Effective filtering and noise reduction, feature extraction and fault diagnosis, and prognostics technology are important to Prognostics and Health Management (PHM) of equipment. Therefore, a multifeature fusion fault diagnosis method based on the combination of quadratic filtering and QPSO-KELM algorithm is proposed. In the quadratic filtering, stable filtering can reduce the impact of noise and fast-kurtogram can filtrate fault frequency bands with rich fault information. Then, the time-domain, frequency-domain, and time-frequency parameters of the secondary filter signal are extracted. MSSST was used to analyze the filtered signal, and the time-frequency image was obtained. The time-frequency parameter was extracted from the time-frequency image by 2DPCA, and all the extracted parameters are taken as the fusion fault feature of the gearbox. Finally, the fault feature parameters are taken as the training sample and testing sample of QPSO-KELM for training and testing to achieve the purpose of fault diagnosis. The experimental results show that the proposed method can effectively filter the noise, complete the fault mode identification of gearbox, and improve the fault diagnosis accuracy better than other methods.

The compressed sampling theory provides a good idea for sampling broadband linear frequency‐modulated (LFM) signal, but the signal reconstruction after sampling should be considered when using the compressed sampling system to sample the signal. For the problem of estimating the parameters of the LFM signal under the condition of nonreconstruction, a method combining random demodulation (RD) and waveform matching (WM) dictionary is proposed in this paper. Firstly, the RD system is used to collect the compressed sampling data of LFM signal. In order to ensure the validity of the compressed sampling data, the value of the compressed sampling rate R in the RD system is discussed. Then, the feasibility of using compressed sampling data to estimate LFM signal parameters is theoretically demonstrated. According to the construction principle of waveform matching dictionary, the corresponding relationship between sparse representation coefficients, dictionary atoms, and signal parameters can be determined. Using this theory, the LFM signal parameters can be estimated. Finally, simulation and real signal experiments verify that the proposed method can realize the estimation of initial frequency and chirp rate of LFM signal when some prior information is known.

A method of estimating linear frequency modulation (LFM) signal parameters using compressed sampling (CS) data of a Modulated Wideband Converter (MWC) system is proposed. The short-time Fourier transform algorithm is used to analyze the CS signal of the MWC system, and the obtained CS signal frequency will present a form of multi-segment distribution. By intercepting the CS signal corresponding to the first segment frequency and analyzing the intercepted segment signal with discrete polynomial transform and Rife algorithm, the chirp rate and initial frequency estimation of the segment CS signal can be preliminarily estimated. According to the random sequence with cyclic displacement, the spectrum shift relationship between the input signal and the output signal can be calculated. Therefore, the parameter of the original signal can be estimated by using single channel CS data. Then, all channels are analyzed with the same method, and a more stable parameter estimation result can be obtained than the single channel output. Finally, combined with the simulation experiment, the proposed method can be used to estimate the initial frequency and chirp rate of the LFM signal using CS data effectively.

In order to estimate the parameters of linear frequency modulation (LFM) signals directly from compressed sampled data, a method combining random demodulator (RD) and discrete fractional Fourier transform (DFRFT) dictionary is proposed in this manuscript. Firstly, according to the characteristics of LFM signal, the RD system parameters are adjusted to obtain effective compressed sampling data; Then, based on the fractional Fourier transform theory, a DFRFT dictionary is constructed, and sparse representation coefficients are obtained by reconstructing the compressed sampling data through the recovery algorithm and DFRFT dictionary. The signal has the characteristics of impact under the optimal fractional transform order, so the problem of signal parameter estimation can be converted into searching the location of the maximum value of sparse representation coefficients, and the location is determined by parameter optimization algorithm, then the initial frequency and frequency modulation (FM) slope of LFM signal can be estimated. Finally, simulation and real data experiments are carried out to verify that the proposed method not only has a good sparse representation ability for LFM signals, but also can directly be used to estimate the parameter of LFM signals with compressed sampling data.

To complete the sparse sampling of linear frequency modulation (LFM) signals and estimate the parameters, the authors proposed an improved finite rate of innovation (FRI) system to achieve the goal. First the authors build a mathematical model based on the Z‐transform, then they input the LFM signal into the modified FRI system and process the output of the system based on this mathematical model, which enables the estimation of the parameters of the LFM signal using only four sampling points. The error of the final experimental results can be controlled within 3%, which greatly improves the efficiency of LFM signal parameter estimation.