Uniform Probability Density Function Research Articles

How to Compute the Information Content of 3-FR, 3-DP Decoupled Designs with Uniform Probability Density Functions for Their FRs

The computation of the information content of decoupled designs implies the use of conditional probability, because the existing design parameters must be adjusted in a certain order, as to fulfil all the existing functional requirements at the first trial. Nevertheless, the computation of the information content is hard to perform when the system range of the functional requirements is denoted by probability density functions. In their works, Suh and Park proposed a graphical method to compute the information content of 2-FR, 2-DP decoupled designs when the probability density functions of the FRs are uniform. This paper introduces an extension to the Suh and Park's previous findings. It presents a method that uses analytical and descriptive geometry techniques to compute the information content of 3-FR, 3-DP decoupled designs with uniform probability density distributions of their FRs, and an illustrative example is presented as well.

Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability‐based design (SRBD)

SummaryThe paper deals with the seismic reliability of elastic structural systems equipped with friction pendulum isolators (friction pendulum system). The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the friction pendulum system device behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. With reference to medium soil condition, the uncertainty in the seismic inputs is taken into account by considering a set of artificial records, obtained through Monte Carlo simulations within the power spectral density method, with different frequency contents and characteristics depending on the soil dynamic parameters and scaled to increasing intensity levels. The sliding friction coefficient at large velocity is also considered as random variable modeled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities exceeding different limit states related to both r.c. superstructure and isolation level defining the seismic fragility curves through an extensive parametric study carried out for different structural system properties.Finally, considering the seismic hazard curves related to a site near L'Aquila (Italy), the seismic reliability of the r.c. superstructure systems is evaluated, and seismic reliability‐based design abacuses are derived with the aim to define the radius in plan of the friction pendulum devices in function of the structural properties and reliability level expected. Copyright © 2016 John Wiley & Sons, Ltd.

Building ensemble representations: How the shape of preceding distractor distributions affects visual search

Perception allows us to extract information about regularities in the environment. Observers can quickly determine summary statistics of a group of objects and detect outliers. The existing body of research has, however, not revealed how such ensemble representations develop over time. Moreover, the correspondence between the physical distribution of features in the external world and their potential internal representation as a probability density function (PDF) by the visual system is still unknown. Here, for the first time we demonstrate that such internal PDFs are built during visual search and show how they can be assessed with repetition and role-reversal effects. Using singleton search for an oddly oriented target line among differently oriented distractors (a priming of pop-out paradigm), we test how different properties of previously observed distractor distributions (mean, variability, and shape) influence search times. Our results indicate that observers learn properties of distractor distributions over and above mean and variance; in fact, response times also depend on the shape of the preceding distractor distribution. Response times decrease as a function of target distance from the mean of preceding Gaussian distractor distributions, and the decrease is steeper when preceding distributions have small standard deviations. When preceding distributions are uniform, however, this decrease in response times can be described by a two-piece function corresponding to the uniform distribution PDF. Moreover, following skewed distributions response times function is skewed in accordance with the skew in distributions. Indeed, internal PDFs seem to be specifically tuned to the observed feature distribution.

Computation tool for assessing the probability characteristics of the stress state of the pipeline part defected by pitting corrosion

