Moment-Based Hybrid Polynomial Chaos Method for Interval and Random Uncertain Analysis of Periodical Composite Structural-Acoustic System with Multi-Scale Parameters

2020 ◽  
pp. 2050041
Author(s):  
Ning Chen ◽  
Jiaojiao Chen ◽  
Shengwen Yin
Keyword(s):  
Polynomial Chaos ◽  
Random Variable ◽  
Acoustic System ◽  
Passenger Compartment ◽  
Scale Parameters ◽  
Multi Scale ◽  
Arbitrary Polynomial ◽  
Random Moment ◽  
The Moment ◽  
Probability Density Function Pdf

An interval and random moment-based arbitrary polynomial chaos method (IRMAPCM) is proposed in this paper for the analysis of periodical composite structural-acoustic systems with multi-scale uncertain-but-bounded parameters. In IRMAPCM, the response of structural-acoustic system is approximated as moment-based arbitrary polynomial chaos (maPC) expansion. IRMAPCM can construct the polynomial basis according to the moment of the random variable without knowing the Probability Density Function (PDF), which can avoid the errors introduced by estimating the PDF. Numerical examples of a hexahedral box and an automobile passenger compartment are given to investigate the effectiveness of IRMAPCM for the prediction of the sound pressure response of structural-acoustic systems.

scholarly journals A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro-Acoustic System

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shengwen Yin ◽  
Xiaohan Zhu ◽  
Xiang Liu
Keyword(s):  
Expansion Coefficient ◽  
Polynomial Chaos ◽  
Sequential Sampling ◽  
Expansion Method ◽  
Sparse Grids ◽  
Polynomial Expansion ◽  
Acoustic System ◽  
Arbitrary Polynomial ◽  
Polynomial Expansion Method ◽  
Random Uncertainties

For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.

scholarly journals Forgery Detection in Digital Images by Multi-Scale Noise Estimation

2021 ◽  
Vol 7 (7) ◽  
pp. 119
Author(s):  
Marina Gardella ◽  
Pablo Musé ◽  
Jean-Michel Morel ◽  
Miguel Colom
Keyword(s):  
Noise Model ◽  
Correlated Noise ◽  
Forgery Detection ◽  
Color Channel ◽  
Image Block ◽  
Multi Scale ◽  
Compressed Images ◽  
Inconsistency Analysis ◽  
Highly Correlated ◽  
The Moment

A complex processing chain is applied from the moment a raw image is acquired until the final image is obtained. This process transforms the originally Poisson-distributed noise into a complex noise model. Noise inconsistency analysis is a rich source for forgery detection, as forged regions have likely undergone a different processing pipeline or out-camera processing. We propose a multi-scale approach, which is shown to be suitable for analyzing the highly correlated noise present in JPEG-compressed images. We estimate a noise curve for each image block, in each color channel and at each scale. We then compare each noise curve to its corresponding noise curve obtained from the whole image by counting the percentage of bins of the local noise curve that are below the global one. This procedure yields crucial detection cues since many forgeries create a local noise deficit. Our method is shown to be competitive with the state of the art. It outperforms all other methods when evaluated using the MCC score, or on forged regions large enough and for colorization attacks, regardless of the evaluation metric.

Uncertainty Quantification and Missing Data for Turbomachinery With Probabilistic Equivalence and Arbitrary Polynomial Chaos, Applied to Scroll Compressors

2021 ◽  
Author(s):  
Nick Pepper ◽  
Francesco Montomoli ◽  
Sanjiv Sharma ◽  
Francesco Giacomel ◽  
Michele Pinelli ◽  
...  
Keyword(s):  
Missing Data ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Arbitrary Polynomial

Markovian Analysis of Aging Distributed Systems Remaining Life

2014 ◽  
Author(s):  
Anna Bushinskaya ◽  
Sviatoslav Timashev
Keyword(s):  
Distributed Systems ◽  
Markov Process ◽  
Residual Life ◽  
Limit State ◽  
Real Life ◽  
Random Variable ◽  
Operating Pressure ◽  
Remaining Life ◽  
Failure Pressure ◽  
The Moment

