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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

Buckling of Particle-Laden Interfaces

Dias Kassuga, Theo 07 November 2014 (has links)
We study the buckling of an oil-water interface populated by micron-sized latex particles using a Langmuir trough. We extend pre-existing results to the micron-range with different capillary length and compare the experimental data to the existing theoretical framework. An unexpected trend for the dominant wavelength of buckling is observed, suggesting that there is a transition between regimes in the micron-range. A mechanism for the new regime is proposed. Cascading is reported, as well as novel kinds of transition between wavelengths within the same particle raft. Lastly, the effect of compression on the macroscopic arrangement of particles is investigated, as well as its effect on the buckling wavelength.
12

The Social Cascades of Exposure to Flood Induced Natech Events on Vulnerable Populations in Hampton Roads, Virginia

Crawford, Margaret Calyer 31 May 2022 (has links)
Coastal flood impacts are increasing in severity with the rising sea levels, causing damage to ecological and human systems. Climate-hazards may also result in cascading impacts, where an initial disaster sets off a chain of events that extends beyond the initial spatiotemporal point of impact. Coastal flood events may result in consecutive disasters in which the initial flood event results in a secondary technological disaster, prompting disruptions to socio-economic systems and resulting in a public health crisis. Flood events that trigger technological emergencies through the inundation and dispersion of hazardous materials are known as Natech disasters. However, current research on the cascading impacts of Natech events is limited. Hampton Roads, Virginia, is experiencing an accelerated rate of sea level rise and a proportionally higher risk of storm surge, potentially leading to a greater risk of Natech disasters. The main objective of this study is to evaluate the impact of Natech events on surrounding communities in Hampton Roads. This study uses geospatial analysis to identify the current (2021) and future (2051) threats of flood-induced Natech disaster and assess its exposure to different coastal populations and ecosystems. The present study calculated the Flood Hazard Density Index (FHDI), using a 1-mile radius around the significantly flooded facilities to determine the spatial dispersion of Natech disasters. The flood risks were determined using the 100-year flood plain and intermediate (RCP 4.5) climate scenario. The risk of a Natech disaster was identified by combining the spatial extent of flood risk with the location of Toxics Release Inventory (TRI) facilities and National Priorities List (NPL) designated Superfund sites. The exposed environmental and social systems to Natech events were chosen through the literature gap analysis. Sociodemographic data from the American Community Survey were collected to examine its correlation with 2021 and 2051 FHDI-affected block groups. Findings reveal that block groups with higher proportions of minorities, people in poverty, and people without a vehicle experience significant exposure to a Natech disaster compared to those who are living further away from the TRI and Superfund facilities. Additionally, open water and wetland environments will also experience significant exposure to Natech events, which could indicate a loss of ecosystem services. This study suggests a need for proactive policy and programmatic interventions to minimize the potential impacts of Natech events on the surrounding communities, such as the remediation of Superfund sites and the development of hazard mitigation plans for TRI facilities. / Master of Science / Coastal flood impacts are increasing in severity with the rising sea levels, causing damage to ecological and human systems. Climate-hazards may also result in cascading impacts, where an initial disaster sets off a chain of events that extends beyond the initial spatial origin of impact, prolonging the effects of the initial disaster. Coastal flood events may result in consecutive disasters, where an initial flood event results in a secondary technological disaster, prompting disruptions to socio-economic systems and resulting in a public health crisis. Flood events that trigger technological emergencies causing the inundation and dispersion of hazardous materials are known as Natech disasters. However, current research on the cascading impacts of Natech events is limited. Hampton Roads, Virginia, is experiencing accelerated sea level rise and a proportionally higher risk of storm surge, potentially leading to a greater risk of Natech disasters. The main objective of this study is to evaluate the impact of Natech events on surrounding communities in Hampton Roads. This study uses geospatial analysis to identify the current (2021) and future (2051) threats of flood-induced Natech disaster and assess its exposure to different coastal populations and ecosystems. The present study used a 1-mile radius around the significantly flooded facilities to determine the spatial dispersion of Natech diasters. The flood risks were determined using the 1 in 100 annual flood risk and an intermediate climate projection. The risk of a Natech disaster was identified by combining the spatial extent of flood risk with the location of U.S. Environmental Protection Agency (U.S. EPA) regulated Toxics Release Inventory (TRI) facilities and National Priorities List (NPL) designated Superfund sites. The most susceptible social, economic, and environmental subsystems to Natech events were identified using a literature gap analysis. Sociodemographic data were collected from the American Community Survey to examine its relationship to the 2021 and 2051 Natech affected census block groups. Findings reveal that block groups with higher proportions of minorities, people in poverty, and people without a vehicle experience significant exposure to a Natech disaster compared to those who are living further away from the TRI and Superfund facilities. Additionally, open water and wetland environments will also experience significant exposure to Natech events, which may indicate a loss of ecosystem services. This study suggests a need for proactive policy and programmatic interventions to minimize the potential impacts of Natech events on the surrounding communities, such as the remediation of Superfund sites and the development of hazard mitigation plans for TRI facilities.
13

