13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- In order to reduce the impact of random noise from the test mode shapes , multi-order efficient modality are used to diagnose structural damage location: ∑ = m ij j DI N DI 1 （23） Where, N is the efficient modal number of selection. A given threshold value of j DI to determine whether the structure has occurred injury can be applied in practical applications. 2.5.Degree of damage calculation After the injury element is determined, the formula (11) can be used to calculated the degree of element damage. The element damage factor jα can be used to represent the degree of damage. If there is only one location injury, assuming k element injury, then ) 0( j k j = ≠ α , only 0≠ kα . The Eq.(11) can be expressed: d ik d i i k MSE MSE ⋅ = δ α （24） If there are multiple locations injury, assuming melement（ 1k 、 2k 、… mk ） injury ) (m n≤ , then need mefficient mode（ 1q 、2q 、… mq ）to be calculated. m equations can solve the corresponding damage factor α. The equations are as follows: MSEDD MSED= ⋅ ⋅ α δ (25) Where, [ ] mq q q q δ δ δ δ δ ... 3 2 1 = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = d q d q d q d q m MSE MSE MSE MSE MSED ... 3 2 1 [ ] mk k k k α α α α α ... 3 2 1 = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = m m m m m m m m q k q k q k q k q k q k q k q k q k q k q k q k q k q k q k q k MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSE MSEDD ... ... ... ... ... ... ... ... ... 3 2 1 3 3 3 2 3 1 3 2 3 2 2 2 1 2 1 3 1 2 1 1 1 If p m< , extended modal can be applied to the calculation. 3. Instance of verification
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