Using chaotic interrogation and attractor nonlinear cross-prediction error to detect fastener preload loss in an aluminum frame

Structural health monitoring is an important field concerned with assessing the current state (or "health") of a structural system or component with regard to its ability to perform its intended function appropriately. One approach to this problem is identifying appropriate features obtained from time series vibration responses of the structure that change as structural degradation occurs. In this work, we present a novel technique adapted from the nonlinear time series prediction community whereby the structure is excited by an applied chaotic waveform, and predictive maps built between structural response attractors are used as the feature space. The structural response is measured at several points on the structure, and pairs of attractors are used to predict each other. As the dynamics of the structure change due to damage, the prediction error rises. This approach is applied to detecting the preload loss in a bolted joint in an aluminum frame structure.     

Multi-affinity and multi-fractality in systems of chaotic elements with long-wave forcing

Multi-scaling properties in quasi-continuous arrays of chaotic maps driven by long-wave random force are studied. The spatial pattern of the amplitude X(x,t) is characterized by multi-affinity, while the field defined by its coarse-grained spatial derivative exhibits multi-fractality. The strong behavioral similarity of the X- and Y-fields respectively to the velocity and energy dissipation fields in fully-developed fluid turbulence is remarkable, still our system is unique in that the scaling exponents are parameter-dependent and exhibit nontrivial q-phase transitions. A theory based on a random multiplicative process is developed to explain the multi-affinity of the X-field, and some attempts are made towards the understanding of the multi-fractality of the Y-field. Received 16 November 1998     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

Using atom interferometry to detect dark energy

We review the tantalising prospect that the first evidence for the dark energy driving the observed acceleration of the universe on giga-parsec scales may be found through metre scale laboratory-based atom interferometry experiments. To do that, we first introduce the idea that scalar fields could be responsible for dark energy and show that in order to be compatible with fifth force constraints, these fields must have a screening mechanism which hides their effects from us within the solar system. Particular emphasis is placed on one such screening mechanism known as the chameleon effect where the field’s mass becomes dependent on the environment. The way the field behaves in the presence of a spherical source is determined and we then go on to show how in the presence of the kind of high vacuum associated with atom interferometry experiments, and when the test particle is an atom, it is possible to use the associated interference pattern to place constraints on the acceleration due to the fifth force of the chameleon field – this has already been used to rule out large regions of the chameleon parameter space and maybe one day will be able to detect the force due to the dark energy field in the laboratory.     

Clustering of arrays of chaotic chemical oscillators by feedback and forcing

Feedback and external forcing are applied to an array of chaotic electrochemical oscillators through variations in the applied potential. We see transitions from intermittent clusters to stable chaotic clusters to stable periodic clusters to synchronized states as the feedback gain and forcing amplitude, respectively, are varied. With forcing up to four clusters are observed in stable states. The transition to synchronization with feedback occurs by the increase in the size of one cluster at the expense of the others.     

Using the modified sample entropy to detect determinism

A modified sample entropy (mSampEn), based on the nonlinear continuous and convex function, has been proposed and proven to be superior to the standard sample entropy (SampEn) in several aspects. In this Letter, we empirically investigate the ability of the mSampEn statistic combined with surrogate data method to detect determinism. The effects of the datasets length and noise on the proposed method to differentiate between deterministic and stochastic dynamics are tested on several benchmark time series. The noise performance of the mSampEn statistic is also compared with the singular value decomposition (SVD) and symplectic geometry spectrum (SGS) based methods. The results indicate that the mSampEn statistic is a robust index for detecting determinism in short and noisy time series.     

Entrainment of a spatially extended nonlinear structure under selective forcing

The response of a nonlinear state to a variable forcing periodic in space is studied in an extended dynamical system consisting of a liquid crystal layer driven to convection. Both the statics and the dynamics of the entrainment and the locking effects are analyzed. The dynamics of the evolution are controlled by topological singularities that allow a diffusion of the phase. The mechanisms involved are related to the role of the defects in systems undergoing spontaneous symmetry breakings.     

