Books on the topic 'Gaussian process regression model'

This article describes a new circuit device, developed in collaboration with scientists at Sandia National Laboratories, based on treed Gaussian processes (TGP). The circuit devices under study are bipolar junction transistors, which are used to amplify electrical current. To aid with the design of the device, a computer model predicts its peak output as a function of the input dosage and a number of design parameters. The methodology also involves a novel sequential design procedure to generate data to fit the emulator. Both physical and computer simulation experiments are performed, and the results show that the TGP model can be useful for spatial data and semiparametric regression in the context of a computer experiment for designing a circuit device, for sequential design of (computer) experiments, sequential robust local optimization, validation, calibration, and sensitivity analysis.

This article discusses an approach that combines monitoring data and computer model outputs for environmental exposure assessment. It describes the application of Bayesian data fusion methods using spatial Gaussian process models in studies of weekly wet deposition data for 2001 from 120 sites monitored by the US National Atmospheric Deposition Program (NADP) in the eastern United States. The article first provides an overview of environmental computer models, with a focus on the CMAQ (Community Multi-Scale Air Quality) Eta forecast model, before considering some algorithmic and pseudo-statistical approaches in weather prediction. It then reviews current state of the art fusion methods for environmental data analysis and introduces a non-dynamic downscaling approach. The static version of the dynamic spatial model is used to analyse the NADP weekly wet deposition data.

Cellulose is the most abundant organic polymer on Earth and a fascinating compound for a vast variety of applications. It is mostly received from wood, thus it is a renewable resource and a CO2 storing material. One of the most important cellulose products are pulp and paper. The major goal of this work was to obtain a material with a high amount of cellulose through a pulping process of wood. Therefore, it is necessary to separate the wood bers and to remove a component of wood, which is called lignin (deligni cation). The conventional way to delignify wood is the Kraft process that causes serval problems like contamination of lignin with sulfur and the emission of toxic volatile sulfur compounds. Hence, there are alternative processes without sulfur, such as the Acetosolv process. It uses simple chemicals like acetic acid and is easy to handle. After cutting a spruce tree (Picea abies L. Karst.), debarking and chipping, the wood chips were cooked in the laboratory. The research included the chemical analysis of the obtained pulp and the manufacturing and testing of paper sheets. The yield of pulp ranged widely due to the di erent parameters of the cooking. FT-IR and Raman spectroscopy were used to observe the decrease of aromatic substances (lignin) and the acetylation of the pulp. With the means of Design of Experiments and statistical analysis the most important factors were identi ed and a mathematical regression model was calculated. The manufactured paper sheets showed good mechanical properties and high transparency. Finally, the Acetosolv process could be considered as a contribution to the upcoming bio-based economy because, in addition to the cellulose bers, the industry would be capable of adding value utilization of the separated lignin. It could be one step to a more sustainable paper and pulp production.

This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.

