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|Title: ||Modeling of nonlinear distributed parameter system for industrial thermal processes|
|Other Titles: ||Gong ye re guo cheng fei xian xing fen bu can shu xi tong jian mo|
|Authors: ||QI, Chenkun (齊臣坤)|
|Department: ||Department of Manufacturing Engineering and Engineering Management|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Distributed parameter systems.|
Nonlinear control theory.
Heat -- Transmission -- Industrial applications.
|Notes: ||CityU Call Number: CityU Call Number:|
xviii, 187 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves 167-187)
|Abstract: ||Distributed parameter system (DPS) becomes important because of advanced
technological needs. Thermal processes in integrated circuit (IC) packaging and other
industry are typical nonlinear DPS where the input and output vary both spatially and
temporally. Modeling is required for prediction, control and optimization of temperature
field. Their complex features: time/space coupling, nonlinear and unknown structure
uncertainties make the modeling of this class of unknown nonlinear DPS very difficult
The physics-based DPS modeling often leads to nominal nonlinear partial differential
equations (PDE) with unknown structure uncertainties. They are infinite-dimensional
systems, thus the reduction to finite-dimensional systems is needed because of finite
actuators/sensors and limited computing power. Though there are many model reduction
methods, e.g., finite difference method (FDM), finite element method (FEM), spectral
method and Karhunen-Loève (KL) method, they require an accurate nominal PDE model
be available. Parameter estimation from input-output data is also not suitable because it
requires the PDE structure be known. Though nonlinear DPS with unknown structure is
very common in the industry, its identification receives a little attention. This problem is
very difficult because both the parameter and structure need determine. Existing DPS
identification approaches have some limitations.
Green’s function based identification leads to a linear spatio-temporal kernel model,
which is only a linear approximation for nonlinear DPS around a working point.
FDM or FEM based identification will lead to a high-order model, which may result
in an unpractical high-order controller.
Spectral or KL based neural identification can lead to a low-order model. Compared
with spectral method, KL method can obtain a lower-order model. However the
complex nonlinear model structure may result in a complicated control design.
On the other hand, the popularly used complexity restricted nonlinear models: Wiener,
Hammerstein and Volterra, are temporal models and only studied for lumped parameter
systems (LPS). Nonlinear principal component analysis (NL-PCA) is a nonlinear
dimension reduction method in machine learning. It can achieve a lower-order and more
accurate model than the KL method. Thus to overcome the limitations in the DPS
identification, it is necessary to develop new nonlinear DPS modeling approaches by
combining the advantages of different modeling and learning techniques.
The objective of this thesis is to extend the traditional Wiener, Hammerstein, Volterra
and neural modeling to DPS with the help of kernel idea, KL method or NL-PCA,
develop some useful data-based spatio-temporal modeling approaches for unknown
nonlinear DPS, and apply the proposed methods on typical thermal processes in IC
packaging and other industry.
Firstly, a KL based Wiener (KL-Wiener) modeling approach is proposed. Traditional
Wiener model is popularly used because of its block-oriented nonlinear structure (a
linear LPS followed by a static nonlinearity). For modeling nonlinear DPS, a spatiotemporal
Wiener model is established with a linear DPS followed by a static
nonlinearity. After the time/space separation, it can be represented by traditional
Wiener system with a set of spatial basis functions. To achieve a low-order model,
the KL method is used for the time/space separation and dimension reduction. Then
the Wiener model is estimated using the least-squares estimation and the
instrumental variables method, which can achieve consistent estimates under process
Secondly, a KL based Hammerstein (KL-Hammerstein) modeling approach is
proposed. Traditional Hammerstein system is also a popular used block-oriented
nonlinear model (a static nonlinearity followed by a linear LPS). To model nonlinear
DPS, a spatio-temporal Hammerstein model (a static nonlinearity followed by a
linear DPS) is constructed. After the time/space separation, it can be represented by
traditional Hammerstein system with a set of spatial basis functions. To obtain a low order model, the KL method is used for the time/space separation and dimension
reduction. Then the compact Hammerstein model structure is determined by
orthogonal forward regression and the parameters are estimated with the leastsquares
estimation and singular value decomposition. This approach can achieve a
low-order parsimonious Hammerstein model.
Thirdly, a kernel based multi-channel spatio-temporal Hammerstein modeling
approach is proposed. A distributed Hammerstein system is constructed with a static
nonlinearity followed by a spatio-temporal kernel. When the model structure is
matched with the system, a basic identification approach using the least-squares
estimation and singular value decomposition can work well. When there is some
unmodeled dynamics, a multi-channel modeling framework is proposed to achieve a
better performance, which can guarantee the convergence under noisy measurements.
Fourthly, a Volterra kernel based spatio-temporal modeling approach is proposed.
Traditional Volterra model consists of a series of temporal kernel. To reconstruct the
spatio-temporal dynamics, a spatio-temporal Volterra model is constructed with a
series of spatio-temporal kernels. It is also a nonlinear extension of Green’s function.
To achieve a low-order model, the KL method is used for the time/space separation
and dimension reduction. Then the model is estimated with a least-squares algorithm,
which can guarantee the convergence under noisy measurements.
Fifthly, a NL-PCA based neural modeling approach is proposed. The KL based
dimension reduction is a linear approximation for a nonlinear system. To get a lowerorder
or more accurate model, a NL-PCA based intelligent modeling framework is
studied. One NL-PCA network is trained for nonlinear dimension reduction and
nonlinear time/space reconstruction, and then the other linear/nonlinear separated
neural model is to learn the system dynamics. With the powerful capability of
dimension reduction and intelligent learning, this approach can model more complex
The simulations and experiments on typical thermal processes in IC packaging and other
industry show that the proposed modeling approaches are effective. Different kinds of
models may be suitable for different system and is usually selected by the performance.
For the snap curing oven system in IC packaging, Volterra model achieves the best
performance. The accuracy of KL-Wiener model is similar to Volterra model. Both
Volterra and Wiener models are more suitable for this process than other models.
This thesis provides several useful modeling frameworks for unknown nonlinear DPS.
The proposed modeling approaches are data-driven and do not need a priori process
knowledge, so they are very flexible and can be easily applied to other distributed
processes. They can obtain low-order and simple nonlinear models. Though the modeling
experiment may need more sensors, once the model has been established a few sensors
will be enough for real-time applications.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2375091|
|Appears in Collections:||MEEM - Doctor of Philosophy |
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