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1 
State space model extraction of thermohydraulic systems / Kenneth R. UrenUren, Kenneth Richard January 2009 (has links)
Many hours are spent by systemand control engineers deriving reduced order dynamicmodels
portraying the dominant systemdynamics of thermohydraulic systems. A need therefore exists
to develop a method that will automate the model derivation process. The model format
preferred for control system design and analysis during preliminary system design is the state
space format. The aim of this study is therefore to develop an automated and generic state
space model extraction method that can be applied to thermohydraulic systems.
Well developed system identiﬁcation methods exist for obtaining state space models from
inputoutput data, but these models are not transparent, meaning the parameters do not
have any physical meaning. For example one cannot identify system parameters such
as heat or mass transfer coefﬁcients. Another approach is needed to derive state space
models automatically. Many commercial thermohydraulic simulation codes follow a network
approach towards the representation of thermohydraulic systems. This approach is probably
one of the most advanced approaches in terms of technical development. It would therefore be
useful to develop a state space extraction algorithm that would be able to derive reduced order
state space models from network representations of thermohydraulic systems. In this regard a
network approach is followed in the development of the state space extraction algorithm. The
advantage of using a networkbased extraction method is that the extracted state space model
is transparent and the algorithm can be embedded in existing simulation software that follow
a network approach.
In this study an existing state space extraction algorithm, used for electrical network analysis, is
modiﬁed and applied in a new way to extract state space models of thermohydraulic systems.
A thermohydraulic system is partitioned into its respective physical domains which, unlike
electrical systems, have multiple variables. Network representations are derived for each
domain. The state space algorithm is applied to these network representations to extract
symbolic state spacemodels. The symbolic parametersmay then be substitutedwith numerical
values. The state space extraction algorithm is applied to small scale thermohydraulic systems
such as a Utube and a heat exchanger, but also to a larger, more complex system such
as the Pebble Bed Modular Reactor Power Conversion Unit (PBMR PCU). It is also shown
that the algorithm can extract linear, nonlinear, timevarying and timeinvariant state space
models. The extracted state space models are validated by solving the state space models
and comparing the solutions with Flownex results. Flownex is an advanced and extensively
validated thermoﬂuid simulation code. The state space models compared well with Flownex
results.
The usefulness of the state space model extraction algorithm in modelbased control system
design is illustrated by extracting a linear timeinvariant state space model of the PBMR PCU.
This model is embedded in an optimal modelbased control scheme called ModelPredictive
Control (MPC). The controller is compared with standard optimised control schemes such as
PID and Fuzzy PID control. The MPC controller shows superior performance compared to
these control schemes.
This study succeeded in developing an automated state space model extraction method that
can be applied to thermohydraulic networks. Hours spent on writing down equations from
ﬁrst principles to derive reduced order models for control purposes can now be replaced
with a click of a button. The need for an automated state space model extraction method for
thermohydraulic systems has therefore been resolved / Thesis (Ph.D. (Computer and Electronical Engineering)NorthWest University, Potchefstroom Campus, 2009.

