Nonlinear Decomposition Method Research Articles

Within the cracks of the cosmic race: Income inequalities by race and ethnicity in Latin America

While a considerable body of literature has studied ethnic inequalities and discrimination in Latin America, it is only in recent years that a growing number of studies examine income inequalities by race, defined as a skin color gradation. Furthermore, most research equates ethnic self-identification with race, leading to confusion on the root of the discrimination. Hardly any studies have addressed ethnicity and race as separate but intertwined characteristics to examine income disparities. It is crucial to address this scarcity to properly comprehend the effect miscegenation narratives have had in the region and the current state of wage inequalities. Hence, in this paper, I employ data from the Americas Barometer to investigate race and ethnicity income gaps in 17 Latin American countries. To do so, I applied non-linear regressions and decomposition methods, which allowed me to (i) separate the observable and non-observable factors of the income gap and (ii) decompose them by race and ethnicity and look at their intersection. In addition to the principal analyses, I conducted a series of robustness checks to evaluate the results’ consistency and perform heterogeneity analysis to examine income inequalities per country. The results show substantial differences in the average income of the different ethnic and racial groups, mainly driven by differences in observable characteristics like years of education and employment status. In addition, the heterogeneity analyses indicate that ethnic and racial disparities vary across Latin America and can be explained partially by unobserved variables like discrimination. Overall, the results suggest that skin color and ethnic self-identification should be accounted for simultaneously when evaluating inequality.

Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

In this paper, we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations.

Distributed Formation Maneuvering Quantized Control of Under-Actuated Unmanned Surface Vehicles with Collision and Velocity Constraints

This paper focuses on a distributed cooperative time-varying formation maneuvering issue of under-actuated unmanned surface vehicles (USVs). A fleet of USVs is guided by a parameterized path with a time-varying formation while avoiding collisions and preserving the connectivity in the environment with multiple obstacles. In some surface missions, due to the obstacles in the external environment, the bandwidth limitations of the communication channel, and the hardware components/performance constraints of the USVs themselves, each vehicle is considered to be subject to model uncertainty, actuator quantization, sensor dead zone, and velocity constraints. During the control design process, the radial basis function (RBF) neural networks (NNs) are utilized to deal with nonlinear terms. Based on a nonlinear decomposition method, the relationship between the control signal and the quantization one is established, which overcomes the difficulty arising from actuator quantization. A Nussbaum function is introduced to handle the unknown output dead zone problem caused by reduced sensor sensitivity. Moreover, a universal-constrained function is employed to satisfy both the constrained and unconstrained requirements during formation keeping and obstacle avoidance. The Lyapunov stability theory confirmed that the error signals are uniformly ultimately bounded (UUB). The simulation results demonstrate the effectiveness of the proposed distributed formation control of multiple USVs.

Validation Of A Nonlinear Wave Decompistion Method Including Shoaling

It is important to decompose the incident and the reflected waves when performing physical or numerical experiments in a wave flume. Especially when large reflection is expected, from for example a breakwater, the total measured signal can significantly deviate from the incident signal. Different techniques exist to decompose a signal into incident and reflected signals. For 1D wave flumes a method based on co-located wave gauges (Nwogu, 1989) or multiple wave gauges (Røge Eldrup and Lykke Andersen, 2019, Zelt and Skjelbreia, 1993) is commonly applied. The latter is the focus of this abstract since recently, the decomposition method based on multiple wave gauges was extended to be applicable to nonlinear irregular waves by including bound waves and amplitude dispersion (Eldrup and Lykke Andersen, 2019). Moreover, the practical requirements for the nonlinear wave decomposition methods were described in De Ridder et al. (2023). Most of the nonlinear wave decomposition methods are only applicable to a flat bed and will introduce an error when it is applied on a sloping foreshore which is typically the case in physical model experiments. Padilla and Alsina (2020) derived a general framework including shoaling of bound waves and Lykke Andersen and Eldrup (2021) presented a method for nonlinear regular waves over a sloping bed. However, a nonlinear decomposition method for irregular waves over a sloping bed has never been verified with physical model experiments. In this abstract the nonlinear decomposition method for irregular waves as presented in De Ridder et al. (2023) is extended with the effects of shoaling and its effects are verified with a physical model experiment.

