Open AccessArticle
Entropy Conditions Involved in the Nonlinear Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows
Entropy 2017, 19(12), 683; doi:10.3390/e19120683 (registering DOI) -
Abstract
The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this
[...] Read more.
The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this study, we first report the important and detailed issues in the use of the H theorem and positive entropy generation in the NCCM. Importantly, the unified nonlinear dissipation model and its relationships to the Rayleigh–Onsager function were demonstrated in the treatment of the collision term of the Boltzmann equation. In addition, we compare the Grad moment method, the Burnett equation, and the NCCM. Next, differences between the NCCM equations and the Navier–Stokes equations are explained in detail. For validation, numerical studies of rarefied and continuum gas flows were conducted. These studies include rarefied and/or continuum gas flows around a two-dimensional (2D) cavity, a 2D airfoil, a 2D cylinder, and a three-dimensional space shuttle. It was observed that the present results of the NCCM are in good agreement with those of the Direct Simulation Monte Carlo (DSMC) method in rarefied cases and are in good agreement with those of the Navier–Stokes equations in continuum cases. Finally, this study can be regarded as a theoretical basis of the NCCM for the development of a unified framework for solving continuum-rarefied gas flows. Full article
Open AccessArticle
Channel Capacity of Coding System on Tsallis Entropy and q-Statistics
Entropy 2017, 19(12), 682; doi:10.3390/e19120682 (registering DOI) -
Abstract
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of
[...] Read more.
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression between code length and code appearance probability and, additionally, a generalized formula of the channel capacity on the basis of Tsallis entropy statistics. This theoretical framework may contribute to data processing techniques and other applications. Full article
Open AccessEditorial
Second-Law Analysis: A Powerful Tool for Analyzing Computational Fluid Dynamics (CFD) Results
Entropy 2017, 19(12), 679; doi:10.3390/e19120679 -
Abstract
Second-law analysis (SLA) is an important concept in thermodynamics, which basically assesses energy by its value in terms of its convertibility from one form to another.[...] Full article
Open AccessArticle
Information Landscape and Flux, Mutual Information Rate Decomposition and Connections to Entropy Production
Entropy 2017, 19(12), 678; doi:10.3390/e19120678 -
Abstract
We explored the dynamics of two interacting information systems. We show that for the Markovian marginal systems, the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the
[...] Read more.
We explored the dynamics of two interacting information systems. We show that for the Markovian marginal systems, the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time-reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviors of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibrium or time-irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts, respectively. This decomposition of the Mutual Information Rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains. Full article
Open AccessArticle
Altered Brain Complexity in Women with Primary Dysmenorrhea: A Resting-State Magneto-Encephalography Study Using Multiscale Entropy Analysis
Entropy 2017, 19(12), 680; doi:10.3390/e19120680 -
Abstract
How chronic pain affects brain functions remains unclear. As a potential indicator, brain complexity estimated by entropy-based methods may be helpful for revealing the underlying neurophysiological mechanism of chronic pain. In this study, complexity features with multiple time scales and spectral features were
[...] Read more.
How chronic pain affects brain functions remains unclear. As a potential indicator, brain complexity estimated by entropy-based methods may be helpful for revealing the underlying neurophysiological mechanism of chronic pain. In this study, complexity features with multiple time scales and spectral features were extracted from resting-state magnetoencephalographic signals of 156 female participants with/without primary dysmenorrhea (PDM) during pain-free state. Revealed by multiscale sample entropy (MSE), PDM patients (PDMs) exhibited loss of brain complexity in regions associated with sensory, affective, and evaluative components of pain, including sensorimotor, limbic, and salience networks. Significant correlations between MSE values and psychological states (depression and anxiety) were found in PDMs, which may indicate specific nonlinear disturbances in limbic and default mode network circuits after long-term menstrual pain. These findings suggest that MSE is an important measure of brain complexity and is potentially applicable to future diagnosis of chronic pain. Full article
Figures

