Stochastic Modelling of Energy Systems

(2000). Experimental design and setup for heat exchanger modelling. International Journal of Heat Exchangers, Accepted for publication. (1999). Identification of continuous time smooth threshold models of physical systems. (2000). A model for the heat dynamics of a radiator. Submitted. (2000). Modeling of a thermostatic valve with hysteresis effects. Submitted. (2000). Modelling the heat dynamics of a building using stochastic differential equations. Energy and Buildings 31 1, 13-24. (2000). The error in variable (EIV) regression approach as a means of identifying unbiased physical parameter estimates. Submitted. iii iv Preface This thesis has been prepared at the Department of Mathematical Modelling (IMM), The Technical University of Denmark (DTU), in fulfilment of the requirements for the degree of Ph.D. in engineering. The thesis is concerned with grey box modelling of heating system components. The main contribution to this field is a discussion on how statistical techniques and physical insight can be combined in building models. As a result, dynamic models of heating system components are presented. Acknowledgements I wish to express my gratitude to all who have contributed to this research. First of all, I want to thank my academic advisor, Professor Henrik Madsen, IMM, DTU, for his help and guidance during this work. Professor Madsen's enthusiasm and insight into the discipline of mathematical modelling has been a source of inspiration and invaluable for this research. I also wish to thank Associate Professor Agami Reddy at Drexel University in Philadelphia, USA, with whom I have spent 9 month as a Visiting Researcher. During the stay at Drexel I have benefited greatly from Dr. Reddy's strong insight in the analysis and modelling of heating systems. During my research I have had the pleasure to work with very competent people from the Danish heating industry. I wish to thank the participants in the joint project IT-Energy, for good advises and interesting discussions. I would like to thank the participants from Grundfos A/S, Danfoss A/S, APV systems A/S, the Danish Technological Institute and the Energy Engineering Department at the Technical University of Denmark. Especially, I would like to thank Mr. Henrik Poulsen, chief of the Energy section at the Danish Technological Institute, for pushing me forward at certain times and for giving me the opportunity to participate in various projects. I am very grateful to Mr. Mads Lundby and Mr. Ole Knop, whom I have been advising and working with during their master's studies. It has …

[1]  Francis J. Doyle,et al.  Friction compensation for a process control valve , 2000 .

[2]  Henrik Aalborg Nielsen,et al.  Parametric and Non-Parametric System Modelling , 1999 .

[3]  Y. Kim.  Parameter estimation in infinite-dimensional stochastic differential equations , 1999 .

[4]  Jakob Birkedal Nielsen,et al.  New developments in the theory of wheel/rail contact mechanics , 1998 .

[5]  Ole Møller Nielsen,et al.  Wavelets in scientific computing , 1998 .

[6]  Frederick W. Faltin,et al.  Statistical Control by Monitoring and Feedback Adjustment , 1999, Technometrics.

[7]  Jørgen Folm-Hansen,et al.  On chromatic and geometrical calibration , 1999 .

[8]  Ragnar Norberg,et al.  Differential equations for moments of present values in life insurance , 1995 .

[9]  Ta‐Hsin Li.  Time‐correlation analysis of nonstationary time series , 1998 .

[10]  P. Dahl.  A Solid Friction Model , 1968 .

[11]  A. Vande Wouwer,et al.  Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design , 1996 .

[12]  Jesper Larsen,et al.  Parallelization of the Vehicle Routing Problem with Time Windows , 1999 .

[13]  Morten Bach Lauritsen,et al.  Delta-Domain Predictive Control and Identification for Control , 1997 .

[14]  Rune A Thorsen,et al.  Restoration of hand function in tetraplegics using myoelectrically controlled functional electrical| stimulation of the controlling muscle , 1997 .

[15]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Allan T. Andersen.  Modelling of packet traffic with matrix analytic methods , 1995 .

[17]  Henrik Melgaard,et al.  Identification of physical models , 1994 .

[18]  G. Jonsson,et al.  An Application of Extended Kalman Filtering to Heat Exchanger Models , 1994 .

[19]  P. Frank.  Robust Model-Based Fault Detection in Dynamic Systems , 1992 .

[20]  Knut Conradsen,et al.  Automated Determination of Crystal Orientations from Electron Backscattering Patterns , 1994 .

[21]  Peter Ulrik Vallø Skands,et al.  Quantitative methods for the analysis of electron microscope images , 1996 .

