54 research outputs found
Identification of low order models for large scale processes
Many industrial chemical processes are complex, multi-phase and large scale in nature. These processes are characterized by various nonlinear physiochemical effects and fluid flows. Such processes often show coexistence of fast and slow dynamics during their time evolutions. The increasing demand for a flexible operation of a complex process, a pressing need to improve the product quality, an increasing energy cost and tightening environmental regulations make it rewarding to automate a large scale manufacturing process. Mathematical tools used for process modeling, simulation and control are useful to meet these challenges. Towards this purpose, development of process models, either from the first principles (conservation laws) i.e. the rigorous models or the input-output data based models constitute an important step. Both types of models have their own advantages and pitfalls. Rigorous process models can approximate the process behavior reasonably well. The ability to extrapolate the rigorous process models and the physical interpretation of their states make them more attractive for the automation purpose over the input-output data based identified models. Therefore, the use of rigorous process models and rigorous model based predictive control (R-MPC) for the purpose of online control and optimization of a process is very promising. However, due to several limitations e.g. slow computation speed and the high modeling efforts, it becomes difficult to employ the rigorous models in practise. This thesis work aims to develop a methodology which will result in smaller, less complex and computationally efficient process models from the rigorous process models which can be used in real time for online control and dynamic optimization of the industrial processes. Such methodology is commonly referred to as a methodology of Model (order) Reduction. Model order reduction aims at removing the model redundancy from the rigorous process models. The model order reduction methods that are investigated in this thesis, are applied to two benchmark examples, an industrial glass manufacturing process and a tubular reactor. The complex, nonlinear, multi-phase fluid flow that is observed in a glass manufacturing process offers multiple challenges to any model reduction technique. Often, the rigorous first principle models of these benchmark examples are implemented in a discretized form of partial differential equations and their solutions are computed using the Computational Fluid Dynamics (CFD) numerical tools. Although these models are reliable representations of the underlying process, computation of their dynamic solutions require a significant computation efforts in the form of CPU power and simulation time. The glass manufacturing process involves a large furnace whose walls wear out due to the high process temperature and aggressive nature of the molten glass. It is shown here that the wearing of a glass furnace walls result in change of flow patterns of the molten glass inside the furnace. Therefore it is also desired from the reduced order model to approximate the process behavior under the influence of changes in the process parameters. In this thesis the problem of change in flow patterns as result of changes in the geometric parameter is treated as a bifurcation phenomenon. Such bifurcations exhibited by the full order model are detected using a novel framework of reduced order models and hybrid detection mechanisms. The reduced order models are obtained using the methods explained in the subsequent paragraphs. The model reduction techniques investigated in this thesis are based on the concept of Proper Orthogonal Decompositions (POD) of the process measurements or the simulation data. The POD method of model reduction involves spectral decomposition of system solutions and results into arranging the spatio-temporal data in an order of increasing importance. The spectral decomposition results into spatial and temporal patterns. Spatial patterns are often known as POD basis while the temporal patterns are known as the POD modal coefficients. Dominant spatio-temporal patterns are then chosen to construct the most relevant lower dimensional subspace. The subsequent step involves a Galerkin projection of the governing equations of a full order first principle model on the resulting lower dimensional subspace. This thesis can be viewed as a contribution towards developing the databased nonlinear model reduction technique for large scale processes. The major contribution of this thesis is presented in the form of two novel identification based approaches to model order reduction. The methods proposed here are based on the state information of a full order model and result into linear and nonlinear reduced order models. Similar to the POD method explained in the previous paragraph, the first step of the proposed identification based methods involve spectral decomposition. The second step is different and does not involve the Galerkin projection of the equation residuals. Instead, the second step involves identification of reduced order models to approximate the evolution of POD modal coefficients. Towards this purpose, two different methods are presented. The first method involves identification of locally valid linear models to represent the dynamic behavior of the modal coefficients. Global behavior is then represented by ‘blending’ the local models. The second method involves direct identification of the nonlinear models to represent dynamic evolution of the model coefficients. In the first proposed model reduction method, the POD modal coefficients, are treated as outputs of an unknown reduced order model that is to be identified. Using the tools from the field of system identification, a blackbox reduced order model is then identified as a linear map between the plant inputs and the modal coefficients. Using this method, multiple local reduced LTI models corresponding to various working points of the process are identified. The working points cover the nonlinear operation range of the process which describes the global process behavior. These reduced LTI models are then blended into a single Reduced Order-Linear Parameter Varying (ROLPV) model. The weighted blending is based on nonlinear splines whose coefficients are estimated using the state information of the full order model. Along with the process nonlinearity, the nonlinearity arising due to the wear of the furnace wall is also approximated using the RO-LPV modeling framework. The second model reduction method that is proposed in this thesis allows approximation of a full order nonlinear model by various (linear or nonlinear) model structures. It is observed in this thesis, that, for certain class of full order models, the POD modal coefficients can be viewed as the states of the reduced order model. This knowledge is further used to approximate the dynamic behavior of the POD modal coefficients. In particular, reduced order nonlinear models in the form of tensorial (multi-variable polynomial) systems are identified. In the view of these nonlinear tensorial models, the stability and dissipativity of these models is investigated. During the identification of the reduced order models, the physical interpretation of the states of the full order rigorous model is preserved. Due to the smaller dimension and the reduced complexity, the reduced order models are computationally very efficient. The smaller computation time allows them to be used for online control and optimization of the process plant. The possibility of inferring reduced order models from the state information of a full order model alone i.e. the possibility to infer the reduced order models in the absence of access to the governing equations of a full order model (as observed for many commercial software packages) make the methods presented here attractive. The resulting reduced order models need further system theoretic analysis in order to estimate the model quality with respect to their usage in an online controller setting
