This work suggests a theoretical principle about the oscillation signal decomposition, which is based on the requirement of a pure oscillation component, in which the mean zero is extracted from the signal. Using this principle, the validity and robustness of the empirical mode decomposition (EMD) method are first proved mathematically. This work also presents a modified version of EMD by the interpolation solution, which is able to improve the frequency decomposition of the signal. The result shows that it can provide a primary theoretical basis for the development of EMD. The simulation signal verifies the effectiveness of the EMD algorithm. At the same time, compared with the existing denoising algorithm, it has achieved good results in the denoising of rolling bearing fault signals. It contributes to the development and improvement of adaptive signal processing theory in the field of fault diagnosis. It provides practical value research results for the rapid development of adaptive technology in the field of fault diagnosis. then theoretically explained briefly how EMD operates on harmonic functions and why it selects the highest frequency oscillation, leaving the lower frequency oscillation in the signal, and also derived the obtainable frequency resolutions of the method and the existence of a critical frequency limit that allows separation of the closest harmonics. In order to improve the frequency resolution and the mode mixing effect [1,18], many efforts have been made for these years. Meanwhile, it has been found that methods associated with the local mean decomposition are more benefit to this purpose [19][20][21].Unfortunately, due to the lack of a complete and generally accepted theoretical framework, the EMD method still gives rise to puzzles, because the local mean of the signal depends on its characteristic local time-scales. To this end, this work suggested a theoretical principle involving the oscillation signal decomposition, which is based on the requirement of the pure oscillation component with mean zero extracted from the signal in it. The principle not only firstly demonstrates the validity and robustness of EMD mathematically, but also provides a theoretical framework for the analysis of EMD.
Theoretical Principle of Oscillation Signal Decomposition
Theoretical PrincipleConsider an oscillation signal x(t) varying with time t and use this signal as a signal for analysis, as shown in Figure 1. Assuming that this signal is composed of a pure oscillation component c(t) of proper rotation, with mean zero and a residual term (the trend or the baseline signal) r(t) from which the oscillation component is removed.Since c(t) is an oscillatory function with mean zero, its integral in the interval of two local maxima (or minima) points t k and t k + 2 should be equal to zero. Therefore, from Equation (1), one has
In this paper, target hunting aims to detect target and surround the detected target in a surface-water using Multiple Autonomous Underwater Vehicles (multi-AUV) in a given area. The main challenge in multi-AUV target hunting is the design of AUV's motion path and coordination mechanism. To conduct the cooperative target hunting by multi-AUV in a surface-water environment, an integrated algorithm based on improved potential field (IPF) is proposed. First, a potential field function is established according to the information of the surface-water environment. Then, the dispersion degree, the homodromous degree, and district-difference degree are introduced to increase the cooperation of the multi-AUV system. Finally, the target hunting is solved by embedding the three kinds of degree into the potential field function. The simulation results show that the proposed approach is applicable and feasible for multi-AUV cooperative target hunting.
To eliminating the safety loophole of gas concentration out-of-limit during ventilation ceasing for mine main fan switchover, we present a main fan hot standby strategy for mine main fan switchover. For the multi-couplings, great lag, nonlinearity of mine ventilation system, to stabilize the ventilation-rate underground to eliminate safety loophole and particle pollution under mine, one of the four air-doors was controlled with Fuzzy-PID, the other air-doors and the working-condition variation of main fans were treated as disturbance. In practical application, it makes good performance for invariant ventilation in the main fan switchover process.
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