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• A method to simulate wind fields is proposed considering probabilistic spectra. • The correlated spectral parameters are decoupled in the proposed method. • The proposed method can combine with the PDEM to assess structural reliability. • The reliability of a tower crane is compared between deterministic and probabilistic spectra. The need for wind-sensitive super-high tower cranes during the construction of high-rise structures has been growing, which makes it critical to assess the wind-resistant reliability of cranes. The accuracy of assessment is dominated by the refined simulation of real stochastic wind fields, which is usually based on the deterministic turbulent spectra including fixed spectral parameters. However, it might cause significant errors to estimate extreme responses of structures. Therefore, a simulation method for stochastic wind fields considering the randomness and correlation of turbulent spectral parameters is proposed in this study. The random functions of correlated spectral parameters are constructed based on several independent elementary random variables. A novel simulation method for stochastic wind fields involving the established random turbulent spectral functions is utilized to generate fluctuating wind samples at the Ma'anshan Yangtze River (MYR) Bridge site. In combination with the probability density evolution method, the stochastic response analysis and reliability assessment of wind-induced vibration of the crane are addressed. Results prove the effectiveness of the proposed approach in depicting probabilistic properties of real wind fields. Meanwhile, the wind-resistant comfort reliability of the tower crane is higher when considering the randomness and correlation of turbulent spectral parameters. [ABSTRACT FROM AUTHOR]

Let be a one-dimensional Brownian motion. We discuss the existence of Ogawa integrals , where is given by a Skorokhod integral and is a deterministic bounded function on. Here the symbol † indicates the ϕ- or u-integrability of the Ogawa integral. If fv is Ogawa integrable, we give an explicit formula for , which shows that the Ogawa integral is an extension of the symmetric integral. [ABSTRACT FROM AUTHOR]

A framework of spectral representation-based dimension reduction for simulating multivariate non-stationary stochastic ground motion processes is addressed in this paper. By means of introducing random functions serving as constraints correlating with the orthogonal random variables in the original spectral representation scheme, the high-dimensional randomness degree involved in the multivariate stochastic processes can thus be reduced substantially. To this aim, three random function forms considering the combination of trigonometric functions and orthogonal polynomials are constructed for simulation purpose. Accordingly, the accurate representation of the original stochastic processes is realized with merely three elementary random variables, overcoming the principal challenge of numerous random variables faced by the Monte Carlo simulation method. Also, the consistency of the statistics between the sample functions of stochastic ground motions and strong motion records is established with update of the ground motion model parameters in stochastic simulation techniques. Numerical investigations involving the comparisons with the Monte Carlo simulation method and the validation based on the strong motion records are presented to demonstrate the superiority and effectiveness of the proposed methodology in practical engineering applications. [ABSTRACT FROM AUTHOR]

A Gaussian random function is a functional version of the normal distribution. This paper proposes a statistical hypothesis test to test whether or not a random function is a Gaussian random function. A parameter that is equal to 0 under Gaussian random function is considered, and its unbiased estimator is given. The asymptotic distribution of the estimator is studied, which is used for constructing a test statistic and discussing its asymptotic power. The performance of the proposed test is investigated through several numerical simulations. An illustrative example is also presented. [ABSTRACT FROM AUTHOR]

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness. [ABSTRACT FROM AUTHOR]

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods. [ABSTRACT FROM AUTHOR]

Conventional Karhunen-Loeve expansions for simulation of stochastic processes often encounter the challenge of dealing with hundreds of random variables. For breaking through the barrier, a random function embedded Karhunen-Loeve expansion method is proposed in this paper. The updated scheme has a similar form to the conventional Karhunen-Loeve expansion, both involving a summation of a series of deterministic orthonormal basis and uncorrelated random variables. While the difference from the updated scheme lies in the dimension reduction of Karhunen-Loeve expansion through introducing random functions as a conditional constraint upon uncorrelated random variables. The random function is expressed as a single-elementary-random-variable orthogonal function in polynomial format (non-Gaussian variables) or trigonometric format (non-Gaussian and Gaussian variables). For illustrative purposes, the simulation of seismic ground motion is carried out using the updated scheme. Numerical investigations reveal that the Karhunen-Loeve expansion with random functions could gain desirable simulation results in case of a moderate sample number, except the Hermite polynomials and the Laguerre polynomials. It has the sound applicability and efficiency in simulation of stochastic processes. Besides, the updated scheme has the benefit of integrating with probability density evolution method, readily for the stochastic analysis of nonlinear structures. [ABSTRACT FROM AUTHOR]

