| 1. |
- Ahlqvist, Max, et al.
(author)
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Probabilistic evaluation of the Step-Stress fatigue testing method considering cumulative damage
- 2023
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In: Probabilistic Engineering Mechanics. - : ELSEVIER SCI LTD. - 0266-8920 .- 1878-4275. ; 74
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Journal article (peer-reviewed)abstract
- A general testing and analysis framework for the Step-Stress fatigue testing method is identified, utilizing interval-censored data and maximum likelihood estimation in an effort to improve estimation of fatigue strength distribution parameters has been performed. The Step-Stress methods limitations are characterized, using a simple material model that considers cumulative damage to evaluate load history effects. In this way, the performance including cumulative damage was evaluated and quantified using a probabilistic approach with Monte-Carlo simulations, benchmarked against the Staircase method throughout the work. It was found that the Step-Stress method, even when cumulative damage occurs to a wide extent, outperforms the Staircase method, especially for small sample sizes. Furthermore, positive results reaches further than the increase performance in estimating fatigue strength distribution parameters, where improvements in secondary information, i.e. S-N data gained from failure specimens, are shown to be distributed more closely to the fatigue life region of interest.
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| 2. |
- Allahvirdizadeh, Reza, et al.
(author)
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Partial safety factor calibration using surrogate models : An application for running safety of ballasted high-speed railway bridges
- 2024
-
In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 75
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Journal article (peer-reviewed)abstract
- Traditionally, regulations employ semi-probabilistic methods with partial safety factors to control design limits. Calibrating these partial safety factors involves estimating the target reliability level and optimizing the partial safety factor values in order to minimize the deviation of the safety index between the considered design scenarios and the target value. This procedure necessitates performing a demanding amount of reliability analyses and is often carried out for simplified design situations. Therefore, high computational costs must be accepted for design problems formulated with complex computational models. This study implements a meta-modeling approach based on active learning in the partial safety calibration procedure, enabling its application to computationally intensive problems. Subsequently, the approach is applied to the running safety of ballasted high-speed railway bridges. This limit state implicitly accounts for the phenomenon of ballast destabilization, the occurrence of which disturbs the load path from the rail level to the bridge structure. The dramatic increase in train operating speeds in recent decades has increased the possibility of this design limit state being violated due to resonance. Despite the evident safety concerns, the adopted safety factors appear to be solely based on engineering judgments rather than calibration through higher-level reliability analysis. Therefore, the proposed calibration method is employed to determine the corresponding partial safety factors for various maximum allowable operating train speeds. The newly calibrated partial safety factors allow for a permissible maximum vertical acceleration of the bridge deck approximately 25% higher than the conventional design approaches. Therefore, incorporating these factors into the design procedure may lead to the construction of lighter bridges.
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| 3. |
- Allahvirdizadeh, Reza, et al.
(author)
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Surrogate-assisted investigation on influence of epistemic uncertainties on running safety of high-speed trains on bridges
- 2024
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 75
-
Journal article (peer-reviewed)abstract
- The operational safety of high-speed trains traversing ballasted bridges is contingent upon the prevention of the ballast destabilization, which can interrupt load transfer from the rail to the bridge. Current design regulations indirectly address this limit-state by specifying a threshold value for the vertical acceleration of the superstructure. This value represents the condition at which the inertial forces induced by train passage exceed the resistive forces. However, this approach is based on limited experimental data and the influence of numerous parameters remains unexplored. As a result, reliability analyses pertaining to running safety are hampered by a lack of knowledge, leading to greater epistemic uncertainties. In this study, the impact of such uncertainties on this dynamic system is investigated using surrogate-based Imprecise Structural Reliability Analysis (ISRA). For this purpose, parametric probability boxes are used to represent lower and upper bounds of the cumulative distribution function for basic random variables with epistemic uncertainties and surrogate models are adaptively trained to reduce computational costs. The obtained results show that neglecting the influence of epistemic uncertainties can lead to permissible operating train speed higher than the speed corresponding to the desired reliability level. In this study, an overestimation of about 13% was observed on average. Furthermore, the rough analyses carried out show that taking epistemic uncertainties into account can lead to a reduction of the system characteristic safety factor by up to 30%. This significant reduction underlines the importance of expanding the available knowledge on the phenomenon of ballast instability.
