Nonlinear Range Research Articles

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

Designing Load-Dependency of Static Friction of Elastomer Covered with Mesh Sheets

The static friction of compliant elastomers has proven important for industrial applications, including seals, and grips on tools and sports equipment. The design of load-dependent contact state may provide characteristic load-dependent frictional properties beyond that found on conventional rubber surfaces. Here we investigate the static friction, over a wide range of normal loads, between a fat glass surface and polyester meshes adhered on an elastomer surface. At low load the glass is supported only by the mesh members and the static friction is low. As normal load increases, the mesh members tend to dent into the elastomer and at the pore of the mesh the elastomer surface may make contact with the glass. The newly created contact with the elastomer makes the static friction increase with the higher friction coefficient. By tuning the structures, e.g., the aperture ratio, of meshes, we can extend the monotonic load-dependency of static friction of rubbers into the highly nonlinear range.

Wide Nonlinear Chirp Scaling Algorithm for Spaceborne Stripmap Range Sweep SAR Imaging

The spaceborne stripmap range sweep synthetic aperture radar (SS-RSSAR) is a new concept spaceborne SAR system that images the region of interest (ROI) with ROI-orientated strips, which, unlike the traditional spaceborne SAR, are allowed to be not parallel with the satellite orbit. The SS-RSSAR imaging is a challenging problem because echoes of a wide region have strong spatial varieties, especially in high-squint geometries, and are hard to be focused by a single swath. The traditional imaging algorithms could solve this problem by cost-ineffectively dividing an ROI into many subswaths for separate processing. In this paper, a new wide nonlinear chirp scaling (W-NLCS) algorithm is proposed to efficiently image the SS-RSSAR data in a single swath. Comparing with the traditional nonlinear chirp scaling algorithm, the W-NLCS algorithm is superior in three major aspects: the nonlinear bulk range migration compensation (RMC), the interpolation-based residual RMC, and the modified azimuth frequency perturbation. Specifically, the interpolation for the residual RMC, the most significant step in achieving the wide-swath imaging performance, is made innovatively in the time domain. The derivation of the W-NLCS algorithm, as well as the performance analyses of the W-NLCS algorithm in aspects of the azimuth resolution, accuracy, and complexity, are all provided. The presented approach is evaluated by the point target simulations.

An equivalent linearization method for nonlinear Van der Pol oscillator subjected to random vibration using orthogonal functions

This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse (BP) function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.

A weighted dual criterion of the equivalent linearization method for nonlinear systems subjected to random excitation

This paper introduces and discusses a weighted form of the dual mean-square error criterion by considering weighted contributions of forward and return replacements adjusted by a specific non-dimensional weight coefficient. The simplicity and accuracy of the proposed weighted dual equivalent linearization technique are checked on several random vibration systems in comparison with other criteria. It is shown that the corresponding accuracy can be significantly improved for a large range of nonlinearity of investigated vibration systems.

Nonlinear correction of the sensor S11639 in mini-spectrometer

Linear array sensor S11639 is often used in mini-spectrometer for UV measurement. However, when the exposure volume of S11639 is relatively bigger, the non-linearity of the spectral response will appear. This nonlinear effect will affect the dynamic range of the mini-spectrometer, and therefore, nonlinear correction must be carried out. Photoelectric response of S11639 is measured with halogen tungsten lamp and deuterium lamp to find out the linear part between the exposure and the A/D conversion output, and straight line fitting of the data is made to obtain the factors of S11639 in the linear range. Based on it, the theoretical value in nonlinear range is got by extrapolation, and the difference between the theoretical value and the actual measurement value was calculated. The nonlinear correction of S11639 is realized by polynomial fitting with the least square method. At the same time, compared with the experimental results, the error causes of the experimental data are analyzed, and the experiment is provided for better utilization of mini-spectrometer based on S11639 for photoelectric detection in the full dynamic range.

Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis

A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of the 2D body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions. The expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2D continuum. To account for the modelling abilities of the 2D continuum in the linear range, the eigenmode and eigenfrequencies of a given specimen are determined. The buckling and post-buckling behaviour of the same specimen, subjected to two different loading conditions are analysed as tests in the nonlinear range. The problems have been solved numerically by means of the COMSOL Multiphysics finite element software.

