Extreme value distributions for nonlinear transformations of vector Gaussian processes

Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

In this contribution, we present the exact asymptotic behavior of the Parisian ruin probability for specific classes of conditionally Gaussian random processes, as the initial capital approaches infinity. We consider a risk process as a mixture of Gaussian and non-Gaussian random processes, where the aggregate claim process is modeled as a Gaussian process (stationary or non-stationary), while the premium income is represented by a different random process that is independent of the claim process.

A spectral method for accurate evaluation of fatigue damage induced by wide-band non-Gaussian random processes

Karhunen-Loeve(KL) expansion of auto-covariance of input Gaussian random process is carried out using standard normal variables as the basis of KL expansion. Input random processes for many practicle problems have non-Gaussian random process description, so an algorithm is developed to find the basis random variables of KL expansion for non-Gaussian processes. The basis random variables of KL expansion are obtained via nonlinear transformation of marginal cumulative distribution function using standard deviation. Results are obtained for three known skewed distributions, Log-Normal, Beta, and Exponential. In all the cases, it is found that the proposed algorithm matches very well with the known solutions and can be applied to solve non-Gaussian process using Spectral Stochastic Finite Element Method.

In this paper, a direct simulation algorithm is presented for the generation of a class of non-Gaussian stochastic processes according to target lower-order moments and prescribed power spectral density (PSD) function. The proposed algorithm is to expand the autoregressive (AR) model and the autoregressive moving average (ARMA) model, which are available to generate Gaussian random process, to simulate directly non-Gaussian stochastic process. The coefficients of the AR or ARMA model are determined based on the prescribed PSD function. It is well known that outputting stochastic process is also non-Gaussian if inputting white noise is non-Gaussian. But the skewness and kurtosis of the outputting non-Gaussian random process are not identical to these of inputting non-Gaussian white noise. In this paper, the relationships of lower-order moments such as skewness and kurtosis between output and input are analyzed and close to linear transformations. To corroborate the feasibility and correctness of the present methodology, numerical examples involving simulation of fluctuating wind pressures are taken into consideration. Numerical results indicate that the skewness and kurtosis of generated wind pressures based on the AR or ARMA model closely match their targets. In addition, the PSD and correlation functions of simulated samples also show considerably good agreement with prescribed functions. Therefore, the proposed algorithm is effective to simulate directly the class of non-Gaussian stochastic process.

A new dissimilarity method integrating multidimensional mutual information and independent component analysis for non-Gaussian dynamic process monitoring

For time-dependent reliability methods, there is a lack of analytical solutions to outcrossing rates of nonstationary and non-Gaussian processes. This paper aims to propose an analytical method to determine this type of outcrossing rate with improved accuracy and efficiency. The novelty of this proposed method is that it can consider the probabilistic properties of non-Gaussian processes by combining a two-component parallel system model with higher-order moments-based reliability indexes. The main contributions of this method are: (1) compared with PHI2+ method, it is more accurate for the calculation of the outcrossing rate of nonstationary and non-Gaussian processes with nonlinear limit state functions; (2) compared with MPHI2 method, it is analytical and not only applicable for the nonstationary stochastic processes but also insensitive to time increments; and (3) it is not only more accurate than the existing methods for nonstationary and non-Gaussian processes but also more computation efficient than the Monte Carlo simulation method. The proposed method has shown its advantages for practical structures with neither Gaussian processes nor linear limit state functions, which are beneficial for both researchers and asset managers to evaluate the time-dependent reliability of structures accurately and to develop risk-informed maintenance schemes with a view to prolonging their service life.

The autocorrelation function (ACF) of a non-Gaussian random process, obtained by the memoryless nonlinear transformation of a Gaussian process with a known ACF, is calculated as a power series with coefficients expressed as one-dimensional integrals. In general these must be evaluated numerically; two analytically tractable special cases are also considered. In cases of practical interest the series has been found to converge rapidly. These results are then used in the simulation of a non-Gaussian process with a specified ACF, which can take values less than the square of its mean. Our approach is compared with other methods in the open literature. Examples are given of time series and random fields with gamma single-point statistics that provide controlled models of high-resolution radar clutter.

