On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.

Nonlinear saturation of ion-acoustic instability

It is proposed that the wave mediated indirect wave-particle interaction may be responsible for nonlinear saturation of current driven low frequency ion-acoustic turbulence. This process decreases the growth rate and increases the damping rate of the wave. Comparison has been made with some experiments.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

R1SVM: A randomised nonlinear approach to large-scale anomaly detection

The problem of unsupervised anomaly detection arises in a wide variety of practical applications. While one-class support vector machines have demonstrated their effectiveness as an anomaly detection technique, their ability to model large datasets is limited due to their memory and time complexity for training. To address this issue for supervised learning of kernel machines, there has been growing interest in random projection methods as an alternative to the computationally expensive problems of kernel matrix construction and sup-port vector optimisation. In this paper we leverage the theory of nonlinear random projections and propose the Randomised One-class SVM (R1SVM), which is an efficient and scalable anomaly detection technique that can be trained on large-scale datasets. Our empirical analysis on several real-life and synthetic datasets shows that our randomised 1SVM algorithm achieves comparable or better accuracy to deep auto encoder and traditional kernelised approaches for anomaly detection, while being approximately 100 times faster in training and testing.

Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.

Transient response of nonlinear magneto-optic rotation in a paraffin-coated Rb vapor cell

We study resonant nonlinear magneto-optic rotation (NMOR) in a paraffin-coated Rb vapor cell as the magnetic field is swept. At low sweep rates, the nonlinear rotation appears as a narrow resonance signal with a linewidth of about ``300 mu G''(2 pi x 420 Hz). At high sweep rates, the signal shows transient response with an oscillatory decay. The decay time constant is of order 100 ms. The behavior is different for transitions starting from the lower or the upper hyperfine level of the ground state because of optical pumping effects.

Jet Engine Health Signal Denoising Using Optimally Weighted Recursive Median Filters

The removal of noise and outliers from health signals is an important problem in jet engine health monitoring. Typically, health signals are time series of damage indicators, which can be sensor measurements or features derived from such measurements. Sharp or sudden changes in health signals can represent abrupt faults and long term deterioration in the system is typical of gradual faults. Simple linear filters tend to smooth out the sharp trend shifts in jet engine signals and are also not good for outlier removal. We propose new optimally designed nonlinear weighted recursive median filters for noise removal from typical health signals of jet engines. Signals for abrupt and gradual faults and with transient data are considered. Numerical results are obtained for a jet engine and show that preprocessing of health signals using the proposed filter significantly removes Gaussian noise and outliers and could therefore greatly improve the accuracy of diagnostic systems. [DOI: 10.1115/1.3200907].

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Laser damage studies in nonlinear optical crystal sodium p-nitrophenolate dihydrate

We report the surface laser damage threshold in sodium p-nitrophenolate dihydrate, a nonlinear optical crystal. The experiment is performed with a pulsed Nd:YAG laser in TEM00 mode. The single shot damage thresholds are 11.16 +/- 0.28GWcm(-2) and 1.25 +/- 0.02GWcm(-2) for 1064 nm and 532 nm laser wavelengths respectively. A close correlation between the laser damage threshold and mechanical hardness is observed. A possible mechanism of laser damage is discussed.

Learning Feature Trajectories Using Gabor Filter Bank for Human Activity Segmentation and Recognition

We describe a novel method for human activity segmentation and interpretation in surveillance applications based on Gabor filter-bank features. A complex human activity is modeled as a sequence of elementary human actions like walking, running, jogging, boxing, hand-waving etc. Since human silhouette can be modeled by a set of rectangles, the elementary human actions can be modeled as a sequence of a set of rectangles with different orientations and scales. The activity segmentation is based on Gabor filter-bank features and normalized spectral clustering. The feature trajectories of an action category are learnt from training example videos using dynamic time warping. The combined segmentation and the recognition processes are very efficient as both the algorithms share the same framework and Gabor features computed for the former can be used for the later. We have also proposed a simple shadow detection technique to extract good silhouette which is necessary for good accuracy of an action recognition technique.

Robust joint precoder/receive filter designs for multiuser MIMO downlink

In this paper, we consider robust joint linear precoder/receive filter designs for multiuser multi-input multi-output (MIMO) downlink that minimize the sum mean square error (SMSE) in the presence of imperfect channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. We consider a stochastic error (SE) model and a norm-bounded error (NBE) model for the CSIT error. In the case of CSIT error following SE model, we compute the desired downlink precoder/receive filter matrices by solving the simpler uplink problem by exploiting the uplink-downlink duality for the MSE region. In the case of the CSIT error following the NBE model, we consider the worst-case SMSE as the objective function, and propose an iterative algorithm for the robust transceiver design. The robustness of the proposed algorithms to imperfections in CSIT is illustrated through simulations.

Citizens breaking out of filter bubbles: Urban screens as civic media

Social media platforms risk polarising public opinions by employing proprietary algorithms that produce filter bubbles and echo chambers. As a result, the ability of citizens and communities to engage in robust debate in the public sphere is diminished. In response, this paper highlights the capacity of urban interfaces, such as pervasive displays, to counteract this trend by exposing citizens to the socio-cultural diversity of the city. Engagement with different ideas, networks and communities is crucial to both innovation and the functioning of democracy. We discuss examples of urban interfaces designed to play a key role in fostering this engagement. Based on an analysis of works empirically-grounded in field observations and design research, we call for a theoretical framework that positions pervasive displays and other urban interfaces as civic media. We argue that when designed for more than wayfinding, advertisement or television broadcasts, urban screens as civic media can rectify some of the pitfalls of social media by allowing the polarised user to break out of their filter bubble and embrace the cultural diversity and richness of the city.