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| 4. |
- Bengtsson, Anders, et al.
(author)
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Uncertainty in fatigue life prediction of structures subject to Gaussian loads
- 2009
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 24:2, s. 224-235
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Journal article (peer-reviewed)abstract
- In this paper we shall concentrate on Gaussian (or close to Gaussian) loads acting on a structure. The goal is to compute a measure of risk for fatigue of a component during a specific time period and the so called "safety index" will be used to combine different types of uncertainties. The presented methodology can be applied in a more general situation of environmental loads which properties may vary with time of the year. The load is assumed to be "locally" stationary such that the mean load is constant (and taken to be zero) but the variance of the load can change slowly with time. Non-stationary hierarchical processes, separable into a stationary Gaussian process and a process describing the load amplitude and period, e.g. processes with Pierson-Moskowitz or JONSWAP spectrum, are treated in detail. The variability of a load, relevant for the fatigue accumulation process, will be described by means of rainflow cycles counted in the load. Moreover, common damage intensity approximations are reviewed and evaluated in a simulation study. © 2008 Elsevier Ltd. All rights reserved.
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| 5. |
- Gibanica, Mladen, 1988, et al.
(author)
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Data-driven modal surrogate model for frequency response uncertainty propagation
- 2021
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 66
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Journal article (peer-reviewed)abstract
- A method is developed for propagation of model parameter uncertainties into frequency response functions based on a modal representation of the equations of motion. Individual local surrogate models of the eigenfrequencies and residue matrix elements for each mode are trained to build a global surrogate model. The computational cost of the global surrogate model is reduced in three steps. First, modes outside the range of interest, necessary to describe the in-band frequency response, are approximated with few residual modes. Secondly, the dimension of the residue matrices for each mode is reduced using principal component analysis. Lastly, multiple surrogate model structures are employed in a mixture. Cheap second-order multivariate polynomial models and more expensive Gaussian process models with different kernels are used to model the modal data. Leave-one-out cross-validation is used for model selection of the local surrogate models. The approximations introduced allow the method to be used for modally dense models at a small computational cost, without sacrificing the global surrogate model's ability to capture mode veering and crossing phenomena. The method is compared to a Monte Carlo based approach and verified on one industrial-sized component and on one assembly of two car components.
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| 6. |
- Gupta, S., et al.
(author)
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Rain-flow fatigue damage due to nonlinear combination of vector Gaussian loads
- 2007
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 22:3, s. 231-249
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Journal article (peer-reviewed)abstract
- The problem of estimating the mean rain-flow fatigue damage in randomly vibrating structures is considered. The excitations are assumed to be through a vector of mutually correlated, stationary Gaussian loadings. The load effect leading to fatigue damage is considered to be a nonlinear function of the vector of excitation loads and is thus non-Gaussian. Its probabilistic characteristics are, however, unknown. The fatigue damage is assumed to follow a linear damage accumulation rule. Though exact expressions for the mean fatigue damage are difficult to determine, approximations and bounds for the mean rain-flow fatigue damage can be developed. Computing these quantities requires the mean level crossing statistics for the associated non-Gaussian response to be estimated. For the special case when the load effect can be expressed as quadratic combinations of Gaussian processes, analytical expressions are developed for computing the level crossing statistics. These, in turn, are used to determine approximations and the bounds for the mean fatigue damage. The applicability of the proposed method is demonstrated through a numerical example. With respect to this example, a comparative study on the quality of the bounds and the approximations is carried out viz-viz the predictions from existing techniques available in the literature. (c) 2007 Elsevier Ltd. All rights reserved.