Correct assessment of the remaining life of distributed systems such as pipeline systems (PS) with defects plays a crucial role in solving the problem of their integrity. Authors propose a methodology which allows estimating the random residual time (remaining life) of transition of a PS from its current state to a critical or limit state, based on available information on the sizes of the set of growing defects found during an in line inspection (ILI), followed by verification or direct assessment. PS with many actively growing defects is a physical distributed system, which transits from one physical state to another. This transition finally leads to failure of its components, each component being a defect. Such process can be described by a Markov process. The degradation of the PS (measured as monotonous deterioration of its failure pressure Pf (t)) is considered as a non-homogeneous pure death Markov process (NPDMP) of the continuous time and discrete states type. Failure pressure is calculated using one of the internationally recognized pipeline design codes: B13G, B31Gmod, DNV, Battelle and Shell-92. The NPDMP is described by a system of non-homogeneous differential equations, which allows calculating the probability of defects failure pressure being in each of its possible states. On the basis of these probabilities the gamma-percent residual life of defects is calculated. In other words, the moment of time tγ is calculated, which is a random variable, when the failure pressure of pipeline defect Pf (tγ) > Pop, with probability γ, where Pop is the operating pressure. The developed methodology was successfully applied to a real life case, which is presented and discussed.

scholarly journals A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021 ◽  
Vol 8 (1) ◽  
pp. 33-44
Author(s):  
Toufik Chaayra ◽  
Hussain Ben-azza ◽  
Faissal El Bouanani
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Performance Metrics ◽  
Approximate Expression ◽  
Maximal Ratio Combining ◽  
Generalized Gamma ◽  
The Moment ◽  
Probability Density Function Pdf ◽  
Closed Form Approximation ◽  
Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Multi-scale Simulation in Railway Planning and Operation

2012 ◽  
Vol 23 (6) ◽  
pp. 511-517 ◽  
Author(s):  
Yong Cui ◽  
Ullrich Martin
Keyword(s):  
Simulation Model ◽  
Process Simulation ◽  
Level Of Detail ◽  
Smooth Transition ◽  
Simulation Methods ◽  
Multi Scale ◽  
Railway Planning ◽  
The Moment ◽  
Discrete Scaling ◽  
Planning And Operation

Simulation methods are widely used in railway planning and operation. However, at the moment there are no applicable solutions in the process simulation for a smooth transition among different infrastructure levels on the basis of a unified structure with consistent algorithm. In this paper, a multi-scale simulation model is designed with consideration of the level of detail of the investigated infrastructure model and the homogeneity of the processes running in the simulation model. A comprehensive and synthesized view of railway planning and operation is therefore obtained. Within the multi-scale simulation model, railway planning and operation processes can be simulated, evaluated and optimized consistently. KEY WORDS: railway planning, simulation, multi-scale, aggregation, discrete scaling, continuous scaling, homogenous process, inhomogeneous process

scholarly journals ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF STOCHASTIC, PARAMETRIC ELLIPTIC MULTISCALE PDEs

2013 ◽  
Vol 11 (01) ◽  
pp. 1350001 ◽  
Author(s):  
V. H. HOANG ◽  
CH. SCHWAB
Keyword(s):  
Polynomial Chaos ◽  
Sufficient Conditions ◽  
Limit Problem ◽  
Elliptic Pdes ◽  
Random Solution ◽  
Anisotropic Conductivity ◽  
Scale Parameters ◽  
Regularity Results ◽  
Analytic Regularity ◽  
Scale Limit

A class of second order, elliptic PDEs in divergence form with stochastic and anisotropic conductivity coefficients and n known, separated microscopic length scales εi, i = 1, …, n in a bounded domain D ⊂ ℝd is considered. Neither stationarity nor ergodicity of these coefficients is assumed. Sufficient conditions are given for the random solution to converge ℙ-a.s, as εi → 0, to a stochastic, elliptic one-scale limit problem in a tensorized domain of dimension (n + 1)d. It is shown that this stochastic limit problem admits best N-term "polynomial chaos" type approximations which converge at a rate σ > 0 that is determined by the summability of the random inputs' Karhúnen–Loève expansion. The convergence of the polynomial chaos expansion is shown to hold ℙ-a.s. and uniformly with respect to the scale parameters εi. Regularity results for the stochastic, one-scale limiting problem are established. An error bound for the approximation of the random solution at finite, positive values of the scale parameters εi is established in the case of two scales, and in the case of n > 2, scales convergence is shown, albeit without giving a convergence rate in this case.

Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process

1984 ◽  
Vol 21 (1) ◽  
pp. 98-107 ◽  
Author(s):  
Minoru Yoshida
Keyword(s):  
Distribution Function ◽  
Stopping Time ◽  
Random Variables ◽  
Secretary Problem ◽  
Independent Random Variables ◽  
Distribution Law ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Random Moment ◽  
The Moment

Before some random moment θ, independent identically distributed random variables x1, · ··, xθ–1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.

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