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18 S Amb hl et al International Journal of Marine Energy 10 2015 17 38. 1 Introduction, Wave energy converters WECs may become an important contributor of electricity from renew. able energy sources in the future Nowadays WECs exist on prototype level and are supposed to be. further developed and improved, Fatigue failures of offshore structures is a common failure mode Fatigue failure often occurs in. consequence of corrosion at welded structures or bolts Background information about corrosion pro. cedures in welds can be found in 1 Due to the fact that failure consequences of a WEC lead to lower. consequences no risk of human life low environmental pollution compared with oil and gas plat. forms WECs can be designed considering a lower safety level than oil and gas platforms The conse. quences of failure of a WEC component can be assumed to be similar to failure consequences of a. broken offshore wind turbine component For offshore wind turbines the dominating load is wind. induced whereas for offshore platforms fatigue is mainly caused by wave loading 2 Due to different. safety levels as well as different dominating load characteristics and different control strategies com. pared with existing offshore structures fatigue impact on WEC substructures need to be assessed and. safety factors need to be calibrated, The scope of this paper is to de ne appropriate partial safety factors fatigue design factors for. steel substructures of WECs In traditional deterministic designs the amount of needed structural. material is determined among others by the value of safety factors which re ect the uncertainties. related to design parameters and the required reliability level Improved designs with consistent reli. ability levels can be obtained by probabilistic design methods A reliability based probabilistic. approach as used e g for offshore wind turbines 3 is used here where uncertainties related to loads. strengths and calculation methods are accounted for A stochastic model for fatigue design has been. established Design and limit state equations are developed based on a SN curve approach Palmgren. Miner rule with linear damage accumulation is used as recommended in most relevant standards see. e g 4 and 5 Also a fracture mechanics approach is used for including different inspection strategies. in order to maintain a given safety target level Inspections can be used to extend the life time as well. as decrease the needed safety level due to better control of fatigue control growth 6 Different. inspection methods are compared as well as different inspection strategies based on an equidistant. inspection plan or a risk based inspection plan where inspections are performed when the annual. probability of failure exceeds the maximum acceptable annual probability of failure are discussed. An example is shown in the paper focusing on the Wavestar device which is located at Hanstholm. DK This kind of device is an offshore bottom xed device which consists of oaters impelling a. hydraulic system The loads are determined using real measured wave states and an in house hydro. dynamic program see 7 for more information to estimate the loads. In Section 2 general background information about probabilistic reliability assessments is given. and Section 3 discusses acceptable reliability levels for fatigue failure of WECs How fatigue can be. modelled including no inspections SN curve approach is shown in Sections 4 1 and 4 2 shows an. approach when including inspections Fracture mechanics In Section 5 the Wavestar example is. shown and resulting FDF values are shown The conclusion from this article is given in Section 6. 2 Probabilistic reliability assessment, In practice material characteristics of a structural detail e g their yield stress loads and environ. mental conditions contain uncertainties which are not directly taken into account in a deterministic. approach Deterministic approaches only consider mean values of a certain parameter Probabilistic. reliability methods enable to model parameters as stochastic variables and take their uncertainties. into account There exist epistemic uncertainties which are related to limited data or limited knowl. edge about the behaviour of the system Epistemic uncertainties can be reduced e g by increasing the. knowledge and collecting more relevant data Aleatory uncertainties are irreducible and account for. physical uncertainties such as the fatigue strength Epistemic and aleatory uncertainties need to be. included in probabilistic reliability assessments, S Amb hl et al International Journal of Marine Energy 10 2015 17 38 19.

Examples of the reliability index b and the corresponding probability of failure PF. b 3 1 3 7 4 3 4 7 5 2,PF 10 3 10 4 10 5 10 6 10 7, For each failure mode of a structural component it is possible to de ne a limit state function g t X. where different uncertainties using stochastic variables X fX 1 X 2 g are de ned. g t X R t S t 0 1, where R t represents the resistance and S t the loads at a certain time t Failure occurs if the limit. state equation is smaller than or equal to zero The probability of failure PF is equal to the probability. that the limit state equation is smaller than or equal to zero. PF t P g t X 6 0 U b t 2, where U is the standardized normal distribution and b the reliability index of the considered com. ponent s failure mode The resulting limit state can be solved using FORM SORM methods as well as. simulation techniques see e g 8 9 FORM SORM methods use a transformation in space where all. stochastic variables become independent as well as standardized normal distributed Therefore the. resulting reliability index b is assumed to be standardized normal distributed see Eq 2 Table 1. shows examples of b values and the resulting probability of failure PF For time dependent failure. probabilities PF t the annual probability of failure DPF t given survival up to time t is obtained from. PF t PF t Dt,where Dt is equal to 1 year and t Dt, 3 Acceptable reliability levels for fatigue failure of wave energy converters. Acceptable reliability levels depend on the application area as well as its impact in case of failure on. human lives and resulting failure costs Unmanned xed offshore structures have according to 10 a. minimal annual reliability index Db in the interval 3 3 3 7 Ref 11 groups the target annual reliabil. ity index for different costs of safety measures dependent on the consequences given failure of the. structure see Table 2 For wave energy converters it can be assumed that failure of the structure only. has economic in uences no pollution and no fatalities WECs are optimized such that the device is. able to produce electricity at a competitive level compared with other devices Therefore costs are. of importance and additional expenses should be prevented if possible Due to the fact that WECs. are most of the time unmanned the relative costs for safety measures are high in order to prevent. fatalities Therefore the resulting target annual reliability indices should be between 3 1 and 3 7. see Table 2 which is in accordance with minimum acceptable reliability levels used for offshore. wind turbines OWTs see e g 12 13, Instead of focusing on the annual probability of failure the probability of failure during the whole.