Application of a Modified Arrhenius Equation to Describe the Time-Temperature Equivalence in Relaxation Analysis of Metal Seals

For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor α. Therefore, the Arrhenius equation is widely used due to its simple form and often leads to suitable results. Where, the Arrhenius equation presents a linear relation for the temperature-dependent shift factor in logarithmic scale ln(α) with the absolute inverse temperature (1/ϑ). However, in cases with a large temperature range which eventually include more complex reaction processes, the functional relation between ln(α) and (1/ϑ) is nonlinear in the ‘Arrhenius plot’. In those cases, the monotone change of the nonlinear range in the ‘Arrhenius plot’ can be interpreted as a transient range between two approximately linear or constant regions. An extended application of the modified Arrhenius equation from Nakamura (1989) is presented in this study for this transient range. The introduced method was applied to describe the time-temperature equivalence in the relaxation analysis of restoring seal force of metal seals, which are used in lid-systems of transport and interim storage casks for radioactive materials. But, the method is widely valid and can be used for different objectives which are characterized by thermorheologically simple behavior with nonlinear sensitivity to inverse temperature.

Input Voltage Mapping Optimized for Resistive Memory-Based Deep Neural Network Hardware

Artificial neural network (ANN) computations based on graphics processing units (GPUs) consume high power. Resistive random-access memory (RRAM) has been gaining attention as a promising technology for implementing power-efficient ANNs, replacing GPU. However, nonlinear ${I}$ – ${V}$ characteristics of RRAM devices have been limiting its use for ANN implementation. In this letter, we propose a method and a circuit to address issues due to the nonlinear ${I}$ – ${V}$ characteristics. We demonstrate the feasibility of the method by simulating its application to multiple neural networks, from multi-layer perceptron to deep convolutional neural network based on a typical RRAM model. Results from classifying datasets including ImageNet show that the proposed method produces much higher accuracy than the naive linear mapping for a wide range of nonlinearity.

A method for measuring the continuous dispersion spectrum of nonlinear refraction coefficients of materials

In this paper, a method for measuring the continuous dispersion spectrum of nonlinear refraction coefficients of materials based on complex refractive index dispersion (CRID) measurement is proposed. This method involves measuring internal reflection spectra with a lab-made apparatus. From the determined CRIDs of a material with and without exciting light, the changes in refractive index over a wide spectral range can be obtained, from which the nonlinear refraction coefficients can be deduced. In addition, the RI changes at wavelengths far from the nonlinear range can be used to monitor the thermal effects. In this study, a methyl-red-doped poly(methyl methacrylate) (MR-PMMA) sample was investigated. A large nonlinear refraction coefficient on the order of 10−1cm2/W was observed. The results also show that the absolute value of nonlinear refraction coefficient of the MR-PMMA sample decreases with the increase of excitation intensity. Consequently, this study provides a powerful approach that has the potential to be applied in the study of the nonlinear properties of materials.

High resolution inverse synthetic aperture radar imaging of three-axis-stabilized space target by exploiting orbital and sparse priors**Project supported by the National Natural Science Foundation of China (Grant Nos. 61601496 and 61401024).

The development of inverse synthetic aperture radar (ISAR) imaging techniques is of notable significance for monitoring, tracking and identifying space targets in orbit. Usually, a well-focused ISAR image of a space target can be obtained in a deliberately selected imaging segment in which the target moves with only uniform planar rotation. However, in some imaging segments, the nonlinear range migration through resolution cells (MTRCs) and time-varying Doppler caused by the three-dimensional rotation of the target would degrade the ISAR imaging performance, and it is troublesome to realize accurate motion compensation with conventional methods. Especially in the case of low signal-to-noise ratio (SNR), the estimation of motion parameters is more difficult. In this paper, a novel algorithm for high-resolution ISAR imaging of a space target by using its precise ephemeris and orbital motion model is proposed. The innovative contributions are as follows. 1) The change of a scatterer projection position is described with the spatial-variant angles of imaging plane calculated based on the orbital motion model of the three-axis-stabilized space target. 2) A correction method of MTRC in slant- and cross-range dimensions for arbitrarily imaging segment is proposed. 3) Coarse compensation for translational motion using the precise ephemeris and the fine compensation for residual phase errors by using sparsity-driven autofocus method are introduced to achieve a high-resolution ISAR image. Simulation results confirm the effectiveness of the proposed method.

