Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Synchronization and Stability of a Nonlinear Vibrating Mechanical System Characterized by Asymmetrical Piecewise Linearity

In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up this drawback,a dynamical model of a nonlinear vibrating mechanical system with double rigid frames(RFs),driven by two vibrators,is proposed to explore the synchronization and stability of the system.In this paper,the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear,where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method.Based on the average method and Hamilton’s principle,the theory conditions to achieve synchronization and stability of two vibrators are deduced.After the theory analyses,some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs.Besides,some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results.Based on the comparisons of the theory,numeric and experiment,the ideal working regions of the system are suggested.Based on the present work,some new types of vibrating equipment,such as vibrating discharging centrifugal dehydrators/conveyers/screens,can be designed.

Linearization of Intrinsically Nonlinear Oscillators

We show that an intrinsically nonlinear oscillator can always be transformed into a linear or harmonic oscillator by addition of a constant force, which shifts the equilibrium position of the oscillator.

Bayesian and Non-Bayesian Analysis for the Sine Generalized Linear Exponential Model under Progressively Censored Data

This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.

On stability analysis of nonlinear ADRC-based control system with application to inverted pendulum problems

This paper mainly focuses on stability analysis of the nonlinear active disturbance rejection control(ADRC)-based control system and its applicability to real world engineering problems.Firstly,the nonlinear ADRC(NLADRC)-based control system is transformed into a multi-input multi-output(MIMO)Lurie-like system,then sufficient condition for absolute stability based on linear matrix inequality(LMI)is proposed.Since the absolute stability is a kind of global stability,Lyapunov stability is further considered.The local asymptotical stability can be deter-mined by whether a matrix is Hurwitz or not.Using the inverted pendulum as an example,the proposed methods are verified by simulation and experiment,which show the valuable guidance for engineers to design and analyze the NL ADRC-based control system.

Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method （HPM） and an ancient Chinese method called the max-rain approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual （numerical） solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.

Non-linearity in the dynamic world of human movement

Non-linear dynamics,fractals,periodic oscillations,bifurcations,chaos,and other terminologies have been used to describe human biological systems in the literature for a few decades.The eight manuscripts included in this special issue discussed the historical background,

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

In this paper we present a synchronization method for chaotic Lur＇e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur＇e systems with deadzone nonlinearity. Based on the Lyapunov-Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality （LMI） formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.

Fundamental and dressed annular solitons in saturable nonlinearity with parity–time symmetric Bessel potential

We theoretically study the existence and stability of optical solitons in saturable nonlinearity with a two-dimensional parity–time（PT） symmetric Bessel potential.Besides the fundamental solitons,a novel type of dressed soliton,whose intensity looks like a ring dressed on an intensity hump,are presented.It is found that both the fundamental solitons and dressed solitons can exist when the propagation constant is beyond a certain critical value.The propagation stability is investigated with a linear stability analysis corroborated by a beam propagation method.All the fundamental solitons are stable,while dressed solitons are unstable for low values of saturable parameter.As the value of saturable parameter increases,the dressed solitons tend to be stable at high powers.

Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation

We present a numerical investigation of the propagation and the switching of ultra-short pulses (100 fs) in a two-core nonlinear coupler of photonic crystal fibers constructed with periodically modulated the non-linearity fiber (PMNL-PFC). Our simulations are taking into account different amplitude and frequency modulations of the PMNL-PFC. A coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics, the compression factor, the crosstalk (Xtalk) and extinction ratio (Xratio) levels of the first order solitons were studied for low to high pump energies considering 2Lc. By an analysis on the reference channel (channel 2), it is observed that at low modulation frequencies an increase occurs in the switching power increasing transmission efficiency. For high modulation frequencies, the transmitted energy efficiency loses. The switching pulses are stronger for low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1). It was observed that this unwanted high-frequency energy increases to lessen the measure of the amplitude modulation. In summary, we have demonstrated that introduction of a non-linearity profile takes the periodically modulated PMNL-PFC to strong variations at transmission efficiency, Xtalk, Xratio a function of frequency and modulation amplitude and the input power.

Studying Effect of Magnetizing Curve Nonlinearity Index on the Occurring Chaotic Ferroresonance Oscillation in Autotransformers

This paper investigates the effect of iron core saturation characteristic degree on the onset of chaotic ferrore-sonance and duration of transient chaos in an autotransformer. The transformer chosen for study has a rating of 50 MVA, 635.1 kV, the magnetization characteristic of the autotransformer is modeled by a single-value two-term polynomial with q = 5, 7, 11. The core loss is modeled by a linear resistance and is considered a fix value for it. Simulation results are derived by using MATLAB software and nonlinear dynamics tool such as bifurcation and phase plan diagrams. It is shown settling down to the chaotic region is increased when degree of core nonlinearity is gone from 5 to 11.

Enhanced Kerr nonlinearity in a quantized four-level graphene nanostructure

In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental,multi-peak,and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity.Two opposite soliton selfbending signals are considered for different families of solitons.Power thresholdless fundamental and multi-peaked solitons are stable in the low power region.The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals.When solitons tend to self-bend toward the waveguide lattice,stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region.Three-peaked twisted solitons are stable in the lower(upper)cutoff region for a shallow(deep)lattice depth.Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.

