non-Gaussian Loads Research Articles

Study on The Response Characteristics of Monopile Offshore Wind Turbines under Non-Gaussian loads in Typhoons

The fan structure is often seriously damaged under typhoon, so the study of the fan structure under typhoon is of great significance for its disaster prevention and mitigation. The actual measurement shows that the typhoon has obvious non-Gaussian characteristics, and the influence mechanism of this characteristic on the fan response characteristics is not clear. Therefore study the response characteristics of fans under non-Gaussian load. First, based on the autoregressive AR model, combined with the Johnson conversion model (JTM); second, the wind load is determined based on the specification; then the wind load. Finally, the response characteristics of 5MW fan are studied by characterizing the numerical cases of non-Gaussian fan with different strength of typhoon. The results show that the non-high characteristics of non-Gaussian wind field and the non-Gaussian characteristics become stronger with the strength of the non-Gaussian characteristics of wind field.

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.

Neural network-aided simulation of non-Gaussian stochastic processes

Simulation of non-Gaussian stochastic processes is of paramount importance to dynamic reliability assessment of structures driven by non-Gaussian loads. In this paper, a novel translation model based on neural network is proposed to convert the target non-Gaussian power spectrum to the underlying Gaussian power spectrum for simulating non-Gaussian stochastic processes. First, a valid neural network model, whose structure is similar to the transformation from a non-Gaussian power spectrum to its underlying Gaussian power spectrum, is established. Then, starting with an initial underlying Gaussian power spectrum, the non-Gaussian power spectrum corresponding to the target non-Gaussian distribution is obtained through the Wiener-Khintchine transform and translation process. After that, the discrete data of non-Gaussian power spectrum is employed as the input layer in the neural network above, while the discrete data of Gaussian power spectrum serves as the output layer. With the trained neural network, the required underlying Gaussian power spectrum can be directly obtained by inputting the target non-Gaussian power spectrum. Finally, Gaussian samples can be generated by using the spectral representation method, which are then converted into non-Gaussian samples via the translation process. The effectiveness, accuracy, and applicability of the proposed method are demonstrated through two numerical examples.

Special mathematical transformation-based fatigue damage estimation under narrowband non-Gaussian random loadings

The frequency-domain method for estimating fatigue damage is important and efficient for engineering applications. However, when dealing with non-Gaussian loadings, the widely used method based on Hermite polynomials model (HPM) has some limitations. To overcome this problem, this paper proposes a new frequency-domain method based on a special mathematical transformation model which was proposed by Johnson (JTM) for narrowband non-Gaussian cases. Numerical simulations are used to validate the new method. Considering different types of spectra and different combinations of kurtosis and skewness, Gaussian and non-Gaussian stress time series are generated for fatigue analysis. The fatigue damage estimates from the time-domain method based on rainflow counting and the frequency-domain methods based on HPM and JTM are compared. The results demonstrate that frequency-domain fatigue damage estimation is effective, but has some errors, which are discussed in this paper. The main finding is that JTM performs as well as HPM when non-Gaussianity is not strong. Therefore, JTM can be used as an alternative to HPM for estimating fatigue damage in the frequency domain under narrowband non-Gaussian conditions.

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.

Offshore Structural Reliability Assessment by Probabilistic Procedures—A Review

Offshore installations must be built to resist fatigue as well as extreme forces caused by severe environmental conditions. The structural reliability analysis is the popular practise to assess a variety of natural waves determined by the long-term probability distribution of wave heights and corresponding periods on the site. In truth, however, these structures are subjected to arbitrary wave-induced forces in the open ocean. Hence, it is much more reasonable to account for the changed loading characteristics by determining the probabilistic characteristics of the random loads and outcomes responses. The key challenges are uncertainties and the non-linearity of Morison’s drag element, which results in non-Gaussian loading and response distributions. This study would analyze advances achieved to date in a comprehensive probabilistic review of offshore fixed jacket-type platforms.

Fatigue Test of 6082 Aluminum Alloy under Random Load with Controlled Kurtosis.

