Improves LMS Algorithm to Detect Heavy Metal Ion Solution

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author: Susan

2022-01-04

Challenge
When the micro spectrometer used to detect high-concentration of trace heavy metal ions, the absorption spectra is easy to be interfered by environment and spectrometer noise. The weak absorbance signal annihilation affects detect result accuracy and repeatability.
How to reduce the noise and SNR by a new LMS algorithm that affects weak reflectance signals, the new LMS algorithm improved to reduce noise value and signal to noise ratio.
It provides a new method to detect high concentration absorption spectra with low SNR micro spectrometer.
Principle and Improvement of LMS algorithm
The LMS algorithm is based on the minimum mean square error criterion and uses a gradient descent method to achieve a denoising algorithm that minimizes the loss function.
Improved LMS algorithm

a. The filter structure is as follows (1):

............(1)

Among them,

, represents the signal vector input by the adaptive filter corresponding to the n position;

, represents the filter weight coefficient vector in the state of the n position;

, represents the order of the improved LMS filter, [] represents rounding down, and L>1.

b. The error calculation module is usually expressed by formula (2):

.............(2)

Use the sigmoid function to constrain the amount of deviation caused by the noise signal to－0.5 to 0.5, as shown in Figure 1, which reduces the algorithmic modulus to a certain extent.
The type is sensitive to noise signals. At the same time, when the weight update iteration is performed, the weight change of the weight coefficient vector of the adaptive filter will not be in an oscillating state, which is conducive to the rapid convergence of the weight coefficient.

Fig. 1 Error constraint

c. Substitute equation (2) into the minimum mean square error function established by the small batch stochastic gradient descent method, and describe it with equation (3):

...............(3)

Fig.2 The relationship between error and loss function

Test Results
Optosky ATP2000P portable miniature spectrometer was selected for the experiment. The light source was a deuterium halogen lamp ATG1020H, and the cuvette was a quartz cuvette ATP0080, figure 3.

Fig. 3 Experiment System

With Zinc hydrometallurgy as the background, mixed standard solutions of Zn²⁺, Cu²⁺, Co²⁺, and Ni²⁺ concentrations were 16g·L-1, 1.4mg·L-1, 0.8mg·L-1, 0.3mg·L-1, respectively. The sampling integration time of the micro-spectrometer is set to 3ms, and the sampling integration interval is 500ms. Under the same experimental conditions, the spectral signal of this concentration was repeatedly collected 4000 times. Figure 4(a) shows the absorption spectrum signal obtained by one sampling. Figure 4(b) is the absorption spectrum signal statistically obtained according to the central limit theorem, which is used here as the reference absorption spectrum signal.

Fig. 4 Absorption spectral signal of mixed solution (a): Measured signal (b): Reference signal

Fig. 5 The denoising results of the simulation data the normal LMS algorithm Fig. 6 The denoising results of the actually measured data the improved LMS algorithm

This method is used to de-noise the measured absorbance spectrum signal of the micro- spectrometer. The de-noising effect is shown in Figure 6. The improved LMS algorithm effectively eliminates the interference of strong noise, and also effectively retains the high concentration ratio in the background. The signal characteristics of the original absorption spectra of trace heavy metal ions.
Conclusion
In the process of processing absorption spectrum signals with low signal-to-noise ratio, the proposed method is superior to the standard LMS algorithm, SG denoising algorithm, wavelet soft threshold algorithm, and wavelet hard threshold algorithm in terms of signal-to-noise ratio and mean square error. Effectively remove the influence of irrelevant noise, retain some important real details in the spectral signal, and avoid the problem of subjective judgment selection of key detail parameters, providing a new solution for the analysis of spectral signals under low signal-to-noise ratio Ideas.
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