Analysis and Probabilistic Modeling of the Stationary Ice Loads Stochastic Process With Lognormal Distribution

2014 ◽  
Author(s):  
Petr Zvyagin ◽  
Kirill Sazonov
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Normal Distribution ◽  
Autocorrelation Function ◽  
Strain Gauge ◽  
Lognormal Distribution ◽  
Probabilistic Modeling ◽  
Stationary Stochastic Process ◽  
Strain Gauge Transducer ◽  
Ice Loads

Until recent times researchers who investigated ice loads stochastic processes usually stated the fact of normal distribution for them. In the paper the model of a stationary stochastic process with a lognormal distribution for ice loads is offered. This model relates to the strain gauge transducer ice loads measurements as well as to some examples considered in different papers that were published earlier. For this model dependencies of the autocorrelation function were found that allows to simulate the ice loads process relatively easily. The procedure of such a simulation is described in details and the example of the analysis and simulation ice loads measurements is provided.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Analysis and Probabilistic Modeling of the Unstationary Ice Loads Stochastic Process, Based on Experiments With Models of Offshore Structures

2015 ◽  
Author(s):  
Petr Zvyagin ◽  
Kirill Sazonov
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Statistical Analysis ◽  
Probabilistic Modeling ◽  
Offshore Structures ◽  
Offshore Structure ◽  
Sample Mean ◽  
Ice Loads ◽  
Time Series Simulation ◽  
Fuzzy C Means Algorithm

Experiments with models of platforms and offshore structures with vertical and inclined panels, which were conducted at Krylov Research Center (St. Petersburg), demonstrated that sometimes ice loads time series registered in these experiments cannot be considered as stationary. At the same time until nowadays methods and algorithms of probabilistic modeling were mainly based on the assumption of ice loads time series stationarity. That is because the analysis and modeling for stationary stochastic process is easier than for those unstationary. In the paper the method for determining the presence of unstationarity in ice loads time series, based on statistical analysis, is described. This method employs sample mean normality. Fuzzy C-means algorithm is used to cluster autocorrelation vectors, which are built for different fragments of time series. In the paper ice loads time series, got in experiments in ice tank with offshore structure columns and basement models, are investigated on their unstationarity. The algorithm of unstationary ice loads time series simulation is offered.

Simulation of Normal Differentiable Stochastic Process of Ice Loads

2017 ◽  
Author(s):  
Petr Zvyagin
Keyword(s):  
Stochastic Process ◽  
Autocorrelation Function ◽  
Critical Level ◽  
Process Approach ◽  
The Other ◽  
Normal Process ◽  
Expected Number ◽  
Stationary Model ◽  
Tank Experiment ◽  
Ice Loads

Ice loads time series should be treated in the other way than separate independent ice loads observations. The stochastic process approach can provide information about such important characteristic as mean length of signal’s outcome beyond some critical level and expected number of such outcomes. The paper considers global ice loads registered in an ice tank experiment with a cylindrical indenter of 100 mm width. The autocorrelation function is fitted in a manner that the observed load process is differentiable. The study conducted in the paper demonstrates that characteristics, such as the number outcomes beyond some critical level and the time spent off this level, are governed in the same way as parameters of a stationary differentiable normal process. Normal stationary model of ice loads process allows its simulation, if autocorrelation function is given. In the paper, such simulation is performed.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (4) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Products of random mappings

2000 ◽  
Vol 20 (2) ◽  
pp. 517-529 ◽  
Author(s):  
DAVID G. LUENBERGER
Keyword(s):  
Stochastic Process ◽  
Normal Distribution ◽  
Stationary Process ◽  
Stationary Stochastic Process ◽  
Common Variance ◽  
Random Mappings ◽  
Special Case ◽  
Nonlinear Mappings

Suppose that $X^1,X^2,\dotsc$ is a stationary stochastic process of positive $k\times k$ matrices, and let ${}^nY^1=X^nX^{n-1}\dots X^1$ be the corresponding product matrices. For a special case, Bellman showed that the elements $[{}^nY^1]_{ij}$ converge in the sense that $n^{-1}\mathrm{E}\{\log[{}^nY^1]_{ij}\}\rightarrow a$ as $n\rightarrow\infty$. The constant $a$ is independent of $i$ and $j$. Bellman also conjectured that, asymptotically, the $n^{-1/2}\{\log[{}^nY^1]_{ij}-na\}$ terms are distributed according to a normal distribution with a common variance, independent of $ij$. Later Furstenberg and Kesten generalized and strengthened Bellman's result and established the validity of his conjecture.This paper extends these results to the case of nonlinear mappings that are monotonic and homogeneous of degree one on $R^k_+$. Specifically, given a stationary process $H^1,H^2,\dots$ of such mappings, we define the composite mappings ${}^nF^1(\cdot)=H^n(H^{n-1}(\dots (H^1(\cdot))\dots)$. Under appropriate conditions, the components $[{}^nF^1(x^0)]_i$ have the property that, almost surely, $n^{-1}\log[{}^nF^1(x^0)]_i\rightarrow a$ independent of $x^0$ and $i$. Furthermore the components $n^{-1/2}\{\log[{}^nF^1(x^0)]_i-na\}$ are asymptotically distributed according to a normal distribution with a common variance.

Simulation of Stochastic Processes by Spectral Representation

1991 ◽  
Vol 44 (4) ◽  
pp. 191-204 ◽  
Author(s):  
Masanobu Shinozuka ◽  
George Deodatis
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Autocorrelation Function ◽  
Structural Engineering ◽  
Spectral Representation ◽  
Target Function ◽  
Mean Value ◽  
Random Loading ◽  
Cosine Series ◽  
Spectral Representation Method

The subject of this paper is the simulation of one-dimensional, uni-variate, stationary, Gaussian stochastic processes using the spectral representation method. Following this methodology, sample functions of the stochastic process can be generated with great computational efficiency using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number N of the terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the temporally-averaged mean value and the autocorrelation function are identical with the corresponding targets, when the averaging takes place over the fundamental period of the cosine series. The most important property of the simulated stochastic process is that it is asymptotically Gaussian as N → ∞. Another attractive feature of the method is that the cosine series formula can be numerically computed efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in engineering mechanics and structural engineering. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

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