Figure 1

Open AccessArticle
Automated Detection of Paroxysmal Atrial Fibrillation Using an Information-Based Similarity Approach
Entropy 2017, 19(12), 677; doi:10.3390/e19120677 -
Abstract
Atrial fibrillation (AF) is an abnormal rhythm of the heart, which can increase heart-related complications. Paroxysmal AF episodes occur intermittently with varying duration. Human-based diagnosis of paroxysmal AF with a longer-term electrocardiogram recording is time-consuming. Here we present a fully automated ensemble model
[...] Read more.
Atrial fibrillation (AF) is an abnormal rhythm of the heart, which can increase heart-related complications. Paroxysmal AF episodes occur intermittently with varying duration. Human-based diagnosis of paroxysmal AF with a longer-term electrocardiogram recording is time-consuming. Here we present a fully automated ensemble model for AF episode detection based on RR-interval time series, applying a novel approach of information-based similarity analysis and ensemble scheme. By mapping RR-interval time series to binary symbolic sequences and comparing the rank-frequency patterns of m-bit words, the dissimilarity between AF and normal sinus rhythms (NSR) were quantified. To achieve high detection specificity and sensitivity, and low variance, a weighted variation of bagging with multiple AF and NSR templates was applied. By performing dissimilarity comparisons between unknown RR-interval time series and multiple templates, paroxysmal AF episodes were detected. Based on our results, optimal AF detection parameters are symbolic word length m = 9 and observation window n = 150, achieving 97.04% sensitivity, 97.96% specificity, and 97.78% overall accuracy. Sensitivity, specificity, and overall accuracy vary little despite changes in m and n parameters. This study provides quantitative information to enhance the categorization of AF and normal cardiac rhythms. Full article
Figures

Figure 1

Open AccessArticle
On the Statistical Mechanics of Alien Species Distribution
Entropy 2017, 19(12), 674; doi:10.3390/e19120674 -
Abstract
Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur’s broken stick). We show
[...] Read more.
Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur’s broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter—some global resource partitioned at random on the two axes of species number and site number. A dynamical model generating this equilibrium is a two-fold stochastic process and suggests a curious and interesting biological interpretation in terms of niche structures fluctuating with time and productivity, with sites and species highly idiosyncratic. Idiosyncrasy implies that attempts to identify a priori those species likely to become naturalised are unlikely to be successful. Although this paper is primarily concerned with a particular problem in population biology, the two-fold stochastic process may be of more general interest. Full article
Figures

Figure 1

Open AccessArticle
Maximum Exergetic Efficiency Operation of a Solar Powered H2O-LiBr Absorption Cooling System
Entropy 2017, 19(12), 676; doi:10.3390/e19120676 -
Abstract
A solar driven cooling system consisting of a single effect H2O-LiBr absorbtion cooling module (ACS), a parabolic trough collector (PTC), and a storage tank (ST) module is analyzed during one full day operation. The pressurized water is used to transfer heat
[...] Read more.
A solar driven cooling system consisting of a single effect H2O-LiBr absorbtion cooling module (ACS), a parabolic trough collector (PTC), and a storage tank (ST) module is analyzed during one full day operation. The pressurized water is used to transfer heat from PTC to ST and to feed the ACS desorber. The system is constrained to operate at the maximum ACS exergetic efficiency, under a time dependent cooling load computed on 15 July for a one storey house located near Bucharest, Romania. To set up the solar assembly, two commercial PTCs were selected, namely PT1-IST and PTC 1800 Solitem, and a single unit ST was initially considered. The mathematical model, relying on the energy balance equations, was coded under Engineering Equation Solver (EES) environment. The solar data were obtained from the Meteonorm database. The numerical simulations proved that the system cannot cover the imposed cooling load all day long, due to the large variation of water temperature inside the ST. By splitting the ST into two units, the results revealed that the PT1-IST collector only drives the ACS between 9 am and 4:30 pm, while the PTC 1800 one covers the entire cooling period (9 am–6 pm) for optimum ST capacities of 90 kg/90 kg and 90 kg/140 kg, respectively. Full article
Figures

Figure 1

Open AccessArticle
A General Symbolic Approach to Kolmogorov-Sinai Entropy
Entropy 2017, 19(12), 675; doi:10.3390/e19120675 -
Abstract
It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back
[...] Read more.
It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back to innovative works of Bandt and Pompe—ordinal symbolic dynamics—plays an increasing role. In this paper, we discuss both approaches novelly in one breath with respect to the theoretical determination of the Kolmogorov-Sinai entropy (KS entropy). For this purpose, we propose and investigate a unifying approach to formalize symbolizations. By doing so, we can emphasize the main advantage of the ordinal approach if no symbolization scheme can be found that characterizes KS entropy directly: the ordinal approach, as well as generalizations of it provide, under very natural conditions, a direct route to KS entropy by default. Full article
Open AccessArticle
Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool
Entropy 2017, 19(12), 673; doi:10.3390/e19120673 -
Abstract
Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement
[...] Read more.
Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement (NREM) sleep. However, other aspects such as change of patterns associated with brain dynamics may not be captured unless a non-linear-based analysis method is used. In this pilot study, Permutation Lempel–Ziv complexity (PLZC), a novel symbolic dynamics analysis method, was used to characterise the changes in the EEG in sleep and wakefulness during baseline and recovery from sleep deprivation (SD). The results obtained with PLZC were contrasted with a related non-linear method, Lempel–Ziv complexity (LZC). Both measure the emergence of new patterns. However, LZC is dependent on the absolute amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates activated brain states associated with wakefulness and REM sleep, which both displayed higher complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations. Full article
Figures

