Fractional order models of leaves

Leaves are mainly responsible for food production in vascular plants. Studying individual leaves can reveal important characteristics of the whole plant, namely its health condition, nutrient status, the presence of viruses and rooting ability. One technique that has been used for this purpose is Electrical Impedance Spectroscopy, which consists of determining the electrical impedance spectrum of the leaf. In this paper we use EIS and apply the tools of Fractional Calculus to model and characterize six species. Two modeling approaches are proposed: firstly, Resistance, Inductance, Capacitance electrical networks are used to approximate the leaves’ impedance spectra; afterwards, fractional-order transfer functions are considered. In both cases the model parameters can be correlated with physical characteristics of the leaves.

Prevalence of syphilis in pregnancy and prenatal syphilis testing in Brazil: Birth in Brazil study

OBJECTIVE Determine the coverage rate of syphilis testing during prenatal care and the prevalence of syphilis in pregnant women in Brazil. METHODS This is a national hospital-based cohort study conducted in Brazil with 23,894 postpartum women between 2011 and 2012. Data were obtained using interviews with postpartum women, hospital records, and prenatal care cards. All postpartum women with a reactive serological test result recorded in the prenatal care card or syphilis diagnosis during hospitalization for childbirth were considered cases of syphilis in pregnancy. The Chi-square test was used for determining the disease prevalence and testing coverage rate by region of residence, self-reported skin color, maternal age, and type of prenatal and child delivery care units. RESULTS Prenatal care covered 98.7% postpartum women. Syphilis testing coverage rate was 89.1% (one test) and 41.2% (two tests), and syphilis prevalence in pregnancy was 1.02% (95%CI 0.84;1.25). A lower prenatal coverage rate was observed among women in the North region, indigenous women, those with less education, and those who received prenatal care in public health care units. A lower testing coverage rate was observed among residents in the North, Northeast, and Midwest regions, among younger and non-white skin-color women, among those with lower education, and those who received prenatal care in public health care units. An increased prevalence of syphilis was observed among women with < 8 years of education (1.74%), who self-reported as black (1.8%) or mixed (1.2%), those who did not receive prenatal care (2.5%), and those attending public (1.37%) or mixed (0.93%) health care units. CONCLUSIONS The estimated prevalence of syphilis in pregnancy was similar to that reported in the last sentinel surveillance study conducted in 2006. There was an improvement in prenatal care and testing coverage rate, and the goals suggested by the World Health Organization were achieved in two regions. Regional and social inequalities in access to health care units, coupled with other gaps in health assistance, have led to the persistence of congenital syphilis as a major public health problem in Brazil.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Tracking of physical activity during adolescence: the 1993 Pelotas Birth Cohort, Brazil

OBJECTIVE To analyze physical activity during adolescence in participants of the 1993 Pelotas Birth Cohort Study, Brazil. METHODS Data on leisure time physical activity at 11, 15, and 18 years of age were analyzed. At each visit, a cut-off point of 300 min/week was used to classify adolescents as active or inactive. A total of 3,736 participants provided data on physical activity at each of the three age points. RESULTS A significant decline in the proportion of active adolescents was observed from 11 to 18 years of age, particularly among girls (from 32.9% to 21.7%). The proportions of girls and boys who were active at all three age points were 28.0% and 55.1%, respectively. After adjustment for sex, economic status, and skin color, participants who were active at 11 and 15 years of age were 58.0% more likely to be active at 18 years of age compared with those who were inactive at 11 and 15 years of age. CONCLUSIONS Physical activity declined during adolescence and inactivity tended to track over time. Our findings reinforce the need to promote physical activity at early stages of life, because active behavior established early tends to be maintained over time.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Fractional order control on a wind turbine benchmark

This paper is about a hierarchical structure with an event-based supervisor in a higher level and a fractional-order proportional integral (FOPI) in a lower level applied to a wind turbine. The event-based supervisor analyzes the operation conditions to determine the state of the wind turbine. This controller operate in the full load region and the main objective is to capture maximum power generation while ensuring the performance and reliability required for a wind turbine to be integrated into an electric grid. The main contribution focus on the use of fractional-order proportional integral controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. Comparisons between fractional-order pitch control and a default proportional integral pitch controller applied to a wind turbine benchmark are given and simulation results by Matlab/Simulink are shown in order to prove the effectiveness of the proposed approach.

