OBJECTIVES:
A time domain model for riser interaction was reported by Huse in 1993 and within the same timeframe a probabilistic model was developed and reported by Niedzwecki and Duggal (1993). Each of the models has limited predictive capabilities that restrict the applicability of the models to practical design. This was recognized and discussed at length at a workshop sponsored by the offshore industry and held in Norway in 1998. As a result, a new round of experiments at Marintek and refinements to the Huse model were pursued. In the experimental study multiple instrumented vertical cylinders were towed at various speeds and cylinder spacing with instrumentation quite similar to the earlier tests performed at the OTRC. However, the focus of the new experiments was on excitation due to uniform current flows. The probabilistic model developed by Duggal and Niedzwecki (1995) considered only deepwater wave excitation of risers with identical properties at various spacings and cylinder positions with respect to the lead cylinder. Issues of variable cylinder pretension and material properties cannot be addressed adequately in part due to the lack of experimental data. Collectively these factors lead to a rethinking of the riser interaction modeling approach by Niedzwecki and Diao in 1998.
A combined preliminary frequency/time domain modeling procedure has been conceived and is presently being explored. The initial results look promising but a serious research effort needs to be initiated to complete the model. Basically, the new model would recognize the nonlinear frequency dependent nature of the wave interactions and utilize classical nonlinear models for interpretive and predictive purposes. The objective of this proposed study is to develop a spacing dependent model that is general enough for potential use in design practice.
APPROACH:
a) analyze select data sets from Marintek experiments
b) extension of probabilistic considerationsANTICIPATED RESULTS:
PROJECT DURATION: 2-3 years
PRINCIPAL INVESTIGATOR: J. Niedzwecki
Date: June 2003
Project Name: Riser Interaction Model: A Combined Time/Frequency Domain Approach
Project Number: 32558-5887A Task Order: 16167
Principal Investigators: J.M. Niedzwecki
Estimated Completion Date: 10/31/03
Project Description:
The primary objective of this research investigation is the development of a new analysis approach to the hydrodynamic modeling of complex fluid-structure interaction phenomena, such as the hydrodynamic interaction of closely spaced risers subject to design seas. Because of the complex nature of the problem, a combined time/frequency domain approach was selected as the basis for the analysis. In particular, the reverse system identification technique for multiple input/ single output nonlinear problems has been developed for use in the analysis of riser measurements and riser simulations. This method was extended to address distributed parameter systems and has been applied to model a marine riser. This approach allows one to illustrate the propagation of various types of nonlinear model considerations along the length of the riser [1].The next logical steps in the development of this methodology were motivated by the need in offshore design to more precisely address the frequency dependence of key parameters such as added mass, stiffness and damping, as well as, the need to exploit the advantages of using fully correlated signals in the process of design parameter estimation. Based an understanding of the analysis requirements and the initial interpretation of some existing multiple riser data, it was concluded that a suitable data set for marine risers was not available at this time. Consequently, other test data sets were considered for possible use and it was determined that it would be possible to utilize a series of recently performed model tests involving complementary model tests of a rigid hull model and its compliant platform counterpart. Background information on the mini-TLP platform, the test program and the analysis and interpretation of some of the research findings can be found in references [2, 3]. Specific details of the most recent developments for the system identification formulation and implementation procedures based upon this research funding are presented in reference [2].
The reverse system identification model has now been adequately developed to the point where it can be applied to investigate complex hydrodynamic aspects of marine riser and floating platform systems. The final objective will be to clearly document the some of the subtle aspects of the methodology that will allow its successful application and the interpretation of practical problems. This will include the utilization of other advanced analysis methods [5] and will be discussed in a forthcoming 2003 OTRC International Symposium [6].
Progress:
Two referred journal articles detailing the analysis procedures and use of the advances made to enhance the findings for the interpretation of the single marine riser problem have been published [1, 2]. These articles document the natural development of the present formulation and the use of partial and cumulative coherence functions to guide the selection and rank the importance of various non-linear terms. An example is presented in Figure 1, where the suggested terms in the equations of motion have been rank ordered and their contribution over the selected frequency range illustrated. This research investigation focused upon the need to address the recovery of key parameters from time series measured during an industry type model basin test program using the reverse multiple input/single output (R-MI/SO) technique. In particular, this study confronts critical problems of practical interest and extends the methodology to address the inclusion of nonlinear coupled systems in which the parameters of interest can be frequency dependent. Due to the lack of suitable riser experimental data it was decided to use the nonlinear coupled equations of motions for a deepwater mini-TLP design and includes the consideration of nonlinear stiffness, quadratic damping, surge/pitch and sway/roll coupling and the frequency dependency of both the hydrodynamic added-mass and damping coefficients. The behavior of the hydrodynamic added-mass and damping coefficients as a function of frequency was simulated for the mini-TLP using an industry standard radiation-diffraction software package. These results were used in evaluating the accuracy of some of the key problem parameters. Examples of the frequency dependency of the system stiffness and damping have been taken from reference [2] and are presented in Figures 2 and 3. In general the results presented in reference [2] demonstrate the methodology as modified in this study is quite robust and yields predictions that are most accurate for the parameters associated with the largest motions of the platform. Practical issues regarding the application of this approach, utilization of both force and moment measurements, and observed strengths and weakness in dealing with data regardless of its source are discussed in reference [6].References:
Niedzwecki, J.M. and Liagre, P-Y. (2002). “System Identification of Distributed-Parameter Marine Riser Models,” Journal of Ocean Engineering, Vol. 30, 1387-1415.Teigen, P. and Niedzwecki, J.M. (1998). "Experimental and Numerical Assessment of Mini-TLP for Benign Environments," 8th International Offshore and Polar Engineering Conference, May, Montreal, Canada.