Hard coal mining is characterised by features that pose numerous challenges to its current operations and cause strategic and operational problems in planning its development. The most important of these include the high capital intensity of mining investment projects and the dynamically changing environment in which the sector operates, while the long-term role of the sector is dependent on factors originating at both national and international level. At the same time, the conditions for coal mining are deteriorating, the resources more readily available in active mines are being exhausted, mining depths are increasing, temperature levels in pits are rising, transport routes for staff and materials are getting longer, effective working time is decreasing, natural hazards are increasing, and seams with an increasing content of waste rock are being mined. The mining industry is currently in a very difficult situation, both in technical (mining) and economic terms. It cannot be ignored, however, that the difficult financial situation of Polish mining companies is largely exacerbated by their high operating costs. The cost of obtaining coal and its price are two key elements that determine the level of efficiency of Polish mines. This situation could be improved by streamlining the planning processes. This would involve striving for production planning that is as predictable as possible and, on the other hand, economically efficient. In this respect, it is helpful to plan the production from operating longwalls with full awareness of the complexity of geological and mining conditions and the resulting economic consequences. The constraints on increasing the efficiency of the mining process are due to the technical potential of the mining process, organisational factors and, above all, geological and mining conditions. The main objective of the monograph is to identify relations between geological and mining parameters and the level of longwall mining costs, and their daily output. In view of the above, it was assumed that it was possible to present the relationship between the costs of longwall mining and the daily coal output from a longwall as a function of onerous geological and mining factors. The monograph presents two models of onerous geological and mining conditions, including natural hazards, deposit (seam) parameters, mining (technical) parameters and environmental factors. The models were used to calculate two onerousness indicators, Wue and WUt, which synthetically define the level of impact of onerous geological and mining conditions on the mining process in relation to: —— operating costs at longwall faces – indicator WUe, —— daily longwall mining output – indicator WUt. In the next research step, the analysis of direct relationships of selected geological and mining factors with longwall costs and the mining output level was conducted. For this purpose, two statistical models were built for the following dependent variables: unit operating cost (Model 1) and daily longwall mining output (Model 2). The models served two additional sub-objectives: interpretation of the influence of independent variables on dependent variables and point forecasting. The models were also used for forecasting purposes. Statistical models were built on the basis of historical production results of selected seven Polish mines. On the basis of variability of geological and mining conditions at 120 longwalls, the influence of individual parameters on longwall mining between 2010 and 2019 was determined. The identified relationships made it possible to formulate numerical forecast of unit production cost and daily longwall mining output in relation to the level of expected onerousness. The projection period was assumed to be 2020–2030. On this basis, an opinion was formulated on the forecast of the expected unit production costs and the output of the 259 longwalls planned to be mined at these mines. A procedure scheme was developed using the following methods: 1) Analytic Hierarchy Process (AHP) – mathematical multi-criteria decision-making method, 2) comparative multivariate analysis, 3) regression analysis, 4) Monte Carlo simulation. The utilitarian purpose of the monograph is to provide the research community with the concept of building models that can be used to solve real decision-making problems during longwall planning in hard coal mines. The layout of the monograph, consisting of an introduction, eight main sections and a conclusion, follows the objectives set out above. Section One presents the methodology used to assess the impact of onerous geological and mining conditions on the mining process. Multi-Criteria Decision Analysis (MCDA) is reviewed and basic definitions used in the following part of the paper are introduced. The section includes a description of AHP which was used in the presented analysis. Individual factors resulting from natural hazards, from the geological structure of the deposit (seam), from limitations caused by technical requirements, from the impact of mining on the environment, which affect the mining process, are described exhaustively in Section Two. Sections Three and Four present the construction of two hierarchical models of geological and mining conditions onerousness: the first in the context of extraction costs and the second in relation to daily longwall mining. The procedure for valuing the importance of their components by a group of experts (pairwise comparison of criteria and sub-criteria on the basis of Saaty’s 9-point comparison scale) is presented. The AHP method is very sensitive to even small changes in the value of the comparison matrix. In order to determine the stability of the valuation of both onerousness models, a sensitivity analysis was carried out, which is described in detail in Section Five. Section Six is devoted to the issue of constructing aggregate indices, WUe and WUt, which synthetically measure the impact of onerous geological and mining conditions on the mining process in individual longwalls and allow for a linear ordering of longwalls according to increasing levels of onerousness. Section Seven opens the research part of the work, which analyses the results of the developed models and indicators in individual mines. A detailed analysis is presented of the assessment of the impact of onerous mining conditions on mining costs in selected seams of the analysed mines, and in the case of the impact of onerous mining on daily longwall mining output, the variability of this process in individual fields (lots) of the mines is characterised. Section Eight presents the regression equations for the dependence of the costs and level of extraction on the aggregated onerousness indicators, WUe and WUt. The regression models f(KJC_N) and f(W) developed in this way are used to forecast the unit mining costs and daily output of the designed longwalls in the context of diversified geological and mining conditions. The use of regression models is of great practical importance. It makes it possible to approximate unit costs and daily output for newly designed longwall workings. The use of this knowledge may significantly improve the quality of planning processes and the effectiveness of the mining process.

