, a new classification method and a segmentation scheme for the 3-D rotated texture patterns are develope