non-Gaussian Loads Research Articles

An exponential model for fast simulation of multivariate non-Gaussian processes with application to structural wind engineering

In order to generate the non-Gaussian loading excitations for time-domain analysis of structural response, an exponential function is used to express the relation between the non-Gaussian process and its underlying Gaussian process. Then, a set of nonlinear equations is derived to determine the coefficients of the exponential function. Based on the property of the joint density of a bivariate Gaussian vector, the relation between correlation functions is obtained. Also, the probability density function for the non-Gaussian process is provided. Therefore the exponential model is established. Further, an algorithm based on the exponential model is proposed for fast simulation of multivariate non-Gaussian processes. A numerical example, wind pressure field simulation of a large-span roof structure, indicates that non-Gaussian wind pressure time histories are generated quickly using the proposed algorithm. Moreover, the correlation functions, the power spectra, the cumulative distribution functions, and the probability histograms of the generated samples coincide well with the corresponding target curves. Hence the proposed algorithm is efficient and accurate.

Peak Factors for Non-Gaussian Load Effects Revisited

The estimation of the extreme of non-Gaussian load effects for design applications has often been treated tacitly by invoking a conventional peak factor on the basis of Gaussian processes. This assumption breaks down when the loading process exhibits non-Gaussianity, in which a conventional peak factor yields relatively nonconservative estimates because of failure to include long tail regions inherent to non-Gaussian processes. To realistically capture the salient characteristics of non-Gaussian load effects and incorporate these in the estimates of their extremes, this study examines the peak factor for non-Gaussian processes, which can be used for estimating the expected value of the positive and negative extremes of non-Gaussian load effects. The efficacy of previously introduced analytical expressions for the peak factor of non-Gaussian processes on the basis of a moment-based Hermite model is evaluated and the variance of the estimates in standard deviation is derived. In addition, some improvements ...

Probability Distribution Analysis of Structural Response under Non-Gaussian Wind Loads

Based on the theory of maximum likelihood estimation, a set of nonlinear equations is first derived for determination of parameters of Weibull distribution. To speed up convergence, an efficient algorithm is proposed for solving the parameters. Further, a large-span roof structure is taken to demonstrate the proposed method. It is proved that the responses of a nonlinear structure have non-Gaussian properties under the excitation of non-Gaussian stochastic wind pressure field. By Weibull distribution fitting, the maximum and minimum values of structural response with a certain assurance rate are computed, and the results are compared with those obtained from normal distribution.

Uncertainty of estimated rainflow damage for random loads

One way to assess the uncertainty in fatigue damage analysis is to use a so-called safety index. In the computation of such an index the coefficient of variation for the accumulated damage is needed. Employing the rainflow cycle count method for fatigue damage leads to, in most cases, complicated calculations. Here we present a new and simplified method to estimate the coefficient of variation for the accumulated damage when only one sample path of the load is available. Non-stationary, slowly changing, Gaussian loads are given special attention. The approach is illustrated by means of stationary Gaussian loads with nine different spectra, a measured non-Gaussian load, a skewed load and the wave load accumulated during one year in a “seasonally changing environment”.

Influence of Non-Gaussian Local Wind Pressures on Fatigue Damage of a Cladding Fastener on a Side Face of a Tall Building

The action of wind pressures is a major consideration in the design of cladding and its connections to building structures. Non-Gaussian environmental loads often may appropriately be reduced to Gaussian loads through the central limit theorem, e.g., integral loads on a building under wind loads. However, for the design load of cladding and its connections to building structures the Gaussian assumption is not valid and loads remain non-Gaussian, especially in separated flow regions. When the loads differ significantly from Gaussian distribution, they may lead to increase expected damage. In this study, the wind-induced high-cycle fatigue damage of a cladding fastener subjected to non-Gaussian local wind pressures and corresponding simulated Gaussian local wind pressures is estimated by using the rainflow cycle counting method and Miner’s rule. The fatigue damage is compared with each other in order to investigate the influence of non-Gaussian local wind pressures on the fatigue damage of a cladding fastener on the side face of a tall building.

Fatigue damage in randomly vibrating jack-up platforms under non-Gaussian loads

The problem of fatigue damage estimation of ageing jack-up platforms is considered, using theories of random processes. The sea-wave excitations are modelled as stationary, Gaussian random processes, with specified power spectral density function. The loads acting on the structure due to the sea waves is calculated using Morison’s equation and are therefore non-Gaussian whose probabilistic properties are not available in explicit form. Assuming linear structure behaviour, the probabilistic properties of the structure response are determined using theories of random vibrations. The simple peak counting method is adopted for estimating the mean fatigue damage. This requires knowledge of the joint probability density function of the structure response and its first and second time derivatives, at the same time instant. A methodology has been presented for developing analytical expressions for this joint pdf. This requires evaluation of multidimensional integrals. A recently developed computational algorithm is presented to deal with integrals for which derivation of closed form analytical expressions may not be feasible. The methodology proposed in this paper provides an alternative and computationally cheaper technique for estimating the fatigue damage in comparison to the Monte Carlo simulation procedure. Numerical results have been presented for illustration of the proposed methodology.

A Practical Formulation for Evaluating Combined Fatigue Damage From High- and Low-Frequency Loads

Based on Gaussian load processes, a new formula suitable for evaluating the combined fatigue damage due to high- and low-frequency loads is derived. Then, by using of the Winterstein’s transformation, the developed formula is extended for the combination of non-Gaussian loads. The numerical simulation shows that the predicted damage by the derived formula is very simple to use and close to the rain-flow prediction.

