Experimental Probability Density Function Research Articles

Time Delay Characterization in Wireless Sensor Networks for Distributed Measurement Applications

This paper investigates the critical aspect of synchronization in wireless sensor networks (WSNs) across diverse industrial applications. The low-cost sensor network topologies are analyzed. The communication delay measurements and quantitative jitter analysis are performed under different conditions, and dependencies of the propagation time delay on the data bitrate and modulation type for different hardware implementations of the WSNs are presented. The time delay distribution influence on the time synchronization error propagation over WSN layers was assessed from the experimental probability density functions. The network synchronization based on the controlled propagation delay jitter approach has been proposed. This research contributes quantitative insights into the complexities of synchronization in WSNs, offering a foundation for optimizing network configurations and parameters to extend the operational life of low-power sensor nodes.

Experimental investigations on an FSO-fiber converged communication system under fog and turbulence

This paper presents experimental results for a free-space optical-fiber converged (FSO-FC) communication system under varying turbulence and foggy conditions. Based on the experimental measurements, we statistically characterize the FSO channel under different levels of turbulence and fog in terms of their respective probability density functions (PDFs). Our experimental PDFs fit well with the theoretical PDFs proposed in the literature. We experimentally evaluate the average bit error rate (ABER) of the considered FSO-FC communication system under different levels of turbulence and fog. Further, to compensate for the effects of turbulence and fog, we use multimode fiber as the receiver and compare the results with single-mode fiber as the receiver. Finally, we show the improvement in ABER under varying turbulence and fog by adding cyclic redundancy check bits to data bits.

Pushing thermal conductivity to its lower limit in crystals with simple structures

Materials with low thermal conductivity usually have complex crystal structures. Herein we experimentally find that a simple crystal structure material AgTlI2 (I4/mcm) owns an extremely low thermal conductivity of 0.25 W/mK at room temperature. To understand this anomaly, we perform in-depth theoretical studies based on ab initio molecular dynamics simulations and anharmonic lattice dynamics. We find that the unique atomic arrangement and weak chemical bonding provide a permissive environment for strong oscillations of Ag atoms, leading to a considerable rattling behaviour and giant lattice anharmonicity. This feature is also verified by the experimental probability density function refinement of single-crystal diffraction. The particularly strong anharmonicity breaks down the conventional phonon gas model, giving rise to non-negligible wavelike phonon behaviours in AgTlI2 at 300 K. Intriguingly, unlike many strongly anharmonic materials where a small propagative thermal conductivity is often accompanied by a large diffusive thermal conductivity, we find an unusual coexistence of ultralow propagative and diffusive thermal conductivities in AgTlI2 based on the thermal transport unified theory. This study underscores the potential of simple crystal structures in achieving low thermal conductivity and encourages further experimental research to enrich the family of materials with ultralow thermal conductivity.

Study of convective air turbulence based on the probability distribution function of angle of arrival fluctuations

This study investigates the probability density function (PDF) of angle of arrival (AoA) fluctuations of a laser beam propagating through convective air turbulence in two settings: indoor turbulence and atmospheric surface layer. The indoor turbulence is generated by an electric heater with a 50 cm × 100 cm surface area placed horizontally on the bottom. The atmospheric turbulence experiments are conducted over a level at 60 cm height from an asphalted area using a slightly divergent laser beam that propagates along 350 m. Image motion monitoring of four sub-apertures installed in front of the receiving telescope aperture is used to record the AoA fluctuations and their PDFs over the entrance pupil at the sub-aperture locations for both types of turbulence. The observations are made in two perpendicular directions to the propagation of the laser beam. The experimental PDFs of the AoA fluctuations are fitted with Gaussian, Lognormal, Weibull, and Gamma distribution functions. The results show that the Weibull and Gamma models are more consistent with the experimental data for the indoor convective air and atmospheric turbulence respectively. For the indoor convective turbulence, the full width at half maximum and the peak location of the measured PDFs increase with the heater temperature, as well as the goodness of fit, which saturates at high temperatures.

