Silverman's Height Inequality for Positive Characteristics

In the paper "Uniformity of Mordell-Lang" by Vesselin Dimitrov, Philipp Habegger and Ziyang Gao (arXiv:2001.10276), they use Silverman's Height Inequality and they give a proof of the same which makes use of Cartier divisors and hence drops the flatness assumption of structure morphisms of abelian schemes. However, their proof makes use of Hironaka's theorem on resolution of singularities which is unknown for fields of positive characteristic. We try to slightly modify their ideas and use blow-ups in place of Hironaka's theorem to make the proof effective for any fields with product formula where heights can be defined.Comment: We corrected a number of mistakes in the last versio

Large Language Model-Based Interpretable Machine Learning Control in Building Energy Systems

The potential of Machine Learning Control (MLC) in HVAC systems is hindered by its opaque nature and inference mechanisms, which is challenging for users and modelers to fully comprehend, ultimately leading to a lack of trust in MLC-based decision-making. To address this challenge, this paper investigates and explores Interpretable Machine Learning (IML), a branch of Machine Learning (ML) that enhances transparency and understanding of models and their inferences, to improve the credibility of MLC and its industrial application in HVAC systems. Specifically, we developed an innovative framework that combines the principles of Shapley values and the in-context learning feature of Large Language Models (LLMs). While the Shapley values are instrumental in dissecting the contributions of various features in ML models, LLM provides an in-depth understanding of rule-based parts in MLC; combining them, LLM further packages these insights into a coherent, human-understandable narrative. The paper presents a case study to demonstrate the feasibility of the developed IML framework for model predictive control-based precooling under demand response events in a virtual testbed. The results indicate that the developed framework generates and explains the control signals in accordance with the rule-based rationale

Opportunities and Challenges of Applying Large Language Models in Building Energy Efficiency and Decarbonization Studies: An Exploratory Overview

In recent years, the rapid advancement and impressive capabilities of Large Language Models (LLMs) have been evident across various domains. This paper explores the application, implications, and potential of LLMs in building energy efficiency and decarbonization studies. The wide-ranging capabilities of LLMs are examined in the context of the building energy field, including intelligent control systems, code generation, data infrastructure, knowledge extraction, and education. Despite the promising potential of LLMs, challenges including complex and expensive computation, data privacy, security and copyright, complexity in fine-tuned LLMs, and self-consistency are discussed. The paper concludes with a call for future research focused on the enhancement of LLMs for domain-specific tasks, multi-modal LLMs, and collaborative research between AI and energy experts

Advancing Building Energy Modeling with Large Language Models: Exploration and Case Studies

The rapid progression in artificial intelligence has facilitated the emergence of large language models like ChatGPT, offering potential applications extending into specialized engineering modeling, especially physics-based building energy modeling. This paper investigates the innovative integration of large language models with building energy modeling software, focusing specifically on the fusion of ChatGPT with EnergyPlus. A literature review is first conducted to reveal a growing trend of incorporating of large language models in engineering modeling, albeit limited research on their application in building energy modeling. We underscore the potential of large language models in addressing building energy modeling challenges and outline potential applications including 1) simulation input generation, 2) simulation output analysis and visualization, 3) conducting error analysis, 4) co-simulation, 5) simulation knowledge extraction and training, and 6) simulation optimization. Three case studies reveal the transformative potential of large language models in automating and optimizing building energy modeling tasks, underscoring the pivotal role of artificial intelligence in advancing sustainable building practices and energy efficiency. The case studies demonstrate that selecting the right large language model techniques is essential to enhance performance and reduce engineering efforts. Besides direct use of large language models, three specific techniques were utilized: 1) prompt engineering, 2) retrieval-augmented generation, and 3) multi-agent large language models. The findings advocate a multidisciplinary approach in future artificial intelligence research, with implications extending beyond building energy modeling to other specialized engineering modeling

Modeling Air Handling Units to Create a Diverse Fault Dataset for FDD Innovation: Lessons Learned and Recommendations

As energy management and information systems (e.g., automated fault detection and diagnostics [AFDD] tools) become more prevalent in the commercial building stock, it is important to determine the effectiveness of these technologies by benchmarking their performance. The authors have been working to develop the largest publicly available dataset of HVAC fault datasets for performance benchmarking applications, covering the most common HVAC systems and designs including chiller plants, rooftop packaged units, dual duct air handling unit and single duct air handling units. This study covers the development, modeling, and validation of a synthetic fault dataset for the air handling unit (AHU), one of the most common HVAC configurations found in the commercial building stock. Despite this being a common system, real-world time series data are scarce and usually do not span a wide range of weather conditions. Due to this limitation, two detailed AHU models, which included the single duct AHU and dual duct AHU developed in the Modelica language and HVACSIM+ were employed to carry out annual simulations of numerous common sensor faults, mechanical faults, and control sequence faults. The fault inclusive data were then validated by comparing fault effects on system performance to expected symptoms. We summarize the nature of each fault and their impacts under different weather and operation conditions. We report some lessons learnt during the efforts of validating the high volumes of the FDD data sets. Finally, we highlight considerations for FDD developers that may want to use this dataset to assess their algorithms’ performance and their improvement over time

