Geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral finite elements with reduced integration

This work presents a geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral isoparametric elements. The main features of the present formulation are: (a) the element matrices are obtained using reduced integrations with hourglass control; (b) an explicit Taylor-Galerkin scheme is used to carry out the dynamic analysis, solving the corresponding equations of motion in terms of velocity components; (c) the Truesdell stress rate tensor is used; (d) the vector processor facilities existing in modern supercomputers were used. The results obtained are comparable with previous solutions in terms of accuracy and computational performance.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Effect of Pursed-Lip Breathing in Patients With COPD: Linear and Nonlinear Analysis of Cardiac Autonomic Modulation

Objective: The aim of the present study was to evaluate the effect of pursed-lip breathing (PLB) on cardiac autonomic modulation in individuals with chronic obstructive pulmonary disease (COPD) while at rest. Methods: Thirty-two individuals were allocated to one of two groups: COPD (n = 17; 67.29 +/- 6.87 years of age) and control (n = 15; 63.2 +/- 7.96 years of age). The groups were submitted to a two-stage experimental protocol. The first stage consisted of the characterization of the sample and spirometry. The second stage comprised the analysis of cardiac autonomic modulation through the recording of R-R intervals. This analysis was performed using both nonlinear and linear heart rate variability (HRV). In the statistical analysis, the level of significance was set to 5% (p = 0.05). Results: PLB promoted significant increases in the SD1, SD2, RMSSD and LF (ms(2)) indices as well as an increase in alpha(1) and a reduction in alpha(2) in the COPD group. A greater dispersion of points on the Poincare plots was also observed. The magnitude of the changes produced by PLB differed between groups. Conclusion: PLB led to a loss of fractal correlation properties of heart rate in the direction of linearity in patients with COPD as well as an increase in vagal activity and impact on the spectral analysis. The difference in the magnitude of the changes produced by PLB between groups may be related to the presence of the disease and alterations in the respiration rate.

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Background: Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods. We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 - 0,04 Hz, low frequency (LF) (0.04-0.15 Hz), and high frequency (HF) (0.15-0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (-ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results: Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms§ssup§2§esup§, RMSSD ≤ 23.9 ms, ApEn ≤-0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion: We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment. © 2012 Pivatelli et al.; licensee BioMed Central Ltd.

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

Impact of artifact correction methods on R-R interbeat signals to quantifying heart rate variability (HRV) according to linear and nonlinear methods.

In the analysis of heart rate variability (HRV) are used temporal series that contains the distances between successive heartbeats in order to assess autonomic regulation of the cardiovascular system. These series are obtained from the electrocardiogram (ECG) signal analysis, which can be affected by different types of artifacts leading to incorrect interpretations in the analysis of the HRV signals. Classic approach to deal with these artifacts implies the use of correction methods, some of them based on interpolation, substitution or statistical techniques. However, there are few studies that shows the accuracy and performance of these correction methods on real HRV signals. This study aims to determine the performance of some linear and non-linear correction methods on HRV signals with induced artefacts by quantification of its linear and nonlinear HRV parameters. As part of the methodology, ECG signals of rats measured using the technique of telemetry were used to generate real heart rate variability signals without any error. In these series were simulated missing points (beats) in different quantities in order to emulate a real experimental situation as accurately as possible. In order to compare recovering efficiency, deletion (DEL), linear interpolation (LI), cubic spline interpolation (CI), moving average window (MAW) and nonlinear predictive interpolation (NPI) were used as correction methods for the series with induced artifacts. The accuracy of each correction method was known through the results obtained after the measurement of the mean value of the series (AVNN), standard deviation (SDNN), root mean square error of the differences between successive heartbeats (RMSSD), Lomb\'s periodogram (LSP), Detrended Fluctuation Analysis (DFA), multiscale entropy (MSE) and symbolic dynamics (SD) on each HRV signal with and without artifacts. The results show that, at low levels of missing points the performance of all correction techniques are very similar with very close values for each HRV parameter. However, at higher levels of losses only the NPI method allows to obtain HRV parameters with low error values and low quantity of significant differences in comparison to the values calculated for the same signals without the presence of missing points.