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1 
Adaptive Identification of Nonlinear SystemsLEHRER, DEVON HAROLD 19 October 2010 (has links)
This work presents three techniques for parameter identification for nonlinear systems. The methods presented are expanded from those presented in Adetola and Guay [3, 4, 5] and are intended to improve the performance of existing adaptive control systems. The first two methods exactly recover openloop system parameters once a defined convergence condition is met. In either case, the true parameters are identified when the regressor matrix is of
full rank and can be inverted. The third case uses a novel method developed in Adetola
and Guay [5] to define a parameter uncertainty set. The uncertainty set is periodically updated to shrink around the true value of the parameters. Each method is shown to be applicable to a large class of linearly parameterized nonlinear discretetime system. In each
case, parameter convergence is guaranteed subject to an appropriate convergence condition, which has been related to a classical persistence of excitation condition. The effectiveness of
the methods is demonstrated using a simulation example. The application of the uncertainty set technique to nonlinearly parameterized systems constitutes the main contribution of the thesis. The parameter uncertainty set method is generalized to the problem of adaptive estimation in nonlinearly parameterized systems, for both continuoustime and discretetime cases. The method is demonstrated to perform well in simulation for a simplified model of a bioreactor operating under Monod kinetics. / Thesis (Master, Chemical Engineering)  Queen's University, 20101019 10:58:24.888

2 
Nonlinear identification and control of building structures equipped with magnetorheological dampersKim, Yeesock 15 May 2009 (has links)
A new system identification algorithm, multiple autoregressive exogenous
(ARX) inputsbased TakagiSugeno (TS) fuzzy model, is developed to identify nonlinear
behavior of structuremagnetorheological (MR) damper systems. It integrates a set of
ARX models, clustering algorithms, and weighted least squares algorithm with a TS
fuzzy model. Based on a set of inputoutput data that is generated from building
structures equipped with MR dampers, premise parameters of the ARXTS fuzzy model
are determined by clustering algorithms. Once the premise part is constructed,
consequent parameters of the ARXTS fuzzy model are optimized by the weighted least
squares algorithm. To demonstrate the effectiveness of the proposed ARXTS fuzzy
model, it is applied to a three, an eight, a twentystory building structures. It is
demonstrated from the numerical simulation that the proposed ARXTS fuzzy algorithm
is effective to identify nonlinear behavior of seismically excited building structures
equipped with MR dampers.
A new semiactive nonlinear fuzzy control (SNFC) algorithm is developed
through integration of multiple Lyapunovbased state feedback gains, a Kalman filter, and a converting algorithm with TS fuzzy interpolation method. First, the nonlinear
ARXTS fuzzy model is decomposed into a set of linear dynamic models that are
operated in only a local linear operating region. Based on the decomposed models,
multiple Lyapunovbased state feedback controllers are formulated in terms of linear
matrix inequalities (LMIs) such that the structureMR damper system is globally
asymptotically stable and the performance on transient responses is guaranteed. Then,
the state feedback controllers are integrated with a Kalman filter and a converting
algorithm using a TS fuzzy interpolation method to construct semiactive output feedback
controllers. To demonstrate the effectiveness of the proposed SNFC algorithm, it is
applied to a three, an eight, and a twentystory building structures. It is demonstrated
from the numerical simulation that the proposed SNFC algorithm is effective to control
responses of seismically excited building structures equipped with MR dampers. In
addition, it is shown that the proposed SNFC system is better than a traditional optimal
algorithm, H2/linear quadratic Gaussianbased semiactive control strategy.

