Nonlinear Dynamic Method Research Articles

Evidence of Chaos in Electroencephalogram Signatures of Human Performance: A Systematic Review.

(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.

Nonlinear dynamic optimization of marine riser system anti-recoil under a flexible multibody framework

Anti-recoil safety of marine risers is critical for deep water offshore drilling. The challenges of riser anti-recoil optimization stem primarily from two factors: (a) nonlinearities of the violent transient response with various system stages and types of design variables and (b) discontinuities of the objective and constraint functions expressed by max–min over the time domain. In this paper, a nonlinear dynamic optimization model and solution method of marine riser system anti-recoil under a flexible multibody framework is proposed. The objective and constraint functions are elaborately designed to protect the system from dynamic buckling and wellhead and riser collision. Corresponding treatments to system state changes and time step sampling are proposed for numerical sensitivity smoothing. In addition, an extra acceleration constraint is imposed to trim and regularize the feasible domain defined by the discontinuous clearance constraint. Following that, the global convergent method of moving asymptotes (GCMMA) is applied. The presented continuous optimization formulation is numerically tested on a real marine riser platform from the X oil field in the South China Sea with a water depth of 1547 m. The numerical results are compared with those computed using a genetic algorithm (GA), surrogate method and interior point method, and the effectiveness and efficiency of the proposed method is demonstrated.

Resistance of Gable Structure of Nuclear Island to Progressive Collapse in Conventional Island Shield Building of Nuclear Power Plants

The gable wall of the conventional island of a nuclear power plant carries various pipeline loads connecting the nuclear island and the conventional island. If the gable wall collapses and is damaged due to the progressive collapse of the main plant structure of the conventional island, it will directly threaten the safety of the nuclear island. Therefore, it is of great significance to systematically study the resistance of the gable structure of the nuclear island to progressive collapse for the safe operation of nuclear power plants. Based on the SAP2000 finite element analysis platform, this paper established a model of the reinforced concrete frame structure of the first span of the shield building on the conventional island of a nuclear power plant, including the gable. According to the alternate path method, the node displacement and bearing capacity responses were used to determine the critical components in the gable, and single column failures of the top four in importance were selected as different analysis conditions. Nonlinear static and dynamic methods were used to analyze the displacement, internal force change, hinge sequence of the gable structure on the side of the nuclear island, and the ability of the gable to resist progressive collapse. The analysis results showed that the gable structure of the nuclear island had good resistance to progressive collapse under four single column failure conditions, whether by nonlinear static or dynamic analysis, and the overall vertical displacement obtained by the nonlinear static analysis was larger than that obtained by the dynamic analysis.

Dynamics in the Reduced Mean-Field Model of Neuron–Glial Interaction

The goal of this study is to propose a new reduced phenomenological model that describes the mean-field dynamics arising from neuron–glial interaction, taking into account short-term synaptic plasticity and recurrent connections in the presence of astrocytic modulation of the synaptic connection. Using computer simulation and numerical methods of nonlinear dynamics, it is shown that the proposed model reproduces a rich set of patterns of population activity, including spiking, bursting and chaotic temporal patterns. These patterns can coexist for specific regions in the parameter space of the model. The main focus of this study was on bifurcation mechanisms that lead to the occurrence of the described types of mean-field dynamics. The proposed phenomenological model can be used to reproduce various patterns of population activity of neurons in a wide range of studies of dynamic memory and information processing. One of the possible applications of such research is the development of new effective methods for the treatment of neurological diseases associated with neuron–glial interactions.

