An Optimization Based Empirical Mode Decomposition Scheme for Images

Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the $\ell_2$ inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema

Forecasting carbon price using empirical mode decomposition and evolutionary least squares support vector regression

Conventional methods are less robust in terms of accurately forecasting non-stationary and nonlineary carbon prices. In this study, we propose an empirical mode decomposition-based evolutionary least squares support vector regression multiscale ensemble forecasting model for carbon price forecasting. Firstly, each carbon price is disassembled into several simple modes with high stability and high regularity via empirical mode decomposition. Secondly, particle swarm optimization-based evolutionary least squares support vector regression is used to forecast each mode. Thirdly, the forecasted values of all the modes are composed into the ones of the original carbon price. Finally, using four different-matured carbon futures prices under the European Union Emissions Trading Scheme as samples, the empirical results show that the proposed model is more robust than the other popular forecasting methods in terms of statistical measures and trading performances

Forecasting carbon price using empirical mode decomposition and evolutionary least squares support vector regression

Conventional methods are less robust in terms of accurately forecasting non-stationary and nonlineary carbon prices. In this study, we propose an empirical mode decomposition-based evolutionary least squares support vector regression multiscale ensemble forecasting model for carbon price forecasting. Firstly, each carbon price is disassembled into several simple modes with high stability and high regularity via empirical mode decomposition. Secondly, particle swarm optimization-based evolutionary least squares support vector regression is used to forecast each mode. Thirdly, the forecasted values of all the modes are composed into the ones of the original carbon price. Finally, using four different-matured carbon futures prices under the European Union Emissions Trading Scheme as samples, the empirical results show that the proposed model is more robust than the other popular forecasting methods in terms of statistical measures and trading performances

A different view on the vector-valued empirical mode decomposition (VEMD)

The empirical mode decomposition (EMD) has achieved its reputation by providing a multi-scale time-frequency representation of nonlinear and/or nonstationary signals. To extend this method to vector-valued signals (VvS) in multidimensional (multi-D) space, a multivariate EMD (MEMD) has been designed recently, which employs an ensemble projection to extract local extremum locations (LELs) of the given VvS with respect to different projection directions. This idea successfully overcomes the problems of locally defining extrema of VvS. Different from the MEMD, where vector-valued envelopes (VvEs) are interpolated based on LELs extracted from the 1-D projected signal, the vector-valued EMD (VEMD) proposed in this paper employs a novel back projection method to interpolate the VvEs from 1-D envelopes in the projected space. Considering typical 4-D coordinates (3-D location and time), we show by numerical simulations that the VEMD outperforms state-of-art methods.Comment: 7th International Congress on Image and Signal Processing (CISP

Sensor-based Nonlinear and Nonstationary Dynaimc Analysis of Online Structural Health Monitoring

This dissertation focuses on robust online Structural Health Monitoring (SHM) framework for civil engineering structures. The proposed framework improves the diagnostic and prognostic schemes for damage-state awareness and structural life prediction in civil engineering structures. The underlying research achieves three main objectives, namely, (1) sensor placement optimization using partial differential equation modeling and Fisher information matrix, (2) structural damage detection using quasi-recursive correlation dimension (QRCD), and (3) structural damage prediction using online empirical mode decomposition (EMD).The research methodology includes three research tasks: Firstly, to formulate the optimal criteria for the sensor placement optimization damage detection problem based upon a partial differential equation (PDE) analytical model. The PDE model is derived and then validated through experimental results using correlation analysis. Secondly, to develop a novel quasi-recursive correlation dimension method for structural damage detection. The QRCD algorithm is integrated with an attractor analysis and overlapping windowing technique. Thirdly, to design an online structural damage prediction method based on empirical mode decomposition. The proposed SHM prediction scheme consists of two steps: prediction based change point detection using Hilbert instantaneous phase, and damage severity prediction using the energy index of the most representative intrinsic mode function (IMF).Study results show that; (1) the proposed optimal sensor placement method leads to an optimal spatial location for a collection of sensors, which are sensitive to structural damage, (2) the proposed damage detection algorithm can significantly alleviate the complexity of computation for correlation dimension to approximate O(N), making the online monitoring of nonlinear/nonstationary processes more applicable and efficient; and (3) the proposed empirical mode decomposition method for online damage prediction overcomes the boundary effects of the sifting process, and it has significant prediction accuracy improvement (greater than 30%) over other commonly used prediction techniques.Industrial Engineering & Managemen

Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

Wind Power Forecasting Methods Based on Deep Learning: A Survey

Accurate wind power forecasting in wind farm can effectively reduce the enormous impact on grid operation safety when high permeability intermittent power supply is connected to the power grid. Aiming to provide reference strategies for relevant researchers as well as practical applications, this paper attempts to provide the literature investigation and methods analysis of deep learning, enforcement learning and transfer learning in wind speed and wind power forecasting modeling. Usually, wind speed and wind power forecasting around a wind farm requires the calculation of the next moment of the definite state, which is usually achieved based on the state of the atmosphere that encompasses nearby atmospheric pressure, temperature, roughness, and obstacles. As an effective method of high-dimensional feature extraction, deep neural network can theoretically deal with arbitrary nonlinear transformation through proper structural design, such as adding noise to outputs, evolutionary learning used to optimize hidden layer weights, optimize the objective function so as to save information that can improve the output accuracy while filter out the irrelevant or less affected information for forecasting. The establishment of high-precision wind speed and wind power forecasting models is always a challenge due to the randomness, instantaneity and seasonal characteristics