[22]  Todd M. Rossi,et al.  A Statistical, Rule-Based Fault Detection and Diagnostic Method for Vapor Compression Air Conditioners , 1997 .

[23]  P. Thomas,et al.  Model Validation , 2020, The Big R‐Book.

[24]  Xin Ma,et al.  Adaptive extremum control and wind turbine control. xix , 1997 .

[25]  Analysis of thermostat models , 1997, European Journal of Applied Mathematics.

[26]  Robert H. Shumway,et al.  The model selection criterion AICu , 1997 .

[27]  Susanne M. Balle.  Distributed-memory matrix computations , 1995 .

[28]  Jeffrey M. Gordon,et al.  How varying condenser coolant flow rate affects chiller performance: thermodynamic modeling and experimental confirmation , 2000 .

[29]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[30]  Allan Larsen,et al.  The Dynamic Vehicle Routing Problem , 2000 .

[31]  W. Wiechert,et al.  Stochastic simulation of biotechnical processes , 1996 .

[32]  Hensen,et al.  Application of Modelling and Simulation to Hva C Systems , 2022 .

[33]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[34]  Lennart Ljung,et al.  Modeling Of Dynamic Systems , 1994 .

[35]  J. Klein Woud,et al.  On-line failure diagnosis for compression refrigeration plants , 1995 .

[36]  A. Benonysson,et al.  Dynamic modelling and operational optimization of district heating systems , 1991 .

[37]  Uffe Høgsbro Thygesen,et al.  Robust Performance And Dissipation of Stochastic Control Systems , 1998 .

[38]  Jerzy Sowa.  Comparison of methods of including stochastic factors into deterministic models of indoor air quality , 1998 .

[39]  W. Wong.  FREQUENCY DOMAIN TESTS OF MULTIVARIATE GAUSSIANITY AND LINEARITY , 1997 .

[40]  Nickos Lazarides,et al.  Nonlinearity in superconductivity and Josephson Junctions , 1995 .

[41]  Wayne A. Fuller,et al.  Statistical analysis of measurement error models and applications : proceedings of the AMS-IMS-SIAM Joint Summer Research conference held June 10-16, 1989, with support from the National Science Foundation and the U.S. Army Research Office , 1990 .

[42]  Jens Moberg Rygaard.  Design and optimization of flexible manufacturing systems , 1994 .

[43]  Anca Daniela Hansen,et al.  Predictive control and identification: Applications to steering dynamics , 1996 .

[44]  Chunyan Wang,et al.  Stochastic differential equations and a biological system , 1994 .

[45]  John Aasted Sørensen,et al.  Signal processing for distribution network monitoring , 1999 .

[46]  Søren Aggerholm,et al.  Varme- og klimateknik: Grundbog , 1997 .

[47]  Philip Haves,et al.  Condition monitoring in HVAC subsystems using first principles models , 1996 .

[48]  K. Ng,et al.  Predictive and diagnostic aspects of a universal thermodynamic model for chillers , 1995 .

[49]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[50]  Kim Ø. Rasmussen,et al.  Nonlinear and stochastic dynamics of coherent structures , 1997 .

[51]  Xin Ma,et al.  Adaptive Extremum Control and Wind Turbine Control , 1997 .

[52]  S. D. Hansen,et al.  Hidden Markov models and neural networks for speech recognition , 1999 .

[53]  Jens Strodl Andersen,et al.  Statistical analysis of biotests - Applied to complex polluted samples , 1998 .

[54]  H.J.A.F. Tulleken.  Grey-box modelling and identification topics , 1992 .

[55]  H. Rake,et al.  Identification of a Large Water-Heated Crossflow Heat Exchanger with Binary Multifrequency Signals , 1985 .

[56]  C. Y. Han,et al.  Fault detection and diagnosis of HVAC systems , 1999 .

[57]  C. Park,et al.  Fault detection in an air-handling unit using residual and recursive parameter identification methods , 1996 .

[58]  Lars Kai Hansen,et al.  Optimization of recurrent neural networks for time series modeling , 1997 .

[59]  R. Khasminskii,et al.  On the estimation of parameters for linear stochastic differential equations , 1999 .

[60]  Hans True,et al.  On the interaction between wheels and rails in railway dynamics , 1995 .

[61]  M. Mcpherson,et al.  Introduction to fluid mechanics , 1997 .

[62]  Brian D. O. Anderson,et al.  On the choice of inputs in identification for robust control , 1999, Autom..

