Analytical and numerical solution to the nonlinear cubic Duffing equation: An application to electrical signal analysis of distribution lines

Zivieri, Roberto; Vergura, Silvano; Carpentieri, Mario

doi:10.1016/j.apm.2016.05.043

Cited by 19 publications

(12 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, in this study, we propose a time-domain quantizer and a classifier for automatic UEVD screening. In time-domain PPG analysis, synchronizing chaotification methods (SCMs), such as the Duffing-Holmes (D-H), Sprott, or Chen-Lee systems [21][22][23][24][25][26][27], have been applied to signal preprocessing and feature extraction. With SCMs, a discrete selfsynchronization dynamic system consisting of a master system (MS) and a slave system (SS) can be established as a time-domain quantizer for extracting different features from normal and abnormal PPG signals, as shown in Figure 2.…”

Section: Methodsmentioning

confidence: 99%

“…SCMs have advantages in the broad frequency spectrum and fractal properties of motion in the phase space for analyzing PPG changes in amplitude (systolic peak) and time delay (systolic peak to diastolic peak). To simplify the high-dimensional SCMs, the D-H system [21,23,24,28,29] can be linearized, simplified, and reduced as a discrete two-dimensional (2D) self-synchronization dynamic system [21,27]. For digital signal processing feeding two different PPG signals into the MS and SS can cause the chaotic system to produce chaotic phenomena.…”

Section: Methodsmentioning

confidence: 99%

“…Based on a forced oscillator, the second-order D-H differential equation can be expressed as follows [21,23,24,28,29]:…”

Section: Duffing-holmes-based Quantizermentioning

confidence: 99%

See 2 more Smart Citations

Photoplethysmography Analysis with Duffing–Holmes Self-Synchronization Dynamic Errors and 1D CNN-Based Classifier for Upper Extremity Vascular Disease Screening

Chen

Sun

et al. 2021

Processes

View full text Add to dashboard Cite

Common upper limb peripheral artery diseases (PADs) are atherosclerosis, embolic diseases, and systemic diseases, which are often asymptomatic, and the narrowed arteries (stenosis) will gradually reduce blood flow in the right or left upper limbs. Upper extremity vascular disease (UEVD) and atherosclerosis are high-risk PADs for patients with Type 2 diabetes or with both diabetes and end-stage renal disease. For early UEVD detection, a fingertip-based, toe-based, or wrist-based photoplethysmography (PPG) tool is a simple and noninvasive measurement system for vital sign monitoring and healthcare applications. Based on time-domain PPG analysis, a Duffing–Holmes system with a master system and a slave system is used to extract self-synchronization dynamic errors, which can track the differences in PPG morphology (in amplitudes (systolic peak) and time delay (systolic peak to diastolic peak)) between healthy subjects and PAD patients. In the preliminary analysis, the self-synchronization dynamic errors can be used to evaluate risk levels based on the reflection index (RI), which includes normal condition, lower PAD, and higher PAD. Then, a one-dimensional convolutional neural network is established as a multilayer classifier for automatic UEVD screening. The experimental results indicated that the self-synchronization dynamic errors have a positive correlation with the RI (R2 = 0.6694). The K-fold cross-validation is used to verify the performance of the proposed classifier with recall (%), precision (%), accuracy (%), and F1 score.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Photoplethysmography Analysis with Duffing–Holmes Self-Synchronization Dynamic Errors and 1D CNN-Based Classifier for Upper Extremity Vascular Disease Screening

Chen

Sun

et al. 2021

Processes

View full text Add to dashboard Cite

show abstract

“…For some of the non-linear variations of the Mathieu, the equation has been presented in [8,9]. Moreover, the oscillations of the mechanical systems under the action of an oscillatory external force may reveal a Duffing problem, for instance, see references [10][11][12][13][14]. Recently, Moatimid [15] attempted to study the stability analysis of a parametric Duffing oscillator.…”

Section: Introductionmentioning

confidence: 99%

Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

El‐Dib¹,

Elgazery²

2022

Sound&Vibration

View full text Add to dashboard Cite

In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.

show abstract

“…Thanks to the availability of big data [1], which require advanced processing techniques [2], the strategies for planning, designing, management, and operating of electrical power systems have been deeply modified and the Smart Grids (SGs) represent the new paradigm. Moreover, it results that the electrical signals of a SG can be linear or nonlinear, stationary or non-stationary, periodic or a-periodic [3][4][5], depending on the loads that are connected to the Power Distribution Systems (PDS) (static, rotating), to the power electronics and to the typology of the energy sources (deterministic or stochastic). In fact, the large penetration of PhotoVoltaic (PV) power in the PDS causes a lack of reactive power [6], introducing specific and not trivial problems for the correct and effective operation of the line, because of the unpredictability of the produced energy [7].…”

Section: Introductionmentioning

confidence: 99%

Phase Coherence Index, HHT and Wavelet Analysis to Extract Features from Active and Passive Distribution Networks

Vergura¹,

Carpentieri²

2018

Applied Sciences

Self Cite

View full text Add to dashboard Cite

The modern Power Distribution Systems (PDS) operate more and more often with distributed generators and the optimal operation of the utility distribution systems has to take into account the possibility of bi-directional energy flows, although this event may only occur for some of the PDS. For this reason, the analysis methods that are usually employed to investigate the electrical behavior of the PDS can be more or less effective, depending on the typology of electrical loads connected to the line and on the presence or absence of Renewable Energy Sources (RES). This paper proposes either a methodology to select the best performing mathematical tool to investigate the electrical behavior of the PDS-depending on their linearity and stationarity-either an index to discriminate the PDS on the basis of a different amount of PV penetration. The proposed approach is applied to three real cases of PDS with different characteristics: residential and commercial, in the presence or absence of PV plants. In addition, two indices that are able to characterize the PDS in terms of periodicity and disturbance of the electrical signal are considered, specifically the phase coherence between two arbitrary signals and the phase coherence between an arbitrary signal and a reference one. The combined use of these indices can give valuable information about the degree of non-linearity and can be a measure of the PV penetration in a distribution circuit.

show abstract

Analytical and numerical solution to the nonlinear cubic Duffing equation: An application to electrical signal analysis of distribution lines

Cited by 19 publications

References 24 publications

Photoplethysmography Analysis with Duffing–Holmes Self-Synchronization Dynamic Errors and 1D CNN-Based Classifier for Upper Extremity Vascular Disease Screening

Photoplethysmography Analysis with Duffing–Holmes Self-Synchronization Dynamic Errors and 1D CNN-Based Classifier for Upper Extremity Vascular Disease Screening

Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

Phase Coherence Index, HHT and Wavelet Analysis to Extract Features from Active and Passive Distribution Networks

Contact Info

Product

Resources

About