Study On The Construction Of Finite Element Based On B-spline Wavelet On The Interval And Pipe Damage Detection

At the end of 20th century, wavelet finite element method (WFEM) has been developed as a new numerical analysis method. It has many advantages because of using the multi-resolution wavelet basis instead of traditional polynomial interpolation function. One is that it keeps the discrete approximation characteristics of traditional finite element method, which can easily solve the complex bounding conditions. The other is that it posses multi-scale and multi-resolution properties of wavelet which can obtain wavelet element at different scale according to different need. So we can see that WFEM is an effective tool of the high performance numerical analysis for resolving practical engineering problems.However, WFEM, which has developed more than ten years, also remain some problems to be solved, such as how to construct more wavelet-based elements and how to embody their advantage for practical engineering problems.Aiming at the first problem, two novel kinds of B-spline wavelet on the interval (BSWI) elements have been constructed. Based on the associated generalized function of potential energy, BSWI scaling functions are adopted to construct three-dimension solid element and plate and shell stability element via variational principle. And the typical numerical examples demonstrate that the BSWI-based element constructed has higher performance and precision than traditional elements.Aiming at the second, a new method based on BSWI shaft element constructed and Support Vector Regression (SVR) is proposed for pipe crack detection. The cracked pipe is modeled by using the wavelet-based element to gain the precise frequencies database according to the crack's location and depth, and then the database is used as training samples to construct the crack prediction model by means of SVR algorithm, at last the first three frequencies obtained inputs to the model to predict the crack location and size. Both the numerical simulation and experimental study have verified the validity of the proposed method.