Presented reasearch aimed to develop and analyse the suitability of the CART models for prediction of the extent and probability of occurrence of damage to outer soil layers caused by timber harvesting performed under varied conditions. Having employed these models, the author identified certain methods of logging works and conditions, under which they should be performed to minimise the risk of damaging forest soils. The analyses presented in this work covered the condition of soils upon completion of logging works, which was investigated in 48 stands located in central and south-eastern Poland. In the stands selected for these studies a few felling treatments were carried out, including early thinning, late thinning and final felling. Logging works were performed with use of the most popular technologies in Poland. Trees were cut down with chainsaws and timber was extracted by means of various skidding methods: with horses, semi-suspended skidding with the use of cable yarding systems, farm tractors equipped with cable winches or tractors of a skidder type, and forwarding employing farm tractors with trailers loaded mechanically by cranes or manually. The analyses also included mechanised forest operation with the use of a harvester and a forwarder. The information about the extent of damage to soil, in a form of wheel-ruts and furrows, gathered in the course of soil condition inventory served for construction of regression tree models using the CART method (Classification and Regression Trees), based on which the area, depth and the volume of soil damage under analysis, wheel-ruts and furrows, were determined, and the total degree of all soil disturbances was assessed. The CART classification trees were used for modelling the probability of occurrence of wheel-ruts and furrows, or any other type of soil damage. Qualitative independent variables assumed by the author for developing the models included several characteristics describing the conditions under which the logging works were performed, mensuration data of the stands and the treatments conducted there. These characteristics covered in particular: the season of the year when logging works were performed, the system of timber harvesting employed, the manner of timber skidding, the means engaged in the process of timber harvesting and skidding, habitat type, crown closure, and cutting category. Moreover, the author took into consideration an impact of the quantitative independent variables on the extent and probability of occurrence of soil disturbance. These variables included the following: the measuring row number specifying a distance between the particular soil damage and communication tracks, the age of a stand, the soil moisture content, the intensity of a particular cutting treatment expressed by units of harvested timber volume per one hectare of the stand, and the mean angle of terrain inclination. The CART models developed in these studies not only allowed the author to identify the conditions, under which the soil damage of a given degree is most likely to emerge, or determine the probability of its occurrence, but also, thanks to a graphical presentation of the nature and strength of relationships between the variables employed in the model construction, they facilitated a recognition of rules and relationships between these variables and the area, depth, volume and probability of occurrence of forest soil damage of a particular type. Moreover, the CART trees served for developing the so-called decision-making rules, which are especially useful in organising logging works. These rules allow the organisers of timber harvest to plan the management-related actions and operations with the use of available technical means and under conditions enabling their execution in such manner as to minimise the harm to forest soils. Furthermore, employing the CART trees for modelling soil disturbance made it possible to evaluate particular independent variables in terms of their impact on the values of dependent variables describing the recorded disturbance to outer soil layers. Thanks to this the author was able to identify, amongst the variables used in modelling the properties of soil damage, these particular ones that had the greatest impact on values of these properties, and determine the strength of this impact. Detailed results depended on the form of soil disturbance and the particular characteristics subject to analysis, however the variables with the strongest influence on the extent and probability of occurrence of soil damage, under the conditions encountered in the investigated stands, enclosed the following: the season of the year when logging works were performed, the volume-based cutting intensity of the felling treatments conducted, technical means used for completion of logging works, the soil moisture content during timber harvest, the manner of timber skidding, dragged, semi-suspended or forwarding, and finally a distance between the soil damage and transportation ducts. The CART models proved to be very useful in designing timber harvesting technologies that could minimise the risk of forest soil damage in terms of both, the extent of factual disturbance and the probability of its occurrence. Another valuable advantage of this kind of modelling is an opportunity to evaluate an impact of particular variables on the extent and probability of occurrence of damage to outer soil layers. This allows the investigator to identify, amongst all of the variables describing timber harvesting processes, those crucial ones, from which any optimisation process should start, in order to minimise the negative impact of forest management practices on soil condition.