This paper presents the results of experimental tests carried out on an electromagnetic shaker where the excited element was a specimen with additional weight attached to the slip table. The load was random with a different kurtosis parameter value, i.e., it was performed for non-Gaussian loads. The experiment was accompanied by basic fatigue calculations in the frequency domain and their verification with experimental results. A significant decrease in fatigue life was found to take place with an increase in kurtosis and the maintenance of the same standard deviation of the specimen load. The fatigue effect, caused by the deviation from the normal distribution that was described by the kurtosis parameter, on the fatigue life of aluminum alloy 6082 was presented. An analysis revealed the different amplitude probability distributions for the loading signal and the recorded deformation signal. It was concluded that there was a lack of sensitivity of the numerical model to the change in the kurtosis parameter of the distribution of random loads.

Fatigue Life Analysis of Vehicle Systems under Non-Gaussian Excitation

Fatigue life analysis is an important work in manufacturing of vehicle systems. The traditional method is to assume that stochastic loads are Gaussian type, then fatigue life is calculated by rain-flow counting, S-N curve and Miner linear damage rule. However, it is difficult to acquire accurate results by this means. In this paper, a numerical methodology is used to simulate non-Gaussian loads considering effects of skewness and kurtosis, as well as to estimate fatigue life under non-Gaussian stresses. Firstly, non-Gaussian inputs are represented by polynomial chaos expansion (PCE) and Karhunen-Loeve (KL) expansion when they are characterised using first four moments, i.e. mean, variance, skewness, kurtosis and a given correlation structure. During this process, we propose spectral decomposition to eliminate the influence of potential imaginary numbers, principal component analysis is also proposed to simplify calculating procedure in KL. Besides, original Monte Carlo sampling is replaced by quasi Monte-Carlo (QMC), which could greatly reduce the workload of numerical simulations. In order to get first four moments and correlation structure of outputs, differential equations of motion are numerically integrated by Runge-Kutta method. Meanwhile, response trajectories are represented based on PCE-KL-QMC approach. Eventually, the rain-flow counting is applied into these trajectories to obtain fatigue life variables, and a convenient formula about the saddlepoint approximations (SPA) represented by first four moments is proposed to provide fatigue life PDF. According to the above way, accurate and effective fatigue life estimation results can be presented

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.

Reliability of controlled linear systems under Gaussian and non-Gaussian loads

Civil and mechanical engineering systems are often subjected to vibrations which could alter their behaviour or even lead to their damage or failure. Generated either by man-made processes, such as traffic or equipment, or by natural processes, such as seismic or ocean waves, vibrations may be represented by stochastic processes defined over certain ranges of frequencies. Vibration-control systems have been developed to reduce the undesired response of systems subjected to random vibrations. The aim of the current paper is to compare comprehensively the performance of three popular passive vibration-suppression devices installed in linear single-degree-of-freedom (SDOF) systems subjected to Gaussian and non-Gaussian random vibrations with general frequency content, characterised by a power-spectral density function. The vibration-control systems analysed in this study are the viscous dampers (VD), the tuned-mass dampers (TMD) and the tuned-inerter dampers (TID), and their performance is assessed in terms of reliability metrics, such as the probability of failure and the first passage time. The twofold goal of this study is reached through (1) the development of explicit analytical relations of the controlled-systems’ responses to the Gaussian input; and (2) Monte Carlo simulation estimates of the reliability metrics for the systems subjected to the non-Gaussian loads.

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.

Combined stochastic lateral and in-plane loading of a stiffened ship panel leading to collapse