One of the factors affecting the life-time of the main pipelines is their susceptibility to different types of corrosion. A common type of pipeline corrosion is pitting corrosion which is a form of localized corrosion – a random process occurring in a certain section of the pipeline, leading to walls thinning under the influence of the external environment. Such a change in the pipeline geometry accompanied by a significant change in the local stress–strain state leads to a large number of emergencies.This work deals with the analysis of probability characteristics of the stress–strain state arising in the areas damaged by pitting corrosion. To determine the parameters of the stress–strain state the finite element method is used. The pipe material is modeled as elastoplastic with a bilinear diagram of plasticity.Pitting corrosion is modeled as a set of randomly positioned half-spheres with the same radius subtracted from the volume of the pipe. Coordinates of pitting defects centers obey to a uniform probability density function (PDF). Using this approach we take into account the mutual influence of defects on the pipe stress–strain state.A special macro was developed to determine the parameters of the stress–strain state of the corroded pipe. It allows performing automatic calculation and processing of the data for pitting corrosion defects. Parameters of the PDF of stress concentration factor depending on the radius of the defect were determined in accordance with the results of simulation. The kernel density estimation and generalized extreme value distribution was chosen as PDF approximation on the basis of the conditions of the Fisher–Tippett–Gnedenko theorem. The change of the PDF shape was investigated for different defect radii. The coefficient of variation, mean and standard deviation of stress concentration factor as function of defect radii were studied as well as reliability function of the pipe part was obtained using the criterion of plastic deformation occurrence.

A probability density function discretization and approximation method for the dynamic load identification of stochastic structures

Aiming at structures containing random parameters with multi-peak probability density functions (PDFs) or great variable coefficients, an analytical method of probability density function discretization and approximation (PDFDA) is proposed for dynamic load identification. Dynamic loads are expressed as the functions of time and random parameters in time domain and the forward model is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions. The PDF of each random parameter is discretized into several subintervals and in each subinterval the original PDF curve is approximated via uniform distribution PDF with equal probability value. Then the joint distribution model is built and hence the equivalent deterministic equations are solved to identify unknown loads. Inverse analysis is operated separately at each variable in the joint distribution model through regularization because of noise-contaminated measured responses. In order to assess the accuracy of identified results, PDF curves and statistical properties of loads are achieved based on the specially assumed distributions of identified loads. Numerical simulations demonstrate the efficiency and superiority of the presented method.

On the uncertainty quantification of the unsteady aerodynamics of 2D free falling plates

The aim of this paper is to conduct a statistical analysis of the effects of the fillet radii on the dynamics of the falling plate using the nonintrusive spectral projection (NISP) method. The free fall of two-dimensional cards immersed in a fluid was studied using a deterministic and stochastic numerical approach. The motion is characterized by the fluid-body interaction described by coupling the Navier–Stokes and rigid body dynamic equations. The model’s predictions have been validated using both experimental and numerical data available in the literature. In the stochastic simulations, the fillet radius of the plate was considered a random variable characterized by a uniform probability density function introducing, in this way, some uncertainties in the plate’s trajectory. To take into account the uncertainties, we employed the NISP method based on polynomial chaos expansion. The analysis was focused on finding the ensemble mean trajectory and error bar for a confidence interval of 95 % for both tumbling and fluttering regimes.

Outage Minimized Joint Power and Channel Allocation in Multihop Cognitive Radio Networks: A Lifetime-Centric Approach

This paper looks for an optimal solution to address joint power and channel allocation problem in a multihop cognitive radio network (CRN). The overall goal is to minimize the end-to-end outage probability of the CRN while meeting simultaneously total transmission power and interference constraints to primary user (PU). Two different forms of interference model, with and without considering spectral distance between PU and secondary user (SU) channels, are considered where the former again uses uniform and triangular probability density functions for determining interference to PU. The problem has been solved using standard technique of solving convex optimization problem (for power allocation) and weighted bipartite matching (for channel allocation). Furthermore, the proposed solution assumes that transmitting nodes are energy constrained. Hence, network lifetime improvement is an additional design challenge. Simulation results show that the proposed scheme not only minimizes outage probability better compared to existing power allocation strategies but also results in savings of SUs power consumption, which helps to extend network lifetime significantly.