3 
Identification Techniques for Mathematical Modeling of the Human Smooth Pursuit SystemJansson, Daniel January 2015 (has links)
This thesis proposes nonlinear system identification techniques for the mathematical modeling of the human smooth pursuit system (SPS) with application to motor symptom quantification in Parkinson's disease (PD). The SPS refers to the complex neuromuscular system in humans that governs the smooth pursuit eye movements (SPEM). Insight into the SPS and its operation is of importance in a wide and steadily expanding array of application areas and research fields. The ultimate purpose of the work in this thesis is to attain a deeper understanding and quantification of the SPS dynamics and thus facilitate the continued development of novel commercial products and medical devices. The main contribution of this thesis is in the derivation and evaluation of several techniques for SPS characterization. While attempts to mathematically model the SPS have been made in the literature before, several key aspects of the problem have been previously overlooked.This work is the first one to devise dynamical models intended for extendedtime experiments and also to consider systematic visual stimuli design in the context of SPS modeling. The result is a handful of parametric mathematical models outperforming current StateoftheArt models in terms of prediction accuracy for rich input signals. As a complement to the parametric dynamical models, a nonparametric technique involving the construction of individual statistical models pertaining to specific gaze trajectories is suggested. Both the parametric and nonparametric models are demonstrated to successfully distinguish between individuals or groups of individuals based on eye movements.Furthermore, a novel approach to Wiener system identification using Volterra series is proposed and analyzed. It is exploited to confirm that the SPS in healthy individuals is indeed nonlinear, but that the nonlinearity of the system is significantly stronger in PD subjects. The nonlinearity in healthy individuals appears to be wellmodeled by a static output function, whereas the nonlinear behavior introduced to the SPS by PD is dynamical.

4 
Particle detection, extraction, and state estimation in single particle tracking microscopyLin, Ye 20 June 2022 (has links)
Single Particle Tracking (SPT) plays an important role in the study of physical and dynamic properties of biomolecules moving in their native environment. To date, many algorithms have been developed for localization and parameter estimation in SPT. Though the performance of these methods is good when the signal level is high and the motion model simple, they begin to fail as the signal level decreases or model complexity increases. In addition, the inputs to the SPT algorithms are sequences of images that are cropped from a large data set and that focus on a single particle. This motivates us to seek machine learning tools to deal with that initial step of extracting data from larger images containing multiple particles. This thesis makes contributions to both data extraction question and to the problem of state and parameter estimation.
First, we build upon the Expectation Maximization (EM) algorithm to create a generic framework for joint localization refinement and parameter estimation in SPT. Under the EMbased scheme, two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo  Expectation Maximization (SMCEM), and Unscented  Expectation Maximization (UEM). The selection of filtering and smoothing algorithms is very flexible so long as they provide the necessary distributions for EM. The versatility and reliability of EM based framework have been validated via dataintensive modeling and simulation where we considered a variety of influential factors, such as a wide range of {\color{red}Signaltobackground ratios (SBRs)}, diffusion speeds, motion blur, camera types, image length, etc.
Meanwhile, under the EMbased scheme, we make an effort to improve the overall computational efficiency by simplifying the mathematical expression of models, replacing filtering/smoothing algorithms with more efficient ones {\color{purple} (trading some accuracy for reduced computation time)}, and using parallel computation and other computing techniques. In terms of localization refinement and parameter estimation in SPT, we also conduct an overall quantitative comparison among EM based methods and standard twostep methods. Regarding the UEM, we conduct transformation methods to make it adapted to the nonlinearities and complexities of measurement model. We also extended the application of UEM to more complicated SPT scenarios, including timevarying parameters and additional observation models that are relevant to the biophysical setting.
The second area of contribution is in the particle detection and extraction problem to create data to feed into the EMbased approaches. Here we build Particle Identification Networks (PINs) covering three different network architectures. The first, \PINCNN{}, is based on a standard Convolutional Neural Network (CNN) structure that has previously been successfully applied in particle detection and localization. The second, \PINRES, uses a Residual Neural Network (ResNet) architecture that is significantly deeper than the CNN while the third, \PINFPN{}, is based on a more advanced Feature Pyramid Network (FPN) that can take advantage of multiscale information in an image. All networks are trained using the same collection of simulated data created with a range of SBRs and fluorescence emitter densities, as well as with three different Point Spread Functions (PSFs): a standard BornWolf model, a model for astigmatic imaging to allow localization in three dimensions, and a model of the DoubleHelix engineered PSF. All PINs are evaluated and compared through dataintensive simulation and experiments under a variety of settings.
In the final contribution, we link all above together to create an algorithm that takes in raw camera data and produces trajectories and parameter estimates for multiple particles in an image sequence.