Study on the frequency modulation phenomenon in the rotor system with blade-casing rub-impact fault

In an aero-engine rotor system, a blade-casing rub-impact fault can lead to a frequency modulation phenomenon of the vibration signal. This paper discusses the extraction of the modulation information in the fault signal using the variational nonlinear chirp mode decomposition (VNCMD) method to detect early rub-impact faults. The regularities of frequency modulation are revealed in both the simulated and experimental blade-casing rubbing signals. According to the frequency modulation law, an empirical formula is summarized to judge the rub-impact fault type. Then, we propose an evaluation index to judge the fault severity based on the energy theory by using the advantage of the VNCMD method that can reconstruct the decomposed fault signal. Finally, the fault severity in the simulated and experimental signals with different parameters is compared. The results show the correctness and reliability of this evaluation index. The research in this paper provides a theoretical basis for the detection and judgment of the rubbing severity of blade-casing rub-impact faults.

Social Groups and Unequal Employment Opportunities in Skilled Occupations in India

Differential labour market outcomes are a major concern in the Indian labour market. This article looks into the caste and ethnicity-based employment gap in skilled jobs in India. The study has used data from two Periodic Labour Force Survey rounds, namely the 2021–2022 round and 2018–2019 round. The employment gap has been decomposed using the non-linear decomposition method. The results suggest that socially forward groups are more likely to participate in skilled jobs than socially backward classes. Moreover, a significant part of the employment gap remains unexplained by characteristic differences, including differences in endowments. However, both the employment gap and the contribution of discriminatory hiring practices are generally less in more skill-oriented jobs. The employment gap in high-skilled occupations is significantly explained by differences in productivity factors. The jobs requiring higher levels of skills are largely prevalent in the public sector that comes under the reservation policy. In the private sector as well, compared to low- or unskilled jobs, high-skilled occupations are more likely to be found in the form of formal jobs to which anti-discrimination laws may be applicable. Low-paying unskilled jobs are mainly dominated by socially backward-class workers in the Indian labour market.

Stability of stochastic reaction-diffusion equation under random influences in high regular spaces

In this paper, we systematically study the high-order stability of the stochastic reaction-diffusion equation driven by additive noise as the noise intensity vanishes. First, with a general assumption on the nonlinear term, we obtain the convergence of solutions and upper semi-continuity of random attractors in L2(RN). Second, by using the nonlinear decomposition method, we technically establish the convergence of solutions in Lp(RN)∩H1(RN)(p>2), and therefore, the upper semi-continuity of random attractors is proved, where p is the growth exponent of the nonlinearity. Finally, by induction argument, we prove that the solution is uniformly bounded near the initial time in Lδ(RN) for arbitrary δ > p, in which space the convergence of solutions and the upper semi-continuity of random attractors are also established.

Validation and practical application of nonlinear wave decomposition methods for irregular waves

Validation and practical application of nonlinear wave decomposition methods for irregular waves

Study of slope integral extension mode decomposition method for bearing-nonlinear vibration signal

This study aims to solve the problem of extreme point ambiguity caused by energy instability at the signal end. Thus, an adaptive nonlinear signal decomposition method based on motion energy accumulation division is proposed, namely slope integral extension mode decomposition (SIEMD). The proposed method considers the fluctuation rate and vibration energy between the peaks of the waveform as its scale. Firstly, the comprehensive index is defined to adaptively select the ideal interval, and the extension characteristics of the waveform signal are obtained. Secondly, the energy of the waveform interval is iterated. Hence, the optimal extension waveform is fitted by combining the edge position information of the curve. The experimental part verifies that the method can extract 92 % of the fault information, and verifies that the proposed method overcomes the limitation of the previous one-dimensional signal waveform dimension. Moreover, from the perspective of signal energy, it eliminates the false information of the intrinsic modal function (IMF) components, more suitable for the randomness of the signal, thereby providing a new way for fault feature extraction.