Determination of mathematical expectations of two weighting statistics for ensemble time scales

The Bureau International des Poids et Mesures uses the ALGOS algorithm to generate the Echelle Atomique Libre. The original and new ALGOS weighting algorithms employ two different statistics to calculate the weights, resulting in different experimental phenomena. These two statistics are believed to be the keys to analyzing these experimental phenomena, because the statistical characteristics (e.g. the mathematical expectations and variances) of the statistics completely determine the statistical characteristics of the weights, and subsequently the experimental phenomena. The core work conducted in this study is to derive the analytical expressions of the mathematical expectations of these two statistics under ideal conditions and to validate them empirically. This paper provides a theoretical analysis of these expressions and discusses the relationships between them and the mathematical expectations of the Allan variances. These expressions theoretically reveal the reasons behind the experimental phenomena, especially why hydrogen masers are assigned lower weights in the original ALGOS weighting algorithm but higher weights in the new one. According to the derivation process, these analytical expressions are universally applicable and can also be applied to time-keeping laboratories. In the future, this work can be extended to determine the theoretical statistic and weight performances of different types of frequency standards quantitatively for time-keeping laboratories under both ideal and non-ideal conditions, providing a theoretical basis for improving the design of ensemble time scale algorithms. In the , a method of obtaining the experimental variances and probability density functions (PDFs) of these two statistics is additionally proposed. The two-sample Kolmogorov–Smirnov test is presented to compare the experimental and theoretical PDFs of an example.

Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

In our previous studies we have examined solar wind and magnetospheric plasma turbulence, including Markovian character on large inertial magnetohydrodynamic scales. Here we present the results of the statistical analysis of magnetic field fluctuations in the Earth’s magnetosheath, based on the Magnetospheric Multiscale mission at much smaller kinetic scales. Following our results on spectral analysis with very large slopes of about −16/3, we apply a Markov-process approach to turbulence in this kinetic regime. It is shown that the Chapman–Kolmogorov equation is satisfied and that the lowest-order Kramers–Moyal coefficients describing drift and diffusion with a power-law dependence are consistent with a generalized Ornstein–Uhlenbeck process. The solutions of the Fokker–Planck equation agree with experimental probability density functions, which exhibit a universal global scale invariance through the kinetic domain. In particular, for moderate scales we have the kappa distribution described by various peaked shapes with heavy tails, which, with large values of the kappa parameter, are reduced to the Gaussian distribution for large inertial scales. This shows that the turbulence cascade can be described by the Markov processes also on very small scales. The obtained results on kinetic scales may be useful for a better understanding of the physical mechanisms governing turbulence.

Dependence of the probability density function of laser radiation power on the scintillation index and the size of a receiver aperture.

Power scintillations of a Gaussian laser beam propagated through a 7 km long horizontal atmospheric path for a wide range of turbulence strengths and different sizes of the receiver aperture were studied experimentally. The probability density function (PDF) and its properties were analyzed for a wide range of scintillation conditions. It was shown that the PDF can be described by the fractional exponential distribution in the strong scintillation regime (scintillation index of power measured on aperture σPIB2>1) for apertures with diameter d < a, where a is the size of the isoplanatic region, and by the gamma distribution in the weak scintillation regime (σPIB2<1), as well as by the lognormal distribution for σPIB2≪1. More than one distribution can be considered as a good approximation for experimental data for some ranges of d/a and σPIB2, but the transition from one distribution to another as the best approximation occurs at certain characteristic values of these parameters. In the strong scintillation regime, the aperture averaging effect resulted in the transition from the fractional exponential distribution to the fractional gamma (FG) distribution when the aperture diameter is about the size of the isoplanatic region (d/a∼1). The FG distribution better approximates the experimental PDF because it accounts for the fact that the probability of zero power values becomes zero due to the averaging effect of the aperture. The fractional gamma distribution is the best approximation of the PDF for a finite aperture when σPIB2>σPIB,crit2=[0.7-0.8], while the gamma distribution is the best approximation for σPIB2<σPIB,crit2.

Rock slope kinematic analysis for planar failure: A probabilistic approach

The probabilistic kinematic analysis for rock slope has been conducted on one slope along USAID road in Aceh Province, Indonesia. This research aims to develop the modelled probability density function (PDF) and determine the probabilistic of planar failure occurrence (Pop). The geometry of discontinuity planes (dip and dip directions) and slope geometry (slope angle and slope face) were collected from our previous study. One slope with planar failure criteria was selected. The Monte Carlo simulations were performed in generating 100 new random values in 100 time iterations to produce modelled PDFs for the geometry of discontinuity plans based on statistical parameters of field observed data. The probabilistic of each experimental PDFs were computed to produce the probabilistic of planar failure occurrence. The result reveals that the distribution of dip and dip directions for experimental PDFs are considered Beta and Normal distributions. The statistical parameters produced in the model are almost likely similar to observed data. It means the model that was developed are reliable and conscientious. The rule ofΦ &lt; βj &lt; βsand dip directions (αj) within ±20° to slope face (αs) are utilised as the boundaries to calculate the probabilistic of planar failure occurrence (Pop) which revealing 0.26.