5 
Modeling and identification of nonlinear and impulsive systemsMattsson, Per January 2016 (has links)
Mathematical modeling of dynamical systems plays a central roll in science and engineering. This thesis is concerned with the process of finding a mathematical model, and it is divided into two parts  one that concentrates on nonlinear system identification and another one where an impulsive model of testosterone regulation is constructed and analyzed. In the first part of the thesis, a new latent variable framework for identification of a large class of nonlinear models is developed. In this framework, we begin by modeling the errors of a nominal predictor using a flexible stochastic model. The error statistics and the nominal predictor are then identified using the maximum likelihood principle. The resulting optimization problem is tackled using a majorizationminimization approach, resulting in a tuning parameterfree recursive identification method. The proposed method learns parsimonious predictive models. Many popular model structures can be expressed within the framework, and in the thesis it is applied to piecewise ARX models. In the first part, we also derive a recursive prediction error method based on the Hammerstein model structure. The convergence properties of the method are analyzed by application of the associated differential equation method, and conditions ensuring convergence are given. In the second part of the thesis, a previously proposed pulsemodulated feedback model of testosterone regulation is extended with infinitedimensional dynamics, in order to better explain testosterone profiles observed in clinical data. It is then shown how the analysis of oscillating solutions for the finitedimensional case can be extended to the infintedimensional case. A method for blind state estimation in impulsive systems is introduced, with the purpose estimating hormone concentrations that cannot be measured in a noninvasive way. The unknown parameters in the model are identified from clinical data and, finally, a method of incorporating exogenous signals portraying e.g. medical interventions is studied.

6 
Nonlinear Latent Variable Models for Video Sequencesrahimi, ali, recht, ben, darrell, trevor 06 June 2005 (has links)
Many highdimensional timevarying signals can be modeled as a sequence of noisy nonlinear observations of a lowdimensional dynamical process. Given highdimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm for estimating the inverse of this mapping. Once this mapping is learned, we can invert it to construct a generative model for the signals. Our algorithm can be thought of as learning a manifold of images by taking into account the dynamics underlying the lowdimensional representation of these images. It also serves as a nonlinear system identification procedure that estimates the inverse of the observation function in nonlinear dynamic system. Our algorithm reduces to a generalized eigenvalue problem, so it does not suffer from the computational or local minimum issues traditionally associated with nonlinear system identification, allowing us to apply it to the problem of learning generative models for video sequences.

7 
Identification of Thermoacoustic Dynamics Exhibiting Limit Cycle BehaviorEisenhower, Bryan A. 07 June 2000 (has links)
Identification of thermoacoustic dynamics that exhibit limit cycle behavior is needed to gain a better intuitive feel of the system, to design complex control strategies, and to validate modeling efforts. Limit cycle oscillations arise in thermoacoustic systems due to the coupling between a nonlinear heat release process and the acoustic dynamics of the combustor. This response arises in lean premixed gaseous power generating turbines and is a concern due to the detrimental effect of the pressure oscillations on the structural integrity of the combustor. Due to the volatile environment intrinsic in the combustor, multiple sensing apparatuses are not available. Therefore, in the current study, an identification approach is assessed considering only a single output from the thermoacoustic system.
As a means to further investigate the thermoacoustic limit cycle behavior, a scaled version of the industrybased turbine was constructed. By anchoring a flame halfway from endtoend of a closedopen tube, a similar nonlinear response is achieved. A harmonic balance technique that linearly incorporates the nonlinearity is developed which uses frequency entrainment to offer sufficient information for the identification. Its validity is assessed on a model, which is based on known dynamics of the thermoacoustic system. The structure of the identification algorithm is based on a twomode acoustic model with both dynamics and nonlinearity in the feedback loop. The limitations of using only a twomode identification structure for a system with more than two modes is discussed as well as future efforts that may alleviate this problem. / Master of Science

