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1

Theoretical probabilistic nonlinear analysis of post-tensioned bridge cross-sections with the application of random fields

Owerko Piotr

Architecture Civil Engineering Environment

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2023

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Vol. 16, no. 2

127--136

EN

The paper presents a proprietary procedure for the analysis of normal stress distributions in post-tensioned cross-sections. It has a significant advantage over conventional commonly used approaches based solely on the envelope analysis as it provides stress levels in all components of the cross-section. The procedure was used in a series of probabilistic analyses with the adoption of random fields. These fields represented uncertainties in strain-stress relationship in concrete. The analysis covered several types of cross-sections and several types of random fields. Key observations from the conducted simulations are as follows: (I) the widest ranges of the probable maximum stresses (i.e. the lowest indexes of reliability) were obtained for sections with relatively low heights of the compressive zone. (II) The highest probabilistic sensitivity to the type of random field used was found in tall sections with a relatively large compressive zone. (III) The greatest sensitivity to batch uncertainties was evident in all cross-sections when using squared exponential random fields. (IV) The greatest relative sensitivity to the batch uncertainties in the form of the random field compliant with the guidelines of the Joint Comity of Structural Safety (JCSS) was evident in the analyses of the tallest cross-section corresponding to the incrementally launched bridges.

2

Exact strong laws of large numbers for independent random fields

Kurasiński P., Matuła P., Adler A.

Bulletin of the Polish Academy of Sciences. Mathematics

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2018

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Vol. 66, no. 2

179--188

EN

Let {Xṉ, ṉ ϵ Nd} be a family of independent random variables with multidimensional indices (a random field) with the same distribution as the r.v. X. A necessary and sufficient condition for the strong law of large numbers in this setting is E|X| logd-1+|X| < ∞. Our goal is to study the almost sure convergence of normalized or weighted sums in the case when this moment condition is not satisfied.

3

Identification and simulation of initial geometrical imperfections of steel cylindrical tanks

Górski J., Mikulski T.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 2

413-434

EN

Critical loads of shell structures can be properly approximated only through including randomness in their geometry. As it is difficult and expensive to measure the initial structure imperfections in situ or in laboratory, a methodology of identification and description of the available data should be provided. The presented procedure provides an opportunity for the reproduction of measured maps of steel cylindrical tank geometrical imperfections. Simulations of nonhomogeneous random fields of imperfections, based on the original conditional-rejection method of simulation, are applied. Using the measured data, an envelope of the imperfections is also estimated. It allows for simulation of extreme but still realistic fields of imperfections. Additionally, nonlinear numerical analyses of tanks with and without initial geometrical imperfections are performed. The results indicate that the initial imperfections influence the solutions.

PL

Wyznaczenie obciążenia granicznego konstrukcji powłokowych wymaga uwzględnienia w obliczeniach odchyłek geometrycznych. Wykonanie pomiarów tego typu odchyłek rzeczywistych obiektów jest trudne i kosztowne. Wyniki uzyskane na podstawie analizy modeli laboratoryjnych nie są wiarygodne. W pracy zaproponowano metodę alternatywną. Wykazano, że na podstawie dostępnych danych można sformułować metody identyfikacji i symulacji wstępnych odchyłek geometrycznych. Zaprezentowane procedury umożliwiają odwzorowanie pomierzonych pól wstępnych odchyłek stalowych cylindrycznych zbiorników o osi pionowej na paliwa płynne. Symulacje niejednorodnych pól losowych imperfekcji wykonano za pomocą oryginalnej warunkowej metody akceptacji i odrzucania. Pomierzone dane pozwoliły także na wyznaczenie obwiedni odchyłek losowych i na tej podstawie wykonano symulację ekstremalnych, realistycznych pól imperfekcji. Dodatkowo przeprowadzono nieliniowe obliczenia numeryczne zbiorników idealnych oraz z imperfekcjami. Porównanie wyników pozwoliło na określenie wpływu odchyłek na mechaniczną odpowiedź powłoki.