PREDICTIVE ANALYSIS OF TIME SERIES WITH LONG-TERM MEMORY

Predictive analysis with the use of nonlinear dynamics methods, chaos theory of real time series, characterizing the prevalence of a certain class of skin pathologies in Ukraine was carried out. The basis for such studies is the Tackens' theorem. The considered time series does not conform to the normal distribution law, and the hypothesis of a trend is not confirmed for them. According to previous studies, the authors calculated the fractality index \mu, the value of which indicates the state of relative stability of the studied process. The assessment of the correlation confirmed the practical absence of the influence of the present on the future in the studied numerical series. The bifurcation of the attractor revealed during the construction of the time series phase portrait allows the system to have such changes in its state that can be interpreted as jump-like or close to them. The value of the Lyapunov characteristic exponent confirms that the trajectory of the studied time series is chaotic. In the presented research, the procedure of qualitative analysis of the time series was carried out. Using the R/S procedure of fractal analysis, the effect of the time series long-term memory was revealed, the «depth of memory of the time series starting point» and the Hurst index were estimated. According to the performed calculations, the behavior of the H trajectory and R/S trajectory is such that it gives grounds to assert that the time series has a long-term memory. When carrying out the R/S procedure of fractal analysis of the time series as a whole, the time series of the family Q(X) of the initial time series X(t) were analyzed. The distribution of the memory depth estimates was constructed, the fuzzy set L(Q(X)) describing «memory depth of the time series X(t)» as a whole was formed, which is received from a sequence of pairs {1;\mu(1)}, where \mu(1) is the value of the membership function «depth l» of the fuzzy set L(Q(X)). The presence in the time series of the long-term memory effect makes it possible to apply the method of cellular automata in predicting its values.

Nonlinear dynamic analysis of a seismic vibrator-ground interaction system considering interval uncertainties

Seismic vibrators have wide prospections in geological exploration which can provide useful information of underground conditions for various geotechnical engineering. The enhancement of the exploration performance of the seismic vibrators closely relates to the dynamic response of the vibrator-ground (VG) system. This paper proposes an effective method for the uncertain nonlinear dynamics of the VG system. Firstly, the dynamic model of the VG system with uncertainties is developed based on the solution of the nonlinear soil-baseplate interaction. Then, the fundamental theory of the Chebyshev-based interval method and its implementation in the simulation of the VG dynamics are described. The efficiency and accuracy of the proposed method are validated by comparing with the scanning method. Finally, the effects of the multiple uncertainty parameters, sourced from both the soil conditions and the vibrator structure, on the dynamic response of the VG system are analyzed and discussed in detail. In addition, an interval sensitivity analysis is developed to evaluate and compare the effects of different uncertain parameters. The results indicate that uncertainties greatly influence the dynamics of the VG system, and their effects change with the excitation frequency and also relate to the sources of the uncertainties.

Two-channel EEG based diagnosis of panic disorder and major depressive disorder using machine learning and non-linear dynamical methods

The current study aimed to investigate the possibility of rapid and accurate diagnoses of Panic disorder (PD) and Major depressive disorder (MDD) using machine learning. The support vector machine method was applied to 2-channel EEG signals from the frontal lobes (Fp1 and Fp2) of 149 participants to classify PD and MDD patients from healthy individuals using non-linear measures as features. We found significantly lower correlation dimension and Lempel-Ziv complexity in PD patients and MDD patients in the left hemisphere compared to healthy subjects at rest. Most importantly, we obtained a 90% accuracy in classifying MDD patients vs. healthy individuals, a 68% accuracy in classifying PD patients vs. controls, and a 59% classification accuracy between PD and MDD patients. In addition to demonstrating classification performance in a simplified setting, the observed differences in EEG complexity between subject groups suggest altered cortical processing present in the frontal lobes of PD patients that can be captured through non-linear measures. Overall, this study suggests that machine learning and non-linear measures using only 2-channel frontal EEGs are useful for aiding the rapid diagnosis of panic disorder and major depressive disorder.

Analysis on the Seismic Behavior of RC Frame with Different Special-shaped Columns at the Bottom

In order to study the seismic behavior of the bottom large-bay frame with different special-shaped columns, the numerical models of the special-shaped columns frame with ordinary, dark and square columns at the bottom are established using the finite element analysis in ANSYS. The three type special-shaped Frame are performed with nonlinear time-history dynamic method under earthquakes. The dynamic characteristics and seismic response of the three type RC Frame are conducted. The weak parts and the development of the plastic hinges on the end of beams and columns are discussed. The results show that the special-shaped frame with bottom square columns can overcome the weak phenomenon at the bottom, and provide outstanding seismic performance compare with the other two frames.The seismic behavior of the special-shaped columns frame with dark columns is better than the normal special-shaped columns, however it can not effectively overcome the weak parts of the bottom floor. The results can provide a theoretical basis for the engineering application of the frame with special-shaped columns.