Fuzzy, integer and fractional-order control: application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Modeling of the lung impedance using a fractional order ladder network with constant phase elements

The self similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. The fractal geometry is typically characterized by a recurrent structure. This study investigates the identification of a model for the respiratory tree by means of its electrical equivalent based on intrinsic morphology. Measurements were obtained from seven volunteers, in terms of their respiratory impedance by means of its complex representation for frequencies below 5 Hz. A parametric modeling is then applied to the complex valued data points. Since at low-frequency range the inertance is negligible, each airway branch is modeled by using gamma cell resistance and capacitance, the latter having a fractional-order constant phase element (CPE), which is identified from measurements. In addition, the complex impedance is also approximated by means of a model consisting of a lumped series resistance and a lumped fractional-order capacitance. The results reveal that both models characterize the data well, whereas the averaged CPE values are supraunitary and subunitary for the ladder network and the lumped model, respectively.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Offshore wind turbine simulation: multibody drive train. Bacl-to-back NPC (Neutral Point Clamped) converters: Fractional-order control

This paper is on offshore wind energy conversion systems installed on the deep water and equipped with back-to-back neutral point clamped full-power converter, permanent magnet synchronous generator with an AC link. The model for the drive train is a five-mass model which incorporates the dynamic of the structure and the tower in order to emulate the effect of the moving surface. A three-level converter and a four-level converter are the two options with a fractional-order control strategy considered to equip the conversion system. Simulation studies are carried out to assess the quality of the energy injected into the electric grid. Finally, conclusions are presented. (C) 2014 Elsevier Ltd. All rights reserved.

Realization of fractional-order controllers: analysis, synthesis and application to the velocity control of a servo system

The synthesis and application of fractional-order controllers is now an active research field. This article investigates the use of fractional-order PID controllers in the velocity control of an experimental modular servo system. The systern consists of a digital servomechanism and open-architecture software environment for real-time control experiments using MATLAB/Simulink. Different tuning methods will be employed, such as heuristics based on the well-known Ziegler Nichols rules, techniques based on Bode’s ideal transfer function and optimization tuning methods. Experimental responses obtained from the application of the several fractional-order controllers are presented and analyzed. The effectiveness and superior performance of the proposed algorithms are also compared with classical integer-order PID controllers.

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Dietary patterns in pregnancy and birth weight

OBJECTIVE To analyze if dietary patterns during the third gestational trimester are associated with birth weight.METHODS Longitudinal study conducted in the cities of Petropolis and Queimados, Rio de Janeiro (RJ), Southeastern Brazil, between 2007 and 2008. We analyzed data from the first and second follow-up wave of a prospective cohort. Food consumption of 1,298 pregnant women was assessed using a semi-quantitative questionnaire about food frequency. Dietary patterns were obtained by exploratory factor analysis, using the Varimax rotation method. We also applied the multivariate linear regression model to estimate the association between food consumption patterns and birth weight.RESULTS Four patterns of consumption – which explain 36.4% of the variability – were identified and divided as follows: (1) prudent pattern (milk, yogurt, cheese, fruit and fresh-fruit juice, cracker, and chicken/beef/fish/liver), which explained 14.9% of the consumption; (2) traditional pattern, consisting of beans, rice, vegetables, breads, butter/margarine and sugar, which explained 8.8% of the variation in consumption; (3) Western pattern (potato/cassava/yams, macaroni, flour/farofa/grits, pizza/hamburger/deep fried pastries, soft drinks/cool drinks and pork/sausages/egg), which accounts for 6.9% of the variance; and (4) snack pattern (sandwich cookie, salty snacks, chocolate, and chocolate drink mix), which explains 5.7% of the consumption variability. The snack dietary pattern was positively associated with birth weight (β = 56.64; p = 0.04) in pregnant adolescents.CONCLUSIONS For pregnant adolescents, the greater the adherence to snack pattern during pregnancy, the greater the baby’s birth weight.