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表4.1：數值模型之理論參數

振動頻率(Hz) 0.679 2.18 3.48 6.00 6.20 7.08 阻尼比(%) 5.00 5.00 5.00 5.00 5.00 5.00 1.000 1.000 -0.902 -0.120 0.118 -0.040 0.920 0.173 1.000 0.632 -0.669 0.307 0.863 -0.185 0.924 -0.550 0.691 -0.552 0.723 -0.696 -0.423 -0.401 0.110 1.000 0.643 -0.765 -0.783 0.383 -0.364 -0.779 模態

0.057 -0.077 -0.102 1.000 1.000 0.198

表4.2：利用 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

2 0.679 2.18 3.48 6.00 6.20 7.08 5.00% 4.98% 4.99% 5.00% 5.00% 4.99% 1.00 1.00 1.00 1.00 1.00 1.00

Nature frequency(Hz) Damping ratio MAC

2 0.679 2.18 3.48 6.00 6.20 7.08 5.01% 5.00% 5.00% 5.00% 4.99% 5.00% 1.00 1.00 1.00 1.00 1.00 1.00

表4.4：利用 a=0.08 所得結果

Nature frequency(Hz) Damping ratio MAC

2 0.680 2.18 3.48 6.00 6.20 7.08 4.87% 5.01% 5.00% 5.00% 5.00% 5.00% 1.00 1.00 1.00 1.00 1.00 1.00

Nature frequency(Hz) Damping ratio MAC

2 0.679 2.18 3.48 6.00 6.20 7.08 4.99% 5.00% 5.00% 5.00% 5.00% 5.00% 1.00 1.00 1.00 1.00 1.00 1.00

表4.6：訊號中包含 10%噪訊比，利用 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

2 0.691 \ \ \ \ \ 7.62% \ \ \ \ \ 1.00 \ \ \ \ \

3 0.678 2.23 \ \ \ \ 5.16% 9.21% \ \ \ \ 1.00 0.97 \ \ \ \

4 0.675 2.21 3.50 \ \ \ 4.49% 8.00% 9.99% \ \ \ 1.00 0.99 1.00 \ \ \ 5 0.677 2.21 3.49 \ \ \ 4.61% 6.87% 8.48% \ \ \ 1.00 0.99 1.00 \ \ \ 6 0.680 2.21 3.49 \ \ \ 4.83% 6.31% 7.66% \ \ \ 1.00 0.99 0.99 \ \ \ 7 0.682 2.21 3.48 \ \ \ 4.98% 5.88% 6.77% \ \ \ 1.00 0.99 0.99 \ \ \ 8 0.682 2.20 3.47 \ \ \ 5.01% 5.62% 6.43% \ \ \ 1.00 0.99 0.99 \ \ \ 9 0.682 2.20 3.47 \ \ \ 5.01% 5.56% 6.43% \ \ \ 1.00 1.00 0.99 \ \ \ 10 0.683 2.20 3.47 \ \ \ 5.06% 5.22% 5.83% \ \ \ 1.00 1.00 0.99 \ \ \ 11 0.682 2.19 3.45 \ \ \ 4.98% 5.57% 5.65% \ \ \ 1.00 1.00 1.00 \ \ \ 12 0.683 2.19 3.45 \ \ \ 5.02% 5.37% 5.72% \ \ \ 1.00 1.00 1.00 \ \ \ 13 0.684 2.19 3.45 \ \ \ 5.05% 5.13% 5.62% \ \ \ 1.00 1.00 0.99 \ \ \ 14 0.683 2.19 3.44 \ \ 7.19 5.02% 5.05% 5.49% \ \ 9.46% 1.00 1.00 1.00 \ \ 0.93 15 0.683 2.20 3.44 \ \ 7.20 5.05% 4.93% 5.52% \ \ 8.66% 1.00 1.00 0.99 \ \ 0.96 16 0.683 2.19 3.43 \ \ 7.15 5.01% 5.04% 5.49% \ \ 7.59% 1.00 1.00 1.00 \ \ 0.97 17 0.682 2.19 3.44 \ \ 7.16 4.97% 5.10% 5.53% \ \ 7.21% 1.00 1.00 1.00 \ \ 0.98 18 0.682 2.19 3.43 6.07 6.21 7.14 4.94% 5.04% 5.54% 7.44% 7.60% 6.63% 1.00 1.00 1.00 0.97 0.75 0.99 19 0.682 2.19 3.43 6.05 6.21 7.15 4.96% 5.08% 5.51% 7.55% 7.13% 6.48% 1.00 1.00 1.00 0.98 0.93 0.99 20 0.682 2.19 3.44 6.04 6.21 7.10 4.96% 5.04% 5.47% 7.42% 6.90% 6.74% 1.00 1.00 1.00 0.98 0.93 0.99 21 0.682 2.19 3.45 6.04 6.19 7.11 4.96% 4.94% 5.49% 7.70% 6.58% 6.74% 1.00 1.00 1.00 0.99 0.93 0.99

註：“\”無法識別

表4.7：訊號中包含 10%噪訊比，利用 a=0.22 所得結果

Nature frequency(Hz) Damping ratio MAC

2 \ 2.18 3.51 \ \ \ \ 6.74% 8.23% \ \ \ \ 1.00 1.00 \ \ \

3 \ 2.17 3.50 6.07 \ 6.07 \ 5.80% 7.23% 5.58% \ 5.58% \ 0.99 1.00 0.85 \ 0.00 4 \ 2.17 3.49 6.07 \ 6.07 \ 5.41% 6.56% 5.68% \ 5.68% \ 0.99 1.00 0.93 \ 0.00 5 \ 2.18 3.49 6.09 \ 6.09 \ 5.23% 5.93% 6.33% \ 7.81% \ 1.00 1.00 0.99 \ 0.01 6 \ 2.18 3.49 6.04 6.14 6.14 \ 5.20% 5.79% 6.76% 6.93% 6.93% \ 1.00 1.00 0.99 0.92 0.04 7 \ 2.18 3.48 5.98 6.17 6.17 \ 5.13% 5.55% 6.87% 6.03% 6.03% \ 1.00 1.00 0.99 0.94 0.02 8 0.605 2.18 3.48 5.96 6.18 6.18 14.69% 5.12% 5.37% 6.41% 5.78% 5.78% 1.00 1.00 1.00 0.99 0.94 0.02 9 0.616 2.18 3.48 5.95 6.18 6.18 11.95% 5.05% 5.31% 6.38% 5.74% 5.74% 1.00 1.00 1.00 0.98 0.93 0.02 10 0.625 2.18 3.48 5.93 6.19 6.19 11.30% 4.97% 5.15% 6.27% 5.52% 5.52% 1.00 1.00 1.00 0.98 0.92 0.01 11 0.622 2.18 3.48 5.95 6.19 6.19 11.48% 4.96% 5.10% 6.64% 5.73% 5.73% 1.00 1.00 1.00 0.99 0.94 0.02 12 0.630 2.18 3.48 5.95 6.19 6.19 10.73% 4.93% 5.03% 6.72% 5.86% 5.86% 1.00 1.00 1.00 0.98 0.93 0.02 13 0.636 2.18 3.48 5.95 6.18 6.18 9.76% 4.92% 4.96% 6.74% 5.92% 5.92% 1.00 1.00 1.00 0.98 0.93 0.02 14 0.635 2.18 3.48 5.97 6.20 6.20 9.29% 4.95% 4.95% 6.59% 6.11% 6.11% 1.00 1.00 1.00 0.99 0.95 0.02 15 0.641 2.18 3.48 5.96 6.19 6.19 8.52% 4.94% 4.96% 6.72% 5.99% 5.99% 1.00 1.00 1.00 0.98 0.94 0.02 16 0.645 2.18 3.48 5.96 6.19 6.19 6.30% 4.93% 4.99% 6.34% 6.05% 6.05% 1.00 1.00 1.00 0.99 0.94 0.02 17 0.650 2.18 3.48 5.96 6.21 6.21 5.21% 4.94% 4.99% 6.16% 6.06% 6.06% 1.00 1.00 1.00 0.99 0.95 0.02 18 0.652 2.18 3.48 5.95 6.20 6.20 4.90% 4.94% 4.98% 6.12% 5.98% 5.98% 1.00 1.00 1.00 0.99 0.94 0.02 19 0.654 2.18 3.48 5.95 6.20 6.20 3.75% 4.96% 4.98% 5.91% 6.04% 6.04% 1.00 1.00 1.00 0.99 0.94 0.02 20 0.658 2.18 3.48 5.95 6.19 6.19 3.72% 4.96% 4.96% 5.89% 6.08% 6.08% 1.00 1.00 1.00 0.99 0.94 0.02 21 0.658 2.18 3.48 5.95 6.20 6.20 3.40% 4.97% 4.94% 5.65% 6.12% 6.12% 1.00 1.00 1.00 0.99 0.95 0.02