Network Modeling Stochastic and Deterministic Approaches

Sansavini, Giovanni 09 November 2010 (has links)
Stochastic and deterministic approaches for modeling complex networks are presented. The methodology combines analysis of the structure formed by the interconnections among the elements of a network with an assessment of the vulnerability towards the propagation of cascading failures. The goal is to understand the mutual interplay between the structure of the network connections and the propagation of cascading failures. Two fundamental issues related to the optimal design and operation of complex networks are addressed. The first concerns the impact that cascading failures have on networks due to the connectivity pattern linking their components. If the state of load on the network components is high, the risk of cascade spreadings becomes significant. In this case, the needed reduction of the connectivity efficiency to prevent the propagation of failures affecting the entire system is quantified. The second issue concerns the realization of the most efficient connectivity in a network that minimizes the propagations of cascading failures. It is found that a system that routinely approaches the critical load for the onset of cascading failures during its operation should have a larger efficiency value. This allows for a smoother transition to the cascade region and for a reasonable reaction time to counteract the onset of significant cascading failures. The interplay between the structure of the network connections and the propagation of cascading failures is assessed also in interdependent networks. In these systems, the linking among several network infrastructures is necessary for their optimal and economical operation. Yet, the interdependencies introduce weaknesses due to the fact that failures may cascade from one system to other interdependent systems, possibly affecting their overall functioning. Inspired by the global efficiency, a measure of the communication capabilities among interdependent systems, i.e. the interdependency efficiency, is defined. The relations between the structural parameters, i.e. the system links and the interdependency links, and the interdependency efficiency, are also quantified, as well as the relations between the structural parameters and the vulnerability towards the propagation of cascading failures. Resorting to this knowledge, the optimal interdependency connectivity is identified. Similar to the spreading of failures, the formation of a giant component is a critical phenomenon emerging as a result of the connectivity pattern in a network. This structural transition is exploited to identify the formation of macrometastases in the developed model for metastatic colonization in tumor growth. The methods of network theory proves particularly suitable to reproduce the local interactions among tumor cells that lead to the emergent global behavior of the metastasis as a community. This model for intercellular sensing reproduces the stepwise behavior characteristic of metastatic colonization. Moreover, it prompts the consideration of a curative intervention that hinders intercellular communication, even in the presence of a significant tumor cell population. / Ph. D.
14

WEB puslapių kūrimo CSS pagrindu mokymas internete / CSS Web pages creation Web based learning

Stankevičius, Stasys 26 August 2010 (has links)
Šiame magistriniame darbe yra pateikiama CSS (Cascading Style Sheeets) apžvalga ir mokymosi galimybių analizė. Taip pat darbe yra pateikiami tyrimo, skirto išsiaiškinti Lietuvoje gyvenančių suinteresuotų asmenų poreikius CSS mokymo kurso teikimui internete ir kurso teikimo aplinkai. Atsižvelgiant į tyrimo rezultatus parengtas pedagoginio kurso teikimo scenarijus ir kursui teikti skirtos virtualios aplinkos projektas bei dirbančios aplinkos vartotojo gidas. / Main aim of this work is to create CSS web-based course pedagogical model and develop web based learning environment ideal for this course. In this document’s project part you will find course, named “CSS usage for web pages creation process”, pedagogical model and web-based learning environment creating process detailed projecting steps. In the end of document you will find created learning environment using and administrating manual.
15

Topological analysis and mitigation strategies for cascading failures in power grid networks

