小波理論應用於平板的破損偵測之研究

A Study of Structural Damage Detection in Plates by Wavelet Transform

本文利用小波轉換之方法，研究對象為含缺陷的長方形平板，經敲擊後產生的彎曲波進行分析，進而預測平板上缺陷的位置。本文以長方形鋁板為測試對象，邊界條件為一對邊固定，另一對邊為自由。將單軸應變規布建於板上，經敲擊後取得各應變規的應變訊號，之後利用小波進行頻域分析找出彎曲波由敲擊點至各應變規的波程時間，進而求得彎曲波在各頻率中的波群速度。當彎曲波在傳遞中遇到結構缺陷時會產生散射波，因此在量得的訊號中含有彎曲波的直接波傳與缺陷引起的散射波傳，再利用直接波傳的波程時間與散射波傳的波程時間差及所計算出的彎曲波群速度，透過簡單尋優方程式得到擁有全域性極小值的等高線圖，反求其破壞位置。本研究方法優點是可運用簡易且不貴之儀器，來求取平板缺陷之位置；而缺點是目前無法探求缺陷大小形狀與深度。未來可利用多點應變規量測並發展平板缺陷散射波頻譜特徵的數值方法來反求缺陷形狀與深度，達到最佳非破壞檢測的效果。 In this study, based on the wavelet transform, a method for detecting the location of a flaw in a rectangular plate is proposed. In the experiment, the strain histories caused by impact loads are measured by strain gauges which are mounted on the rectangular plate with two longitudinal-side clamps while leaving the other two sides free. The wavelet transforms are applied to identify the group velocity of flexural wave which were measured and recorded by the strain gauges and a computer. Since the flexural waves in the plate will produce scattered waves when they propagate through the flaw of a plate, the measured signals of a strain gauge content 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 can 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 can be found by the contour map containing the global minimum. The advantage of the method is that less expensive equipments may be used to detect the crack or flaw on a structural plate. However, it 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. It is believed that by utilizing multiple-array measurement and certain numerical analysis to evaluate the scatter waves' spectrum, the flawed shape and depth in a plate may be found in the future.