應用粒子群演算法與搜尋策略於剪力構架之結構勁度參數修正

Applying Particle Swarm Optimization and Searching Strategy Approach in Structural Stiffness Parameter Updating

陳國禎(Guo-Zhen Chen)

指導教授 ： 洪士林

國立交通大學/工學院/土木工程系所/碩士(2018年)

摘要

本研究利用結構自然頻率及模態振型推導之具有物理意義之目標函數，在各樓層質量已知且固定，亦不考慮阻尼影響之假設條件下，針對不完全量測情況之剪力構架進行結構勁度參數識別，求解過程中不需反覆求解特徵值問題及模態參數比對，從而減少計算量，本研究之目的即為探討此目標函數之可行性與使用限制。方法流程先對振型單純之第一模態進行三次方雲線擬合，產生近似之完整振型，搭配已知質量快速推算出一組初始之各樓層參考勁度，以此勁度組合作為輔助選擇適當之演算法搜尋範圍，最後應用所推導之目標函數與粒子群演算法來求取最佳解。演算法中亦加入些許搜尋策略，以平衡收斂速度並避開陷入局部最佳解之問題。本研究將以一6層樓的剪力構架數值案例來進行測試方法之準確性與可行性，並探討雜訊對此目標函數識別勁度結果之影響。測試結果顯示，當自然頻率與模態振型足夠正確時，可以準確識別出各個案例之勁度參數。另外為了測試方法對破壞位置檢測之效能，再以6層樓之勁度折減數值案例，及兩組實驗模型(3層樓剪力構架與8層樓鋼構架振動台試驗)來進行測試。測試結果顯示，本研究方法在藉由比較健康結構與破壞或加勁結構之勁度差異，可檢測出結構主要勁度改變之位置。

關鍵字

模型修正 ； 最佳化問題 ； 粒子群優化演算法 ； 不完全量測 ； 破壞位置檢測

並列摘要

This work propose an approach that uses structure’s natural frequency and mode shape to derive an objective function, which is for identifying structural stiffness parameters of shear building model from measured incomplete modal data. This study assumes that the mass matrix is known and unchanged and no damping effect. This objective function retains the physical meaning of structural system and also reduce the computation by avoiding eigenvalue analysis and modal parameters comparing process. The aim of this work is to analyze the stiffness parameters from measured incomplete modal data also to test the feasibility and the working limitation of the objective function. It’s started with using cubic spline interpolation and the first mode shape to generate an approximately complete mode shape. In the next step, one set of reference stiffness is calculated by approximately mode shape and mass, and used to determine the appropriate searching range. Finally, a particle swarm optimization (PSO) with the derived objective function is applied to find the optimal stiffness solution. Two strategies of PSO are also proposed to balance converging speed and avoid being stuck in the local minimum. A six-story numerical case is employed to verify the accuracy and feasibility of the proposed approach, and also to investigate the influence of noise. The analyzing results revealed the approach can identify the corresponding stiffness parameters accurately when the modal parameters are correct enough. Moreover, the six-story numerical case and two experimental models (three-story and eight-story shear buildings shaking table experiments) are utilized to verify the capability to detect the damage locations of simulated structural models. The results revealed that the approach can identify the locations of the major stiffness changes through comparing the stiffness differences of healthy structures and damaged or strengthened structures.

並列關鍵字

Model Updating ； Optimization ； Particle Swarm Optimization ； Incomplete Measurement ； Structural Damage Detection

參考文獻

[1] Kennedy, J., and Eberhart, R. C. (1995). “Particle swarm optimization.” Proc., IEEE Int. Conf. on Neural Networks. IEEE service center, Piscataway, NJ, Vol. 4, 1942-1948.

[2] Baruch, M., and Itzhack, Y. B. (1978). “Optimal weighted orthogonalization of measured modes.” AIAA Journal, 16(4), 346-351.

[3] Berman, A., and Nagy, E. J. (1983). “Improvement of a large analytical model using test data.” AIAA Journal, 21(8), 1168-1173.

[4] Kabe, A. M. (1985). “Stiffness matrix adjustment using mode data.” AIAA Journal, 23(9), 143l-1436.

[5] Smith, S. W., and Beattie, C. A. (1991). “Secant-method adjustment for structural models.” AIAA Journal, 29(1), 119-126.