State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

A review of surrogate models and their application to groundwater modeling

The spatially and temporally variable parameters and inputs to complex groundwater models typically result in long runtimes which hinder comprehensive calibration, sensitivity, and uncertainty analysis. Surrogate modeling aims to provide a simpler, and hence faster, model which emulates the specified output of a more complex model in function of its inputs and parameters. In this review paper, we summarize surrogate modeling techniques in three categories: data-driven, projection, and hierarchical-based approaches. Data-driven surrogates approximate a groundwater model through an empirical model that captures the input-output mapping of the original model. Projection-based models reduce the dimensionality of the parameter space by projecting the governing equations onto a basis of orthonormal vectors. In hierarchical or multifidelity methods the surrogate is created by simplifying the representation of the physical system, such as by ignoring certain processes, or reducing the numerical resolution. In discussing the application to groundwater modeling of these methods, we note several imbalances in the existing literature: a large body of work on data-driven approaches seemingly ignores major drawbacks to the methods; only a fraction of the literature focuses on creating surrogates to reproduce outputs of fully distributed groundwater models, despite these being ubiquitous in practice; and a number of the more advanced surrogate modeling methods are yet to be fully applied in a groundwater modeling context

Block matching algorithm for motion estimation based on Artificial Bee Colony (ABC)

Block matching (BM) motion estimation plays a very important role in video coding. In a BM approach, image frames in a video sequence are divided into blocks. For each block in the current frame, the best matching block is identified inside a region of the previous frame, aiming to minimize the sum of absolute differences (SAD). Unfortunately, the SAD evaluation is computationally expensive and represents the most consuming operation in the BM process. Therefore, BM motion estimation can be approached as an optimization problem, where the goal is to find the best matching block within a search space. The simplest available BM method is the full search algorithm (FSA) which finds the most accurate motion vector through an exhaustive computation of SAD values for all elements of the search window. Recently, several fast BM algorithms have been proposed to reduce the number of SAD operations by calculating only a fixed subset of search locations at the price of poor accuracy. In this paper, a new algorithm based on Artificial Bee Colony (ABC) optimization is proposed to reduce the number of search locations in the BM process. In our algorithm, the computation of search locations is drastically reduced by considering a fitness calculation strategy which indicates when it is feasible to calculate or only estimate new search locations. Since the proposed algorithm does not consider any fixed search pattern or any other movement assumption as most of other BM approaches do, a high probability for finding the true minimum (accurate motion vector) is expected. Conducted simulations show that the proposed method achieves the best balance over other fast BM algorithms, in terms of both estimation accuracy and computational cost.Comment: 22 Pages. arXiv admin note: substantial text overlap with arXiv:1405.4721, arXiv:1406.448

Automatic Circle Detection on Images Based on an Evolutionary Algorithm That Reduces the Number of Function Evaluations

This paper presents an algorithm for the automatic detection of circular shapes from complicated and noisy images with no consideration of the conventional Hough transform principles. The proposed algorithm is based on a newly developed evolutionary algorithm called the Adaptive Population with Reduced Evaluations (APRE). Our proposed algorithm reduces the number of function evaluations through the use of two mechanisms: (1) adapting dynamically the size of the population and (2) incorporating a fitness calculation strategy, which decides whether the calculation or estimation of the new generated individuals is feasible. As a result, the approach can substantially reduce the number of function evaluations, yet preserving the good search capabilities of an evolutionary approach. Experimental results over several synthetic and natural images, with a varying range of complexity, validate the efficiency of the proposed technique with regard to accuracy, speed, and robustness

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Surrogate Groundwater Models

The spatially and temporally variable parameters and inputs to complex groundwater models typically result in long runtimes which hinder comprehensive analysis. These analyses typically involving calibration, sensitivity analysis and uncertainty propagation. Surrogate modelling aims to provide a simpler, and hence faster, model which emulates the specified output of a more complex model as a function of its inputs and parameters. A faster model enables more model runs, critical for understanding models through methods such as sensitivity and uncertainty analysis. Three broad categories of surrogate models are data-driven, projection, and hierarchical-based. Data-driven surrogates approximate a groundwater model through an empirical model that captures the input-output mapping of the original model. Projection-based models reduce the dimensionality of the parameter space by projecting the governing equations onto basis vectors. In hierarchical or multi-fidelity methods the surrogate is created by simplifying the representation of the physical system, such as by ignoring certain processes, or reducing the numerical resolution. A surrogate method can only be of practical value if it significantly reduces model runtimes, robustly emulates the output and can be implemented simply. A gamut of surrogate techniques have been applied to groundwater and similar partial differential equation based simulators, but the practicability of all approaches is not clear. Among the promising approaches are Polynomial Chaos Expansions (PCE), Multi-fidelity Stochastic Collocation (MFSC) and modern Deep Learning (DL) Neural Networks (NN). These are investigated in the thesis. They represent the three categories above as projection-based (depending on implementation), multi-fidelity and data-driven methods respectively. However all three methods are black box in that they do not require re-implementation of the complex model, making them relevant to practitioners. PCEs are an efficient and statistically rigorous approach with a number of well developed methods for their calibration. In the framework we present, they are suited to accelerating sensitivity analysis and uncertainty propagation of models with a moderate number of parameters. MFSC overcomes many shortcomings of other surrogate methods by employing a lower resolution model as the surrogate. The approach is shown to faithfully emulate spatially and temporally distributed parameters, and allows simply parallelization. While traditional NN are not the most promising surrogate technique, there is potential in the DL software frameworks associated with the recent boom in their popularity. This promise extends not just to efficient uncertainty analysis and data assimilation for groundwater modelling, but numerical modelling in general. Emulation using either PCE, MFSC or DL as demonstrated in this thesis will add value to practical groundwater modelling by not only reducing model runtimes but deepening understanding of the underlying model. The PCE approach iteratively selects the underlying model samples, training a surrogate with less than 1% error in under 200 model runs. The MFSC method achieves similar accuracy with less than 30 full model runs. The DL approaches are less efficient, requiring 500 model runs. However they emulate the full spatially distributed output of the underlying model, and can be applied in situations with 100s of uncertain parameters. Further contributions of this work include two improvements to the MFSC algorithm, reducing surrogate error by two orders of magnitude. We identify a gap between existing research in applied DL, theory-rich applied mathematics and the increasing quantity of spatially distributed data. We create a new surrogate form which combines PCE theory with a DL implementation, and develop another which captures physical aquifer properties during the training of a state of the art DL architecture

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p