Analysis of diagnostic climate model cloud parametrizations using large‐eddy simulations

Current climate models often predict fractional cloud cover on the basis of a diagnostic probability density function (PDF) describing the subgrid‐scale variability of the total water specific humidity, qt, favouring schemes with limited complexity. Standard shapes are uniform or triangular PDFs, the widths of which are assumed to scale with the grid‐box mean qt or the grid‐box mean saturation specific humidity, qs. In this study, the qt variability is analysed from large‐eddy simulations for two stratocumulus, two shallow cumulus, and one deep convective cases. We find that, in most cases, triangles are a better approximation to the simulated PDFs than uniform distributions. In 2 of the 24 slices examined, the actual distributions were so strongly skewed that the simple symmetric shapes could not capture the PDF at all. The distribution width for either shape scales acceptably well with both the mean values of qt and qs, the former being a slightly better choice. The qt variance is underestimated by the fitted PDFs, but overestimated by the existing parametrizations. While the cloud fraction is in general relatively well diagnosed from fitted or parametrized uniform or triangular PDFs, it fails to capture cases with small partial cloudiness, and in 10–30% of the cases misdiagnoses clouds in clear skies or vice versa. The results suggest choosing a parametrization with a triangular shape, where the distribution width would scale with the grid‐box mean qt using a scaling factor of 0.076. However, this is subject to the caveat that the reference simulations examined here were partly for rather small domains and driven by idealised boundary conditions.

Pseudo‐Zernike polynomials for numerically stable PA modeling using 3G+ signals

ABSTRACTThis article presents pseudo‐Zernike polynomials for numerically stable modeling and predistortion of high power amplifiers that, along with lesser coefficient dispersion, is capable of better model stability. Due to inherent properties of proposed basis function, orthogonality property of proposed basis function is independent of any phase rotation, which finds its use in baseband polynomial modeling. Moreover, in contrast to previously proposed orthogonal polynomial models, theoretically, presented model is independent from assumptions of Gaussian or uniform probability density function of the input signal unlike previous models. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:2569–2572, 2014

Psychometric function of jittered rate pitch discrimination

The impact of jitter on rate pitch discrimination (JRPD) is still a matter of debate. Previous studies have used adaptive procedures to assess pitch discrimination abilities of jittered rate pulses (Dobie and Dillier, 1985; Chen et al., 2005) or have used jitter detection thresholds (Fearn, 2001). Previous studies were conducted in a relatively small number of subjects using either a single-electrode cochlear implant (Dobie and Dillier, 1985, n = 2) or the Nucleus multi-channel devices (Fearn, 2001, n = 3; Chen et al., 2005, n = 5). The successful application of an adaptive procedure requires a monotone psychometric function to achieve asymptotic results. The underlying psychometric function of rate jitter has not been investigated so far. In order to close this knowledge gap, the present study determines psychometric functions by measuring of JRPD with a fixed stimulus paradigm. A rather large range of temporal, Gaussian distributed jitter standard deviation 0, 1, 2, 3, 4 ms was applied to electrical pulse patterns. Since the shape of the underlying probability density function (PDF) may also effect JRPD, a uniform PDF was alternatively applied. 7 CI users (8 ears, high-level performers with open-speech perception, MED-EL Pulsar/Sonata devices, Innsbruck, Austria) served as subjects for the experiment. JRPD was assessed with a two-stage forced choice procedure. Gross results showed decreasing JRPD with increasing amounts of jitter independent of the applied jitter distribution. In conclusion, pulse rate jitter affects JRPD and therefore should be considered in current coding strategies.

A production inventory model with flexible manufacturing, random machine breakdown and stochastic repair time

Article history: Received January 26 2014 Received in Revised Format July 5 2014 Accepted July 5 2014 Available online July 12 2014 This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory. © 2014 Growing Science Ltd. All rights reserved

A Hybrid Stochastic-Deterministic Approach For Active Fault Diagnosis Using Scenario Optimization

Active fault diagnosis can improve the diagnosability of potential faults by injecting a suitable input into the system. This input can be designed using either a stochastic or a deterministic framework. The stochastic approach aims to maximize the probability of a correct diagnosis at a certain time, whereas the deterministic approach aims to guarantee diagnosis within a certain time interval. Recently, a hybrid stochastic-deterministic approach has been developed in which all uncertainties are described by uniform probability density functions (PDFs) with finite support on zonotopes. This method is able to provide a guaranteed diagnosis at a given time N, while approximately maximizing the probability of diagnosis at some earlier time M < N. In this article, the hybrid stochastic-deterministic method is extended to arbitrary PDFs using a sampling approach based on scenario optimization.

