NL2031067B1 - Hybrid bi-modal non-gaussian response amplitude probability distribution model based method for estimating fatigue damage of offshore structure - Google Patents

Hybrid bi-modal non-gaussian response amplitude probability distribution model based method for estimating fatigue damage of offshore structure Download PDF

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NL2031067B1
NL2031067B1 NL2031067A NL2031067A NL2031067B1 NL 2031067 B1 NL2031067 B1 NL 2031067B1 NL 2031067 A NL2031067 A NL 2031067A NL 2031067 A NL2031067 A NL 2031067A NL 2031067 B1 NL2031067 B1 NL 2031067B1
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response amplitude
probability distribution
response
moment
fatigue damage
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Guo Yuanzhi
Tao Wei
Song Xiancang
Zhao Yixiang
Hou Yuyao
Wang Shuqing
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Ocean Univ China
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B21/00—Tying-up; Shifting, towing, or pushing equipment; Anchoring
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B79/00—Monitoring properties or operating parameters of vessels in operation
    • B63B79/20—Monitoring properties or operating parameters of vessels in operation using models or simulation, e.g. statistical models or stochastic models
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B79/00—Monitoring properties or operating parameters of vessels in operation
    • B63B79/30—Monitoring properties or operating parameters of vessels in operation for diagnosing, testing or predicting the integrity or performance of vessels
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B21/00—Tying-up; Shifting, towing, or pushing equipment; Anchoring
    • B63B2021/003—Mooring or anchoring equipment, not otherwise provided for
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing

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Abstract

Disclosed is a hybrid bi-modal non-Gaussian response amplitude probability distribution model based method for estimating fatigue damage of offshore structure. The method takes the standard deviation of the wave frequency response of the system as a parameter to construct a Rayleigh distribution function, and takes the standard deviation of the total tension response of the system as a parameter to construct an Exponential distribution function. Given statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system, the method can accurately describe the probability distribution of the lowfrequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system synchronously, and the precision of the fatigue damage assessment of the structure with the method is far higher than that of fatigue damage assessment through a traditional method, thereby enabling high engineering application prospects.

Description

HYBRID BI-MODAL NON-GAUSSIAN RESPONSE AMPLITUDE PROBABILITY
DISTRIBUTION MODEL BASED METHOD FOR ESTIMATING FATIGUE
DAMAGE OF OFFSHORE STRUCTURE
TECHNICAL FIELD
[01] The present invention belongs to the field of ocean engineering, and in particular relates to a hybrid bi-modal non-Gaussian response amplitude probability distribution model based method for estimating fatigue damage of offshore structure.
BACKGROUND
[02] The deep-water floating system is prone to cumulative fatigue damage under complex environmental loads, and therefore, it is of vital importance to accurately describe response characteristics of the deep-water floating system, quickly and accurately predict the fatigue damage of the deep-water floating system, and reduce the uncertain factors in the design and analysis procedure, so as to ensure the safety of the floating system.
[03] The existing probability distribution function (PDF) cannot accurately describe the probability distribution of the bi-modal non-Gaussian response amplitude of the deep-water floating system, making it urgent to develop a novel probability distribution model to quickly and accurately estimate the structural fatigue damage, so as to provide support for safety design and assessment of the deep-water floating system.
SUMMARY
[04] Aiming at the problem that the existing probability distribution model cannot accurately describe probability distribution of the bi-modal non-Gaussian response amplitude of the deep-water floating system, the present invention develops a hybrid bi- modal non-Gaussian response amplitude probability distribution model based method for estimating structural fatigue damage, which is used to improve the precision of fatigue damage assessment of the mooring system in a process of designing and analyzing a floating structure.
