# 加權配置法 (Weighting Sensors Placement, WSP )

In document 建築物微振量測之最佳感測器配置 (Page 90-98)

## 第四章 最佳化感測器配置 - 利用模擬試驗數據

### 4.5.2 加權配置法 (Weighting Sensors Placement, WSP )

(4.21)

(4.22) 依耐震設計規範裡提到，有效模態質量總和需超過 90%：

(4.23)

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4-13. 有效模態質量表

mode 5F 10F 15F 20F 30F

1st 0.88 0.85 0.82 0.80 0.77 2nd 0.09 0.09 0.09 0.11 0.12 3rd 0.02 0.03 0.04 0.03 0.05

4-15. 5 層樓加權配置法之穩態圖

4-17. 15 層樓加權配置法之穩態圖

1st 2nd 3rd 4th 5th Avg.(1st -5th ) Modal frequency (Hz) 3.005 8.771 13.827 17.762 20.259

Reference frequency (Hz) 3.006 8.724 13.781 17.539 20.224 OSP[1,4] (Hz) 3.012 8.75 13.698 17.684 19.895

OSP Error(%) 0.23 0.24 0.94 0.44 1.80 0.73 WSP[1,2] (Hz) 3.003 8.756 13.734 17.529 20.743

WSP Error(%) 0.07 0.18 0.67 1.31 2.39 0.92

4-15. 10 層樓加權配置模態頻率誤差表

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Average

Modal frequency (Hz) 1.578 4.698 7.714 10.557 13.165 15.478 17.445 19.023 20.176 20.878 Reference frequency (Hz) 1.580 4.695 7.708 10.510 13.094 15.369 17.319 19.008 20.267 21.142 OSP [2 5] (Hz) 1.579 4.694 7.703 10.514 13.045 15.327 17.33 18.655 19.866 20.522 － OSP Error (%) 0.06 0.09 0.14 0.41 0.91 0.98 0.66 1.93 1.54 1.71 0.84 WSP[1,7] (Hz) 1.580 4.696 7.706 10.499 13.053 15.367 17.285 18.830 21.890 23.416 WSP Error (%) 0.13 0.04 0.10 0.55 0.85 0.72 0.92 1.01 8.49 12.16 2.50

4-16. 15 層樓加權配置模態頻率誤差表(前 10 個模態)

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Avg.(1st -10th ) Modal frequency (Hz) 1.052 2.938 4.923 6.854 8.58 10.444 11.925 13.523 14.775 15.986 Reference frequency (Hz) 1.054 2.933 4.92 6.826 8.55 10.355 11.914 13.491 14.863 15.783 OSP[10,15] (Hz) 1.051 2.939 4.906 6.838 8.529 10.428 11.851 13.426 14.578 15.846 － OSP Error(%) 0.10 0.03 0.35 0.23 0.59 0.15 0.62 0.72 1.33 0.88 0.50 WSP[12,14] (Hz) 1.053 2.933 4.933 6.831 8.572 10.456 11.841 13.437 14.632 16.183

WSP Error(%) 0.09 0.16 0.20 0.34 0.09 0.26 0.71 1.64 3.97 4.23 1.17

4-17. 20 層樓加權配置模態頻率誤差表(前 14 個模態)

(Hz) 1st 2nd 3rd 4th 5th 6th 7th

Modal frequency (Hz) 0.773 2.147 3.653 5.037 6.429 7.815 9.048 Reference frequency (Hz) 0.773 2.156 3.646 5.036 6.388 7.783 9.015 OSP [1,13] (Hz) 0.773 2.142 3.64 5.031 6.432 7.812 8.981 OSP Error(%) 0.03 0.26 0.34 0.11 0.05 0.04 0.74 WSP[11,13] (Hz) 0.773 2.153 3.643 5.048 6.418 7.072 9.006

WSP Error(%) 0 0.30 0.28 0.21 0.18 9.51 0.46

(Hz) 8th 9th 10th 11th 12th 13th 14th Avg.(1st -14th ) Modal frequency (Hz) 10.39 11.472 12.66 13.671 14.556 15.516 16.146

Reference frequency (Hz) 10.224 11.537 12.699 13.554 14.176 15.245 15.858 OSP [1,13] (Hz) 10.359 11.437 12.596 13.59 14.408 15.447 16.123

OSP Error(%) 0.3 0.31 0.50 0.59 1.02 0.45 0.15 0.35 WSP[11,13] (Hz) 10.353 11.483 12.646 13.4777 14.4115 15.4078 15.9761

WSP Error(%) 0.36 0.10 0.11 1.41 0.99 0.70 1.05 1.12

(Hz) 1st 2nd 3rd 4th 5th 6th 7th

Modal frequency (Hz) 0.488 1.315 2.174 3.061 3.926 4.807 5.55 Reference frequency (Hz) 0.492 1.321 2.172 3.078 3.926 4.841 5.582

OSP [19,27] (Hz) 0.493 1.321 2.172 3.072 3.92 4.798 5.569 OSP Error(%) 0.98 0.41 0.09 0.33 0.17 0.18 0.33 WSP[21,26] (Hz) 0.492 1.321 2.172 3.058 3.888 4.798 5.538

WSP Error(%) 0.82 0.41 0.09 0.11 0.97 0.19 0.23

(Hz) 8th 9th 10th 11th 12th 13th 14th

Modal frequency (Hz) 6.442 7.236 8.005 8.746 9.45 10.241 10.823 Reference frequency (Hz) 6.409 7.22 7.925 8.842 9.409 10.073 11.029 OSP [19,27] (Hz) 6.406 7.225 7.886 8.79 9.457 10.135 10.832 OSP Error(%) 0.57 0.15 1.5 0.51 0.07 1.04 0.08 WSP[21,26] (Hz) 6.452 7.206 7.989 8.720 9.427 10.226 10.731

WSP Error(%) 0.16 0.41 0.20 0.30 0.24 0.14 0.85

(Hz) 15th 16th 17th 18th 19th 20th 21th Avg.(1st-21th) Modal frequency (Hz) 11.492 12 12.674 13.091 13.576 13.901 14.099

Reference frequency (Hz) 12.037 12.266 12.68 13.296 13.98 14.334 15.293 OSP [19,27] (Hz) 11.408 11.715 12.589 13.21 13.883 14.371 15.738

OSP Error(%) 0.74 2.43 0.68 0.90 2.21 3.27 10.41 1.29 WSP[21,26] (Hz) 11.415 11.939 12.854 13.729 14.646 15.128 15.740

WSP Error(%) 0.67 0.51 1.42 4.87 7.88 8.83 11.64 1.95

### 4.5.3 模態振型配置法(Modal Shape Sensor Placement,

In document 建築物微振量測之最佳感測器配置 (Page 90-98)