Optimal analog wavelet bases construction using hybrid optimization algorithm

An approach for the construction of optimal analog wavelet bases is presented. First, the definition of an analog wavelet is given. Based on the definition and the least-squares error criterion, a general framework for designing optimal analog wavelet bases is established, which is one of difficult nonlinear constrained optimization problems. Then, to solve this problem, a hybrid algorithm by combining chaotic map particle swarm optimization (CPSO) with local sequential quadratic programming (SQP) is proposed. CPSO is an improved PSO in which the saw tooth chaotic map is used to raise its global search ability. CPSO is a global optimizer to search the estimates of the global solution, while the SQP is employed for the local search and refining the estimates. Benefiting from good global search ability of CPSO and powerful local search ability of SQP, a high-precision global optimum in this problem can be gained. Finally, a series of optimal analog wavelet bases are constructed using the hybrid algorithm. The proposed method is tested for various wavelet bases and the improved performance is compared with previous works.Peer reviewedFinal Published versio

Shannon Wavelet Chaotic Neural Network with Nonlinear Self-feedback

Shannon wavelet chaotic neural network is a kind of chaotic neural network with non-monotonous activation function composed by Sigmoid and Wavelet. In this paper, wavelet chaotic neural network models with different nonlinear self-feedbacks are proposed and the effects of the different self-feedbacks on simulated annealing are analyzed respectively. Then the proposed models are applied to the 10-city traveling salesman problem (TSP) and by comparison the performance of the model with wavelet self-feedback is superior to that of the rest others presented in this paper. Moreover, the performance of the model with wavelet self-feedback is improved by the scale index and the location index of the wavelet. Finally, the dynamics of an internal state of the model for the 10-city TSP is researched, including chaotic area distribution, the largest Lyapunov exponents and the effects of the chaotic distribution on the performance of the network for 10-city TSP. The numerical simulations show that the models can converge to the global minimum or approximate solutions more efficiently than the Hopfield network, and the performance of the model with wavelet self-feedback is superior to that of the others

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

Generalised cellular neural networks (GCNNs) constructed using particle swarm optimisation for spatio-temporal evolutionary pattern identification

Particle swarm optimization (PSO) is introduced to implement a new constructive learning algorithm for training generalized cellular neural networks (GCNNs) for the identification of spatio-temporal evolutionary (STE) systems. The basic idea of the new PSO-based learning algorithm is to successively approximate the desired signal by progressively pursuing relevant orthogonal projections. This new algorithm will thus be referred to as the orthogonal projection pursuit (OPP) algorithm, which is in mechanism similar to the conventional projection pursuit approach. A novel two-stage hybrid training scheme is proposed for constructing a parsimonious GCNN model. In the first stage, the orthogonal projection pursuit algorithm is applied to adaptively and successively augment the network, where adjustable parameters of the associated units are optimized using a particle swarm optimizer. The resultant network model produced at the first stage may be redundant. In the second stage, a forward orthogonal regression (FOR) algorithm, aided by mutual information estimation, is applied to re. ne and improve the initially trained network. The effectiveness and performance of the proposed method is validated by applying the new modeling framework to a spatio-temporal evolutionary system identification problem

Blind image separation based on exponentiated transmuted Weibull distribution

In recent years the processing of blind image separation has been investigated. As a result, a number of feature extraction algorithms for direct application of such image structures have been developed. For example, separation of mixed fingerprints found in any crime scene, in which a mixture of two or more fingerprints may be obtained, for identification, we have to separate them. In this paper, we have proposed a new technique for separating a multiple mixed images based on exponentiated transmuted Weibull distribution. To adaptively estimate the parameters of such score functions, an efficient method based on maximum likelihood and genetic algorithm will be used. We also calculate the accuracy of this proposed distribution and compare the algorithmic performance using the efficient approach with other previous generalized distributions. We find from the numerical results that the proposed distribution has flexibility and an efficient resultComment: 14 pages, 12 figures, 4 tables. International Journal of Computer Science and Information Security (IJCSIS),Vol. 14, No. 3, March 2016 (pp. 423-433

Doctor of Philosophy

dissertationThis dissertation consists of three independent essays on cyclical fluctuations of functional income distribution and effective demand in the Post-Keynesian tradition. The first essay investigates the longer run relationship between wage share and measurements of economic activity. Our main tools are wavelet covariance and multiresolution analysis. Results indicate that (1) Goodwin type cycles are observed even at longer run and (2) when considering smooth trends for periodicities longer than 32 years, a long Goodwin cycle seems to appear from the 1940s to mid-1990s that collapses afterwards. The second and third essays are related in the sense that they empirically investigate the possibility of strong internal dynamics in the business cycle model of effective demand and income distribution. Specifically, in the second essay, we study wage share and output gap in an univariate setting. Each time series is examined through chaos theory. The main tools are the nonlinear autoregressive neural network model, the dominant Lyapunov exponent, coefficient of determination, and local Lyapunov exponent. Results indicate that output gap might behave quasi-chaotically and wage share noisy-stable. Finally, the third essay inquires into the possibility of limit cycle in the two-dimensional model on wage share and output gap. For that, we use the multivariate nonlinear autoregressive neural network model. Our results indicate that limit cycle behavior describes well their dynamics and, furthermore, the instability is located on the wage share isocline. Chapters 1 through 3 open several questions that we hope further research will address. In Chapter 1, we conjecture that globalization plays a crucial role in the stagnation of the trends in the late 1990s. However, further research is required. Chapter 2 concludes that instability is rooted in the goods market dynamics rather than the distributive dynamics. Results on Chapter 3 indicate that the demand regime is stable and wage share locally unstable. This possibility remains largely unexplored both in the theoretical and empirical literature, and it creates a contradiction with the results found in Chapter 2. Further research is necessary on the robustness of the result, and possible mechanisms

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Solar mean magnetic field variability: A wavelet approach to Wilcox Solar Observatory and SOHO/Michelson Doppler Imager observations

Solar mean magnetic field (SMMF) measurements from the Wilcox Solar Observatory and with the SOHO/MDI instrument are described and analyzed. Even though two completely different methods of observation are used, the two data sets obtained show a strong similarity. Using continuous wavelet transforms, SMMF variability is found at a number of temporal scales. Detected SMMF signals with a 1–2 year period are considered to be linked to variations in the internal rotation of the Sun. Intermediate SMMF oscillations with a period of 80–200 days are probably connected to the evolution of large active regions. We also find evidence for 90 min variations with coronal mass ejections as a suggested origin