Fractional Fourier transform pre-processing for neural networks and its application to object recognition

New Criteria on Finite-Time Stability of Fractional-Order Hopfield Neural Networks With Time Delays

In this article, the finite-time stability (FTS) of fractional-order Hopfield neural networks with time delays (FHNNTDs) is studied. A widely used inequality in investigating the stability of the fractional-order neural networks is fractional-order Gronwall inequality related to the Mittag-Leffler function, which cannot be directly used to study the stability of the factional-order neural networks with time delays. In the existing works related to fractional-order Gronwall inequality with time delays, the order was divided into two cases: λ ∈ (0,0.5] and λ ∈ (0.5,+∞) . In this article, a new fractional-order Gronwall integral inequality with time delay and the unified form for all the fractional order is developed, which can be widely applied to investigate FTS of various fractional-order systems with time delays. Based on this new inequality, a new criterion for the FTS of FHNNTDs is derived. Compared with the existing criteria, in which fractional order λ ∈ (0,1) was divided into two cases, λ ∈ (0,0.5] and λ ∈ (0.5,1) , the obtained results in this article are presented in the unified form of fractional order λ ∈ (0,1) and convenient to verify. More importantly, the criteria in this article are less conservative than some existing ones. Finally, two numerical examples are given to demonstrate the validity of the proposed results.

Boundary Mittag-Leffler stabilization of fractional reaction-diffusion cellular neural networks

Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.

Fluid flow signals processing based on fractional Fourier transform in a stirred tank reactor

The analysis of fluid flow signals and the characterization of fluid flow behavior are of great importance for two-phase flow studies. In this work, the fractional Fourier transform (FRFT), which was based on the optimum order calculated by stepping search method, was proposed to extract the characteristics of fluid flow signals. Meanwhile, the largest Lyapunov exponent (LLE), which is an indication of the chaotic degree of mixing process, was adopted to quantify fluid flow behavior. The maximum amplitude (MA) and LLE value were taken together to inquire into the relationship between the characteristics of fluid flow signals and the characterization of fluid flow behavior. In addition, differences between the two adjacent values (AD) and the maximum differences (MD) are employed to further analyze the differences in behavioral characterization with MA and LLE. The results show that the MA value performs the same increasing trend as the LLE value when the gas flow rate and agitation speed increase. AD and MD values of the MA are one to two orders of magnitude greater than those of the LLE. The eigenvalues (MA) solved by the FRFT method is facilitates capturing small changes owing to changes in external conditions. These findings can provide new ideas for the extraction and characterization of fluid flow behavior.

Mobile Robot Sonar Backscatter Algorithm for Automatically Distinguishing Walls, Fences, and Hedges

We present an algorithm to distinguish several types of brick walls, picket fences, and hedges based on the analysis of backscattered sonar echoes. The echo data are acquired by a mobile robot with a single-transducer 50 kHz pulse-echo sonar computer-controlled scanning system packaged as its sensor head. For several locations along a wall, fence, or hedge, a fan of backscatter sonar echoes is acquired, digitized, and stored on a computer as the sonar transducer is swept over a horizontal arc. Off-line, each digitized echo waveform is then rectified, smoothed, and summed to give a measure of the backscatter strength. This backscatter is then plotted versus scan angle, with a series of N-peak deformable templates fit to these data for each scan. The number of peaks in the best-fitting N-peak template indicates the presence and location of retro-reflectors, and allows automatic categorization of the various fences, hedges, and brick walls.

Perceptrons with Hebbian learning based on wave ensembles in spatially patterned potentials

A general scheme to realize a perceptron for hardware neural networks is presented, where multiple interconnections are achieved by a superposition of Schrödinger waves. Spatially patterned potentials process information by coupling different points of reciprocal space. The necessary potential shape is obtained from the Hebbian learning rule, either through exact calculation or construction from a superposition of known optical inputs. This allows implementation in a wide range of compact optical systems, including (1) any nonlinear optical system, (2) optical systems patterned by optical lithography, and (3) exciton-polariton systems with phonon or nuclear spin interactions.

Embolic Doppler ultrasound signal detection via fractional Fourier transform

Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.

Wall-corner classification using sonar: a new approach based on geometric features

Ultrasonic signals coming from rotary sonar sensors in a robot gives us several features about the environment. This enables us to locate and classify the objects in the scenario of the robot. Each object and reflector produces a series of peaks in the amplitude of the signal. The radial and angular position of the sonar sensor gives information about location and their amplitudes offer information about the nature of the surface. Early works showed that the amplitude can be modeled and used to classify objects with very good results at short distances—80% average success in classifying both walls and corners at distances less than 1.5 m. In this paper, a new set of geometric features derived from the amplitude analysis of the echo is presented. These features constitute a set of characteristics that can be used to improve the results of classification at distances from 1.5 m to 4 m. Also, a comparative study on classification algorithms widely used in pattern recognition techniques has been carried out for sensor distances ranging between 0.5 to 4 m, and with incidence angles ranging between 20° to 70°. Experimental results show an enhancement on the success in classification rates when these geometric features are considered.