With harshening ocean environments and the push to extend the service life of vessels and platforms, lifetime structural design performance is an increasingly important factor to differentiate between design options. But despite many advancements in structural modeling, reliability analysis may still be too time consuming and computationally expensive to be employed for local design choices. Reliability analysis for stiffened ship panels is additionally complicated as the collapse mechanism is due to combined stochastic lateral and in-plane loading effects [1]. This paper employs the non-linear Design Loads Generator (NL-DLG) process [2] to efficiently estimate the probability of stiffened ship panel collapse while retaining the wave profiles which lead to lifetime responses. This information allows a direct comparison between panel options and highlights critical panel parameters which are strongly related to design robustness. The resulting ensemble of short NL-DLG wave profiles lead to similar statistical characteristics of the panel designs as do brute-force Monte Carlo Simulations, but reduce the required simulation time by a factor of nearly 87,000 for the same number of simulations. These directed wave profiles offer naval architects the opportunity to efficiently examine rare complex structural responses by linking high-fidelity structural and hydrodynamic models. The potential of the NL-DLG process is that relevant information about complex marine structures, even those with limit surfaces excited by combined non-Gaussian loading, can be obtained efficiently and in earlier stages of the design process via low-order surrogate models.

The importance of dynamic behaviour of vibrating systems on the response in case of non-Gaussian random excitations

Dynamic response of vibrating system subjected to non-Gaussian random loads was investigated through a set of numerical simulation on several lumped systems aimed to determine whether and in what form the dynamic behaviour of a vibrating system transfers or masks non-Gaussianity features of the input to the output response. Indeed, in several numerical and experimental activities performed on a Y-shaped specimen it was observed how the system response, both in terms of displacement or stress, changed according to an input variation (stationary and non-stationary Gaussian and non-Gaussian load time histories) and according to a change of the system frequency response function. Moreover, it was observed that even if the system was excited in its frequency range, the response remains unchanged and similar to the input in case of non-stationary and non-Gaussian load, removing preliminarily the possibility to use spectral methods for damage evaluation, going necessarily back to a more “expensive” time-domain analysis. Since the system response characteristics may change significantly according to the input excitation features and to the dynamic system parameters allowing, in some cases, the use of spectral techniques for fatigue damage evaluation also in case of non-Gaussian input loads, the aim of this paper is to understand whether and how the dynamic behaviour of a generic mechanical system transforms the non-Gaussian input excitations into a Gaussian response. To this aim several numerical displacement responses of 1-dof lumped systems characterized by different frequency response functions (resonance frequency position and damping) were analysed and investigated for different stationary and non-stationary Gaussian and non-Gaussian excitations. In such a way, it was possible to a-priori establish under what circumstances the frequency-domain approaches can be adopted to compute the fatigue damage of real mechanical systems.

The relevance of non-stationarities and non-Gaussianities in vibration fatigue

In classical fatigue of materials, the frequency contents of dynamic loading are well below the natural frequencies of the observed structure or test specimen. However, when dealing with vibration fatigue the frequency contents of dynamic loading and structure's dynamic response overlap, resulting in amplified stress loads of the structure. For such cases, frequency counting methods are especially convenient. Gaussianity and stationarity assumptions are applied in frequency-domain methods for obtaining dynamic structure's response and frequency-domain methods for calculating damage accumulation rate. Since it is common in real environments for the structure to be excited with non-Gaussian and non-stationary loads, this study addresses the effects of such dynamic excitation to experimental time-to-failure of a structure. Initially, the influence of non-Gaussian stationary excitation is experimentally studied via excitation signals with equal power density spectrum and different values of kurtosis. Since no relevant changes of structure's time-to-failure were observed, the study focused on non-stationary excitation signals that are also inherently non-Gaussian. The non-stationarity of excitation was achieved by amplitude modulation and significantly shorter times-to-failure were observed when compared to experiments with stationary non-Gaussian excitation. Additionally, the structure's time-to-failure varied with the rate of the amplitude modulation. To oversee this phenomenon the presented study proposes a non-stationarity index which can be obtained from the excitation time history. The non-stationarity index was experimentally confirmed as a reliable estimator for severity of non-stationary excitation. The non-stationarity index is used to determine if the frequencydomain methods can safely be applied for time-to-failure calculation.

Reliability Analysis of Nonlinear Vibratory Systems Under Non-Gaussian Loads

A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on polynomial chaos expansion (PCE), Karhunen–Loeve (KL) expansion, and quasi Monte Carlo (QMC). The latter is used to estimate multidimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness, and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion (EOM) are time integrated for each of the M points, and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE–KL–QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.

