Bayesian estimation of diameter distribution during harvesting

Abstract

Bayesian classification of forest ecological type from satellite data

The main objective of this study was todo a statistical analysis of ecological type from optical satellite data, using Tipping's sparse Bayesian algorithm. This thesis uses "the Relevence Vector Machine" algorithm in ecological classification betweenforestland and wetland. Further this bi-classification technique was used to do classification of many other different species of trees and produces hierarchical classification of entire subclasses given as a target class. Also, we carried out an attempt to use airborne image of same forest area. Combining it with image analysis, using different image processing operation, we tried to extract good features and later used them to perform classification of forestland and wetland.

Fusion weld metal solidification:Continuum from weld interface to centerline

We present a brief résumé of the history of solidification research and key factors affecting the solidification of fusion welds. There is a general agreement of the basic solidification theory, albeit differing - even confusing - nomenclatures do exist, and Cases 2 and 3 (the Chalmers' basic boundary conditions for solidification, categorized by Savage as Cases) are variably emphasized. Model Frame, a tool helping to model the continuum of fusion weld solidification from start to end, is proposed. It incorporates the general solidification models, of which the pertinent ones are selected for the actual modeling. The basic models are the main solidification Cases 1…4. These discrete Cases are joined with Sub-Cases: models of Pfann, Flemings and others, bringing needed Sub-Case variables into the model. Model Frame depicts a grain growing from the weld interface to its centerline. Besides modeling, the Model Frame supports education and academic debate. The new mathematical modeling techniques will extend its use into multi-dimensional modeling, introducing new variables and increasing the modeling accuracy. We propose a model: melting/solidification-model (M/S-model) - predicting the solute profile at the start of the solidification of a fusion weld. This Case 3-based Sub-Case takes into account the melting stage, the solute back-diffusion in the solid, and the growth rate acceleration typical to fusion welds. We propose - based on works of Rutter & Chalmers, David & Vitek and our experimental results on copper - that NEGS-EGS-transition is not associated only with cellular-dendritic-transition. Solidification is studied experimentally on pure and doped copper with welding speed range from 0 to 200 cm/min, with one test at 3000 cm/min. Found were only planar and cellular structures, no dendrites - columnar or equiaxed. Cell sub structures: rows of cubic elements we call "cubelettes", "cell-bands" and "micro-cells", as well as an anomalous crack morphology "crack-eye", were detected, as well as microscopic hot crack nucleus we call "grain-lag cracks", caused by a grain slightly lagging behind its neighbors in arrival to the weld centerline. Varestraint test and R-test revealed a change of crack morphologies from centerline cracks to grainand cell boundary cracks with an increasing welding speed. High speed made the cracks invisible to bare eye and hardly detectable with light microscope, while electron microscope often revealed networks of fine micro-cracks.

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.

Reaction Kinetics and Viscosity Modelling in the Fusion Syntheses of Ca- and Ca/Mg-resinates

Rosin is a natural product from pine forests and it is used as a raw material in resinate syntheses. Resinates are polyvalent metal salts of rosin acids and especially Ca- and Ca/Mg- resinates find wide application in the printing ink industry. In this thesis, analytical methods were applied to increase general knowledge of resinate chemistry and the reaction kinetics was studied in order to model the non linear solution viscosity increase during resinate syntheses by the fusion method. Solution viscosity in toluene is an important quality factor for resinates to be used in printing inks. The concept of critical resinate concentration, c crit, was introduced to define an abrupt change in viscosity dependence on resinate concentration in the solution. The concept was then used to explain the non-inear solution viscosity increase during resinate syntheses. A semi empirical model with two estimated parameters was derived for the viscosity increase on the basis of apparent reaction kinetics. The model was used to control the viscosity and to predict the total reaction time of the resinate process. The kinetic data from the complex reaction media was obtained by acid value titration and by FTIR spectroscopic analyses using a conventional calibration method to measure the resinate concentration and the concentration of free rosin acids. A multivariate calibration method was successfully applied to make partial least square (PLS) models for monitoring acid value and solution viscosity in both mid-infrared (MIR) and near infrared (NIR) regions during the syntheses. The calibration models can be used for on line resinate process monitoring. In kinetic studies, two main reaction steps were observed during the syntheses. First a fast irreversible resination reaction occurs at 235 °C and then a slow thermal decarboxylation of rosin acids starts to take place at 265 °C. Rosin oil is formed during the decarboxylation reaction step causing significant mass loss as the rosin oil evaporates from the system while the viscosity increases to the target level. The mass balance of the syntheses was determined based on the resinate concentration increase during the decarboxylation reaction step. A mechanistic study of the decarboxylation reaction was based on the observation that resinate molecules are partly solvated by rosin acids during the syntheses. Different decarboxylation mechanisms were proposed for the free and solvating rosin acids. The deduced kinetic model supported the analytical data of the syntheses in a wide resinate concentration region, over a wide range of viscosity values and at different reaction temperatures. In addition, the application of the kinetic model to the modified resinate syntheses gave a good fit. A novel synthesis method with the addition of decarboxylated rosin (i.e. rosin oil) to the reaction mixture was introduced. The conversion of rosin acid to resinate was increased to the level necessary to obtain the target viscosity for the product at 235 °C. Due to a lower reaction temperature than in traditional fusion synthesis at 265 °C, thermal decarboxylation is avoided. As a consequence, the mass yield of the resinate syntheses can be increased from ca. 70% to almost 100% by recycling the added rosin oil.