表4.8：訊號中包含 10%噪訊比，利用 a=0.08 所得結果

Nature frequency(Hz) Damping ratio MAC

6 \ 2.16 3.58 6.06 6.20 7.20 \ 13.13% 12.76% 5.77% 6.28% 6.87% \ 1.00 0.99 0.99 0.85 0.99 7 \ 2.16 3.56 6.05 6.21 7.17 \ 11.16% 10.40% 5.67% 5.95% 6.14% \ 0.99 0.99 1.00 0.88 0.99 8 \ 2.17 3.54 6.03 6.20 7.14 \ 9.91% 9.29% 5.45% 5.58% 5.66% \ 0.99 1.00 1.00 0.95 0.99 9 \ 2.17 3.53 6.02 6.21 7.14 \ 8.67% 8.37% 5.26% 5.39% 5.33% \ 0.99 1.00 1.00 0.99 1.00 10 \ 2.17 3.52 6.01 6.21 7.12 \ 7.77% 7.88% 5.05% 5.31% 5.07% \ 0.99 1.00 1.00 1.00 1.00 11 \ 2.18 3.52 6.00 6.22 7.12 \ 7.56% 7.61% 4.97% 5.15% 4.82% \ 0.99 1.00 1.00 1.00 0.99 12 \ 2.20 3.58 6.02 6.24 7.15 \ 10.47% 9.46% 5.06% 5.33% 5.02% \ 0.99 1.00 0.99 1.00 0.99 13 \ 2.21 3.60 6.01 6.25 7.18 \ 11.12% 9.38% 4.98% 5.27% 4.82% \ 0.99 0.99 0.98 1.00 0.98 14 \ 2.18 3.53 5.99 6.23 7.14 \ 8.16% 7.29% 5.02% 5.15% 4.96% \ 0.99 1.00 0.99 1.00 0.98 15 \ 2.17 3.51 6.01 6.21 7.14 \ 6.87% 6.78% 5.01% 5.44% 5.05% \ 0.98 1.00 1.00 1.00 0.99 16 \ 2.16 3.50 6.02 6.21 7.12 \ 6.30% 6.38% 4.92% 5.51% 5.06% \ 0.98 1.00 1.00 1.00 0.99 17 \ 2.16 3.49 6.01 6.20 7.11 \ 6.13% 6.05% 4.91% 5.49% 5.21% \ 0.98 1.00 1.00 1.00 1.00 18 \ 2.16 3.49 6.01 6.20 7.10 \ 5.89% 5.81% 4.93% 5.28% 5.28% \ 0.99 1.00 1.00 1.00 1.00 19 \ 2.17 3.49 6.00 6.20 7.10 \ 5.76% 5.73% 4.93% 5.23% 5.32% \ 0.99 1.00 1.00 1.00 1.00 20 \ 2.17 3.48 6.00 6.20 7.09 \ 5.61% 5.61% 4.95% 5.13% 5.32% \ 1.00 1.00 1.00 1.00 1.00 21 \ 2.17 3.49 6.00 6.20 7.08 \ 5.55% 5.38% 4.99% 5.05% 5.31% \ 1.00 1.00 1.00 1.00 1.00 22 \ 2.17 3.48 5.99 6.20 7.08 \ 5.41% 5.29% 5.02% 5.05% 5.31% \ 1.00 1.00 1.00 1.00 1.00 23 \ 2.17 3.48 5.99 6.20 7.07 \ 5.27% 5.11% 5.01% 5.01% 5.31% \ 1.00 1.00 1.00 1.00 1.00 24 \ 2.17 3.49 5.99 6.20 7.08 \ 5.44% 5.20% 5.01% 5.05% 5.12% \ 1.00 1.00 1.00 1.00 1.00 25 \ 2.17 3.49 5.99 6.20 7.09 \ 5.58% 5.13% 5.11% 4.95% 4.94% \ 1.00 1.00 1.00 1.00 1.00

表4.9：訊號中包含 10%噪訊比，利用 a=0.08、a=0.22 以及 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

11 0.669 2.19 3.51 6.02 6.22 7.16 7.33% 5.38% 6.60% 6.41% 6.19% 8.65% 1.00 1.00 1.00 1.00 0.99 0.98 12 0.673 2.19 3.50 5.99 6.22 7.14 8.00% 5.22% 6.56% 6.51% 5.66% 8.36% 1.00 1.00 1.00 0.99 0.96 0.98 13 0.673 2.19 3.50 5.98 6.20 7.09 6.46% 5.01% 5.77% 6.56% 5.72% 8.69% 1.00 1.00 1.00 1.00 0.97 0.98 14 0.671 2.18 3.50 5.98 6.19 7.09 5.17% 5.00% 5.65% 6.54% 5.99% 9.03% 1.00 1.00 1.00 0.99 0.97 0.97 15 0.672 2.18 3.50 5.98 6.20 7.12 4.90% 4.97% 5.55% 6.48% 6.09% 9.14% 1.00 1.00 1.00 0.99 0.97 0.98 16 0.674 2.18 3.50 6.00 6.18 7.14 4.99% 4.86% 5.49% 6.70% 6.07% 9.53% 1.00 1.00 1.00 0.98 0.97 0.99 17 0.674 2.18 3.49 6.01 6.19 7.15 4.87% 4.83% 5.47% 6.74% 6.17% 9.43% 1.00 1.00 1.00 0.99 0.97 0.99 18 0.674 2.19 3.49 6.00 6.20 7.17 4.89% 4.73% 5.47% 6.57% 6.08% 8.20% 1.00 1.00 1.00 0.99 0.96 0.99 19 0.675 2.18 3.49 5.99 6.20 7.19 4.95% 4.73% 5.41% 6.40% 5.81% 7.58% 1.00 1.00 1.00 1.00 0.97 0.99 20 0.676 2.18 3.49 6.00 6.21 7.18 5.01% 4.76% 5.45% 6.50% 5.89% 7.67% 1.00 1.00 1.00 1.00 0.97 0.99 21 0.676 2.18 3.49 6.00 6.21 7.20 4.88% 4.77% 5.50% 6.33% 5.85% 7.28% 1.00 1.00 1.00 1.00 0.97 0.99 22 0.676 2.18 3.49 5.99 6.21 7.15 4.64% 4.82% 5.44% 5.95% 5.58% 6.40% 1.00 1.00 1.00 1.00 1.00 0.99 23 0.676 2.18 3.49 5.99 6.21 7.12 4.82% 4.83% 5.33% 5.83% 5.41% 5.81% 1.00 1.00 1.00 1.00 1.00 0.99 24 0.676 2.18 3.49 5.98 6.21 7.12 4.76% 4.78% 5.36% 5.66% 5.32% 5.53% 1.00 1.00 1.00 1.00 1.00 0.99 25 0.677 2.18 3.49 5.99 6.22 7.13 4.69% 4.81% 5.29% 5.60% 5.33% 5.57% 1.00 1.00 1.00 0.99 1.00 0.99 26 0.676 2.18 3.49 5.98 6.21 7.12 4.54% 4.86% 5.27% 5.50% 5.26% 5.40% 1.00 1.00 1.00 1.00 0.99 0.99 27 0.677 2.18 3.49 5.98 6.20 7.11 4.64% 4.89% 5.21% 5.42% 5.26% 5.36% 1.00 1.00 1.00 1.00 0.99 0.99 28 0.677 2.18 3.49 5.97 6.20 7.10 4.70% 4.92% 5.17% 5.43% 5.24% 5.39% 1.00 1.00 1.00 1.00 0.99 0.99 29 0.678 2.18 3.49 5.97 6.20 7.10 4.71% 4.94% 5.14% 5.43% 5.31% 5.50% 1.00 1.00 1.00 1.00 0.99 0.99 30 0.678 2.18 3.49 5.96 6.20 7.09 4.72% 4.95% 5.14% 5.32% 5.27% 5.41% 1.00 1.00 1.00 1.00 0.98 0.99