2 
State space model extraction of thermohydraulic systems / Kenneth R. UrenUren, Kenneth Richard January 2009 (has links)
Many hours are spent by systemand control engineers deriving reduced order dynamicmodels
portraying the dominant systemdynamics of thermohydraulic systems. A need therefore exists
to develop a method that will automate the model derivation process. The model format
preferred for control system design and analysis during preliminary system design is the state
space format. The aim of this study is therefore to develop an automated and generic state
space model extraction method that can be applied to thermohydraulic systems.
Well developed system identiﬁcation methods exist for obtaining state space models from
inputoutput data, but these models are not transparent, meaning the parameters do not
have any physical meaning. For example one cannot identify system parameters such
as heat or mass transfer coefﬁcients. Another approach is needed to derive state space
models automatically. Many commercial thermohydraulic simulation codes follow a network
approach towards the representation of thermohydraulic systems. This approach is probably
one of the most advanced approaches in terms of technical development. It would therefore be
useful to develop a state space extraction algorithm that would be able to derive reduced order
state space models from network representations of thermohydraulic systems. In this regard a
network approach is followed in the development of the state space extraction algorithm. The
advantage of using a networkbased extraction method is that the extracted state space model
is transparent and the algorithm can be embedded in existing simulation software that follow
a network approach.
In this study an existing state space extraction algorithm, used for electrical network analysis, is
modiﬁed and applied in a new way to extract state space models of thermohydraulic systems.
A thermohydraulic system is partitioned into its respective physical domains which, unlike
electrical systems, have multiple variables. Network representations are derived for each
domain. The state space algorithm is applied to these network representations to extract
symbolic state spacemodels. The symbolic parametersmay then be substitutedwith numerical
values. The state space extraction algorithm is applied to small scale thermohydraulic systems
such as a Utube and a heat exchanger, but also to a larger, more complex system such
as the Pebble Bed Modular Reactor Power Conversion Unit (PBMR PCU). It is also shown
that the algorithm can extract linear, nonlinear, timevarying and timeinvariant state space
models. The extracted state space models are validated by solving the state space models
and comparing the solutions with Flownex results. Flownex is an advanced and extensively
validated thermoﬂuid simulation code. The state space models compared well with Flownex
results.
The usefulness of the state space model extraction algorithm in modelbased control system
design is illustrated by extracting a linear timeinvariant state space model of the PBMR PCU.
This model is embedded in an optimal modelbased control scheme called ModelPredictive
Control (MPC). The controller is compared with standard optimised control schemes such as
PID and Fuzzy PID control. The MPC controller shows superior performance compared to
these control schemes.
This study succeeded in developing an automated state space model extraction method that
can be applied to thermohydraulic networks. Hours spent on writing down equations from
ﬁrst principles to derive reduced order models for control purposes can now be replaced
with a click of a button. The need for an automated state space model extraction method for
thermohydraulic systems has therefore been resolved / Thesis (Ph.D. (Computer and Electronical Engineering)NorthWest University, Potchefstroom Campus, 2009.

3 
Knowledge Discovery Through Probabilistic ModelsRistovski, Kosta January 2012 (has links)
Probabilistic models are dominant in many research areas. To learn those models we need to find a way to determine parameters of distributions over variables which are included in the model. The main focus of my research is related to continuous variables. Thus, Gaussian distribution over variables is the most dominant factor in all models used in this document. I have been working on different and important reallife problems such as Uncertainty of Neural Network Based Aerosol Retrieval, Regression Learning with Multiple Noise Oracles and Model Predictive Control (MPC) for Sepsis Treatment, Clustering Causes of Action in Federal Courts. These problems will be discussed in the following chapters. Aerosols, small particles emanating from natural and manmade sources, along with green house gases have been recognized as very important factors in ongoing climate changes. Accurate estimation of aerosol composition and concentration is one of the main challenges in current climate research. Algorithm for prediction of aerosol designed by domain scientists does not provide quantitative information about aerosol estimation uncertainty. We deployed algorithm which uses neural networks to determine both uncertainty and the estimation of the aerosol. The uncertainty estimator has been built under an assumption that uncertainty is a function of variables used for aerosol prediction. Also, the uncertainty of predictions has been computed as the variance of the conditional distribution of targets given the input data. In regression learning, it is often difficult to obtain the true values of the label variables, while multiple sources of noisy estimates of lower quality are readily available. To address this problem, I propose a new Bayesian approach that learns a regression model from a data with noisy labels which are provided by multiple oracles. This method gives closed form solution for model parameters and it is applicable to both linear and nonlinear regression problems. Sepsis is a medical condition characterized as a systemic inflammatory response to an infection. High mortality rate (3035%) of septic patients is usually caused by inadequate treatment. Thus, development of tools that can aid clinicians in designing optimal strategies for inflammation treatments is of utmost importance. Towards this objective I developed a data driven approach for therapy optimization where a predictive model for patients' behavior is learned directly from historical data. As such, the predictive model is incorporated into a model predictive control optimization algorithm to find optimal therapy, which will lead the patient to a healthy state. A more careful targeting of specific therapeutic strategies to more biologically homogeneous groups of patients is essential to developing effective sepsis treatment. We propose a kernelbased approach to characterize dynamics of inflammatory response in a heterogeneous population of septic patients. The method utilizes Linear State Space Control (LSSC) models to take into account dynamics of inflammatory response over time as well as the effect of therapy applied to the patient. We use a similarity measure defined on kernels of LSSC models to find homogeneous groups of patients. In addition to clustering of dynamics of inflammatory response we also explored a clustering of civil litigation from its inception by examining the content of civil complaints. We utilize spectral cluster analysis on a newly compiled federal district court dataset of causes of action in complaints to illustrate the relationship of legal claims to one another, the broader composition of lawsuits in trial courts, and the breadth of pleading in individual complaints. Our results shed light not only on the networks of legal theories in civil litigation but also on how lawsuits are classified and the strategies that plaintiffs and their attorneys employ when commencing litigation. / Computer and Information Science

