Measured Probability Density Research Articles

Stochastic characterisation of unstable lean hydrogen–air annular premixed flames

This study is devoted to the characterisation of lean premixed hydrogen–air laminar flames stabilised on an annular burner. The flames studied are chosen to lie close to the lean flammability limit, spanning a range of Damköhler and Reynolds numbers, and correspond to situations where instabilities arise. The experimental characterisation is achieved by examining the statistical moments of the flame hydroxyl radical (OH*) chemiluminescence and schlieren. The standard deviation and the skewness, that are needed to fully characterise the measured probability density functions, are shown to exhibit a non-monotonic behaviour with the distance from the burner surface, first increasing, then decreasing downstream the flame tip. An exponentially modified Gaussian distribution model is proposed to describe the skewed schlieren fluctuations probability density function. This model is closed by developing relations for the probability density function parameters based on the Damköhler and Reynolds numbers, and then used to describe the OH* stochastic behaviour. The relation between the distribution parameters and the transport equation of a reactive scalar gradient is addressed also.

Statistical laws of stick-slip friction at mesoscale

Friction between two rough solid surfaces often involves local stick-slip events occurring at different locations of the contact interface. If the apparent contact area is large, multiple local slips may take place simultaneously and the total frictional force is a sum of the pinning forces imposed by many asperities on the interface. Here, we report a systematic study of stick-slip friction over a mesoscale contact area using a hanging-beam lateral atomic-force-microscope, which is capable of resolving frictional force fluctuations generated by individual slip events and measuring their statistical properties at the single-slip resolution. The measured probability density functions (PDFs) of the slip length δxs, the maximal force Fc needed to trigger the local slips, and the local force gradient {k}^{{prime} } of the asperity-induced pinning force field provide a comprehensive statistical description of stick-slip friction that is often associated with the avalanche dynamics at a critical state. In particular, the measured PDF of δxs obeys a power law distribution and the power-law exponent is explained by a new theoretical model for the under-damped spring-block motion under a Brownian-correlated pinning force field. This model provides a long-sought physical mechanism for the avalanche dynamics in stick-slip friction at mesoscale.

Scanning near-field optical spectroscopy and carrier transport based analysis in mesoscopic regions for two-dimensional semiconductors

The measurements of photoexcited transport in mesoscopic regimes reveal the states and properties of mesoscopic systems. In this study, we focused on direct measurements of electromagnetic energy transports in the mesoscopic regions and constructed a scanning tunnelling microscope-assisted multi-probe scanning near-field optical microscope spectroscopy system. After producing an emission energy map through a single-probe measurement, two-probe measurement enables us to observe and analyse carrier transport characteristics. It suggests that exciton generation and transport in the mesoscopic region of semiconductors with quantum structure changes, such as the bias of dopant, affect the excited carrier emission recombination process. The measured probability density of the carrier transported with quantum effects can be used for applications in natural intelligence research by combining it with the analysis using tournament structures. Our developed measurement and analysis methods are expected to clarify the details of carrier's behaviour in the mesoscopic region in various materials and lead to applications for novel optoelectronic devices.

K-Means algorithm-based detection for wavelength division multiplexed OOK PD-NOMA system over turbulent optical channel

We have experimentally demonstrated the efficacy of k-means algorithm-based detection scheme in a two-user-based wavelength division multiplexed (WDM) on-off keying (OOK) power-division non-orthogonal multiple access (PD-NOMA) system over turbulent free-space optical (FSO) channels. The proposed system utilizes both power and wavelength division multiplexing to enhance the capacity of the transmission system. The proposed system also incorporates successive interference cancellation technique that utilizes unsupervised machine learning technique, which is K-means clustering, to detect the signal. Two different weak turbulence conditions in the free-space optical channels have been realized in the laboratory environment having link lengths of 2.2 m (near user) and 3.2 m (far user). The results show that the measured probability density function of intensity fluctuation closely matches the log-normal distribution. The experimental results also show that the K-means-based detection provides the BER, which is well below the Pre-FEC limit. The maximum power penalty for the near (far) user is found to be 3.1 dB (4.2 dB) at a BER of 10 − 3 for weak turbulence conditions. The proposed and implemented k-means-based detection scheme for the WDM-OOK PD-NOMA system can also be used for FSO communication systems.