表4.10：訊號中包含 20%噪訊比，利用 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

2 0.671 \ \ 6.12 \ \ 2.30% \ \ 4.69% \ \ 1.00 \ \ 0.65 \ \

3 0.682 \ \ 6.09 \ \ 3.45% \ \ 5.62% \ \ 1.00 \ \ 0.61 \ \

4 0.676 \ \ 6.08 \ \ 2.63% \ \ 6.52% \ \ 1.00 \ \ 0.71 \ \

5 0.678 \ 3.47 6.08 \ \ 3.27% \ 13.28% 6.40% \ \ 1.00 \ 0.97 0.58 \ \ 6 0.674 \ 3.47 6.06 \ \ 2.82% \ 14.36% 6.76% \ \ 1.00 \ 0.96 0.73 \ \ 7 0.683 \ 3.46 6.06 \ \ 4.19% \ 9.27% 6.25% \ \ 1.00 \ 0.98 0.60 \ \ 8 0.681 \ 3.45 6.06 \ \ 3.88% \ 10.17% 6.29% \ \ 1.00 \ 0.98 0.74 \ \ 9 0.686 2.27 3.45 6.06 \ \ 4.66% 10.17% 7.74% 5.91% \ \ 1.00 0.90 0.98 0.60 \ \ 10 0.684 2.29 3.46 6.05 \ \ 4.42% 12.20% 8.37% 5.83% \ \ 1.00 0.89 0.98 0.60 \ \ 11 0.685 2.27 3.44 6.06 \ \ 4.58% 10.74% 7.66% 5.72% \ \ 1.00 0.92 0.98 0.61 \ \ 12 0.686 2.26 3.45 6.05 \ \ 4.66% 10.52% 7.79% 5.67% \ \ 1.00 0.96 0.98 0.78 \ \ 13 0.686 2.24 3.43 6.05 \ \ 4.72% 8.72% 7.26% 5.35% \ \ 1.00 0.97 0.99 0.79 \ \ 14 0.686 2.24 3.43 6.05 \ \ 4.76% 8.16% 6.99% 5.36% \ \ 1.00 0.97 0.99 0.80 \ \ 15 0.685 2.23 3.42 6.05 \ \ 4.81% 7.26% 6.70% 5.33% \ \ 1.00 0.98 0.99 0.80 \ \ 16 0.684 2.25 3.43 6.04 6.56 \ 4.72% 7.45% 6.60% 5.28% 13.72% \ 1.00 0.98 0.99 0.83 0.71 \ 17 0.684 2.25 3.42 6.05 6.49 \ 4.74% 7.12% 6.57% 5.30% 13.31% \ 1.00 0.98 0.99 0.85 0.71 \ 18 0.683 2.23 3.42 6.04 6.47 \ 4.72% 7.05% 6.38% 5.18% 12.08% \ 1.00 0.98 0.99 0.86 0.81 \ 19 0.683 2.22 3.42 6.04 6.36 \ 4.70% 6.87% 6.36% 5.12% 11.05% \ 1.00 0.99 1.00 0.89 0.81 \ 20 0.682 2.22 3.43 6.04 6.40 \ 4.73% 6.71% 6.45% 5.21% 11.27% \ 1.00 0.99 1.00 0.89 0.73 \ 21 0.682 2.21 3.44 6.05 6.33 6.97 4.72% 6.57% 6.57% 5.17% 11.58% 13.69% 1.00 0.99 1.00 0.91 0.69 0.67

表4.11：訊號中包含 20%噪訊比，利用 a=0.22 所得結果

Nature frequency(Hz) Damping ratio MAC

6 \ 2.18 3.51 6.05 6.16 \ \ 6.86% 9.94% 7.20% 8.43% \ \ 0.99 1.00 0.98 0.94 \ 7 \ 2.18 3.51 5.99 6.17 \ \ 6.19% 8.65% 7.64% 7.31% \ \ 1.00 1.00 0.98 0.95 \ 8 \ 2.19 3.50 5.94 6.18 \ \ 5.94% 7.74% 7.12% 6.84% \ \ 1.00 1.00 0.96 0.95 \ 9 \ 2.18 3.49 5.92 6.18 \ \ 5.68% 7.44% 6.85% 6.82% \ \ 1.00 1.00 0.95 0.94 \ 10 \ 2.18 3.49 5.91 6.16 \ \ 5.48% 6.91% 7.06% 6.89% \ \ 1.00 1.00 0.92 0.94 \ 11 \ 2.18 3.49 5.89 6.16 \ \ 5.29% 6.60% 7.10% 6.60% \ \ 1.00 1.00 0.91 0.94 \ 12 \ 2.18 3.49 5.89 6.15 \ \ 5.19% 6.23% 6.77% 6.40% \ \ 1.00 1.00 0.89 0.92 \ 13 \ 2.18 3.49 5.92 6.15 \ \ 5.15% 6.03% 6.57% 6.47% \ \ 1.00 1.00 0.91 0.94 \ 14 \ 2.18 3.49 5.92 6.15 \ \ 5.16% 5.78% 6.76% 6.64% \ \ 1.00 1.00 0.90 0.94 \ 15 \ 2.18 3.49 5.93 6.16 \ \ 5.08% 5.68% 6.60% 6.68% \ \ 1.00 1.00 0.94 0.95 \ 16 \ 2.18 3.49 5.93 6.15 \ \ 5.07% 5.55% 6.64% 6.65% \ \ 1.00 1.00 0.92 0.95 \ 17 0.598 2.18 3.48 5.94 6.16 \ 11.74% 5.06% 5.44% 6.43% 6.75% \ 1.00 1.00 1.00 0.95 0.96 \ 18 0.605 2.18 3.48 5.95 6.16 \ 10.01% 5.03% 5.35% 6.23% 6.65% \ 1.00 1.00 1.00 0.95 0.97 \ 19 0.618 2.18 3.48 5.95 6.16 \ 5.38% 5.00% 5.29% 6.08% 6.57% \ 1.00 1.00 1.00 0.96 0.97 \ 20 0.624 2.18 3.48 5.93 6.18 \ 2.50% 5.00% 5.35% 5.77% 6.15% \ 1.00 1.00 1.00 0.98 0.96 \ 21 0.629 2.18 3.48 5.92 6.17 \ 2.34% 5.02% 5.31% 5.94% 6.12% \ 1.00 1.00 1.00 0.97 0.95 \ 22 0.631 2.18 3.49 5.91 6.17 \ 2.32% 5.02% 5.28% 6.03% 6.15% \ 1.00 1.00 1.00 0.97 0.95 \ 23 0.632 2.18 3.48 5.91 6.16 \ 1.86% 5.02% 5.15% 5.85% 6.22% \ 1.00 1.00 1.00 0.96 0.95 \ 24 0.629 2.18 3.48 5.91 6.16 \ 3.68% 5.02% 5.05% 5.74% 6.39% \ 1.00 1.00 1.00 0.96 0.95 \ 25 0.624 2.18 3.48 5.94 6.17 \ 5.24% 5.00% 4.98% 5.76% 6.38% \ 1.00 1.00 1.00 0.96 0.97 \

