Parameter and State Estimation of Shear Buildings Using Spline Interpolation and Linear Integral Filters

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<div>Functions <svg height="12.5794pt" id="M428" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 30.2654 12.5794" width="30.2654pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.076,2.976)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path></g><g transform="matrix(.013,0,0,-0.013,14.36,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,18.858,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path></g><g transform="matrix(.013,0,0,-0.013,25.58,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg> and <svg height="12.4698pt" id="M429" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 28.95 12.4698" width="28.95pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.007,3.031)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M504 0V39C460 43 432 59 396 115L305 260C341 307 363 339 385 361C421 395 430 399 486 407V445H300V407C336 400 341 393 327 371C316 353 300 326 279 297L233 369C219 392 225 400 257 407V445H17V407C71 400 83 390 111 344L198 202C167 161 142 127 116 98C84 60 61 48 8 39V0H200V39C161 46 159 58 174 84C187 105 205 138 224 164L273 83C291 54 287 44 249 39V0H504Z" id="g22-118"></path></g><g transform="matrix(.013,0,0,-0.013,13.045,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,17.543,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path></g><g transform="matrix(.013,0,0,-0.013,24.265,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg> computed with four instrumented floors.</div>

Shock and Vibration

fig5

Figure 5

Figure 5: Parameter and State Estimation of Shear Buildings Using Spline Interpolation and Linear Integral Filters 