Sensor Fusion of Proprioception, Force and Vision in Estimation and Robot

Sensor-based robot control allows manipulation in dynamic environments with uncertainties. Vision is a versatile low-cost sensory modality, but low sample rate, high sensor delay and uncertain measurements limit its usability, especially in strongly dynamic environments. Force is a complementary sensory modality allowing accurate measurements of local object shape when a tooltip is in contact with the object. In multimodal sensor fusion, several sensors measuring different modalities are combined to give a more accurate estimate of the environment. As force and vision are fundamentally different sensory modalities not sharing a common representation, combining the information from these sensors is not straightforward. In this thesis, methods for fusing proprioception, force and vision together are proposed. Making assumptions of object shape and modeling the uncertainties of the sensors, the measurements can be fused together in an extended Kalman filter. The fusion of force and visual measurements makes it possible to estimate the pose of a moving target with an end-effector mounted moving camera at high rate and accuracy. The proposed approach takes the latency of the vision system into account explicitly, to provide high sample rate estimates. The estimates also allow a smooth transition from vision-based motion control to force control. The velocity of the end-effector can be controlled by estimating the distance to the target by vision and determining the velocity profile giving rapid approach and minimal force overshoot. Experiments with a 5-degree-of-freedom parallel hydraulic manipulator and a 6-degree-of-freedom serial manipulator show that integration of several sensor modalities can increase the accuracy of the measurements significantly.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Communicative and Anticipatory Decision-Making Supported by Bayesian Networks

The purpose of this research is to draw up a clear construction of an anticipatory communicative decision-making process and a successful implementation of a Bayesian application that can be used as an anticipatory communicative decision-making support system. This study is a decision-oriented and constructive research project, and it includes examples of simulated situations. As a basis for further methodological discussion about different approaches to management research, in this research, a decision-oriented approach is used, which is based on mathematics and logic, and it is intended to develop problem solving methods. The approach is theoretical and characteristic of normative management science research. Also, the approach of this study is constructive. An essential part of the constructive approach is to tie the problem to its solution with theoretical knowledge. Firstly, the basic definitions and behaviours of an anticipatory management and managerial communication are provided. These descriptions include discussions of the research environment and formed management processes. These issues define and explain the background to further research. Secondly, it is processed to managerial communication and anticipatory decision-making based on preparation, problem solution, and solution search, which are also related to risk management analysis. After that, a solution to the decision-making support application is formed, using four different Bayesian methods, as follows: the Bayesian network, the influence diagram, the qualitative probabilistic network, and the time critical dynamic network. The purpose of the discussion is not to discuss different theories but to explain the theories which are being implemented. Finally, an application of Bayesian networks to the research problem is presented. The usefulness of the prepared model in examining a problem and the represented results of research is shown. The theoretical contribution includes definitions and a model of anticipatory decision-making. The main theoretical contribution of this study has been to develop a process for anticipatory decision-making that includes management with communication, problem-solving, and the improvement of knowledge. The practical contribution includes a Bayesian Decision Support Model, which is based on Bayesian influenced diagrams. The main contributions of this research are two developed processes, one for anticipatory decision-making, and the other to produce a model of a Bayesian network for anticipatory decision-making. In summary, this research contributes to decision-making support by being one of the few publicly available academic descriptions of the anticipatory decision support system, by representing a Bayesian model that is grounded on firm theoretical discussion, by publishing algorithms suitable for decision-making support, and by defining the idea of anticipatory decision-making for a parallel version. Finally, according to the results of research, an analysis of anticipatory management for planned decision-making is presented, which is based on observation of environment, analysis of weak signals, and alternatives to creative problem solving and communication.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

