Spectral estimation method for noisy data using a noise reference

The development of array processing methods to extract the useful characteristics of acoustic sources such as their locations and absolute levels, starting from the measured sound field is one of the main issues in aero-acoustics. The conventional beamforming method is a very popular technique investigated to solve the power level estimation problem. It has the advantage of being robust, easy to implement and cheap in computation time. However, this technique is also known for having poor spatial resolution capabilities which prevents the correct source levels being obtained for numerous practical applications. Deconvolution techniques of the result computed with CBF, with the point spread function of the array manifold, may restore the power levels of the acoustic sources that would be observed in the absence of the array resolution effects. However, the accuracy of the results provided by deconvolution methods is very sensitive to background noise, always present in acoustic measurements. This process should be carried out after the additive noise has been suitably attenuated and, ideally, the deconvolution operator should amplify the noise as little as possible. Another approach is described in the article. It consists in using a noise reference and a new technique called spectral estimation method with additive noise to remove both the smearing effect produced by the array response and the background noise. The technique has been applied to computer and experimental simulations conducted both in an anechoic chamber and in the test section of an open wind tunnel involving acoustic sources radiating in a noisy environment. The levels of the sources were found with a good level of accuracy and the background noise greatly reduced, confirming the validity of the approach and the satisfactory performance of the method proposed.     

Nonequilibrium potential for arbitrary-connected networks of FitzHugh-Nagumo elements

We study an array of N units with FitzHugh-Nagumo dynamics linearly coupled. The system is submitted to a subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. In the limit of adiabatic driving, we analytically calculate the system’s nonequilibrium potential for arbitrary linear coupling. We illustrate its applicability by investigating noise-induced effects in an excitable regular network with extended antiphase coupling. In particular, the levels of noise for short-wavelength phase-instability, network’s synchronization and depinning of “defects” (groups of contiguous inhibited neurons on an antiphase background) are theoretically predicted and numerically confirmed. The origin of these collective effects and the dependence with parameters of the most probable length of defects are explained in terms of the system’s nonequilibrium potential.     

Parameter estimation using balanced synchronization

Synchronization between experimental observations and a dynamical model with undetermined parameters can assist in completing the specification of the model parameters. The quality of the synchronization, a cost function to be minimized, typically depends on the difference between the data time series and the model time series. If the coupling between the data and the model is too strong, this cost function is small for any data and any model, and the variation of the cost function with respect to the parameters of interest is too small to permit selection of a value of the parameters. If the coupling is too small, synchronization is lost. We introduce two methods for balancing the competing desires of a small cost function and the numerical ability to determine parameters accurately. One method of ‘balanced’ synchronization adds a requirement that the conditional Lyapunov exponent of the model system, conditioned on being driven by the data, remain negative but small. The other method allows the coupling to vary in time according to the error in synchronization. This second method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined.     

Street categorization for the estimation of day levels using short-term measurements

Day time noise level computation by traffic noise model requires realistic traffic data that is hardly ever available for every single street, therefore direct noise levels measurements may be the alternative. However, direct, continuous measurement of the day time noise level (equivalent level from 7 am to 7 pm) is an expensive strategy if a whole city must be assessed. To overcome this situation, short-term measurements of variable duration are often taken in order to estimate the day time noise level (L_d) because they are less expensive and resource demanding than continuous measurements over a whole day or more. From a set of continuous measurements over more than 48 h in 137 streets of nine different cities, the present work quantifies the error committed when using short-term noise measurements as a function of interval length measurement. To enhance estimation accuracy, both a street categorization and a temporal categorization have been attempted: in first place, it is found that the difference between the short-term noise level and L_d follows a different distribution for main roads than for ordinary streets, therefore the error committed depends on the street category. To be specific, when estimating L_d from a 15 min short time measurement the error committed would be ±2 dB with a percent population coverage of 90%, in the case of main streets and in the case of ordinary streets the same error range covers 72.5% of the population. In second place, if the measurement range time is restricted (temporal categorization) from 9 am to 1 pm and from 2 pm to 5 pm in the case of ordinary streets, the percent population coverage increases to 90% when the error range is ±3 dB. When referring to main streets, the measurement range of time is limited from 10 am to 5 pm to obtain an increase of 2% of the percent population coverage when the error is ±1 and ±2 dB.     

Parameter estimation in dynamic Casimir force measurements with known periodicity

It is important to have an accurate estimate of the unknown parameters such as the separation distance between interacting materials in Casimir force measurements. Current methods tend to produce large estimation errors. In this Letter, we present a novel method based on an adaptive control approach to estimate the unknown parameters using large amplitude dynamic Casimir measurements at separation distances of below 1 μm where both electrostatic force and Casimir force are significant. The estimate is proved to be accurate and the effectiveness of our method is demonstrated via a numerical example.     

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

We propose a method to estimate the average fidelity using the unitary 2t-design of a twirled noisy channel, which is suitable for large-scale quantum circuits. Compared with the unitary 2-design in randomized benchmarking, the unitary2t-design for the twirling of noisy channels is more flexible in construction and can provide more information. In addition,we prove that the proposed method provides an efficient and reliable estimation of the average fidelity in benchmarking multistage quantum gates and estimating the weakly gate-and time-dependent noise. For time-dependent noise, we provide a scheme of moment superoperator to analyze the noise in different experiments. In particular, we give a lower bound on the average fidelity of a channel with imperfect implementation of benchmarking and state preparation and measurement errors(SPAM).     

