Fractal Analysis

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

A novel numerical framework for simulation of multiscale spatio-temporally non-linear systems in additive manufacturing processes.

New computationally efficient numerical techniques have been formulated for multi-scale analysis in order to bridge mesoscopic and macroscopic scales of thermal and mechanical responses of a material. These numerical techniques will reduce computational efforts required to simulate metal based Additive Manufacturing (AM) processes. Considering the availability of physics based constitutive models for response at mesoscopic scales, these techniques will help in the evaluation of the thermal response and mechanical properties during layer-by-layer processing in AM. Two classes of numerical techniques have been explored. The first class of numerical techniques has been developed for evaluating the periodic spatiotemporal thermal response involving multiple time and spatial scales at the continuum level. The second class of numerical techniques is targeted at modeling multi-scale multi-energy dissipative phenomena during the solid state Ultrasonic Consolidation process. This includes bridging the mesoscopic response of a crystal plasticity finite element framework at inter- and intragranular scales and a point at the macroscopic scale. This response has been used to develop an energy dissipative constitutive model for a multi-surface interface at the macroscopic scale. An adaptive dynamic meshing strategy as a part of first class of numerical techniques has been developed which reduces computational cost by efficient node element renumbering and assembly of stiffness matrices. This strategy has been able to reduce the computational cost for solving thermal simulation of Selective Laser Melting process by ~100 times. This method is not limited to SLM processes and can be extended to any other fusion based additive manufacturing process and more generally to any moving energy source finite element problem. Novel FEM based beam theories have been formulated which are more general in nature compared to traditional beam theories for solid deformation. These theories have been the first to simulate thermal problems similar to a solid beam analysis approach. These are more general in nature and are capable of simulating general cross-section beams with an ability to match results for complete three dimensional analysis. In addition to this, a traditional Cholesky decomposition algorithm has been modified to reduce the computational cost of solving simultaneous equations involved in FEM simulations. Solid state processes have been simulated with crystal plasticity based nonlinear finite element algorithms. This algorithm has been further sped up by introduction of an interfacial contact constitutive model formulation. This framework has been supported by a novel methodology to solve contact problems without additional computational overhead to incorporate constraint equations averting the usage of penalty springs

Human Activity Recognition for AI-Enabled Healthcare Using Low-Resolution Infrared Sensor Data

This paper explores the feasibility of using low-resolution infrared (LRIR) image streams for human activity recognition (HAR) with potential application in e-healthcare. Two datasets based on synchronized multichannel LRIR sensors systems are considered for a comprehensive study about optimal data acquisition. A novel noise reduction technique is proposed for alleviating the effects of horizontal and vertical periodic noise in the 2D spatiotemporal activity profiles created by vectorizing and concatenating the LRIR frames. Two main analysis strategies are explored for HAR, including (1) manual feature extraction using texture-based and orthogonal-transformation-based techniques, followed by classification using support vector machine (SVM), random forest (RF), k-nearest neighbor (k-NN), and logistic regression (LR), and (2) deep neural network (DNN) strategy based on a convolutional long short-term memory (LSTM). The proposed periodic noise reduction technique showcases an increase of up to 14.15% using different models. In addition, for the first time, the optimum number of sensors, sensor layout, and distance to subjects are studied, indicating the optimum results based on a single side sensor at a close distance. Reasonable accuracies are achieved in the case of sensor displacement and robustness in detection of multiple subjects. Furthermore, the models show suitability for data collected in different environments

Physics-Guided Deep Learning for Dynamical Systems: A survey

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are interpretable but rely on rigid assumptions. And the direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, it does not necessarily obey the governing laws of physical systems, nor do they generalize well across different systems. Thus, the study of physics-guided DL emerged and has gained great progress. It aims to take the best from both physics-based modeling and state-of-the-art DL models to better solve scientific problems. In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL and discuss the emerging opportunities

Rupture Reactivation during the 2011 M_w 9.0 Tohoku Earthquake: Dynamic Rupture and Ground-Motion Simulations

Near‐source ground‐motion observations and kinematic source inversions suggest that the rupture process of the 2011 M_w 9.0 Tohoku earthquake involved rupture reactivation, that is, repeated rupture nucleation in the same hypocentral area. This unusual phenomenon may have provided a second breath to the rupture that enhanced its final size. Here, we propose that rupture reactivation may have been governed by a slip‐weakening friction model with two sequential strength drops, the second one being activated at large slip. Such frictional behavior has been previously observed in laboratory experiments and attributed to pressurization of fault‐zone fluids by mineral decomposition reactions activated by shear heating, such as dehydration and decarbonation. Further evidence of this double‐slip‐weakening friction model is obtained here from the dynamic stress changes in the hypocentral region derived from a finite source inversion model. We incorporate this friction model in a dynamic rupture simulation comprising two main asperities constrained by source inversion models and several deep small asperities constrained by backprojection source imaging studies. Our simulation produces ground‐motion patterns along the Japanese coast consistent with observations and rupture patterns consistent with a kinematic source model featuring rupture reactivation. The deep small asperities serve as a bridge to connect the two main asperities, and the rupture reactivation mechanism is needed to reproduce the observed ground‐motion pattern. Therefore, we argue that rupture reactivation during the 2011 Tohoku earthquake is consistent with a second strength drop, possibly caused by activation of thermochemical weakening processes at large slip