表4.12：訊號中包含 20%噪訊比，利用 a=0.08 所得結果

Nature frequency(Hz) Damping ratio MAC

14 \ \ \ 6.09 6.36 7.45 \ \ \ 5.29% 9.66% 7.80% \ \ \ 0.89 0.74 0.96 15 \ \ \ 6.10 6.42 7.54 \ \ \ 5.25% 10.11% 8.46% \ \ \ 0.87 0.74 0.96 16 \ \ \ 6.10 6.47 7.56 \ \ \ 5.26% 10.03% 8.45% \ \ \ 0.87 0.73 0.97 17 \ \ \ 6.07 6.33 7.30 \ \ \ 5.14% 7.86% 6.87% \ \ \ 0.94 0.92 0.97 18 \ \ \ 6.07 6.30 7.26 \ \ \ 5.23% 7.58% 6.68% \ \ \ 0.96 0.88 0.98 19 \ 2.16 \ 6.08 6.25 7.21 \ 14.74% \ 5.24% 6.96% 6.07% \ 0.99 \ 0.99 0.85 0.99 20 \ 2.18 \ 6.06 6.22 7.16 \ 11.26% \ 5.24% 5.97% 5.27% \ 0.99 \ 1.00 0.92 0.99 21 \ 2.17 \ 6.08 6.20 7.17 \ 12.06% \ 5.31% 6.06% 5.39% \ 0.99 \ 0.99 0.83 0.99 22 \ 2.18 \ 6.05 6.21 7.17 \ 13.04% \ 5.26% 5.97% 5.41% \ 0.99 \ 0.99 0.93 0.98 23 \ 2.19 \ 6.05 6.24 7.18 \ 13.20% \ 5.17% 5.86% 5.48% \ 0.99 \ 0.99 0.96 0.97 24 \ 2.20 3.67 6.04 6.24 7.17 \ 13.16% 14.93% 5.16% 5.76% 5.42% \ 0.99 0.99 0.99 0.97 0.97 25 \ 2.18 3.57 6.01 6.22 7.12 \ 9.94% 11.59% 5.04% 5.35% 5.36% \ 0.99 0.99 1.00 1.00 0.97 26 \ 2.18 3.56 6.01 6.21 7.11 \ 8.87% 10.00% 4.95% 5.40% 5.51% \ 0.99 1.00 1.00 1.00 0.98 27 \ 2.17 3.54 6.00 6.20 7.07 \ 7.48% 8.27% 4.83% 5.38% 5.44% \ 0.99 1.00 1.00 0.99 0.98 28 \ 2.17 3.54 6.00 6.21 7.08 \ 7.51% 8.17% 4.86% 5.52% 5.67% \ 0.98 1.00 1.00 0.99 0.98 29 \ 2.17 3.54 6.00 6.21 7.11 \ 7.59% 8.47% 4.84% 5.41% 5.63% \ 0.99 1.00 1.00 0.99 0.98 30 \ 2.16 3.53 5.99 6.21 7.11 \ 7.43% 8.09% 4.88% 5.29% 5.61% \ 0.99 1.00 1.00 0.99 0.98 31 \ 2.16 3.52 5.99 6.21 7.12 \ 7.09% 7.69% 4.96% 5.34% 5.34% \ 0.99 1.00 1.00 0.99 0.98 32 \ 2.16 3.52 6.00 6.21 7.13 \ 6.87% 7.18% 4.90% 5.29% 5.17% \ 0.99 1.00 1.00 0.99 0.98 33 \ 2.17 3.51 5.99 6.20 7.13 \ 6.11% 6.52% 4.94% 5.24% 5.65% \ 0.99 1.00 1.00 0.99 0.98

表4.13：訊號中包含 20%噪訊比，利用 a=0.08、a=0.22 以及 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

46 0.678 2.18 3.48 5.97 6.21 7.09 4.24% 5.20% 5.36% 4.70% 5.44% 5.94% 1.00 1.00 1.00 1.00 0.97 0.97 47 0.678 2.18 3.48 5.97 6.21 7.09 4.24% 5.17% 5.35% 4.68% 5.41% 6.05% 1.00 1.00 1.00 1.00 0.97 0.96 48 0.678 2.18 3.48 5.97 6.21 7.10 4.23% 5.23% 5.31% 4.67% 5.43% 5.82% 1.00 1.00 1.00 1.00 0.96 0.95 49 0.679 2.18 3.48 5.97 6.21 7.11 4.28% 5.14% 5.25% 4.54% 5.45% 5.83% 1.00 1.00 1.00 1.00 0.95 0.95 50 0.679 2.18 3.48 5.96 6.20 7.14 4.35% 5.14% 5.20% 4.45% 5.47% 5.97% 1.00 1.00 1.00 1.00 0.94 0.94 51 0.679 2.18 3.48 5.96 6.20 7.14 4.33% 5.22% 5.18% 4.48% 5.41% 5.89% 1.00 1.00 1.00 1.00 0.94 0.95 52 0.679 2.18 3.48 5.96 6.20 7.18 4.34% 5.20% 5.09% 4.51% 5.42% 5.94% 1.00 1.00 1.00 1.00 0.95 0.95 53 0.679 2.18 3.48 5.96 6.20 7.20 4.41% 5.27% 5.13% 4.40% 5.35% 6.03% 1.00 1.00 1.00 1.00 0.93 0.94 54 0.680 2.18 3.48 5.96 6.20 7.20 4.40% 5.32% 5.11% 4.55% 5.40% 5.99% 1.00 1.00 1.00 1.00 0.95 0.96 55 0.680 2.18 3.48 5.95 6.20 7.19 4.46% 5.31% 5.08% 4.56% 5.25% 6.05% 1.00 1.00 1.00 0.99 0.95 0.97 56 0.680 2.18 3.48 5.95 6.21 7.17 4.45% 5.23% 5.00% 4.62% 5.17% 5.53% 1.00 1.00 1.00 0.99 0.96 0.97 57 0.680 2.18 3.48 5.94 6.21 7.15 4.47% 5.14% 5.09% 4.76% 5.24% 5.56% 1.00 1.00 1.00 0.99 0.96 0.98 58 0.680 2.18 3.48 5.94 6.21 7.14 4.49% 5.18% 5.11% 4.70% 5.20% 5.48% 1.00 1.00 1.00 0.99 0.96 0.97 59 0.679 2.18 3.48 5.95 6.21 7.14 4.43% 5.12% 5.14% 4.88% 5.38% 5.50% 1.00 1.00 1.00 0.99 0.97 0.97 60 0.680 2.18 3.49 5.95 6.22 7.15 4.45% 5.19% 5.12% 4.92% 5.35% 5.23% 1.00 1.00 1.00 0.99 0.98 0.97 61 0.680 2.18 3.48 5.95 6.22 7.15 4.48% 5.20% 5.06% 5.01% 5.37% 5.00% 1.00 1.00 1.00 0.99 0.98 0.98 62 0.680 2.18 3.48 5.95 6.23 7.15 4.50% 5.15% 5.03% 4.99% 5.23% 4.80% 1.00 1.00 1.00 0.99 0.98 0.98 63 0.681 2.18 3.48 5.95 6.22 7.15 4.53% 5.04% 5.02% 4.97% 5.16% 4.70% 1.00 1.00 1.00 0.99 0.99 0.98 64 0.680 2.18 3.48 5.95 6.21 7.16 4.51% 5.03% 5.02% 4.93% 5.18% 5.00% 1.00 1.00 1.00 0.99 0.99 0.97 65 0.681 2.18 3.48 5.95 6.21 7.17 4.55% 5.04% 4.99% 5.10% 5.16% 4.99% 1.00 1.00 1.00 0.99 0.99 0.98