Non-linear stress-orientation behavior of flexible chain polymers under fast elongational flow

Closed-form analytical formulas are proposed for non-linear stress-orientation relation valid in the entire range of tensile stresses, intermediate and high, basing on the inverse Langevin chain statistics. Tensile force and orientation characteristics for single, flexible chain macromolecule are reconsidered in a closed-form Padè approximation of the inverse Langevin function in the entire range of chain extensions, as well as the dynamics of molecular deformation and orientation for systems of chains subjected to uniaxial elongational flow. Average stress and orientation tensors, not collinear in the non-linear range, as well as the tensile stress and axial orientation factor of the chain segments in the system are calculated. For the intermediate tensile stresses, the closed-form formula is derived in the first non-Gaussian term approximation of the inverse Langevin function with the assumption of dominating longitudinal elongation of the chains. The high-stress non-linearity formula is derived with the Padè and Peterlin modulus approximations and aligned chain end-to-end vectors by the flow. Both formulas are validated by exact numerical calculations without the assumptions and influence of the approximations is estimated. Ranges of applicability of the formulas are illustrated and examples of their application are presented.

Hardware Implementation of Single Iterated Multiplicative Inverse Square Root

Inverse square root has played an important role in Cholesky decomposition, which devoted to hardware efficient compressed sensing. However, the performance is usually limited by the trade-off between throughput and precision. This paper presents hardware implementation of fixed-point single iterated multiplicative inverse square root. Multiple piecewise linear approximation in softly nonlinear range is used to compute the initial value. Single iterated Newton-Raphson method is employed to obtain high precision. Multiple constants multiplication technique is proposed to achieve high throughput. The combination of these techniques yields high performance in terms of throughput and precision. It obtains more than 70 % of throughput improvement and almost 100 × higher precision over the inverse square root Intellectual Property (IP) from Altera. In addition, Cholesky decomposition has been presented to validate the proposed architecture, which shows that 42 % of throughput improvement is achieved compared with the IP.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18717

Simple Homogenization-Topology Optimization Approach for the Pushover Analysis of Masonry Walls

ABSTRACTA topology optimized rigid triangular FE macro-model with non-linear homogenized interfaces for the pushover analysis of in plane loaded masonry is presented. The shape of the mesh and the position of the interfaces is evaluated through a topology optimization approach that detects the main compressive stress fluxes in the structure. Different values of the horizontal action are considered to derive an adaptive mesh or an optimal discretization that is suitable for multiple loads. Masonry properties are calibrated by means of a homogenization approach in the nonlinear range. To tackle elastic and inelastic deformations, interfaces are assumed to behave as elasto-plastic with softening in both tension and compression, with orthotropic behavior. The two-step procedure competes favorably with classic equivalent frame approaches because it does not require a-priori assumptions on the mesh and on the length of the rigid offsets. An example of technical relevance is discussed, relying into a multi-story masonry wall loaded up to failure.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Fractional Order Linear Variable Differential Transformer: Design and analysis

Linear Variable Differential Transformer (LVDT) is the most preferred displacement measurement transducer used in industries because of its simple design and proven reliability. The major challenge faced in LVDT is linearity in limited stroke range. In this paper, a fractional order model of LVDT is developed and its characteristics like sensitivity, nonlinearity and stroke range are analysed by considering fractional behaviour only in self-inductance, mutual inductance and both. The results presented in this paper shows that Fractional Order Linear Variable Differential Transformer (FOLVDT) provides high sensitivity with reduced nonlinearity compared to the conventional LVDT. The results also demonstrate that the FOLVDT can be operated for increased stroke range without compromising on sensitivity and linearity.