Novel adaptive fault detection method based on kernel entropy component analysis integrating moving window of dissimilarity for nonlinear dynamic processes

Fault detection of nonlinear dynamic processes can ensure the safety of industrial production processes. Industrial process data are mostly autocorrelated along with strong nonlinear characteristics. And these significant characteristics interact with each other and limit the fault detection performance of traditional methods. Therefore, this paper presents a novel adaptive fault detection method for nonlinear dynamic processes based on kernel entropy component analysis (KECA) integrating the moving window of dissimilarity (DMW) (KECA-DMW). The KECA is used to map the raw data and capture the nonlinear features of the data, which combine with moving window techniques to build the fault detection model. In the process of updating the data in the moving window, the data information of the historical window is combined with that of the current window to obtain a more comprehensive judgment of the current moment. Then a dynamic update fusion method with adaptive weight allocation based on the dissimilarity index is proposed by analyzing the data characteristics of window information at different moments through the dissimilarity. Finally, three example studies with a numerical example, a closed-loop continuously stirred tank reactor and a Tennessee-Eastman process are used to validate the effectiveness of the proposed method. Compared with other nonlinear dynamic process fault detection methods, the results verify the effectiveness of the proposed method in the process monitoring performance of nonlinear dynamic processes in terms of false alarm rate and fault detection rate, where the false alarm rates of the proposed method are only 2%, 1.83%, and 4.33%, while the fault detection rates are 97.4%, 96.83%, and 86.25%, respectively.

Use of two-dimensional refined composite multi-scale time-frequency dispersion entropy for rolling bearing condition monitoring

Rolling bearing vibration signals with local failure usually contain rich fault characteristic in the time and frequency domains. Two-dimensional multi-scale dispersion entropy (MDE2D) is a nonlinear dynamic analysis method widely used in image signal processing. However, the multi-scale coarse-grained process of MDE2D is relatively complex and the computational cost is high. Therefore, this paper develops a two-dimensional multi-scale time-frequency dispersion entropy (MTFDE2D) to solve the problem of high calculation cost of MDE2D. Unfortunately, the length of the coarse-grained sequence used in MTFDE2D will become shorter as the scale factor increases, resulting in a loss of potential useful information. To address this, a two-dimensional refined composite multi-scale time–frequency dispersion entropy (RCMTFDE2D) is proposed. In RCMTFDE2D, the utilization of information contained in the original date is first effectively improved through the coarse-grained process of sliding values of adjacent elements, and then the refined process is used to avoid the fluctuation of entropy on large scale factors. Furthermore, the rolling bearing test data under two different operating conditions are analyzed. The results illustrate that RCMTFDE2D can successfully extract the rolling bearing fault information in time–frequency domain, and the condition monitoring method based on RCMTFDE2D can effectively identify the rolling bearings in different health states and has the highest recognition rate.

Design and analysis of a double-helix tensegrity spherical lander

This paper presents design and dynamics analysis methods for a Double-Helix tensegrity (DHT) spherical lander. First, we give the topology description of the DHT lander with a payload modeled as a point mass. Then, based on the finite element method for nonlinear tensegrity dynamics and ground dynamics, a DHT lander carrying the payload dynamics is derived during the impact. After analyzing the dynamics, we check the failure of the structure members and iterate the design process. Non-dimensional structure parameters, such as elements material, cross-section area, and stiffness, are studied in the generality of the approaches. Finally, the numerical studies indicate the maximum acceleration of the payload is around 10 g. The methods developed here can also be used for various impact problems for tensegrity structures.

