Toward Optimal Stratification for Stratified Monte-Carlo Integration

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More precisely, it is interesting to refine the partition of the domain in area where the noise to the function, or where the variations of the function, are very heterogeneous. On the other hand, having a (too) refined stratification is not optimal. Indeed, the more refined the stratification, the more difficult it is to adjust the allocation of the samples to the stratification, i.e. sample more points where the noise or variations of the function are larger. We provide in this paper an algorithm that selects online, among a large class of partitions, the partition that provides the optimal trade-off, and allocates the samples almost optimally on this partition

Toward optimal stratification for stratified monte-carlo integration

International audienceWe consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More precisely, it is interesting to refine the partition of the domain in area where the noise to the function, or where the variations of the function, are very heterogeneous. On the other hand, having a (too) refined stratification is not optimal. Indeed, the more refined the stratification, the more difficult it is to adjust the allocation of the samples to the stratification, i.e. sample more points where the noise or variations of the function are larger. We provide in this paper an algorithm that selects online, among a large class of partitions, the partition that provides the optimal trade-off, and allocates the samples almost optimally on this partitio

Recipes for replication:Applying open science principles to research software development and data collection with cognitive tasks

During the past decade, science witnessed a replication crisis where many findings of published research could not be reproduced by other researchers. Attempts to address this "replication crisis" have identified several avenues for improvement, such as making science more open. This allows for more transparency in the scientific workflow, thus reducing a researcher's degrees of freedom and enabling researchers to check each other's work more extensively. Open science is a multifaceted concept, but in practice, there seems to be a strong focus on pre-registration of research designs, open data, and open access publications. However, between the research design and data/publication, there is the phase of data collection. So far, this phase has received relatively little attention even though it is an essential part of the scientific workflow. Hence, this dissertation focuses on open data collection in the behavioral domain, with an emphasis on cognitive tasks. In modern behavioral science, cognitive task procedures are often automated by software running on a computer. Hence, the focus is on research software development and data collection with cognitive tasks, which are evaluated from the perspective of five schools of thought on open science: the democratic, infrastructure, pragmatic, measurement, and public school. I discuss how applying open science principles to research software development and behavioral data collection with cognitive tasks may address the replication crisis and may improve the quality of science in general

An Integrated Risk Analysis Methodology in a Multidisciplinary Design Environment

Design of complex, one-of-a-kind systems, such as space transportation systems, is characterized by high uncertainty and, consequently, high risk. It is necessary to account for these uncertainties in the design process to produce systems that are more reliable. Systems designed by including uncertainties and managing them, as well, are more robust and less prone to poor operations as a result of parameter variability. The quantification, analysis and mitigation of uncertainties are challenging tasks as many systems lack historical data. In such an environment, risk or uncertainty quantification becomes subjective because input data is based on professional judgment. Additionally, there are uncertainties associated with the analysis tools and models. Both the input data and the model uncertainties must be considered for a multi disciplinary systems level risk analysis. This research synthesizes an integrated approach for developing a method for risk analysis. Expert judgment methodology is employed to quantify external risk. This methodology is then combined with a Latin Hypercube Sampling - Monte Carlo simulation to propagate uncertainties across a multidisciplinary environment for the overall system. Finally, a robust design strategy is employed to mitigate risk during the optimization process. This type of approach to risk analysis is conducive to the examination of quantitative risk factors. The core of this research methodology is the theoretical framework for uncertainty propagation. The research is divided into three stages or modules. The first two modules include the identification/quantification and propagation of uncertainties. The third module involves the management of uncertainties or response optimization. This final module also incorporates the integration of risk into program decision-making. The risk analysis methodology, is applied to a launch vehicle conceptual design study at NASA Langley Research Center. The launch vehicle multidisciplinary environment consists of the interface between configuration and sizing analysis outputs and aerodynamic parameter computations. Uncertainties are analyzed for both simulation tools and their associated input parameters. Uncertainties are then propagated across the design environment and a robust design optimization is performed over the range of a critical input parameter. The results of this research indicate that including uncertainties into design processes may require modification of design constraints previously considered acceptable in deterministic analyses

The Role of Low Carbon Alcohol Fuels in Advanced Combustion

The production of alcohol fuels from bioderived feedstocks and the performance of next generation stratified low temperature combustion (LTC) modes for internal combustion engines are two research areas that have recently undergone rapid growth independently. Now, there is a need to bridge these two fields and identify the optimal combustion strategy for these low-carbon and carbon-neutral alcohol fuels as well as potential synergies. The large set of next generation stratified LTC modes are generalized into two groups based on how the heat release process proceeds in the compositionally stratified combustion chamber: lean-to-rich or rich-to-lean burn stratified combustion. It was found that the C1-C4 alcohol fuels are prime candidates to enable lean-to-rich burn stratified combustion based on their high cooling potentials and lack of cool flame reactivity (pre-ignition reactions). Previous experimental work by the author showed that a lean-to-rich burn stratified combustion mode, thermally stratified compression ignition (TSCI), can be enabled using a split injection of wet ethanol to gain control over the heat release process. The current work further investigates TSCI with wet ethanol experimentally on a diesel engine architecture, finding that the effectiveness of TSCI’s heat release control strategy is not affected by the use of external, cooled exhaust gas recirculation or intake boost. Further, it was shown that the effectiveness of TSCI’s heat release control strategy is highly coupled to the hardware used. Specifically, an injector whose spray targets high local heat transfer regions in the cylinder during the compression stroke is more effective at controlling the heat release process than an injector whose spray targets the adiabatic core. Additionally, a piston whose geometry allows regions with high compression stroke heat transfer to be distinct from the adiabatic core, such as a re-entrant bowl piston, will also increase the effectiveness of TSCI’s heat release control strategy. Using a split injection strategy to enable TSCI is not the only way to increase natural thermal stratification and control the heat release process. In this work, high-load LTC is experimentally enabled with wet ethanol on a light-duty gasoline engine architecture by employing a side-mounted, single hole injector with a relatively low injection pressure in a fairly quiescent combustion chamber. The low mixing propensity of this architecture results in a self-sustaining increase of thermal stratification that allows the high-load limit of LTC to be oxygen limited rather than noise limited. Following the experimental work with TSCI with wet ethanol, the LTC performance of seven bio-synthesizable C1-C4 alcohol fuels (methanol, ethanol, n-propanol, isopropanol, n-butanol, isobutanol, and sec-butanol) is experimentally characterized, showing that with the exception of n-butanol, the LTC performance of these fuels are similar, implying the remaining six fuels could form an equivalence class of fuels for LTC. To further explore this possibility, two previously proposed LTC fuel metrics are considered: critical compression ratio, a metric that describes the ignition propensity of a fuel in LTC, and normalized φ-sensitivity, a metric that describes how the local ignition delay time responds to a change in φ. The critical compression ratio, experimentally measured on a cooperative fuel research (CFR) engine, was shown to accurately predict the HCCI ignition propensity of the alcohol fuels near the critical compression ratio operating conditions. Similarly, the normalized φ-sensitivity showed the potential to predict the effectiveness of a fuel to control the heat release process of LTC using small amounts of in-cylinder stratification. The normalized φ-sensitivity could then serve as a blending benchmark for multi-alcohol water fuel blends