On Bayesian predictive modeling : with applications on the analysis of chromatography data in forensic investigations

Med prediktion avses att man skattar det framtida värdet på en observerbar storhet. Kännetecknande för det bayesianska paradigmet är att osäkerhet gällande okända storheter uttrycks i form av sannolikheter. En bayesiansk prediktiv modell är således en sannolikhetsfördelning över de möjliga värden som en observerbar, men ännu inte observerad storhet kan anta. I de artiklar som ingår i avhandlingen utvecklas metoder, vilka bl.a. tillämpas i analys av kromatografiska data i brottsutredningar. Med undantag för den första artikeln, bygger samtliga metoder på bayesiansk prediktiv modellering. I artiklarna betraktas i huvudsak tre olika typer av problem relaterade till kromatografiska data: kvantifiering, parvis matchning och klustring. I den första artikeln utvecklas en icke-parametrisk modell för mätfel av kromatografiska analyser av alkoholhalt i blodet. I den andra artikeln utvecklas en prediktiv inferensmetod för jämförelse av två stickprov. Metoden tillämpas i den tredje artik eln för jämförelse av oljeprover i syfte att kunna identifiera den förorenande källan i samband med oljeutsläpp. I den fjärde artikeln härleds en prediktiv modell för klustring av data av blandad diskret och kontinuerlig typ, vilken bl.a. tillämpas i klassificering av amfetaminprover med avseende på produktionsomgångar.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Energy and raw material consumption analysis of powder bed fusion: case study: CNC machining and laser additive manufacturing

Laser additive manufacturing (LAM), known also as 3D printing, is a powder bed fusion (PBF) type of additive manufacturing (AM) technology used to manufacture metal parts layer by layer by assist of laser beam. The development of the technology from building just prototype parts to functional parts is due to design flexibility. And also possibility to manufacture tailored and optimised components in terms of performance and strength to weight ratio of final parts. The study of energy and raw material consumption in LAM is essential as it might facilitate the adoption and usage of the technique in manufacturing industries. The objective this thesis was find the impact of LAM on environmental and economic aspects and to conduct life cycle inventory of CNC machining and LAM in terms of energy and raw material consumption at production phases. Literature overview in this thesis include sustainability issues in manufacturing industries with focus on environmental and economic aspects. Also life cycle assessment and its applicability in manufacturing industry were studied. UPLCI-CO2PE! Initiative was identified as mostly applied exiting methodology to conduct LCI analysis in discrete manufacturing process like LAM. Many of the reviewed literature had focused to PBF of polymeric material and only few had considered metallic materials. The studies that had included metallic materials had only measured input and output energy or materials of the process and compared to different AM systems without comparing to any competitive process. Neither did any include effect of process variation when building metallic parts with LAM. Experimental testing were carried out to make dissimilar samples with CNC machining and LAM in this thesis. Test samples were designed to include part complexity and weight reductions. PUMA 2500Y lathe machine was used in the CNC machining whereas a modified research machine representing EOSINT M-series was used for the LAM. The raw material used for making the test pieces were stainless steel 316L bar (CNC machined parts) and stainless steel 316L powder (LAM built parts). An analysis of power, time, and the energy consumed in each of the manufacturing processes on production phase showed that LAM utilises more energy than CNC machining. The high energy consumption was as result of duration of production. Energy consumption profiles in CNC machining showed fluctuations with high and low power ranges. LAM energy usage within specific mode (standby, heating, process, sawing) remained relatively constant through the production. CNC machining was limited in terms of manufacturing freedom as it was not possible to manufacture all the designed sample by machining. And the one which was possible was aided with large amount of material removed as waste. Planning phase in LAM was shorter than in CNC machining as the latter required many preparation steps. Specific energy consumption (SEC) were estimated in LAM based on the practical results and assumed platform utilisation. The estimated platform utilisation showed SEC could reduce when more parts were placed in one build than it was in with the empirical results in this thesis (six parts).

Metal additive manufacturing of internal flow channels with powder bed fusion processes

This thesis studies the advantages, disadvantages and possibilities of additive manufacturing in making components with internal flow channels. These include hydraulic components, components with cooling channels and heat exchangers. Processes studied in this work are selective laser sintering and selective laser melting of metallic materials. The basic principles of processes and parameters involved in the process are presented and different possibilities of internal channel manufacturing and flow improvement are introduced