Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network.

Blind Characterisation of Sensors with Second-Order Dynamic Response

Compensation for the dynamic response of a temperature sensor usually involves the estimation of its input on the basis of the measured output and model parameters. In the case of temperature measurement, the sensor dynamic response is strongly dependent on the measurement environment and fluid velocity. Estimation of time-varying sensor model parameters therefore requires continuous textit{in situ} identification. This can be achieved by employing two sensors with different dynamic properties, and exploiting structural redundancy to deduce the sensor models from the resulting data streams. Most existing approaches to this problem assume first-order sensor dynamics. In practice, however second-order models are more reflective of the dynamics of real temperature sensors, particularly when they are encased in a protective sheath. As such, this paper presents a novel difference equation approach to solving the blind identification problem for sensors with second-order models. The approach is based on estimating an auxiliary ARX model whose parameters are related to the desired sensor model parameters through a set of coupled non-linear algebraic equations. The ARX model can be estimated using conventional system identification techniques and the non-linear equations can be solved analytically to yield estimates of the sensor models. Simulation results are presented to demonstrate the efficiency of the proposed approach under various input and parameter conditions.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Analysis of steel structures for first- and second-order element (displacement and force) solutions

Finite element method (FEM) relies on an approximate function to fit into a governing equation and minimizes the residual error in the integral sense in order to generate solutions for the boundary value problems (nodal solutions). Because of this FEM does not show simultaneous capacities for accurate displacement and force solutions at node and along an element, especially when under the element loads, which is of much ubiquity. If the displacement and force solutions are strictly confined to an element’s or member’s ends (nodal response), the structural safety along an element (member) is inevitably ignored, which can definitely hinder the design of a structure for both serviceability and ultimate limit states. Although the continuous element deflection and force solutions can be transformed into the discrete nodal solutions by mesh refinement of an element (member), this setback can also hinder the effective and efficient structural assessment as well as the whole-domain accuracy for structural safety of a structure. To this end, this paper presents an effective, robust, applicable and innovative approach to generate accurate nodal and element solutions in both fields of displacement and force, in which the salient and unique features embodies its versatility in applications for the structures to account for the accurate linear and second-order elastic displacement and force solutions along an element continuously as well as at its nodes. The significance of this paper is on shifting the nodal responses (robust global system analysis) into both nodal and element responses (sophisticated element formulation).

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

The statistics of the second order response of an FPSO in spreading seas

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman's approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly. Copyright © 2009 by ASME.

The effect of the group delay ripple of chirped fiber grating on composite second-order in optical fiber CATV system

The effect of group delay ripple of chirped fiber gratings on composite second-order (CSO) performance in optical fiber CATV system is investigated. We analyze the system CSO performances for different ripple amplitudes, periods and residual dispersion amounts in detail. It is found that the large ripple amplitude and small ripple period will deteriorate the system CSO performance seriously. Additionally, the residual dispersion amount has considerable effect on CSO performance in the case of small ripple amplitude and large ripple period. (c) 2004 Elsevier B.V. All rights reserved.

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Effect of the electrostatic interactions of chromophores on the macroscopic second-order nonlinear optical properties of the polymer films

The polyetherketone (PEK-c) guest-host system thin films doped with 3-(1,1-dicyanothenyl)-1-phenyl-4,5-dihydro-1H-pryazole (DCNP) were prepared. Their second-order nonlinear optical (NLO) coefficients chi(33)((2)) were measured by using Maker fringe method for the polymer films doped with different weight percents of DCNP. Experimental results indicate that the second-order NLO properties of the poled polymer films could decrease with the chromophore loading increasing when the chromophore loading reaches a fairly high level. In this paper, the relationship between the macroscopic second-order NLO coefficient and the chromophore number density was modified under considering the role of the electrostatic interactions of chromophores in the polymer film. According to the modified relationship, the macroscopic second-order NLO coefficient is no longer in direct proportion with the chromophore number density in the polymer film. The effect of the electrostatic interactions of chromophores on second-order NLO properties was discussed. The attenuation of the macroscopic second-order NLO activity can be demonstrated by the role of the chromophore electrostatic interactions at high loading of chromophore in the polymer systems.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.