The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

System Identification I

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

Thank you for reading stochastic processes and filtering theory. Maybe you have knowledge that, people have look numerous times for their favorite novels like this stochastic processes and filtering theory, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their computer. stochastic processes and filtering theory is available in our digital library an online access to it is set as public so you can download it instantly. Our digital library saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the stochastic processes and filtering theory is universally compatible with any devices to read.

Stochastic Processes And Filtering Theory

Modelica is an object oriented, acausal equation-based language for describing complex, hybrid dynamic models. From a control systems point of view, the support of models with inputs and outputs is of particular importance. About ten Modelica implementations exist, of which most are commercial and two are open source; the implementations have varying levels of tool functionality. Many Modelica implementations have limited support for model analysis. It is therefore of interest to integrate Modelica tools with a powerful scripting and programming language, such as Julia. Julia is a modern and free language for scientific computing. Julia has very good support for plotting, linear algebra, random numbers/statistics, automatic differentiation, optimization, machine learning, differential equations, signal processing, data frames, graph algorithms, file handling/databases, etc. Although support for control tools is lacking compared to MATLAB, control packages are more developed and simpler to install than, e.g., in Python. In summary, integration of Modelica with Julia facilitates many needed analysis possibilities and can speed up the development of effient simulation models. A number of design choices for interaction between Julia and Modelica tools are discussed. The simplest approach is to interact via text strings of command code. A more convenient approach is to use an API in Julia (the script tool) which hides the interaction code details. For simulation, both of these approaches lead to interaction between Julia and compiled Modelica code, with some resulting run-time overhead in the call. A third approach could be to translate Modelica code into Julia code instead of C code. The produced Julia code can then be included in a Julia session, and can take advantage of Julia tools with no run-time overhead for the simulation. A fourth possibility is to utilize meta programming capabilities of Julia and extend Julia with the possibilities of Modelica (as in the Modia project). Some advantages and disadvantages of the approaches are discussed. In this paper, the second approach is taken, and Julia package OMJulia is introduced with an API for interaction between OpenModelica and Julia. Some discussion of the reasoning behind the OMJulia design is given. The API is based on a new class ModelicaSystem within package OMJulia, with systematic methods which operate on instantiated models. OMJulia supports handling of FMU and Modelica models, setting and getting model values, as well as some model operations such as simulate and linearize. Results are available in Julia for further analysis. OMJulia is a further development of a previous OMPython package; a key advantage of Julia over Python is that Julia has better support for control engineering packages. OMJulia represents a first effort to interface a relatively complete Modelica tool to Julia, giving access to an open source set-up for modeling and analysis, including control synthesis, easily installable from a unified package manager. In addition to documenting OMJulia with some basic examples, slightly more advanced examples are included to illustrate the possibilities of implementing dynamic models in OpenModelica and carry out control systems analysis in Julia. Because Python has poor design for control systems analysis, Modelica-Julia interaction is more intersting for control applications. The examples illustrate use of Julia for linearization of Modelica models, control analysis, controller synthesis, and comparison of the control design. Although not shown in the paper, the Modelica-Julia integration makes it straightforward to do state estimation (random number generators, linear algebra), test out optimal control and model predictive control (control systems package, optimization code), develop surrogate models (machine learning), carry out structural analysis (graph theory algorithms), etc. Some of the methods take advantage of OpenModelica’s algorithm for translating DAE models to state space models. The Julia API/OMJulia makes it possible to utilize a mature Modelica implementation (OpenModelica) out of the box, and add tools that are not part of Modelica. The approaches for tighter integration of Modelica with Julia (Modelica-to-Julia translation, Modia) are, of course, also interesting — tighter integration promises better performance compared to the OMJulia approach. These tighter integration approaches are currently limited in scope, but are interesting developments for the near future.

/pdf/omjulia-an-openmodelica-api-for-julia-modelica-interaction-33z6hvtx8d.pdf

OMJulia: An OpenModelica API for Julia-Modelica Interaction

Optimal design and operation of a UASB reactor for dairy cattle manure

Models of synchronous generators with excitation system, for transient power system studies

A mechanistic nonlinear model of the wet end of paper machine 6 (PM6) at Norske Skog Saugbrugs, Norway has been developed, and used in an MPC application. The MPC provides reduced variability in many key variables, and better efficiency through faster grade changes, start ups, and improved control during periods of poor measurements. The model and controller can be rolled-out to other paper machines, as found by studying and fitting the model to data from PM4 at Norske Skog Saugbrugs, and PM3 at Norske Skog Skogn, Norway. No changes to the model, except for parameter values, were introduced, and still the validation results were good. The time spent on fitting and validating the PM6 model to PM4 and PM3 are approximately 1% of the time spent on developing the original model. This should be a strong incentive for focusing on mechanistic modeling in industries were there are many similar production lines or units.

/pdf/paper-machine-modeling-at-norske-skog-saugbrugs-a-3z28skrp1s.pdf

Paper Machine Modeling at Norske Skog Saugbrugs: A Mechanistic Approach

Optimal operation and control of a run-of-river hydro power plant depends on good knowledge of the elements of the plant in the form of models. River reaches are often considered shallow channels with free surfaces. A typical model for such reaches use the Saint Venant model, which is a 1D distributed model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. The finite volume method with staggered grid was compared with the Kurganov-Petrova central upwind scheme, and was used to illustrate the dynamics of the river upstream from the Gronvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi AS. In an experiment on the Gronvollfoss run-of-river power plant, a step was injected in the upstream inlet flow at Arlifoss, and the resulting change in level in front of the dam at the Gronvollfoss plant was logged. The results from the theoretical Saint Venant model was then compared to the experimental results. Because of uncertainties in the geometry of the river reach (river bed slope, etc.), the slope and length of the varying slope parts were tuned manually to improve the fit. Then, friction factor, river width and height drop of the river was tuned by minimizing a least squares criterion. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.

/pdf/model-based-control-for-run-of-river-system-part-1-model-31a5zekhzu.pdf

Bernt Lie

Papers

OMJulia: An OpenModelica API for Julia-Modelica Interaction

Optimal design and operation of a UASB reactor for dairy cattle manure

Models of synchronous generators with excitation system, for transient power system studies

Paper Machine Modeling at Norske Skog Saugbrugs: A Mechanistic Approach

Model based control for run-of-river system. Part 1: Model implementation and tuning