Figure 1

Open AccessArticle
Association between Multiscale Entropy Characteristics of Heart Rate Variability and Ischemic Stroke Risk in Patients with Permanent Atrial Fibrillation
Entropy 2017, 19(12), 672; doi:10.3390/e19120672 -
Abstract
Multiscale entropy (MSE) profiles of heart rate variability (HRV) in patients with atrial fibrillation (AFib) provides clinically useful information for ischemic stroke risk assessment, suggesting that the complex properties characterized by MSE profiles are associated with ischemic stroke risk. However, the meaning of
[...] Read more.
Multiscale entropy (MSE) profiles of heart rate variability (HRV) in patients with atrial fibrillation (AFib) provides clinically useful information for ischemic stroke risk assessment, suggesting that the complex properties characterized by MSE profiles are associated with ischemic stroke risk. However, the meaning of HRV complexity in patients with AFib has not been clearly interpreted, and the physical and mathematical understanding of the relation between HRV dynamics and the ischemic stroke risk is not well established. To gain a deeper insight into HRV dynamics in patients with AFib, and to improve ischemic stroke risk assessment using HRV analysis, we study the HRV characteristics related to MSE profiles, such as the long-range correlation and probability density function. In this study, we analyze the HRV time series of 173 patients with permanent AFib. Our results show that, although HRV time series in patients with AFib exhibit long-range correlation (1/f fluctuations)—as observed in healthy subjects—in a range longer than 90 s, these autocorrelation properties have no significant predictive power for ischemic stroke occurrence. Further, the probability density function structure of the coarse-grained times series at scales greater than 2 s is dominantly associated with ischemic stroke risk. This observation could provide valuable information for improving ischemic stroke risk assessment using HRV analysis. Full article
Figures

Figure 1

Open AccessArticle
Inspecting Non-Perturbative Contributions to the Entanglement Entropy via Wavefunctions
Entropy 2017, 19(12), 671; doi:10.3390/e19120671 -
Abstract
In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with
[...] Read more.
In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunneling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases with the number of minima. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunneling system, we also extract the exponentially-suppressed tail contribution, the analogue of instantons. To understand the effects of multiple minima in a field theory, we are inspired to inspect wavefunctions in a toy model of a bosonic field describing quasi-particles of two different condensates related by Bogoliubov transformations. We find that the area law is naturally preserved. This is probably a useful set of perspectives that promise wider applications. Full article
Figures

Figure 1

Open AccessArticle
Oscillations in Multiparticle Production Processes
Entropy 2017, 19(12), 670; doi:10.3390/e19120670 -
Abstract
We discuss two examples of oscillations apparently hidden in some experimental results for high-energy multiparticle production processes: (i) the log-periodic oscillatory pattern decorating the power-like Tsallis distributions of transverse momenta; (ii) the oscillations of the modified combinants obtained from the measured multiplicity distributions.
[...] Read more.
We discuss two examples of oscillations apparently hidden in some experimental results for high-energy multiparticle production processes: (i) the log-periodic oscillatory pattern decorating the power-like Tsallis distributions of transverse momenta; (ii) the oscillations of the modified combinants obtained from the measured multiplicity distributions. Our calculations are confronted with pp data from the Large Hadron Collider (LHC). We show that in both cases, these phenomena can provide new insight into the dynamics of these processes. Full article
Figures

Figure 1

Open AccessArticle
Thermoelectrics of Interacting Nanosystems—Exploiting Superselection Instead of Time-Reversal Symmetry
Entropy 2017, 19(12), 668; doi:10.3390/e19120668 -
Abstract
Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager’s results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems—deriving from the fundamental fermion-parity superselection principle of quantum
[...] Read more.
Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager’s results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems—deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems—provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here. Full article
Figures

Figure 1

Open AccessArticle
Formation of Photo-Responsive Liquid Crystalline Emulsion by Using Microfluidics Device
Entropy 2017, 19(12), 669; doi:10.3390/e19120669 -
Abstract
Photo-responsive double emulsions made of liquid crystal (LC) were prepared by a microfluidic device, and the light-induced processes were studied. The phase transition was induced from the center of the topological defect for an emulsion made of (N-(4-methoxybenzylidene)-4-butylaniline (MBBA), and strange
[...] Read more.
Photo-responsive double emulsions made of liquid crystal (LC) were prepared by a microfluidic device, and the light-induced processes were studied. The phase transition was induced from the center of the topological defect for an emulsion made of (N-(4-methoxybenzylidene)-4-butylaniline (MBBA), and strange texture change was observed for an emulsion made of 4-cyano-4′-pentylbiphenyl (5CB) doped with azobenzene. The results suggest that there are defect-involved processes in the phase change of LC double emulsions. Full article
Figures