Uncertainty Quantification of Compressor Map Using the Monte Carlo Approach Accelerated by an Adjoint-Based Nonlinear Method

Precise and inexpensive uncertainty quantification (UQ) is crucial for robust optimization of compressor blades and to control manufacturing tolerances. This study looks into the suitability of MC−adj−nonlinear, a nonlinear adjoint-based approach, to precisely and rapidly assess the performance discrepancies of a transonic compressor blade section, arising from geometric alterations, and building upon previous research. In order to assess the practicality and illustrate the benefits of the adjoint-based nonlinear approach, its proficiency and precision are gauged against two other methodologies, the adjoint-based linear approach (MC−adj−linear) and the high-fidelity nonlinear Computational Fluid Dynamics (MC−CFD) method. The MC−adj−nonlinear methodology exhibits impressive generalization capabilities. The MC−adj−nonlinear method offers a great balance between precision and time efficiency, since it is more precise than the MC−adj−linear method in both design and near-stall conditions, yet requires approximately a thirtieth of the time of the MC−CFD method. Finally, the MC−adj−nonlinear method was utilized to conduct fast UQ analyses of the section at four distinct speeds to quantify the performance uncertainty for the compressor map. It is found that aerodynamic performance is more sensitive to geometric deviations at high speeds than at low speeds. The impact of the geometric deviations is generally detrimental to the mean efficiency.

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane and the electron temperature at the outer divertor . Note that is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in and 5%–10% in for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

Visualization of oscillatory electron dynamics on the surface of liquid helium

We investigate the time traces of currents induced in five segmented electrodes by the motion of electrons on the surface of liquid $^{4}\mathrm{He}$ at $\ensuremath{\sim}0.3$ K, that are placed in a perpendicular magnetic field and exposed to microwave radiation. Nonlinear dynamics methods are utilized to explore the characteristic features of the current oscillations in the electrodes for different electron densities and pressing voltages. The wavelet phase coherence and phase shift are calculated to obtain the coherence relationships between the signals in all five electrodes as functions of the pressing voltage. Coupling analysis of the ridge-extracted instantaneous frequencies revealed the directions of motion of electrons inside the cell and provided evidence of strong phase coupling at a pressing voltage of 4.20 V. These classical methods reveal that the motion is oscillatory, with a varying frequency subject to a constant frequency modulation. High harmonics due to nonlinearity arise at higher frequencies where the resonance condition is satisfied at a pressing voltage of 4.20 V for low-electron density. Our approach provides a platform for investigating these phenomena analytically. We show that slow gravity waves on the helium surface modulate the electronic oscillatory behavior and illustrate that the model in fact produces three-dimensional dynamics. Motion of electrons on the surface of liquid helium is shown to be a paradigmatic example of a chronotaxic system, i.e., a system that undergoes continuous perturbation but is nonetheless capable of maintaining its stability.

In search of a data-driven symbolic multi-fluid ten-moment model closure

The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally, the pressure tensor is reduced to a scalar which is an approximation used to aid in the modelling of large scale global systems such as the Earth's magnetosphere. This unfortunately omits important kinetic physics which have been shown to play a crucial role in collisionless regimes. The multi-fluid ten-moment model, however, retains the full symmetric pressure tensor. The ten-moment model is constructed by taking moments of the Vlasov equation up to second order, and includes the scalar density, the vector bulk-flow and the symmetric pressure tensor for a total of ten separate components. Use of the multi-fluid ten-moment model requires a closure which truncates the cascading system of equations. Here we look to leverage data-driven methodologies to seek a closure which may improve the physical fidelity of the ten-moment multi-fluid model in collisionless regimes. Specifically, we use the sparse identification of nonlinear dynamics (SINDy) method for symbolic equation discovery to seek the truncating closure from fully kinetic particle-in-cell simulation data, which inherently retains the relevant kinetic physics. We verify our method by reproducing the ten-moment model from the particle-in-cell (PIC) data and use the method to generate a closure truncating the ten-moment model which is analysed through the nonlinear phase of reconnection.

Effect of trapping in coupled kinetic Alfven-acoustic waves in a partially degenerate plasma with quantizing magnetic field

Inclusion of a quantizing magnetic field in a partially degenerate plasma has interesting effects on the propagation of solitary and nonlinear periodic structures in coupled kinetic Alfven acoustic waves. In this paper, we use two-potential theory to investigate the nonlinear structures using Sagdeev potential approach and further analyze it using nonlinear dynamical methods. It is shown that the existence of solitary structure is sensitive to small temperature effects and quantizing magnetic field in a dense plasma with adiabatically trapped electrons. The work presented here is useful in understanding the low frequency wave propagation in a dense astrophysical environment like white dwarf stars and in low beta laboratory plasmas e.g. intense laser-plasma interactions.