[63]  Peter L. Brooks,et al.  Visualizing data , 1997 .

[64]  H. Chaté,et al.  Statistical analysis of the transition to turbulence in plane Couette flow , 1998 .

[65]  C. Granger,et al.  USING THE MUTUAL INFORMATION COEFFICIENT TO IDENTIFY LAGS IN NONLINEAR MODELS , 1994 .

[66]  J. Shao.  Linear Model Selection by Cross-validation , 1993 .

[67]  Asok Ray,et al.  A stochastic model of fatigue crack propagation under variable-amplitude loading , 1999 .

[68]  Gábor Szederkényi,et al.  Grey box fault detection of heat exchangers , 2000 .

[69]  Torben Skov Nielsen,et al.  Online prediction and control in nonlinear stochastic systems , 2002 .

[70]  Helle Mølgaard Sommer,et al.  Variability in microbiological degradation experiments, analysis and case study , 1997 .

[71]  Katalin M. Hangos,et al.  Grey-Box Modeling for Identification and Control: An Emerging Discipline or an Established Technology? , 1994 .

[72]  Herbert J. A. F. Tulleken,et al.  Grey-box modelling and identification using physical knowledge and bayesian techniques , 1993, Autom..

[73]  Henrik Madsen,et al.  Fiction and reality in the modelling world – Balance between simplicity and complexity, calibration and identifiability, verification and falsification , 1999 .

[74]  Theis Leth Larsen,et al.  Phosphorus diffusion in float zone silicon crystal growth , 2000 .

[75]  Karsten Hartelius,et al.  Analysis of irregularly distributed points , 1996 .

[76]  Carlos Canudas de Wit,et al.  Friction Models and Friction Compensation , 1998, Eur. J. Control.

[77]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[78]  Robert Tenno,et al.  State and parameter estimation for wastewater treatment processes using a stochastic model , 1995 .

[79]  Martin B. Zarrop,et al.  Optimal experiment design for dynamic system identification , 1977 .

[80]  Dynamic analysis of a low energy test house and a central heating system , 1996 .

[81]  Keith R. Godfrey,et al.  Perturbation signals for system identification , 1993 .

[82]  Allan Aasbjerg Nielsen,et al.  Analysis of Regularly and Irregularly Sampled Spatial, Multivariate, and Multi-temporal Data , 1994 .

[83]  Jan Nygaard Nielsen,et al.  Parameter estimation in stochastic differential equations: An overview , 2000 .

[84]  Finn Aarup Nielsen.  Neuroinformatics in Functional Neuroimaging , 2002 .

[85]  Lars Kai Hansen,et al.  A probabilistic framework for classification of dermatoscopic images , 1999 .

[86]  Preben Kidmose,et al.  Blind separation of heavy tail signals , 2001 .

[87]  Sandro Macchietto,et al.  Statistical tools for optimal dynamic model building , 2000 .

[88]  H. Madsen,et al.  Identification of a Linear Continuous Time Stochastic Model of the Heat Dynamics of a Greenhouse , 1998 .

[89]  J. Roux,et al.  Elastic wave propagation in anisotropic materials , 1990, IEEE Symposium on Ultrasonics.

[90]  Hugh W. Coleman,et al.  Experimentation and Uncertainty Analysis for Engineers , 1989 .

[91]  Michael Pilegaard Hansen,et al.  Metaheuristics for multiple objective combinatorial optimization , 1998 .

[92]  Torsten Bohlin,et al.  Issues in Nonlinear Stochastic Grey-Box Identification , 1994 .

[93]  Daves.  What is Condition Monitoring , 1990 .

[94]  Sami Karjalainen,et al.  Performance factors as a basis of practical fault detection and diagnostic methods for air-handling units , 1999 .

[95]  Jens Christian Jensen,et al.  Teoretiske og eksperimentelle dynamiske undersøgelser af jernbanekøretøjer , 1995 .

[96]  Tim Helge Hultberg.  Topics in computational linear optimization , 2000 .

[97]  H. Bechmann.  Modelling of wastewater systems , 1999 .

[98]  Kaj Madsen,et al.  Automatic Validation of Numerical Solutions , 1997 .

[99]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[100]  Niklas Kohl,et al.  Exact methods for time constrained routing and related scheduling problems , 1995 .

[101]  Per Grove Thomsen,et al.  Hemodynamic simulation of the heart using a 2D model and MR data , 2002 .

