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Design of Digital Lock-In Amplifier Based on Wiener Filter

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Design of Digital Lock-In Amplifier Based on Wiener Filter 2020 International Conference on Computer Intelligent Systems and Network Remote Control (CISNRC 2020) ISBN: 978-1-60595-683-1 Design of Digital Lock-in Amplifier Based on Wiener Filter Meng Zhang, Minxiang Wei, Xinda Chen, Kai Chen ABSTRACT This paper introduced the design of a digital lock-in amplifier for weak crack detection. Due to the limitation of flicker noise and low pass filter performance, the error of the traditional lock-in amplifier in detecting weak signal will be large. In order to solve this problem, this paper designed an algorithm according to the source of noise. First, an orthogonal vector digital phase locked amplifier has been built. In addition, we have proposed and implemented a noise removal method based on Wiener filter, and optimized the anti-interference performance of the lock- in amplifier by sliding mean algorithm. The simulation results show that the proposed design can effectively extract the weak crack signals submerged in noise, optimize the performance of the traditional lock-in amplifier, improve the accuracy and reduce the noise interference. KEYWORDS Lock-in Amplifier, Weak Signal, Wiener Filtering, Sliding Median Filtering. INTRODUCTION Many components of construction machinery are subject to external conditions ___________________ Meng Zhang, Minxiang Wei, Xinda Chen, Kai Chen College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 99 such as high temperature, high pressure and sudden load in the process of work, which are prone to crack faults. Such cracks also occur in important structures like bridges. If the early crack fault is not detected and treated, the crack will continue to grow under the action of alternating load and so on, which will eventually lead to serious faults. Early crack fault detection can transform non-electric signals such as micro-displacement and micro-vibration into electric signals such as micro-current and low-voltage by sensors. Usually in this case, the signal is weak and mixed with a large number of noise signals, and the amplitude of external interference is much larger than the useful signal. The amplifier amplifies the measured signal and also amplifies the noise. Therefore, only by increasing the amplitude of the weak signal under the condition of effectively suppressing the noise can the useful signal be extracted. As shown in Figure 1, lock-in amplifier uses the principle of cross- correlation detection between the measured signal and the reference signal, which can effectively filter out the noise interference and complete the detection of crack signal. Literature [1] verified this detection method by using a lock-in amplifier for nondestructive detection of cast iron, and successfully extracted the signal of 31uV from the noise of 1000 times. Test signal PSD1 LPF1 GDC1 I 90° phase Reference shift Signal Reference Channel PSD2 LPF2 GDC2 Q Figure 1. Principle of orthogonal vector-type lock-in amplifier. Orthogonal vector lock-in amplifier is biphasic lock-in amplifier. There are two reference signals corresponding to two phase-sensitive phase-frequency detection units. Through signal processing of these two channels, the amplitude of the weak target component in the detected signal and the phase difference between the detected signal and the reference signal can be finally obtained. The realization of the lock-in amplification technique has a high requirement for the signal source to be detected. If there are large low-frequency noise and DC noise components in the signal acquired by the sensor, the result will have a large error due to the same frequency superposition. And the final detected amplitude is the sum of the original amplitude and noise signal amplitude in the target signal frequency band. 100 Literature [2] uses adaptive algorithm and particle swarm optimization (PSO) to search for the most matched and optimal particles to realize digital lock-in amplifier. This algorithm relies on a large amount of computation, and when Gabor particles are selected, the sampling point of the system is limited to 512 and the SNR is -5dB. In the research on the processing of weak signals by lock-in amplifier technology, literature3, based on the analysis of noise source, designed a single- power analog lock-in amplifier to restore signals doped with white noise, flicker noise and interference pollution. The results show that the amplifier can effectively recover the SNR information less than -24dB with an error of less than 6%. In this design, the error is mainly caused by the fact that the lock-in amplifier cannot completely eliminate the superposition of certain noises in the signal, such as flicker noise. Literature4 pointed out that by introducing a trans-impedance amplifier (TIA) and change the passive components