"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:048cb071-3f03-484b-a20d-c688e23067a8","http://resolver.tudelft.nl/uuid:048cb071-3f03-484b-a20d-c688e23067a8","Learning to simulate and predict chaotic dynamical systems","Bakker, R.","Van den Bleek, C.M. (promotor); Schouten, J.C. (promotor)","2007","With precise knowledge of the rules which govern a deterministic chaotic system, it is possible to interact with the system and change its dynamics. This research is part of a larger project, in which chaos control is used to improve the bubbling behavior of multi-phase chemical reactors. Chaos control requires models which capture the complete behavior of the system. If we replace the system by its model, or vice versa, we should not notice a change in dynamical behavior. We restrict ourselves to data-driven models, which learn both their structure and parameters from measured data. In cooperation with Robert Jan de Korte [1], we use a neural network model to control the chaotic dynamics of an experimental, driven and damped pendulum. The neural network provides a nearly perfect model for this system. The gas-solids fluidized bed is a much more difficult system, because it has a large number of state variables, while the pendulum has only three. To get a good predictive model, the neural network approach is improved with several enhancements: (1) Inputs are compressed by weighted Principal Component Analysis. (2) An 'error propagation"" scheme is introduced, in the which the model synchronizes itself with the data. (3) The neural network is connected in parallel to a linear predictive model. (4) A new pruning algorithm removes unused nodes from the network. (5) A statistical test by Diks et. al. [3] compares the chaotic attractors of the model-generated and measured time series. The approach is succesfully applied to benchmark tests. But Diks' test reveals that during training, the correctness of the model's attractor jumps from right to wrong from one iteration to another. We investigate why this is, and present an example of a model which can predict the measured data with zero error, but yet has a very different attractor. This has far-reaching consequences. It turns out that the learning of an attractor from measured data is a very ill-posed problem, in which the data covers all available dimensions globally, but locally the data is confined to low-dimensional structures. When a global nonlinear model is trained on this data, it locally has too many degrees of freedom, and this leads to arbitrary dynamics. A Nonlinear Principal Component Regression (NLPCR) algorithm is needed, which locally detects and eliminates the unused dimensions. We develop the 'Split & Fit' (S&F) algorithm, based on a fuzzy partitioning of the input space. In each region, unused dimensions are detected with Principal Component Analysis (PCA). This algorithm is shown to keep an otherwise unstable model for a chaotic laser onto the desired trajectory. Meanwhile, Robert Jan de Korte found that deterministic prediction of gas-solids fluidized beds is not feasible. But the S&F algorithm does learn the attractor of another experimental reactor, a gas-liquid bubble column with a single train of rising bubbles [2]. The S&F model paves the way for robust learning of chaotic attractors. However, real-world systems rarely meet the requirement of determinism and low-dimensionality. For these systems, we recommend to develop algorithms which find structure in 'noisy' nonlinear behavior. A good starting point is to have a probabilistic representation (kernel smoother or mixture density) of how the measured data are distributed in state space. [1] R.J. De Korte (2000), ""Controlling the Chaotic Hydrodynamics of Fluidized Beds"", PhD thesis, Delft Unversity of Technology [2] S. Kaart (2002), ""Controlling Chaotic Bubbles"", PhD thesis, Delft Unversity of Technology [3] C. Diks, W.R. van Zwet, F. Takens, J. de Goede (1996), ""Detecting differences between delay vector distributions, pp. 2169--2176","deterministic chaos; time-series; dynamical system; chaotic attractor; multi-phase reactor; fluidized bed; chaos control; pendulum; bubble column","en","doctoral thesis","","","","","","","","","Applied Sciences","","","","",""
"uuid:6dd67142-c893-485a-b384-6ec500b51d72","http://resolver.tudelft.nl/uuid:6dd67142-c893-485a-b384-6ec500b51d72","Bubble columns: Structures or stability?","Harteveld, W.K.","Van den Akker, H.E.A. (promotor); Mudde, R.F. (promotor)","2005","The aim of the thesis is to contribute to the understanding of the hydrodynamics of the gravity driven bubbly flow that can be found in bubble columns. Special attention is paid to the large scale structures that have a strong impact on several key parameters such as the degree of mixing, mass and heat transfer. An experimental investigation has been performed in a bubble column with a needle sparger that allows for gas injection in well controlled patterns. Experimental teechniques such as Laser Doppler Anemometry (LDA) and glass fiber probes are employed, and their accuracy for application to bubbly flows is investigated and improved. Signal processing techniques are evaluated and improved, with special attention for techniques to determine turbulence power spectra for LDA signals obtained in bubbly flows. The hydrodynamics for uniform gas injection have been studied, with particular attention for the stability of the flow regime. The importance of the lift force for stability is discussed. The importance of non-uniformities in the gas injection on the flow is investigated, focusing on the behavior of both the entrance region and the bulk region. Finally, liquid velocity flucuations are studied: both the strength of the pseudo-turbulence and the turbulence power spectra are explored.","bubble column; bubbly flow; laser doppler anemometry; glass fiber probe; turbulence","en","doctoral thesis","","","","","","","","","Applied Sciences","","","","",""
"uuid:10486dfd-24f4-4044-bc1b-754dbc2bea70","http://resolver.tudelft.nl/uuid:10486dfd-24f4-4044-bc1b-754dbc2bea70","Scales and structures in bubbly flows. Experimental analysis of the flow in bubble columns and in bubbling fluidized beds","Groen, J.S.","Mudde, R.F. (promotor); Van den Akker, H.E.A. (promotor)","2004","In this project a detailed experimental analysis was performed of the dynamic flow field in bubbly flows, with the purpose of determining local hydrodynamics and scale effects. Measurements were done in gas-liquid systems (air-water bubble columns) and in gas-solid systems (air-sand bubbing fluidized beds) of different size. Amongst others with the help of lasers and glass fibres the behaviour was studied of single bubbles, bubble swarms and the continuous phase. These techniques were combined with advanced signal processing such as correlation analysis. A striking new phenomenon was the anisotropy or orientation dependence of experimental results. A detailed experimental study into the applicability of laser Doppler anemometry (LDA) in bubble columns showed that virtually only the liquid phase is recorded with LDA. The measurements show a pronouncedly turbulent flow field, but it is striking that this complex view can be characterized by a small number of fixed parameters. These parameters can also be used quite well for describing several physical phenomena and for scaling up these reactors.","bubble column; fluidized bed; bubbly flow; turbulence; laser doppler anemometry; glass fibre; coherent structures; dispersion; scale-up","en","doctoral thesis","","","","","","","","","Applied Sciences","","","","",""