利用系統識別技術進行外力評估：遞迴式卡氏過濾理論與時域褶積法

Abstract

本研究介紹不同之外力識別法，以藉由量測所得之系統反應評估作用於系統之外力歷時。本文推導之時域褶積識別法，假設外力由傅立葉級數組成，藉由建立系統之褶積向量，並結合Matlab之最佳化工具，以識別外力。並採用遞迴式卡氏過濾理論（RLS-KF Method）識別外力，並與時域褶積識別法進行比較。不同於前述之方法，外力參數之敏感度識別法假設外力由正弦波組成，藉由建立系統反應對外力參數之敏感度矩陣，以識別外力參數。外力參數之最佳化以Matlab之最佳化工具取代敏感度矩陣，以改善外力參數之敏感度識別法之效率。功率譜密度函數識別法則是以系統反應之交叉功率譜密度函數識別外力之交叉功率譜密度函數。由於有限的量測資料，本文介紹卡氏重建器與結合分段式立方Hermite型插值多項式之奇異值分解重建法，以重建未量測點之反應歷時，以利進行部分量測系統之外力識別。 首先，由數值模擬建立一多自由度之系統、輸入隨機外力與系統反應，以驗證外力識別法。接著，將驗證之外力識別法與反應重建法應用於振動台之土壤－樁基礎互制實驗中。對土壤－樁基礎系統施予白噪音並量測系統反應，並以系統識別技術建立樁基礎之系統矩陣。最後，以介紹之外力識別法評估土壤與樁基礎之作用力。本研究最終証明，可先由量測之反應進行系統識別後，由識別之系統與本文介紹之外力識別法間接求得作用於系統之外來刺激力。

In this study several input force identification methods is presented using the direct response meausrements. First, by assuming the input force as a summation of sine and cosine functions, the time domain convolution method is derived. Based on the system convolution vector and the optimization scheme are presented for identifying the input forces. Then a different input force identification approach which employs the Recursive Least Square with Kalman Filter (RLS-KF) method is used for comparison. Different to the above two proposed methods, a sensitivity method with respect to the input force parameters is also presented for identify the force parameters by estabilishing sensitivity matrix of dynamic response. Optimization with respect to the force parameters can improve the efficiency of sensitivity method is also investigated. PSD method for identifying cross power spectral density of distributed excitation force is discussed by calculating cross power spectral density of measured response. Due to the limited number of measurements on the response data, both Kalman Estimator technique and Singular Value Decomposition (SVD) incopoerated with piecewise cubic Hermite Polynomial curve fitting method are used to reconstruct the unmeasured reponses and establish the full response measurement. The proposed input force identification methods were verified first using numerical simulation of a MDOF system subjected to limited number of input forces. Second, data from the shaking table tests of soil-pile interaction are used to idrntify the interaction forces. For this large-scale shaking table test, the ambient vibration measurements of the pile are used to estabilish the structural system matrix. Based on the proposed identification methods in this study, soil-pile force is identified.