Toward Circumventing Collinearity Effect in Nonlinear Spectral Mixture Analysis by Using a Spectral Shape Measure

Nonlinear spectral mixture analysis (NSMA) is a widely used unmixing algorithm. It can fit the mixed spectra adequately, but collinearity effect among true and virtual endmembers will decrease the retrieval accuracies of endmember fractions. Use of linear spectral mixture analysis (LSMA) can effectively reduce the degree of collinearity in the NSMA. However, the inadequate modeling of mixed spectra in the LSMA will also yield retrieval errors, especially for the cases where the multiple scattering is not ignorable. In this study, a generalized spectral unmixing scheme based on a spectral shape measure, i.e. spectral information divergence (SID), was applied to overcome the limitations of the conventional NSMA and LSMA. Two simulation experiments were undertaken to test the performances of the SID, LSMA and NSMA in the mixture cases of treesoil, tree-concrete and tree-grass. Results demonstrated that the SID yielded higher accuracies than the LSMA for almost all the mixture cases in this study. On the other hand, performances of the SID method were comparable with the NSMA for the tree-soil and tree-grass mixture cases, but significantly better than the NSMA for the tree-concrete mixture case. All the results indicate that the SID method is fairly effective to circumvent collinearity effect within the NSMA, and compensate the inadequate modeling of mixed spectra within the LSMA.

Intensity and composition-dependent sign reversal of non-linearity in TiO_2/CeO_2 nanocomposites

CeO2/TiO2 composite nanoparticles with different Ce/Ti molar ratios have been successfully synthesized via sol-gel method. It was found that the band gap of the nanocomposite is tunable by varying Ce/Ti content. The nonlinear response of the sample was studied by using the nanosecond laser pulses from a Q switched Nd：Yag laser employing the Z-scan method. Open aperture Z-scan experiment revealed that with the increase in the CeO2 amount in the nanocomposite, the non-linearity of the composite increases, and it was assumed that this could be due to the modification of TiO2 dipole symmetry by the addition of CeO2. Closed aperture Z-scan experiment showed that when the CeO2 amount increases, positive nonlinear refraction decreases, and this could be attributed to the increase in the two photon absorption which subsequently suppresses the nonlinear refraction.

Nonlinear Resistance Circuit Subsection Linearity Decomposition Fitting Analysis

The analysis of circuits is frequently required in the electricity of physics. When analyzing circuits, the general idea is to study the issues related to nonlinear resistance circuits based on commonly used physical and electrical theory. Generally, circuits can be divided into linear resistance circuits and nonlinear resistance circuits. However, for some nonlinear resistance circuit, a small part of them are decomposed through subsection linearity while most of them are adopted the form of hieroglyph combination for subsection decomposition fitting analysis. For the following contents, the author will adopt curve layout method to analyze nonlinear resistance element and relation characteristics of voltage and current;to state the characteristics and nature of common electronic elements in our life, and concepts of concave resistance and convex resistance;to analyze the characteristics of nonlinear resistance circuits through electrical circuit analysis method based on the electrical theorem of physics;finally, to analyze referring to actual cases, study the veracity, verify the feasibility and scientificity of the adopted analytical approach, apply image graphics of the resistance circuits in the convenient way to solve complicated design problems among actual electrical problems.

TianXing:A Linear Complexity Transformer Model with Explicit Attention Decay for Global Weather Forecasting

In this paper,we introduce TianXing,a transformer-based data-driven model designed with physical augmentation for skillful and efficient global weather forecasting.Previous data-driven transformer models such as Pangu-Weather,FengWu,and FuXi have emerged as promising alternatives for numerical weather prediction in weather forecasting.However,these models have been characterized by their substantial computational resource consumption during training and limited incorporation of explicit physical guidance in their modeling frameworks.In contrast,TianXing applies a linear complexity mechanism that ensures proportional scalability with input data size while significantly diminishing GPU resource demands,with only a marginal compromise in accuracy.Furthermore,TianXing proposes an explicit attention decay mechanism in the linear attention derived from physical insights to enhance its forecasting skill.The mechanism can reweight attention based on Earth's spherical distances and learned sparse multivariate coupling relationships,promptingTianXing to prioritize dynamically relevant neighboring features.Finally,to enhance its performance in mediumrange forecasting,TianXing employs a stacked autoregressive forecast algorithm.Validation of the model's architecture is conducted using ERA5 reanalysis data at a 5.625°latitude-longitude resolution,while a high-resolution dataset at 0.25°is utilized for training the actual forecasting model.Notably,the TianXing exhibits excellent performance,particularly in the Z500(geopotential height)and T850(temperature)fields,surpassing previous data-driven models and operational fullresolution models such as NCEP GFS and ECMWF IFS,as evidenced by latitude-weighted RMSE and ACC metrics.Moreover,the TianXing has demonstrated remarkable capabilities in predicting extreme weather events,such as typhoons.

Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors

As an extension of linear regression in functional data analysis,functional linear regression has been studied by many researchers and applied in various fields.However,in many cases,data is collected sequentially over time,for example the financial series,so it is necessary to consider the autocorrelated structure of errors in functional regression background.To this end,this paper considers a multiple functional linear model with autoregressive errors.Based on the functional principal component analysis,we apply the least square procedure to estimate the functional coeficients and autoregression coeficients.Under some regular conditions,we establish the asymptotic properties of the proposed estimators.A simulation study is conducted to investigate the finite sample performance of our estimators.A real example on China's weather data is applied to illustrate the validity of our model.