Nonlinear dynamic mode decomposition from time-resolving snapshots based on deep convolutional autoencoder

A novel nonlinear decomposition method of flow field is proposed based on the dynamic mode decomposition (DMD) and nonlinear mode decomposition autoencoder. The flow fields are indexed in time order and then input to the nonlinear neural networks to learn the connected observables and decomposed fields. The reconstructions of input fields are assumed to be the summation of the nonlinear decomposed fields. The nonlinear decoders are regarded as the nonlinear modes, which concentrate most of the total energy of the flow field data. The resulting nonlinear dynamic mode decomposition autoencoder reports a series of orderly low-dimensional representations and decomposition fields. Besides, the proposed method can be used for dynamic modeling and returns more stable and accurate predictions with a few number of low-dimensional representations. The present method is tested with the benchmark case, flow around a circular cylinder at Reynolds number Re = 100. The results in this example indicate that the proposed method achieves higher reconstruction accuracy using fewer modes, while retaining similar temporal dynamics and mode information as proper orthogonal decomposition and DMD.

Adaptive neural prescribed performance control for switched pure-feedback non-linear systems with input quantization

Purpose This paper aims to investigate an adaptive prescribed performance control problem for switched pure-feedback non-linear systems with input quantization. Design/methodology/approach By using the semi-bounded continuous condition of non-affine functions, the controllability of the system can be guaranteed. Then, a constraint variable method is introduced to ensure that the tracking error satisfies the prescribed performance requirements. Meanwhile, to avoid the design difficulties caused by the input quantization, a non-linear decomposition method is adopted. Finally, the feasibility of the proposed control scheme is verified by a numerical simulation example. Findings Based on neural networks and prescribed performance control method, an adaptive neural control strategy for switched pure-feedback non-linear systems is proposed. Originality/value The complex deduction and non-differentiable problems of traditional prescribed performance control methods can be solved by using the proposed error transformation approach. Besides, to obtain more general results, the restrictive differentiability assumption on non-affine functions is removed.

Adaptive Nonlinear Domain Decomposition Methods with an Application to the $p$-Laplacian

In this article, different nonlinear domain decomposition methods are applied to nonlinear problems with highly heterogeneous coefficient functions with jumps. In order to obtain a robust solver with respect to nonlinear as well as linear convergence, adaptive coarse spaces are employed. First, as an example for a nonlinearly left-preconditioned domain decomposition method, the two-level restricted nonlinear Schwarz method H1-RASPEN (Hybrid Restricted Additive Schwarz Preconditioned Exact Newton) is combined with an adaptive GDSW (generalized Dryja--Smith--Widlund) coarse space. Second, as an example for a nonlinearly right-preconditioned domain decomposition method, a nonlinear FETI-DP (Finite Element Tearing and Interconnecting--Dual Primal) method is equipped with an edge-based adaptive coarse space. Both approaches are compared with the respective nonlinear domain decomposition methods with classical coarse spaces as well as with the respective Newton--Krylov methods with adaptive coarse spaces. For some two-dimensional $p$-Laplace model problems with different spatial coefficient distributions, it can be observed that the best linear and nonlinear convergence can only be obtained when combining the nonlinear domain decomposition methods with adaptive coarse spaces.

