On the Use of Singular Vectors for the Flexibility-Based Damage Detection under the Assumption of Unknown Structural Masses

<table class="fixed-width table-group" id="tab14"><tr><td><table class="table"><colgroup><col style="width:3.98em"/><col style="width:3.73em"/><col style="width:3.40em"/><col style="width:3.26em"/><col style="width:3.51em"/><col style="width:3.51em"/><col style="width:3.56em"/><col style="width:3.33em"/><col style="width:3.43em"/></colgroup><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td class="align_left">Sensor</td><td class="align_center"><span style="width: 10.2525ptpx;"><svg height="12.4307pt" id="M298" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 10.2525 12.4307" width="10.2525pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.548,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M401 397C401 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style="vertical-align:-3.29109pt" version="1.1" viewbox="-0.0498162 -9.24921 10.2525 12.5403" width="10.2525pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.548,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z" id="g113-227"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.187,3.132)"><path d="M453 623H65C60 580 56 530 46 472H80C103 538 110 548 175 548H389C310 380 195 168 90 0L98 -12L175 -2C273 206 366 408 462 610L453 623Z" 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class="align_center">-</td><td class="align_center">−7.43</td><td class="align_center">-</td><td class="align_center">−1.26</td><td class="align_center">-</td><td class="align_center">+0.86</td><td class="align_center">-</td><td class="align_center">−1.85</td></tr><tr><td class="align_left">Case <svg height="8.39864pt" id="M307" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.34882 6.36303 8.39864" width="6.36303pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path></g></svg></td><td class="align_center">−14.81</td><td class="align_center">−0.71</td><td class="align_center">+1.16</td><td class="align_center">+3.54</td><td class="align_center">+2.29</td><td class="align_center">−2.09</td><td class="align_center">+1.55</td><td class="align_center">+1.06</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Damage evaluation in case of 4 and 8 sensors on the continuous shear-deflecting structure, by using SVD-based algorithm.</div>

Shock and Vibration

tab14

Table 14

Table 14: On the Use of Singular Vectors for the Flexibility-Based Damage Detection under the Assumption of Unknown Structural Masses 