In the fault diagnosis field, the fault feature signal is weak and contaminated by the noise. The lock-in amplifier is a useful tool for weak signal detection. Aiming to the amplitude error of the lock-in amplifier caused by frequency deviation between the measured signal and the reference signal, a DFT-based automatic signal frequency estimation method is studied to improve the frequency accuracy of the reference signal. Based on this frequency estimation method, a software digital lock-in amplifier method is proposed to detect the multiple frequencies signals. This proposed method can automatically measure the frequency value of the measured signal without prior frequency information. Then, the reference signals are generated through this frequency value to make the digital lock-in amplifier estimate the amplitude of the measured signal. Moreover, an iterative structure is used to implement the multiple frequencies signal measurement. The frequencies and amplitudes measurement accuracies are tested. Under different SNR conditions, the frequency relative error is less than 0.1%. In addition, the amplitude relative error with different signal frequencies is less than 1.7% when the SNR is −1 dB. This proposed software digital lock-in amplifier method has a higher signal frequency tracking ability and amplitude measurement accuracy.
The frequency of a weak signal is used for fault diagnosis and target identification in various fields. By introducing particle swarm optimization (PSO) and spectral entropy (SE), an automated weak signal frequency estimation method based on the Duffing oscillator is proposed. The proposed method uses the differential structure to enhance the timing difference of the Duffing oscillator between the chaotic and large-scale periodic states, which is quantitatively distinguished by SE. Then, the frequency of the internal driving force is adaptively adjusted by the PSO to allow the SE to reach a minimum value where the driving frequency equals the weak signal frequency. A group of weak signals with different frequencies has been tested. The maximum relative frequency error is only 0.68%. Unlike other chaotic oscillator-based frequency estimation methods, the proposed method does not need to determine the phase state manually. A rough initial frequency search range is sufficient for automatic frequency measurement of the proposed method in this paper.
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