小波分析方法於平板疲勞裂縫檢測之應用

The Application of Wavelet Transform Method on the Fatigue Crack Detection in Plates

本文旨在探討如何應用小波分析方法偵測平板的疲勞裂縫位置。本研究是以長方形鋁合金板為偵測對象，此平板的邊界條件為一對邊固定，另一對邊為自由。佈建於鋁合金板表面的應變規，是用以偵測經激震器衝擊平板後所產生的應變波訊號。藉由小波轉換進行訊號的時頻分析，進而求得彎曲波由衝擊點至各應變規的波程時間，並計算出彎曲波在各頻率中的波群速度。當彎曲波在傳遞時遇到平板裂縫則會產生散射波，因此含有裂縫平板的板波訊號即包括彎曲波的直接波傳與裂縫引起的散射波傳。而直接波傳與散射波傳的時間差可運用簡單的計算程序求得。以直接波傳與散射波傳的波程時間差及波群速度，可求得具有唯一全域性極小值（目標函數）的等高線圖，而該極小值之位置即為平板裂縫的位置。本研究方法是利用簡易而價值不高的實驗儀器，而達到非破壞檢測的效果。雖然本方法無法探測出裂縫的形狀與深度，但仍不失為一種簡易的非破壞檢測裂縫位置之方法。 In this study, based on the wavelet transform, a method for detecting the location of a flaw in a rectangular plate is proposed. The strain histories caused by impact loads are measured by strain gauges which are mounted on the aluminum alloy rectangular plate with two longitudinal-side clamps while leaving the other two sides free. The wavelet transforms were applied to identify the group velocity of flexural waves which were measured and recorded by the strain gauges and a computer. Since the flexural waves in the plate would produce scattered waves when they propagated through the flaw of a plate, the measured signals of a strain gauge contented the direct waves propagated from the impact source and the scattered waves propagated from the flaw. The time lag between the direct wave and the scattered wave could be computed by using the simplex algorithm method. By comparing the group velocities of the flexural waves, and the time lag between the direct wave and the scattered wave, the exact location of the flaw could be found by the contour map containing the global minimum. The advantage of the method is that less expensive equipments is required to detect a crack or flaw on a structural plate. However, the method cannot detect the shape and the depth of flaws at the present stage. The proposed method may become a feasible alternative among non-destructive inspection methods for damage detection of structural members.