Journal of Engineering Mechanics-asce, Aug 1, 2008
... (2007). Clustering effects on the extreme response statistics for dynamical systems. Proc.,... more ... (2007). Clustering effects on the extreme response statistics for dynamical systems. Proc., 5th Int. ... (2007). An importance sampling procedure for estimating failure probabilities of nonlinear dynamic systems subjected to random noise. Int. J. Non-Linear Mech., 42, 848863. ...
The paper describes a novel approach to the problem of estimating the extreme response statistics... more The paper describes a novel approach to the problem of estimating the extreme response statistics of a drag-dominated offshore structure exhibiting a pronounced dynamic behaviour when subjected to harsh weather conditions. It is shown that the key quantity for extreme response prediction is the mean upcrossing rate function, which can be simply extracted from simulated response time histories. A commonly adopted practice for obtaining adequate extremes for design purposes requires the execution of 20 or more 3-h time domain analyses for several extreme sea states. For early phase considerations, it would be convenient if extremes of a reasonable accuracy could be obtained based on shorter and fewer simulations. The aim of the work reported in the present paper has therefore been to develop specific methods which make it possible to extract the necessary information about the extreme response from relatively short time histories. The method proposed in this paper opens up the possibility to predict simply and efficiently both short-term and long-term extreme response statistics. The results presented are based on extensive simulation results for the Kvitebjørn jacket structure, in operation on the Norwegian Continental Shelf. Specifically, deck response time histories for different sea states simulated from an MDOF model were used as the basis for our analyses.
Extreme value prediction of the load-effect responses of complex offshore structures such as the ... more Extreme value prediction of the load-effect responses of complex offshore structures such as the floating wind turbine (FWT) is crucial in ultimate limit state (ULS) design. This paper considers two cases to understand the feasibility of the bivariate correction on the extreme load and motion responses of a 10-MW semi-submersible type FWT. The empirical anchor tension force and surge motion used in this study are obtained from the FAST simulation tool (developed by the National Renewable Energy Laboratory) with the load cases stimulated at underrated , rated and above rated speeds. Then, the bivariate correction method is applied to model FWT extreme response for a 5-years return period prediction with a 95% confidence interval (CI), based on just 2 min short response record. The proposed methodology permits accurate correction of the bivariate extreme value in case of, for example, corrupted measurement sensor data. Based on the proposed novel method's performance, it is concluded that the bivariate correction method can offer better robust and precise bivariate predictions of coupled surge motion and anchor tension of the FWT.
Introduction The first step in planning response analysis is whether the analysis can be accompli... more Introduction The first step in planning response analysis is whether the analysis can be accomplished as a static one or whether a dynamic model must be used. Dynamic analyses are generally necessary in connection with transient loads; otherwise, the results may be significantly conservative or nonconservative. For load processes consisting of several harmonic components, the main criterion is whether the load process contains energy in the range of eigenfrequencies of the system. Figure 14.1 shows an overview of the largest eigenperiod (natural period) of vibration or motion of offshore structures, as well as the relevant range of periods of dynamic loads associated with waves. Solution of Equations of Motion General The equations of motion for a linear structural system (Section 4.10) may be solved in the time or frequency domain. The choice of formulation especially depends on: The nature of the loading; i.e., whether it is steady state or transient (which often involves response in a wide frequency band). Frequency dependence of the dynamic properties (mass, damping, Nonlinear features of the loading or dynamic properties. In Chapter 2, solutions of the equation of motion for SDOF systems with different load conditions are described. If the solution method either in time or frequency domain is formulated for the coupled system of equations in Eq. (14.1), the method is denoted as direct.