Teigen, P. and Niedzwecki, J.M. (2003). “Wave Diffraction Effects and Wave Runup around Multicolumn Structure,” ISOPE 2003, May 25-30, 2003, Honolulu, Hawaii.
Liagre, P-Y. and Niedzwecki, J.M. (2003). "Estimating Nonlinear Coupled Frequency Dependent Parameters in Offshore Engineering,” Applied Ocean Research, in press.
Sibetheros, I. A. and Niedzwecki, J.M. (2003). “System Analysis of the Interactive Behavior of Flexible Cylinders under Unidirectional Wave Loading,” ISOPE 2003, Vol. 3, May 25-30, 2003, Honolulu, Hawaii.
Niedzwecki, J.M. and Liagre P-Y. (2003). “Interpreting Data on Marine Riser Response Behavior Using System Identification, OTRC Deepwater Mooring Symposium, October 2-3, 2003, Houston, TX.
Figure 1. Cumulative coherence functions for the R-MI/SO model using the inline force as output
Figure 2. Comparison of the frequency-dependent surge linear damping.
Figure 3. Comparison of the frequency-dependent surge linear stiffness
Date: November, 2002
Project Name: Riser Interaction Model: A Combined Time/Frequency Domain Approach
Project Number: 32558 / 588A / CE Task Order: 16167
Principal Investigators: J.M. Niedzwecki
Estimated Completion Date: 10/31/03
Project Description:
The primary objective of this research investigation is the development of a new approach to the hydrodynamic modeling to account for the interaction of groups of closely space risers subject to design seas. A formulation based upon the reverse system identification technique for multiple input/ single output nonlinear problems have been developed for use in the analysis of riser measurements and riser simulations. This combined time/frequency method has been applied to model a marine riser and used to illustrate the propagation of various types of nonlinear model considerations along the length of the riser. The model is now being applied to investigate multiple riser experimental data and frequency dependent parameters. The intent is to further develop this methodology to allow for the interpretation of practical considerations associated with riser arrays.Progress:
A journal article detailing the analysis procedures and findings for the interpretation of the single marine riser problem is in press (Niedzwecki and Liagre 2002). The technical paper presents an alternate formulation of the wave force excitation. In this approach, all of the non-linear contributions of the wave force and wave-structure interaction are concentrated in a single nonlinear force term on the left hand side of the equations of motion. The actual expression of this force can take a variety of nonlinear forms selected by the engineer. Modal decomposition is introduced and shown to be quite useful in verifying the values of the coefficients associated with the various nonlinear contributions. Basic information about the system, such as mass, stiffness and damping are recovered. Interestingly, it is possible to follow the propagation of the nonlinear term with depth along the marine riser and this is shown in Figure 1.In the process of developing the present formulation it was decided to address the identification of frequency dependent parameters that are often found in this and other offshore problems. Of particular interest is the frequency dependent hydrodynamic added mass and damping. As a result a new approach has been developed and is being tested using other OTRC data sets more suitable to illustrate this new formulation. This research finding has broad implications in the interpretation of experimental data as will be discussed in the next report.
Reference:
Niedzwecki, J.M. and Liagre, P-Y. (2002). “System Identification of Distributed-Parameter Marine Riser Models,” Journal of Ocean Engineering, in press.
Figure 1. Probability density function profiles at various depths along a single 873m long marine riser illustrating the role of various types of nonlinearities as a function of depth.
