Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Short communication: estimation of the financial benefit of using Jersey milk at different inclusion rates for Cheddar cheese production using partial budgeting

Partial budgeting was used to estimate the net benefit of blending Jersey milk in Holstein-Friesian milk for Cheddar cheese production. Jersey milk increases Cheddar cheese yield. However, the cost of Jersey milk is also higher; thus, determining the balance of profitability is necessary, including consideration of seasonal effects. Input variables were based on a pilot plant experiment run from 2012 to 2013 and industry milk and cheese prices during this period. When Jersey milk was used at an increasing rate with Holstein-Friesian milk (25, 50, 75, and 100% Jersey milk), it resulted in an increase of average net profit of 3.41, 6.44, 8.57, and 11.18 pence per kilogram of milk, respectively, and this additional profit was constant throughout the year. Sensitivity analysis showed that the most influential input on additional profit was cheese yield, whereas cheese price and milk price had a small effect. The minimum increase in yield, which was necessary for the use of Jersey milk to be profitable, was 2.63, 7.28, 9.95, and 12.37% at 25, 50, 75, and 100% Jersey milk, respectively. Including Jersey milk did not affect the quantity of whey butter and powder produced. Althoug further research is needed to ascertain the amount of additional profit that would be found on a commercial scale, the results indicate that using Jersey milk for Cheddar cheese making would lead to an improvement in profit for the cheese makers, especially at higher inclusion rates.

Simulating the impact on health of internalising the cost of carbon in food prices combined with a tax on sugar-sweetened beverages

Rising greenhouse gas emissions (GHGEs) have implications for health and up to 30 % of emissions globally are thought to arise from agriculture. Synergies exist between diets low in GHGEs and health however some foods have the opposite relationship, such as sugar production being a relatively low source of GHGEs. In order to address this and to further characterise a healthy sustainable diet, we model the effect on UK non-communicable disease mortality and GHGEs of internalising the social cost of carbon into the price of food alongside a 20 % tax on sugar sweetened beverages (SSBs). Developing previously published work, we simulate four tax scenarios: (A) a GHGEs tax of £2.86/tonne of CO2 equivalents (tCO2e)/100 g product on all products with emissions greater than the mean across all food groups (0.36 kgCO2e/100 g); (B) scenario A but with subsidies on foods with emissions lower than 0.36 kgCO2e/100 g such that the effect is revenue neutral; (C) scenario A but with a 20 % sales tax on SSBs; (D) scenario B but with a 20 % sales tax on SSBs. An almost ideal demand system is used to estimate price elasticities and a comparative risk assessment model is used to estimate changes to non-communicable disease mortality. We estimate that scenario A would lead to 300 deaths delayed or averted, 18,900 ktCO2e fewer GHGEs, and £3.0 billion tax revenue; scenario B, 90 deaths delayed or averted and 17,100 ktCO2e fewer GHGEs; scenario C, 1,200 deaths delayed or averted, 18,500 ktCO2e fewer GHGEs, and £3.4 billion revenue; and scenario D, 2,000 deaths delayed or averted and 16,500 ktCO2e fewer GHGEs. Deaths averted are mainly due to increased fibre and reduced fat consumption; a SSB tax reduces SSB and sugar consumption. Incorporating the social cost of carbon into the price of food has the potential to improve health, reduce GHGEs, and raise revenue. The simple addition of a tax on SSBs can mitigate negative health consequences arising from sugar being low in GHGEs. Further conflicts remain, including increased consumption of unhealthy foods such as cakes and nutrients such as salt.

Analyses of cataract surgery performed by the Unified Health System in Brazil, 2006-2007

Objective. Estimate cataract surgical rates (CSR) for Brazil and each federal unit in 2006 and 2007 based on the number of surgeries performed by the Unified Health System to help plan a comprehensive ophthalmology network in order to eliminate cataract blindness in compliance with the target set by the World Health Organization (WHO) of 3 000 cataract surgeries per million inhabitants per year. Methods. This descriptive study calculates CSR by using the number of cataract surgeries carried out by the Brazilian Unified Health System for each federal unit and estimates the need for cataract surgery in Brazil for 2006-2007, with official population data provided by the Brazilian Institute of Geography and Statistics. The number of cataract surgeries was compared with the WHO target. Results. To reach the WHO goal for eliminating age-related cataract blindness in Brazil, 560 312 cataract surgeries in 2006 and 568 006 surgeries in 2007 needed to be done. In 2006, 179 121 cataract surgeries were done by the Unified Health System, corresponding to a CSR of 959 per million population; in 2007, 223 317 were performed, with a CSR of 1 179. With the Brazilian Council of Ophthalmology estimation of 165 000 surgeries each year by the non-public services, the CSR for Brazil would be 1 842 for 2006 and 2 051 for 2007. The proportions needed to achieve the proposed target were 38.6% in 2006 and 31.6% in 2007. Conclusions. Human resources, technical expertise, and equipment are crucial to reach the WHO goal. Brazil has enough ophthalmologists but needs improved planning and infrastructure in order to eliminate the problem, aspects that require greater financial investment and stronger political commitment.

