Time Intervals for Maintenance of Offshore Structures Based on Multiobjective Optimization

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Solution</td><td align="center">Time interval (years)</td><td align="center">Damage index<br/>(DI)</td><td align="center">Confidence factor (<svg height="16.450001" id="M128" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 31.125 16.450001" width="31.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5
q27 -249 51 -392q7 -46 23 -46q24 0 70 60z" id="x1D706"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.45,16.25)"><path d="M390 111l17 -21q-34 -45 -80 -73.5t-89 -28.5q-91 0 -146 62t-55 147q0 118 101 195q74 57 149 57h1q59 0 90 -27q16 -14 16 -30q0 -15 -12 -29t-21 -14q-8 0 -19 11q-44 41 -101 41q-52 0 -87.5 -42.5t-35.5 -117.5q0 -49 15 -87t39 -58t49 -30t48 -10q33 0 60.5 12
t60.5 43z" id="x63"></path></g><g transform="matrix(.012,-0,0,-.012,14.483,16.25)"><path d="M257 449q92 0 154 -65t62 -158q0 -112 -67 -175t-150 -63q-98 0 -158.5 66.5t-60.5 154.5q0 59 21 106.5t54.5 75.5t71 43t73.5 15zM244 416q-48 0 -81 -47t-33 -128q0 -96 38 -158t99 -62q51 0 82 43.5t31 139.5q0 91 -36 151.5t-100 60.5z" id="x6F"></path></g><g transform="matrix(.012,-0,0,-.012,20.409,16.25)"><path d="M524 0h-209v26q44 5 55 18t11 65v167q0 114 -91 114q-50 0 -109 -51v-235q0 -50 10 -61.5t55 -16.5v-26h-217v26q51 5 62 17t11 61v206q0 47 -9.5 58.5t-50.5 19.5v23q82 15 139 40v-79l67 47q47 30 83 30q60 0 94.5 -40t34.5 -112v-193q0 -50 10 -61.5t54 -16.5v-26z
" id="x6E"></path></g><g transform="matrix(.012,-0,0,-.012,26.917,16.25)"><path d="M54 437h47v21q0 48 11 83q23 72 77 118q55 46 110 53q53 -3 79 -34q13 -16 5 -35q-5 -13 -19 -24t-27 3q-37 37 -81 37q-34 0 -53 -29q-24 -37 -23 -153v-40h118q5 -7 1.5 -21t-11.5 -19h-108v-287q0 -55 13 -67t73 -18v-25h-236v26q49 5 60 16.5t11 60.5v294h-70l-4 11z
" id="x66"></path></g>
</svg>)</td><td align="center">Expected cumulative total cost  <svg height="11.175" id="M129" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.8625 11.175" width="10.8625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
</svg>[CTC] <br/>(USD)</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left"><span style="width: 15.2px;"><svg height="12.25" id="M130" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 15.2 12.25" width="15.2" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.1)"><path d="M463 54l10 10l15 -21q-52 -57 -112 -57q-37 0 -55.5 15.5t-26.5 53.5q-76 -69 -159 -69q-52 0 -81 27t-29 79q0 67 67 112q48 32 201 76v68q0 49 -18.5 71t-62.5 22q-28 0 -46.5 -10t-18.5 -27q0 -10 11 -23q19 -22 19 -42q0 -26 -19 -43t-49 -17q-31 0 -48 18t-17 50
q0 59 52 92.5t139 33.5q92 0 144 -35t52 -99v-261q0 -28 21 -28q7 0 11 4zM293 97v148q-122 -35 -122 -121q0 -32 14 -49.5t38 -17.5q42 0 70 40z" id="x1D41A"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.562,12.188)"><path d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" id="x1D7D0"></path></g>
</svg></span></td><td align="center"><b>10</b></td><td align="center">0.2284</td><td align="center"><b>1.0827</b></td><td align="center">2133420</td></tr><tr><td align="left"><span style="width: 16.15px;"><svg height="15.7" id="M131" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 16.15 15.7" width="16.15" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M17 676h194v-259q53 56 122 56q82 0 135 -65t53 -169q0 -113 -63 -183t-163 -70q-71 0 -132 57l-79 -56h-12v607q0 30 -10 40.5t-45 17.5v24zM211 360v-263q0 -36 19 -57.5t50 -21.5q94 0 94 203q0 198 -93 198q-47 0 -70 -59z" id="x1D41B"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.512,15.637)"><path d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" id="x1D7D0"></path></g>
</svg></span></td><td align="center"><b>9</b></td><td align="center">0.2309</td><td align="center"><b>1.0886</b></td><td align="center">2040560</td></tr><tr><td align="left"><span style="width: 14.25px;"><svg height="12.25" id="M132" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 14.25 12.25" width="14.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.1)"><path d="M412 109l18 -18q-41 -56 -86 -80.5t-105 -24.5q-95 0 -155 65q-59 65 -59 171q0 109 68 180t169 71q66 0 110 -31t44 -79q0 -29 -18.5 -46.5t-49.5 -17.5q-26 0 -41 19t-15 54q0 31 -3 44q-4 26 -39 26q-39 0 -61.5 -45t-22.5 -124q0 -102 37 -161t102 -59q57 0 107 56z
" id="x1D41C"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.613,12.188)"><path d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" id="x1D7D0"></path></g>
</svg></span></td><td align="center"><b>8</b></td><td align="center">0.2371</td><td align="center"><b>1.1200</b></td><td align="center">1870170</td></tr><tr><td align="left"><span style="width: 16.15px;"><svg height="15.7" id="M133" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 16.15 15.7" width="16.15" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M534 43v-23l-62 -8q-74 -9 -133 -25v65q-35 -37 -64 -51.5t-69 -14.5q-79 0 -130 66t-51 169q0 109 54 180q55 72 138 72q34 0 60.5 -13.5t58.5 -48.5v183q0 35 -13 44q-12 9 -63 14v24h215v-575q0 -32 12.5 -44t46.5 -14zM336 112v243q-24 62 -78 62q-85 0 -85 -188
q0 -187 78 -187q36 0 66 37q19 25 19 33z" id="x1D41D"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.512,15.637)"><path d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" id="x1D7D0"></path></g>
</svg></span></td><td align="center"><b>7</b></td><td align="center">0.2375</td><td align="center"><b>1.1255</b></td><td align="center">1813980</td></tr><tr><td align="left">e<sub>2</sub></td><td align="center">5</td><td align="center">0.2680</td><td align="center">1.2029</td><td align="center">1665650</td></tr><tr><td align="left">f<sub>2</sub></td><td align="center">4</td><td align="center">0.2734</td><td align="center">1.2284</td><td align="center">1523060</td></tr><tr><td align="left">g<sub>2</sub></td><td align="center">4</td><td align="center">0.2980</td><td align="center">1.2458</td><td align="center">1554500</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Comparison between solutions a<sub>2</sub>, b<sub>2</sub>, c<sub>2</sub>, d<sub>2</sub>, e<sub>2</sub>, f<sub>2</sub>, and g<sub>2</sub>. ICD corresponding to 5 years.

Mathematical Problems in Engineering

tab6

Table 6

Table 6: Time Intervals for Maintenance of Offshore Structures Based on Multiobjective Optimization 