From GPT-4 to Gemini and Beyond: Assessing the Landscape of MLLMs on Generalizability, Trustworthiness and Causality through Four Modalities

Multi-modal Large Language Models (MLLMs) have shown impressive abilities in generating reasonable responses with respect to multi-modal contents. However, there is still a wide gap between the performance of recent MLLM-based applications and the expectation of the broad public, even though the most powerful OpenAI's GPT-4 and Google's Gemini have been deployed. This paper strives to enhance understanding of the gap through the lens of a qualitative study on the generalizability, trustworthiness, and causal reasoning capabilities of recent proprietary and open-source MLLMs across four modalities: ie, text, code, image, and video, ultimately aiming to improve the transparency of MLLMs. We believe these properties are several representative factors that define the reliability of MLLMs, in supporting various downstream applications. To be specific, we evaluate the closed-source GPT-4 and Gemini and 6 open-source LLMs and MLLMs. Overall we evaluate 230 manually designed cases, where the qualitative results are then summarized into 12 scores (ie, 4 modalities times 3 properties). In total, we uncover 14 empirical findings that are useful to understand the capabilities and limitations of both proprietary and open-source MLLMs, towards more reliable downstream multi-modal applications

Advanced Solver Development for Large-Scale Dynamic Building System Simulation

Efficiently, robustly and accurately solving large and sparse nonlinear algebraic and differential equation system for dynamic building simulation is becoming more and more essential due to increasing demands to simulate large-scale problems for multiple buildings coupled with various levels of strength either through the smart grid or other means, such as district heating/cooling and shared distributed energy resources. This study is interested in advancing solving techniques that either improve the quality and efficiency of a dynamic building simulation model generically or improve the performance of the underlying equation solver. Nowadays, many commonly used tools for dynamic building system simulation still employ direct Newton methods. These methods are not only lack of convergence for stiff problems or cold starts, but also fail to meet the increased memory requirements associated with large-scale problems or more specific issues that arise in problems where the nonlinear equations resulted from the discretization of an underlying engineering differential equation. Therefore, a Newton-Krylov method that satisfies the computational need for large-scale dynamic building system simulation is investigated. An ideal preconditioner and an automatic update scheme are employed to ensure fast and robust simulation by way of the Newton-Krylov method. In addition to the comparison study focuses on the numerical solution methods, a generic function smoothing technique for the rare occasion that discontinuous functions are encountered is also investigated. Four testbeds, namely, 4Z5B, 4Z1B, 12Z5B, and 40Z5B, are developed in an HVACSIM+ environment to evaluate the advancement techniques. All testbeds simulate the airflow and thermal behaviour of building zones (from four zones, 4Z, to forty zones, 40Z) that are served by air handling unit (AHU) and variable air volume (VAV) systems. 4Z5B and 4Z1B testbeds simulate the same building system with the same number of equations but with different equation groupings while 4Z5B. 12Z5B and 40Z5B testbeds have the same equation grouping but are corresponding to very different building system sizes (four, twelve, and forty zones, respectively) and therefore different numbers of equations to be solved. The following tasks are completed and summarized in this report: (1) Develop numerical testbeds to evaluate solution methods and techniques. (2) Investigate potential numerical issues in a typical dynamic building system simulation model and seek generic techniques to improve the quality of the model. (3) Examine the performance of a Newton-Krylov method on solving dynamic building system simulation equations. (4) Improve the performance of the Newton-Krylov method by developing and employing proper preconditioning techniques. (5) Investigate potential strategies to construct physics-based preconditioners. (6) Investigate the impact of finite difference step size in Jacobian approximation on the performance of dynamic building system simulation. The major numerical issue found in the testbeds mentioned above is the discontinuity of the simple coil component model. A generic smoothing technique is employed to improve the performance of the discontinuous simple coil component model, and the smoothed model results in a more stable and more accurate solution. A Newton-Krylov method is employed to increase the computational speed of a large-scale simulation. However, the direct implementation of the Newton-Krylov method results in stability issues. Therefore, a preconditioned Newton-Krylov method that employs the ideal preconditioner and an automatic update scheme is developed in this study, referred to as INB-PSGMRES(m). This method performs as robust as the default Powell's Hybrid (PH) method in HVACSIM+ while saving a significant amount of computational time. Its computational time saving against the PH method is at least 49.7%, 91.8%, 88.7%, and 97.1% for 4Z5B, 4Z1B, 12Z5B, and 40Z5B testbeds, respectively. It is found that because of the employment of preconditioning, two important parameters of the INB-PSGMRES(m) method, i.e., the forcing term and the restarting parameter, have little impact on the simulation performance. A few potential partitioning strategies for developing a physics-based preconditioner are investigated. Due to the strong coupling of mass flow rates and pressures between each nodal point of the airflow network system, it is difficult to construct an effective physics-based preconditioner for the airflow network of an AHU-VAV system. On the other hand, the thermal network can be effectively exploited. A preconditioner that targets the coil related equations is found effective at reducing the condition number of the Jacobian (which typically leads to fast linear convergence in a Krylov method) due to the high nonlinearity of the coil component model and its strong impact on the temperature and humidity in the HVAC system. Four finite difference step sizes for the Jacobian approximation and four finite difference step sizes for the Jacobian-vector approximation are investigated. For the Jacobian approximation, the current finite difference step size employed by HVACSIM+ is effective for the operating period. Its performance can be improved for the nonoperating period by adding a lower bound to the finite difference step size.Ph.D., Architectural Engineering -- Drexel University, 201