life time can be considered For fatigue limit states Ref 14 requires minimal cumulative reliability. Target annual reliability index Db according to 11. Relative cost of safety measure Consequences of failure. Minor Moderate Large,Large 3 1 3 3 3 7,Normal 3 7 4 2 4 4. Small 4 2 4 4 4 7, 20 S Amb hl et al International Journal of Marine Energy 10 2015 17 38. Fatigue Design Factor FDF values proposed by 15,FDF Structural element. 1 Internal structure accessible and not welded directly to the submerged part. 1 External structure accessible for regular inspection and repair in dry and clean conditions. 2 Internal structure accessible and welded directly to the submerged part. 2 External structure not accessible for inspection and repair in dry and clean conditions. 3 Non accessible areas areas not planned to be accessible for inspection and repair during operation. indices b between 2 3 and 3 1 dependent on the possibility of inspections For OWTs minimal cumu. lative reliability indices between 2 5 and 3 1 are considered see 13 This minimal cumulative reli. ability indices range is assumed to be transferrable from OWTs to WECs due to the same consequences. in case of failure no fatalities and low impact on environment. The fatigue design criteria depends on whether the detail can be inspected and the location of the. detail in uence of corrosion as well as the resulting consequences if the structural detail fails. Table 3 shows suggested FDF values proposed by DNV Carbon Trust 15 for WEC steel structures. based on failures with low consequences, A more general overview is shown in Table 4 where different FDF values are compared from differ. ent standards used for different offshore applications The FDF values for oil and gas structures are. taken from 10 Fatigue design factors used for OWTs are taken from 16 for bottom xed turbines. and for oating wind turbines from 17 Fatigue design factors in 17 including inspections assume. inspection intervals between four and ve years The FDF values for WECs are taken from 15 As. expected the required FDF values for offshore oil and gas structures are higher than or equal for WECs. Due to the fact that WEC concepts designs are still under development different development. stages which lead to different uncertainty levels should be considered when calibrating structural. safety factors There might be a prototype level where high uncertainties related to the overall per. formance exist The main purpose at that development stage is to show functionality of the device. In a developed stage the target needs to be adjusted more towards cost optimization and also. decreasing the uncertainties due to gained knowledge For different development stages different. required FDF values result due to different uncertainty levels The target reliability levels remain. the same over the whole development process see e g 18. Also the effect of using different materials different SN curves as well as the effect of corrosion. need to be considered in the design stage There are design features coating cathodic protection or. plate thickness allowance which reduce the effect of corrosion Whether or not such protection fea. tures are used should be de ned and considered when de ning FDF values. In summary the following points in uence the calibration of FDF values. Consequences when structural detail fails,Considered inspection method and inspection plan.

Location of considered detail submerged internal external effect of corrosion cathodic protec. Fatigue Design Factors FDFs required for different offshore industries and conditions criticality and inspections of external. structures OWT offshore wind turbine WEC wave energy converter. Failure critical detail Inspections Oil and gas 10 OWT WEC 15. Bottom xed 16 Floating 17,Yes No 10 3 6 3,Yes Yes 5 2 3 2. No No 5 2 3 2,No Yes 2 1 2 1, S Amb hl et al International Journal of Marine Energy 10 2015 17 38 21. Development stage of system developed prototype and the resulting uncertainties. 4 Reliability modelling of fatigue, This section focuses on approaches used to model fatigue reliability When no inspections are con. sidered SN curves together with Palmgren Miner hypothesis which assumes linear damage accumu. lation can be used SN curves show the number of cycles with a certain stress amplitude leading to. fatigue failure of the component If inspections at a certain detail are performed more information. about the different stages of crack growth is needed In this case fracture mechanics approaches. which are calibrated using SN curves can be used, 4 1 Reliability modelling of fatigue failure using SN curves. In this section the SN approach which is generally recommended for the design of offshore steel. structures see e g 10 but also for offshore wind turbine designs see e g 19 21 is considered. If a bilinear SN curve which has a slope change at DrD where the number of cycles to failure N D is. considered the SN relation can be written as,N K 1 S m1 for S P DrD ND.

N K 2 S m2 for S DrD ND, where N is equal the number of cycle leading to failure for a given stress amplitude S The parameters. K 1 K 2 m1 as well as m2 are SN curve parameters, It is assumed that the stress range Dr DQ z can be obtained on basis of load effect range DQ e g. normal force and the design parameter z e g cross sectional area Further it is assumed that the. total number of stress ranges for a given fatigue critical detail can be grouped into groups intervals. of stress amplitudes such that the number of stress ranges in group i is ni per year DQ i ni is obtained. by rain ow counting see e g 22, The code based design equation which is needed to calibrate the design parameter z using Palm. gren Miner rule can be written as,X X X T FAT nijk m X X X T FAT nijk m. sijk11 P HSi T Pj 2,sijk22 P HSi T Pj 0 5,i j k1 K1 i j k2 K c2.

sijk PDrD sijk DrD,where K c1, are the characteristic values of K 1 and K 2 nijk is the number of cycles per year of stress. range k given a certain wave state signi cant wave height HSi and peak period T Pj sijk DQ ijk z is the. safety factors There might be a prototype level where high uncertainties related to the overall per formance exist The main purpose at that development stage is to show functionality of the device In a developed stage the target needs to be adjusted more towards cost optimization and also decreasing the uncertainties due to gained

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