non-Gaussian Random Loadings Research Articles

An approach for fatigue damage estimation under broadband non-Gaussian random loadings based on the Johnson transformation model

Estimating fatigue damage of marine structures using spectral methods under broadband random loadings is a complex and challenging task. In the presence of non-Gaussian loading, the spectral method typically employs the Hermite polynomial model (HPM) to address the non-Gaussianity. However, the applicability of HPM is limited in certain non-Gaussian cases due to the requirement of monotonicity. This paper adopts the Johnson transformation model (JTM) instead of HPM and integrates it with the non-Gaussian TB method (Ding and Chen, 2015) to overcome the constraints in broadband non-Gaussian fatigue estimation. To verify the performance of the new approach, this paper analyses the transformation accuracy of the two models. Additionally, taking the time-domain fatigue damage obtained by the rainflow counting method and the linear damage accumulation rule as a benchmark, this paper compares the fatigue damage estimates obtained from the spectral methods. The comparative assessment encompasses various spectra, S-N curves, and non-Gaussian characteristics. The results indicate the performance of JTM within the non-Gaussian TB method is comparable to HPM in most cases and even surpasses it in hardening non-Gaussian cases. Given the broader applicability of JTM across ranges of skewness and kurtosis, it emerges a superior option for the non-Gaussian TB method in estimating broadband non-Gaussian fatigue damage. Furthermore, the limitations of the proposed approach are discussed.

Study of the kurtoses transmission of linear structures under stationary non-Gaussian random loadings

Recent research has discovered that the kurtoses of non-Gaussian stress loadings can significantly impact the fatigue life of in-service structures. To predict potential damage, a fatigue life estimation method based on Gaussian damage and a kurtosis-related corrective coefficient has been developed. However, the transmission of kurtoses from excitations to responses has not been well studied, particularly in multi-input cases. This hinders efforts to accelerate fatigue damage by controlling input kurtoses. Therefore, this paper aims to establish a kurtoses transmission model for a linear structure under multiple uncorrelated stationary non-Gaussian excitations generated by zero-memory non-linear method. Firstly, a single-input kurtosis transmission equation is proposed to establish the relationship between excitation kurtosis and response kurtosis. Using this equation, the response kurtosis is formulated with input kurtosis and the system parameters of a linear structure. Secondly, the response kurtosis of multi-input cases is deduced, and the study shows that the response kurtosis is the weighted sum of the kurtosis induced by each excitation. Finally, numerical validation and experimental studies are conducted to verify the accuracy of both the single-input and multi-input kurtoses transmission models. The validations demonstrate that the proposed models can predict the response kurtoses with satisfactory precision, regardless of the input spectral shape and the number of uncorrelated input forces.

On the transmission of non-Gaussian random loading through linear structures

The kurtosis finds popular application for characterizing the non-Gaussianity of random loading. Commonly overseen is that the kurtosis has a spectral representation – the trispectrum, which provides substantial information regarding the specific nature of the non-Gaussianity and the affected frequencies. This becomes crucial when estimating the degree of non-Gaussianity that transfers into structural responses and consequently affects fatigue damage. To shed light on the mechanisms that describe the transmission of the kurtosis into structural responses of linear systems, this paper covers three central aspects. The first is an overview on estimation and visualization techniques of the trispectrum. Secondly, the transfer characteristic of the trispectrum through linear structures is examined. Lastly, on this basis, popular kurtosis control algorithms are employed to demonstrate that mechanical structures with relevant resonances are more sensitive to non-stationary non-Gaussian loading than to stationary non-Gaussian loading.

Fatigue life prediction of ship and offshore structures under wide-banded non-Gaussian random loadings: Part II: extension to wide-banded non-Gaussian random processes

Ships and offshore structures are exposed to various cyclic loads such as winds, waves and currents in their lifetime. These loads can result in fatigue failures at hot spots, and to prevent such failures, accurate estimates of the fatigue life of hot spots should be performed in the design stage. The cycle distribution indicative of the probability distribution of cycles is an important factor in estimation of fatigue damage to mechanical systems in frequency-domain methods. It depends on not only the counting method but also the statistical properties of random processes. Many studies deriving both theoretical and approximate models of rainflow-counted cycle distributions in wide-banded non-Gaussian processes have been conducted. However, some of the existing models require multi-dimensional integrations with much computational time or yield inaccurate representations of rainflow-cycle distributions. Therefore, a new model providing accurate cycle distributions is needed for fatigue analysis of offshore structures under wide-banded non-Gaussian random loadings.This paper consists of two parts: Part I is devoted to the development of a new approximation model for the joint probability distribution of mean and amplitude of rainflow-counted cycles in wide-band Gaussian random processes. This probabilistic model derived in Gaussian random processes could be transformed to the corresponding non-Gaussian processes through non-linear transformation technique. Part II discusses the detailed procedure and accuracy of the proposed model in fatigue damage assessment of offshore structures under non-Gaussian random loading. Rainflow cycle distribution in wide-band non-Gaussian processes is derived using the Hermite transformation function. The accuracy of the proposed model is verified through two numerical examples, and compared to other existing models.