Analysis of rain fade characteristics from experimental satellite measurements at Ka/Q bands for a temperate location Vigo, Spain

Rain is one of the most dominant factors for satellite communication systems link performance at frequencies above 10 GHz, increasing rapidly at higher frequencies. The prediction of time dynamics of the rain attenuation is required to improve the efficiency of various fade mitigation techniques (FMTs) to reduce signal fading. Fade duration and fade slope statistics are used to describe the dynamic behavior of attenuation experienced by radio communication links. The present study is based on experimental measurements from a Ka band (KaSAT) and Q band (AlphaSAT) beacon receiver at the frequencies 19. 7 GHz and 39. 4 GHz respectively. In this paper, annual and monthly variation of rain attenuation statistics for a temperate location Vigo, Spain is presented. Monthly variation of rain attenuation statistics is much larger than the yearly variation for the present location. This paper also analyzes the fade duration and fade slope statistics for both the bands. The conditional probability density function (PDF) of fade slope shows general symmetry between positive and negative slope values for both Ka and Q bands. All the measured statistics (1st order and 2nd order) are compared with the existing ITU-R and COST-205 models. Predictions of rain attenuation by both the models are close to the measured data. For fade duration statistics, as attenuation threshold increases, performance of both ITU-R and COST-205 models improves for Ka band. For Q band, COST model performs better compared to ITU-R model. Measured probability density function of fade slope fits with the ITU-R model more closely for Q band compared to Ka band.

Reliability Assessment Method of Complex Electronic Equipment with Multivariate Competing Failure

This paper presents a generalized reliability assessment model for complex electronic equipment with multivariate competing failure. The key of multivariate competing failure model is separated into two parts, multi-degradation measure probability density function (MDM-PDF) and traumatic failure reliability function (TFRF) related to degradation level. Principal component analysis is used to solve the calculation problem of MDM-PDF; Logistic function and least square method are introduced to solve the problem of TFRF. Finally, a case study of sine-wave oscillation circuit is given to validate the effectiveness of the model.

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder.

Mechanical unfolding of single polyubiquitin molecules subjected to a constant stretching force showed nonexponentiality in the measured probability density of unfolding (waiting time distribution) and the survival probability of the folded state during the course of the measurements. These observations explored the relevance of disorder present in the system under study with implications for a static disorder approach to rationalize the experimental results. Here, an approach for dynamic disorder is presented based on Zwanzig’s fluctuating bottleneck (FB) model, in which the rate of the reaction is controlled by the passage through the cross-sectional area of the bottleneck. The radius of the latter undergoes stochastic fluctuations that in turn is described in terms of the end-to-end distance fluctuations of the Rouse-like dynamics using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our results are comprised of analytical expressions for the survival probability and waiting time distribution, which show excellent agreement with the experimental data throughout the range of the applied forces. In addition, by fitting the survival probabilities at different stretching forces, we quantify two system parameters, namely, the average free energy ΔGav and the average distance to the transition state Δxav, both perfectly recovered the experimental estimates. These agreements validate the present model of polymer dynamics, which captures the very essence of dynamic disorder in single-molecule pulling experiments.

On the electrical conductivity of composites with a polymeric matrix and a non-uniform concentration of carbon nanotubes

We present a multiscale modelling approach to explore the effects of a non-uniform concentration of carbon nanotubes (CNTs) on the electrical conductivity of CNT-polymer composites. Realistic three-dimensional representative volume elements (RVEs) are generated from a two-dimensional CNT concentration map, obtained via microscopy techniques. The RVEs capture the measured probability density function of the CNT concentration and include a length-scale to represent the details of the spatial distribution of the concentration. The homogenized conductivity of the RVEs is computed via multiscale FE analyses for different values of such length-scale, and it is compared to measurements. The modelling strategy is then used to explore the effects of the microstructural features of these materials on their electrical conductivity.

Statistics of Colloidal Suspensions Stirred by Microswimmers.

We present a statistical analysis of the experimental trajectories of colloids in a dilute suspension of the green algae Chlamydomonas reinhardtii. The measured probability density function (pdf) of the displacements of colloids covers 7 orders of magnitude. The pdfs are characterized by non-Gaussian tails for intermediate time intervals, but nevertheless they collapse when scaled with their standard deviation. This diffusive scaling breaks down for longer time intervals and the pdf becomes Gaussian. However, the mean squared displacements of tracer positions are linear over the complete measurement time interval. Experiments are performed for various tracer diameters, swimmer concentrations, and mean swimmer velocities. This allows a rigorous comparison with several theoretical models. We can exclude a description based on an effective temperature and other mean field approaches that describe the irregular motion as a sum of the fluctuating far field of many microswimmers. The data are best described by the microscopic model by J.-L. Thiffeault, Distribution of particle displacements due to swimming microorganisms, Phys. Rev. E 92, 023023 (2015)PRESCM1539-375510.1103/PhysRevE.92.023023.