表4.14：訊號中包含 20%噪訊比，小波函數為 Meyer，分別利用 a=0.1、a=0.26 以及 a=1 所得結果

Nature frequency(Hz) Damping ratio MAC

3 \ 2.19 3.47 6.09 6.49 7.28 \ 7.66% 7.10% 5.19% 6.23% 4.42% \ 1.00 1.00 0.84 0.88 0.93 4 \ 2.18 3.47 6.09 6.48 7.30 \ 6.13% 6.02% 5.28% 5.61% 4.02% \ 1.00 1.00 0.82 0.85 0.93 5 0.736 2.18 3.48 6.10 \ 7.33 9.66% 5.51% 5.71% 5.30% \ 4.26% 1.00 1.00 1.00 0.85 \ 0.94 6 0.730 2.18 3.48 6.12 \ 7.37 7.33% 5.26% 5.56% 5.20% \ 4.64% 1.00 1.00 1.00 0.85 \ 0.96 7 0.720 2.18 3.48 6.12 6.65 7.42 6.44% 5.08% 5.44% 5.10% 7.68% 5.22% 1.00 1.00 1.00 0.60 0.90 0.96 8 0.709 2.18 3.48 6.13 6.67 7.46 6.08% 5.00% 5.35% 5.06% 7.65% 5.59% 1.00 1.00 1.00 0.59 0.90 0.95 9 0.699 2.18 3.48 6.12 6.58 7.48 6.07% 4.95% 5.31% 5.00% 8.22% 5.66% 1.00 1.00 1.00 0.88 0.91 0.95 10 0.693 2.18 3.47 6.11 6.48 7.44 5.86% 4.89% 5.26% 5.03% 8.11% 6.05% 1.00 1.00 1.00 0.91 0.89 0.94 11 0.687 2.18 3.47 6.10 6.40 7.38 5.51% 4.87% 5.23% 5.10% 7.85% 6.14% 1.00 1.00 1.00 0.93 0.86 0.95 12 0.686 2.18 3.47 6.07 6.33 7.28 5.36% 4.85% 5.23% 5.06% 7.17% 6.04% 1.00 1.00 1.00 0.96 0.91 0.96 13 0.684 2.18 3.48 6.06 6.29 7.20 5.14% 4.86% 5.19% 5.02% 6.32% 5.83% 1.00 1.00 1.00 0.98 0.95 0.97 14 0.682 2.18 3.48 6.04 6.27 7.16 5.15% 4.87% 5.18% 4.94% 5.88% 5.33% 1.00 1.00 1.00 0.98 0.98 0.97 15 0.682 2.18 3.48 6.02 6.26 7.14 5.14% 4.88% 5.16% 4.70% 5.60% 5.11% 1.00 1.00 1.00 0.98 0.99 0.96 16 0.681 2.18 3.48 6.02 6.26 7.14 5.06% 4.90% 5.14% 4.70% 5.54% 4.93% 1.00 1.00 1.00 0.98 0.99 0.96 17 0.681 2.18 3.48 6.01 6.26 7.14 4.96% 4.90% 5.14% 4.60% 5.44% 4.77% 1.00 1.00 1.00 0.98 0.99 0.96 18 0.680 2.18 3.48 6.01 6.25 7.13 4.94% 4.91% 5.14% 4.60% 5.36% 4.75% 1.00 1.00 1.00 0.98 0.99 0.96 19 0.680 2.18 3.48 6.01 6.25 7.14 4.93% 4.92% 5.16% 4.65% 5.27% 4.69% 1.00 1.00 1.00 0.98 1.00 0.95 20 0.680 2.18 3.48 6.02 6.25 7.17 4.91% 4.91% 5.17% 4.69% 5.24% 4.52% 1.00 1.00 1.00 0.98 1.00 0.97 21 0.680 2.18 3.48 6.01 6.25 7.18 4.86% 4.91% 5.21% 4.84% 5.19% 4.44% 1.00 1.00 0.99 0.98 0.99 0.96 22 0.679 2.18 3.48 6.01 6.24 7.16 4.94% 4.90% 5.20% 4.89% 5.21% 4.56% 1.00 1.00 0.99 0.98 0.99 0.92