Pahwa, Sakshi January 1900 (has links)
Master of Science / Department of Electrical and Computer Engineering / Caterina M. Scoglio / In recent times, research in the field of complex networks has advanced by leaps and bounds. Researchers have developed mathematical models for different networks such as epidemic networks, computer networks, power grid networks, and so on. In this thesis, the power grid has been modeled as a complex network. The power grid is being used extensively in every field today. Our dependence on the power grid has exceeded to an extent that we cannot think of survival without electricity. Recently, there has been an increasing concern about the growing possibility of cascading failures, due to the fact that the power grid is works close to full utilization. Furthermore, the problem will be exacerbated by the need to transfer a large amount of power generated by renewable sources from the regions where it is produced to the regions where it is consumed. Many researchers have studied these networks to find a solution to the problem of network robustness. Topological analysis may be considered as one of the components of analysis of a system's robustness. In the first part of this thesis, to study the cascading effect on power grid networks from a topological standpoint, we developed a simulator and used the IEEE standard networks for our analysis. The cascading effect was simulated on three standard networks, the IEEE 300 bus system, the IEEE 118 bus test system, and the WSCC 179 bus equivalent model. To extend our analysis to a larger set of networks with different topologies, we developed a first approximation network generator the creates networks with characteristics similar to the standard networks but with different topologies. The generated networks were then compared with the standard networks to show the effect of topology on the robustness of power grid networks. A comparison of the network metrics for the standard and the generated networks indicate that the generated networks are more robust than the standard ones. However, even if the generated topologies show an increased robustness with respect to the standard topologies, the real implementation and design of power grids based on those topologies requires further study, and will be considered as future work. In the second part of this thesis, we studied two mitigation strategies based on load reduction, Homogeneous load reduction and Targeted range-based load reduction. While the generic Homogeneous strategy will only mitigate the severity of the cascade when a non-negligible load reduction is performed, our newly proposed targeted load reduction strategy is much more efficient, reducing the load only in a small portion of the grid. The determination of this special portion of the grid is based on an algorithm, which finds the paths supplying power from the generators to the nodes. This algorithm is described in details in the Appendix B. While the Homogeneous strategy is easier to implement, efficient results can be obtained using the targeted strategy.
16

Dynamics on complex networks with application to power grids

Pahwa, Sakshi January 1900 (has links)
Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / The science of complex networks has significantly advanced in the last decade and has provided valuable insights into the properties of real world systems by evaluating their structure and construction. Several phenomena occurring in real technological and social systems can be studied, evaluated, quantified, and remedied with the help of network science. The electric power grid is one such real technological system that can be studied through the science of complex networks. The electric grid consists of three basic sub-systems: Generation, Transmission, and Distribution. The transmission sub-system is of particular interest in this work because its mesh-like structure offers challenging problems to complex networks researchers. Cascading dynamics of power grids is one of the problems that can be studied through complex networks. The North American Electric Reliability Corporation (NERC) defines a cascading failure as the uncontrolled successive loss of system elements triggered by an incident at any location. In this dissertation, we primarily discuss the dynamics of cascading failures in the power transmission grid, from a complex networks perspective, and propose possible solutions for mitigating their effects. We evaluate the grid dynamics for two specific scenarios, load growth and random fluctuations in the grid, to study the behavior of the grid under critical conditions. Further, we propose three mitigation strategies for reducing the damage caused by cascading failures. The first strategy is intentional islanding in the power transmission grid. The aim of this method is to intentionally split the grid into two or more separate self- sustaining components such that the initial failure is isolated and the separated components can function independently, with minimum load shedding. The second mitigation strategy involves controlled placement of distributed generation (DG) in the transmission system in order to enhance robustness of the grid. The third strategy requires the addition of a link in the transmission grid by reduction of the average spectral distance, utilizing the Ybus matrix of the grid and a novel algorithm. Through this dissertation, we aim to successfully cover the gap present in the complex networks domain, with respect to the vulnerability analysis of power grid networks.
17

Estudo da comunidade fitoplanctônica como bioindicador de poluição em três reservatórios em série do Parque Estadual das Fontes do Ipiranga (PEFI), São Paulo, SP / Phytoplankton community’s study as bioindicator of pollution in three cascading reservoir system in Parque Estadual das Fontes do Ipiranga (PEFI), São Paulo, SP