RESPONSE STATISTICS OF OCEAN STRUCTURES TO NON-LINEAR HYDRODYNAMIC LOADING PART II: NON-GAUSSIAN OCEAN WAVES

In radar problems involving weak signal detection conventional space-time processing cannot be used to separate the target from the clutter when the spatial and Doppler spectra of the target and clutter overlap. In such problems the concept of the locally optimum detector (LOD) is useful in coming up with a decision rule to discriminate between the two hypotheses of signal present or signal absent. The clutter, which may be correlated, can arise from either a non-Gaussian or Gaussian random process. For correlated multivariate K-distributed clutter it is shown in this paper that performance improvements can be obtained with an LOD receiver compared to the conventional Gaussian linear receiver.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, a new multivariate counting process model (called Multivariate Poisson Generalized Gamma Process) is developed and its main properties are studied. Some basic stochastic properties of the number of events in the new multivariate counting process are initially derived. It is shown that this new multivariate counting process model includes the multivariate generalized Pólya process as a special case. The dependence structure of the multivariate counting process model is discussed. Some results on multivariate stochastic comparisons are also obtained.

We set up a general framework for modeling non-Gaussian multivariate stochastic processes by transforming underlying multivariate Gaussian processes. This general framework includes multivariate spatial random fields, multivariate time series, and multivariate spatio-temporal processes, whereas the respective univariate processes can also be seen as special cases. We advocate joint modeling of the transformation and the cross-/auto-correlation structure of the latent multivariate Gaussian process, for better estimation and prediction performance. We provide two useful models, the Tukey g-and-h transformed vector autoregressive model and the sinh-arcsinh-transformed multivariate Matérn random field. We evaluate them with a simulation study. Finally, we apply the two models to a wind data set for modeling the two perpendicular components of wind speed vectors. Both the simulation study and data analysis show the advantages of the joint modeling approach.

The aim of this article is to find a rational solution for increasing the safety of level crossings in the Czech Republic on the basis of a set of representative level crossings. The Czech Republic was deliberately chosen because of its geographical location, the number of level crossings on the network, and because, according to statistics from the Rail Safety Inspection Office, the country ranks as one of the highest for the number of accidents at level crossings. The rational solution being sought is one that achieves a balance between legislative, technical, and awareness-raising measures. In the practical part, great emphasis is placed on the assessment of the current state of Czech legislation. The identified discrepancies are resolved by adjusting calculations for overview distances and proposing changes to incorrect provisions. The main contribution of this paper is the comprehensive overview that it provides of level crossings and their safety. This overview includes a description of the current state of affairs, i.e., the number of level crossings, their location, classification, construction and type of equipment used, as well as an analysis of accidents and their frequency. The latter is in relation to the proposed construction and technical solution and subsequent assessment of the rationalisation possibilities and investments required to reconstruct or remove existing level crossings, thereby affecting the accident rate.

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. To this end, the conventional (Monte Carlo) time simulation technique (CTS) is frequently used for predicting the probability distribution of the extreme values of response. However, this technique suffers from excessive sampling variability and hence a large number of simulated extreme responses (hundreds of simulated response records) are required to reduce the sampling variability to acceptable levels. A more efficient version of the time simulation technique (ETS) was recently introduced which takes advantage of the correlation between the extreme surface elevations and their corresponding extreme responses by dividing the simulated extreme responses into a number of groups based on the magnitude of their associated extreme surface elevations. The probability distribution of response extreme values for each group is then calculated individually based on a relatively small number of simulations, and then the total probability theorem is used to derive the probability distribution of response extreme values. The ETS procedure is found to be many times more efficient than the CTS method. However, its efficiency and accuracy reduces for sea states of lower intensity. In this paper, a more efficient version of the ETS technique is introduced which takes advantage of the correlation between extreme values of the nonlinear response and their corresponding linear response extreme values (both quasi-static and dynamic linear responses are considered)). The three different versions of the ETS technique are compared by exposing a test structure to sea states of different intensity. It is demonstrated that the extreme linear response versions of the ETS technique are more accurate and efficient than the version based on surface elevation extreme values.

Importance sampling for reliability assessment of dynamic systems under general random process excitation