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| 7. |
- Hildeman, Anders, 1984, et al.
(author)
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Joint spatial modeling of significant wave height and wave period using the SPDE approach
- 2022
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 68
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Journal article (peer-reviewed)abstract
- The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with this journey. Two important characteristics of the sea state are significant wave height and mean wave period. We propose a joint spatial model of these two quantities on the north Atlantic ocean. The model describes the distribution of the logarithm of the two quantities as a bivariate Gaussian random field, modeled as a solution to a system of coupled fractional stochastic partial differential equations. The bivariate random field is non-stationary and allows for arbitrary, and different, smoothness for the two marginal fields. The parameters of the model are estimated from data using a stepwise maximum likelihood method. The fitted model is used to derive the distribution of accumulated fatigue damage for a ship sailing a transatlantic route. Also, a method for estimating the risk of capsizing due to broaching-to based on the joint distribution of the two sea state characteristics is investigated. The risks are calculated for a transatlantic route between America and Europe using both data and the fitted model. The results show that the model compares well with observed data. It further shows that the bivariate model is needed and cannot simply be approximated by a model of significant wave height alone. © 2022 Elsevier Ltd
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| 8. |
- Jith, J., et al.
(author)
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Crossing Statistics of Quadratic Transformations of LMA Processes
- 2013
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 33, s. 9-17
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Journal article (peer-reviewed)abstract
- Random loads that exhibit significant non-Gaussianity in terms of asymmetric distributions with high kurtosis can be modeled as Laplace Moving Average (LMA) processes. Examples of such loads are the wave loadings in ships, wind loads on wind turbines, loads arising due to surface roughness in vehicular systems, etc. The focus of this paper is on estimating the crossing statistics of second-order response of structures subjected to LMA loads. Following the Kac–Siegert representation, a second order approximation of the Volterra expansion of the system enables representing the response as a quadratic combination of vector LMA processes. The mean crossing rate of the response is then computed using a hybrid approach. The proposed method is illustrated through two numerical examples.
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| 9. |
- Johannesson, Pär, 1969, et al.
(author)
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AR(1) time series with autoregressive gamma variance for road topography modeling
- 2016
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 43, s. 106-116
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Journal article (peer-reviewed)abstract
- A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) process with randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal. A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed. The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressive process is fitted from the autocorrelation of the squared values of the model. The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution. Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method. It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely Gaussian model.
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| 10. |
- Kvarnström, Mats, 1974, et al.
(author)
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Laplace moving average model for multi-axial responses applied to fatigue analysis of a cultivator
- 2013
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In: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 34, s. 12-25
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Journal article (peer-reviewed)abstract
- Modeling of loads on a vehicle through Laplace moving averages is extended to the multivariate setting and efficient methods of computing the damage indexes are discussed. Multivariate Laplace moving averages are used as statistical models of multi-axial loads represented by forces and moments measured at some locations of a cultivator. As opposed to models based on the Gaussian distribution, these models account explicitly for transients that have a common origin—vibrations that can be caused by large obstacles encountered by a cultivator or a vehicle driving into potholes. The model is characterized by a low number of parameters accounting for fundamental characteristics of multivariate signals: the covariance matrix representing size of loads and their mutual dependence, the excess kurtosis that in the model is related to relative size of transients, and the time scale that accounts for the vehicle speed. These parameters can be used to capture diversity of environmental conditions in which the vehicle operates. Distributions of parameter values that are specific to a given market or encountered by specific customers can be then used to describe the long term loading. The model is validated by analysis of the resulting damage index. It is shown that the parameters enter this index in a multiplicative and explicit manner and, for a given damage exponent, only the factor representing dependence on the kurtosis has to be obtained through regression approximation based on Monte Carlo simulations. An example of actual cultivator data is used to illustrate the accuracy of damage and fatigue life prediction.
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