Fatigue-damage prediction for ship and offshore structures under wide-banded non-Gaussian random loadings part I: Approximation of cycle distribution in wide-banded gaussian random processes

Ships and offshore structures are exposed to various cyclic loads such as winds, waves and currents in their lifetime. These loads can result in fatigue failures at hot spots, and so to prevent such failures, accurate estimates of the fatigue life of hot spots should be performed in the design stage. The cycle distribution indicative of the probability distribution of cycles is an important factor in estimation of fatigue damage to mechanical systems in frequency-domain methods. It depends on not only the counting method but also the statistical properties of random processes. Many studies deriving both theoretical and approximate models of rainflow-counted cycle distributions in wide-banded non-Gaussian processes have been conducted. However, some of the existing models require multi-dimensional integrations that require much computational time or yield inaccurate representations of rainflow-cycle distributions. Therefore, a new model providing accurate cycle distributions is needed for fatigue analysis of offshore structures under wide-banded non-Gaussian random loadings.This paper consists of two parts: Part I is devoted to the development of a new approximate model of the joint probability distribution (JPD) of mean and amplitude of rainflow-counted cycles in wide-banded Gaussian random processes. Nonlinear regression analysis is performed to approximate the conditional probability density function (PDF) of the cycle mean value. The accuracy of the proposed model was verified through two numerical examples. This probabilistic model derived in Gaussian random processes could be transformed to the corresponding non-Gaussian processes through a non-linear transformation technique. In the forthcoming Part II, the accuracy of the proposed model for fatigue-damage assessment of offshore structures under non-Gaussian random loading will be discussed.

More on variance of fatigue damage in non-Gaussian random loadings – effect of skewness and kurtosis

This work investigates the variance of fatigue damage in stationary random loadings with non-Gaussian probability distribution and narrow-band power spectral density. It presents an approach exploiting a non-linear time-invariant transformation that links Gaussian and non-Gaussian domains and that is calibrated on the skewness and kurtosis values of the non-Gaussian process. The transformation allows determining the joint probability distribution of two peaks and the cycle amplitude distribution in the non-Gaussian process, from which the variance of damage is calculated. Monte Carlo numerical simulations are finally discussed to demonstrate the correctness of the proposed model and to investigate the sensitivity of the damage variance to several parameters (S-N inverse slope, skewness and kurtosis of non-Gaussian loading).

Artificial neural network for Gaussian and non-Gaussian random fatigue loading analysis

There has been a lot of work done on the analysis of Gaussian loading analysis perhaps because its occurrence is more common than non-Gaussian loading problems. It is nevertheless known that non-Gaussian load occurs in many instances especially in various forms of transport, land, sea and space. Part of the challenge with non-Gaussian loading analysis is the increased number of variables that are needed to model the loading adequately. Artificial neural network approach provides a versatile means to develop models that may require many input variables in order to achieve applicable predictive generalisation capabilities. Artificial neural network has been shown to perform much better than existing frequency domain methods for random fatigue loading under stationary Gaussian load forms especially when mean stress effects are included. This paper presents an artificial neural network model with greater predictive capability than existing frequency domain methods for both Gaussian and non-Gaussian loading analysis. Both platykurtic and leptokurtic non-Gaussian loading cases were considered to demonstrate the scope of application. The model was also validated with available SAE experimental data, even though the skewness and kurtosis of the signal in this case were mild.