[03] In order to achieve the above objective, the present invention provides a hybrid bi- modal non-Gaussian response amplitude probability distribution model based method for estimating fatigue damage of offshore structure. The method mainly includes: S1,
processing the bi-modal non-Gaussian tension response (the tension response of mooring lines resulted from the dynamic analysis of floating system under the actual stochastic wave) of a deep-water floating system to obtain the zeroth moment my, first moment m,, second moment m, and fourth moment m, of the total response, and the zeroth moment mgy > and standard deviation owr = \Mowr Of the wave frequency response of the system (the above parameters being capable of being obtained according to their mathematical definition); S2, utilizing the standard deviation of the wave frequency response of the system to construct the Rayleigh distribution function, Pic(y) = pr exp(- =) (y is the tension response amplitude variable of mooring line), which is used to accurately describe 10 probability distribution of the low-frequency high-tension response amplitude of the system;
S3, utilizing a standard deviation of the total response of the system to construct an
Exponential distribution function, Psc = op (- 72) (y is the tension response amplitude variable of mooring line), which is adopted to correct probability distribution of the high-frequency low-tension response amplitude of the system, where wri =0wr + Or, 0 = 1-0, and a, = my, /Jmom, (Gr is the standard deviation of the low-frequency response of mooring line); S4, utilizing the zeroth moment, the first moment, the second moment and the fourth moment of the total response of the system to construct a coupling parameter A considering statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency 20° low-tension response amplitude of the system; S5, utilizing the coupling parameter 4 to couple the Rayleigh distribution function and the Exponential distribution function together to create a hybrid bi-modal non-Gaussian response amplitude probability distribution model, 2 p(y) = dga XP (- oe) + (1-3) To (- 2) (y is the tension response amplitude variable of mooring line); S6, utilizing the hybrid bi-modal non-
Gaussian response amplitude probability distribution model to determine the annual fatigue damage D=», [a (2805, T(m +1) + (1 = 2) (2VZ0wr,) T(m/2 + 1) [of structure under the 7 sea state, where Vp = M4/m; is a peak rate of the total response,
A is a fatigue strength coefficient, m is a fatigue strength coefficient, and TC) is a gamma function; and S7, performing fatigue assessment over all the sea states in the wave scatter diagram in which the structure is located, and summing damage of the sea states to obtain an annual fatigue damage degree = Ni; D; = Zi: 2x fy, (286we15,) r(m+ 1)|of the structure.
[06] In the present invention, in S4, a process for determining the coupling parameter considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system is as follows: S41, establishing a bandwidth parameter a, = m;/ mom, for describing the response of the system based on the zeroth moment, the first moment and the second moment of the total response of the system; S42, constructing an irregular coefficient a, =m, [moms of the response of the system based on the zeroth moment, the second moment and the fourth moment of the response of the system; and S43, establishing the coupling parameter A = 2a,(a; — a2)/(1 + a?) considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system based on the bandwidth parameter and the irregular coefficient of the total response of the system. 13 [07] In the present invention, in S6, I'(-) used is the gamma function, an expression of which is Fa) = Jy t*lexp(t)dt , the low-frequency high-tension annual fatigue damage Dye, = 22204 (1 = A) [ype (dy = (1 (QV Zo) T(n/2+1) of the structure of the system under the 7! sea state can be estimated by utilizing the constructed
Rayleigh distribution function p;c(y) = 2 exp (- pa and the coupling parameter A,
WF 20yp and moreover, the high-frequency low-tension annual fatigue damage Dymo * Ay *
Jy™s po ()dy = pO xj (2e0 wer) T(m +1) of the structure of the system under the /™ sea state can be estimated by utilizing the constructed Exponential distribution function psc = EE exp (- i) and the coupling parameter A, thereby acquiring the annual fatigue damage degree D = XD; = Zin “2200 (266509, Tm +1) + 2 (1-2)(2VZowr,)"T0n/2+ 1)] of the structure.