Analysis of the in-cylinder flow of a DISI engine using high-speed particle image velocimetry

In addition to exploring electric drives, it is crucial to minimize emissions and improve the efficiency of transport based on internal combustion engines (ICE). For these, in particular, a significant reduction of emissions as well as a considerable efficiency of ICE are required. A reliable formation of an effective mixture prior to ignition and a fast, steady combustion process are two key elements that influence emissions and efficiency. While on the one hand, the air-fuel mixture is formed by strongly three-dimensional, time-dependent flow phenomena during the intake and compression stroke, the turbulence level of the flow near the approaching flame front has a direct impact on turbulent flame propagation. The flow field in the combustion chamber, on the other hand, is highly turbulent and sensitive to cycle-to-cycle variations (CCV). In order to understand the fundamental processes and interactions of the flow field, flow measurements with high spatial and temporal resolution are required. To analyze CCV, the resulting flow field data must be decomposed into its scales, since CCVs are different from random fluctuations due to turbulent flow motions. Besides velocity decomposition based on traditional Reynolds decomposition, which provides an average flow velocity and a fluctuation velocity, most studies include statistical and linear approaches such as proper orthogonal decomposition (POD) and Fast Fourier transformation (FFT). In this paper, time-resolved high-speed stereoscopic PIV (HS-SPIV) measurements on an optical single-cylinder engine are processed using a new nonlinear and transient decomposition method, namely the multivariate empirical mode decomposition (NA-MEMD) based on a data-driven decomposition algorithm. The decomposition is based on the inherent scales of the data and generates physically valid modal representations known as intrinsic mode functions (IMFs), which are arranged with respect to the contained scale values. The approach and the IMFs generated are described in detail using one engine cycle as an example. According to the results, three modes are obtained, the measurement noise and extremely tiny short-term scales, the turbulent scales, and the large-scale tumble vortex.

Gravity Wave Generation in Balanced Sheared Flow Revisited

Abstract The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates. Significance Statement We aim to understand the generation of internal gravity waves in the atmosphere and ocean from a flow field that is initially balanced, i.e., free from any internal gravity waves. To examine this process, we use simulations from idealized numerical models and nonlinear flow decomposition method to identify waves. Our results show that a prominent mechanism by which waves can be generated is related to symmetric or ageostrophic instabilities of the balanced flow possibly occurring during frontogenesis. This process can be a significant mechanism to dissipate the energy of the geostrophic flow in the ocean.

The optimal decomposition method (ODM) for nonlinear problems

The herein coined Optimal Decomposition Method (ODM) is presented; an analytic decomposition approach to solve nonlinear problems that circumvents the well-known convergence barrier within nonlinear decomposition methods, e.g., Adomian Decomposition Method (ADM) and Duan –Rach ADM. ODM initially concerns removing the unknown coefficients from the recursion scheme. In addition, it is powered by multiple Convergence-Control Parameters (CCP) through insertion of an ‘artificial’ parameter. The series of CCPs results in the deployment of the entire convergence potential of the decomposition method. It is shown, in a detailed manner, that ADM and Duan-Rach ADM, i.e., a modified approach preventing the appearance of the unknown coefficients in the Adomian recursion scheme for an l-point BVP ( l≥2), can be generalized only as the special cases of ODM. Therefore, ODM, by itself, moves beyond generalization of the aforementioned methods. The CCPs are computed by minimizing the universal system error. For this purpose, a gradient-based contraction search is exploited together with Genetic Algorithm (GA) to facilitate procuring the CCPs in strongly divergent examples involving several CCPs. Indeed, through examples, namely, a generalized Boundary Value Problem (BVP) test case, the Falkner-Skan equation, a two-state optimal control problem, the Burgers’ equation and a strongly nonlinear problem governing electrohydrodynamic flow of a fluid in a circular cylindrical conduit, it is exemplified that CCPs expand the radius of convergence substantially. In the considered examples, ADM and D-R ADM are strictly divergent with the addition of series terms; on the contrary, ODM serves as a successful remedy on these occasions. In practice, it was found that for most of the nonlinearities, minimizing the system error containing CCPs for lower orders of approximation gives rise to a natural minimization of the system error in higher orders of approximation, i.e., natural convergence.