[102]  Lars Kai Hansen,et al.  A Multivariate Approach to Functional Neuro Modeling , 1998 .

[103]  G. Reuter,et al.  A stochastic model of global atmospheric response to enhanced greenhouse warming with cloud feedback , 1998 .

[104]  Peter Thyregod,et al.  MODELLING AND MONITORING IN INJECTION MOLDING , 2001 .

[105]  C. Bendtsen,et al.  Parallel Numerical Algorithms for the Solution of Systems of Ordinary Differential Equations , 1996 .

[106]  Claus Gramkow,et al.  2D and 3D object measurement for control and quality assurance in the industry , 1999 .

[107]  Vlad Bally,et al.  Construction of asymptotically optimal controls for control and game problems , 1998 .

[108]  Kenneth Arisman.  An Experiment in Design , 1936 .

[109]  Claus Jørgensen,et al.  Driftsoptimering på kraftvarmesystemer , 1997 .

[110]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

[111]  Per S. Sørensen,et al.  Spatial distribution maps for benthic communities , 1999 .

[112]  Olafur P. Palsson,et al.  Modeling and Parameter Estimation of Heat Exchangers—A Statistical Approach , 1992 .

[113]  C. Bianchi,et al.  Indirect estimation of stochastic differential equation models: some computational experiments , 1996 .

[114]  Damir Čemerin,et al.  IV , 2011 .

[115]  Karina Edith Schramm-Nielsen,et al.  Environmental reference materials methods and case studies , 1998 .

[116]  J. Timmer,et al.  Parameter estimation in nonlinear stochastic differential equations , 2000 .

[117]  Keith R. Godfrey,et al.  Correlation methods , 1980, Autom..

[118]  Lars Henrik Hansen,et al.  Stochastic modelling of central heating systems , 1997 .

[119]  Anders Rosholm,et al.  Statistical methods for segmentation and classification of images , 1997 .

[120]  Jeffrey M. Gordon,et al.  Thermodynamic modeling of reciprocating chillers , 1994 .

[121]  Aleksey V. Nenarokomov,et al.  Uncertainties in parameter estimation: the optimal experiment design , 2000 .

[122]  K. Lindsay,et al.  Estimating the parameters of stochastic differential equations , 1999 .

[123]  Henrik Madsen,et al.  VALIDATION OF GREY BOX MODELS , 1993 .

[124]  Robert Luxmore Payne,et al.  Optimal experiment design for dynamic system identification , 1974 .

[125]  J. Holst,et al.  Input design for linear dynamic systems using maxmin criteria , 1998 .

[126]  Sven Kreiborg,et al.  Surface-bounded growth modeling applied to human mandibles , 2000, IEEE Transactions on Medical Imaging.

[127]  Lennart Ljung,et al.  Tools for Semi-Physical Modeling , 1994 .

[128]  Ulrik Kjems,et al.  Bayesian Signal Processing and Interpretation of Brain Scans , 1998 .

[129]  Gudmundur Jonsson.  Parameter Estimation in Models of Heat Exchangers and Geothermal Reservoirs , 1990 .

[130]  M. Freidlin,et al.  A threshold estimation problem for processes with hysteresis , 1998 .

[131]  Henrik Madsen,et al.  Estimation of continuous-time models for the heat dynamics of a building , 1995 .

[132]  Kai Dirscherl,et al.  Online correction of scanning probe microscopes with pixel accuracy , 2000 .

[133]  K. Lindsay,et al.  Estimating the parameters of stochastic differential equations by Monte Carlo methods , 1997 .

[134]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[135]  Wai Keung Li,et al.  Robust residual cross correlation tests for lagged relations in time series , 1994 .

[136]  Henrik Madsen,et al.  A generalization of some classical time series tools , 2001 .

[137]  George Tauchen,et al.  Estimation of Continuous Time Models for Stock Returns and Interest Rates , 1997 .

[138]  Peter Søren Kirk Hansen,et al.  Signal subspace methods for speech enhancement , 1998 .

[139]  Lars Kai Hansen,et al.  Approximating methods for intractable probabilistic models: Applications in neuroscience , 2002 .

[140]  J. Bennetsen,et al.  Numerical simulation of turbulent airflow in livestock buildings , 2000 .

[141]  Lennart Ljung,et al.  Ensuring monotonic gain characteristics in estimated models by fuzzy model structures , 2000, Autom..

[142]  Rune Fisker.  Making Deformable Template Models Operational , 2000 .