Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Estimates of genetic parameters of trotting performance traits for repeated annual records

Selostus: Ravihevosten jalostettavia ominaisuuksia kuvaavien kilpailumittojen perinnölliset tunnusluvut

Progeny Trial Estimates of Genetic Parameters for Growth and Quality Traits in Scots Pine

Summary

Empirical errors of small area estimates from the multisource National Forest Inventory in Eastern Finland

Abstract

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

Accuracy Analysis of Frequency Converter Estimates in Diagnostic Applications

Transportation of fluids is one of the most common and energy intensive processes in the industrial and HVAC sectors. Pumping systems are frequently subject to engineering malpractice when dimensioned, which can lead to poor operational efficiency. Moreover, pump monitoring requires dedicated measuring equipment, which imply costly investments. Inefficient pump operation and improper maintenance can increase energy costs substantially and even lead to pump failure. A centrifugal pump is commonly driven by an induction motor. Driving the induction motor with a frequency converter can diminish energy consumption in pump drives and provide better control of a process. In addition, induction machine signals can also be estimated by modern frequency converters, dispensing with the use of sensors. If the estimates are accurate enough, a pump can be modelled and integrated into the frequency converter control scheme. This can open the possibility of joint motor and pump monitoring and diagnostics, thereby allowing the detection of reliability-reducing operating states that can lead to additional maintenance costs. The goal of this work is to study the accuracy of rotational speed, torque and shaft power estimates calculated by a frequency converter. Laboratory tests were performed in order to observe estimate behaviour in both steady-state and transient operation. An induction machine driven by a vector-controlled frequency converter, coupled with another induction machine acting as load was used in the tests. The estimated quantities were obtained through the frequency converter’s Trend Recorder software. A high-precision, HBM T12 torque-speed transducer was used to measure the actual values of the aforementioned variables. The effect of the flux optimization energy saving feature on the estimate quality was also studied. A processing function was developed in MATLAB for comparison of the obtained data. The obtained results confirm the suitability of this particular converter to provide accurate enough estimates for pumping applications.

Value at Risk in Foreign Exchange Risk Management

This thesis examines the suitability of VaR in foreign exchange rate risk management from the perspective of a European investor. The suitability of four different VaR models is evaluated in respect to have insight if VaR is a valuable tool in managing foreign exchange rate risk. The models evaluated are historical method, historical bootstrap method, variance-covariance method and Monte Carlo simulation. The data evaluated are divided into emerging and developed market currencies to have more intriguing analysis. The foreign exchange rate data in this thesis is from 31st January 2000 to 30th April 2014. The results show that the previously mentioned VaR models performance in foreign exchange risk management is not to be considered as a single tool in foreign exchange rate risk management. The variance-covariance method and Monte Carlo simulation performs poorest in both currency portfolios. Both historical methods performed better but should also be considered as an additional tool along with other more sophisticated analysis tools. A comparative study of VaR estimates and forward prices is also included in the thesis. The study reveals that regardless of the expensive hedging cost of emerging market currencies the risk captured by VaR is more expensive and thus FX forward hedging is recommended