表4.15：訊號中包含 20%噪訊比，小波函數為 Meyer，利用 a=0.1、a=0.26 以及 a=1 所得結果

Nature frequency(Hz) Damping ratio MAC

31 0.678 2.18 3.48 5.97 6.19 7.06 6.92% 4.75% 5.28% 5.21% 5.10% 6.86% 1.00 1.00 1.00 1.00 1.00 0.98 32 0.676 2.18 3.49 5.97 6.20 7.09 6.21% 4.74% 5.33% 5.20% 5.19% 6.62% 1.00 1.00 1.00 0.99 0.99 0.97 33 0.675 2.18 3.48 5.97 6.21 7.09 5.71% 4.80% 5.28% 5.09% 5.33% 6.06% 1.00 1.00 1.00 0.99 0.99 0.98 34 0.672 2.18 3.48 5.97 6.21 7.11 5.36% 4.82% 5.26% 4.90% 5.15% 6.12% 1.00 1.00 1.00 0.99 0.98 0.97 35 0.674 2.18 3.48 5.98 6.21 7.11 5.45% 4.77% 5.25% 4.89% 5.23% 5.66% 1.00 1.00 1.00 0.99 0.99 0.97 36 0.674 2.18 3.48 5.98 6.22 7.10 5.23% 4.82% 5.23% 4.63% 5.19% 5.40% 1.00 1.00 1.00 0.99 0.97 0.97 37 0.677 2.18 3.47 5.99 6.23 7.09 5.25% 4.83% 5.15% 4.40% 5.20% 5.01% 1.00 1.00 1.00 0.99 0.95 0.97 38 0.675 2.18 3.47 5.99 6.23 7.10 5.13% 4.85% 5.17% 4.48% 5.18% 5.00% 1.00 1.00 1.00 0.99 0.95 0.97 39 0.678 2.18 3.47 6.00 6.23 7.10 5.44% 4.86% 5.17% 4.43% 5.23% 4.73% 1.00 1.00 1.00 0.99 0.95 0.98 40 0.679 2.18 3.47 6.01 6.23 7.10 5.52% 4.87% 5.16% 4.35% 5.29% 4.68% 1.00 1.00 1.00 0.99 0.94 0.98 41 0.680 2.18 3.47 6.01 6.23 7.09 5.52% 4.86% 5.14% 4.22% 5.41% 4.55% 1.00 1.00 1.00 1.00 0.92 0.98 42 0.681 2.18 3.47 6.01 6.23 7.09 5.64% 4.89% 5.19% 4.29% 5.44% 4.47% 1.00 1.00 1.00 1.00 0.94 0.97 43 0.680 2.18 3.47 6.01 6.23 7.09 5.56% 4.90% 5.14% 4.26% 5.29% 4.53% 1.00 1.00 1.00 0.99 0.93 0.98 44 0.680 2.18 3.48 6.01 6.22 7.10 5.56% 4.85% 5.12% 4.35% 5.31% 4.68% 1.00 1.00 1.00 0.99 0.95 0.99 45 0.679 2.18 3.47 6.01 6.22 7.10 5.52% 4.86% 5.22% 4.44% 5.48% 4.62% 1.00 1.00 1.00 1.00 0.96 0.98 46 0.681 2.18 3.47 6.01 6.23 7.09 5.61% 4.87% 5.20% 4.24% 5.42% 4.67% 1.00 1.00 1.00 1.00 0.92 0.98 47 0.679 2.18 3.47 6.01 6.22 7.11 5.42% 4.88% 5.13% 4.43% 5.29% 4.76% 1.00 1.00 1.00 0.99 0.96 0.99 48 0.679 2.18 3.48 6.01 6.21 7.12 5.40% 4.90% 5.08% 4.57% 5.37% 4.67% 1.00 1.00 1.00 1.00 0.98 0.98 49 0.680 2.18 3.48 6.01 6.21 7.12 5.50% 4.90% 5.19% 4.60% 5.38% 4.79% 1.00 1.00 1.00 1.00 0.98 0.97 50 0.679 2.18 3.48 6.00 6.22 7.11 5.36% 4.87% 5.16% 4.55% 5.35% 4.71% 1.00 1.00 1.00 1.00 0.98 0.97

表4.16：於 ARMAX 模型階數下訊號中包含 20%噪訊比，小波函數為 Harr，利用 a=0.08 所得結果

Nature frequency(Hz) Damping ratio MAC

11 \ \ \ 6.10 6.71 \ \ \ 5.34% 5.34% 12.55% \ \ \ \ 0.60 0.64 \ 12 \ \ \ 6.09 6.55 7.91 \ \ 10.91% 5.38% 10.95% 10.91% \ \ \ 0.85 0.68 0.97 13 \ \ \ 6.08 6.41 7.65 \ \ 9.45% 5.40% 9.30% 9.45% \ \ \ 0.90 0.75 0.98 14 \ \ \ 6.07 6.32 7.42 \ \ 7.93% 5.39% 7.93% 7.56% \ \ \ 0.94 0.84 0.98 15 \ \ \ 6.07 6.28 7.33 \ \ 7.35% 5.38% 7.35% 6.80% \ \ \ 0.97 0.83 0.98 16 \ \ \ 6.07 6.25 7.27 \ \ 6.88% 5.37% 6.88% 6.06% \ \ \ 0.99 0.83 0.99 17 \ \ 3.67 6.07 6.25 7.24 \ \ 13.92% 5.34% 6.58% 5.79% \ \ 0.99 0.99 0.83 0.99 18 \ 2.22 3.66 6.06 6.24 7.21 \ 14.73% 13.09% 5.33% 6.21% 5.66% \ 0.99 0.99 0.99 0.87 0.99 19 \ 2.21 3.61 6.04 6.22 7.17 \ 11.72% 10.51% 5.12% 5.72% 5.22% \ 0.99 1.00 1.00 0.97 0.99 20 \ 2.23 3.67 6.04 6.25 7.23 \ 14.90% 12.57% 5.24% 5.89% 5.24% \ 0.99 1.00 0.99 0.95 0.98 21 \ 2.21 3.64 6.04 6.25 7.23 \ 14.02% 11.75% 5.19% 5.82% 5.18% \ 0.99 1.00 0.99 0.96 0.98 22 \ 2.21 3.58 6.03 6.24 7.20 \ 12.21% 10.24% 5.19% 5.67% 5.33% \ 0.99 1.00 0.99 0.98 0.98 23 \ 2.19 3.56 6.02 6.23 7.17 \ 10.24% 8.83% 5.05% 5.37% 5.34% \ 0.99 1.00 0.99 1.00 0.99 24 \ 2.20 3.55 6.02 6.22 7.16 \ 9.76% 8.03% 4.97% 5.46% 5.32% \ 0.99 1.00 1.00 1.00 0.99 25 \ 2.19 3.54 6.01 6.22 7.14 \ 8.80% 7.31% 4.95% 5.52% 5.50% \ 0.99 1.00 1.00 1.00 0.99 26 \ 2.18 3.53 6.01 6.21 7.15 \ 8.10% 7.00% 4.95% 5.42% 5.71% \ 0.99 1.00 1.00 1.00 0.99 27 \ 2.18 3.52 6.00 6.21 7.10 \ 7.34% 6.39% 4.95% 5.32% 5.80% \ 0.99 1.00 1.00 1.00 0.99 28 \ 2.17 3.51 5.99 6.21 7.07 \ 6.74% 6.21% 4.88% 5.35% 5.66% \ 0.99 1.00 1.00 0.99 0.99 29 \ 2.18 3.50 5.99 6.20 7.05 \ 6.51% 5.97% 4.83% 5.28% 5.52% \ 0.99 1.00 1.00 0.99 0.99 30 \ 2.17 3.51 5.99 6.21 7.10 \ 6.78% 5.94% 4.92% 5.24% 5.42% \ 0.99 1.00 1.00 1.00 0.99