Hierarchical Dirichlet Process Based Gamma Mixture Modeling for Terahertz Band Wireless Communication Channels

Due to the unique channel characteristics of Terahertz (THz), comprehensive propagation channel modeling is essential to understand the spectrum and develop reliable communication systems in these bands. In this work, we propose the utilization of the hierarchical Dirichlet Process Gamma Mixture Model (DPGMM) to characterize THz channels statistically in the absence of any prior knowledge. DPGMM provides mixture component parameters and the required number of components. A revised expectation-maximization (EM) algorithm is also proposed as a pre-step for DPGMM. Kullback-Leibler Divergence (KL-divergence) is utilized as an error metric to examine the amount of inaccuracy of the EM algorithm and DPGMM when modeling the experimental probability density functions (PDFs). DPGMM and EM algorithm are implemented over the measurements taken at frequencies between 240 GHz and 300 GHz. By comparing the results of the DPGMM and EM algorithms for the measurement datasets, we demonstrate how well the DPGMM fits the target distribution. It is shown that the proposed DPGMM can accurately describe the various THz channels as well as the EM algorithm, and its flexibility allows it to represent more complex distributions better than the EM algorithm. We also demonstrated that DPGMM can be used to model any wireless channel due to its versatility.

Experimental study on spray characteristics of pressure-swirl nozzle in China advanced PWR containment

Pressurized Water Reactor (PWR) is the most mature technology for nuclear power plants and nuclear power devices. Spray systems play an essential role in the safety of a PWR. The spray characteristics of the nozzle are of crucial importance for the performance of the spray system. In the present study, a test loop with four rotatable branches was established to obtain spray characteristics data, including flow characteristic, spray cone angle (SCA), spray flux distribution and droplet size spectrum. The effect of inclined angles was taken into consideration when designing and conducting the experiment. A specific type of pressure-swirl nozzle used in China advanced PWR was employed for the study. According to experimental data, variations of pressure drop and the spray angles versus volume flow rate were obtained, and typical curves of spray flux distribution were plotted, and the change in the flux distribution was evident with the change in inclined angle. The flux distribution results were used to build 3D spray flux distribution models together with the spray cone angles tested. The droplet size spectrum was measured by laser diffraction analysis. Typical droplet size distributions were obtained by the relevant software, and the experimental Probability Density Function (PDF) of droplet size was derived and compared with several empirical distributions.

Aggregation of GPS, WLAN, and BLE Localization Measurements for Mobile Devices in Simulated Environments.

There are multiple available technologies to find the location of a mobile device, such as the Global Positioning System (GPS), Bluetooth Low-Energy beacons (BLE), and Wireless LAN (WLAN) localization. We propose a novel method to estimate the location of a moving device by aggregating information from multiple positioning systems into a single, more precise location estimation. The aggregated location is calculated as the place in which the product of the probability density functions (PDF) of individual methods has the maximum value. The experimental probability density functions of the three analyzed technologies are fitted by gamma distributions based on error histograms found in the literature and measurement data. The location measurements of the individual technologies are provided at different time instants, so the weighted product of the PDFs is used to improve aggregation accuracy. The discrete event-simulation model was used to evaluate the aggregation method with the Gauss–Markov mobility model. Simulations demonstrated that the calculated aggregated location was more accurate than any of the methods taken as the input, and average error was decreased by almost 13% compared to an arithmetic mean of the three considered localization methods, and by more than 36% compared to the single method with the highest accuracy.

Inverse Gaussian gamma distribution model for turbulence-induced fading in free-space optical communication

We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.