Fatigue life assessment in non-Gaussian random loadings

This paper treats the theoretical fatigue analysis of non-Gaussian random loadings. It first reviews a method recently developed by the Authors, which is capable to account for the effect of load bandwidth and non-normality. Fatigue lives from simulated Gaussian and non-Gaussian loadings, as well as data from experiments taken from the literature, are compared with theoretical estimations. The non-Gaussian loading was modelled as a transformed Gaussian process. The results show how the load non-normality has a great effect on both the cycle distribution and the fatigue damage; the proposed method seems able to account for this effect correctly. Furthermore, the theoretical predictions are shown to be substantially comparable (with some exceptions) with the experimental data.

Fatigue lifetime of welded joints under random loading: rainflow cycle vs. cycle sequence method

The evaluation of fatigue lifetime is a complex problem due to the loading cycle sequence effect influencing the fatigue damage process. In the literature two different approaches are usually adopted to solve the fatigue crack growth under time varying loading: the rainflow cycle (RFC) and the cycle sequence (CSQ) model. In this paper the performance of the recently proposed stochastic version of these methods is compared and applied to the evaluation of the fatigue lifetime of the welded cruciform tested in the literature. Non-Gaussianity and bandwidth effect are correctly captured by both methods but only the CSQ model enables us to examine the influence of the load sequence effect on the fatigue lifetime. Numerical results show that the retardation effect can be neglected for Gaussian and non-Gaussian loading as the bandwidth increases. Finally, this work shows the greater performance and flexibility of the CSQ model compared to the RFC model.

Random response of Duffing oscillator to periodic excitation with random disturbance

This paper discusses the random response of a non-linear Duffing oscillator subjected to a periodic excitation with random phase modulation. Effects of uncertainty in the periodic excitation and level of the system non-linearity on the response moments and non-Gaussian nature of the response caused by both the system non-linearity and the non-Gaussian loading are investigated. Results are presented in terms of the second- and the fourth-order moments as well as the excess factor of the response and some results are compared with those from the Monte Carlo simulation. An iterated linearisation technique is proposed to improve the accuracy of the numerical results for strongly non-linear systems.

Simulation of Correlated Non-Gaussian Pressure Fields

Abstract. Among a host of techniques developed for the analysis and prediction of nonlinear structural response, simulation methods are gaining popularity as computational efficiency increases. Implementation of time domain methods require simulated load time histories with case-specific statistical and spectral characteristics. When the assumption of Gaussian wind loading is inappropriate, techniques for simulating non-Gaussian loading must be sought. Over a larger expanse of building surface, simulation of correlated loads at several spatially separated locations is required. This work introduces a multi-variate non-Gaussian simulation method capable of producing realizations with a wide range of spectral and probabilistic characteristics. The correlation between multiple locations is accurately simulated simultaneously, while retaining the appropriate spectral and probabilistic content at each location.

Markov based correlations of damage cycles in Gaussian and non-Gaussian loads

The sequence of peaks and troughs in a load process acting on a material, contains important information about the damage caused by the load, e.g. on the growth rate of a widening crack. The stress range, i.e. the difference between a peak and the following trough, is one of the variables that is used to describe e.g. fatigue life under random loading. The moments, in particular the mean and variance, of the load range are important variables that determine the total damage caused by a sequence of stress cycles, and they give the parameters in the distribution of the time to fatigue failure. However, for many random load processes, the successive stress ranges can show considerable correlation, which affects the failure time distribution. In this paper we derive the modified failure time distribution under correlated stress ranges, under a realistic approximation that the sequence of peaks and troughs forms a Markov chain. We use the regression method to calculate the transition probabilities of the Markov chain for Gaussian load processes with known spectral density. Simulations of Gaussian processes with Pierson-Moscowitz spectrum, and linear and the Duffing oscillators driven by Gaussian white noise, show very good agreement between observed correlations and those calculated from the Markov approximation. Also the numerically calculated transition probabilities lead to good agreement with simulation.

Fatigue of welded joints under narrowband non-Gaussian loadings

Analytical and experimental results are presented to determine the effect of non-normality of the loading process on the rate of fatigue damage accumulation in welded steel joints. All stochastic loadings used are narrowband and the parameter kurtosis is used to measure the degree of non-normality of the loading processes. Non-normal loadings are generated by passing Gaussian loadings through non-linear transformation functions. p] Results of the analytical study as well as results of fatigue experiments on welded cruciform specimens indicate that non-normality can significantly influence the rate of fatigue damage accumulation. Errors in fatigue life prediction can vary from slightly conservative to very unconservative by assuming a normal response when it is not. Results of random load experiments indicate that an endurance limit observed under constant amplitude tests does not convey to random load response.

Extreme wind load distributions for linear and nonlinear design

Ever increasing demand for economical design and construction has led to the use of more sophisticated design methods which take into account nonlinear effects. Strictly speaking, for these design methods the known procedures to estimate the wind-induced reactions fail since their applicability is limited to linear systems. A new method, the load-response-correlation (LRC) method, which is presented in this paper, helps to bridge this gap, and enables the designing engineer to take into account a realistic spatial distribution of the wind loads which produce accurate peak structural responses for the linear design and a good approximation for nonlinear effects. Although the identification of the critical load distribution is based on the assumption of Gaussian properties of the load process, the method gives a very close approximation of the real load pattern for non-Gaussian load processes so that, for practical purposes, the confinement to Gaussian properties will be sufficient.

A study of linear combination of load effects

The performance of a combination formula, extensively used in stochastic dynamics for estimating extreme values of linear combination of load effects, is investigated. It is shown that this combination formula is nearly optimal in the case of independent Gaussian load effect components. For non-Gaussian load effects the performance is investigated by studying specific examples, and it is shown that the accuracy deteriorates significantly.