4 
Towards smooth particle filters for likelihood estimation with multivariate latent variablesLee, Anthony 11 1900 (has links)
In parametrized continuous statespace models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change.
When the state variables are univariate, a method exists that gives an estimator of the loglikelihood that is continuous in the parameters. We present a nontrivial generalization of this method using treebased o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers.
Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous.
In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous statespace models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical treebased resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

5 
Towards smooth particle filters for likelihood estimation with multivariate latent variablesLee, Anthony 11 1900 (has links)
In parametrized continuous statespace models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change.
When the state variables are univariate, a method exists that gives an estimator of the loglikelihood that is continuous in the parameters. We present a nontrivial generalization of this method using treebased o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers.
Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous.
In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous statespace models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical treebased resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

6 
Towards smooth particle filters for likelihood estimation with multivariate latent variablesLee, Anthony 11 1900 (has links)
In parametrized continuous statespace models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change.
When the state variables are univariate, a method exists that gives an estimator of the loglikelihood that is continuous in the parameters. We present a nontrivial generalization of this method using treebased o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers.
Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous.
In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous statespace models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical treebased resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion. / Science, Faculty of / Computer Science, Department of / Graduate

7 
Point process modeling and estimation: advances in the analysis of dynamic neural spiking dataDeng, Xinyi 12 August 2016 (has links)
A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecondtimescale spike patterns of neurons to understand higher brain functions.
Such relationships can often be formulated within the framework of statespace models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of statespace models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using historydependent structure, 2) to model population spike activity using marked point process models, 3) to allow for realtime decision making, and 4) to take into account the need for dimensionality reduction for highdimensional state and observation processes.
We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in realtime (for example, to stimulate the neurons or not) based on various sources of information present in population spiking data. Lastly, we proposed a general threestep paradigm that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas, which is a step towards closedloop therapies for psychological diseases using realtime neural stimulation. These methods are suitable for realtime implementation for contentbased feedback experiments.

8 
Forecast Comparison of Models Based on SARIMA and the Kalman Filter for InflationNikolaisen Sävås, Fredrik January 2013 (has links)
Inflation is one of the most important macroeconomic variables. It is vital that policy makers receive accurate forecasts of inflation so that they can adjust their monetary policy to attain stability in the economy which has been shown to lead to economic growth. The purpose of this study is to model inflation and evaluate if applying the Kalman filter to SARIMA models lead to higher forecast accuracy compared to just using the SARIMA model. The BoxJenkins approach to SARIMA modelling is used to obtain wellfitted SARIMA models and then to use a subset of observations to estimate a SARIMA model on which the Kalman filter is applied for the rest of the observations. These models are identified and then estimated with the use of monthly inflation for Luxembourg, Mexico, Portugal and Switzerland with the target to use them for forecasting. The accuracy of the forecasts are then evaluated with the error measures mean squared error (MSE), mean average deviation (MAD), mean average percentage error (MAPE) and the statistic Theil's U. For all countries these measures indicate that the Kalman filtered model yield more accurate forecasts. The significance of these differences are then evaluated with the DieboldMariano test for which only the difference in forecast accuracy of Swiss inflation is proven significant. Thus, applying the Kalman filter to SARIMA models with the target to obtain forecasts of monthly inflation seem to lead to higher or at least not lower predictive accuracy for the monthly inflation of these countries.

9 
Bayesian Model Discrimination and Bayes Factors for Normal Linear State Space ModelsFrühwirthSchnatter, Sylvia January 1993 (has links) (PDF)
It is suggested to discriminate between different state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. Practical implementation of this procedures requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters which is carried out by Markov chain Monte Carlo methods. Application to some nonstandard situations such as testing hypotheses on the boundary of the parameter space, discriminating nonnested models and discrimination of more than two models is discussed in detail. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

10 
Data Augmentation and Dynamic Linear ModelsFrühwirthSchnatter, Sylvia January 1992 (has links) (PDF)
We define a subclass of dynamic linear models with unknown hyperparameters called dinversegamma models. We then approximate the marginal p.d.f.s of the hyperparameter and the state vector by the data augmentation algorithm of Tanner/Wong. We prove that the regularity conditions for convergence hold. A sampling based scheme for practical implementation is discussed. Finally, we illustrate how to obtain an iterative importance sampling estimate of the model likelihood. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

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