The deposition of fly ash in the tube-bundle heat exchanger has become an urgent problem that must be resolved. During the deposition process, the fly ash particles will alter the physical properties and geometry of the heat exchange surface. A random function model combined with the dynamic mesh method is proposed to improve the existing particle deposition model. The effects of various flow velocities and particle sizes on particle deposition are analyzed. The results indicated that the total deposition mass of large particles decreases and the small particles increases as the flow velocity increases. With increasing particle size at the same flow velocity, the total particle deposition mass increases first and then decreases for in-line tube bundles. Local analysis indicates that the initial deposition occurs primarily on the windward side of the tube, with a greater number of particles deposited on the upstream tube bundles than on the downstream tube bundles. A random function model combined with the dynamic mesh method is proposed to improve the existing particle deposition model. [Display omitted] • A random function model combined with the dynamic mesh method is proposed. • Account for changes in physical properties and geometry of the heat exchange surface. • The improved deposition model is validated by comparison with experimental data. • Effects of flow velocities and particle sizes on ash deposition characteristics are analyzed. [ABSTRACT FROM AUTHOR]

At present the major secure sum protocol has high communication complexity. Based on the public key encryption technology and random algorithm, this paper proposed a new secure sum protocol in the semi-honest model, which improved safety and reduced communication complexity, and it proved the correctness and security. Compared with other protocols, this protocol has more advantages. [ABSTRACT FROM AUTHOR]

In conjunction with the formulation of random functions, a family of renewed spectral representation schemes is proposed. The selected random function serves as a random constraint correlating the random variables included in the spectral representation schemes. The objective stochastic process can thus be completely represented by a dimension-reduced spectral model with just few elementary random variables, through defining the high-dimensional random variables of conventional spectral representation schemes (usually hundreds of random variables) into the low-dimensional orthogonal random functions. To highlight the advantages of this scheme, orthogonal trigonometric functions with one and two random variables are constructed. Representative-point set of the dimension-reduced spectral model is derived by employing the probability-space partition techniques. The complete set with assigned probabilities of points gains a low-number-sample stochastic process. For illustrative purposes, the stochastic modeling of seismic acceleration processes is proceeded, of which the stationary and non-stationary cases are investigated. It is shown that the spectral acceleration of simulated processes matches well with the target spectrum. Stochastic seismic response analysis, moreover, and reliability assessment of a framed structure with Bouc-Wen behaviors are carried out using the probability density evolution method. Numerical results reveal the applicability and efficiency of the proposed simulation technique. [ABSTRACT FROM AUTHOR]

A random function of a variabletinT(or, a random function onT) is known as a functionfwhose values are random variables all defined on a common probability space, whereTis an arbitrary set. A random function is also called a stochastic (random) process. In this work, we base ourselves on a random function ofE-process type and such a function is also called a random function, briefly. In this approach, the domain of such a random function isor an interval of, and the set of values of this random function is considered as a special probabilistic metric (PM) space (more precisely, anE-space) of metric space-valued random variables, and all our definitions and results are presented using the tools of PM spaces. In this context, we introduce the concept of an exhaustive family of such random functions, which is a natural generalization of equicontinuity, and we investigate its basic properties. We also examine some of the properties related to the continuous convergence in probability for a sequence of such random functions and certain conditions which give rise to the continuity in probability of the limit of a sequence of such random functions. [ABSTRACT FROM PUBLISHER]