[08] Preferably, in S4, on the basis of the bandwidth parameter and the irregular coefficient of the dynamic response of the system, after the coupling parameter considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system is introduced, the Rayleigh distribution function for describing the probability distribution of the low-frequency high-tension response amplitude of the system and the Exponential distribution function for describing the probability distribution of the high-frequency low- tension response amplitude of the system are coupled together, and therefore a hybrid bi- modal non-Gaussian response amplitude probability distribution model is established.
Further, a linear fatigue damage accumulation rule (e.g. P-M rule) is utilized and a bandwidth correction parameter is introduced to establish a hybrid Rayleigh and Exponential probability distribution model based method for estimating structural fatigue damage, such that the method may accurately estimate low-frequency high-tension fatigue damage and high-frequency low-tension fatigue damage of the system simultaneously, and precision of structural fatigue damage obtained based on the method is far higher than that of fatigue damage estimated by means of the traditional method.
[09] Beneficial effects: the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system may be accurately described simultaneously with the proposed probability distribution model, and the low-frequency high-tension fatigue damage and the high-frequency low- tension fatigue damage of the system may be accurately estimated with the proposed method.
The model based method for structural fatigue assessment can be used for estimating the fatigue damage of the mooring lines for various floating system with different mooring lines layouts, and has high engineering application prospects.
BRIEF DESCRIPTION OF THE DRAWINGS
[10] FIG. 1 is a flow-chart of the method provided by the present invention;
[11] FIG. 2 is a flow-chart of determining the coupling parameter in S4 of FIG. 1;
[12] FIG. 3 1s probability distribution of a tension response amplitude of a mooring line of a moored floater;
[13] FIG. 4 is accumulative probability distribution of the tension response amplitude of the mooring line of a moored floater;
[14] FIG. 5 is the normalized fatigue damage of mooring lines of the moored floater.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[15] With reference to FIG. 1, which is a flow-chart of the method provided by the present invention, the method mainly includes: S1, process a bi-modal non-Gaussian tension response (the tension response of mooring lines resulted from the dynamic analysis under the simulated actual stochastic wave) of a deep-water floating system to obtain zeroth moment my, first moment m4, second moment m, and fourth moment m, of a total response, and zeroth moment mgr and a standard deviation Gyr = Mowr of a wave 5 frequency response of the system (the above parameters being capable of being obtained according to their mathematical definition); S2, utilize the standard deviation of the wave frequency response of the system to construct a Rayleigh distribution function, pic(y) = exp (- =) (y is the tension response amplitude variable of mooring line), which is used to accurately describe the probability distribution of a low-frequency high-tension response amplitude of the system; S3, utilize the standard deviation of the total response of the system to construct an Exponential distribution function, pg = ee exp (- rr) (v being the tension response amplitude variable of mooring line), which is used to correct probability distribution of the high-frequency low-tension response amplitude of the system, where Orie =Owr +01, 8 =1—a,, and a, =m,/
Moms (ar being a standard deviation of a low-frequency response of the mooring line);
S4, utilize the zeroth moment, the first moment, the second moment and the fourth moment of the total response of the system to construct a coupling parameter A considering statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system;
S5, utilize the coupling parameter A to couple the Rayleigh distribution function and the
Exponential distribution function together to create a hybrid bi-modal non-Gaussian response amplitude probability distribution p(y) = A; To exp (- az) +H1—Àà) exp (- ] (y being the tension response amplitude variable of (ows) 2(owr,) mooring line); S6, utilize the hybrid bi-modal non-Gaussian response amplitude probability distribution model to determine annual fatigue damage
Dj = XEN |, (26i00wrsimr,) Mm +1) + (1 =A) (2VZoye) "T(m/2 + 1D] of the structure under the i" sea state, where Vp = My/m, is a peak rate of the total response, 4 is a fatigue strength coefficient, m is a fatigue strength coefficient, and I'(a) is a gamma function; and S7, perform fatigue estimation over all the sea states in a wave scatter diagram in which the structure is located, and sum the fatigue damage resulted from the individual sea states to obtain an annual fatigue damage degree D= ze * [x (26051; ) T+) +(1- A) (2V2owr,)"T(m/2 + 1)|of the structure.