Improving tool wear and surface covering in polishing via toolpath optimization

Polishing operations are commonly carried out manually, thus inducing variability on the surface quality. The aim of this paper is to automate the polishing of free-form surfaces in order to obtain high quality surfaces. Tool wear and toolpath surface covering have a great impact on surface properties. The current work proposes therefore a toolpath which optimizes both tool wear and surface covering. This toolpath is composed of an optimized elementary pattern repeated along a 5-axis carrier trajectory. Usually, trochoid patterns are used. Non uniform wear of the tool and uneven probability density function of the surface covering are the main inconvenients of such pattern. So, this paper proposes two optimized patterns: Spade and Triangular. Both of them lead to uniform tool wear. Our paper also demonstrates that the second solution provides a uniform probability density function. All presented computations are validated experimentally.

Pulse signal detection in cognitive UWB system

According to the problem of cognitive ultra wide-band (UWB) spectrum sensing, a novel UWB pulse signal detection algorithm based on cumulative sum (CUSUM) test is proposed in this paper. Based on the analysis of the existing spectrum sensing schemes for cognitive UWB system, some obvious facts are obtained that it is difficult to detect UWB pulse signal with conventional spectrum sensing schemes, due to its low average signal to noise ratio (SNR), large bandwidth, and low duty ratio. In this paper the detection algorithm of signal distribution change, which is application of CUSUM test, is considered to be applied to cognitive UWB spectrum sensing. But CUSUM test request that the pre-change and the post-change distributions are i.i.d, which cannot be satisfied in the detection process of UWB pulse signal. Since there are two time domain descriptions on UWB pulse signal, namely one contains only noise and the other one contains pulse signal plus noise, the existing detection algorithm of signal distribution change cannot be directly applied to detect UWB pulse signal. Hence the uniform probability density function expression of UWB pulse signal is first deduced, then CUSUM test is applied to cognitive UWB spectrum sensing. The proposed algorithm is a time sequential detection algorithm, with low complexity and minimal detection delay, which is suitable to detect the low duty ratio signal. Its performance is evaluated through theoretical analysis and numerical simulations. It is shown that this algorithm outperforms the conventional energy detection algorithm and conquers SNR wall phenomenon.

Variations of the specific barrier model—part II: effect of isochron distributions

The specific barrier model (SBM) is a particular case of a composite earthquake source model where the seismic moment is distributed in a deterministic manner on a rectangular fault plane on the basis of moment and area constraints. It is assumed that the fault surface is composed of an aggregate of subevents of equal diameter, the ‘barrier interval’. Furthermore, the subevents are assumed to rupture randomly and statistically independent of one another as the rupture front sweeps the fault plane. In the formulation of the far-field source spectrum of the SBM the ‘arrival time’ of the seismic radiation emitted by each subevent is specified via a probability density function (PDF). In the SBM the subevents are assumed to be of equal sizes (an assumption relaxed in a companion paper, referred to as Part I) and the PDF of ‘arrival times’ is assumed to be uniform. In this study we investigate the effects of different PDFs of ‘arrival times’ on the far-field source spectrum of the SBM. Different PDFs of ‘arrival times’ affect the source spectra primarily at the intermediate frequency range (between the first and second corner frequencies). Such effects become more pronounced as the earthquake magnitude increases. The far-field spectrum of seismic energy observed/recorded at a site depends on the location of the site relative to the causative fault plane, the location of rupture initiation (hypocenter) and the onset times of the rupturing subevents. All the above factors are effectively taken into account by the ‘isochrons’, which vary with source-site geometry. We investigate the selection of the appropriate PDF of seismic energy arrival times at a given site by computing isochrons for a grid of stations surrounding the earthquake fault, represented by the SBM. We show that only for stations located in a direction normal to the fault plane is the assumption of uniform PDF of ‘arrival times’ valid. At other sites non-uniform PDFs of ‘arrival times’ are observed. We identify and categorize the prevalent types of PDFs by directivity (forward vs. backward vs. neutral) and source-site distance (near-fault vs. far-field), show examples in which we group the stations accordingly. We investigate the effects of the different PDF-groups on the SBM source spectrum. Selection of the appropriate PDF for a given source-site configuration when simulating strong ground motions using the SBM in the context of the stochastic method is expected to yield more self-consistent, and physically realistic simulations.

