1、Guidance Notes on Selecting Design Wave by Long Term Stochastic Method GUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD OCTOBER 2016 American Bureau of Shipping Incorporated by Act of Legislature of the State of New York 1862 2016 American Bureau of Shipping. All rights reserve
2、d. ABS Plaza 16855 Northchase Drive Houston, TX 77060 USA Foreword Foreword The purpose of these Guidance Notes is to supplement the determination of design wave by long term stochastic approach for the ABS Rules for Building and Classing Mobile Offshore Drilling Units (MODU Rules). These Guidance N
3、otes provide users with step-by-step procedures for selecting design wave using long term stochastic method for non-ship type offshore structures. This methodology has been implemented in the ABS Eagle Offshore Structural Assessment Program (OSAP). These Guidance Notes become effective on the first
4、day of the month of publication. Users are advised to check periodically on the ABS website www.eagle.org to verify that this version of these Guidance Notes is the most current. We welcome your feedback. Comments or suggestions can be sent electronically by email to rsdeagle.org. ii ABSGUIDANCE NOT
5、ES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 Table of Contents GUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD CONTENTS SECTION 1 Introduction 1 1 General . 1 3 Features 1 5 Application 1 SECTION 2 Waves 2 1 General . 2 3 Wave Spectra (Short-term Wave Stati
6、stics) . 2 3.1 Unidirectional Spectra . 2 3.3 Directional Spectra (Wave Spreading) 3 3.5 Wave Spectral Formulation . 4 3.7 Wave Scatter Diagram and Rosette (Long-Term Wave Statistics) . 7 FIGURE 1 Definition of Spreading Angles 3 SECTION 3 Wave Data for Long Term Design Wave . 8 1 General . 8 3 Wave
7、 Data for Long Term Design Wave Analysis . 8 5 Load Cases and Dominant Load Parameters 8 7 Unit Motion and Wave Load Response Amplitude Operators (RAOs) 9 SECTION 4 Methodology . 10 1 General . 10 3 Extreme Values for Long Term Wave Analysis 11 5 Equivalent Design Wave . 13 5.1 Equivalent Wave Ampli
8、tude . 13 5.3 Equivalent Wave Frequency, Length and Direction . 13 5.5 Phase Angle and Wave Crest Position 14 ABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 iii FIGURE 1 Long Term Design Wave Analysis Procedure 10 FIGURE 2 Determination of Equivalent Wave Amplitude 1
9、4 FIGURE 3 Equivalent Wave Length and Crest Position 14 FIGURE 4 Definition of Wave Heading 15 APPENDIX 1 References 16 APPENDIX 2 Torsethaugen Spectrum 17 1 General . 17 3 General Spectrum Form . 18 3.1 Wind Dominated Sea (Tp Tf) 18 3.3 Swell Dominated Sea (Tp Tf) . 19 5 Simplified Spectrum Form .
10、19 5.1 Wind Dominated Sea (Tp Tf) 20 5.3 Swell Dominated Sea (Tp Tf) . 20 iv ABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 Section 1: Introduction SECTION 1 Introduction 1 General The design wave calculation by the short term stochastic method is provided in the ABS
11、 Rules for Building and Classing Mobile Offshore Drilling Units (MODU Rules). The ABS Rules for Building and Classing Floating Production Installations (FPI Rules) require the installations hull strength and fatigue assessment in the site-specific environmental conditions, considering both 100-year
12、return period environmental events and wave scatter diagram data of wave height/period joint occurrence distributions. As a supplement to select the design wave from the site specific environmental conditions, these Guidance Notes provide the detailed procedures to determine the design wave by the l
13、ong term stochastic method for non-ship type offshore structures. 3 Features Information related to the long term stochastic method includes: loading conditions, load cases, dominant load parameters, response RAOs, waves, wave spectra, sea state, wave scatter diagram, design wave, etc. The primary f
14、eatures of these Guidance Notes include: Wave spectrum and wave characteristics for site specific environment Wave data for long term design wave analysis Methodology for determining long term design wave 5 Application These Guidance Notes describe procedures to select the design waves based on the
15、long term stochastic approach. The procedures can be used for Response analysis selecting design waves for non-ship type offshore structures. Assistance in non-ship type offshore structure design. These Guidance Notes should be used in association with ABS Rules and Guides for non-ship type offshore
16、 structure analysis, such as the MODU Rules and FPI Rules. ABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 1 Section 2: Waves SECTION 2 Waves 1 General For offshore structures, the most dominant source of dynamic loads is waves. During the service life of an offshore
17、unit, it will experience a large number of cyclic loads due to waves, from very small wavelets to possibly giant waves. A practical way to describe these unceasingly changing waves is to divide them into various categories (sea states), and use short term wave statistics to depict each sea state and