[16] The present invention introduces a coupling parameter considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system. With l0 reference to FIG. 2, in $4, a process for determining the coupling parameter A considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system is as follows: S41, utilize the zeroth moment, the first moment and the second moment of the response of the system to construct a bandwidth parameter a; = m, mom of the response of the system; S42, utilize the zeroth moment, the second moment and the fourth moment of the response of the system to estimate an irregular coefficient a, = Mm; Moms of the response of the system; and S43, create a coupling parameter A = 2a,(a; — a;)/(1+ a?) considering the statistical influences of the probability distribution of the low-frequency high-tension response amplitude and the high-frequency low-tension response amplitude of the system based on the bandwidth parameter and the irregular coefficient of the response of the system.
[17] In order to illustrate the technical effect of the present invention more clearly, a dynamic analysis model of a moored floater is established by taking a deep-water semi- submersible platform as an example, and the tension response of mooring lines of the moored floater under the stochastic waves is obtained by means of coupling dynamic analysis. The tension response of the mooring line is analyzed to obtain the zeroth moment my, the first moment m,, the second moment m, and the fourth moment m, of the total response of the mooring line and the standard deviation gy, of the wave frequency response of the mooring line. The standard deviation oyr+;p of the total tension response of the mooring line is utilized to construct the Exponential distribution function, the standard deviation Oy of the wave frequency response of the mooring line is utilized to construct the Rayleigh distribution function, and the zeroth moment my, the first moment m,, the second moment m, and the fourth moment m, of the total response of the mooring line are utilized to create the coupling parameter A, which couples the Exponential distribution function and the Rayleigh distribution function together to obtain the probability distribution 3 of the tension amplitude of the mooring line represented by a hybrid Rayleigh and
Exponential probability distribution model.
[18] FIGs. 3 and 4 provide a statistical result of the probability distribution of the tension response amplitude of the mooring line and a predicted value of the probability distribution of the tension response amplitude represented by Rayleigh distribution and the 10° hybrid Rayleigh and Exponential probability distribution model (CRE). A comparative result shows that the Rayleigh distribution remarkably underestimates probability of the high-frequency low-tension response amplitude and remarkably overestimates probability of the low-frequency high-tension response amplitude, and a prediction result of the probability distribution of the tension response amplitude of the mooring line represented by the hybrid Rayleigh and Exponential probability distribution model is satisfactorily consistent with the statistical results.
[19] FIG. 5 provides a fatigue damage result of the mooring line estimated based on different distribution functions. In the figure, a narrow-band (NB) model 1s fatigue damage of the mooring line obtained based on the Rayleigh distribution, the CRE model is fatigue damage of the mooring line assessed based on the hybrid Rayleigh and Exponential probability distribution model provided by the present invention, and the dotted line presents the fatigue damage of mooring lines obtained through the time domain fatigue assessment method. The comparative results show that the Rayleigh distribution function based method remarkably overestimates the fatigue damage of the mooring lines, and the fatigue damage of the mooring line obtained based on the hybrid Rayleigh and Exponential probability distribution model based method is very close to fatigue damage obtained by the time domain fatigue assessment method.