In shallow geothermal systems, the main equivalent underground thermal properties are commonly calculated with a thermal response test (TRT). This is a borehole heat exchanger production test where the temperature of a heat transfer fluid is recorded over time at constant power heat injection/extraction. The equivalent thermal parameters (thermal conductivity, heat capacity) are simply deduced from temperature data regression analysis that theoretically is a logarithmic function in the time domain, or else a linear function in the log-time domain. By interpreting the recorded temperatures as a regionalized variable whose drift is the regression function, in both cases the formal problem is a linear estimation of the mean. If the autocorrelation function (variogram, covariance) of residuals is known, coefficient variance can be directly deduced. Coefficient estimates are independent of the drift form adopted, and the residuals are the same in the same points. The random function is different in the time domain, however, and in the log-time domain. In fact, residual variograms are different due to the transformation of the coordinate space. This paper uses a TRT case study to examine the consequences of coordinate space transformation for a random function, namely its variogram. The specific question addressed is the choice of coordinate space and variogram. [ABSTRACT FROM AUTHOR]

We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area equivalence, wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual variance and hazard. Beside this, we discuss important aspects of classical approaches and discover discrepancies with the state of the art of stochastics and statistics (model selection and significance, test of distribution assumptions, extreme value statistics). We criticize especially the assumption of logarithmic normally distributed residuals of maxima like the peak ground acceleration (PGA). The natural distribution of its individual random component (equivalent to exp( ε) of Joyner and Boore, Bull Seism Soc Am 83(2):469-487, ) is the generalized extreme value. We show by numerical researches that the actual distribution can be hidden and a wrong distribution assumption can influence the PSHA negatively as the negligence of area equivalence does. Finally, we suggest an estimation concept for GMRs of PSHA with a regression-free variance estimation of the individual random component. We demonstrate the advantages of event-specific GMRs by analyzing data sets from the PEER strong motion database and estimate event-specific GMRs. Therein, the majority of the best models base on an anisotropic point source approach. The residual variance of logarithmized PGA is significantly smaller than in previous models. We validate the estimations for the event with the largest sample by empirical area functions, which indicate the appropriate modeling of the GMR by an anisotropic point source model. The constructed distances like the Joyner-Boore distance do not work well for event-specific GMRs. We discover also a strong relation between magnitude and the squared expectation of the PGAs being integrated in the geo-space for the event-specific GMRs. One of our secondary contributions is the simple modeling of anisotropy for a point source model. [ABSTRACT FROM AUTHOR]

At Eurocrypt 2004, Bellare and Kohno presented the concept of a regular hash function. For a hash function to be regular, every hash value must have the same number of preimages in the domain. The findings of their paper remained unchallenged for over six years, and made their way into several research papers and textbooks. In their paper, Bellare and Kohno claim that regular hash functions are more resistant against the birthday attack than random hash functions. We counter their arguments, by showing that the success probability of the birthday attack against a regular hash function can be made arbitrarily close to that of a random hash function (for the same number of trials). Our analysis uses the fact that the choices of the attacker can be limited to any subset of the domain. Furthermore, we prove that it is not possible to construct a hash function that is regular for only a small fraction of subsets of the domain. In order to avoid these problems, we propose to model hash functions as random functions. Compared to regular functions, we argue that the statistics of random functions are more similar to hash functions used in practice, regardless of how the attacker chooses the domain points. [ABSTRACT FROM AUTHOR]

Geostatistics is a branch of statistics dealing with spatial phenomena. Kriging consists in estimating or predicting a spatial phenomenon at non-sampled locations from an estimated random function. It is assumed that, under some well-chosen simplifying hypotheses of stationarity, the probabilistic model, i.e. the random function describing spatial variability dependencies, can be completely assessed from the dataset. However, in the usual kriging approach, the choice of the random function is mostly made at a glance by the experts (i.e. geostatisticians), via the selection of a variogram from a thorough descriptive analysis of the dataset. Although information necessary to properly select a unique random function model seems to be partially lacking, geostatistics, in general, and the kriging methodology, in particular, does not account for the incompleteness of the information that seems to pervade the procedure. The paper proposes an approach to handle epistemic uncertainty appearing in the kriging methodology. On the one hand, the collected data may be tainted with errors that can be modelled by intervals or fuzzy intervals. On the other hand, the choice of parameter values for the theoretical variogram, an essential step, contains some degrees of freedom that are seldom acknowledged. In this paper, we propose to account for epistemic uncertainty pervading the variogram parameters, and possibly the dataset, and lay bare its impact on the kriging results, improving on previous attempts by Bardossy and colleagues in the late 1980s. [ABSTRACT FROM AUTHOR]