Using permutations to detect dependence between time series

In this paper, we propose an independence test between two time series which is based on permutations. The proposed test can be carried out by means of different common statistics such as Pearson’s chi-square or the likelihood ratio. We also point out why an exact test is necessary. Simulated and real data (return exchange rates between several currencies) reveal the capacity of this test to detect linear and nonlinear dependences.     

Using feature vectors to detect frog calls in wireless sensor networks

A method for detecting vocalization of giant barred frogs (Mixophyes iteratus) in noisy audio is proposed. Audio recordings from remote wireless sensor nodes were segmented into individual sounds and from each sound a small set of features was extracted. Feature vectors were compared to those of example calls using a Euclidean distance formula as a detection system. The system achieved a sensitivity of 0.85 with specificity of 0.92 when distinguishing M. iteratus calls from other species' calls and sensitivity of 0.88 with specificity 0.82 against background noise.     

A game theoretic algorithm to detect overlapping community structure in networks

Community detection can be used as an important technique for product and personalized service recommendation. A game theory based approach to detect overlapping community structure is introduced in this paper. The process of the community formation is converted into a game, when all agents (nodes) cannot improve their own utility, the game process will be terminated. The utility function is composed of a gain and a loss function and we present a new gain function in this paper. In addition, different from choosing action randomly among join, quit and switch for each agent to get new label, two new strategies for each agent to update its label are designed during the game, and the strategies are also evaluated and compared for each agent in order to find its best result. The overlapping community structure is naturally presented when the stop criterion is satisfied. The experimental results demonstrate that the proposed algorithm outperforms other similar algorithms for detecting overlapping communities in networks.     

Topological description of a chaotic attractor with spiral structure

We compute the template of a chaotic attractor with spiral structure. The template describes the topological properties of periodic orbits embedded in the attractor. It is confirmed by investigating orbits of higher period.     

Integrator-based circuit-independent chaotic oscillator structure

An integrator-based chaotic oscillator structure composed of three cascaded inverting, noninverting, and differential integrators is presented. The nonlinearity responsible for folding the trajectories is introduced by a single switching diode which is controlled by the output of the first integrator in the cascade. Chaotic behavior is verified on the functional level of the structure rendering it circuit-independent. A possible circuit realization is given and a canonical single-parameter-controlled ordinary differential equation capturing the qualitative dynamics of similar fourth-order integrator-based chaotic oscillators is proposed.     

Using white noise to enhance synchronization of coupled chaotic systems

In the paper, complete synchronization of two chaotic oscillators via unidirectional coupling determined by white noise distribution is investigated. It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling. The established theoretical result supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators. Furthermore, numerical examples are provided to illustrate some possible applications of the theoretical result.     

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Planck's over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Planck's over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker's map, for which the probability density in position space is observed to have self-similarity properties.     

Subharmonic and chaotic bifurcation structure in optical bistability

We provide a global view of optical bistability in the domain described by the Ikeda finite difference equation through a study of the boundary structure for marginally stable period N solutions in the parameter space.     

Using Berry's phase to detect the Unruh effect at lower accelerations

We show that a detector acquires a Berry phase due to its motion in spacetime. The phase is different in the inertial and accelerated case as a direct consequence of the Unruh effect. We exploit this fact to design a novel method to measure the Unruh effect. Surprisingly, the effect is detectable for accelerations 10(9) times smaller than previous proposals sustained only for times of nanoseconds.     

Laser induced damage threshold derived from chaotic electron dynamics

The small metallic inclusions whose presence is thought to be responsible for the onset of laser induced damage of a dielectric are modeled by one-dimensional square well potentials. The known fact that this system turns chaotic in the presence of a sufficiently strong external field allows for a rather simple estimate of the damage threshold.     

Using multiple attractor chaotic systems for communication

In recent work with symmetric chaotic systems, we synchronized two such systems with one-way driving. The drive system had two possible attractors, but the response system always synchronized with the drive system. In this work, we show how we may combine two attractor chaotic systems with a multiplexing technique first developed by Tsimring and Suschick to make a simple communications system. We note that our response system is never synchronized to our drive system (not even in a generalized sense), but we are still able to transmit information. We characterize the performance of the communications system when noise is added to the transmitted signal.