The Cramer-Rao Bound and DMT Signal Optimisation for the Identification of a Wiener-Type Model

In linear system identification, optimal excitation signals can be determined using the Cramer-Rao bound. This problem has not been thoroughly studied for the nonlinear case. In this work, the Cramer-Rao bound for a factorisable Volterra model is derived. The analytical result is supported with simulation examples. The bound is then used to find the optimal excitation signal out of the class of discrete multitone signals. As the model is nonlinear in the parameters, the bound depends on the model parameters themselves. On this basis, a three-step identification procedure is proposed. To illustrate the procedure, signal optimisation is explicitly performed for a third-order nonlinear model. Methods of nonlinear optimisation are applied for the parameter estimation of the model. As a baseline, the problem of optimal discrete multitone signals for linear FIR filter estimation is reviewed

Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect

A characteristic feature of the Portevin - Le Chatelier effect or the jerky flow is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to result from the competition of a few relevant time scales controlling the dynamics of jerky flow. We address the issue of time scales and its connection to the negative strain rate sensitivity of the flow stress within the framework of a model for the jerky flow which is known to reproduce several experimentally observed features including the negative strain rate sensitivity of the flow stress. We attempt to understand the above issues by analyzing the geometry of the slow manifold underlying the relaxational oscillations in the model. We show that the nature of the relaxational oscillations is a result of the atypical bent geometry of the slow manifold. The analysis of the slow manifold structure helps us to understand the time scales operating in different regions of the slow manifold. Using this information we are able to establish connection with the strain rate sensitivity of the flow stress. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity.Comment: 7 figures, To appear in Phys. Rev.

Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape

It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force function. By including the kinetic energy of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier equations. Our analysis also shows that mass of the ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication

Testing the assumptions of linear prediction analysis in normal vowels

This paper develops an improved surrogate data test to show experimental evidence, for all the simple vowels of US English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modelling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modelling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance

The hidden order behind jerky flow

Jerky flow, or the Portevin-Le Chatelier effect, is investigated at room temperature by applying statistical, multifractal and dynamical analyses to the unstable plastic flow of polycrystalline Al-Mg alloys with different initial microstructures. It is shown that a chaotic regime is found at medium strain rates, whereas a self-organized critical dynamics is observed at high strain rates. The cross-over between these two regimes is signified by a large spread in the multifractal spectrum. Possible physical mechanisms leading to this wealth of patterning behavior and their dependence on the strain rate and the initial microstructure are discussed

High order amplitude equation for steps on creep curve

We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential equations describing the evolution of three types of dislocations. The transition to the instability has been shown to be via Hopf bifurcation leading to limit cycle solutions with respect to physically relevant drive parameters. Here we use reductive perturbative method to extract an amplitude equation of up to seventh order to obtain an approximate analytic expression for the order parameter. The analysis also enables us to obtain the bifurcation (phase) diagram of the instability. We find that while supercritical bifurcation dominates the major part of the instability region, subcritical bifurcation gradually takes over at one end of the region. These results are compared with the known experimental results. Approximate analytic expressions for the limit cycles for different types of bifurcations are shown to agree with their corresponding numerical solutions of the equations describing the model. The analysis also shows that high order nonlinearities are important in the problem. This approach further allows us to map the theoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.

PVDF/BaTiO3 composite foams with high content of β phase by thermally induced phase separation (TIPS)

Poly(vinylidene fluoride) (PVDF) displays ferroelectric, piezoelectric and pyroelectric behavior and it is widely used in high-tech applications including sensors, transducers, energy harvesting devices and actuators. The crystallization of this polymer into highly polar β phase is desirable but is hard to achieve without applying specific thermo-mechanical treatments. Indeed, fabrication processes directly affect PVDF molecular chain conformation, inducing distinct polymorphs. In this paper, we present the fabrication of PVDF/BaTiO3 composite foams by thermally induced phase separation method (TIPS). Different compositions are tested and characterized. The crystallinity, and in particular the development of electroactive β crystal phase is monitored by FTIR, DSC and XRD measurements. Dielectric properties are also evaluated. It turns out that TIPS is a straightforward method that clearly promotes the spontaneous growth of the β phase in PVDF and its composite foams, without the need to apply additional treatments, and also significantly improves the degree of crystallinity. BaTiO3 content gives additional value to the development of β phase and total crystallinity of the systems. The low permittivity values (between 2 and 3), combined with the cellular morphology makes these materials suitable as lightweight components of microelectronic circuits

Dynamics of stick-slip in peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. We derive the equations of motion for the angular speed of the roller tape, the peel angle and the pull force used in earlier investigations using a Lagrangian. Due to the constraint between the pull force, peel angle and the peel force, it falls into the category of differential-algebraic equations requiring an appropriate algorithm for its numerical solution. Using such a scheme, we show that stick-slip jumps emerge in a purely dynamical manner. Our detailed numerical study shows that these set of equations exhibit rich dynamics hitherto not reported. In particular, our analysis shows that inertia has considerable influence on the nature of the dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a phenomenological peel force function which includes the influence of the pull speed. This reproduces the decreasing nature of the rupture force with the pull speed observed in experiments. This rich dynamics is made transparent by using a set of approximations valid in different regimes of the parameter space. The approximate solutions capture major features of the exact numerical solutions and also produce reasonably accurate values for the various quantities of interest.Comment: 12 pages, 9 figures. Minor modifications as suggested by refere