表4.17：於 ARMAX 模型階數下訊號中包含 20%噪訊比，小波函數為 Harr，，利用 a=0.22 所得結果

Nature frequency(Hz) Damping ratio MAC

2 \ \ \ 6.11 \ \ \ \ \ 5.29% 5.29% \ \ \ \ 0.59 \ \

3 \ \ \ 6.10 \ \ \ \ \ 5.32% 5.32% \ \ \ \ 0.60 \ \

4 \ 2.20 \ 6.09 \ \ \ 13.51% \ 5.61% 5.61% \ \ 1.00 \ 0.60 \ \ 5 \ 2.19 3.56 6.09 6.31 \ \ 9.83% 11.65% 5.93% 13.03% \ \ 1.00 1.00 0.87 0.80 \ 6 \ 2.18 3.53 6.07 6.26 \ \ 8.21% 9.57% 6.16% 10.50% \ \ 0.99 1.00 0.92 0.89 \ 7 \ 2.18 3.52 6.05 6.21 \ \ 7.02% 8.25% 6.49% 8.94% \ \ 1.00 1.00 0.96 0.96 \ 8 \ 2.18 3.51 6.00 6.20 \ \ 6.31% 7.31% 6.75% 7.34% \ \ 1.00 1.00 0.99 0.96 \ 9 \ 2.18 3.50 5.98 6.20 \ \ 5.93% 6.96% 6.70% 7.09% \ \ 1.00 1.00 0.99 0.96 \ 10 \ 2.18 3.49 5.97 6.18 \ \ 5.66% 6.39% 6.84% 6.97% \ \ 1.00 1.00 0.98 0.96 \ 11 \ 2.18 3.49 5.96 6.18 \ \ 5.45% 6.16% 6.95% 6.88% \ \ 1.00 1.00 0.98 0.95 \ 12 \ 2.18 3.49 5.94 6.17 \ \ 5.31% 5.82% 6.96% 6.45% \ \ 1.00 1.00 0.95 0.94 \ 13 \ 2.18 3.48 5.94 6.16 \ \ 5.25% 5.65% 6.85% 6.35% \ \ 1.00 1.00 0.95 0.94 \ 14 \ 2.18 3.48 5.94 6.17 \ \ 5.21% 5.32% 6.84% 6.33% \ \ 1.00 1.00 0.94 0.94 \ 15 \ 2.18 3.48 5.94 6.17 \ \ 5.14% 5.19% 6.72% 6.37% \ \ 1.00 1.00 0.96 0.94 \ 16 \ 2.18 3.48 5.93 6.17 \ \ 5.09% 5.17% 6.59% 6.37% \ \ 1.00 1.00 0.96 0.94 \ 17 \ 2.18 3.48 5.93 6.18 \ \ 5.04% 5.10% 6.48% 6.43% \ \ 1.00 1.00 0.97 0.94 \ 18 0.61 2.17 3.48 5.94 6.18 \ 12.44% 5.00% 5.08% 6.38% 6.44% \ 1.00 1.00 1.00 0.98 0.95 \ 19 0.62 2.17 3.48 5.94 6.19 \ 8.25% 4.96% 5.05% 6.31% 6.47% \ 1.00 1.00 1.00 0.99 0.95 \ 20 0.63 2.17 3.48 5.94 6.19 \ 5.43% 4.96% 5.06% 6.16% 6.39% \ 1.00 1.00 1.00 0.99 0.95 \ 21 0.63 2.17 3.48 5.92 6.18 \ 3.91% 4.96% 5.08% 6.23% 6.38% \ 1.00 1.00 1.00 0.99 0.94 \

表4.18：於 ARMAX 模型階數下訊號中包含 20%噪訊比，小波函數為 Harr，利用 a=0.9 所得結果

Nature frequency(Hz) Damping ratio MAC

2 \ \ \ 6.10 \ \ \ \ \ 7.72% \ \ \ \ \ 0.53 \ \

3 0.673 \ \ 6.06 \ \ 9.07% \ \ 5.88% \ \ 1.00 \ \ 0.55 \ \

4 0.683 \ \ 6.06 \ \ 7.10% \ \ 6.18% \ \ 1.00 \ \ 0.71 \ \

5 0.687 \ \ 6.05 \ \ 6.67% \ \ 6.12% \ \ 1.00 \ \ 0.72 \ \

6 0.683 \ \ 6.05 \ \ 6.02% \ \ 6.26% \ \ 1.00 \ \ 0.72 \ \

7 0.682 \ 3.51 6.06 \ \ 5.58% \ 10.21% 6.07% \ \ 1.00 \ 0.98 0.72 \ \ 8 0.685 \ 3.48 6.05 \ \ 5.87% \ 11.04% 6.06% \ \ 1.00 \ 0.97 0.74 \ \ 9 0.683 \ 3.48 6.06 \ \ 5.49% \ 7.72% 5.89% \ \ 1.00 \ 0.99 0.60 \ \ 10 0.685 \ 3.49 6.05 \ \ 5.54% \ 8.47% 5.80% \ \ 1.00 \ 0.99 0.75 \ \ 11 0.686 2.25 3.46 6.05 \ \ 5.46% 11.26% 7.47% 5.72% \ \ 1.00 0.98 0.99 0.61 \ \ 12 0.687 2.25 3.46 6.04 \ \ 5.53% 11.67% 7.25% 5.67% \ \ 1.00 0.98 0.99 0.76 \ \ 13 0.687 2.23 3.45 6.05 \ \ 5.43% 9.76% 6.74% 5.51% \ \ 1.00 0.99 0.99 0.77 \ \ 14 0.688 2.22 3.45 6.05 \ \ 5.50% 9.94% 6.28% 5.57% \ \ 1.00 0.99 0.99 0.78 \ \ 15 0.685 2.23 3.45 6.05 \ \ 5.33% 7.75% 6.02% 5.50% \ \ 1.00 0.99 0.99 0.77 \ \ 16 0.686 2.23 3.45 6.05 \ \ 5.35% 8.57% 6.16% 5.55% \ \ 1.00 0.99 0.99 0.81 \ \ 17 0.685 2.23 3.44 6.05 \ \ 5.30% 7.69% 6.06% 5.58% \ \ 1.00 0.99 0.99 0.82 \ \ 18 0.684 2.23 3.44 6.04 6.54 \ 5.20% 7.66% 5.89% 5.47% 13.64% \ 1.00 0.99 1.00 0.84 0.78 \ 19 0.684 2.22 3.44 6.04 6.53 \ 5.18% 7.41% 5.90% 5.54% 12.25% \ 1.00 0.99 1.00 0.86 0.81 \ 20 0.683 2.23 3.44 6.05 6.52 \ 5.10% 7.28% 6.00% 5.55% 11.87% \ 1.00 1.00 1.00 0.87 0.74 \ 21 0.683 2.22 3.45 6.04 6.43 \ 5.09% 7.03% 6.10% 5.47% 11.63% \ 1.00 1.00 1.00 0.89 0.72 \