Characterizing non-Gaussian vibration loading using the trispectrum

This paper addresses the use of higher-order spectra to study the non-Gaussian nature of random vibration loading. Since the power spectral density is only a full description for stationary Gaussian processes, specifying non-Gaussian random vibration loading requires a sophisticated statistical description. In recent research higher-order statistical moments such as skewness and kurtosis have been used to define non-Gaussian properties of vibration loading. However, useful information contained in the spectral representation of these moments is neglected. This paper introduces the trispectrum as a tool for analyzing vibration loading. It is the spectral representation of the fourth-order moment and thus extends the information content of the kurtosis. For demonstration several common methods for generating non-Gaussian loading are reviewed and used to derive loads that reproduce the power spectral density and kurtosis of a real in-service loading. These loads are analyzed using Fatigue Damage Spectra and trispectra to relate structural response behavior to their non-Gaussian nature. The results suggest that the trispectrum is a valuable tool for analyzing and classifying non-Gaussian random loading.

A method for estimating rainflow fatigue damage of narrowband non-Gaussian random loadings

We describe efforts to improve the accuracy of fatigue damage estimation methods of narrowband non-Gaussian random loading. The available analytical solutions are reviewed and briefly summarized, and the reasons for the occurrence of computational errors during nonlinear transformation-based methods are determined. The computational errors are mainly due to inconsistencies in the statistical moments above fourth order. A new approach is proposed for the evaluation of rainflow fatigue damage. This approach avoids the problem of transformation-based methods and provides accurate estimation for fatigue damage of narrowband leptokurtic non-Gaussian random loading. Additionally, the applicability of the proposed method to Gaussian random loading is investigated. Finally, two examples are carried out and comparisons are made to more commonly used methods to demonstrate the capabilities and brevity of the proposed algorithm.

On the background and biresonant components of the random response of single degree-of-freedom systems under non-Gaussian random loading

The variance of the response of a single degree-of-freedom system subjected to a low frequency excitation is usually decomposed into its background and resonant contributions. In this paper we aim at the formulation of such a decomposition for the third statistical moment, which should in principle sidestep the heavy double integration of the bispectrum of the response. In large finite element models, the estimation of the bispectrum of the loading for a given frequency ( ω 1 , ω 2 ) , which is a necessary stage towards estimation of the response, is the most expensive computational task. We therefore formulate the problem with the underlying constraint that the number of estimations of the bispectrum of the force be kept as small as possible. Invoking the perturbation theory in the context of the computation of integrals, we propose to decompose the third moment into background and biresonant components with expressions that are not trivially adapted from the decomposition of the variance. Thanks to the proposed method, the double integration of the bispectrum is avoided and represents accurately the response of lightly to moderately damped structures under a low-frequency loading. The formal expression for the biresonant component still requires an integration that should preferably be avoided. In the second part of the paper, we then investigate the practical implementation of the proposed formula and study the possible application of local, global or hybrid numerical approximations of that remaining integral, so as to further increase the computational efficiency. Finally two numerical experiments illustrate the prospect of the proposed method: the third statistical moment of the response is accurately computed with less than 20 estimates of the bispectrum of the loading, whereas an advanced numerical procedure for the double integration would require a mesh of probably more than (a) thousand(s) points.

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 life under non-Gaussian random loading from various models

Fatigue test results on the 10HNAP steel under constant amplitude and random loading with non-Gaussian probability distribution function, zero mean value and wide-band frequency spectrum have been used to compare the life time estimation of the models proposed by Bannantine, Fatemi–Socie, Socie, Wang–Brown, Morel and Łagoda–Macha. Except the Morel proposal which accumulates damage step by step with a proper methodology, all the other models use a cycle counting method. The rainflow algorithm is used to extract cycles from random histories of damage parameters in time domain. In the last model, where a strain energy density parameter is employed, additionally spectral method is evaluated for fatigue life calculation in the frequency domain. The best and very similar results of fatigue life assessment have been obtained using the models proposed by Socie and by Łagoda–Macha, both in time and frequency domains for the last one.

Frequency-Domain Analysis of Offshore Platform in Non-Gaussian Seas

A frequency-domain solution approach for the response of a system whose inputs are nonlinear transformations of non-Gaussian (nonlinear) wave kinematic processes is introduced. Particularly, this paper compares the probabilistic response characteristics of jacket-type platforms in deep water that are subjected to both Gaussian and non-Gaussian random wave loadings. Unlike earlier analytical treatments of this class of system, a statistical description of the wave forces is first developed to reflect nonlinearities and associated non-Gaussianity in the wave field kinematics. The kinematics are derived from Laplace's equation and nonlinear boundary conditions using a second-order Stokes' perturbation expansion. The deck response resulting particularly because of the effects of the second-order contribution to the loads on an idealized platform is computed. Consideration is given to the importance of the spacing of the legs to the response of the structure. The impact of swell in addition to locally wind-gen...