Claims (6)

ConclusiesConclusions 1. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een structuur in zee, waarbij de werkwijze het volgende omvat: Sl, het verwerken van een bi-modale niet-Gaussiaanse spanningsrespons (de spanningsrespons van trossen die resulteert uit de dynamische analyse van een drijvend systeem onder de huidige stochastische golf) van een op diep water drijvend systeem om nulde moment 7%, eerste moment #:;, tweede moment #22 en vierde moment #24 van een totale respons en nulde moment moi en een standaarddeviatie oye = / (Mowr) van een golffrequentierespons van het systeem te verkrijgen (waarbij de bovenstaande parameters in staat zijn volgens de wiskundige definitie ervan verkregen te worden), S2, het gebruikmaken van de standaarddeviatie van de golffrequentierespons van het systeem om een Rayleigh-verdelingsfunctie, “ss CN Swe? te construeren (waarbij y een spanningsresponsamplitudevariabele van een tros is), die gebruikt wordt om de waarschijnlijkheidsdistributie van een lage frequentie-hoge spanning responsamplitude van het systeem nauwkeurig te beschrijven; S3, het gebruiken van een standaarddeviatie van de totale respons van het systeem 3 of py A om een exponentiële distributiefunctie, PSE = grais PVT Geeste) ‚ te construeren (waarbij y de spanningsresponsamplitudevariabele van een tros is), die gebruikt wordt om een waarschijnlijkheidsdistributie van een hoge frequentie-lage spanning responsamplitude van het systeem te corrigeren, waarbij owe: = our + or, 0= 1 —00, en az = ma/y/ (Mom) (waarbij a: een standaarddeviatie van een lagefrequentierespons van de tros is); S4, het gebruikmaken van het nulde moment, het eerste moment, het tweede moment en het vierde moment van de totale respons van het systeem om een koppelparameter A te construeren rekening houdend met statistische invloeden van de waarschijnlijkheidsdistributie van de lage frequentie-hoge spanning responsamplitude en de hoge frequentie-lage spanning responsamplitude van het systeem; S5, het gebruikmaken van de koppelaparameter A om de Rayleigh-distributiefunctie en de exponentiële distributiefunctie samen te koppelen om een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude te creéren, ECT ea tend ment (waarbij y de spanningsresponsamplitudevariabele van een tros is); S6, het gebruikmaken van het hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude om jaarlijkse vermoeiingsschade n=, 2 ereen] Pim + 1) + (1 — 403 Ta) Toyz + £)} van de structuur onder de i° zeetoestand te bepalen, waarbij vp = 14/92 een pieksnelheid van de totale respons is, 4 een vermoeingssterktecoëfficiënt is, m een vermoeiingssterktecoëfficiënt is en T'(*) een gammafunctie is; en S7, het uitvoeren van vermoeiingsschatting op alle zeetoestanden in een golfverspreidingsdiagram van een zeegebied waarin de structuur zich bevindt, en het optellen van schade van de zeetoestanden om een jaarlijksevermoeiingsschademate ee eN { Ee Pon +13 + LAND) Timf2 + 13] van de structuur te verkrijgen.1. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of a marine structure, the method comprising: Sl, processing a bi-modal non-Gaussian stress response ( the tension response of bunches resulting from the dynamic analysis of a floating system under the current stochastic wave) of a deep water floating system at zeroth moment 7%, first moment #:;, second moment #22 and fourth moment #24 of a total response and zeroth moment moi and a standard deviation oye = / (Mowr) of a wave frequency response of the system (where the above parameters are capable of being obtained according to their mathematical definition), S2, using the standard deviation of the wave frequency response of the system to a Rayleigh distribution function, “ss CN Swe? construct (where y is a bunch voltage response amplitude variable), which is used to accurately describe the low frequency-high voltage response amplitude probability distribution of the system; S3, using a standard deviation of the total response of the system 3 or py A to construct an exponential distribution function, PSE = free PVT Geeste) ‚ (where y is the voltage response amplitude variable of a bunch), which is used to calculate a probability distribution of to correct a high frequency-low voltage response amplitude of the system, where owe: = our + or, 0= 1 —00, and az = ma/y/ (Mom) (where a: is a standard deviation of a low frequency response of the bunch ); S4, using the zeroth moment, the first moment, the second moment and the fourth moment of the total response of the