Abstract: Computer models simulating a physical process are used in many areas of science. Due to the complex nature of these codes it is often necessary to approximate the code, which is typically done using a Gaussian process. In many situations the number of code runs available to build the Gaussian process approximation is limited. When the initial design is small or the underlying response surface is complicated this can lead to poor approximations of the code output. In order to improve the fit of the model, sequential design strategies must be employed. In this paper we introduce two simple distance based metrics that can be used to augment an initial design in a batch sequential manner. In addition we propose a sequential updating strategy to an orthogonal array based Latin hypercube sample. We show via various real and simulated examples that the distance metrics and the extension of the orthogonal array based Latin hypercubes work well in practice. [Copyright &y& Elsevier]

Self-stochasticity theory, established for certain classes of deterministic finite-dimensional dynamical systems, is extended to the continuous time difference equations [image omitted] with [image omitted] and f being continuous interval map. For such equations, self-stochasticity lies in the existence of eventually unpredictable solutions (as smooth as desired) whose long-term behaviour is described with some stochastic processes. [ABSTRACT FROM AUTHOR]

We provide reasons and evidence supporting the informal rule that the number of runs for an effective initial computer experiment should be about 10 times the input dimension. Our arguments quantify two key characteristics of computer codes that affect the sample size required for a desired level of accuracy when approximating the code via a Gaussian process (GP). The first characteristic is the total sensitivity of a code output variable to all input variables; the second corresponds to the way this total sensitivity is distributed across the input variables, specifically the possible presence of a few prominent input factors and many impotent ones (i.e., effect sparsity). Both measures relate directly to the correlation structure in the GP approximation of the code. In this way, the article moves toward a more formal treatment of sample size for a computer experiment. The evidence supporting these arguments stems primarily from a simulation study and via specific codes modeling climate and ligand activation of G-protein. [ABSTRACT FROM AUTHOR]

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimation (MLE) in the presence of ‘nuisance’ parameters. A direct application to phylogeny reconstruction is given. [ABSTRACT FROM AUTHOR]

An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained. [ABSTRACT FROM AUTHOR]

Abstract: Estimating concentrations or flow rates along a stream network requires specific models. Two classes of models, recently proposed in the literature, are generalized, to the intrinsic case in particular. We present a global construction by ‘streams’, i.e. on the whole set of paths between sources and outlet. Combining stationary or intrinsic one-dimensional random functions leads to stationary or intrinsic models on segments, with discontinuities at the forks. A construction from outlet to sources, leads to stationary or intrinsic models on each stream, without any discontinuity at the forks. The linear variogram is found as a particular case. The extension to the linear model of coregionalization is immediate, allowing a multivariate modelling of concentrations. To cite this article: C. de Fouquet, C. Bernard-Michel, C. R. Geoscience 338 (2006). [Copyright &y& Elsevier]

A method is presented for creating randomly generated polynomial functions to be used as a test bed of simulated response surfaces. The need for the test bed to perform empirical comparisons of experimental design strategies is discussed and the methods used to create the surfaces are explained. An important feature of the test bed is that the user can control some of the characteristics of the surfaces without directly controlling the surface functions. This allows the user to choose the types of surfaces on which a simulation study is run while preserving the random nature of the surfaces needed for a valid simulation study. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The geostatistical estimation proposed by the Kriging process is the best possible estimation because it provides the best linear unbiased estimation. A good example of it is the increasing number of applications in the Earth Sciences where it is used nowadays: mining industry, petrol industry, environmental study, etc. This estimator, under the condition which is obtained, shows a smoother representation of the reality that is being studied. So, an alternative for this situation is the simulation, which main aim is to present one of the possible realization of the Random Function with the same spatial variability characteristics of the reality. The principal topics of the Conditional Simulation Theory are presented in this paper. [ABSTRACT FROM AUTHOR]