Dynamics of Aeromonas species isolated from wastewater treatment system

Aeromonas are widely distributed in the aquatic environment, and are considered to be emerging organisms that can produce a series of virulence factors. The present study was carried out in a sanitary sewage stabilization pond treatment system, located in Lins, State of Sao Paulo, Brazil. Most probable number was applied for estimation of the genus Aeromonas. Colony isolation was carried out on blood agar ampicillin and confirmed by biochemical characterization. Aeromonas species were isolated in 72.4% of influent samples, and in 55.2 and 48.3% of effluent from anaerobic and facultative lagoons, respectively. Thirteen Aeromonas species were isolated, representing most of the recognized species of these organisms. Even though it was possible to observe a tendency of decrease, total elimination of these organisms from the studied system was not achieved. Understanding of the pathogenic organism`s dynamics in wastewater treatment systems with a reuse potential is especially important because of the risk it represents.

DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

Bayesian Estimation for Performance Measures of Two Diagnostic Tests in the Presence of Verification Bias

Sensitivity and specificity are measures that allow us to evaluate the performance of a diagnostic test. In practice, it is common to have situations where a proportion of selected individuals cannot have the real state of the disease verified, since the verification could be an invasive procedure, as occurs with biopsy. This happens, as a special case, in the diagnosis of prostate cancer, or in any other situation related to risks, that is, not practicable, nor ethical, or in situations with high cost. For this case, it is common to use diagnostic tests based only on the information of verified individuals. This procedure can lead to biased results or workup bias. In this paper, we introduce a Bayesian approach to estimate the sensitivity and the specificity for two diagnostic tests considering verified and unverified individuals, a result that generalizes the usual situation based on only one diagnostic test.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

Applicatiion of Almost ideal demand system for a pharmaceutical

This thesis is an application of the Almost Ideal Demand System approach of Deaton and Muellbauer,1980, for a particular pharmaceutical, Citalopram, in which GORMAN´s (1971) multi-stage budgeting approach is applied basically since it is one of the most useful approach in estimating demand for differentiated products. Citalopram is an antidepressant drug that is used in the treatment of major depression. As for most other pharmaceuticals whose the patent has expired, there exist branded and generic versions of Citalopram. This paper is aimed to define its demand system with two stage models for the branded version and five generic versions, and to show whether generic versions are able to compete with the branded version. I calculated the own price elasticities, and it made me possible to compare and make a conclusion about the consumers’ choices over the brand and generic drugs. Even though the models need for being developed with some additional variables, estimation results of models and uncompensated price elasticities indicated that the branded version has still power in the market, and generics are able to compete with lower prices. One important point that has to be taken into consideration is that the Swedish pharmaceutical market faced a reform on October 1, 2002, that aims to make consumer better informed about the price and decrease the overall expenditures for pharmaceuticals. Since there were not significantly enough generic sales to take into calculation before the reform, my paper covers sales after the reform.

The actual status of the development of a Danish/Swedish system concept of a solar combisystem

At the beginning of 2003 the four year long research project REBUS on education, research, development and demonstration of competitive solar combisystems was launched. Research groups in Norway, Denmark, Sweden and Latvia are working together with partners from industry on innovative solutions for solar heating in the Nordic countries. Existing system concepts have been analyzed and based on the results new system designs have been developed. The proposed solutions have to fulfill country specific technical, sociological and cost requirements. Due to the similar demands on the systems in Denmark and Sweden it has been decided to develop a common system concept for both countries, which increases the market potential for the manufacturer. The focus of the development is on systems for the large number of rather well insulated existing single family houses. In close collaboration with the industrial partners a system concept has been developed that is characterized by its high compactness and flexibility. It allows the use of different types of boilers, heating distribution systems and a variable store and collector size. Two prototypes have been built, one for the Danish market with a gas boiler, and one for the Swedish market with a pellet boiler as auxiliary heater. After intensive testing and eventual further improvements at least two systems will be installed and monitored in demonstration houses. The systems have been modeled in TRNSYS and the simulation results will be used to further improve the system and evaluate the system performance.

A Cost Model for the Effect of Setup Time Reduction in Stainless Steel Strip Production

Setup time reduction facilitate the flexibility needed for just-in-time production. An integrated steel mill with meltshop, continuous caster and hot rolling mill is often operated as decoupled processes. Setup time reduction provides the flexibility needed to reduce buffering, shorten lead times and create an integrated process flow. The interdependency of setup times, process flexibility and integration were analysed through system dynamics simulation. The results showed significant reductions of energy consumption and tied capital. It was concluded that setup time reduction in the hot strip mill can aid process integration and hence improve production economy while reducing environmental impact.