Bistability of ultrashort pulses in FBG under different nonlinearity profiles

In this work, we studied the optical bistability of Fiber Bragg Grating (FBG) under nonlinear regime, considering three increasing and decreasing profiles of nonlinearity: linear, quadratic and exponential. We varied the nonlinearity range in each profile, and obtained different curves of bistability and reflectivity. We analyzed the powers [Formula: see text] and [Formula: see text], as well as the width of the photonic band gap ([Formula: see text] of each device under different nonlinearity profiles, and we observed the changes in reflectivity of the FBG. The power intensities [Formula: see text] and [Formula: see text] obtained for the bistability of decreasing profiles were lower than those obtained for the increasing profiles, and the values of [Formula: see text] were also lower in decreasing profiles, which is useful for optical switching applications.

α-Synuclein fibril-induced inclusion spread in rats and mice correlates with dopaminergic Neurodegeneration

Proteinaceous inclusions in neurons, composed primarily of α-synuclein, define the pathology in several neurodegenerative disorders. Neurons can internalize α-synuclein fibrils that can seed new inclusions from endogenously expressed α-synuclein. The factors contributing to the spread of pathology and subsequent neurodegeneration are not fully understood, and different compositions and concentrations of fibrils have been used in different hosts. Here, we systematically vary the concentration and length of well-characterized α-synuclein fibrils and determine their relative ability to induce inclusions and neurodegeneration in different hosts (primary neurons, C57BL/6J and C3H/HeJ mice, and Sprague Dawley rats). Using dynamic-light scattering profiles and other measurements to determine fibril length and concentration, we find that femptomolar concentrations of fibrils are sufficient to induce robust inclusions in primary neurons. However, a narrow and non-linear dynamic range characterizes fibril-mediated inclusion induction in axons and the soma. In mice, the C3H/HeJ strain is more sensitive to fibril exposures than C57BL/6J counterparts, with more inclusions and dopaminergic neurodegeneration. In rats, injection of fibrils into the substantia nigra pars compacta (SNpc) results in similar inclusion spread and dopaminergic neurodegeneration as injection of the fibrils into the dorsal striatum, with prominent inclusion spread to the amygdala and several other brain areas. Inclusion spread, particularly from the SNpc to the striatum, positively correlates with dopaminergic neurodegeneration. These results define biophysical characteristics of α-synuclein fibrils that induce inclusions and neurodegeneration both in vitro and in vivo, and suggest that inclusion spread in the brain may be promoted by a loss of neurons.

Influence of seismic incident angle on response of symmetric in plan buildings

The objective of this paper is the investigation of the influence of the seismic incident angle on the response values of symmetric in plan buildings subjected to bi-directional horizontal ground motion. Firstly, a set of symmetric buildings is studied by means of linear response history analysis. The maximum response values over all incident angles are determined using well established analytical formulae. It is demonstrated that for symmetric buildings possessing equal stiffness along two orthogonal horizontal axes the maximum value of some vectorial response quantities (resultant displacements, resultant moments of some columns) does not depend on the orientation of the seismic action. On the contrary, the seismic incident angle is essential for the rest response quantities of such buildings, as well as for all the response quantities of symmetric buildings with different stiffness along the two structural axes. In addition, the same buildings are analyzed by means of non-linear response history analysis, with seismic components having several different orientations with regard to the structural axes. Similar conclusions are derived for the nonlinear range of behaviour too.

Non‐linear fuzzy predictive control of hydroelectric system

This study brings out a brand new non-linear predictive control method, a fuzzy generalised predictive control, for hydroelectric plant systems. Takagi-Sugeno (T-S) fuzzy method and generalised predictive control are implemented in the non-linear control method. The basic concept of the method is generalised predictive control, which is a linear system based method. However, the authors novelty adopt fuzzy model, especially the T-S model, as the prediction model to broaden the applications of the predictive control to non-linear range. Therefore, the proposed method inherits the advantages of generalised predictive control, but it can also effectively control a complex non-linear system. Its effectiveness and efficiency are verified by Lyapunov stability theory. Applying the control method on the non-linear hydroelectric system, the different experiments show that this control method succeeds in maintaining the hydroelectric system stable. Those experimental results accord with theoretic analysis. Thus, the proposed control method enjoys the capacity to govern a non-linear system. A comparison experiment between the proposed method and PID method illustrates the advantages of the authors' method, which are its smooth treatment, less overshoot and fast to be stable of response. In addition, discussions about the tuning control parameters facilitate the usages of the proposed method.