Examples of measurement uncertainty evaluations in accordance with the revised GUM

The paper presents examples of the evaluation of uncertainty components in accordance with the current and revised Guide to the expression of uncertainty in measurement (GUM). In accordance with the proposed revision of the GUM a Bayesian approach was conducted for both type A and type B evaluations.The law of propagation of uncertainty (LPU) and the law of propagation of distribution applied through the Monte Carlo method, (MCM) were used to evaluate associated standard uncertainties, expanded uncertainties and coverage intervals. Furthermore, the influence of the non-Gaussian dominant input quantity and asymmetric distribution of the output quantity y on the evaluation of measurement uncertainty was analyzed. In the case when the probabilistically coverage interval is not symmetric, the coverage interval for the probability P is estimated from the experimental probability density function using the Monte Carlo method. Key highlights of the proposed revision of the GUM were analyzed through a set of examples.

Experimental Study on Atomizing and Reaction Performance of Pressure Swirl Nozzles in Ethoxylation Reactor

Abstract Spray Tower Loop Reactors is one of the most advanced ethoxylation reactors in the world. The special pressure swirl nozzles are the core component and important for production efficiency and product quality. A test rig was established, which was divided into four parts: spray system, laser measurement system, photographic system and flux distribution test system. An experimental study on the atomizing performances was conducted, including discharge coefficient, spray cone angle, spray flux distribution, Sauter mean droplets size and droplets size distribution. According to the measurement data, the correlation of volume flow rate, discharge coefficient, spray cone angle and Sauter mean droplets size versus pressure drop were respectively gained. The spray flow distributions of all measured nozzles are classified as a unimodal、bimodal and trimodal distribution due to the different structure. And the experimental Probability Density Function (PDF) of the droplets size was gained by a split-type spray laser droplets size analyzer and compared with five empirical distributions. The log-hyperbolic distribution has a most agreement with the measured PDF. At same time, reaction performance of the special nozzles was measured in the industrial STLR ethoxylation reactor. It is indicated that Sauter mean diameter determines the number of EO and the width of droplets size distribution determines the width of the molecular weight distributions. The present paper exhibits the measurement way and outcomes of spray characteristics of the nozzles in ethoxylation reaction and it is instructive for the optimization design of SPLT ethoxylation reaction.

Statistics of the optical intensity of a chaotic external-cavity DFB laser

We study experimentally and theoretically the first- and second-order statistics of the optical intensity of a chaotic external-cavity semiconductor DFB laser in fully developed coherence-collapse. The second-order statistic is characterized by the autocorrelation, where we achieve consistent experimental and theoretical results over the entire parameter range considered. For the first-order statistic, we find that the experimental probability-density function is significantly more concentrated around the mean optical power and robust to parameter changes than theory predicts.

Time Dependent Classification of Solar Radiation Sequences Using Best Information Criterion

Large and frequent variations of solar radiation can be observed in tropical climates with amplitudes reaching 800W/m2 and occurring within a short time interval, from few seconds to few minutes, according to the geographical location. Such fluctuations can be due for example to the dynamic of clouds which can be very complex and depend on cloud type, size, speed and spatial distribution and, more generally, due to some specific local meteorological conditions.In this work, we have led a statistical and dynamical analysis of time dependent global solar radiation sequences in Guadeloupe (F.W.I.) located in the East part of the lesser Antilles. It's the first land to receive the transported clouds by the trade winds, there is also cloud generation by convection process. This process is strongly time dependent. Consequently there is direct relation between this process and fluctuations on ground measured solar radiation signals. In this analysis we have used solar radiation data measured at 1 hz. We have classified time conditioned probability density functions (pdf) the clearness index kt. to ensure that the experimental probability density function (pdf) is well defined we have use the best information criterion to find the appropriate number of bins for each pdf. This classification allowed to identify different regimes of solar radiation at specific hours of the day.

EMG AMPLITUDE ESTIMATORS BASED ON PROBABILITY DISTRIBUTION FOR MUSCLE–COMPUTER INTERFACE

To develop an advanced muscle–computer interface (MCI) based on surface electromyography (EMG) signal, the amplitude estimations of muscle activities, i.e., root mean square (RMS) and mean absolute value (MAV) are widely used as a convenient and accurate input for a recognition system. Their classification performance is comparable to advanced and high computational time-scale methods, i.e., the wavelet transform. However, the signal-to-noise-ratio (SNR) performance of RMS and MAV depends on a probability density function (PDF) of EMG signals, i.e., Gaussian or Laplacian. The PDF of upper-limb motions associated with EMG signals is still not clear, especially for dynamic muscle contraction. In this paper, the EMG PDF is investigated based on surface EMG recorded during finger, hand, wrist and forearm motions. The results show that on average the experimental EMG PDF is closer to a Laplacian density, particularly for male subject and flexor muscle. For the amplitude estimation, MAV has a higher SNR, defined as the mean feature divided by its fluctuation, than RMS. Due to a same discrimination of RMS and MAV in feature space, MAV is recommended to be used as a suitable EMG amplitude estimator for EMG-based MCIs.