Simulation of Photovoltaic Panel Production as Complement to Ground Source Heat Pump System

This master thesis presents a new technological combination of two environmentally friendly sources of energy in order to provide DHW, and space heating. Solar energy is used for space heating, and DHW production using PV modules which supply direct current directly to electrical heating elements inside a water storage tank. On the other hand a GSHP system as another source of renewable energy provides heat in the water storage tank of the system in order to provide DHW and space heating. These two sources of renewable energy have been combined in this case-study in order to obtain a more efficient system, which will reduce the amount of electricity consumed by the GSHP system.The key aim of this study is to make simulations, and calculations of the amount ofelectrical energy that can be expected to be produced by a certain amount of PV modules that are already assembled on a house in Vantaa, southern Finland. This energy is then intended to be used as a complement to produce hot water in the heating system of the house beside the original GSHP system. Thus the amount of electrical energy purchased from the grid should be reduced and the compressor in the GSHP would need fewer starts which would reduce the heating cost of the GSHP system for space heating and providing hot water.The produced energy by the PV arrays in three different circuits will be charged directly to three electrical heating elements in the water storage tank of the existing system to satisfy the demand of the heating elements. The excess energy can be used to heat the water in the water storage tank to some extent which leads to a reduction of electricity consumption by the different components of the GSHP system.To increase the efficiency of the existing hybrid system, optimization of different PV configurations have been accomplished, and the results are compared. Optimization of the arrays in southern and western walls shows a DC power increase of 298 kWh/year compared with the existing PV configurations. Comparing the results from the optimization of the arrays on the western roof if the intention is to feed AC power to the components of the GSHP system shows a yearly AC power production of 1,646 kWh.This is with the consideration of no overproduction by the PV modules during the summer months. This means the optimized PV systems will be able to cover a larger part of summer demand compared with the existing system.

Energy Storage for a Grid-Connected PV-System: A Feasibility Study

The work presented in this thesis concerns the dimensioning of an Energy Storage System (ESS) which will be used as an energy buffer for a grid-connected PV plant. This ESS should help managing the PV plant to inject electricity into the grid according to the requirements of the grid System Operator. It is desired to obtain a final production not below 1300kWh/kWp with a maximum ESS budget of 0.9€/Wp. The PV plant will be sited in Martinique Island and connected to the main grid. This grid is a small one where the perturbations due clouds in the PV generation are not negligible anymore. A software simulation tool, incorporating a model for the PV-plant production, the ESS and the required injection pattern of electricity into the grid has been developed in MS Excel. This tool has been used to optimize the relevant parameters defining the ESS so that the feed-in of electricity into the grid can be controlled to fulfill the conditions given by the System Operator. The inputs used for this simulation tool are, besides the conditions given by the System Operator on the allowed injection pattern, the production data from a similar PV-plant in a close-by location, and variables for defining the ESS. The PV production data used is from a site with similar climate and weather conditions as for the site on the Martinique Island and hence gives information on the short term insolation variations as well as expected annual electricity production. The ESS capacity and the injected electric energy will be the main figures to compare while doing an economic study of the whole plant. Hence, the Net Present Value, Benefit to Cost method and Pay-back period studies are carried on as dependent of the ESS capacity. The conclusion of this work is that it is possible to obtain the requested injection pattern by using an ESS. The design of the ESS can be made within an acceptable budget. The capacity of ESS to link with the PV system depends on the priorities of the final output characteristics, and it also depends on which economic parameter that is chosen as a priority.

Jämförelsestudie avseende stomsystem : Ramverk eller fackverk/balk/pelar-system

Projektet omfattade en jämförelsestudie avseende stomsystem. Studien undersökte ramverk och fackverk/balk/pelar-system och genomfördes självständigt med stöttning av Ramböll AB´s kontor i Falun. Syftet var främst att undersöka vilka skillnader det finns mellan tvåledsramar och fackverk/balk/pelar-system för lätta hallbyggnader och försöka få klarhet i varför fackverk/balk/pelar-system är det dominerande systemet i Sverige eftersom övriga Europa har tagit en annan utveckling och domineras av tvåledsramar. Studien undersöker skillnaderna mellan systemen i en hallbyggnad med förutbestämda mått i stål.Inledningsvis gjordes en litteraturstudie för att få en bredare bakgrund av systemen och en bättre förståelse om förutsättningarna för varje system. Efter litteraturstudien kunde sedan ett typhus och beräkningsunderlag för jämförelsestudien tas fram. Även en enkätstudie gjordes med syftet att skapa en tydlig bild av vilket stomsystem konstruktörer i Sverige oftast väljer och varför. Resultatet av studien visade att tvåledsramar ger en ökad kostnad jämfört med fackverk/balk/pelar-system i materialåtgång och framställning samt att beräkningarna blir mer komplicerade. Skulle fortsatta studier göras med dessa system i byggnader med andra mått skulle det kanske gå att få fram speciella mått på byggnader där kostnaden för tvåledsramar blir densamma som för fackverk/balk/pelar-system och därför är ett likvärdigt alternativ som stomsystem.En viktig slutsats från projektet är att tvåledsramar används mycket mer sällan än fackverk/balk/pelar-system som stomsystem i lätta hallbyggnader i Sverige på grund av att kostnaderna blir mycket högre med tvåledsramar och att det är ett mer komplicerat system i beräkningsarbetet. De viktigaste slutsatserna från jämförelsestudien går att sammafatta som följande: Tvåledsramar är dyrare att använda. Tvåledsramar är ett mer komplicerat system beräkningsmässigt. Traditionen av att använda tvåledsramar finns inte och därför används inte systemet.