Figure 1

Open AccessArticle
Fault Diagnosis of Rolling Bearings Based on EWT and KDEC
Entropy 2017, 19(12), 633; doi:10.3390/e19120633 -
Abstract
This study proposes a novel fault diagnosis method that is based on empirical wavelet transform (EWT) and kernel density estimation classifier (KDEC), which can well diagnose fault type of the rolling element bearings. With the proposed fault diagnosis method, the vibration signal of
[...] Read more.
This study proposes a novel fault diagnosis method that is based on empirical wavelet transform (EWT) and kernel density estimation classifier (KDEC), which can well diagnose fault type of the rolling element bearings. With the proposed fault diagnosis method, the vibration signal of rolling element bearing was firstly decomposed into a series of F modes by EWT, and the root mean square, kurtosis, and skewness of the F modes were computed and combined into the feature vector. According to the characteristics of kernel density estimation, a classifier based on kernel density estimation and mutual information was proposed. Then, the feature vectors were input into the KDEC for training and testing. The experimental results indicated that the proposed method can effectively identify three different operative conditions of rolling element bearings, and the accuracy rates was higher than support vector machine (SVM) classifier and back-propagation (BP) neural network classifier. Full article
Figures

Open AccessArticle
Assessment of Component Selection Strategies in Hyperspectral Imagery
Entropy 2017, 19(12), 666; doi:10.3390/e19120666 -
Abstract
Hyperspectral imagery (HSI) integrates many continuous and narrow bands that cover different regions of the electromagnetic spectrum. However, the main challenge is the high dimensionality of HSI data due to the ’Hughes’ phenomenon. Thus, dimensionality reduction is necessary before applying classification algorithms to
[...] Read more.
Hyperspectral imagery (HSI) integrates many continuous and narrow bands that cover different regions of the electromagnetic spectrum. However, the main challenge is the high dimensionality of HSI data due to the ’Hughes’ phenomenon. Thus, dimensionality reduction is necessary before applying classification algorithms to obtain accurate thematic maps. We focus the study on the following feature-extraction algorithms: Principal Component Analysis (PCA), Minimum Noise Fraction (MNF), and Independent Component Analysis (ICA). After a literature survey, we have observed a lack of a comparative study on these techniques as well as accurate strategies to determine the number of components. Hence, the first objective was to compare traditional dimensionality reduction techniques (PCA, MNF, and ICA) in HSI of the Compact Airborne Spectrographic Imager (CASI) sensor and to evaluate different strategies for selecting the most suitable number of components in the transformed space. The second objective was to determine a new dimensionality reduction approach by dividing the CASI HSI regarding the spectral regions covering the electromagnetic spectrum. The components selected from the transformed space of the different spectral regions were stacked. This stacked transformed space was evaluated to see if the proposed approach improves the final classification. Full article
Figures

Figure 1

Open AccessArticle
L1-Minimization Algorithm for Bayesian Online Compressed Sensing
Entropy 2017, 19(12), 667; doi:10.3390/e19120667 -
Abstract
In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to
[...] Read more.
In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning. Full article
Figures

Figure 1

Open AccessArticle
Entropic Updating of Probabilities and Density Matrices
Entropy 2017, 19(12), 664; doi:10.3390/e19120664 -
Abstract
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel.
[...] Read more.
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information. Full article
Open AccessArticle
An Improved Chaotic Optimization Algorithm Applied to a DC Electrical Motor Modeling
Entropy 2017, 19(12), 665; doi:10.3390/e19120665 -
Abstract
The chaos-based optimization algorithm (COA) is a method to optimize possibly nonlinear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by means of nonlinear, discrete-time dynamical systems to explore the
[...] Read more.
The chaos-based optimization algorithm (COA) is a method to optimize possibly nonlinear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by means of nonlinear, discrete-time dynamical systems to explore the search space while looking for the global minimum of a complex criterion function. The aim of the present research is to investigate the numerical properties of the COA, both on complex optimization test-functions from the literature and on a real-world problem, to contribute to the understanding of its global-search features. In addition, the present research suggests a refinement of the original COA algorithm to improve its optimization performances. In particular, the real-world optimization problem tackled within the paper is the estimation of six electro-mechanical parameters of a model of a direct-current (DC) electrical motor. A large number of test results prove that the algorithm achieves an excellent numerical precision at a little expense in the computational complexity, which appears as extremely limited, compared to the complexity of other benchmark optimization algorithms, namely, the genetic algorithm and the simulated annealing algorithm. Full article
Figures

Figure 1