(a)
(b)
(c)
Date: June 2002Project Name: Riser Interference: A Combined Time/Frequency Domain Approach
Task Order: 16167 Project Number: 5887A
Principal Investigators: J.M. Niedzwecki
Estimated Completion Date: October, 2002
Project Description:
The primary objective of this research investigation is the development of a new approach to the hydrodynamic modeling to account for the interaction of groups of closely space risers subject to design seas. The approach has been to study combined frequency/time domain modeling procedures based upon a system identification approach to nonlinear problems. Of particular concern is to develop a methodology that will allow for practical considerations such as variable riser spacing and array geometrical arrangement so that it has the potential for use in design practice.Progress:
A journal article detailing the findings in the initial phase of this research investigation was recently submitted (Niedzwecki and Liagre 2002). An alternative formulation of the wave force excitation was proposed and investigated that is more suitable for use with system identification methods. Basically, all of the non-linear contributions to wave force and wave-structure interaction are concentrated in nonlinear terms introduced on the side where the inertia, damping and stiffness forces are expressed. Further, modal decomposition is introduced and shown to be quite useful in verifying the values of the coefficients associated with the various nonlinear contributions. Basic information about the system, such as mass, stiffness and damping are recovered. An example of the mass recovery using this reverse system identification method is shown in Figure 1. In that figure one sees that frequency ranges are an important for interpreting the results and that the answers for the first five modes converge quite well. Unfortunately, not all parameters are so cleanly evaluated and presently we are investigating the frequency dependence of hydrodynamic added-mass and damping. Another interesting aspect of the present formulation is the ability to study the role of various types of non-linearity in modifying the response behavior of the riser response. An example is presented in Figure 2. Note that information at specified depths is obtained and the depth dependence of various fluid-structure interactions can be followed.The research is now moving from the distributed parameter single riser model to a much more complex multi-degree-of-freedom identification formulation that more accurately addresses the design of riser arrays and the fluid/structure interaction of the various risers in the array. Based upon the research results reported in the initial technical paper by Niedzwecki and Liagre (2002), efficiencies in computational procedures and extension of the basic methodology beyond that reported in the open literature are underway. Data from earlier OTRC model basin tests is being used in this phase of the research as well.
Figure 1. Modal estimates of the mass per unit length obtained using reverse system identification.
Figure 2. Probability density function profiles at a depth of 100m on a single riser 873m long
Publication:
Niedzwecki, J.M. and Liagre, P-Y. (2002). “System Identification of Distributed-Parameter Marine Riser Models,” submitted Journal of Ocean Engineering, April 2002.
Date: December 2001Project Name: Riser Interference: A Combined Time/Frequency Domain Approach
Task Order: 16167 Project Number: 5887A
Principal Investigators: J.M. Niedzwecki
Estimated Completion Date: October, 2002
Project Description:
The primary research objective of this research study is the development of a new hydrodynamic model to account for the interaction of groups of closely space risers subject to design seas. The approach has been to study combined frequency/time domain modeling procedures based upon a system identification approach to nonlinear problems. A major objective of this study is to develop a spacing dependent model that is general enough to potentially be used in design practice.
Progress:
Two different yet complementary analysis approaches are being pursued to study riser inference. In the first approach, only a single riser is modeled with non-linear terms to account for the influence of other risers in close proximity. The interactive behavior is modeled using classic non-linear models involving a cubic nonlinear displacement term combined with another term involving the products the riser displacement and velocity. The interference effects of risers on one another are reflected in changes to measured quantities of tension, reaction force and displacement behavior. This formulation is combined with system identification for non-linear systems.
System identification techniques have been developed and reported in the open literature, for example Bendat (1998). These time-frequency domain techniques utilize measured data to back figure structural properties such as mass, stiffness and damping. In this research investigation, the additional problem of spatial variation has been analyzed and a new methodology has been developed riser systems. Presently a technical paper describing the approach and presenting examples of increasingly complex interpretations of riser problem is being written for journal publication. One of the more important results of this study is the ability to introduce a variety of non-linear models into the analysis procedures and to view the results in the graphical environment of Matlab. Both experimental and numerical simulations can be investigated using the methodology. For example, in the case of a complete numerical simulation of riser response to random design seas, kinematics information along the riser at specified elevations along the riser. Based upon this information it is possible to develop probabilistic mappings of the results allowing one to explore and interpret the influence of different types of non-linear models on the system overall system behavior.
In Figure 1, shown on the next page, a contour plot of the cumulative probability density functions for the same riser systems are presented. It is important to note that the contours for the case where a non-linear model, consistent with the multiple riser interaction, is introduced the variation of the riser response is quite different from the results for a single isolated riser subject to the same random sea excitation. Work is proceeding to refine this new formulation and its use in the interpretation of riser problems.
Figure 1. Contour plots of the cumulative probability of a single riser.
In the second approach, a formulation for a grouping of two or more closely spaced risers is being developed. This approach is more physically appealing because engineers may relate it more readily to riser arrays. The interference effects are modeled as combinations of linear springs and dampers. In this multi-year research study more attention to this approach will follow completion of the first approach.
Reference:
Bendat, J.S. (1998). Nonlinear Systems Techniques and Applications, Wiley Interscience, New York, NY.