International Journal of Mechanical Sciences, Jul 1, 2018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights A unique analytical solution available for biaxially excited Jeffcott rotor system was used to validate the proposed advanced path integration technique Dynamic system stability and extreme response statistics have been studied Novel improvements to an existing Path Integration scheme have been discussed (e.g. using MC preestimated initial PDF) Numerical results were in a good agreement with analytical results, therefore main contribution of this paper is a 100 percent reliable and independent confirmation of the path integration technique as a tool for assessing the dynamics of the kind of stochastic mechanical models considered in this paper
Introduction This chapter deals with vibrations of structures that can be represented as a single... more Introduction This chapter deals with vibrations of structures that can be represented as a single degree-of-freedom (SDOF) system. This means that the oscillatory response can be completely described by one displacement variable. This may seem like a gross oversimplification for structures of engineering interest that leads to a theory of little practical significance. However, the theory of vibrations for systems of an SDOF is crucial for understanding the vibration response of more complex structures. Frequently, it is also the case that one may investigate the vibration response characteristics of apparently complex structures by directly applying the theory of vibrations of SDOF systems. This is demonstrated in Chapter 3 on multi-degrees-of-freedom (MDOF) structures. The word “vibration” used in this chapter should be interpreted as meaning oscillatory response in a fairly general sense, e.g., as applied to marine structures. Harmonic Oscillator – Free Vibrations Free vibrations or oscillations occur when there are no external forces imposed on the structure, e.g., after an initial displacement and release. Two different situations are discussed: translational oscillations and rotational oscillations. Motions of Marine Structures Because the main focus of this book is the motion response of marine structures, it is expedient to define the terms commonly used to describe the rigid-body motions of floating structures. This is most easily done by referring to Fig. 2.1. For a shiplike structure, it is common practice to place the x -axis along the beam of the ship (for the body-fixed coordinate system), and call the corresponding translational motion for surge.
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white nois... more Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
The paper discusses the problem, of linearization for the purpose of simplified calculation of lo... more The paper discusses the problem, of linearization for the purpose of simplified calculation of long-term fatigue damage in offshore structures. Specific linearization procedures are proposed that may be better suited to deal with the problem of fatigue life calculation than the standard mean square stochastic linearization (MSSL). These are based on minimizing higher order moments of the linearization error, and it is indicated how the optimal order is linked to the street exponent of the S-N curve. It is shown by specific example studies that the proposed method may lead to substantial improvement over MSSL in estimating fatigue damage.
Journal of Engineering Mechanics-asce, Aug 1, 2008
... (2007). Clustering effects on the extreme response statistics for dynamical systems. Proc.,... more ... (2007). Clustering effects on the extreme response statistics for dynamical systems. Proc., 5th Int. ... (2007). An importance sampling procedure for estimating failure probabilities of nonlinear dynamic systems subjected to random noise. Int. J. Non-Linear Mech., 42, 848863. ...
The paper describes a novel approach to the problem of estimating the extreme response statistics... more The paper describes a novel approach to the problem of estimating the extreme response statistics of a drag-dominated offshore structure exhibiting a pronounced dynamic behaviour when subjected to harsh weather conditions. It is shown that the key quantity for extreme response prediction is the mean upcrossing rate function, which can be simply extracted from simulated response time histories. A commonly adopted practice for obtaining adequate extremes for design purposes requires the execution of 20 or more 3-h time domain analyses for several extreme sea states. For early phase considerations, it would be convenient if extremes of a reasonable accuracy could be obtained based on shorter and fewer simulations. The aim of the work reported in the present paper has therefore been to develop specific methods which make it possible to extract the necessary information about the extreme response from relatively short time histories. The method proposed in this paper opens up the possibility to predict simply and efficiently both short-term and long-term extreme response statistics. The results presented are based on extensive simulation results for the Kvitebjørn jacket structure, in operation on the Norwegian Continental Shelf. Specifically, deck response time histories for different sea states simulated from an MDOF model were used as the basis for our analyses.
Extreme value prediction of the load-effect responses of complex offshore structures such as the ... more Extreme value prediction of the load-effect responses of complex offshore structures such as the floating wind turbine (FWT) is crucial in ultimate limit state (ULS) design. This paper considers two cases to understand the feasibility of the bivariate correction on the extreme load and motion responses of a 10-MW semi-submersible type FWT. The empirical anchor tension force and surge motion used in this study are obtained from the FAST simulation tool (developed by the National Renewable Energy Laboratory) with the load cases stimulated at underrated , rated and above rated speeds. Then, the bivariate correction method is applied to model FWT extreme response for a 5-years return period prediction with a 95% confidence interval (CI), based on just 2 min short response record. The proposed methodology permits accurate correction of the bivariate extreme value in case of, for example, corrupted measurement sensor data. Based on the proposed novel method's performance, it is concluded that the bivariate correction method can offer better robust and precise bivariate predictions of coupled surge motion and anchor tension of the FWT.