Relative information contributions of model vs. data to short- and long-term forecasts of forest carbon dynamics

Biogeochemical models have been used to evaluate long-term ecosystem responses to global change on decadal and century time scales. Recently, data assimilation has been applied to improve these models for ecological forecasting. It is not clear what the relative information contributions of model (structure and parameters) vs. data are to constraints of short- and long-term forecasting. In this study, we assimilated eight sets of 10-year data (foliage, woody, and fine root biomass, litter fall, forest floor carbon [C], microbial C, soil C, and soil respiration) collected from Duke Forest into a Terrestrial Ecosystem model (TECO). The relative information contribution was measured by Shannon information index calculated from probability density functions (PDFs) of carbon pool sizes. The null knowledge without a model or data was defined by the uniform PDF within a prior range. The relative model contribution was information content in the PDF of modeled carbon pools minus that in the uniform PDF, while the relative data contribution was the information content in the PDF of modeled carbon pools after data was assimilated minus that before data assimilation. Our results showed that the information contribution of the model to constrain carbon dynamics increased with time whereas the data contribution declined. The eight data sets contributed more than the model to constrain C dynamics in foliage and fine root pools over the 100-year forecasts. The model, however, contributed more than the data sets to constrain the litter, fast soil organic matter (SOM), and passive SOM pools. For the two major C pools, woody biomass and slow SOM, the model contributed less information in the first few decades and then more in the following decades than the data. Knowledge of relative information contributions of model vs. data is useful for model development, uncertainty analysis, future data collection, and evaluation of ecological forecasting.

Assessment methodology for confidence in safety margin for large break loss of coolant accident sequences

Deterministic Safety Analysis and Probabilistic Safety Assessment (PSA) analyses are used to assess the Nuclear Power Plant (NPP) safety. The conventional deterministic analysis is conservative. The best estimate plus uncertainty analysis (BEPU) is increasingly being used for deterministic calculation in NPPs. The PSA methodology integrates information about the postulated accident, plant design, operating practices, component reliability and human behavior. The deterministic and probabilistic methodologies are combined by analyzing the accident sequences within design basis in the event trees of a postulated initiating event (PIE) by BEPU. The peak clad temperature (PCT) distribution provides an insight into the confidence in safety margin for an initiating event. The paper deals with calculating the safety margin with 95% confidence and 95% probability in large break loss of coolant accident (LBLOCA). In the present study, five uncertain input parameters were selected. Uniform probability density function was assigned to the uncertain parameters in the selected range and these uncertainties are propagated using Latin Hypercube Sampling (LHS) technique. The sampled data for five parameters was randomly mixed by LHS to obtain 25 input sets. An event tree for the initiating event, LBLOCA inside containment, has been used from a VVER study on Level-1 PSA and four non-core damage (NCD) accident sequences were identified for this study. In the accident analysis the success and failure of safety systems reflected in event tree was appropriately modeled in the system thermal hydraulics code runs. The PCT was obtained for each of 25 code runs for each accident sequence. A Kolmogorov – Smirnov goodness-of-fit test carried out for PCTs indicated that they followed normal distribution for each of the accident sequences. The probability distribution of safety margin (difference between acceptable value and PCT) in each accident sequence was also obtained. The values of safety margin for the 95% confidence and 95% probability are estimated. The robustness of the system can be judged based on this. This paper describes the methodology. LBLOCA in a VVER type reactor is considered as an example.