8 
Nonlinear model predictive control using automatic differentiationAl Seyab, Rihab Khalid Shakir January 2006 (has links)
Although nonlinear model predictive control (NMPC) might be the best choice for a
nonlinear plant, it is still not widely used. This is mainly due to the computational
burden associated with solving online a set of nonlinear differential equations and a
nonlinear dynamic optimization problem in real time. This thesis is concerned with
strategies aimed at reducing the computational burden involved in different stages
of the NMPC such as optimization problem, state estimation, and nonlinear model
identification.
A major part of the computational burden comes from function and derivative evaluations
required in different parts of the NMPC algorithm. In this work, the problem is
tackled using a recently introduced efficient tool, the automatic differentiation (AD).
Using the AD tool, a function is evaluated together with all its partial derivative from
the code defining the function with machine accuracy.
A new NMPC algorithm based on nonlinear least square optimization is proposed.
In a first–order method, the sensitivity equations are integrated using a linear formula
while the AD tool is applied to get their values accurately. For higher order
approximations, more terms of the Taylor expansion are used in the integration for
which the AD is effectively used. As a result, the gradient of the cost function against
control moves is accurately obtained so that the online nonlinear optimization can be
efficiently solved.
In many real control cases, the states are not measured and have to be estimated for
each instance when a solution of the model equations is needed. A nonlinear extended
version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose.
The AD tool is used to calculate the required derivatives in the local linearization
step of the filter automatically and accurately.
Offset is another problem faced in NMPC. A new nonlinear integration is devised
for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct
the plant/model mismatch. The time response of the controller is also improved as a
by–product.
The proposed NMPC algorithm has been applied to an evaporation process and a
two continuous stirred tank reactor (two–CSTR) process with satisfactory results to
cope with large setpoint changes, unmeasured severe disturbances, and process/model
mismatches.
When the process equations are not known (black–box) or when these are too complicated
to be used in the controller, modelling is needed to create an internal model for
the controller. In this thesis, a continuous time recurrent neural network (CTRNN)
in a state–space form is developed to be used in NMPC context. An efficient training
algorithm for the proposed network is developed using AD tool. By automatically
generating Taylor coefficients, the algorithm not only solves the differentiation equations
of the network but also produces the sensitivity for the training problem. The
same approach is also used to solve online the optimization problem of the NMPC.
The proposed CTRNN and the predictive controller were tested on an evaporator
and two–CSTR case studies. A comparison with other approaches shows that the
new algorithm can considerably reduce network training time and improve solution
accuracy.
For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is
implemented to control the system. In this work a nonlinear state–space class Wiener
model is used to identify the black–box model of the gasifier. A linear model of the
plant at zero–load is adopted as a base model for prediction. Then, a feedforward
neural network is created as the static gain for a particular output channel, fuel gas
pressure, to compensate its strong nonlinear behavior observed in open–loop simulations.
By linearizing the neural network at each sampling time, the static nonlinear
gain provides certain adaptation to the linear base model. The AD tool is used here
to linearize the neural network efficiently. Noticeable performance improvement is
observed when compared with pure linear MPC. The controller was able to pass all
tests specified in the benchmark problem at all load conditions.