表4.19：於 ARMAX 模型階數下訊號中包含 20%噪訊比，小波函數為 Meyer，分別利用 a=0.1、a=0.26 以及 a=1 所得結果

Nature frequency(Hz) Damping ratio MAC

4 \ \ \ 6.06 6.31 7.30 \ \ \ 5.34% 7.87% 9.78% \ \ \ 0.95 0.83 0.95 5 0.682 2.18 3.48 6.03 6.23 7.27 4.48% 6.32% 6.19% 4.91% 5.89% 5.81% 1.00 1.00 1.00 0.99 0.99 0.95 6 0.677 2.18 3.48 6.04 6.25 7.22 6.77% 5.78% 5.88% 4.83% 5.41% 4.82% 1.00 1.00 1.00 0.98 0.98 0.98 7 0.720 2.18 3.48 6.03 6.25 7.23 4.77% 5.45% 5.63% 4.76% 5.25% 4.36% 1.00 1.00 1.00 0.97 0.99 0.99 8 0.716 2.18 3.48 6.03 6.26 7.22 2.88% 5.27% 5.54% 4.77% 5.29% 4.29% 1.00 1.00 1.00 0.97 0.99 0.98 9 0.708 2.18 3.48 6.03 6.27 7.25 2.88% 5.16% 5.44% 4.88% 5.25% 4.33% 1.00 1.00 1.00 0.96 0.98 0.99 10 0.693 2.18 3.48 6.02 6.28 7.25 4.55% 5.03% 5.38% 4.70% 5.24% 4.41% 1.00 1.00 1.00 0.96 1.00 0.99 11 0.686 2.18 3.48 6.03 6.27 7.26 5.56% 4.95% 5.25% 5.15% 5.24% 4.36% 1.00 1.00 1.00 0.96 0.94 0.99 12 0.688 2.18 3.48 6.02 6.28 7.25 5.19% 4.90% 5.24% 4.91% 5.22% 4.34% 1.00 1.00 1.00 0.95 0.99 0.99 13 0.688 2.18 3.48 6.03 6.26 7.24 4.92% 4.89% 5.24% 4.83% 5.38% 4.58% 1.00 1.00 1.00 0.97 0.99 0.99 14 0.682 2.18 3.48 6.02 6.25 7.24 4.94% 4.87% 5.22% 4.84% 5.28% 4.30% 1.00 1.00 1.00 0.98 0.99 0.99 15 0.674 2.18 3.48 6.02 6.25 7.22 4.73% 4.89% 5.17% 4.91% 5.32% 4.61% 1.00 1.00 1.00 0.98 0.99 0.98 16 0.683 2.18 3.48 6.02 6.25 7.22 5.16% 4.91% 5.16% 4.84% 5.36% 4.54% 1.00 1.00 1.00 0.98 0.99 0.99 17 0.678 2.18 3.48 6.02 6.24 7.20 4.81% 4.87% 5.13% 4.93% 5.37% 4.60% 1.00 1.00 1.00 0.99 0.99 0.99 18 0.676 2.18 3.48 6.03 6.25 7.20 4.78% 4.91% 5.15% 4.82% 5.24% 4.64% 1.00 1.00 1.00 0.98 0.99 0.99 19 0.676 2.18 3.47 6.01 6.23 7.17 4.94% 4.90% 5.11% 4.85% 5.36% 4.73% 1.00 1.00 1.00 0.99 1.00 0.99 20 0.675 2.18 3.48 6.01 6.22 7.16 4.83% 4.91% 5.11% 4.86% 5.26% 4.65% 1.00 1.00 1.00 0.99 1.00 0.98 21 0.676 2.18 3.48 6.01 6.21 7.14 4.67% 4.93% 5.17% 4.88% 5.28% 4.67% 1.00 1.00 1.00 1.00 1.00 0.99 22 0.677 2.18 3.48 6.00 6.20 7.10 4.66% 4.92% 5.18% 4.91% 5.34% 4.83% 1.00 1.00 1.00 1.00 1.00 0.98 23 0.677 2.18 3.48 6.00 6.19 7.07 4.52% 4.91% 5.22% 4.97% 5.39% 4.54% 1.00 1.00 0.99 1.00 1.00 0.96

表5.1 以 SAP2000 所得 Benchmark C1 之理論模態與振形

X director Y director

frequency(Hz) 1.05 3.23 5.10 1.45 4.66 7.79 1.00 -0.82 -0.44 1.00 -0.85 0.40

0.77 0.54 1.00 0.73 0.69 -0.97

Mode shape

0.38 1.00 -0.89 0.32 1.00 1.00

表5.2 識別 Benchmark C1 之模態

mode frequency(Hz) Damping

ratio MAC

1 1.08 2.00% 1.00

2 3.27 0.18% 1.00

X director

3 5.14 0.16% 1.00

1 1.40 2.07% 1.00

2 4.66 0.20% 1.00

Y director

3 8.21 0.20% 1.00

表5.3 以 Harr 小波函數識別白噪輸入之結果（Benchmark C2）

ratio MAC Frequency (Hz)

Damping

ratio MAC Frequency (Hz)

表5.5 以 Meyer 小波函數識別白噪輸入之結果（Benchmark C2）

ratio MAC Frequency (Hz)

Damping

ratio MAC Frequency (Hz)

表5.7 以 SAP2000 所得 Benchmark C2 之理論模態與振形

fq.(Hz) 3.18 5.44 10.67 13.88 20.08 24.76 25.60 37.31 46.85 Damping 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00%

1.00 -0.09 -0.07 -0.79 0.08 0.28 0.30 -0.01 -0.13

frequency(Hz) Damping ratio MAC

3.18 5.00% 1.00

表5.9 萬版大橋垂直向之模態

（林,2000） FEM

Mode（FEM） f(Hz) damping(%) f(Hz) damping(%) f(Hz) 1（8） 1.49 3.39 1.49 3.27 1.18 2（10） 1.87 4.57 1.84 4.40 1.90 3（11） 2.67 3.28 2.64 3.70 2.07 4（14） 3.03 3.32 \ \ 2.39 5（15） 3.75 3.22 3.63 2.90 2.52 6（22） 4.35 1.93 4.36 2.20 \ 7（14） 5.78 2.70 \ \ 2.39

“\”未收錄於文獻

圖2.1：

L

²

( ) R

分解之子空間式意圖

( ) R L

²

V

1

W

1

V

2

W

2

V

3

W

3

O

⊕

⊕

⊕

( )0

DOF

圖4.2：數值模擬輸入之訊號及頻譜圖

圖4.3：各自由度相對加速度之輸出反應

圖4.4：各自由度相對加速度輸出反應之頻譜圖

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1.5 -1 -0.5 0 0.5 1 1.5

ψ(t)

time(sec)

圖4.5：Haar 基底小波函數

0 1 2 3 4 5 6 7 8 9 10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Am p

frequency(Hz)

圖4.6：Haar 基底小波函數之頻譜圖

圖4.7：加入 10%噪訊比之輸入及頻譜圖

圖4.8：加入 10%噪訊比之各自由度相對加速度反應

圖4.9：加入 10%噪訊比下各自由度相對加速度反應之頻譜圖

圖4.10：以 Harr 小波函數配合分別取 a=0.08、0.22 或 0.9 之結果（NSR=10%）

圖4.11：以 Harr 小波函數配合同時取 a=0.08、0.22 或 0.9 之結果（NSR=10%）

圖4.12：加入 20%噪訊比之輸入及頻譜圖

圖4.13：加入 20%噪訊比之各自由度相對加速度反應

圖4.14：加入 20%噪訊比下各自由度相對加速度反應之頻譜圖

圖4.15：以 Harr 小波函數配合分別取 a=0.08、0.22 或 0.9 之結果（NSR=20%）

圖4.16：以 Harr 小波函數配合同時取 a=0.08、0.22 或 0.9 之結果（NSR=20%）

-8 -6 -4 -2 0 2 4 6 8 -1

-0.5 0 0.5 1 1.5

Meyer wavelet

time(sec) ψ (t)

圖4.17：Meyer 基底小波函數

0 1 2 3 4 5 6 7 8 9 10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

frequency(Hz)

Am p

Meyer wavelet

圖4.18：Meyer 基底小波函數之頻譜圖

圖4.19：以 Meyer 小波函數配合分別取 a=0.1、0.26 或 1 之結果（NSR=20%）

圖4.20：以 Meyer 小波函數配合同時取 a=0.1、0.26 或 1 之結果（NSR=20%）

圖4.21：利用 ARMAX 模式以 Harr 小波，配合分別取 a= 0.08、0.22 或 0.9 之結 果（NSR=20%）

圖4.22：利用 ARMAX 模式以 Meyer 小波，配合分別取 a= 0.1、0.26 或 1 之結 果（NSR=20%）

圖5.1：進行振動台試驗之各種結構模型

在文檔中 結構健康診斷及控制研究---大型結構實驗驗証---子計畫：發展基於小波轉換之系統識別方法(I)線性系統 (頁 44-90)