Lopes, Adriana Guidetti Dias 13 August 2007 (has links)
Os três reservatórios rasos e em série localizam-se no Parque Estadual das Fontes do Ipiranga (PEFI), região sudoeste do município de São Paulo, numa unidade de conservação que abriga as nascentes do histórico riacho do Ipiranga. O primeiro reservatório recebe água do Lago das Garças, um sistema artificial eutrófico, onde já foram detectadas florações de cianobactérias potencialmente tóxicas e com problemas ecológicos, sanitários e estéticos. Objetivo. Analisar a variação sazonal da comunidade fitoplanctônica de três reservatórios rasos subseqüentes a um lago hipereutrófico localizado no município de São Paulo/SP, visando avaliar a qualidade da água durante o sistema em série. Material e Métodos. As coletas foram realizadas trimensalmente durante o período de um ano (outubro/2005 a julho/2006), em uma estação de amostragem em cada um dos três reservatórios e a duas profundidades: superfície e fundo. Foram determinadas variáveis morfométricas (área superficial, perímetro, comprimento máximo e profundidade), climatológicas (temperatura do ar e precipitação), físicas e químicas (temperatura da água, transparência, zona eufótica, pH, condutividade, turbidez, oxigênio dissolvido, demanda bioquímica de oxigênio, fósforo total e ortofosfato, nitrogênio total e amoniacal), biológicas (coliformes totais e termotolerantes, clorofila-a, feofitina, composição florística, densidade total, biovolume, estimativa do número de células e espécies descritoras) e aplicações de índices biológicos. Na análise qualitativa foi empregada a rede de malha de 20 µm e identificação em microscópio óptico binocular com câmara clara. Na análise quantitativa, foi utilizado a garrafa coletora e método de sedimentação em câmara de volume definido e contagem em microscópio invertido. A ordenação dos dados foi realizada por meio da análise de componentes principais (ACP) e análise de correspondência canônica (ACC). Resultados. Como conseqüência da floração de cianobactérias registradas nos três reservatórios, foram identificados 125 táxons distribuídos em 12 classes. A classe com maior representatividade foi Chlorophyceae com 38,8%, seguida por Cyanobacteria (23,8%), Euglenophyceae (8,7%), Cryptophyceae (6,3%), Zygnemaphyceae (5,5%), Bacillariophyceae (4,7%) e 11,1% para as demais classes (Chrysophyceae, Coscinodiscophyceae, Dinophyceae, Xanthophyceae, Craspedomonadophyceae e Fragilariophyceae). Os táxons que apresentaram 100% de freqüência foram: Microcystis aeruginosa, Cylindrospermopsis raciborskii, Planktothrix agardhii (Cyanobacteria). As espécies descritoras que podem ser consideradas como bioindicadoras de poluição foram Cylindrospermopsis raciborskii e Chroococcus minutus, que juntas contribuíram com 79,4% de toda densidade deste estudo. Conclusões. A comunidade fitoplanctônica respondeu sazonalmente às estações do ano, predominando a classe Cyanophyceae na primavera e a classe Chlorophyceae nas demais estações e não houve melhoria na qualidade da água durante a série. / The three shallow cascading reservoir system are located in Parque Estadual das Fontes do Ipiranga (PEFI) Biological Reserve in the southern of São Paulo city where located headwater Ipiranga Stream. The first reservoir is linked to Lago das Garças, a shallow and eutrophic environment, where have become frequent blooms of Cyanobacteria that produce aggressive toxins which cause problems to environment and public health. Objective. This study aimed to analyze the sazonal variation of the phytoplankton community of three shallow cascading reservoir system subsequent of a eutrophic lake and avaliated the water quality. Material and Methods. Samples were collected quarterly during the period of one year (October/2005 to July/2006), in the deepest part of the each lake, in two depths. Morphometric variables (superficial area, perimeter, maximum length and depth), climatic variables (air temperature and precipitation), physical and chemical variables (water temperature, transparence of water, euphotic zone, pH, conductivity, turbidity, dissolved oxygen, biochemical oxygen demand, nutrients), biological variables (total and fecal coliforms, chlorophyll-a, pheopigments, species composition, density, biovolume, cells number and descriptions species) were determined. Qualitative samples were collected at the surface using planktonic net (20 µm) and identificated using a binocular optic microscope. Quantitative samples were obtained by collecting bottle and counting in inverted microscope. Multivariate statistical analysis was applied to calculate the correlations between biological and environmental data. Results. The phytoplankton community was composed of 125 taxons distributed in 12 classes: Chlorophyceae (38,8%) was the main class regarding species richness and density, followed by the Cyanobacteria (23,8%), Euglenophyceae (8,7%), Cryptophyceae (6,3%), Zygnemaphyceae (5,5%), Bacillariophyceae (4,7%) and 11,1% for others classes (Chrysophyceae, Coscinodiscophyceae, Dinophyceae, Xanthophyceae, Craspedomonadophyceae and Fragilariophyceae). Taxons that had appeared during all study are: Microcystis aeruginosa, Cylindrospermopsis raciborskii, Planktothrix agardhii (Cyanobacteria). Cylindrospermopsis raciborskii and Chroococcus minutus are descriptions species and they can be considered bioindicator of pollution because their density are elevated (79,4% of total density). Conclusions. The phytoplankton community as well as the environmental variables responded to the seasonality, predominance of Cyanophyceae in spring and Chlorophyceae in others stations. It didn’t have improvement in the quality of the water during the serie.
18