Fault detection for non-Gaussian stochastic distribution fuzzy systems by an event-triggered mechanism

This paper studies an event-triggered fault detection (FD) problem for non-Gaussian stochastic distribution fuzzy systems. Different from other systems, the available information of the stochastic distribution systems is the measurable output probability density functions (PDFs) rather than the output itself. This increases the difficulty of the event-triggered-based observer synthesis. To overcome the difficulty, a new event-triggered observer approach based on the information of the output PDFs is proposed. First, a B-spline model is employed to approximate the output PDFs. Second, a novel event-triggered scheme (ETS) is designed to save the limited communication source. Then, a finite-frequency H_∕L∞ fault detection observer is constructed such that the effect of the PDFs approximation error on the residual signal can be attenuated and the FD performance can be increased. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.

Compressive Sensing Based Device-Free Multi-Target Localization Using Quantized Measurement

Device-free localization (DFL), requiring no extra devices equipped with a target, is an important field of research on the Internet of Thing (IoT). Energy efficiency issue is essential for the development of the IoT, but seldom of the existing papers are focus on it. So we investigate this issue with quantized data of only several bits under the compressive sensing (CS) framework, which can both reduce the required wireless link number and the bit number in the DFL scheme. First, through exploiting the discrete property of CS theory, we calculate the discrete measurement probability bypass computing the complex or uncalculated measurement probability density function (pdf), which can well represent the measurement distribution characteristic. Second, we design a unique quantization scheme for each wireless link according to their measurement probability and build a novel DFL model by analyzing the quantization error. Third, a new DF-QVBI algorithm is proposed to recover the target location, which can make great use of the quantization error. Finally, numerical simulations show the superiority and robustness of the proposed method.

Probabilistic analytical modelling of predator-prey interactions in fishes.

Predation is a fundamental interaction between species, yet it is largely unclear what tactics are successful for the survival or capture of prey. One challenge in this area comes with how to test theoretical ideas about strategy with experimental measurements of features such as speed, flush distance and escape angles. Tactics may be articulated with an analytical model that predicts the motion of predator or prey as they interact. However, it may be difficult to recognize how the predictions of such models relate to behavioural measurements that are inherently variable. Here, we present an alternative approach for modelling predator-prey interactions that uses deterministic dynamics, yet incorporates experimental kinematic measurements of natural variation to predict the outcome of biological events. This technique, called probabilistic analytical modelling (PAM), is illustrated by the interactions between predator and prey fish in two case studies that draw on recent experiments. In the first case, we use PAM to model the tactics of predatory bluefish ( Pomatomus saltatrix) as they prey upon smaller fish ( Fundulus heteroclitus). We find that bluefish perform deviated pure pursuit with a variable pursuit angle that is suboptimal for the time to capture. In the second case, we model the escape tactics of zebrafish larvae ( Danio rerio) when approached by adult predators of the same species. Our model successfully predicts the measured patterns of survivorship using measured probability density functions as parameters. As these results demonstrate, PAM is a data-driven modelling approach that can be predictive, offers analytical transparency, and does not require numerical simulations of system dynamics. Though predator-prey interactions demonstrate the use of this technique, PAM is not limited to studying biological systems and has broad utility that may be applied towards understanding a wide variety of natural and engineered dynamical systems where data-driven modelling is beneficial.

Five kHz thermometry in turbulent spray flames using chirped-probe-pulse femtosecond CARS, part II: Structure of reaction zones

Temperature was measured in turbulent spray flames of ethanol and acetone stabilized on the piloted Sydney Needle Spray Burner (SYNSBURNTM) using single-laser-shot, chirped-probe-pulse femtosecond coherent anti-Stokes Raman spectroscopy (CPP-fs-CARS) with a repetition rate of 5 kHz. The burner features air-blast atomization of liquid injected from a needle that can be translated by a length Lr within a co-flowing air stream so that piloted spray flames ranging from dilute to dense can be studied. Part I of these investigations has reported on the CPP-fs-CARS technique and extensive details of data processing methodology. Part II is concerned with the structure of the reaction zones at different spray loadings and for different departures from blow-off. While not performed simultaneously, measurements of the size distribution of liquid fragments are also reported and discussed in conjunction with the measured temperature. Measured probability density functions of temperature show that for flames with the same liquid loading but different recess lengths, Lr, the near-field spray structure that forms upstream of x/D = 10 affects flame structure and stability further downstream. As the spray exiting the burner becomes denser, with a higher proportion of ligaments and ‘irregular’ shaped objects, the entrainment of hot pilot gases into the spray envelope is affected, hence changing the rates of vaporization and subsequent combustion. The reported results will also form a useful platform for validating sub-models of atomization and combustion in turbulent, dilute to dense spray flames.