system to construct a coupling parameter A taking into account statistical influences of the probability distribution of the low frequency-high voltage response amplitude and the high frequency-low voltage response amplitude of the system; S5, using the coupling parameter A to couple the Rayleigh distribution function and the exponential distribution function together to create a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude, ECT ea tend ment (where y is the voltage response amplitude variable of a bunch) ; S6, using the hybrid probability distribution model of a bi-modal non-Gaussian response amplitude to estimate annual fatigue damage n=, 2 eren] Pim + 1) + (1 — 403 Ta) Toyz + £)} of the structure under the i° sea state where vp = 14/92 is a peak velocity of the total response, 4 is a fatigue strength coefficient, m is a fatigue strength coefficient and T'(*) is a gamma function; and S7, performing fatigue estimation on all sea states in a wave dispersion diagram of a sea area in which the structure is located, and summing damage from the sea states to obtain an annual fatigue damage rate ee eN { Ee Pon +13 + LAND) Timf2 + 13] of the structure to obtain. 2. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een aflandige structuur volgens conclusie 1, waarbij een werkwijze voor het bepalen van de koppelparameter 1 rekening houdend met de statistische invloeden van de waarschijnlijkheidsdistributie van lage frequentie-hoge spanning responsamplitude en de hoge frequentie-lage spanning responsamplitude van het systeem in S4 als volgt is: S41, het vaststellen van een bandbreedteparameter a: =m1// (mgm, van een respons van het systeem op basis van het nulde moment, het eerste moment en het tweede moment van de totale respons van het systeem; S42, het construeren van een onregelmatige coéfficiént 02 = 2/,/ (Mom, ) voor het beschrijven van de respons van het systeem op basis van het nulde moment, het tweede moment en het vierde moment van de totale respons van het systeem, en S43, het vaststellen van de koppelparameter rekening houdend met de statistische invloeden van de waarschijnlijkheidsdistributie van de lage frequentie-hoge spanning responsamplitude en de hoge frequentie-lage spanning responsamplitude van het systeem op basis van de bandbreedteparameter en de onregelmatige coëfficiënt van de respons van het systeem, à = 202(02 - 02)/(1 + a2).2. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of an offshore structure according to claim 1, wherein a method for determining the coupling parameter 1 taking into account the statistical influences of the probability distribution of low frequency-high voltage response amplitude and the high frequency-low voltage response amplitude of the system in S4 is as follows: S41, establishing a bandwidth parameter a: =m1// (mgm, of a response of the system based on the zeroth moment, the first moment and the second moment of the total response of the system; S42, constructing an irregular coefficient 02 = 2/,/ (Mom, ) for describing the response of the system based on the zeroth moment, the second moment and the fourth moment of the total response of the system, and S43, determining the torque parameter taking into account the statistical influences of the probability distribution of the low frequency-high voltage response amplitude and the high frequency-low voltage response amplitude of the system based on the bandwidth parameter and the irregular coefficient of the system response, à = 202(02 - 02)/(1 + a2). 3. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een aflandige structuur volgens conclusie 1, waarbij T'(:) die gebruikt wordt in S6 de gammafunctie is, waarvan een uitdrukking 73 = fy = expltyde3. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of an offshore structure according to claim 1, where T'(:) used in S6 is the gamma function, an expression of which is 73 =fy=expltyde 4. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een aflandige structuur volgens conclusie 1, waarbij jaarlijkse lage frequentie-hoge spanning vermoeiingsschade van de structuur van het systeem onder de i zeetoestand geschat kan worden door middel Ce Bic) =p (- van de geconstrueerde Rayleigh-distributiefunctie TNE . Zy en de koppelparameter 4 in S6.4. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of an offshore structure according to claim 1, wherein annual low frequency-high stress fatigue damage of the structure of the system under the i sea state is estimated can be obtained by means of Ce Bic) = p (- from the constructed Rayleigh distribution function TNE . Zy and the coupling parameter 4 in S6. 5. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een aflandige structuur volgens conclusie 1, waarbij jaarlijkse hoge frequentie-lage spanning vermoeiingsschade Boge = ee vas [yap yidy = RE a + A {28, SiMF+EE) 3 Fim + 1} van de structuur van het systeem onder de i zeetoestand geschat kan worden door middel u 1 of yo van de geconstrueerde exponentiéle distributiefunctie Se Gogpe 7 (- Cr, en de koppelparameter 4 in S6.5. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of an offshore structure according to claim 1, where annual high frequency-low voltage fatigue damage Boge = ee vas [yap yidy = RE a + A {28, SiMF+EE) 3 Fim + 1} of the structure of the system under the i sea state can be estimated using u 1 or yo of the constructed exponential distribution function Se Gogpe 7 (- Cr, and the coupling parameter 4 in S6 . 6. Werkwijze op basis van een hybride waarschijnlijkheidsdistributiemodel van een bi-modale niet-Gaussiaanse responsamplitude voor het schatten van vermoeiingsschade van een aflandige structuur volgens conclusie 1, waarbij de koppelparameter A die in S4 geconstrueerd wordt rekening houdt met de statistische invloeden van de waarschijnlijkheidsdistributie van de lage frequentie-hoge spanning responsamplitude en de hoge frequentie-lage spanning responsamplitude van het systeem, zodat de waarschijnlijkheidsdistributie van de lage frequentie-hoge spanning responsamplitude6. Method based on a hybrid probability distribution model of a bi-modal non-Gaussian response amplitude for estimating fatigue damage of an offshore structure according to claim 1, wherein the coupling parameter A constructed in S4 takes into account the statistical influences of the probability distribution of the low frequency-high voltage response amplitude and the high frequency-low voltage response amplitude of the system, so that the probability distribution of the low frequency-high voltage response amplitude S11 - en de hoge frequentie-lage spanning responsamplitude van het systeem nauwkeurig gelijktijdig beschreven kunnen worden, en de precisie van het voorspellen van de waarschijnlijkheidsdistributie van de responsamplitude middels de werkwijze veel hoger is dan die van het afzonderlijk voorspellen van de waarschijnlijkheidsdistributie van de responsamplitude van het systeem middels de Rayleigh-distributiefunctie, en de werkwijze op basis van het model voor het schatten van vermoeiing een schattingsefficiëntie heeft die veel hoger is dan die van een traditionele werkwijze voor de tijdsdomeinvermoeiingsbeoordelingswerkwijze met het dynamische koppelanalysemodel onder de veronderstelling van het verzekeren van voldoende precisie, schattingsnauwkeurigheid zeer verbetert in vergelijking met een traditionele werkwijze op basis van een Rayleigh-distributie voor vermoeiingsbeoordeling, gebruikt kan worden voor het schatten van vermoeiingsschade van het drijvendestructuuraanmeersysteem, en nauwkeurigheid en efficiëntie van het schatten van de vermoeiingsschade van het drijvendstructuuraanmeersysteem opmerkelijk verbetert.S11 - and the high frequency-low voltage response amplitude of the system can be accurately described simultaneously, and the precision of predicting the probability distribution of the response amplitude by the method is much higher than that of predicting the probability distribution of the response amplitude separately from the system through the Rayleigh distribution function, and the method based on the fatigue estimation model has an estimation efficiency much higher than that of a traditional method for the time domain fatigue assessment method with the dynamic torque analysis model under the assumption of ensuring sufficient precision , greatly improves estimation accuracy compared with a traditional method based on Rayleigh distribution for fatigue assessment, can be used for estimating fatigue damage of the floating structure mooring system, and remarkably improves accuracy and efficiency of estimating the fatigue damage of the floating structure mooring system.
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ZHAO YULIANG ET AL: "Probabilistic fatigue surrogate model of bimodal tension process for a semi-submersible platform", OCEAN ENGINEERING, PERGAMON, AMSTERDAM, NL, vol. 220, 21 December 2020 (2020-12-21), XP086445671, ISSN: 0029-8018, [retrieved on 20201221], DOI: 10.1016/J.OCEANENG.2020.108501 *

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