The frequency domain estimate of fatigue damage of combined load effects based on the rain-flow counting

Based on the rain-flow counting technique, a frequency domain method is developed for calculating the fatigue damages caused by the combined loads, which can be linear or nonlinear and Gaussian or non-Gaussian loads. Firstly, the new method is developed for the fatigue damage estimates of the combination of high and low frequency Gaussian loads, by which the ranges of the small rain-flow cycles are obtained as high frequency cycles with considering the reduction effect of low frequency loads on them; the ranges of the large rain-flow cycles are determined by means of Turkstra's rule of load combination. Secondly, the method is extended to calculate the fatigue damages caused by the nonlinear Morison load which is the combination of linear inertial and nonlinear drag forces. The method is benchmarked against the rain-flow damage estimates and compared with the existing ones. The numerical analyses show that the damages estimated by the new method are close to the rain-flow damages.

Time-Dependent Reliability Analysis Using a Vine-ARMA Load Model

A common strategy for the modeling of stochastic loads in time-dependent reliability analysis is to describe the loads as independent Gaussian stochastic processes. This assumption does not hold for many engineering applications. This paper proposes a Vine-autoregressive-moving average (Vine-ARMA) load model for time-dependent reliability analysis, in problems with a vector of correlated non-Gaussian stochastic loads. The marginal stochastic processes are modeled as univariate ARMA models. The correlations among different univariate ARMA models are captured using the Vine copula. The ARMA model maintains the correlation over time. The Vine copula represents not only the correlation among different ARMA models but also the tail dependence of different ARMA models. Therefore, the developed Vine-ARMA model can flexibly model a vector of high-dimensional correlated non-Gaussian stochastic processes with the consideration of tail dependence. Due to the complicated structure of the Vine-ARMA model, new challenges are introduced in time-dependent reliability analysis. In order to overcome these challenges, the Vine-ARMA model is integrated with a single-loop Kriging (SILK) surrogate modeling method. A hydrokinetic turbine blade subjected to a vector of correlated river flow loads is used to demonstrate the effectiveness of the proposed method.

The Use of Spectral Method for Fatigue Life Assessment for Non-Gaussian Random Loads

Abstract The well-known problem with the fatigue lifetime assessment of non-Gaussian loading signals with the use of spectral method has been presented in the paper. A correction factors that transform the non-Gaussian signal into an equivalent Gaussian signal proposed by Bracessi et al. (2009) has been used for the purpose of lifetime calculations together with Palmgren-Miner Hypothesis. The calculations have been performed for the 10HNAP steel under random non-Gaussian load with four dominating frequencies. The signal has been generated on the test stand SHM250 for random tension-compression tests. The results with zero and non-zero mean stresses have been used to calculate the fatigue life with the frequency domain method based on Dirlik’s model and with a time domain method with the use of the rainflow cycle counting algorithm. The obtained calculation results have been compared with experimental results.

Numerical simulation of non-Gaussian wind load

Compared with Gaussian wind loads, there is a higher probability of strong suction fluctuations occurrence for non-Gaussian wind pressures. These instantaneous and intermittent fluctuations are the initial cause of local damage to roof structures, particularly at the edges and corners of long-span roofs. Thus, comparative errors would occur if a Gaussian model is used to describe a non-Gaussian wind load, and structural security would not be guaranteed. This paper presents a simplified method based on the inverse fast Fourier transform (IFFT), in which the amplitude spectrum is established via a target power spectrum. Also, the phase spectrum is constructed by introducing the exponential peak generation (EPG) model. Finally, a random process can be generated via IFFT that meets the specified power spectral density (PSD), skewness and kurtosis. In contrast to a wind tunnel experiment, this method can avoid the coupled relation between the non-Gaussian and the power spectrum characteristics, and lead to the desired computational efficiency. Its fitting accuracy is not affected by phase spectrum. Moreover, the fitting precision of the kurtosis and PSD parameters can be guaranteed. In a few cases, the fitting precision of the skewness parameter is fairly poor, but kurtosis is more important than skewness in the description of the non-Gaussian characteristics. Above all, this algorithm is simple and stable and would be an effective method to simulate a non-Gaussian signal.