Estudo da comunidade fitoplanctônica como bioindicador de poluição em três reservatórios em série do Parque Estadual das Fontes do Ipiranga (PEFI), São Paulo, SP / Phytoplankton community’s study as bioindicator of pollution in three cascading reservoir system in Parque Estadual das Fontes do Ipiranga (PEFI), São Paulo, SP

Adriana Guidetti Dias Lopes 13 August 2007 (has links)
Os três reservatórios rasos e em série localizam-se no Parque Estadual das Fontes do Ipiranga (PEFI), região sudoeste do município de São Paulo, numa unidade de conservação que abriga as nascentes do histórico riacho do Ipiranga. O primeiro reservatório recebe água do Lago das Garças, um sistema artificial eutrófico, onde já foram detectadas florações de cianobactérias potencialmente tóxicas e com problemas ecológicos, sanitários e estéticos. Objetivo. Analisar a variação sazonal da comunidade fitoplanctônica de três reservatórios rasos subseqüentes a um lago hipereutrófico localizado no município de São Paulo/SP, visando avaliar a qualidade da água durante o sistema em série. Material e Métodos. As coletas foram realizadas trimensalmente durante o período de um ano (outubro/2005 a julho/2006), em uma estação de amostragem em cada um dos três reservatórios e a duas profundidades: superfície e fundo. Foram determinadas variáveis morfométricas (área superficial, perímetro, comprimento máximo e profundidade), climatológicas (temperatura do ar e precipitação), físicas e químicas (temperatura da água, transparência, zona eufótica, pH, condutividade, turbidez, oxigênio dissolvido, demanda bioquímica de oxigênio, fósforo total e ortofosfato, nitrogênio total e amoniacal), biológicas (coliformes totais e termotolerantes, clorofila-a, feofitina, composição florística, densidade total, biovolume, estimativa do número de células e espécies descritoras) e aplicações de índices biológicos. Na análise qualitativa foi empregada a rede de malha de 20 µm e identificação em microscópio óptico binocular com câmara clara. Na análise quantitativa, foi utilizado a garrafa coletora e método de sedimentação em câmara de volume definido e contagem em microscópio invertido. A ordenação dos dados foi realizada por meio da análise de componentes principais (ACP) e análise de correspondência canônica (ACC). Resultados. Como conseqüência da floração de cianobactérias registradas nos três reservatórios, foram identificados 125 táxons distribuídos em 12 classes. A classe com maior representatividade foi Chlorophyceae com 38,8%, seguida por Cyanobacteria (23,8%), Euglenophyceae (8,7%), Cryptophyceae (6,3%), Zygnemaphyceae (5,5%), Bacillariophyceae (4,7%) e 11,1% para as demais classes (Chrysophyceae, Coscinodiscophyceae, Dinophyceae, Xanthophyceae, Craspedomonadophyceae e Fragilariophyceae). Os táxons que apresentaram 100% de freqüência foram: Microcystis aeruginosa, Cylindrospermopsis raciborskii, Planktothrix agardhii (Cyanobacteria). As espécies descritoras que podem ser consideradas como bioindicadoras de poluição foram Cylindrospermopsis raciborskii e Chroococcus minutus, que juntas contribuíram com 79,4% de toda densidade deste estudo. Conclusões. A comunidade fitoplanctônica respondeu sazonalmente às estações do ano, predominando a classe Cyanophyceae na primavera e a classe Chlorophyceae nas demais estações e não houve melhoria na qualidade da água durante a série. / The three shallow cascading reservoir system are located in Parque Estadual das Fontes do Ipiranga (PEFI) Biological Reserve in the southern of São Paulo city where located headwater Ipiranga Stream. The first reservoir is linked to Lago das Garças, a shallow and eutrophic environment, where have become frequent blooms of Cyanobacteria that produce aggressive toxins which cause problems to environment and public health. Objective. This study aimed to analyze the sazonal variation of the phytoplankton community of three shallow cascading reservoir system subsequent of a eutrophic lake and avaliated the water quality. Material and Methods. Samples were collected quarterly during the period of one year (October/2005 to July/2006), in the deepest part of the each lake, in two depths. Morphometric variables (superficial area, perimeter, maximum length and depth), climatic variables (air temperature and precipitation), physical and chemical variables (water temperature, transparence of water, euphotic zone, pH, conductivity, turbidity, dissolved oxygen, biochemical oxygen demand, nutrients), biological variables (total and fecal coliforms, chlorophyll-a, pheopigments, species composition, density, biovolume, cells number and descriptions species) were determined. Qualitative samples were collected at the surface using planktonic net (20 µm) and identificated using a binocular optic microscope. Quantitative samples were obtained by collecting bottle and counting in inverted microscope. Multivariate statistical analysis was applied to calculate the correlations between biological and environmental data. Results. The phytoplankton community was composed of 125 taxons distributed in 12 classes: Chlorophyceae (38,8%) was the main class regarding species richness and density, followed by the Cyanobacteria (23,8%), Euglenophyceae (8,7%), Cryptophyceae (6,3%), Zygnemaphyceae (5,5%), Bacillariophyceae (4,7%) and 11,1% for others classes (Chrysophyceae, Coscinodiscophyceae, Dinophyceae, Xanthophyceae, Craspedomonadophyceae and Fragilariophyceae). Taxons that had appeared during all study are: Microcystis aeruginosa, Cylindrospermopsis raciborskii, Planktothrix agardhii (Cyanobacteria). Cylindrospermopsis raciborskii and Chroococcus minutus are descriptions species and they can be considered bioindicator of pollution because their density are elevated (79,4% of total density). Conclusions. The phytoplankton community as well as the environmental variables responded to the seasonality, predominance of Cyanophyceae in spring and Chlorophyceae in others stations. It didn’t have improvement in the quality of the water during the serie.
19

