Ten lectures on wavelets
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
IEEE Computational Science & Engineering
Haar Wavelet-Based Approach for Optimal Control of Second-Order Linear Systems in Time Domain
Journal of Dynamical and Control Systems
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Nowadays, each newly produced car must conform to the appropriate safety standards and norms. The most direct way to observe how a car behaves during a collision and to assess its crashworthiness is to perform a crash test. This paper deals with the wavelet-based performance analysis of the safety barrier for use in a full-scale test. The test involves a vehicle, a Ford Fiesta, which strikes the safety barrier at a prescribed angle and speed. The vehicle speed before the collision was measured. Vehicle accelerations in three directions at the centre of gravity were measured during the collision. The yaw rate was measured with a gyro meter. Using normal speed and high-speed video cameras, the behavior of the safety barrier and the test vehicle during the collision was recorded. Based upon the results obtained, the tested safety barrier, has proved to satisfy the requirements for an impact severity level. By taking into account the Haar wavelets, the property of integral operational matrix is utilized to find an algebraic representation form for calculate of wavelet coefficients of acceleration signals. It is shown that Haar wavelets can construct the acceleration signals well.