The Sensor Roller: A Piezoelectric Energy Harvesting Roller in a Bearing for Self-Sustained IoT Sensors

With the high-speed development of the Internet of Things (IoT), powering such a massive number of wireless IoT sensors with chemical batteries become more and more unpractical. To make the IoT sensors self-sustained, Piezoelectric Energy Harvesting (PEH) technology provides an excellent solution to power the devices with a relatively long service time. By harvesting the ambient mechanical vibrations, PEH could generate a stable power source without wind or light.Currently, the famous bearing manufacturer, SKF, collaborates with TU Delft to design a self-sustained smart IoT roller with PEH technology, which will be implanted in huge bearings, such as the bearing in the wind turbines. This thesis project is a feasibility study investigating the possibility of replacing the chemical battery with the Piezoelectric Energy Harvester in SKF's smart IoT roller, called Sensor Roller. The objective of this project includes the system design of two generations of the prototype harvester. The first prototype concentrates on the properties of the piezoelectric material, while the second prototype focuses on the structure of the harvester. The design work consists of the raw data analysis of the target roller from SKF and the prototype construction and simulation in COMSOL Multiphysics. Besides, to make the results more reliable, two stages of the test with the practical components are made to study the harvester's performance under the actual working condition of the roller in the bearing. As a result, a tube shape Piezoelectric Energy Harvester with suitable materials and parameters is built. According to the simulation results, under a safe pressure level of the piezoelectric material, the proposed harvester achieves 8.1mW output power, which is enough for the loading sensors. The designed Piezoelectric Energy Harvester is being manufactured at present, and it is planned to be installed in the target roller to get the system-level test in the future.In addition to the harvester, some rectifiers are designed and taped out to improve the performance of the proposed Piezoelectric Energy Harvesting system. Three rectifiers are made with the Silicon Carbide (SiC) process to obtain a high voltage and temperature tolerance: a Full Bridge Rectifier (FBR), a Passive Rectifier, and a Synchronized Switch Harvesting on Inductor (SSHI) rectifier. Meanwhile, another SSHI rectifier is made with the 0.18um Silicon BCD process that focuses on solving the cold-startup problem. Consequently, simulated with the real transducer of the proposed harvester, both the FBR circuit and the Passive Rectifier circuit with the SiC process achieve over 10mW output power, and the SiC SSHI circuit achieves 37.1mW output power. As for the cold-startup SSHI rectifier circuit, it successfully reduces the required open circuit voltage by 4x to start up the SSHI system from the cold state.The results of this project show the great potential for applying the Piezoelectric Energy Harvesting technology to power the IoT sensors in the roller of bearing. Although some future works should be finished to build the commercial version of the energy harvesting roller, we are convinced that the fully self-sustained Sensor Roller with Piezoelectric Energy Harvesting technology will possibly show up in the near future.Electrical Enginee

A Highly Efficient Fully Integrated Active Rectifier for Ultrasonic Wireless Power Transfer

Ultrasonic wireless power transfer (WPT) has been proved to be a promising approach to power biomedical implants. To extract the energy generated from the transducer, a rectifier is typically required. Previous inductor-based rectifiers (SSHI and SECE) require a large off-chip inductor to achieve good performance, which is not desired for miniaturization and safety reasons. Synchronized switch harvesting on capacitors (SSHC) rectifiers have been proved to achieve high performance without inductors; however, they are mainly designed for low-frequency kinetic energy harvesting. In this paper, an improved SSHC rectifier is designed to achieve a fully integrated design with all flying capacitors implemented on-chip. The proposed SSHC rectifier can properly operate at ultrasonic excitation frequency (100 KHz) with precise switching time control and ultrafast voltage flipping techniques. In addition, an on-chip ultralow-power LDO allows the system to be self-sustained. The system is designed in a TSMC 180nm BCD technology and post-layout simulation results are presented.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Electronic Instrumentatio