時間と周波数領域情報に基づいたシステムモデリングとその応用
System modeling is required to deal with the time-varying system dynamics or the experimental data with insufficient information. However, the existing methods cannot construct satisfactory models for rapidly varying systems or severely band-limited signals. This thesis focuses on the new approaches to solve such system modeling problems based on time and frequency-domain information and illustrates their applications in time-varying channel identification and localization system. For the rapid time-varying systems, parameters can be approximated by the cosine series using virtual even periodic functions. Following the orthogonality of the trigonometric functions, the parameter estimation is recursively implemented by estimating the coefficients of each degree of the cosine harmonic term. For the localization system with insufficient frequency components, the spectral characteristics including phase information in frequency domain and the information evaluation in time domain are applied to improve the convergence performance. Numerical simulations demonstrate the effectiveness of the new approaches.北九州市立大
Machine Learning-based Brokers for Real-time Classification of the LSST Alert Stream
The unprecedented volume and rate of transient events that will be discovered
by the Large Synoptic Survey Telescope (LSST) demands that the astronomical
community update its followup paradigm. Alert-brokers -- automated software
system to sift through, characterize, annotate and prioritize events for
followup -- will be critical tools for managing alert streams in the LSST era.
The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is
one such broker. In this work, we develop a machine learning pipeline to
characterize and classify variable and transient sources only using the
available multiband optical photometry. We describe three illustrative stages
of the pipeline, serving the three goals of early, intermediate and
retrospective classification of alerts. The first takes the form of variable vs
transient categorization, the second, a multi-class typing of the combined
variable and transient dataset, and the third, a purity-driven subtyping of a
transient class. While several similar algorithms have proven themselves in
simulations, we validate their performance on real observations for the first
time. We quantitatively evaluate our pipeline on sparse, unevenly sampled,
heteroskedastic data from various existing observational campaigns, and
demonstrate very competitive classification performance. We describe our
progress towards adapting the pipeline developed in this work into a real-time
broker working on live alert streams from time-domain surveys.Comment: 33 pages, 14 figures, submitted to ApJ
Validation practices for satellite based earth observation data across communities
Assessing the inherent uncertainties in satellite data products is a challenging task. Different technical approaches have been developed in the Earth Observation (EO) communities to address the validation problem which results in a large variety of methods as well as terminology. This paper reviews state-of-the-art methods of satellite validation and documents their similarities and differences. First the overall validation objectives and terminologies are specified, followed by a generic mathematical formulation of the validation problem. Metrics currently used as well as more advanced EO validation approaches are introduced thereafter. An outlook on the applicability and requirements of current EO validation approaches and targets is given
Continuous time model identification using sinusoidal response
System identification is an interface that unites the mathematical world of control theory
and practical applications of control; as such its significance is omnipresent. Identification
techniques involve differential equations where the coefficients are closely
related to the physical parameters in the system; continuous time models have greater
appeal than its discrete-time counterpart in understanding these interpretations. In
this study, we have considered sinusoidal input for identification purpose as it has
been discussed in the context of designing optimal input and also because it facilitates
to excite processes with particular frequencies of interest. The primary objective
of this work focuses on process parameter estimation. At first, integer order model
is studied due to its simplicity, as order estimation is not necessary and thus the
structure of the model. In addition, a comparison between different identification
methods for better parameter estimates is performed on integer order model. Following
on, fractional order model is taken into consideration with known and unknown
order estimates. When solving for unknown model order, more emphasis is given on
the logarithmic derivative term. According to literature, the unknown model order
is estimated numerically whereas we provide an analytical expression of logarithmic
derivative of sinusoidal inputs considering deterministic approach. For integer order
model, although satisfactory results were achieved in terms of parameter estimates
for different approaches varying different input constraints, it was evident that the performances varied with data length, and more importantly with the frequency of
the input signal. The developed methodology for fractional order model identification
with known model order lead fairly accurate estimates of the process parameters and
when extended for unknown model order, exhibited highly satisfactory results as well
but with higher computational time. The main challenge of this study was optimizing
process parameters based on convergence; this issue was studied in simulation and
corresponding numerical results for diverse noise levels met our expectations
Multichannel Analysis of Intracardiac Electrograms - Supporting Diagnosis and Treatment of Cardiac Arrhythmias
Cardiologists diagnose and treat atrial tachycardias using electroanatomical mapping systems. These can be combined with multipolar catheters to record intracardiac electrograms. Within this thesis, various signal processing techniques were implemented and benchmarked to analyze electrograms. They support the physician in diagnosis and treatment of atrial flutter and atrial fibrillation. The developed methods were assessed using simulated data and demonstrated on clinical cases
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