On-line prognosis of fatigue crack propagation based on Gaussian weight-mixture proposal particle filter

Accurate on-line prognosis of fatigue crack propagation is of great meaning for prognostics and health management (PHM) technologies to ensure structural integrity, which is a challenging task because of uncertainties which arise from sources such as intrinsic material properties, loading, and environmental factors. The particle filter algorithm has been proved to be a powerful tool to deal with prognostic problems those are affected by uncertainties. However, most studies adopted the basic particle filter algorithm, which uses the transition probability density function as the importance density and may suffer from serious particle degeneracy problem. This paper proposes an on-line fatigue crack propagation prognosis method based on a novel Gaussian weight-mixture proposal particle filter and the active guided wave based on-line crack monitoring. Based on the on-line crack measurement, the mixture of the measurement probability density function and the transition probability density function is proposed to be the importance density. In addition, an on-line dynamic update procedure is proposed to adjust the parameter of the state equation. The proposed method is verified on the fatigue test of attachment lugs which are a kind of important joint components in aircraft structures.

An information based feedback control for audio-motor binaural localization

In static scenarios, binaural sound localization is fundamentally limited by front-back ambiguity and distance non-observability. Over the past few years, “active” schemes have been shown to overcome these shortcomings, by combining spatial binaural cues with the motor commands of the sensor. In this context, given a Gaussian prior on the relative position to a source, this paper determines an admissible motion of a binaural head which leads, on average, to the one-step-ahead most informative audio-motor localization. To this aim, a constrained optimization problem is set up, which consists in maximizing the entropy of the next predicted measurement probability density function over a cylindric admissible set. The method is appraised through geometrical arguments, and validated in simulations and on real-life robotic experiments.

Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms.

The invariant measure and stationary probability density computing model based analysis of the governor system

In this paper, the stochastic stability and bifurcation of a stochastic differential equation modeling a hexagonal governor system are investigated. More precisely, we introduced the stochasticity into the model based on the parameter perturbation, and simplified the stochastic hexagonal governor system by using the stochastic center manifold theory and stochastic average theory. Besides, we investigated the local stochastic stability and global stochastic stability of the stochastic hexagonal governor system through the use of the Lyapunov exponent and singular boundary theory. And based on the invariant measure and stationary probability density, we studied the stochastic bifurcation of the stochastic hexagonal governor system. Finally, we obtained some new criteria to ensure the stochastic pitchfork bifurcation and P-bifurcation of the stochastic hexagonal governor system.

Mixture Proposal Particle Filtering for Guided Wave Based Fatigue Crack Propagation Prognosis

For on-line prognosis of fatigue crack propagation with guided wave based structural health morning, uncertainties always exist in the process of fatigue crack propagation and crack monitoring. The particle filtering is demonstrated as a powerful tool to deal with these uncertainties. However, most literatures adopt the standard sequential importance sampling resampling algorithm, which uses the transition probability density function as the importance density and neglects current measurement information. Satisfactory results may be unable to be achieved if particles are drawn from an inferior transition probability density. This paper proposes a kind of mixture proposal distribution as the importance density that linearly combines the measurement probability density with the transition probability density. In addition, the damage index of the on-line monitored guided wave signal is adopted for quantifying the crack length. Each time a new damage index is available, the mixture proposal particle filtering is adopted to evaluate the posterior probability density estimate of the crack length, as well as the crack propagation prognosis. Simulated crack propagation data is used for validation, and the result shows that the mixture proposal particle filtering outperforms the standard particle filtering algorithm.

Micromixing model performance for nonreacting flows using a consistent Monte Carlo method

ABSTRACTIn this paper, several micromixing models are applied to the prediction of turbulent nonreacting flows. All micromixing models predict the mean mixture fraction and root mean squared (RMS) mixture fraction well. For higher mixture fraction moments, there is a tendency to overpredict the skewness and kurtosis field. The exception to this is a modification to the Langevin model which produces predictions more consistent with the measured fields. Where intermittency effects do not dominate the flow, the modified Curl model and the limited Langevin model can accurately predict the measured probability density function. Of the micromixing models tested for nonhomogeneous flows, the modified Curl model represents an appropriate balance between predictive capabilities, ease of implementation, and short run times for simulating nonreacting flows.

Nanomechanical fluctuations of microcantilever under turbulent mixing

Here, we describe the motion of a microcantilever under water, being stirred by a rotating stir bar. Specifically, the thermomechanical fluctuations of the microcantilever are monitored as a function of the rotation frequency of the stir bar and compared with those under stationary water and in air. While the measured probability density functions both in air and stationary water show well-defined Gaussian distributions in displacement, with increasing rotation frequency of the stir bar, we note the growing tail of the probability density function as well as high level of the noise power spectral density, which can be attributed to the turbulent fluctuation within the water, caused by the motion of the stir bar. The work presented demonstrates the cantilever-based mechanical probing of the fluid motion.