Experimental study on spray characteristics of pressure-swirl nozzles in pressurizer

Spraying system in the pressurizer of Pressurized Water Reactor (PWR) power plant system is of great importance for system pressure control. An experimental study on the spray characteristics, including mass flow rate, spray flux distribution, spray cone angle and drop size spectrum, was conducted. A testing loop with nine swirling nozzles was established for the study. In order to measure the spray cone angle and drop size spectrum, two original devices including a spray droplet collector and a photographic chamber were designed and employed. The former was used to collect the spray droplet along the cross-section diameter, and the latter was made to isolate and measure the targeted spray droplet. Based on the experimental data, the curves of flow rate and spray cone angle versus nozzle pressure drop were obtained. Several typical spray flux distributions were derived and the results indicated that the flux distribution changes significantly with even small pressure changes. Thus, it was proposed that instability of the spray flux distribution should be considered in the pressurizer. Based on the spray drop pictures recorded by the high speed camera, Probability Density Function (PDF) of the drop size was obtained and compared with four ‘standard’ empirical distributions. It was found that the Nukiyama–Tanasawa distribution provides a better fit to the experimental PDF of the spray drop size. The present work introduces the experimental methodology and results of spray behaviour of the nozzle in pressurizer. The work is expected to be helpful for the optimization design of spraying systems.

Resolvability of Isotropic Component in Regional Seismic Moment Tensor Inversion

We propose a new approach to resolve the isotropic component of the seismic moment tensor and its uncertainty. In linearized inversion problems, where the earthquake or explosive-source location and origin time are fixed (e.g., assumed to be known), the uncertainty of the moment tensor can be studied through the eigenvalues and the eigenvectors of the design matrix, which allows the representation of the theo- retical misfit by means of a 6D error ellipsoid. Because the design matrix depends only on the structural model and receiver source geometry, the analysis can be performed using recorded seismic waveforms, or without. In the nonlinear inversion problems, where the free parameters are eight (e.g., the six elements of the moment tensor, depth, and origin time), we propose a waveform-inversion scheme in which the trace of the moment tensor varies systematically and the remaining seven free parameters are opti- mized for each specific value of the trace. In this way, a 1D experimental probability density function of the moment tensor trace is constructed. To demonstrate the appli- cability of the method, we apply it to two shallow earthquakes (Mw 4.9 and 4.7) with epicenters close to the Columbo volcano, located 20 km northeast of the island of Santorini, Aegean Sea, Greece. We use 15 near-regional (60-310 km) records at frequencies below 0.1 Hz and two alternative crustal models. We conclude that the main uncertaintiesare attributed to the crustal modeland tothe trade-off betweenthe isotropic component and the source depth.

How gravity and size affect the acceleration statistics of bubbles in turbulence

We report the results of the first systematic Lagrangian experimental investigation in a previously unexplored regime of very light (air bubbles in water) and large (D/η ≫ 1) particles in turbulence. Using a traversing camera setup and particle tracking, we study the Lagrangian acceleration statistics of ∼3 mm diameter (D) bubbles in a water tunnel with nearly homogeneous and isotropic turbulence generated by an active grid. The Reynolds number (Reλ) is varied from 145 to 230, resulting in size ratios, D/η, in the range of 7.3–12.5, where η is the Kolmogorov length scale. The experiments reveal that gravity increases the acceleration variance and reduces the intermittency of the probability density function (PDF) in the vertical direction. Once the gravity offset has been subtracted, the variances of both the horizontal and vertical acceleration components are about 5 ± 2 times larger than those measured in the same flow for fluid tracers. Moreover, for these light particles, the experimental acceleration PDF shows a substantial reduction of intermittency at growing size ratios, in contrast with neutrally buoyant or heavy particles. All these results closely match numerical simulations of finite-sized bubbles with the Faxén corrections.