MAGNETIC FIELDS IN INTERSTELLAR CLOUDS FROM ZEEMAN OBSERVATIONS: INFERENCE OF TOTAL FIELD STRENGTHS BY BAYESIAN ANALYSIS

The only direct measurements of interstellar magnetic field strengths depend on the Zeeman effect, which samples the line-of-sight component B{sub z} of the magnetic vector. In this paper, we use a Bayesian approach to analyze the observed probability density function (PDF) of B{sub z} from Zeeman surveys of H I, OH, and CN spectral lines in order to infer a density-dependent stochastic model of the total field strength B in diffuse and molecular clouds. We find that at n 300 cm{sup -3}, with an uncertainty at the 50% level in the power-law exponent of about {+-}0.05. This break-point density could be interpreted as the average density at which parsec-scale clouds become self-gravitating. Both the uniform PDF of total field strengths and the scalingmore » with density suggest that magnetic fields in molecular clouds are often too weak to dominate the star formation process. The stochasticity of the total field strength B implies that many fields are so weak that the mass/flux ratio in many clouds must be significantly supercritical. A two-thirds power law comes from isotropic contraction of gas too weakly magnetized for the magnetic field to affect the morphology of the collapse. On the other hand, our study does not rule out some clouds having strong magnetic fields with critical mass/flux ratios.« less

Pavement Rehabilitation Project Ranking Approach Using Probabilistic Long-Term Performance Indicators

A probabilistic performance-based approach for generating a priority ranking of pavement rehabilitation project candidates is presented. The deployed probabilistic approach uses a discrete-time Markovian model to predict pavement conditions at the network level. The expected future distress rating associated with a particular pavement project is determined as the mean of a compound uniform probability density function derived from the corresponding future state probabilities. The expected future distress ratings for a particular pavement project are then used to construct the corresponding performance curve. The generated performance curves form the basis for developing an effective mechanism for prioritizing potential rehabilitation projects. A priority ranking system is presented with two alternatives. The first priority ranking alternative requires a fixed analysis period wherein project candidates are evaluated by using three different long-term performance indicators derived from the corresponding performance curves. The deployed performance indicators include the area under the performance curve, the average distress rating, and the terminal distress rating. The second priority ranking alternative requires a fixed terminal distress rating for the pavement network under consideration. The time required for each project to reach the terminal distress rating is determined as the rehabilitation scheduling time, which is used to establish project priority ranking. Pavement rehabilitation project candidates are then scheduled according to their priority rankings and available budget. The developed probabilistic approach is demonstrated by considering a project sample from the two-lane highway system in Ohio.

Three-dimensional speckle-noise reduction by using coherent integral imaging

We present a 3D imaging method to reduce speckle noise that exists in coherent imaging systems. This approach is based on integral imaging (II). The elemental images set having speckle-noise patterns of a 3D object is obtained by II technique under coherent illumination. The computational geometrical ray-propagation algorithm is applied to the elemental images in order to reconstruct the original 3D object. A uniform probability-density function is assumed for modeling the phase distribution of the speckle patterns. The statistical point estimator is used for 3D speckle removal. Speckle index is calculated to compare the computational reconstruction using the proposed method with that of conventional coherent image degraded by speckle patterns for 3D object reconstruction and by object recognition. Experimental results are presented. The speckle index, mean square error, and signal-to-noise ratio are used as performance metrics and are shown to have been significantly improved by the proposed method to reduce speckle noise in the 3D object reconstruction. 3D reconstruction experiments of objects with reduced speckle noise are presented. To the best of our knowledge, this is the first report on 3D speckle removal using II and statistical estimation algorithms.