Sensitivity boundary integral equations with applications in engineering mechanics

In sensitivity analysis for problems involving thin domains or domains with cracks, conventional boundary integral equations must be supplemented and/or replaced by hypersingular ones. This is due to the fact that the conventional equations become nearly-degenerate for thin domains and actually degenerate for cracks. Such degenerate character follows from the close proximity to each other, or actual coincidence, of two defining surfaces in each case. Hypersingular boundary integral equations for sensitivity analysis are developed in two forms in this thesis, using a global regularization and a local regularization. The regularizations are facilitated by observing that the singularity order of the sensitivity BIE. formulas is no more than that of the ordinary BIE formulas. One motivation for this work is the computation of stress-intensity-factor sensitivities with respect to crack-growth. Other motivations would include optimization and design applications wherein sensitivities would be needed, but would otherwise be unavailable, for any reason, from conventional integral equations alone. In this thesis, examples of stress-intensity-sensitivities with respect to the size of a crack are given. Specifically, sensitivity values for a circular bar with an embedded penny-shaped crack under tension, bending, and torsion loadings are obtained and shown to be accurate. These examples verify the formulas and the codes developed in this dissertation

Design and Operation of an Islanded Microgrid at Constant Frequency

This chapter presents a method for operating an islanded microgrid at a constant frequency. The proposed method uses de-coupled PQ control plus real power reference generation based on voltage variation to control the grid-forming generator and grid-supporting generators. Its effectiveness has been validated by a three-phase microgrid system where there is one grid-forming generator, one grid-supporting, and one grid-feeding generator. The grid-forming generator produces its own voltage reference with a constant frequency of 50 Hz, while the grid-supporting and grid-feeding generators take the voltage as a reference at their respective coupling point with the microgrid. It is found that the grid-forming and grid-supporting generators work collaboratively to keep voltages at each bus around the rated value. For a practical microgrid, it is necessary to determine the location and sizing of each grid-supporting generator in order to keep the voltage profile within specification under all operating conditions. To achieve these two purposes and also to reduce the computational demand of modeling and to shorten simulation time, a single-phase equivalent microgrid has been adopted in this research. Such approach is useful for the design of a practical microgrid

Detecting Floating-Point Errors via Atomic Conditions

This paper tackles the important, difficult problem of detecting program inputs that trigger large floating-point errors in numerical code. It introduces a novel, principled dynamic analysis that leverages the mathematically rigorously analyzed condition numbers for atomic numerical operations, which we call atomic conditions, to effectively guide the search for large floating-point errors. Compared with existing approaches, our work based on atomic conditions has several distinctive benefits: (1) it does not rely on high-precision implementations to act as approximate oracles, which are difficult to obtain in general and computationally costly; and (2) atomic conditions provide accurate, modular search guidance. These benefits in combination lead to a highly effective approach that detects more significant errors in real-world code (e.g., widely-used numerical library functions) and achieves several orders of speedups over the state-of-the-art, thus making error analysis significantly more practical. We expect the methodology and principles behind our approach to benefit other floating-point program analysis tasks such as debugging, repair and synthesis. To facilitate the reproduction of our work, we have made our implementation, evaluation data and results publicly available on GitHub at https://github.com/FP-Analysis/atomic-condition.ISSN:2475-142

Complexity and Approximation Results for the Min-Sum and Min-Max Disjoint Paths Problems

Given a graph G=(V, E) and k source-sink pairs (s1, t1), …, (sk, tk) with each si, ti  V, the Min-Sum Disjoint Paths problem asks to find k disjoint paths connecting all the source-sink pairs with minimized total length, while the Min-Max Disjoint Paths problem asks for k disjoint paths connecting all the source-sink pairs with minimized length of the longest path. We show that the weighted Min-Sum Disjoint Paths problem is FPNP-complete in general graphs, and the unweighted Min-Sum Disjoint Paths problem and the unweighted Min-Max Disjoint Paths problem cannot be approximated within m(m1-1) for any constant   > 0 even in planar graphs, assuming P P NP, where m is the number of edges in G. We give for the first time a simple bicriteria approximation algorithm for the unweighted Min-Max Edge-Disjoint Paths problem and the weighted Min-Sum Edge-Disjoint Paths problem, w

IsoTree: A New Framework for De novo Transcriptome Assembly from RNA-seq Reads

High-throughput sequencing of mRNA has made the deep and efficient probing of transcriptome more affordable. However, the vast amounts of short RNA-seq reads make de novo transcriptome assembly an algorithmic challenge. In this work, we present IsoTree, a novel framework for transcripts reconstruction in the absence of reference genomes. Unlike most of de novo assembly methods that build de Bruijn graph or splicing graph by connecting $k-mers$ which are sets of overlapping substrings generated from reads, IsoTree constructs splicing graph by connecting reads directly. For each splicing graph, IsoTree applies an iterative scheme of mixed integer linear program to build a prefix tree, called isoform tree. Each path from the root node of the isoform tree to a leaf node represents a plausible transcript candidate which will be pruned based on the information of paired-end reads. Experiments showed that in most cases IsoTree performs better than other leading transcriptome assembly programs. IsoTree is available at https://github.com/Jane110111107/IsoTree

PI parameter tuning of converters for sub-synchronous interactions existing in grid-connected DFIG wind turbines

As a clean energy, wind power has been extensively exploited in the past few years. However, oscillations in wind turbines, particularly those from controllers, could severely affect the stability of power systems. Therefore, oscillation suppression is a recent research focus. Based on the small-signal model eigenvalues and participation factors, this paper detects the sub-synchronous interactions (SSI) mainly determined by converters' PI parameters in a grid-connected doubly fed induction generator (DFIG). With the aim of oscillation restraint, a novel optimization model with the reference-point based non-dominated sorting genetic algorithm (NSGA-III) and the t-distributed stochastic neighbour embedding (t-SNE) is developed to explore and visualize optimal ranges of PI parameters, facilitating the selection of the appropriate PI parameters to augment the damping. Additionally, to study the adaptability of the optimal PI parameters, interactions performance of the system that uses optimal parameters is studied with different output levels of the wind turbine. Finally, a time domain simulation and a practical experiment are conducted to demonstrate the effectiveness of the proposed approach. Results illustrate that the SSI of a grid-connected DFIG is suppressed by the optimization model. This study is highly beneficial to power system operators in integrating wind power and maintaining system stability.</p

Can a permutation be sorted by best short swaps?

A short swap switches two elements with at most one element caught between them. Sorting permutation by short swaps asks to find a shortest short swap sequence to transform a permutation into another. A short swap can eliminate at most three inversions. It is still open for whether a permutation can be sorted by short swaps each of which can eliminate three inversions. In this paper, we present a polynomial time algorithm to solve the problem, which can decide whether a permutation can be sorted by short swaps each of which can eliminate 3 inversions in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time, where n is the number of elements in the permutation. A short swap can cause the total length of two element vectors to decrease by at most 4. We further propose an algorithm to recognize a permutation which can be sorted by short swaps each of which can cause the element vector length sum to decrease by 4 in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time. This improves upon the O(n^2) algorithm proposed by Heath and Vergara to decide whether a permutation is so called lucky