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Based on Lyapunov Exponents of a car engine fault diagnosis

Details of the wave packet transform can be found in the literature accompanying this article. Wavelet packet transform themselves according to changes in the signal adaptive scale parameter, especially for non-stationary signal representation and processing. Wavelet packet can signal a number of different forms of decomposition, the decomposition of all possible forms is unrealistic, the signal using wavelet packet decomposition purpose is to select the appropriate wavelet packet basis functions, in order to be able to describe the basic function of a signal These features, and then the signal in the basement under the given decomposition, to analyze the time-frequency characteristics. Of interest is for a standard, to find an optimal signal decomposition. Time-frequency analysis of the decomposition of the signal quality is good or bad depends largely on fundamental function of the selected good or bad, the traditional entropy (Entropy) of the standard can be used as the standard signal decomposition,[link widoczny dla zalogowanych], thermodynamic entropy is an important concept had been introduction of information theory to describe the degree of uncertainty given signal. To minimize the amount of information to complete the decomposition of the signal, all signal components to achieve the classification of economic rationality,[link widoczny dla zalogowanych], rather than an unconditional decomposition of the signal band down. In signal processing, commonly used Shannon entropy entropy standards, dead norm, log energy entropy, entropy threshold. This example is Shannon entropy criterion used entropy minimization,[link widoczny dla zalogowanych], with representatives of the signal S, with S. Representative of the signal in a wavelet packet based on the projection coefficient, the signal S on wavelet packet decomposition Shan-non entropy is defined as follows: W (s) one by one>: s ~ log (5), agreed i0log (0) a 0.2 Test and Engineering Simulation examples to illustrate the wavelet packet-based non-destructive stress wave testing method is effective, the numerical simulation carried out the necessary tests and actual application. 2.1 Numerical experiments complete selection of defective piles and the central model in both cases the numerical simulation test, the specific parameters such as Bian shows. Pile length: 8.0m; design cross-sectional area: 0.1m; pile of concrete density: 2500kg / m. ; Pile longitudinal wave velocity: 3600m / s; pile lateral stiffness: 2.5e6N / m. ; Pile side damping: 1.0e4N · s / m. ; Pile stiffness: 3.0e7N / m; pile damping: 2. Oe6N · s / m; here,[link widoczny dla zalogowanych], the equivalent cross-sectional area of pile defects change, given a model for the complete pile, two models from the top of the pile located at the cross-sectional area reduced 4.5 ~ 5.0m to 0.05m. . Signal to anyone, as the top of the pile to encourage, through the finite element method (direct integration) are top of the pile simulation speed response Ls]. Used by several wavelet basis function of wavelet series to compare, choose one of Daubechies wavelet series D7 wavelet as wavelet packet basis functions to solve this problem satisfy smoothness and locality requirements. Simulated signal will be based on minimum entropy (Shannon entropy) standard optimal wavelet packet decomposition, limit the maximum decomposition level is 4 layers (space is limited, this decomposition is not listed, the best wavelet packet basis tree). Decomposition based on the actual results, test the best wavelet packet basis corresponding to each set of decomposition coefficients,[link widoczny dla zalogowanych], selected to reflect the stress from the decomposition coefficient reconstruction of this part of the signal components, the reconstructed signal can reveal the reflection of stress wave signals The distribution of wave characteristics in the timeline. Thanks to the best wavelet packet decomposition corresponds to a specific set of wavelet packet basis, so this group of just the corresponding wavelet packet decomposition coefficients-based test. A model pile driving forces, pile top speed of response signal and the results shown in Figure 1. Figure 1, c} signal reconstruction from wavelet coefficients are included in the top of the pile revealed in the pile response signal reflection information, A, B, C three signal time interval is 4.4ms, A place for the direct wave, B, c correspond reflected in two pile information, you can determine the structural integrity of the pile. lO00.02O. Ol reputation o. o. 0120-2-400.0050.0l0.0l50.020.025t / s top of the pile driving signal of a lf ll ~ if/J00.0050.0l0.0l50.020.025s pile item response simulation results 00. oo50.0l0.0l50.020.025sC wavelet packet decomposition coefficient reconstruction Figure 11 exciting force, response and analysis of the pile 2 model pile driving forces, pile top speed of response signal and the results shown in Figure 2. Figure 2, c} signal reconstruction from wavelet coefficients revealed defects and bottom parts of the reflection information, A place for the direct wave, B corresponds to the pile at the defect reflection reflection, C corresponds to the pile at the bottom reflection reflection, can determine the pile in 4.5m defects.

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