Fast finite‐time adaptive fuzzy control for quantized stochastic uncertain nonlinear systems

SummaryThe issue of fast finite‐time adaptive control is studied for quantized stochastic nonlinear systems. Unlike the existing works about fast finite‐time control, the input signals are quantized, and the stochastic disturbances and nonlinear functions are unknown. According to universal approximation capacity of fuzzy logic system, combined with backstepping technique, a novel fast finite‐time adaptive fuzzy control strategy of quantized stochastic nonlinear system is proposed. The nonlinear decomposition method is introduced to set up the relationship among the control signals and the quantization signals, which overcomes the technical difficulties result from the piecewise quantization input. The proposed tactics can assure the tracking error situate in a neighborhood of the origin point and the closed‐loop system signals keep bounded. Finally, an algorithm simulation is conducted to test the validity of the method.

Understanding Harmonic Structures Through Instantaneous Frequency.

The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.

Adaptive robust design for nonlinear switched systems with unmodeled dynamics and input quantization

AbstractIn this paper, we focus on the adaptive robust input quantized control problem for a class of uncertain nonlinear switched systems under a state‐dependent switching law. The considered systems admit the non‐ISS unmodeled dynamics, the unknown virtual control coefficients, and an unknown parameter. In order to reduce the conservativeness of the common Lyapunov function, the multiple Lyapunov functions method is used to design a state‐dependent switching law. Besides, to overcome the design difficulty arising from the quantization behavior, a nonlinear decomposition method is used to establish the relationship between the control signal and the quantized signal. We put forward the adaptive robust controllers for the individual subsystems, based on which the resulted closed‐loop system is uniformly ultimately bounded. Finally, to verify the effectiveness of the proposed control scheme, two examples are given to construct the adaptive robust controllers.

Decomposing the urban\u2013rural inequalities in the utilisation of maternal health care services: evidence from 27 selected countries in Sub-Saharan Africa

BackgroundThere has been a substantial improvement in reducing maternal mortality in the Sub-Saharan African region. The vast rural-urban gap in maternal health outcomes, however, is obscured by this average achievement. This study attempts to measure the contribution of identified risk factors to describe the average rural-urban difference in the use of antenatal care, health facilities for delivery, and health professional assistance at delivery.MethodTo achieve this objective, we used descriptive analysis and Fairlie non-linear decomposition method to quantify covariates’ contribution in explaining the urban–rural difference in maternal healthcare services utilisation.ResultThe study’s finding shows much difference between urban and rural areas in the use of maternal healthcare services. Socio-economic factors such as household wealth index, exposure to media, and educational level of women and their husbands/partners contributed the most in explaining the gap between urban and rural areas in healthcare services utilisation.ConclusionsInterventions to bridge the gap between urban and rural areas in maternal healthcare services utilisation in Sub-Saharan Africa should be centred towards socio-economic empowerment. Government can enforce targeted awareness campaigns to encourage women in rural communities in Sub-Sharan Africa to take the opportunity and use the available maternal health care services to be at par with their counterparts in urban areas.

Explaining caste-based digital divide in India

With the increasing importance of information and communication technologies in access to basic services like education and health, the question of digital divide based on caste assumes importance in India where large socioeconomic disparities persist between different caste groups. Studies on caste-based digital inequality are still scanty in India. Using nationally representative survey data, this paper analyzes the first-level digital divide (ownership of computer and access to the Internet) and the second-level digital divide (individuals skills to use computer and the Internet) between the disadvantaged caste groups and Others. Further, this paper identifies the caste-based differences in socioeconomic factors that contribute to the digital divide between these groups using a non-linear decomposition method. The results show that there exists large first-level and second-level digital divide between the disadvantaged caste groups and Others in India. The non-linear decomposition results indicate that caste-based digital divide in India is rooted in historical socioeconomic deprivation of disadvantaged caste groups. More than half of the caste-based digital gap is attributable to differences in educational attainment and income between the disadvantaged caste groups and Others. Findings of this study highlight the urgent need for addressing educational and income inequality between the different caste groups in India in order to bridge the digital divide.