Search results for: approximate controllability

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 154

Authors: Luzie Krings

Abstract:

The electrification of the transport sector is increasingly recognized as a vital strategy for decarbonization. However, integrating electric vehicles (EVs) into the energy grid poses challenges due to decentralized power units and the intermittent nature of renewable energy sources. Vehicle-to-grid (V2G) technology offers a compelling solution by enabling EVs to function as mobile storage units, providing system services, reducing grid congestion, and offering economic incentives. This potential is particularly significant in freight transport, which accounts for 38% of transport-related emissions. The aggregated use of energy storage in this sector can facilitate grid stability and renewable energy integration. Despite this, existing optimization methods for energy markets frequently overlook operational constraints, such as fixed schedules and state-of-charge requirements, while redispatch markets remain underutilized. This study introduces a risk-averse optimization model for marketing EV flexibilities across multiple energy markets in Germany. Using a linear optimization framework, the model incorporates technical, regulatory, and user constraints. EVs are modeled as energy storage units, and the integration of renewable energy sources, such as photovoltaic (PV) and wind energy, is evaluated. To benchmark performance, unidirectional charging with dynamic tariffs is used as the reference scenario. The research examines four distinct logistics depot fleets, each with varying capacities and schedules, to simulate commercial EV operations. The methodology employs a multi-market optimization model that integrates Day-Ahead, Intraday, and Redispatch energy markets, each with specific trading conditions and temporal offsets. The tool, developed using the Python-based library energy pilot by Fraunhofer IEE, also explores scenarios where proprietary renewable energy sources are incorporated to maximize benefits. By accounting for charging schedules, market requirements, and technical constraints, the study aims to enhance grid stability and improve economic outcomes and integration of renewable energies. The findings highlight the economic, environmental, and grid-related advantages of optimizing EV flexibility. Compared to the reference scenario of unidirectional charging, bidirectional strategies delivered an approximate economic benefit of 20%. Furthermore, the integration of proprietary renewable energy sources increased by 15%, demonstrating the potential for environmental gains. The study revealed that the duration of a single charging cycle has a greater impact on economic benefits than the total daily charging time spread across multiple cycles. This underscores the marketing potential of vehicles with extended idle times rather than frequent charging cycles. In conclusion, optimizing energy trading through flexible EV portfolios and efficient charging infrastructure offers substantial cost savings, particularly by increasing the number of charging stations and extending charging cycle durations. By leveraging multiple marketing options, high investment costs can be offset through enhanced revenues. Further gains could be achieved by simultaneously optimizing all trading options, though this approach introduces risks from price volatility and unreliable redispatch capacities. As electrified trucks are modeled as energy storage units, the study's findings are applicable to other forms of energy storage, offering a scalable and transferable framework for future energy systems.

Keywords: electric vehicles, energy markets, energy storage, energy grid

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Authors: Lauti Dwita Santy, Hermes Panggabean, Syahrir Andi Mangga

Abstract:

The Bengkulu Basin is part of the Sunda Arc system, which is a classic convergent type margin that occur around the southern rim of the Eurasian continental (Sundaland) plate. The basin is located between deep sea trench (Mentawai Outer Arc high) and the volvanic/ magmatic Arc of the Barisan Mountains Range. To the northwest it is bounded by Padang High, to the northest by Barisan Mountains (Sumatra Fault Zone) to the southwest by Mentawai Fault Zone and to the southeast by Semangko High/ Sunda Strait. The stratigraphic succession and tectonic development can be broadly divided into four stage/ periods, i.e Late Jurassic- Early Cretaceous, Late Eocene-Early Oligocene, Late Oligocene-Early Miocene, Middle Miocene-Late Miocene and Pliocene-Plistocene, which are mainly controlled by the development of subduction activities. The Pre Tertiary Basement consist of sedimentary and shallow water limestone, calcareous mudstone, cherts and tholeiitic volcanic rocks, with Late Jurassic to Early Cretaceous in age. The sedimentation in this basin is depend on the relief of the Pre Tertiary Basement (Woyla Terrane) and occured into two stages, i.e. transgressive stage during the Latest Oligocene-Early Middle Miocene Seblat Formation, and the regressive stage during the Latest Middle Miocene-Pleistocene (Lemau, Simpangaur and Bintunan Formations). The Pre-Tertiary Faults were more intensive than the overlying cover, The Tertiary Rocks. There are two main fault trends can be distinguished, Northwest–Southwest Faults and Northeast-Southwest Faults. The NW-SE fault (Ketaun) are commonly laterally persistent, are interpreted to the part of Sumatran Fault Systems. They commonly form the boundaries to the Pre Tertiary basement highs and therefore are one of the faults elements controlling the geometry and development of the Tertiary sedimentary basins.The Northeast-Southwest faults was formed a conjugate set to the Northwest–Southeast Faults. In the earliest Tertiary and reactivated during the Plio-Pleistocene in a compressive mode with subsequent dextral displacement. The Block Faulting accross these two sets of faults related to approximate North–South compression in Paleogene time and produced a series of elongate basins separated by basement highs in the backarc and forearc region. The Bengkulu basin is interpreted having evolved from pull apart feature in the area southwest of the main Sumatra Fault System related to NW-SE trending in dextral shear.Based on Pyrolysis Yield (PY) vs Total Organic Carbon (TOC) diagram show that Seblat and Lemau Formation belongs to oil and Gas Prone with the quality of the source rocks includes into excellent and good (Lemau Formation), Fair and Poor (Seblat Formation). The fine-grained carbonaceous sediment of the Seblat dan Lemau Formations as source rocks, the coarse grained and carbonate sediments of the Seblat and Lemau Formations as reservoir rocks, claystone bed in Seblat and Lemau Formation as caprock. The source rocks maturation are late immature to early mature, with kerogen type II and III (Seblat Formation), and late immature to post mature with kerogen type I and III (Lemau Formation). The burial history show to 2500 m in depthh with paleo temperature reached 80oC. Trapping mechanism occur during Oligo–Miocene and Middle Miocene, mainly in block faulting system.

Keywords: fore arc, bengkulu, sumatra, sundaland, hydrocarbon, trapping mechanism

Procedia PDF Downloads 559