Modeling Cascading Failures in Power Systems in the Presence of Uncertain Wind Generation

Athari, Mir Hadi 01 January 2019 (has links)
One of the biggest threats to the power systems as critical infrastructures is large-scale blackouts resulting from cascading failures (CF) in the grid. The ongoing shift in energy portfolio due to ever-increasing penetration of renewable energy sources (RES) may drive the electric grid closer to its operational limits and introduce a large amount of uncertainty coming from their stochastic nature. One worrisome change is the increase in CFs. The CF simulation models in the literature do not allow consideration of RES penetration in studying the grid vulnerability. In this dissertation, we have developed tools and models to evaluate the impact of RE penetration on grid vulnerability to CF. We modeled uncertainty injected from different sources by analyzing actual high-resolution data from North American utilities. Next, we proposed two CF simulation models based on simplified DC power flow and full AC power flow to investigate system behavior under different operating conditions. Simulations show a dramatic improvement in the line flow uncertainty estimation based on the proposed model compared to the simplified DC OPF model. Furthermore, realistic assumptions on the integration of RE resources have been made to enhance our simulation technique. The proposed model is benchmarked against the historical blackout data and widely used models in the literature showing similar statistical patterns of blackout size.
20

Statistical Inference in Inverse Problems

Xun, Xiaolei 2012 May 1900 (has links)
Inverse problems have gained popularity in statistical research recently. This dissertation consists of two statistical inverse problems: a Bayesian approach to detection of small low emission sources on a large random background, and parameter estimation methods for partial differential equation (PDE) models. Source detection problem arises, for instance, in some homeland security applications. We address the problem of detecting presence and location of a small low emission source inside an object, when the background noise dominates. The goal is to reach the signal-to-noise ratio levels on the order of 10^-3. We develop a Bayesian approach to this problem in two-dimension. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov chain Monte Carlo simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source. Differential equation (DE) models are widely used to model dynamic processes in many fields. The forward problem of solving equations for given parameters that define the DEs has been extensively studied in the past. However, the inverse problem of estimating parameters based on observed state variables is relatively sparse in the statistical literature, and this is especially the case for PDE models. We propose two joint modeling schemes to solve for constant parameters in PDEs: a parameter cascading method and a Bayesian treatment. In both methods, the unknown functions are expressed via basis function expansion. For the parameter cascading method, we develop the algorithm to estimate the parameters and derive a sandwich estimator of the covariance matrix. For the Bayesian method, we develop the joint model for data and the PDE, and describe how the Markov chain Monte Carlo technique is employed to make posterior inference. A straightforward two-stage method is to first fit the data and then to estimate parameters by the least square principle. The three approaches are illustrated using simulated examples and compared via simulation studies. Simulation results show that the proposed methods outperform the two-stage method.

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