Research On Feature Detection Of Time-Varying Non-stationary Signal Based On Fractional Transform

Gear vibration signal during acceleration and ECG signals are typical time-varying non-stationary signals,and their characteristics contain a lot of useful information.How to use the corresponding signal processing methods to detect their characteristics has become a research hotspot.For the processing of time-varying non-stationary signals,the traditional fourier transform and integer-order differential are weak and often fail to achieve the desired effect.In order to solve this problem,the fractional fourier transform and fractional differential theory are proposed.They are the extension and expansion of the traditional fourier transform and integer order differentiation.Compared with the traditional fourier transform and integer-order differentiation,the fractional fourier transform and the fractional differential have one more free parameter,that is,the transformation order p,which has greater choice in signal processing and is more suitable for Processing of time-varying non-stationary signals.In this paper,the fractional fourier transform is applied to the gear fault feature detection in the acceleration process,and a fault sideband detection method combining the fractional fourier transform and time-frequency ridge extraction is proposed to analyze the gear vibration signal.The weak sideband caused by the partial failure of the gear was effectively detected,and the evaluation of the degree of the gear failure was completed.On this basis,the research has been extended to the processing of biomedical signals,and the accuracy of R peak feature detection of ECG signals has been improved by using fractional differentiation.The main research contents are as follows:(1)Application of fractional fourier transform in chirp signal detection.The frequency of the chirp signal changes with time,and there is a large broadening in the time domain and the frequency domain.The method of processing stationary signals—traditional fourier transform often does not achieve good results.The fractional fourier transform has a chirp kernel,which can be understood as a chirp basis decomposition,and is especially suitable for processing chirp signals.Based on the research on the definition of the fractional fourier transform and the discretization algorithm,this paper has completed the filtering of the chirp signal and the detection of the multi-component chirp signal,and the ideal effect has been obtained.(2)Obtain the optimal order of the fractional fourier transform based on time-frequency ridge extraction.Chirp signal only exhibits impulse characteristics in the fractional fourier domain under the optimal order.In order to obtain the optimal order quickly and accurately,an optimal order acquisition algorithm based on time-frequency ridge extraction is proposed.Compared with the traditional two-dimensional peak search algorithm under variable order,the initial frequency and frequency modulation slope can be estimated in advance through ridge extraction,which improves the calculation efficiency,does not generate a lot of redundant data,and is suitable for the analysis of multi-component signals.At the same time,the proposed ridgeline extraction algorithm can be used to estimate the instantaneous frequency of non-stationary signals such as gear vibration signals,which plays an important role in the interception of gear vibration signal segments in the subsequent analysis process.(3)Application of fractional fourier transform in gear fault detection in acceleration process..Aiming at the problem that the gear fault sideband is difficult to detect during acceleration,a sideband detection method based on fractional fourier transform is proposed,which can effectively detect the gear fault sideband.According to the principle of minimum linearity error,the collected gear vibration signals of different failure degrees(healthy state,tooth root cracks,gear tooth breakage)are intercepted and analyzed,and the fractional fourier transform of the corresponding optimal order was performed on it,and the meshing frequency and sideband of the gear are successfully detected.The energy ratio of the sideband to the meshing frequency is used as an index to judge the degree of failure.The experimental results show that the deeper the degree of failure of the gear,the greater the energy ratio of the sideband to the meshing frequency,which effectively evaluate the degree of gear failure.(4)Application of fractional differentiation in R peak detection of ECG Signal.On the basis of the above research,the research is further extended to biomedical signal processing.Designed and implemented a fractional digital differentiator,and used it in the preprocessing stage of ECG signal R peak detection,which enhanced the R peak characteristics of ECG signal,and at the same time reduced noise interference and suppressed the influence of P wave and T wave on the detection result.Improve the accuracy of R peak detection,and evaluate its effectiveness in the MIT/BIH arrhythmia database.