in TIA to control the frequency range. The effects of flicker noise is reduced, because the TIA has feedback structure of the operational amplifier. And its gain, stability, is a trade-off relationship between bandwidth and noise performance. This scheme needs for each target signal to be detected to select different input capacitors and feedback network to obtain the minimum noise gain. In addition, the function of low-pass filter in orthogonal vector Lock-in amplifier is to filter out the AC component of Phase-Sensitive Detector (PSD) output signal, so a low-pass filter with low cut-off frequency and fast attenuation velocity is needed5. However, limited by the performance of the filter, the unfiltered AC signal will lead to inaccurate results. The above error is unacceptable for the precision detection technique of weak signal detection. In order to overcome the above problems, the first stage of the orthogonal vector lock-in amplifier is designed to make the actual signal output of the sensor close to the expected signal as far as possible under the minimum mean square error criterion, so that the phase-sensitive detector can obtain a relatively pure signal source. The output signal is filtered by sliding mean method at the back stage of the phase-sensitive detector to eliminate the AC component, thus the accuracy of the detection results of the whole lock-in amplifier is improved. SYSTEM MODELING BASED ON CORRELATION DETECTION PRINCIPLE Cross-correlation detection is a method of spectrum migration, that is, a reference signal is designed through the known signal frequency, the target signal 101 frequency band is migrated to the noiseless band by mathematical calculation, and then the output signal can only contain the target signal information. According to this principle, an orthogonal vector lock-in amplifier can be built. Its core component is the phase-sensitive detector, which is essentially a multiplier. It is assumed that the input signal is the superposition of the target signal to be measured and the noise signal: x(t) U sin(t ) n(t) x (1) The reference signal shall be the same frequency signal of the target signal: r(t) U sint R (2) Therefore, after the phase-sensitive detector multiplies the two signals, it can be obtained as follows: U U U U x(t)r(t) x R cos x R cos(2 t ) U n(t)sin t 2 2 0 R o (3) After the signal is processed by a phase-sensitive detector, it enters into a low- pass filter. The low-pass filter filters out the noise components and the components whose frequency is two times of the reference signal frequency, therefore: U U u x R cos x 2 (4) Because the amplitude of the reference signal is known, a DC signal containing the amplitude and phase information of the weak crack signal can be obtained. 102 In this design, the phase difference between the two reference signals is 90 u x u x degrees. The DC signals output by the two PSDs are 1 and 2 , based on equation (4). Then the amplitude and phase information of the target signal can be extracted as: 2 2 2 U x ux ux U 1 2 R (5) ux arctan( 1 ) ux 2 (6) In engineering applications, the introduction of noise will have a great impact on the results under certain circumstances. For example, the flicker noise, which can be widely found in passive devices, also known as 1/f noise, is characterized by the inverse ratio between noise power and frequency6, so it has a great influence in low frequency band. In practical application, the amplitude detected by lock-in amplifier is the sum of the amplitude of target signal and the amplitude of flicker noise at this frequency. In addition, the low-pass filter cannot filter out all AC signals in practice, so the output signals of two phase-sensitive detectors are actually the expected DC signals and the noise of AC components. DESIGN OF DIGITAL LOCK-IN AMPLIFIER Overall Design Based on the analysis in chapter 2, the simulation platform of orthogonal vector digital lock-in amplifier has been built, as shown in Figure 2. 103 Figure 2. Simulation platform of orthogonal vector Lock-in amplifier. As shown in Figure 2, in the established simulation platform, wiener filter processes the input signals of the whole system so that a relatively pure signal source can be obtained from the lock-in amplifier for crack detection and target signal to be measured. The reference signal sent by the two reference signal sources with a phase difference of 90 degrees is processed into a DC signal containing the original signal information in the phase-sensitive detector and then the noise is reduced in the low-pass filter and Anti-AC module. Finally, the amplitude and phase information of the target signal to be measured can be obtained through mathematical operation. The First Stage Channel Algorithm Based on Wiener Filtering In order to reduce the error of the result, the orthogonal vector lock-in amplifier needs to obtain the purest detection signal in low frequency band.
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