Introduction The first step in planning response analysis is whether the analysis can be accompli... more Introduction The first step in planning response analysis is whether the analysis can be accomplished as a static one or whether a dynamic model must be used. Dynamic analyses are generally necessary in connection with transient loads; otherwise, the results may be significantly conservative or nonconservative. For load processes consisting of several harmonic components, the main criterion is whether the load process contains energy in the range of eigenfrequencies of the system. Figure 14.1 shows an overview of the largest eigenperiod (natural period) of vibration or motion of offshore structures, as well as the relevant range of periods of dynamic loads associated with waves. Solution of Equations of Motion General The equations of motion for a linear structural system (Section 4.10) may be solved in the time or frequency domain. The choice of formulation especially depends on: The nature of the loading; i.e., whether it is steady state or transient (which often involves response in a wide frequency band). Frequency dependence of the dynamic properties (mass, damping, Nonlinear features of the loading or dynamic properties. In Chapter 2, solutions of the equation of motion for SDOF systems with different load conditions are described. If the solution method either in time or frequency domain is formulated for the coupled system of equations in Eq. (14.1), the method is denoted as direct.
International Journal of Mechanical Sciences, Jul 1, 2018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights A unique analytical solution available for biaxially excited Jeffcott rotor system was used to validate the proposed advanced path integration technique Dynamic system stability and extreme response statistics have been studied Novel improvements to an existing Path Integration scheme have been discussed (e.g. using MC preestimated initial PDF) Numerical results were in a good agreement with analytical results, therefore main contribution of this paper is a 100 percent reliable and independent confirmation of the path integration technique as a tool for assessing the dynamics of the kind of stochastic mechanical models considered in this paper
Introduction This chapter deals with vibrations of structures that can be represented as a single... more Introduction This chapter deals with vibrations of structures that can be represented as a single degree-of-freedom (SDOF) system. This means that the oscillatory response can be completely described by one displacement variable. This may seem like a gross oversimplification for structures of engineering interest that leads to a theory of little practical significance. However, the theory of vibrations for systems of an SDOF is crucial for understanding the vibration response of more complex structures. Frequently, it is also the case that one may investigate the vibration response characteristics of apparently complex structures by directly applying the theory of vibrations of SDOF systems. This is demonstrated in Chapter 3 on multi-degrees-of-freedom (MDOF) structures. The word “vibration” used in this chapter should be interpreted as meaning oscillatory response in a fairly general sense, e.g., as applied to marine structures. Harmonic Oscillator – Free Vibrations Free vibrations or oscillations occur when there are no external forces imposed on the structure, e.g., after an initial displacement and release. Two different situations are discussed: translational oscillations and rotational oscillations. Motions of Marine Structures Because the main focus of this book is the motion response of marine structures, it is expedient to define the terms commonly used to describe the rigid-body motions of floating structures. This is most easily done by referring to Fig. 2.1. For a shiplike structure, it is common practice to place the x -axis along the beam of the ship (for the body-fixed coordinate system), and call the corresponding translational motion for surge.
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white nois... more Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
The paper discusses the problem, of linearization for the purpose of simplified calculation of lo... more The paper discusses the problem, of linearization for the purpose of simplified calculation of long-term fatigue damage in offshore structures. Specific linearization procedures are proposed that may be better suited to deal with the problem of fatigue life calculation than the standard mean square stochastic linearization (MSSL). These are based on minimizing higher order moments of the linearization error, and it is indicated how the optimal order is linked to the street exponent of the S-N curve. It is shown by specific example studies that the proposed method may lead to substantial improvement over MSSL in estimating fatigue damage.
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