利用神經網路識別時變系統之瞬時模態參數

Abstract

時變系統被非常廣泛地應用於很多領域裡。在機械和土木工程中，修正剛度或阻尼的主動控制裝置是時變系統。當一個結構在動力荷載的作用下受到損害，結構亦通常展現剛度和阻尼隨著時間改變。因此，在結構物的損害評估中，由時變系統識別瞬時模態參數是一個很重要的課題。 本文發展建立一個時變類神經網路，並且從架構的神經網路，根據系統識別的程序來估算瞬時模態參數。程序步驟是首先將位移反應及外力輸入倒傳遞神經網路，其連結的權重和門檻值假設為時間的函數，並以多項式展開。然後，利用權重最小平方差法來決定各多項式之係數。由於採用權重最小平方差法，各多項式的係數亦時間之函數；因此，不須高階多項式。 為了驗證此程序的可行性，先用時變線性系統及非線性系統之數值模擬來驗證本文所建立的程序；探討對權重最小平方差法中之加權函數、多項式階數，以及雜訊對建立一個合適的時變類神經網路程序，或估算瞬時模態參數之影響。最後，將本程序應用至分析鋼筋混凝土結構的振動台試驗，此實驗結構的反應進入非線性行為。所估算瞬時模態參數隨時間之變化趨勢與量測力-位移數據之斜率變化趨勢一致。

Time varying systems find many applications in various fields. In mechanical and civil engineering, a system with active control devices of modifying stiffness or damping of the system is a time varying system. When a structure is damaged under dynamic loading, the structure normally displays changes in stiffness and damping with time. The changes with time in stiffness and damping of a system result in time varying instantaneous model parameters is an important issue in damage assessment of a structure. The present work develops a novel procedure of establishing BP neural network of a time varying system and estimating instantaneous model parameters of the system from established neural network. The connective weights and thresholds in a neural network are assumed as functions of time and are expanded by polynomials. A weighted least-squares approach is applied to determine the coefficients of the polynomials. Because of using the weighted least-squares approach, the coefficients of the polynomials also depend on time. Consequently, only low orders of polynomials are needed to expand the connective weights and thresholds. The feasibility of the proposed procedure is demonstrated by processing numerically simulated dynamic responses of a nonlinear system and a time-varying linear system. It is also performed to investigate the effects of weighting function in the weighted least-square approach, polynomial order, and noise on establishing a suitable neural network and determining instantaneous model parameters. Finally, the proposed procedure is applied to process measured dynamics responses of a RC structure under shaking table tests. The experimental structure has been shaken to perform nonlinear behaviors. When dramatic changes are observed in the slope of the measured relationship between force and displacement for the experimental structure, the identified instantaneous model parameters also show significant changes.