9 
Nonlinear System Identification and Analysis with Applications to Power Amplifier Modeling and Power Amplifier PredistortionRaich, Raviv 07 April 2004 (has links)
Power amplifiers (PAs) are important components of communication
systems and are inherently nonlinear. When a nonconstant modulus
signal goes through a nonlinear PA, spectral regrowth (broadening)
appears in the PA output, which in turn causes adjacent channel
interference (ACI). Stringent limits on the ACI are imposed by
regulatory bodies, and thus the extent of the PA nonlinearity must
be controlled. PA linearization is often necessary to suppress
spectral regrowth, contain adjacent channel interference, and
reduce bit error rate (BER). This dissertation addresses the
following aspects of power amplifier research: modeling,
linearization, and spectral regrowth analysis.
We explore the passband and baseband PA input/output relationships
and show that they manifest differently when the PA exhibits
longterm, shortterm, or no memory effects. The socalled
quasimemoryless case is especially clarified. Four particular
nonlinear models with memory are further investigated. We provide
experimental results to support our analysis.
The benefits of using the orthogonal polynomials as opposed to the
conventional polynomials are explored, in the context of digital
baseband PA modeling and predistorter design. A closedform
expression for the orthogonal polynomial basis is derived. We
demonstrate the improvement in numerical stability associated with
the use of orthogonal polynomials for predistortion.
Spectral analysis can help to evaluate the suitability of a given
PA for amplifying certain signals or to assist in predistortion
linearization algorithm design. With the orthogonal polynomials
that we derived, spectral analysis of the nonlinear PA becomes a
straightforward task. We carry out nonlinear spectral analysis
with digitally modulated signal as input. We demonstrate an
analytical approach for evaluating the power spectra of filtered
QPSK and OQPSK signals after nonlinear amplification.
Many communications devices are nonlinear and have a peak power or
peak amplitude constraint. In addition to possibly amplifying the
useful signal, the nonlinearity also generates distortions. We
focus on signaltonoiseanddistortion ratio (SNDR) optimization
within the family of amplitude limited memoryless nonlinearities.
We obtain a link between the capacity of amplitudelimited
nonlinear channels with Gaussian noise to the SNDR.

10 
Multiresolution methods for high fidelity modeling and control allocation in largescale dynamical systemsSingla, Puneet 16 August 2006 (has links)
This dissertation introduces novel methods for solving highly challenging model
ing and control problems, motivated by advanced aerospace systems. Adaptable, ro
bust and computationally effcient, multiresolution approximation algorithms based
on Radial Basis Function Network and GlobalLocal Orthogonal Mapping approaches
are developed to address various problems associated with the design of large scale
dynamical systems. The main feature of the Radial Basis Function Network approach
is the unique direction dependent scaling and rotation of the radial basis function via
a novel Directed Connectivity Graph approach. The learning of shaping and rota
tion parameters for the Radial Basis Functions led to a broadly useful approximation
approach that leads to global approximations capable of good local approximation
for many moderate dimensioned applications. However, even with these refinements,
many applications with many high frequency local input/output variations and a
high dimensional input space remain a challenge and motivate us to investigate an
entirely new approach. The GlobalLocal Orthogonal Mapping method is based upon
a novel averaging process that allows construction of a piecewise continuous global
family of local leastsquares approximations, while retaining the freedom to vary in
a general way the resolution (e.g., degrees of freedom) of the local approximations.
These approximation methodologies are compatible with a wide variety of disciplines
such as continuous function approximation, dynamic system modeling, nonlinear signal processing and time series prediction. Further, related methods are developed
for the modeling of dynamical systems nominally described by nonlinear differential
equations and to solve for static and dynamic response of Distributed Parameter Sys
tems in an effcient manner. Finally, a hierarchical control allocation algorithm is
presented to solve the control allocation problem for highly overactuated systems
that might arise with the development of embedded systems. The control allocation
algorithm makes use of the concept of distribution functions to keep in check the
"curse of dimensionality". The studies in the dissertation focus on demonstrating,
through analysis, simulation, and design, the applicability and feasibility of these ap
proximation algorithms to a variety of examples. The results from these studies are
of direct utility in addressing the "curse of dimensionality" and frequent redundancy
of neural network approximation.

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