18、 long term wave statistics, usually in the form of a wave scatter diagram and wave direction rosette, to delineate the rate at which a sea state occurs. In a similar way, there are two levels in the description of wave directionality (i.e., wave directional spectrum or wave spreading for short-term,
19、 and wave rosette for long term, respectively). There are numerous texts that present information on ocean waves and the statistically based parameters that are used to define sea states. The key concepts resulting from the application of these theoretical developments are the characterization of a
20、sea state as spectra comprised of numerous individual wave components, and the use of spectra moments to establish sea state defining parameters such as significant wave height and peak or zero crossing periods. For more details on this subject, refer to 5. 3 Wave Spectra (Short-term Wave Statistics
21、) 3.1 Unidirectional Spectra A wave spectrum describes the energy distribution among wave components of different frequencies of a sea state. Wave spectra can be obtained directly from measured data. However, various mathematical formulae of wave spectra have been available based on analysis of meas
22、ured data, such as ISSC Wave Spectrum, Bretschneider Spectrum (or Pierson-Moskowitz (P-M) spectrum), JONSWAP spectrum and Ochis six-parameter spectrum, etc. These spectrum formulae are suitable for different sea states. A fully-developed sea is a sea state that will not change if wind duration or fe
23、tch is further increased (for a fixed wind speed). The Bretschneider spectrum is applicable to fully-developed seas. For most of the ships and offshore structures in ABSs classification, either the Bretschneider spectrum for open ocean areas with fully-developed seas, or the JONSWAP spectrum for fet
24、ch-limited regions is used, respectively. For example, the Bretschneider wave spectrum is usually employed to describe tropical storm waves, such as those generated by hurricanes in the Gulf of Mexico or typhoons in the South China Sea. The JONSWAP wave spectrum is used to describe winter storm wave
25、s of the North Sea. In some cases, it can also be adjusted to represent waves in Offshore Eastern Canada and swells, such as those in West Africa and Offshore Brazil. A suitable wave spectrum should be chosen based on a partially or fully developed sea state for selecting design waves. In general, t
26、he Bretschneider spectrum has a greater frequency bandwidth than the JONSWAP spectrum. Therefore, the selection of a spectrum should be based on the frequency characteristics of the wave environment. The above-described two spectra are single-modal spectra, which are usually used to represent pure w
27、ind waves or swell-only cases. When wind waves co-exist with swells (i.e., there are multi-modes in the spectrum), no single-modal spectrum can match the spectral shape very well. In this case, recourse can be made to the use of the Ochi-Hubble 6-Parameter Spectrum or other wave spectrum. 2 ABSGUIDA
28、NCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 Section 2 Waves 3.3 Directional Spectra (Wave Spreading) 3.3.1 Long-crested Waves This is a simple case where the observed wave pattern at a fixed point neglects different directions of wave components. It is equivalent to assum
29、ing that all wave components travel in the same direction. These waves are called long-crested since the wave motion is two-dimensional and the wave crests are parallel. Waves produced by swell are almost long-crested in many situations since the crests of the wave become nearly parallel as the obse
30、rvation point recedes from the storm area which produced the waves. 3.3.2 Short-crested Waves If the observation station is inside the storm area, different waves will come from different directions, and the combined wave system will be short-crested waves. The spreading of wave directions should be
31、 taken into account to describe the short-crested waves. 3.3.3 Wave Spreading Considering the wave spreading, the wave energy spectrum can be obtained by integrating the spreading wave spectrum over the range of directions from maxto +max(maxcan be typically taken as 90). The general expression for
32、wave spreading is given by: S() = maxmaxS (,)d( ) where denotes the predominant wave direction and is the wave spreading angle, as shown in Section 2, Figure 1. FIGURE 1 Definition of Spreading Angles 0VmaxmaxABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 3 Section 2
33、 Waves In general, directional short-crested wave spectra S(,) may be expressed in terms of the uni-directional wave spectra: S(,) = S()D(,) = S()D() Where the latter equality represents a simplification often used in practice. D(,) and D() are spreading functions and fulfils the requirement: D (,)d
