A statistical strategy to select optimal structural health monitoring data in operational modal analysis

Operational modal analysis (OMA) is prevalent in modal identifi cation of civil structures. It asks for response measurements of the underlying structure under ambient loads. A valid OMA method requires the excitation be white noise in time and space. Although there are numerous applications of OMA in the literature, few have investigated the statistical distribution of a measurement and the infl uence of such randomness to modal identifi cation. This research has attempted modifi ed kurtosis to evaluate the statistical distribution of raw measurement data. In addition, a windowing strategy employing this index has been proposed to select quality datasets. In order to demonstrate how the data selection strategy works, the ambient vibration measurements of a laboratory bridge model and a real cable-stayed bridge have been respectively considered. The analysis incorporated with frequency domain decomposition (FDD) as the target OMA approach for modal identifi cation. The modal identifi cation results using the data segments with different randomness have been compared. The discrepancy in FDD spectra of the results indicates that, in order to fulfi l the assumption of an OMA method, special care shall be taken in processing a long vibration measurement data. The proposed data selection strategy is easy-to-apply and verifi ed effective in modal analysis.

Differential entrainment of neuroelectric delta oscillations in developmental dyslexia

Oscillatory entrainment to the speech signal is important for language processing, but has not yet been studied in developmental disorders of language. Developmental dyslexia, a difficulty in acquiring efficient reading skills linked to difficulties with phonology (the sound structure of language), has been associated with behavioural entrainment deficits. It has been proposed that the phonological ‘deficit’ that characterises dyslexia across languages is related to impaired auditory entrainment to speech at lower frequencies via neuroelectric oscillations (<10 Hz, ‘temporal sampling theory’). Impaired entrainment to temporal modulations at lower frequencies would affect the recovery of the prosodic and syllabic structure of speech. Here we investigated event-related oscillatory EEG activity and contingent negative variation (CNV) to auditory rhythmic tone streams delivered at frequencies within the delta band (2 Hz, 1.5 Hz), relevant to sampling stressed syllables in speech. Given prior behavioural entrainment findings at these rates, we predicted functionally atypical entrainment of delta oscillations in dyslexia. Participants performed a rhythmic expectancy task, detecting occasional white noise targets interspersed with tones occurring regularly at rates of 2 Hz or 1.5 Hz. Both groups showed significant entrainment of delta oscillations to the rhythmic stimulus stream, however the strength of inter-trial delta phase coherence (ITC, ‘phase locking’) and the CNV were both significantly weaker in dyslexics, suggestive of weaker entrainment and less preparatory brain activity. Both ITC strength and CNV amplitude were significantly related to individual differences in language processing and reading. Additionally, the instantaneous phase of prestimulus delta oscillation predicted behavioural responding (response time) for control participants only.

Decision making in social neurobiological systems modeled as transitions in dynamic pattern formation

Extant models of decision making in social neurobiological systems have typically explained task dynamics as characterized by transitions between two attractors. In this paper, we model a three-attractor task exemplified in a team sport context. The model showed that an attacker–defender dyadic system can be described by the angle x between a vector connecting the participants and the try line. This variable was proposed as an order parameter of the system and could be dynamically expressed by integrating a potential function. Empirical evidence has revealed that this kind of system has three stable attractors, with a potential function of the form V(x)=−k1x+k2ax2/2−bx4/4+x6/6, where k1 and k2 are two control parameters. Random fluctuations were also observed in system behavior, modeled as white noise εt, leading to the motion equation dx/dt = −dV/dx+Q0.5εt, where Q is the noise variance. The model successfully mirrored the behavioral dynamics of agents in a social neurobiological system, exemplified by interactions of players in a team sport.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Coalescence of rigid droplets in a stirred dispersion-II. Band-limited force fluctuations

The coalescence of nearly rigid liquid droplets in a turbulent flow field is viewed as the drainage of a thin film of liquid under the action of a stochastic force representing the effect of turbulence. The force squeezing the drop pair is modelled as a correlated random function of time. The drops are assumed to coalesce once the film thickness becomes smaller than a critical thickness while they are regarded as separated if their distance of separation is larger than a prescribed distance. A semi-analytical solution is derived to determine the coalescence efficiency. The veracity of the solution procedure is established via a Monte-Carlo solution scheme. The model predicts a reversing trend of the dependence of the coalescence efficiency on the drop radii, the film liquid viscosity and the turbulence energy dissipation per unit mass, as the relative fluctuation increases. However, the dependence on physical parameters is weak (especially at high relative fluctuation) so that for the smallest droplets (which are nearly rigid) the coalescence efficiency may be treated as an empirical constant. The predictions of this model are compared with those of a white-noise force model. The results of this paper and those in Muralidhar and Ramkrishna (1986, Ind. Engng Chem. Fundam. 25, 554-56) suggest that dynamic drop deformation is the key factor that influences the coalescence efficiency.

Nondiffusive Quantum Transport in a Dynamically Disordered Medium

For a dynamically disordered continuum it is found that the exact quantum mechanical mean square displacement 〈x2(t)〉∼t3, for t→∞. A Gaussian white-noise spectrum is assumed for the random potential. The result differs qualitatively from the diffusive behavior well known for the one-band lattice Hamiltonian, and is understandable in terms of the momentum cutoff inherent in the lattice, simulating a "momentum bath."

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.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Experimental Demonstration of H{infty} Control based Active Vibration Suppression in Composite Fin-tip of Aircraft using Optimally Placed Piezoelectric Patch Actuators

The goal of this study is the multi-mode structural vibration control in the composite fin-tip of an aircraft. Structural model of the composite fin-tip with surface bonded piezoelectric actuators is developed using the finite element method. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes accurately. A model order reduction technique is employed for reducing the finite element structural matrices before developing the controller. Particle swarm based evolutionary optimization technique is used for optimal placement of piezoelectric patch actuators and accelerometer sensors to suppress vibration. H{infty} based active vibration controllers are designed directly in the discrete domain and implemented using dSpace® (DS-1005) electronic signal processing boards. Significant vibration suppression in the multiple bending modes of interest is experimentally demonstrated for sinusoidal and band limited white noise forcing functions.

On the duality between rate and power optimizations

Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.

First passage probability during random vibration

The probability that a random process crosses an arbitrary level for the first time is expressed as a Gram—Charlier series, the leading term of which is the Poisson approximation. The coefficients of this series are related to the moments of the number of level crossings. The results are applicable to both stationary and non-stationary processes. Some numerical results are presented for the response process of a linear single-degree-of-freedom oscillator under Gaussian white noise excitation.

Prediction of inplane damping from deterministic and stochastic models

This paper reviews computational reliability, computer algebra, stochastic stability and rotating frame turbulence (RFT) in the context of predicting the blade inplane mode stability, a mode which is at best weakly damped. Computational reliability can be built into routine Floquet analysis involving trim analysis and eigenanalysis, and a highly portable special purpose processor restricted to rotorcraft dynamics analysis is found to be more economical than a multipurpose processor. While the RFT effects are dominant in turbulence modeling, the finding that turbulence stabilizes the inplane mode is based on the assumption that turbulence is white noise.

Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Stochastic Analysis of Yielding System

The probability distribution of the instantaneous incremental yield of an inelastic system is characterized in terms of a conditional probability and average rate of crossing. The detailed yield statistics of a single degree-of-freedom elasto-plastic system under a Gaussian white noise are obtained for both nonstationary and stationary response. The present analysis indicates that the yield damage is sensitive to viscous damping. The spectra of mean and mean square damage rate are presented.