Forecasting Models for Integration of Large-Scale Renewable Energy Generation to Electric Power Systems

Amid growing concerns about climate change and non-renewable energy sources deple¬tion, vari¬able renewable energy sources (VRESs) are considered as a feasible substitute for conventional environment-polluting fossil fuel-based power plants. Furthermore, the transition towards clean power systems requires additional transmission capacity. Dynamic thermal line rating (DTLR) is being considered as a potential solution to enhance the current transmission line capacity and omit/postpone transmission system expansion planning, while DTLR is highly dependent on weather variations. With increasing the accommodation of VRESs and application of DTLR, fluctuations and variations thereof impose severe and unprecedented challenges on power systems operation. Therefore, short-term forecasting of large-scale VERSs and DTLR play a crucial role in the electric power system op¬eration problems. To this end, this thesis devotes on developing forecasting models for two large-scale VRESs types (i.e., wind and tidal) and DTLR. Deterministic prediction can be employed for a variety of power system operation problems solved by deterministic optimization. Also, the outcomes of deterministic prediction can be employed for conditional probabilistic prediction, which can be used for modeling uncertainty, used in power system operation problems with robust optimization, chance-constrained optimization, etc. By virtue of the importance of deterministic prediction, deterministic prediction models are developed. Prevalently, time-frequency decomposition approaches are adapted to decompose the wind power time series (TS) into several less non-stationary and non-linear components, which can be predicted more precisely. However, in addition to non-stationarity and nonlinearity, wind power TS demonstrates chaotic characteristics, which reduces the predictability of the wind power TS. In this regard, a wind power generation prediction model based on considering the chaosity of the wind power generation TS is addressed. The model consists of a novel TS decomposition approach, named multi-scale singular spectrum analysis (MSSSA), and least squares support vector machines (LSSVMs). Furthermore, deterministic tidal TS prediction model is developed. In the proposed prediction model, a variant of empirical mode decomposition (EMD), which alleviates the issues associated with EMD. To further improve the prediction accuracy, the impact of different components of wind power TS with different frequencies (scales) in the spatiotemporal modeling of the wind farm is assessed. Consequently, a multiscale spatiotemporal wind power prediction is developed, using information theory-based feature selection, wavelet decomposition, and LSSVM. Power system operation problems with robust optimization and interval optimization require prediction intervals (PIs) to model the uncertainty of renewables. The advanced PI models are mainly based on non-differentiable and non-convex cost functions, which make the use of heuristic optimization for tuning a large number of unknown parameters of the prediction models inevitable. However, heuristic optimization suffers from several issues (e.g., being trapped in local optima, irreproducibility, etc.). To this end, a new wind power PI (WPPI) model, based on a bi-level optimization structure, is put forward. In the proposed WPPI, the main unknown parameters of the prediction model are globally tuned based on optimizing a convex and differentiable cost function. In line with solving the non-differentiability and non-convexity of PI formulation, an asymmetrically adaptive quantile regression (AAQR) which benefits from a linear formulation is proposed for tidal uncertainty modeling. In the prevalent QR-based PI models, for a specified reliability level, the probabilities of the quantiles are selected symmetrically with respect the median probability. However, it is found that asymmetrical and adaptive selection of quantiles with respect to median can provide more efficient PIs. To make the formulation of AAQR linear, extreme learning machine (ELM) is adapted as the prediction engine. Prevalently, the parameters of activation functions in ELM are selected randomly; while different sets of random values might result in dissimilar prediction accuracy. To this end, a heuristic optimization is devised to tune the parameters of the activation functions. Also, to enhance the accuracy of probabilistic DTLR, consideration of latent variables in DTLR prediction is assessed. It is observed that convective cooling rate can provide informative features for DTLR prediction. Also, to address the high dimensional feature space in DTLR, a DTR prediction based on deep learning and consideration of latent variables is put forward. Numerical results of this thesis are provided based on realistic data. The simulations confirm the superiority of the proposed models in comparison to traditional benchmark models, as well as the state-of-the-art models