34、 = 1 A common cosine spreading function used for the wave spectrum is: D() = )2/2/1()2/1(nn+cosn( ) where = Gamma function | | 2n = wave spreading parameter, which is a positive integer. Typical values for wind sea are n = 2 to n = 4. If used for swell waves, n 6 is more appropriate. 3.5 Wave Spectr
35、al Formulation The shape of a spectrum supplies useful information about the characteristics of the ocean wave system to which it corresponds. There exist many wave spectral formulations (e.g., Bretschneider spectrum, Pierson-Moskowitz spectrum, ISSC spectrum, ITTC spectrum, JONSWAP spectrum, Ochi-H
36、ubble 6-parameter spectrum, etc.). 3.5.1 Bretschneider or Two-Parameter Pierson-Moskowitz Spectrum The Bretschneider spectrum or two-parameter Pierson-Moskowitz spectrum, also known as ISSC spectrum (representing by significant wave height and mean period), or ITTC spectrum (representing by signific
37、ant wave height and one of energy period, peak period, mean period and zero-crossing period) is the spectrum recommended for open-ocean wave conditions (e.g., the Atlantic Ocean). S() = 454245exp165ppsHin m2/(rad/s) (ft2/(rad/s) or S() = 4445221exp241zzsTTHin m2/(rad/s) (ft2/(rad/s) where p= 2/Tpmod
38、al (peak) frequency corresponding to the highest peak of the spectrum, in rad/s Hs= significant wave height, in m (ft) = circular frequency of the wave, in rad/s Tz= average zero up-crossing period of the wave, in seconds 4 ABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2
39、016 Section 2 Waves 3.5.2 JONSWAP Spectrum The JONSWAP spectrum is derived from the Joint North Sea Wave Project (JONSWAP) and constitutes a modification to the Pierson-Moskowitz spectrum to account for the regions that have geographical boundaries that limit the fetch in the wave generating area (e
40、.g., the North Sea). S() = 454245exp165ppsH( ) ln287.01ain m2/(rad/s) (ft2/(rad/s) where a = ( )2222exppp = when 09.0when 07.0pp = circular frequency of the wave, in rad/s = peakedness parameter, typically 1 to 7 p= 2/Tpmodal (peak) frequency corresponding to the highest peak of the spectrum, in rad
41、/s Here, the factor (1 0.287ln ) limits its practical application, because for =32.6, the spectral value from above formula becomes zero. For the peakedness larger than 7, it is recommended that an adjustment to the formula has to be made. The formula of the JONSWAP spectrum can be then given by: S(
42、) = 45245exp pgain m2/(rad/s) (ft2/(rad/s) where = peakedness parameter, representing the ratio of the maximum spectral density to that of the corresponding Pierson-Moskowitz spectrum. This means that for = 1 the JONSWAP spectrum defaults to the Pierson-Moskowitz spectrum g = gravitational accelerat
43、ion = 9.8 m/s2(32.2 ft/s2) = parameter to be determined as a function of the significant wave height, through the expression provided in the formula of Hsbelow, since the integral is a function of Hs= 0)(4 dS 3.5.3 Gaussian-Swell Spectrum The design sea state may come from intensification of the loc
44、al wind seas (waves) and/or swell propagating with different directions. In general, both are statistically independent. The wind seas are often characterized with the Bretschneider or the JONSWAP spectrum while the Gaussian distribution function can be used to describe swells. The spectral formulat
45、ion for the swell can be represented by the Gaussian-Swell spectrum: S()= 222)2(2)(exp22)4/(psHin m2/(rad/s) (ft2/(rad/s) ABSGUIDANCE NOTES ON SELECTING DESIGN WAVE BY LONG TERM STOCHASTIC METHOD .2016 5 Section 2 Waves where Hs= significant wave height, in m (ft) = peakedness parameter for Gaussian
46、 spectral width p= 2/Tpmodal (peak) frequency corresponding to the highest peak of the spectrum, in rad/s 3.5.4 Ochi-Hubble 6-Parameter Spectrum The Ochi-Hubble 6-Parameter spectrum covers shapes of wave spectra associated with the growth and decay of a storm, including swells. As may be seen in som
47、e wave records, the variability in the form of spectra can be great. Multi-modal spectra are common, and a single-modal Bretschneider form may not match the shape of such spectrum in an accurate manner. In order to cover a variety of shapes of wave spectra associated with the growth and decay of a s
48、torm, including the existence of swell, the following 6-parameter spectrum was developed by Ochi and Hubble: S() = ( ) + +=4142214414exp41441pjjsjjjpjjHjjin m2/(rad/s) (ft2/(rad/s) where j = 1, 2 stands for lower (swell part) and higher (wind seas part) frequency components. The six parameters, Hs1, Hs2, p1, p2, 1, 2, are determined numerically to minimize the difference between theoretical and observed spectra. Note that the modal frequency of the first component, p1, must be less than that of the second, p2. The significant wave height of the first component, Hs1, sh