4

Conditional simulation of spatiotemporal random fields of environmental contamination

Jankowski R., Walukiewicz H.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 1

21-26

EN

The paper considers a method of conditional simulation of spatiotemporal scalar random fields of certain environmental phenomena. The method can be used to predict field values at given space points at specified time, on the basis of field values at other locations and data on second order moment functions in the domain. This approach has been applied to a space-time prognosis of soil contamination fields. The assessment of the spatiotemporal variability of heavy metals' concentrations provides the knowledge needed to monitor and control soil contamination. Empirical data of heavy metal (viz. chromium) concentration in the soil of northern Poland have been used in the study. The acceptance-rejection method has been applied to generate covariance matrices and vectors of discrete field values, taking into account conditional probability distributions. The results of the study show that the considered method can be successfully used to model conditional, spatiotemporal random fields of contamination with relatively small simulation errors.

5

Curse of dimensionality in approximation of random fields

Lifshits M. A., Tulyakova V.

Probability and Mathematical Statistics

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2006

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Vol. 26, Fasc. 1

97--112

EN

Consider a random field of tensor product-type X(t), t∈[0,1]d, given by [formula] where (λ(i))i>0∈l2(φi)i>0 is an orthonormal system in L2 [0, 1] and (ξk)k∈Nd are non-correlated random variables with zero mean and unit variance. We investigate the quality of approximation (both in the average and in the probabilistic sense) to X by the n-term partial sums Xn minimizing the quadratic error E‖X‒Xn‖2, In the first part of the paper we consider the case of fixed dimension d. In the second part, following the suggestion of H. Woźniakowski, we consider the same problem for d→∞. We show that, for any fixed level of relative error, approximation complexity increases exponentially and we find the ex- plosion coefficient. We also show that the behavior of the probabilistic and average complexity is essentially the same in the large domain of parameters.

6

Convergence rate in CLT for vector-valued random fields with self-normalization

Bulinski A., Kryzhanovskaya N.

Probability and Mathematical Statistics

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2006

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Vol. 26, Fasc. 2

261--281

EN

Statistical version of the central limit theorem (CLT) with random matrix normalization is established for random fields with values in a space Rk (k ≥ 1). Dependence structure of the field under consideration is described in terms of the covariance inequalities for the class of bounded Lipschitz ”test functions” defined on finite disjoint collections of random vectors constituting the field. The main result provides an estimate of the convergence rate, over a family of convex bounded sets, in the CLT with random normalization.

7

Central limit theorem for diffusion processes in an anisotropic random environment

Nieznaj E.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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Vol. 53, no 2

187-205

EN

We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. [18], [7]. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.

8

Linearly additive random fields with independent increments on time like curves

Takenaka S.

Probability and Mathematical Statistics

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2003

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Vol. 23, Fasc. 1

1--5

EN

Let V be a convex cone in Rn. A curve L = {l(t); t ∈ R+} ⊂ Rn is called a time-like curve if {l(s); s ≥ t} ⊂ l(t) + V holds for any t. A random field {X(t); t ∈ Rn} whose restriction X|L(t) = X (l(t)) on time-like curve L becomes an additive process is considered and it is characterized as a set-indexed random field on the dual cone V∗.

9

Gaussian semiparametric estimation for random fields with singular spectrum

Marinucci D.

Probability and Mathematical Statistics

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2003

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Vol. 23, Fasc. 1

105--138

EN

We analyze the asymptotic behaviour of the tapered discrete Fourier transforms for random fields with singular spectrum. The results are used to establish consistency and asymptotic normality for semiparametric estimates of the singularity parameter under broad conditions.

10

Informational entropy in simulation of one-dimensional random fields

Opoka Sz., Walukiewicz H.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2002

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Vol. 6, No 3

379-385

EN

The entropy H of a continuous distribution with probability density function f* is defined as a function of the number of nodes (n) in a one-dimensional scalar random field. For the second order theory this entropy is expressed by the determinants of the covariance matrices and simulated for several types of correlation functions. In the numerical example the propagation of the entropy for the static response of linear elastic, randomly loaded beam has been considered. Two unexpected results have been observed: - function H(n) is entirely different for differentiable (m.s.) and non-differentiable fields, with the same parameters in the correlation functions, - in some cases, the greater randomness at the input (measured by the entropy) does not lead to the greater randomness at the output.

11

Marcinkiewicz-type strong law of large numbers for pairwise independent random fields

Czerebak-Mrozowicz E. B., Klesov O. I., Rychlik Z.

Probability and Mathematical Statistics

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2002

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Vol. 22, Fasc. 1

127--139

EN

We present the Marcinkiewicz-type strong law of large numbers for ran-dom fields{Xn, n ∈Zd+}of pairwise independent random variables, where Zd+, d≥1, is the set of positived-dimensional lattice points with coordinatewise partial ordering.