Base Isolation Compared to Capacity Design for Long Corner Periods and Pulse-Type Seismic Records

Southern Romania is a geographic region with alluvial deposits. This soil type leads to rather long corner periods and provides as a particularity of the response spectrum an enlarged plateau. These conditions produce large displacement demands. Moreover, pulse-type ground acceleration records make this seismic area more unique. Research on the seismic behaviour of structures built under such unusual conditions is limited and Romanian engineers are not confident to apply alternative solutions such as base isolation. Although capacity design is still the regular design method applied in Romania, modern base isolation solutions may overcome the large displacement demand expectation produced by seismic events and fulfil immediate occupancy requirements. This study presents the seismic performance of an existing hospital from Bucharest, for which two seismic design solutions were applied: (i) classical approach based on capacity design and (ii) base isolation. Both approaches are compared in terms of drift, acceleration and base shear values. Static as well as non-linear dynamic analysis methods were applied.

A new fractional fuzzy dispersion entropy and its application in muscle fatigue detection.

Recently, fuzzy dispersion entropy (DispEn) has attracted much attention as a new nonlinear dynamics method that combines the advantages of both DispEn and fuzzy entropy. However, it suffers from limitation of insensitivity to dynamic changes. To solve this limitation, we proposed fractional fuzzy dispersion entropy (FFDispEn) based on DispEn, a novel fuzzy membership function and fractional calculus. The fuzzy membership function was defined based on the Euclidean distance between the embedding vector and dispersion pattern. Simulated signals generated by the one-dimensional (1D) logistic map were used to test the sensitivity of the proposed method to dynamic changes. Moreover, 29 subjects were recruited for an upper limb muscle fatigue experiment, during which surface electromyography (sEMG) signals of the biceps brachii muscle were recorded. Both simulated signals and sEMG signals were processed using a sliding window approach. Sample entropy (SampEn), DispEn and FFDispEn were separately used to calculate the complexity of each frame. The sensitivity of different algorithms to the muscle fatigue process was analyzed using fitting parameters through linear fitting of the complexity of each frame signal. The results showed that for simulated signals, the larger the fractional order q, the higher the sensitivity to dynamic changes. Moreover, DispEn performed poorly in the sensitivity to dynamic changes compared with FFDispEn. As for muscle fatigue detection, the FFDispEn value showed a clear declining tendency with a mean slope of -1.658 × 10-3 as muscle fatigue progresses; additionally, it was more sensitive to muscle fatigue compared with SampEn (slope: -0.4156 × 10-3) and DispEn (slope: -0.1675 × 10-3). The highest accuracy of 97.5% was achieved with the FFDispEn and support vector machine (SVM). This study provided a new useful nonlinear dynamic indicator for sEMG signal processing and muscle fatigue analysis. The proposed method may be useful for physiological and biomedical signal analysis.

Seismic Performance Analysis of Meru (Bali Pagoda): Preliminary Study

This study evaluates the earthquake-resistant performance of Meru, specifically level eleven, located in the Ulun Danu Batur Kintamani Temple Area, Bali Province. Despite the upper layer’s construction with wooden frames and panels, and the base layer’s masonry walls, Meru has remained remarkably undamaged by earthquakes since its establishment in 1968. The analysis encompasses Meru’s architectural forms, structural systems, building materials, and dynamic response to seismic activity. A 3D finite element model and nonlinear time history dynamic analysis methods were employed to investigate its earthquake resistance. The findings indicate that Meru can withstand credible maximum seismicity for a return period of 2500 years, and the natural period and modes of Meru have been determined. This study serves as an initial investigation into predicting and monitoring the behavior of Meru structures during earthquakes. Future research could involve experimental analysis of individual components and the overall structure to further validate the analytical model. As a result, this study offers significant insights into the upkeep and preservation of traditional Balinese historic buildings in an earthquake-prone area.