Accuracy enhancement of parameter estimation for noisy NMR spectra

An ARMA(M,M-1) modeling is implemented by the multi-stage linear least squares. This modeling technique is applied to the analysis of noisy NMR signals. A new method is proposed to eliminate the spurious peaks by utilizing the phase angle difference between the real and imaginary data. The proposed method is tested to simulated and experimental¹⁷O, NMR spectra with seven peaks. The results are compared to those by the autoregressive (AR) Householder triangularization decomposition (QRD). The proposed ARMA(M,M-1) model yields more accurate and consistent parameter estimation than AR model in the noisy spectra.     

Parameter estimation for hysteretic systems

The differential system characterization of hysteretic system is well known. The problem of estimating the parameters of this system on the basis of input-output data, possibly noise corrupted, is considered. It turns out that the estimation problem is a non-linear optimization problem. The Gauss Newton method is used in setting up a two-stage iterative least squares algorithm. The usefulness of the algorithm is validated through its application to various simulated time histories from the hysteretic model.     

The simplified FitzHugh-Nagumo model with action potential duration restitution: Effects on 2D wave propagation

A modification of the simplified FitzHugh-Nagumo (FN) equations is proposed for introducing a residual component of the slow variable, which determines the restitution of action potential duration (APD) also known as the interval-excitation duration relationship. The three-step-wise approximation of ε(E) which is widely used in current publications is replaced in a new model by a four-step approximation. This change is used for studying by computer simulation the effects of APD restitution properties independently of the APD and refractory period on 2D wave propagation in an isotropic matrix (made by 128 × 128 nodes). The method for fitting the model to the given experimental restitution data (obtained from myocardial cells) is presented. The computer simulations implemented on a massively parallel computer (Connection Machine) showed at least three important qualitative distinctions in behavior which demonstrate the effect of APD restitution: changes in the speed and wavelength of propagated waves with the period of stimulation, non-stationary propagation of spiral waves, and site-specific induction of spiral waves with premature stimulation not on the tail of the previous wave. Quantitative effects of differing restitution properties are expressed in the size and location of a window of vulnerability in 2D excitable media. These windows are characterized by the appearance of single and double spiral waves in response to premature stimulation applied inside the window. Thus the APD restitution incorporated in the FN model produces a significant effect on the formation and propagation of spiral waves.     

Parameter estimation and multivariable model building for the non-destructive, on-line determination of eggshell strength

In the non-destructive quality assessment of agro-products using vibration analysis, the resonant frequency and the damping of the vibration are the main interest. Those parameters are usually calculated starting from the frequency spectrum, obtained after a fast Fourier transformation (FFT) of the time signal. However, this method faces several drawbacks when applied to short-time signals, as in the case of impact testing of highly damped specimen. An alternative to the FFT method is used for the high-resolution estimation of both resonant frequency and damping. Furthermore, the mass-spring model that is used in the literature for non-destructive quality assessment of various agro-products is extended with the incorporation of the damping and a shape characteristic. As a practical example, eggshell stiffness was estimated using vibration measurements. A data set consisting of 229 eggs was measured. It is shown that both the damping and the shape characteristics are of major importance to explain eggshell strength. This paper makes clear that a univariable model, as is mostly used in the literature, is not always satisfactory to describe the vibration behaviour of biological products.     

The noisy Hegselmann-Krause model for opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause’s rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model [G. Deffuant, D. Neu, F. Amblard, G. Weisbuch, Adv. Compl. Syst. 3, 87 (2000)] for continuous-opinion dynamics.     

Assessment of membrane potential using confocal microspectrofluorimetry

Some slow potentiometric dyes, e.g., 3,3-dipropylthiacarbocyanine and tetramethylrhodamine methyl ester, exhibit fluorescence spectral changes on redistributing from aqueous medium to cells. This effect has been used for spectroscopic discrimination of the emissions from free and bound dyes in cells. Such a discrimination can, in principle, allow for the assessment of cell membrane potential in individual cells, using the Nernst equation applied to the ratio of free dye fluorescence intensities inside and outside of the cell.     

分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程 关键词： 分数阶 Hopf分岔 FitzHugh-Nagumo模型 同步     

Parameter estimation for chaotic systems with and without noise using differential evolution-based method

We present an approach in which the differential evolution (DE) algorithm is used to address identification problems in chaotic systems with or without delay terms. Unlike existing considerations, the scheme is able to simultaneously extract (i) the commonly considered parameters, (ii) the delay, and (iii) the initial state. The main goal is to present and verify the robustness against the common white Guassian noise of the DE-based method. Results of the time-delay logistic system, the Mackey-Glass system and the Lorenz system are also presented.     

Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method

We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.     

Sine-Gordon solitons in the presence of a noisy potential

We study the interaction of sine-Gordon solitons with two kinds of impurity potentials localized in space and varying randomly in time. the production of modified kink-antikink pairs is observed with different features depending respectively on the additive or multiplicative nature of the noise.     

Bifurcation analysis of the travelling waveform of FitzHugh-Nagumo nerve conduction model equation

The FitzHugh-Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z(2) symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (c) 1997 American Institute of Physics.     

Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform

Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton׳s rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.